TPTP Problem File: SEV651+1.p

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%------------------------------------------------------------------------------
% File     : SEV651+1 : TPTP v9.3.1. Released v9.3.0.
% Domain   : Set theory
% Problem  : CoqHammer - Mapc MapDom Split 2 c
% Version  : [Kal26] axioms : Especial.
% English  :

% Refs     : [CK18]  Czajka L. & Kaliszyk (2018), Hammer for Coq: Automatio
%          : [Kal26] Kalizyk (2026), Email to G. Sutcliffe
% Source   : [Kal26]
% Names    : Mapc.MapDom.Split.2.c.p [Kal26]

% Status   : Theorem
% Rating   : 0.91 v9.3.0
% Syntax   : Number of formulae    : 2744 (1126 unt;   0 def)
%            Number of atoms       : 8875 (2683 equ)
%            Maximal formula atoms :  257 (   3 avg)
%            Number of connectives : 6242 ( 111   ~; 632   |;1280   &)
%                                         ( 891 <=>;3328  =>;   0  <=;   0 <~>)
%            Maximal formula depth :  258 (   6 avg)
%            Maximal term depth    :   23 (   1 avg)
%            Number of predicates  :  463 ( 462 usr;   0 prp; 1-23 aty)
%            Number of functors    : 1596 (1596 usr; 977 con; 0-22 aty)
%            Number of variables   : 8988 (8511   !; 477   ?)
% SPC      : FOF_THM_RFO_SEQ

% Comments : This is an export from CoqHammer, Naive-Bayes premise selection,
%            with 1024 premises.
%------------------------------------------------------------------------------
fof('_HAMMER_COQ_TRUE',axiom,
    p(c_24True) ).

fof('_HAMMER_COQ_FALSE',axiom,
    ~ p(c_24False) ).

fof('_HAMMER_COQ_TYPE_TYPE',axiom,
    cType___24t(cType) ).

fof('$_case_Coq.Init.Datatypes.bool$13267',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4] :
      ( cType___24t(Vv__CANONICAL__0)
     => ( cIntMap_2eMap_2ead___24t(Vv__CANONICAL__4)
       => ( ( cCoq_2eNArith_2eBinNatDef_2eN_2eodd___24a1(Vv__CANONICAL__4) = cCoq_2eInit_2eDatatypes_2etrue
            & c_24__case__Coq_2eInit_2eDatatypes_2ebool_2413267___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4) = cIntMap_2eMap_2eMapGet___24a3(Vv__CANONICAL__0,cIntMap_2eMap_2eM2___24a3(Vv__CANONICAL__0,Vv__CANONICAL__2,Vv__CANONICAL__1),Vv__CANONICAL__4) )
          | ( cCoq_2eNArith_2eBinNatDef_2eN_2eodd___24a1(Vv__CANONICAL__4) = cCoq_2eInit_2eDatatypes_2efalse
            & c_24__case__Coq_2eInit_2eDatatypes_2ebool_2413267___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4) = cIntMap_2eMap_2eMapGet___24a3(Vv__CANONICAL__0,cIntMap_2eMap_2eM2___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__3),Vv__CANONICAL__4) ) ) ) ) ).

fof('$_case_Coq.Init.Datatypes.bool$13293',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] :
      ( cType___24t(Vv__CANONICAL__0)
     => ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__1)
       => ( ( Vv__CANONICAL__1 = cCoq_2eInit_2eDatatypes_2etrue
            & c_24__case__Coq_2eInit_2eDatatypes_2ebool_2413293___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = Vv__CANONICAL__2 )
          | ( Vv__CANONICAL__1 = cCoq_2eInit_2eDatatypes_2efalse
            & c_24__case__Coq_2eInit_2eDatatypes_2ebool_2413293___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = Vv__CANONICAL__3 ) ) ) ) ).

fof('$_case_Coq.Init.Datatypes.bool$13299',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4] :
      ( cType___24t(Vv__CANONICAL__0)
     => ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__1)
       => ( ( Vv__CANONICAL__1 = cCoq_2eInit_2eDatatypes_2etrue
            & c_24__case__Coq_2eInit_2eDatatypes_2ebool_2413299___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4) = cIntMap_2eMap_2eMapGet___24a3(Vv__CANONICAL__0,Vv__CANONICAL__2,Vv__CANONICAL__4) )
          | ( Vv__CANONICAL__1 = cCoq_2eInit_2eDatatypes_2efalse
            & c_24__case__Coq_2eInit_2eDatatypes_2ebool_2413299___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4) = cIntMap_2eMap_2eMapGet___24a3(Vv__CANONICAL__0,Vv__CANONICAL__3,Vv__CANONICAL__4) ) ) ) ) ).

fof('$_case_Coq.Init.Datatypes.bool$13303',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] :
      ( cType___24t(Vv__CANONICAL__0)
     => ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__2)
       => ( ( Vv__CANONICAL__2 = cCoq_2eInit_2eDatatypes_2etrue
            & c_24__case__Coq_2eInit_2eDatatypes_2ebool_2413303___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = Vv__CANONICAL__1 )
          | ( Vv__CANONICAL__2 = cCoq_2eInit_2eDatatypes_2efalse
            & c_24__case__Coq_2eInit_2eDatatypes_2ebool_2413303___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = Vv__CANONICAL__1 ) ) ) ) ).

fof('$_case_Coq.Init.Datatypes.bool$13309',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4] :
      ( cType___24t(Vv__CANONICAL__0)
     => ( cIntMap_2eMap_2ead___24t(Vv__CANONICAL__4)
       => ( ( cCoq_2eNArith_2eBinNatDef_2eN_2eodd___24a1(Vv__CANONICAL__4) = cCoq_2eInit_2eDatatypes_2etrue
            & c_24__case__Coq_2eInit_2eDatatypes_2ebool_2413309___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4) = cIntMap_2eMap_2eM2___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) )
          | ( cCoq_2eNArith_2eBinNatDef_2eN_2eodd___24a1(Vv__CANONICAL__4) = cCoq_2eInit_2eDatatypes_2efalse
            & c_24__case__Coq_2eInit_2eDatatypes_2ebool_2413309___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4) = cIntMap_2eMap_2eM2___24a3(Vv__CANONICAL__0,Vv__CANONICAL__2,Vv__CANONICAL__3) ) ) ) ) ).

fof('$_case_Coq.Init.Datatypes.bool$1994',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] :
      ( cType___24t(Vv__CANONICAL__0)
     => ( cIntMap_2eMap_2ead___24t(Vv__CANONICAL__3)
       => ( ( cCoq_2eNArith_2eBinNatDef_2eN_2eodd___24a1(Vv__CANONICAL__3) = cCoq_2eInit_2eDatatypes_2etrue
            & c_24__case__Coq_2eInit_2eDatatypes_2ebool_241994___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = cIntMap_2eMap_2eMapGet___24a3(Vv__CANONICAL__0,Vv__CANONICAL__2,cCoq_2eNArith_2eBinNatDef_2eN_2ediv2___24a1(Vv__CANONICAL__3)) )
          | ( cCoq_2eNArith_2eBinNatDef_2eN_2eodd___24a1(Vv__CANONICAL__3) = cCoq_2eInit_2eDatatypes_2efalse
            & c_24__case__Coq_2eInit_2eDatatypes_2ebool_241994___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = cIntMap_2eMap_2eMapGet___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,cCoq_2eNArith_2eBinNatDef_2eN_2ediv2___24a1(Vv__CANONICAL__3)) ) ) ) ) ).

fof('$_case_Coq.Init.Datatypes.bool$2000',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4] :
      ( cType___24t(Vv__CANONICAL__0)
     => ( cIntMap_2eMap_2ead___24t(Vv__CANONICAL__3)
       => ( ( cCoq_2eNArith_2eBinNatDef_2eN_2eodd___24a1(Vv__CANONICAL__3) = cCoq_2eInit_2eDatatypes_2etrue
            & c_24__case__Coq_2eInit_2eDatatypes_2ebool_242000___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4) = cIntMap_2eMap_2eM2___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,cIntMap_2eMap_2eMapPut__behind___24a4(Vv__CANONICAL__0,Vv__CANONICAL__2,cCoq_2eNArith_2eBinNatDef_2eN_2ediv2___24a1(Vv__CANONICAL__3),Vv__CANONICAL__4)) )
          | ( cCoq_2eNArith_2eBinNatDef_2eN_2eodd___24a1(Vv__CANONICAL__3) = cCoq_2eInit_2eDatatypes_2efalse
            & c_24__case__Coq_2eInit_2eDatatypes_2ebool_242000___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4) = cIntMap_2eMap_2eM2___24a3(Vv__CANONICAL__0,cIntMap_2eMap_2eMapPut__behind___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,cCoq_2eNArith_2eBinNatDef_2eN_2ediv2___24a1(Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__2) ) ) ) ) ).

fof('$_case_Coq.Init.Datatypes.bool$2675',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] :
      ( cType___24t(Vv__CANONICAL__0)
     => ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__1)
       => ( ( cCoq_2eInit_2eDatatypes_2enegb___24a1(Vv__CANONICAL__1) = cCoq_2eInit_2eDatatypes_2etrue
            & c_24__case__Coq_2eInit_2eDatatypes_2ebool_242675___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = Vv__CANONICAL__2 )
          | ( cCoq_2eInit_2eDatatypes_2enegb___24a1(Vv__CANONICAL__1) = cCoq_2eInit_2eDatatypes_2efalse
            & c_24__case__Coq_2eInit_2eDatatypes_2ebool_242675___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = Vv__CANONICAL__3 ) ) ) ) ).

fof('$_case_Coq.Init.Datatypes.bool$2680',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] :
      ( cType___24t(Vv__CANONICAL__0)
     => ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__1)
       => ( ( Vv__CANONICAL__1 = cCoq_2eInit_2eDatatypes_2etrue
            & c_24__case__Coq_2eInit_2eDatatypes_2ebool_242680___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = Vv__CANONICAL__3 )
          | ( Vv__CANONICAL__1 = cCoq_2eInit_2eDatatypes_2efalse
            & c_24__case__Coq_2eInit_2eDatatypes_2ebool_242680___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = Vv__CANONICAL__2 ) ) ) ) ).

fof('$_case_Coq.Init.Datatypes.bool$282',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4] :
      ( cType___24t(Vv__CANONICAL__0)
     => ( cIntMap_2eMap_2ead___24t(Vv__CANONICAL__3)
       => ( ( cCoq_2eNArith_2eBinNatDef_2eN_2eodd___24a1(Vv__CANONICAL__3) = cCoq_2eInit_2eDatatypes_2etrue
            & c_24__case__Coq_2eInit_2eDatatypes_2ebool_24282___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4) = cIntMap_2eMap_2eM2___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,cIntMap_2eMap_2eMapPut___24a4(Vv__CANONICAL__0,Vv__CANONICAL__2,cCoq_2eNArith_2eBinNatDef_2eN_2ediv2___24a1(Vv__CANONICAL__3),Vv__CANONICAL__4)) )
          | ( cCoq_2eNArith_2eBinNatDef_2eN_2eodd___24a1(Vv__CANONICAL__3) = cCoq_2eInit_2eDatatypes_2efalse
            & c_24__case__Coq_2eInit_2eDatatypes_2ebool_24282___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4) = cIntMap_2eMap_2eM2___24a3(Vv__CANONICAL__0,cIntMap_2eMap_2eMapPut___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,cCoq_2eNArith_2eBinNatDef_2eN_2ediv2___24a1(Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__2) ) ) ) ) ).

fof('$_case_Coq.Init.Datatypes.bool$36649',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4] :
      ( cType___24t(Vv__CANONICAL__0)
     => ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__3)
       => ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__4)
         => ( ( cCoq_2eInit_2eDatatypes_2eandb___24a2(Vv__CANONICAL__3,Vv__CANONICAL__4) = cCoq_2eInit_2eDatatypes_2etrue
              & c_24__case__Coq_2eInit_2eDatatypes_2ebool_2436649___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4) = Vv__CANONICAL__1 )
            | ( cCoq_2eInit_2eDatatypes_2eandb___24a2(Vv__CANONICAL__3,Vv__CANONICAL__4) = cCoq_2eInit_2eDatatypes_2efalse
              & c_24__case__Coq_2eInit_2eDatatypes_2ebool_2436649___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4) = Vv__CANONICAL__2 ) ) ) ) ) ).

fof('$_case_Coq.Init.Datatypes.bool$36660',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4] :
      ( cType___24t(Vv__CANONICAL__0)
     => ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__3)
       => ( ( cType___24t(Vv__CANONICAL__0)
           => ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__4)
             => ( Vv__CANONICAL__3 = cCoq_2eInit_2eDatatypes_2etrue
                & ( ( Vv__CANONICAL__4 = cCoq_2eInit_2eDatatypes_2etrue
                    & c_24__case__Coq_2eInit_2eDatatypes_2ebool_2436660___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4) = Vv__CANONICAL__1 )
                  | ( Vv__CANONICAL__4 = cCoq_2eInit_2eDatatypes_2efalse
                    & c_24__case__Coq_2eInit_2eDatatypes_2ebool_2436660___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4) = Vv__CANONICAL__2 ) ) ) ) )
          | ( Vv__CANONICAL__3 = cCoq_2eInit_2eDatatypes_2efalse
            & c_24__case__Coq_2eInit_2eDatatypes_2ebool_2436660___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4) = Vv__CANONICAL__2 ) ) ) ) ).

fof('$_case_Coq.Init.Datatypes.bool$36665',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] :
      ( cType___24t(Vv__CANONICAL__0)
     => ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__3)
       => ( ( cCoq_2eInit_2eDatatypes_2enegb___24a1(Vv__CANONICAL__3) = cCoq_2eInit_2eDatatypes_2etrue
            & c_24__case__Coq_2eInit_2eDatatypes_2ebool_2436665___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = Vv__CANONICAL__1 )
          | ( cCoq_2eInit_2eDatatypes_2enegb___24a1(Vv__CANONICAL__3) = cCoq_2eInit_2eDatatypes_2efalse
            & c_24__case__Coq_2eInit_2eDatatypes_2ebool_2436665___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = Vv__CANONICAL__2 ) ) ) ) ).

fof('$_case_Coq.Init.Datatypes.bool$36670',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] :
      ( cType___24t(Vv__CANONICAL__0)
     => ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__3)
       => ( ( Vv__CANONICAL__3 = cCoq_2eInit_2eDatatypes_2etrue
            & c_24__case__Coq_2eInit_2eDatatypes_2ebool_2436670___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = Vv__CANONICAL__2 )
          | ( Vv__CANONICAL__3 = cCoq_2eInit_2eDatatypes_2efalse
            & c_24__case__Coq_2eInit_2eDatatypes_2ebool_2436670___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = Vv__CANONICAL__1 ) ) ) ) ).

fof('$_case_Coq.Init.Datatypes.bool$577',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5] :
      ( cType___24t(Vv__CANONICAL__0)
     => ( cIntMap_2eMap_2ead___24t(Vv__CANONICAL__1)
       => ( ( cCoq_2eNArith_2eBinNatDef_2eN_2eodd___24a1(Vv__CANONICAL__1) = cCoq_2eInit_2eDatatypes_2etrue
            & c_24__case__Coq_2eInit_2eDatatypes_2ebool_24577___24a6(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5) = cIntMap_2eMap_2eM2___24a3(Vv__CANONICAL__0,cIntMap_2eMap_2eM0___24a1(Vv__CANONICAL__0),c_24__let__var__8__m__567__570___24a6(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5)) )
          | ( cCoq_2eNArith_2eBinNatDef_2eN_2eodd___24a1(Vv__CANONICAL__1) = cCoq_2eInit_2eDatatypes_2efalse
            & c_24__case__Coq_2eInit_2eDatatypes_2ebool_24577___24a6(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5) = cIntMap_2eMap_2eM2___24a3(Vv__CANONICAL__0,c_24__let__var__8__m__567__570___24a6(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5),cIntMap_2eMap_2eM0___24a1(Vv__CANONICAL__0)) ) ) ) ) ).

fof('$_case_Coq.Init.Datatypes.nat$23372',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__2)
     => ( ( Vv__CANONICAL__2 = cCoq_2eInit_2eDatatypes_2eO
          & c_24__case__Coq_2eInit_2eDatatypes_2enat_2423372___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = cCoq_2eNumbers_2eBinNums_2eZ0 )
        | ? [Vvar__0___24Anonymous__23373] :
            ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__23373)
            & Vv__CANONICAL__2 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__23373)
            & c_24__case__Coq_2eInit_2eDatatypes_2enat_2423372___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eof__succ__nat___24a1(Vvar__0___24Anonymous__23373)) ) ) ) ).

fof('$_case_Coq.Init.Datatypes.nat$23394',axiom,
    ! [Vv__CANONICAL__0] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
     => ( ( Vv__CANONICAL__0 = cCoq_2eInit_2eDatatypes_2eO
          & c_24__case__Coq_2eInit_2eDatatypes_2enat_2423394___24a1(Vv__CANONICAL__0) = cCoq_2eNumbers_2eBinNums_2eZ0 )
        | ? [Vvar__0___24Anonymous__23395] :
            ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__23395)
            & Vv__CANONICAL__0 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__23395)
            & c_24__case__Coq_2eInit_2eDatatypes_2enat_2423394___24a1(Vv__CANONICAL__0) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eof__succ__nat___24a1(Vvar__0___24Anonymous__23395)) ) ) ) ).

fof('$_case_Coq.Init.Datatypes.option$13336',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] :
      ( cType___24t(Vv__CANONICAL__0)
     => ( cIntMap_2eMap_2eMap___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
       => ( cIntMap_2eMap_2ead___24t(Vv__CANONICAL__2)
         => ( ? [Vvar__1___24Anonymous__13339] :
                ( t(Vvar__1___24Anonymous__13339,Vv__CANONICAL__0)
                & cIntMap_2eMap_2eMapGet___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = cCoq_2eInit_2eDatatypes_2eSome___24a2(Vv__CANONICAL__0,Vvar__1___24Anonymous__13339)
                & c_24__case__Coq_2eInit_2eDatatypes_2eoption_2413336___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = cCoq_2eInit_2eDatatypes_2eSome___24a2(Vv__CANONICAL__0,Vvar__1___24Anonymous__13339) )
            | ( cIntMap_2eMap_2eMapGet___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = cCoq_2eInit_2eDatatypes_2eNone___24a1(Vv__CANONICAL__0)
              & c_24__case__Coq_2eInit_2eDatatypes_2eoption_2413336___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = cCoq_2eInit_2eDatatypes_2eSome___24a2(Vv__CANONICAL__0,Vv__CANONICAL__3) ) ) ) ) ) ).

fof('$_case_Coq.Init.Datatypes.option$2237',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] :
      ( cType___24t(Vv__CANONICAL__0)
     => ( cIntMap_2eMapiter_2ealist___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
       => ( cIntMap_2eMap_2ead___24t(Vv__CANONICAL__3)
         => ( ? [Vvar__1___24Anonymous__2240] :
                ( t(Vvar__1___24Anonymous__2240,Vv__CANONICAL__0)
                & cIntMap_2eMapiter_2ealist__semantics___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__3) = cCoq_2eInit_2eDatatypes_2eSome___24a2(Vv__CANONICAL__0,Vvar__1___24Anonymous__2240)
                & c_24__case__Coq_2eInit_2eDatatypes_2eoption_242237___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = cCoq_2eInit_2eDatatypes_2eSome___24a2(Vv__CANONICAL__0,Vvar__1___24Anonymous__2240) )
            | ( cIntMap_2eMapiter_2ealist__semantics___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__3) = cCoq_2eInit_2eDatatypes_2eNone___24a1(Vv__CANONICAL__0)
              & c_24__case__Coq_2eInit_2eDatatypes_2eoption_242237___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = cIntMap_2eMapiter_2ealist__semantics___24a3(Vv__CANONICAL__0,Vv__CANONICAL__2,Vv__CANONICAL__3) ) ) ) ) ) ).

fof('$_case_Coq.Numbers.BinNums.Z$23389',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__2)
     => ( ( c_24__case__Coq_2eInit_2eDatatypes_2enat_2423394___24a1(Vv__CANONICAL__2) = cCoq_2eNumbers_2eBinNums_2eZ0
          & c_24__case__Coq_2eNumbers_2eBinNums_2eZ_2423389___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = cCoq_2eNumbers_2eBinNums_2eZ0 )
        | ? [Vvar__0___24Anonymous__23390] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__23390)
            & c_24__case__Coq_2eInit_2eDatatypes_2enat_2423394___24a1(Vv__CANONICAL__2) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__23390)
            & c_24__case__Coq_2eNumbers_2eBinNums_2eZ_2423389___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__23390) )
        | ? [Vvar__0___24Anonymous__23391] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__23391)
            & c_24__case__Coq_2eInit_2eDatatypes_2enat_2423394___24a1(Vv__CANONICAL__2) = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__23391)
            & c_24__case__Coq_2eNumbers_2eBinNums_2eZ_2423389___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__23391) ) ) ) ).

fof('$_case_Coq.Numbers.BinNums.positive$33555',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1] :
      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__1)
     => ( ? [Vvar__0___24Anonymous__33556] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__33556)
            & Vv__CANONICAL__1 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__33556)
            & c_24__case__Coq_2eNumbers_2eBinNums_2epositive_2433555___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = cCoq_2eNumbers_2eBinNums_2exO___24a1(c_24__fix__33571__v__CANONICAL__0___24a1(Vvar__0___24Anonymous__33556)) )
        | ? [Vvar__0___24Anonymous__33563] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__33563)
            & Vv__CANONICAL__1 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__33563)
            & c_24__case__Coq_2eNumbers_2eBinNums_2epositive_2433555___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__33563) )
        | ( Vv__CANONICAL__1 = cCoq_2eNumbers_2eBinNums_2exH
          & c_24__case__Coq_2eNumbers_2eBinNums_2epositive_2433555___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2eNumbers_2eBinNums_2exH) ) ) ) ).

fof('$_def_$_cast_1811',axiom,
    ! [V1__b2] : c_24__cast__1811___24a1(V1__b2) = cCoq_2eInit_2eSpecif_2eleft___24a2(c_24__prop__1812,c_24__prop__1813___24a1(V1__b2)) ).

fof('$_def_$_cast_1814',axiom,
    ! [V1__b2] : c_24__cast__1814___24a1(V1__b2) = cCoq_2eInit_2eSpecif_2eright___24a2(c_24__prop__1815___24a1(V1__b2),c_24__prop__1816___24a1(V1__b2)) ).

fof('$_def_$_let_var_6_p_28906_28909',axiom,
    ! [V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__28905] : c_24__let__var__6__p__28906__28909___24a4(V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__28905) = cCoq_2esetoid__ring_2eRing__theory_2epow__pos___24a4(V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__28905) ).

fof('$_def_$_let_var_6_p_28908_28910',axiom,
    ! [V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__28907] : c_24__let__var__6__p__28908__28910___24a4(V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__28907) = cCoq_2esetoid__ring_2eRing__theory_2epow__pos___24a4(V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__28907) ).

fof('$_def_$_let_var_8_m_567_570',axiom,
    ! [V0__A,V2__a,V3__y,V4__a_27,V5__y_27,Vvar__0___24Anonymous__565] : c_24__let__var__8__m__567__570___24a6(V0__A,V2__a,V3__y,V4__a_27,V5__y_27,Vvar__0___24Anonymous__565) = cIntMap_2eMap_2eMapPut1___24a6(V0__A,cCoq_2eNArith_2eBinNatDef_2eN_2ediv2___24a1(V2__a),V3__y,cCoq_2eNArith_2eBinNatDef_2eN_2ediv2___24a1(V4__a_27),V5__y_27,Vvar__0___24Anonymous__565) ).

fof('$_def_Coq.Arith.EqNat.eq_nat',axiom,
    ! [V1__n,V2__m] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
     => ( ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__m)
         => ( V1__n = cCoq_2eInit_2eDatatypes_2eO
            & ( ( V2__m = cCoq_2eInit_2eDatatypes_2eO
                & ( cCoq_2eArith_2eEqNat_2eeq__nat___24a2(V1__n,V2__m)
                <=> p(c_24True) ) )
              | ? [Vvar__0___24Anonymous__20060] :
                  ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__20060)
                  & V2__m = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__20060)
                  & ( cCoq_2eArith_2eEqNat_2eeq__nat___24a2(V1__n,V2__m)
                  <=> p(c_24False) ) ) ) ) )
        | ? [Vvar__0___24Anonymous__20061] :
            ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__20061)
            & ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__m)
             => ( V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__20061)
                & ( ( V2__m = cCoq_2eInit_2eDatatypes_2eO
                    & ( cCoq_2eArith_2eEqNat_2eeq__nat___24a2(V1__n,V2__m)
                    <=> p(c_24False) ) )
                  | ? [Vvar__0___24Anonymous__20064] :
                      ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__20064)
                      & V2__m = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__20064)
                      & ( cCoq_2eArith_2eEqNat_2eeq__nat___24a2(V1__n,V2__m)
                      <=> cCoq_2eArith_2eEqNat_2eeq__nat___24a2(Vvar__0___24Anonymous__20061,Vvar__0___24Anonymous__20064) ) ) ) ) ) ) ) ) ).

fof('$_def_Coq.Arith.PeanoNat.Nat.divide',axiom,
    ! [V0__x,V1__y] :
      ( cCoq_2eArith_2ePeanoNat_2eNat_2edivide___24a2(V0__x,V1__y)
    <=> ? [V2__z] :
          ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__z)
          & V1__y = cCoq_2eInit_2eNat_2emul___24a2(V2__z,V0__x) ) ) ).

fof('$_def_Coq.Arith.PeanoNat.Nat.eqf',axiom,
    ! [V0__f,V1__g] :
      ( cCoq_2eArith_2ePeanoNat_2eNat_2eeqf___24a2(V0__f,V1__g)
    <=> ! [V2__n] :
          ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__n)
         => happ(V0__f,V2__n) = happ(V1__g,V2__n) ) ) ).

fof('$_def_Coq.Arith.PeanoNat.Nat.le_alt',axiom,
    ! [V0__n,V1__m] :
      ( cCoq_2eArith_2ePeanoNat_2eNat_2ele__alt___24a2(V0__n,V1__m)
    <=> ? [V2__p] :
          ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__p)
          & cCoq_2eInit_2eNat_2eadd___24a2(V2__p,V0__n) = V1__m ) ) ).

fof('$_def_Coq.Bool.Bool.Is_true',axiom,
    ! [V0__b] :
      ( cCoq_2eInit_2eDatatypes_2ebool___24t(V0__b)
     => ( ( V0__b = cCoq_2eInit_2eDatatypes_2etrue
          & ( cCoq_2eBool_2eBool_2eIs__true___24a1(V0__b)
          <=> p(c_24True) ) )
        | ( V0__b = cCoq_2eInit_2eDatatypes_2efalse
          & ( cCoq_2eBool_2eBool_2eIs__true___24a1(V0__b)
          <=> p(c_24False) ) ) ) ) ).

fof('$_def_Coq.Bool.Bool.eqb',axiom,
    ! [V0__b1,V1__b2] :
      ( cCoq_2eInit_2eDatatypes_2ebool___24t(V0__b1)
     => ( ( cCoq_2eInit_2eDatatypes_2ebool___24t(V1__b2)
         => ( V0__b1 = cCoq_2eInit_2eDatatypes_2etrue
            & ( ( V1__b2 = cCoq_2eInit_2eDatatypes_2etrue
                & cCoq_2eBool_2eBool_2eeqb___24a2(V0__b1,V1__b2) = cCoq_2eInit_2eDatatypes_2etrue )
              | ( V1__b2 = cCoq_2eInit_2eDatatypes_2efalse
                & cCoq_2eBool_2eBool_2eeqb___24a2(V0__b1,V1__b2) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) )
        | ( cCoq_2eInit_2eDatatypes_2ebool___24t(V1__b2)
         => ( V0__b1 = cCoq_2eInit_2eDatatypes_2efalse
            & ( ( V1__b2 = cCoq_2eInit_2eDatatypes_2etrue
                & cCoq_2eBool_2eBool_2eeqb___24a2(V0__b1,V1__b2) = cCoq_2eInit_2eDatatypes_2efalse )
              | ( V1__b2 = cCoq_2eInit_2eDatatypes_2efalse
                & cCoq_2eBool_2eBool_2eeqb___24a2(V0__b1,V1__b2) = cCoq_2eInit_2eDatatypes_2etrue ) ) ) ) ) ) ).

fof('$_def_Coq.Bool.Bool.leb',axiom,
    ! [V0__b1,V1__b2] :
      ( cCoq_2eInit_2eDatatypes_2ebool___24t(V0__b1)
     => ( ( V0__b1 = cCoq_2eInit_2eDatatypes_2etrue
          & ( cCoq_2eBool_2eBool_2eleb___24a2(V0__b1,V1__b2)
          <=> V1__b2 = cCoq_2eInit_2eDatatypes_2etrue ) )
        | ( V0__b1 = cCoq_2eInit_2eDatatypes_2efalse
          & ( cCoq_2eBool_2eBool_2eleb___24a2(V0__b1,V1__b2)
          <=> p(c_24True) ) ) ) ) ).

fof('$_def_Coq.Bool.Bool.orb_true_elim',axiom,
    ! [V0__b1] :
      ( cCoq_2eInit_2eDatatypes_2ebool___24t(V0__b1)
     => ( ( V0__b1 = cCoq_2eInit_2eDatatypes_2etrue
          & cCoq_2eBool_2eBool_2eorb__true__elim___24a1(V0__b1) = c_24__cast__1811 )
        | ( V0__b1 = cCoq_2eInit_2eDatatypes_2efalse
          & cCoq_2eBool_2eBool_2eorb__true__elim___24a1(V0__b1) = c_24__cast__1814 ) ) ) ).

fof('$_def_Coq.Bool.Sumbool.sumbool_of_bool',axiom,
    ! [V0__b] :
      ( cCoq_2eInit_2eDatatypes_2ebool___24t(V0__b)
     => ( ( V0__b = cCoq_2eInit_2eDatatypes_2etrue
          & cCoq_2eBool_2eSumbool_2esumbool__of__bool___24a1(V0__b) = cCoq_2eInit_2eSpecif_2eleft___24a3(c_24__prop__426,c_24__prop__427,cCoq_2eInit_2eLogic_2eeq__refl___24a2(cCoq_2eInit_2eDatatypes_2ebool,cCoq_2eInit_2eDatatypes_2etrue)) )
        | ( V0__b = cCoq_2eInit_2eDatatypes_2efalse
          & cCoq_2eBool_2eSumbool_2esumbool__of__bool___24a1(V0__b) = cCoq_2eInit_2eSpecif_2eright___24a3(c_24__prop__428,c_24__prop__429,cCoq_2eInit_2eLogic_2eeq__refl___24a2(cCoq_2eInit_2eDatatypes_2ebool,cCoq_2eInit_2eDatatypes_2efalse)) ) ) ) ).

fof('$_def_Coq.FSets.FSetPositive.PositiveSet.In',axiom,
    ! [V0__i,V1__t] :
      ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eIn___24a2(V0__i,V1__t)
    <=> cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2emem___24a2(V0__i,V1__t) = cCoq_2eInit_2eDatatypes_2etrue ) ).

fof('$_def_Coq.FSets.FSetPositive.PositiveSet.elt',axiom,
    ! [Vvar__19219] :
      ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(Vvar__19219)
    <=> cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__19219) ) ).

fof('$_def_Coq.FSets.FSetPositive.PositiveSet.t',axiom,
    ! [Vvar__19245] :
      ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(Vvar__19245)
    <=> cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree___24t(Vvar__19245) ) ).

fof('$_def_Coq.Init.Datatypes.IDProp',axiom,
    ( p(cCoq_2eInit_2eDatatypes_2eIDProp)
  <=> ! [V0__A] :
        ( cProp___24t(V0__A)
       => ( p(V0__A)
         => p(V0__A) ) ) ) ).

fof('$_def_Coq.Init.Datatypes.andb',axiom,
    ! [V0__b1,V1__b2] :
      ( cCoq_2eInit_2eDatatypes_2ebool___24t(V0__b1)
     => ( ( V0__b1 = cCoq_2eInit_2eDatatypes_2etrue
          & cCoq_2eInit_2eDatatypes_2eandb___24a2(V0__b1,V1__b2) = V1__b2 )
        | ( V0__b1 = cCoq_2eInit_2eDatatypes_2efalse
          & cCoq_2eInit_2eDatatypes_2eandb___24a2(V0__b1,V1__b2) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ).

fof('$_def_Coq.Init.Datatypes.app',axiom,
    ! [V0__A,V2__l,V3__m] :
      ( cType___24t(V0__A)
     => ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l)
       => ( ( V2__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)
            & cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V2__l,V3__m) = V3__m )
          | ? [Vvar__1___24Anonymous__10979] :
              ( t(Vvar__1___24Anonymous__10979,V0__A)
              & ? [Vvar__2___24Anonymous__10980] :
                  ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__10980)
                  & V2__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__10979,Vvar__2___24Anonymous__10980)
                  & cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V2__l,V3__m) = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__10979,cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,Vvar__2___24Anonymous__10980,V3__m)) ) ) ) ) ) ).

fof('$_def_Coq.Init.Datatypes.fst',axiom,
    ! [V0__A,V1__B,V2__p] :
      ( cType___24t(V0__A)
     => ( cType___24t(V1__B)
       => ( cCoq_2eInit_2eDatatypes_2eprod___24t(V0__A,V1__B,V2__p)
         => ? [Vvar__2___24Anonymous__10891] :
              ( t(Vvar__2___24Anonymous__10891,V0__A)
              & ? [Vvar__3___24Anonymous__10892] :
                  ( t(Vvar__3___24Anonymous__10892,V1__B)
                  & V2__p = cCoq_2eInit_2eDatatypes_2epair___24a4(V0__A,V1__B,Vvar__2___24Anonymous__10891,Vvar__3___24Anonymous__10892)
                  & cCoq_2eInit_2eDatatypes_2efst___24a3(V0__A,V1__B,V2__p) = Vvar__2___24Anonymous__10891 ) ) ) ) ) ).

fof('$_def_Coq.Init.Datatypes.is_true',axiom,
    ! [V0__b] :
      ( cCoq_2eInit_2eDatatypes_2eis__true___24a1(V0__b)
    <=> V0__b = cCoq_2eInit_2eDatatypes_2etrue ) ).

fof('$_def_Coq.Init.Datatypes.length',axiom,
    ! [V0__A,V2__l] :
      ( cType___24t(V0__A)
     => ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l)
       => ( ( V2__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)
            & cCoq_2eInit_2eDatatypes_2elength___24a2(V0__A,V2__l) = cCoq_2eInit_2eDatatypes_2eO )
          | ? [Vvar__1___24Anonymous__10969] :
              ( t(Vvar__1___24Anonymous__10969,V0__A)
              & ? [Vvar__2___24Anonymous__10970] :
                  ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__10970)
                  & V2__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__10969,Vvar__2___24Anonymous__10970)
                  & cCoq_2eInit_2eDatatypes_2elength___24a2(V0__A,V2__l) = cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2elength___24a2(V0__A,Vvar__2___24Anonymous__10970)) ) ) ) ) ) ).

fof('$_def_Coq.Init.Datatypes.negb',axiom,
    ! [V0__b] :
      ( cCoq_2eInit_2eDatatypes_2ebool___24t(V0__b)
     => ( ( V0__b = cCoq_2eInit_2eDatatypes_2etrue
          & cCoq_2eInit_2eDatatypes_2enegb___24a1(V0__b) = cCoq_2eInit_2eDatatypes_2efalse )
        | ( V0__b = cCoq_2eInit_2eDatatypes_2efalse
          & cCoq_2eInit_2eDatatypes_2enegb___24a1(V0__b) = cCoq_2eInit_2eDatatypes_2etrue ) ) ) ).

fof('$_def_Coq.Init.Datatypes.orb',axiom,
    ! [V0__b1,V1__b2] :
      ( cCoq_2eInit_2eDatatypes_2ebool___24t(V0__b1)
     => ( ( V0__b1 = cCoq_2eInit_2eDatatypes_2etrue
          & cCoq_2eInit_2eDatatypes_2eorb___24a2(V0__b1,V1__b2) = cCoq_2eInit_2eDatatypes_2etrue )
        | ( V0__b1 = cCoq_2eInit_2eDatatypes_2efalse
          & cCoq_2eInit_2eDatatypes_2eorb___24a2(V0__b1,V1__b2) = V1__b2 ) ) ) ).

fof('$_def_Coq.Init.Datatypes.prod_rect',axiom,
    ! [V0__A,V1__B,V2__P,V3__f,V4__p] :
      ( cType___24t(V0__A)
     => ( cType___24t(V1__B)
       => ( c_24__type__10849___24t(V0__A,V1__B,V2__P,V2__P)
         => ( cCoq_2eInit_2eDatatypes_2eprod___24t(V0__A,V1__B,V4__p)
           => ? [Vvar__2___24Anonymous__10842] :
                ( t(Vvar__2___24Anonymous__10842,V0__A)
                & ? [Vvar__3___24Anonymous__10843] :
                    ( t(Vvar__3___24Anonymous__10843,V1__B)
                    & V4__p = cCoq_2eInit_2eDatatypes_2epair___24a4(V0__A,V1__B,Vvar__2___24Anonymous__10842,Vvar__3___24Anonymous__10843)
                    & cCoq_2eInit_2eDatatypes_2eprod__rect___24a5(V0__A,V1__B,V2__P,V3__f,V4__p) = happ(happ(V3__f,Vvar__2___24Anonymous__10842),Vvar__3___24Anonymous__10843) ) ) ) ) ) ) ).

fof('$_def_Coq.Init.Datatypes.snd',axiom,
    ! [V0__A,V1__B,V2__p] :
      ( cType___24t(V0__A)
     => ( cType___24t(V1__B)
       => ( cCoq_2eInit_2eDatatypes_2eprod___24t(V0__A,V1__B,V2__p)
         => ? [Vvar__2___24Anonymous__10903] :
              ( t(Vvar__2___24Anonymous__10903,V0__A)
              & ? [Vvar__3___24Anonymous__10904] :
                  ( t(Vvar__3___24Anonymous__10904,V1__B)
                  & V2__p = cCoq_2eInit_2eDatatypes_2epair___24a4(V0__A,V1__B,Vvar__2___24Anonymous__10903,Vvar__3___24Anonymous__10904)
                  & cCoq_2eInit_2eDatatypes_2esnd___24a3(V0__A,V1__B,V2__p) = Vvar__3___24Anonymous__10904 ) ) ) ) ) ).

fof('$_def_Coq.Init.Datatypes.xorb',axiom,
    ! [V0__b1,V1__b2] :
      ( cCoq_2eInit_2eDatatypes_2ebool___24t(V0__b1)
     => ( ( cCoq_2eInit_2eDatatypes_2ebool___24t(V1__b2)
         => ( V0__b1 = cCoq_2eInit_2eDatatypes_2etrue
            & ( ( V1__b2 = cCoq_2eInit_2eDatatypes_2etrue
                & cCoq_2eInit_2eDatatypes_2exorb___24a2(V0__b1,V1__b2) = cCoq_2eInit_2eDatatypes_2efalse )
              | ( V1__b2 = cCoq_2eInit_2eDatatypes_2efalse
                & cCoq_2eInit_2eDatatypes_2exorb___24a2(V0__b1,V1__b2) = cCoq_2eInit_2eDatatypes_2etrue ) ) ) )
        | ( cCoq_2eInit_2eDatatypes_2ebool___24t(V1__b2)
         => ( V0__b1 = cCoq_2eInit_2eDatatypes_2efalse
            & ( ( V1__b2 = cCoq_2eInit_2eDatatypes_2etrue
                & cCoq_2eInit_2eDatatypes_2exorb___24a2(V0__b1,V1__b2) = cCoq_2eInit_2eDatatypes_2etrue )
              | ( V1__b2 = cCoq_2eInit_2eDatatypes_2efalse
                & cCoq_2eInit_2eDatatypes_2exorb___24a2(V0__b1,V1__b2) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ) ) ).

fof('$_def_Coq.Init.Nat.add',axiom,
    ! [V1__n,V2__m] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
     => ( ( V1__n = cCoq_2eInit_2eDatatypes_2eO
          & cCoq_2eInit_2eNat_2eadd___24a2(V1__n,V2__m) = V2__m )
        | ? [Vvar__0___24Anonymous__787] :
            ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__787)
            & V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__787)
            & cCoq_2eInit_2eNat_2eadd___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eNat_2eadd___24a2(Vvar__0___24Anonymous__787,V2__m)) ) ) ) ).

fof('$_def_Coq.Init.Nat.div2',axiom,
    ! [V1__n] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
     => ( ( V1__n = cCoq_2eInit_2eDatatypes_2eO
          & cCoq_2eInit_2eNat_2ediv2___24a1(V1__n) = cCoq_2eInit_2eDatatypes_2eO )
        | ? [Vvar__0___24Anonymous__14600] :
            ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__14600)
            & ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__14600)
             => ( V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__14600)
                & ( ( Vvar__0___24Anonymous__14600 = cCoq_2eInit_2eDatatypes_2eO
                    & cCoq_2eInit_2eNat_2ediv2___24a1(V1__n) = cCoq_2eInit_2eDatatypes_2eO )
                  | ? [Vvar__0___24Anonymous__14603] :
                      ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__14603)
                      & Vvar__0___24Anonymous__14600 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__14603)
                      & cCoq_2eInit_2eNat_2ediv2___24a1(V1__n) = cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eNat_2ediv2___24a1(Vvar__0___24Anonymous__14603)) ) ) ) ) ) ) ) ).

fof('$_def_Coq.Init.Nat.double',axiom,
    ! [V0__n] : cCoq_2eInit_2eNat_2edouble___24a1(V0__n) = cCoq_2eInit_2eNat_2eadd___24a2(V0__n,V0__n) ).

fof('$_def_Coq.Init.Nat.eqb',axiom,
    ! [V1__n,V2__m] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
     => ( ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__m)
         => ( V1__n = cCoq_2eInit_2eDatatypes_2eO
            & ( ( V2__m = cCoq_2eInit_2eDatatypes_2eO
                & cCoq_2eInit_2eNat_2eeqb___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2etrue )
              | ? [Vvar__0___24Anonymous__21838] :
                  ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__21838)
                  & V2__m = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__21838)
                  & cCoq_2eInit_2eNat_2eeqb___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) )
        | ? [Vvar__0___24Anonymous__21839] :
            ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__21839)
            & ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__m)
             => ( V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__21839)
                & ( ( V2__m = cCoq_2eInit_2eDatatypes_2eO
                    & cCoq_2eInit_2eNat_2eeqb___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2efalse )
                  | ? [Vvar__0___24Anonymous__21842] :
                      ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__21842)
                      & V2__m = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__21842)
                      & cCoq_2eInit_2eNat_2eeqb___24a2(V1__n,V2__m) = cCoq_2eInit_2eNat_2eeqb___24a2(Vvar__0___24Anonymous__21839,Vvar__0___24Anonymous__21842) ) ) ) ) ) ) ) ).

fof('$_def_Coq.Init.Nat.even',axiom,
    ! [V1__n] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
     => ( ( V1__n = cCoq_2eInit_2eDatatypes_2eO
          & cCoq_2eInit_2eNat_2eeven___24a1(V1__n) = cCoq_2eInit_2eDatatypes_2etrue )
        | ? [Vvar__0___24Anonymous__21851] :
            ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__21851)
            & ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__21851)
             => ( V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__21851)
                & ( ( Vvar__0___24Anonymous__21851 = cCoq_2eInit_2eDatatypes_2eO
                    & cCoq_2eInit_2eNat_2eeven___24a1(V1__n) = cCoq_2eInit_2eDatatypes_2efalse )
                  | ? [Vvar__0___24Anonymous__21854] :
                      ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__21854)
                      & Vvar__0___24Anonymous__21851 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__21854)
                      & cCoq_2eInit_2eNat_2eeven___24a1(V1__n) = cCoq_2eInit_2eNat_2eeven___24a1(Vvar__0___24Anonymous__21854) ) ) ) ) ) ) ) ).

fof('$_def_Coq.Init.Nat.max',axiom,
    ! [V1__n,V2__m] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
     => ( ( V1__n = cCoq_2eInit_2eDatatypes_2eO
          & cCoq_2eInit_2eNat_2emax___24a2(V1__n,V2__m) = V2__m )
        | ? [Vvar__0___24Anonymous__14582] :
            ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__14582)
            & ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__m)
             => ( V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__14582)
                & ( ( V2__m = cCoq_2eInit_2eDatatypes_2eO
                    & cCoq_2eInit_2eNat_2emax___24a2(V1__n,V2__m) = V1__n )
                  | ? [Vvar__0___24Anonymous__14585] :
                      ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__14585)
                      & V2__m = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__14585)
                      & cCoq_2eInit_2eNat_2emax___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eNat_2emax___24a2(Vvar__0___24Anonymous__14582,Vvar__0___24Anonymous__14585)) ) ) ) ) ) ) ) ).

fof('$_def_Coq.Init.Nat.min',axiom,
    ! [V1__n,V2__m] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
     => ( ( V1__n = cCoq_2eInit_2eDatatypes_2eO
          & cCoq_2eInit_2eNat_2emin___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2eO )
        | ? [Vvar__0___24Anonymous__14588] :
            ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__14588)
            & ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__m)
             => ( V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__14588)
                & ( ( V2__m = cCoq_2eInit_2eDatatypes_2eO
                    & cCoq_2eInit_2eNat_2emin___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2eO )
                  | ? [Vvar__0___24Anonymous__14591] :
                      ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__14591)
                      & V2__m = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__14591)
                      & cCoq_2eInit_2eNat_2emin___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eNat_2emin___24a2(Vvar__0___24Anonymous__14588,Vvar__0___24Anonymous__14591)) ) ) ) ) ) ) ) ).

fof('$_def_Coq.Init.Nat.mul',axiom,
    ! [V1__n,V2__m] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
     => ( ( V1__n = cCoq_2eInit_2eDatatypes_2eO
          & cCoq_2eInit_2eNat_2emul___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2eO )
        | ? [Vvar__0___24Anonymous__14579] :
            ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__14579)
            & V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__14579)
            & cCoq_2eInit_2eNat_2emul___24a2(V1__n,V2__m) = cCoq_2eInit_2eNat_2eadd___24a2(V2__m,cCoq_2eInit_2eNat_2emul___24a2(Vvar__0___24Anonymous__14579,V2__m)) ) ) ) ).

fof('$_def_Coq.Init.Nat.pow',axiom,
    ! [V1__n,V2__m] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__m)
     => ( ( V2__m = cCoq_2eInit_2eDatatypes_2eO
          & cCoq_2eInit_2eNat_2epow___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO) )
        | ? [Vvar__0___24Anonymous__21856] :
            ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__21856)
            & V2__m = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__21856)
            & cCoq_2eInit_2eNat_2epow___24a2(V1__n,V2__m) = cCoq_2eInit_2eNat_2emul___24a2(V1__n,cCoq_2eInit_2eNat_2epow___24a2(V1__n,Vvar__0___24Anonymous__21856)) ) ) ) ).

fof('$_def_Coq.Init.Nat.pred',axiom,
    ! [V0__n] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
     => ( ( V0__n = cCoq_2eInit_2eDatatypes_2eO
          & cCoq_2eInit_2eNat_2epred___24a1(V0__n) = V0__n )
        | ? [Vvar__0___24Anonymous__21830] :
            ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__21830)
            & V0__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__21830)
            & cCoq_2eInit_2eNat_2epred___24a1(V0__n) = Vvar__0___24Anonymous__21830 ) ) ) ).

fof('$_def_Coq.Init.Nat.sub',axiom,
    ! [V1__n,V2__m] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
     => ( ( V1__n = cCoq_2eInit_2eDatatypes_2eO
          & cCoq_2eInit_2eNat_2esub___24a2(V1__n,V2__m) = V1__n )
        | ? [Vvar__0___24Anonymous__21832] :
            ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__21832)
            & ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__m)
             => ( V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__21832)
                & ( ( V2__m = cCoq_2eInit_2eDatatypes_2eO
                    & cCoq_2eInit_2eNat_2esub___24a2(V1__n,V2__m) = V1__n )
                  | ? [Vvar__0___24Anonymous__21835] :
                      ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__21835)
                      & V2__m = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__21835)
                      & cCoq_2eInit_2eNat_2esub___24a2(V1__n,V2__m) = cCoq_2eInit_2eNat_2esub___24a2(Vvar__0___24Anonymous__21832,Vvar__0___24Anonymous__21835) ) ) ) ) ) ) ) ).

fof('$_def_Coq.Init.Nat.testbit',axiom,
    ! [V1__a,V2__n] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__n)
     => ( ( V2__n = cCoq_2eInit_2eDatatypes_2eO
          & cCoq_2eInit_2eNat_2etestbit___24a2(V1__a,V2__n) = cCoq_2eInit_2eNat_2eodd___24a1(V1__a) )
        | ? [Vvar__0___24Anonymous__14605] :
            ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__14605)
            & V2__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__14605)
            & cCoq_2eInit_2eNat_2etestbit___24a2(V1__a,V2__n) = cCoq_2eInit_2eNat_2etestbit___24a2(cCoq_2eInit_2eNat_2ediv2___24a1(V1__a),Vvar__0___24Anonymous__14605) ) ) ) ).

fof('$_def_Coq.Init.Peano.ge',axiom,
    ! [V0__n,V1__m] :
      ( cCoq_2eInit_2ePeano_2ege___24a2(V0__n,V1__m)
    <=> cCoq_2eInit_2ePeano_2ele___24a2(V1__m,V0__n) ) ).

fof('$_def_Coq.Init.Peano.gt',axiom,
    ! [V0__n,V1__m] :
      ( cCoq_2eInit_2ePeano_2egt___24a2(V0__n,V1__m)
    <=> cCoq_2eInit_2ePeano_2elt___24a2(V1__m,V0__n) ) ).

fof('$_def_Coq.Init.Peano.lt',axiom,
    ! [V0__n,V1__m] :
      ( cCoq_2eInit_2ePeano_2elt___24a2(V0__n,V1__m)
    <=> cCoq_2eInit_2ePeano_2ele___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(V0__n),V1__m) ) ).

fof('$_def_Coq.Init.Specif.sigT_rect',axiom,
    ! [V0__A,V1__P,V2__P,V3__f,V4__s] :
      ( cType___24t(V0__A)
     => ( c_24__type__18778___24t(V0__A,V1__P,V2__P,V1__P)
       => ( c_24__type__18786___24t(V0__A,V1__P,V2__P,V2__P)
         => ( cCoq_2eInit_2eSpecif_2esigT___24t(V0__A,V1__P,V4__s)
           => ? [Vvar__2__x__18770] :
                ( t(Vvar__2__x__18770,V0__A)
                & ? [Vvar__3___24Anonymous__18771] :
                    ( t(Vvar__3___24Anonymous__18771,happ(V1__P,Vvar__2__x__18770))
                    & V4__s = cCoq_2eInit_2eSpecif_2eexistT___24a4(V0__A,V1__P,Vvar__2__x__18770,Vvar__3___24Anonymous__18771)
                    & cCoq_2eInit_2eSpecif_2esigT__rect___24a5(V0__A,V1__P,V2__P,V3__f,V4__s) = happ(happ(V3__f,Vvar__2__x__18770),Vvar__3___24Anonymous__18771) ) ) ) ) ) ) ).

fof('$_def_Coq.Init.Specif.sig_rec',axiom,
    ! [V0__A,V1__P,V2__P] : cCoq_2eInit_2eSpecif_2esig__rec___24a3(V0__A,V1__P,V2__P) = cCoq_2eInit_2eSpecif_2esig__rect___24a3(V0__A,V1__P,V2__P) ).

fof('$_def_Coq.Init.Specif.sig_rect',axiom,
    ! [V0__A,V1__P,V2__P,V3__f,V4__s] :
      ( cType___24t(V0__A)
     => ( c_24__type__2277___24t(V0__A,V1__P,V2__P,V1__P)
       => ( c_24__type__2285___24t(V0__A,V1__P,V2__P,V2__P)
         => ( cCoq_2eInit_2eSpecif_2esig___24t(V0__A,V1__P,V4__s)
           => ? [Vvar__2__x__2269] :
                ( t(Vvar__2__x__2269,V0__A)
                & p(happ(V1__P,Vvar__2__x__2269))
                & V4__s = cCoq_2eInit_2eSpecif_2eexist___24a3(V0__A,V1__P,Vvar__2__x__2269)
                & cCoq_2eInit_2eSpecif_2esig__rect___24a5(V0__A,V1__P,V2__P,V3__f,V4__s) = happ(V3__f,Vvar__2__x__2269) ) ) ) ) ) ).

fof('$_def_Coq.Init.Specif.sumbool_rec',axiom,
    ! [V0__A,V1__B,V2__P] : cCoq_2eInit_2eSpecif_2esumbool__rec___24a3(V0__A,V1__B,V2__P) = cCoq_2eInit_2eSpecif_2esumbool__rect___24a3(V0__A,V1__B,V2__P) ).

fof('$_def_Coq.Init.Specif.sumbool_rect',axiom,
    ! [V0__A,V1__B,V2__P,V3__f,V4__f,V5__s] :
      ( cProp___24t(V0__A)
     => ( cProp___24t(V1__B)
       => ( c_24__type__2320___24t(V0__A,V1__B,V2__P,V2__P)
         => ( cCoq_2eInit_2eSpecif_2esumbool___24t(V0__A,V1__B,V5__s)
           => ( ( p(V0__A)
                & V5__s = cCoq_2eInit_2eSpecif_2eleft___24a2(V0__A,V1__B)
                & cCoq_2eInit_2eSpecif_2esumbool__rect___24a6(V0__A,V1__B,V2__P,V3__f,V4__f,V5__s) = V3__f )
              | ( p(V1__B)
                & V5__s = cCoq_2eInit_2eSpecif_2eright___24a2(V0__A,V1__B)
                & cCoq_2eInit_2eSpecif_2esumbool__rect___24a6(V0__A,V1__B,V2__P,V3__f,V4__f,V5__s) = V4__f ) ) ) ) ) ) ).

fof('$_def_Coq.Init.Specif.sumor_rec',axiom,
    ! [V0__A,V1__B,V2__P] : cCoq_2eInit_2eSpecif_2esumor__rec___24a3(V0__A,V1__B,V2__P) = cCoq_2eInit_2eSpecif_2esumor__rect___24a3(V0__A,V1__B,V2__P) ).

fof('$_def_Coq.Init.Specif.sumor_rect',axiom,
    ! [V0__A,V1__B,V2__P,V3__f,V4__f,V5__s] :
      ( cType___24t(V0__A)
     => ( cProp___24t(V1__B)
       => ( c_24__type__2359___24t(V0__A,V1__B,V2__P,V2__P)
         => ( cCoq_2eInit_2eSpecif_2esumor___24t(V0__A,V1__B,V5__s)
           => ( ? [Vvar__2___24Anonymous__2350] :
                  ( t(Vvar__2___24Anonymous__2350,V0__A)
                  & V5__s = cCoq_2eInit_2eSpecif_2einleft___24a3(V0__A,V1__B,Vvar__2___24Anonymous__2350)
                  & cCoq_2eInit_2eSpecif_2esumor__rect___24a6(V0__A,V1__B,V2__P,V3__f,V4__f,V5__s) = happ(V3__f,Vvar__2___24Anonymous__2350) )
              | ( p(V1__B)
                & V5__s = cCoq_2eInit_2eSpecif_2einright___24a2(V0__A,V1__B)
                & cCoq_2eInit_2eSpecif_2esumor__rect___24a6(V0__A,V1__B,V2__P,V3__f,V4__f,V5__s) = V4__f ) ) ) ) ) ) ).

fof('$_def_Coq.Lists.List.In',axiom,
    ! [V0__A,V2__a,V3__l] :
      ( cType___24t(V0__A)
     => ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l)
       => ( ( V3__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)
            & ( cCoq_2eLists_2eList_2eIn___24a3(V0__A,V2__a,V3__l)
            <=> p(c_24False) ) )
          | ? [Vvar__1___24Anonymous__21693] :
              ( t(Vvar__1___24Anonymous__21693,V0__A)
              & ? [Vvar__2___24Anonymous__21694] :
                  ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__21694)
                  & V3__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__21693,Vvar__2___24Anonymous__21694)
                  & ( cCoq_2eLists_2eList_2eIn___24a3(V0__A,V2__a,V3__l)
                  <=> ( Vvar__1___24Anonymous__21693 = V2__a
                      | cCoq_2eLists_2eList_2eIn___24a3(V0__A,V2__a,Vvar__2___24Anonymous__21694) ) ) ) ) ) ) ) ).

fof('$_def_Coq.Lists.List.fold_left',axiom,
    ! [V0__A,V1__B,V2__f,V4__l,V5__a0] :
      ( cType___24t(V0__A)
     => ( cType___24t(V1__B)
       => ( cCoq_2eInit_2eDatatypes_2elist___24t(V1__B,V4__l)
         => ( ( V4__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V1__B)
              & cCoq_2eLists_2eList_2efold__left___24a5(V0__A,V1__B,V2__f,V4__l,V5__a0) = V5__a0 )
            | ? [Vvar__1___24Anonymous__12917] :
                ( t(Vvar__1___24Anonymous__12917,V1__B)
                & ? [Vvar__2___24Anonymous__12918] :
                    ( cCoq_2eInit_2eDatatypes_2elist___24t(V1__B,Vvar__2___24Anonymous__12918)
                    & V4__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V1__B,Vvar__1___24Anonymous__12917,Vvar__2___24Anonymous__12918)
                    & cCoq_2eLists_2eList_2efold__left___24a5(V0__A,V1__B,V2__f,V4__l,V5__a0) = cCoq_2eLists_2eList_2efold__left___24a5(V0__A,V1__B,V2__f,Vvar__2___24Anonymous__12918,happ(happ(V2__f,V5__a0),Vvar__1___24Anonymous__12917)) ) ) ) ) ) ) ).

fof('$_def_Coq.Lists.List.fold_right',axiom,
    ! [V0__A,V1__B,V2__f,V3__a0,V5__l] :
      ( cType___24t(V0__A)
     => ( cType___24t(V1__B)
       => ( cCoq_2eInit_2eDatatypes_2elist___24t(V1__B,V5__l)
         => ( ( V5__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V1__B)
              & cCoq_2eLists_2eList_2efold__right___24a5(V0__A,V1__B,V2__f,V3__a0,V5__l) = V3__a0 )
            | ? [Vvar__1___24Anonymous__12948] :
                ( t(Vvar__1___24Anonymous__12948,V1__B)
                & ? [Vvar__2___24Anonymous__12949] :
                    ( cCoq_2eInit_2eDatatypes_2elist___24t(V1__B,Vvar__2___24Anonymous__12949)
                    & V5__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V1__B,Vvar__1___24Anonymous__12948,Vvar__2___24Anonymous__12949)
                    & cCoq_2eLists_2eList_2efold__right___24a5(V0__A,V1__B,V2__f,V3__a0,V5__l) = happ(happ(V2__f,Vvar__1___24Anonymous__12948),cCoq_2eLists_2eList_2efold__right___24a5(V0__A,V1__B,V2__f,V3__a0,Vvar__2___24Anonymous__12949)) ) ) ) ) ) ) ).

fof('$_def_Coq.Logic.Decidable.decidable',axiom,
    ! [V0__P] :
      ( cCoq_2eLogic_2eDecidable_2edecidable___24a1(V0__P)
    <=> ( p(V0__P)
        | ~ p(V0__P) ) ) ).

fof('$_def_Coq.Logic.EqdepFacts.Eq_dep_eq_on',axiom,
    ! [V0__U,V1__P,V2__p,V3__x] :
      ( cCoq_2eLogic_2eEqdepFacts_2eEq__dep__eq__on___24a4(V0__U,V1__P,V2__p,V3__x)
    <=> ! [V4__y] :
          ( t(V4__y,happ(V1__P,V2__p))
         => ( cCoq_2eLogic_2eEqdepFacts_2eeq__dep___24a6(V0__U,V1__P,V2__p,V3__x,V2__p,V4__y)
           => V3__x = V4__y ) ) ) ).

fof('$_def_Coq.Logic.EqdepFacts.Eq_rect_eq_on',axiom,
    ! [V0__U,V1__p,V2__Q,V3__x] :
      ( cCoq_2eLogic_2eEqdepFacts_2eEq__rect__eq__on___24a4(V0__U,V1__p,V2__Q,V3__x)
    <=> ( V1__p = V1__p
       => V3__x = cCoq_2eInit_2eLogic_2eeq__rect___24a5(V0__U,V1__p,V2__Q,V3__x,V1__p) ) ) ).

fof('$_def_Coq.Logic.EqdepFacts.Streicher_K_',axiom,
    ! [V0__U] :
      ( cCoq_2eLogic_2eEqdepFacts_2eStreicher__K_____24a1(V0__U)
    <=> ! [V1__x] :
          ( t(V1__x,V0__U)
         => ! [V2__P] :
              ( c_24__type__11430___24t(V0__U,V1__x,V2__P)
             => cCoq_2eLogic_2eEqdepFacts_2eStreicher__K__on_____24a3(V0__U,V1__x,V2__P) ) ) ) ).

fof('$_def_Coq.Logic.EqdepFacts.Streicher_K_on_',axiom,
    ! [V0__U,V1__x,V2__P] :
      ( cCoq_2eLogic_2eEqdepFacts_2eStreicher__K__on_____24a3(V0__U,V1__x,V2__P)
    <=> ( p(happ(V2__P,cCoq_2eInit_2eLogic_2eeq__refl___24a2(V0__U,V1__x)))
       => ( V1__x = V1__x
         => p(V2__P) ) ) ) ).

fof('$_def_Coq.Logic.EqdepFacts.UIP_on_',axiom,
    ! [V0__U,V1__x,V2__y] :
      ( cCoq_2eLogic_2eEqdepFacts_2eUIP__on_____24a3(V0__U,V1__x,V2__y)
    <=> ( V1__x = V2__y
       => c_24Proof = c_24Proof ) ) ).

fof('$_def_Coq.NArith.BinNat.N.divide',axiom,
    ! [V0__p,V1__q] :
      ( cCoq_2eNArith_2eBinNat_2eN_2edivide___24a2(V0__p,V1__q)
    <=> ? [V2__r] :
          ( cCoq_2eNumbers_2eBinNums_2eN___24t(V2__r)
          & V1__q = cCoq_2eNArith_2eBinNatDef_2eN_2emul___24a2(V2__r,V0__p) ) ) ).

fof('$_def_Coq.NArith.BinNat.N.eqf',axiom,
    ! [V0__f,V1__g] :
      ( cCoq_2eNArith_2eBinNat_2eN_2eeqf___24a2(V0__f,V1__g)
    <=> ! [V2__n] :
          ( cCoq_2eNumbers_2eBinNums_2eN___24t(V2__n)
         => happ(V0__f,V2__n) = happ(V1__g,V2__n) ) ) ).

fof('$_def_Coq.NArith.BinNat.N.le',axiom,
    ! [V0__x,V1__y] :
      ( cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(V0__x,V1__y)
    <=> cCoq_2eNArith_2eBinNatDef_2eN_2ecompare___24a2(V0__x,V1__y) != cCoq_2eInit_2eDatatypes_2eGt ) ).

fof('$_def_Coq.NArith.BinNat.N.lt',axiom,
    ! [V0__x,V1__y] :
      ( cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V0__x,V1__y)
    <=> cCoq_2eNArith_2eBinNatDef_2eN_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eLt ) ).

fof('$_def_Coq.NArith.BinNatDef.N.add',axiom,
    ! [V0__n,V1__m] :
      ( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
     => ( ( V0__n = cCoq_2eNumbers_2eBinNums_2eN0
          & cCoq_2eNArith_2eBinNatDef_2eN_2eadd___24a2(V0__n,V1__m) = V1__m )
        | ? [Vvar__0___24Anonymous__18985] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__18985)
            & ( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
             => ( V0__n = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__18985)
                & ( ( V1__m = cCoq_2eNumbers_2eBinNums_2eN0
                    & cCoq_2eNArith_2eBinNatDef_2eN_2eadd___24a2(V0__n,V1__m) = V0__n )
                  | ? [Vvar__0___24Anonymous__18988] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__18988)
                      & V1__m = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__18988)
                      & cCoq_2eNArith_2eBinNatDef_2eN_2eadd___24a2(V0__n,V1__m) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(Vvar__0___24Anonymous__18985,Vvar__0___24Anonymous__18988)) ) ) ) ) ) ) ) ).

fof('$_def_Coq.NArith.BinNatDef.N.div2',axiom,
    ! [V0__n] :
      ( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
     => ( ( V0__n = cCoq_2eNumbers_2eBinNums_2eN0
          & cCoq_2eNArith_2eBinNatDef_2eN_2ediv2___24a1(V0__n) = cCoq_2eNumbers_2eBinNums_2eN0 )
        | ? [Vvar__0___24Anonymous__443] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__443)
            & ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__443)
             => ( V0__n = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__443)
                & ( ? [Vvar__0___24Anonymous__447] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__447)
                      & Vvar__0___24Anonymous__443 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__447)
                      & cCoq_2eNArith_2eBinNatDef_2eN_2ediv2___24a1(V0__n) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__447) )
                  | ? [Vvar__0___24Anonymous__448] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__448)
                      & Vvar__0___24Anonymous__443 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__448)
                      & cCoq_2eNArith_2eBinNatDef_2eN_2ediv2___24a1(V0__n) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__448) )
                  | ( Vvar__0___24Anonymous__443 = cCoq_2eNumbers_2eBinNums_2exH
                    & cCoq_2eNArith_2eBinNatDef_2eN_2ediv2___24a1(V0__n) = cCoq_2eNumbers_2eBinNums_2eN0 ) ) ) ) ) ) ) ).

fof('$_def_Coq.NArith.BinNatDef.N.double',axiom,
    ! [V0__n] :
      ( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
     => ( ( V0__n = cCoq_2eNumbers_2eBinNums_2eN0
          & cCoq_2eNArith_2eBinNatDef_2eN_2edouble___24a1(V0__n) = cCoq_2eNumbers_2eBinNums_2eN0 )
        | ? [Vvar__0___24Anonymous__1810] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__1810)
            & V0__n = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__1810)
            & cCoq_2eNArith_2eBinNatDef_2eN_2edouble___24a1(V0__n) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__1810)) ) ) ) ).

fof('$_def_Coq.NArith.BinNatDef.N.eqb',axiom,
    ! [V1__n,V2__m] :
      ( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__n)
     => ( ( cCoq_2eNumbers_2eBinNums_2eN___24t(V2__m)
         => ( V1__n = cCoq_2eNumbers_2eBinNums_2eN0
            & ( ( V2__m = cCoq_2eNumbers_2eBinNums_2eN0
                & cCoq_2eNArith_2eBinNatDef_2eN_2eeqb___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2etrue )
              | ? [Vvar__0___24Anonymous__435] :
                  ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__435)
                  & V2__m = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__435)
                  & cCoq_2eNArith_2eBinNatDef_2eN_2eeqb___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) )
        | ? [Vvar__0___24Anonymous__436] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__436)
            & ( cCoq_2eNumbers_2eBinNums_2eN___24t(V2__m)
             => ( V1__n = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__436)
                & ( ( V2__m = cCoq_2eNumbers_2eBinNums_2eN0
                    & cCoq_2eNArith_2eBinNatDef_2eN_2eeqb___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2efalse )
                  | ? [Vvar__0___24Anonymous__439] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__439)
                      & V2__m = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__439)
                      & cCoq_2eNArith_2eBinNatDef_2eN_2eeqb___24a2(V1__n,V2__m) = cCoq_2ePArith_2eBinPosDef_2ePos_2eeqb___24a2(Vvar__0___24Anonymous__436,Vvar__0___24Anonymous__439) ) ) ) ) ) ) ) ).

fof('$_def_Coq.NArith.BinNatDef.N.lxor',axiom,
    ! [V0__n,V1__m] :
      ( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
     => ( ( V0__n = cCoq_2eNumbers_2eBinNums_2eN0
          & cCoq_2eNArith_2eBinNatDef_2eN_2elxor___24a2(V0__n,V1__m) = V1__m )
        | ? [Vvar__0___24Anonymous__990] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__990)
            & ( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
             => ( V0__n = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__990)
                & ( ( V1__m = cCoq_2eNumbers_2eBinNums_2eN0
                    & cCoq_2eNArith_2eBinNatDef_2eN_2elxor___24a2(V0__n,V1__m) = V0__n )
                  | ? [Vvar__0___24Anonymous__993] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__993)
                      & V1__m = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__993)
                      & cCoq_2eNArith_2eBinNatDef_2eN_2elxor___24a2(V0__n,V1__m) = cCoq_2ePArith_2eBinPosDef_2ePos_2elxor___24a2(Vvar__0___24Anonymous__990,Vvar__0___24Anonymous__993) ) ) ) ) ) ) ) ).

fof('$_def_Coq.NArith.BinNatDef.N.max',axiom,
    ! [V0__n,V1__n_27] :
      ( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
     => ( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__n_27)
       => ( ( cCoq_2eNArith_2eBinNatDef_2eN_2ecompare___24a2(V0__n,V1__n_27) = cCoq_2eInit_2eDatatypes_2eEq
            & cCoq_2eNArith_2eBinNatDef_2eN_2emax___24a2(V0__n,V1__n_27) = V1__n_27 )
          | ( cCoq_2eNArith_2eBinNatDef_2eN_2ecompare___24a2(V0__n,V1__n_27) = cCoq_2eInit_2eDatatypes_2eLt
            & cCoq_2eNArith_2eBinNatDef_2eN_2emax___24a2(V0__n,V1__n_27) = V1__n_27 )
          | ( cCoq_2eNArith_2eBinNatDef_2eN_2ecompare___24a2(V0__n,V1__n_27) = cCoq_2eInit_2eDatatypes_2eGt
            & cCoq_2eNArith_2eBinNatDef_2eN_2emax___24a2(V0__n,V1__n_27) = V0__n ) ) ) ) ).

fof('$_def_Coq.NArith.BinNatDef.N.min',axiom,
    ! [V0__n,V1__n_27] :
      ( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
     => ( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__n_27)
       => ( ( cCoq_2eNArith_2eBinNatDef_2eN_2ecompare___24a2(V0__n,V1__n_27) = cCoq_2eInit_2eDatatypes_2eEq
            & cCoq_2eNArith_2eBinNatDef_2eN_2emin___24a2(V0__n,V1__n_27) = V0__n )
          | ( cCoq_2eNArith_2eBinNatDef_2eN_2ecompare___24a2(V0__n,V1__n_27) = cCoq_2eInit_2eDatatypes_2eLt
            & cCoq_2eNArith_2eBinNatDef_2eN_2emin___24a2(V0__n,V1__n_27) = V0__n )
          | ( cCoq_2eNArith_2eBinNatDef_2eN_2ecompare___24a2(V0__n,V1__n_27) = cCoq_2eInit_2eDatatypes_2eGt
            & cCoq_2eNArith_2eBinNatDef_2eN_2emin___24a2(V0__n,V1__n_27) = V1__n_27 ) ) ) ) ).

fof('$_def_Coq.NArith.BinNatDef.N.mul',axiom,
    ! [V0__n,V1__m] :
      ( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
     => ( ( V0__n = cCoq_2eNumbers_2eBinNums_2eN0
          & cCoq_2eNArith_2eBinNatDef_2eN_2emul___24a2(V0__n,V1__m) = cCoq_2eNumbers_2eBinNums_2eN0 )
        | ? [Vvar__0___24Anonymous__18990] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__18990)
            & ( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
             => ( V0__n = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__18990)
                & ( ( V1__m = cCoq_2eNumbers_2eBinNums_2eN0
                    & cCoq_2eNArith_2eBinNatDef_2eN_2emul___24a2(V0__n,V1__m) = cCoq_2eNumbers_2eBinNums_2eN0 )
                  | ? [Vvar__0___24Anonymous__18993] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__18993)
                      & V1__m = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__18993)
                      & cCoq_2eNArith_2eBinNatDef_2eN_2emul___24a2(V0__n,V1__m) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2emul___24a2(Vvar__0___24Anonymous__18990,Vvar__0___24Anonymous__18993)) ) ) ) ) ) ) ) ).

fof('$_def_Coq.NArith.BinNatDef.N.odd',axiom,
    ! [V0__n] : cCoq_2eNArith_2eBinNatDef_2eN_2eodd___24a1(V0__n) = cCoq_2eInit_2eDatatypes_2enegb___24a1(cCoq_2eNArith_2eBinNatDef_2eN_2eeven___24a1(V0__n)) ).

fof('$_def_Coq.NArith.BinNatDef.N.pred',axiom,
    ! [V0__n] :
      ( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
     => ( ( V0__n = cCoq_2eNumbers_2eBinNums_2eN0
          & cCoq_2eNArith_2eBinNatDef_2eN_2epred___24a1(V0__n) = cCoq_2eNumbers_2eBinNums_2eN0 )
        | ? [Vvar__0___24Anonymous__33480] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__33480)
            & V0__n = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__33480)
            & cCoq_2eNArith_2eBinNatDef_2eN_2epred___24a1(V0__n) = cCoq_2ePArith_2eBinPosDef_2ePos_2epred__N___24a1(Vvar__0___24Anonymous__33480) ) ) ) ).

fof('$_def_Coq.NArith.BinNatDef.N.succ',axiom,
    ! [V0__n] :
      ( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
     => ( ( V0__n = cCoq_2eNumbers_2eBinNums_2eN0
          & cCoq_2eNArith_2eBinNatDef_2eN_2esucc___24a1(V0__n) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(cCoq_2eNumbers_2eBinNums_2exH) )
        | ? [Vvar__0___24Anonymous__18984] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__18984)
            & V0__n = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__18984)
            & cCoq_2eNArith_2eBinNatDef_2eN_2esucc___24a1(V0__n) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2esucc___24a1(Vvar__0___24Anonymous__18984)) ) ) ) ).

fof('$_def_Coq.NArith.BinNatDef.N.succ_double',axiom,
    ! [V0__x] :
      ( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__x)
     => ( ( V0__x = cCoq_2eNumbers_2eBinNums_2eN0
          & cCoq_2eNArith_2eBinNatDef_2eN_2esucc__double___24a1(V0__x) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(cCoq_2eNumbers_2eBinNums_2exH) )
        | ? [Vvar__0___24Anonymous__1809] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__1809)
            & V0__x = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__1809)
            & cCoq_2eNArith_2eBinNatDef_2eN_2esucc__double___24a1(V0__x) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__1809)) ) ) ) ).

fof('$_def_Coq.NArith.BinNatDef.N.testbit',axiom,
    ! [V0__a,V1__n] :
      ( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__a)
     => ( ( V0__a = cCoq_2eNumbers_2eBinNums_2eN0
          & cCoq_2eNArith_2eBinNatDef_2eN_2etestbit___24a2(V0__a,V1__n) = cCoq_2eInit_2eDatatypes_2efalse )
        | ? [Vvar__0___24Anonymous__33482] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__33482)
            & V0__a = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__33482)
            & cCoq_2eNArith_2eBinNatDef_2eN_2etestbit___24a2(V0__a,V1__n) = cCoq_2ePArith_2eBinPosDef_2ePos_2etestbit___24a2(Vvar__0___24Anonymous__33482,V1__n) ) ) ) ).

fof('$_def_Coq.NArith.BinNatDef.N.to_nat',axiom,
    ! [V0__a] :
      ( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__a)
     => ( ( V0__a = cCoq_2eNumbers_2eBinNums_2eN0
          & cCoq_2eNArith_2eBinNatDef_2eN_2eto__nat___24a1(V0__a) = cCoq_2eInit_2eDatatypes_2eO )
        | ? [Vvar__0___24Anonymous__19005] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__19005)
            & V0__a = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__19005)
            & cCoq_2eNArith_2eBinNatDef_2eN_2eto__nat___24a1(V0__a) = cCoq_2ePArith_2eBinPosDef_2ePos_2eto__nat___24a1(Vvar__0___24Anonymous__19005) ) ) ) ).

fof('$_def_Coq.NArith.Ndigits.Nless',axiom,
    ! [V0__a,V1__a_27] :
      ( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__a)
     => ( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__a_27)
       => ( ( cCoq_2eNArith_2eBinNatDef_2eN_2elxor___24a2(V0__a,V1__a_27) = cCoq_2eNumbers_2eBinNums_2eN0
            & cCoq_2eNArith_2eNdigits_2eNless___24a2(V0__a,V1__a_27) = cCoq_2eInit_2eDatatypes_2efalse )
          | ? [Vvar__0___24Anonymous__14617] :
              ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__14617)
              & cCoq_2eNArith_2eBinNatDef_2eN_2elxor___24a2(V0__a,V1__a_27) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__14617)
              & cCoq_2eNArith_2eNdigits_2eNless___24a2(V0__a,V1__a_27) = cCoq_2eNArith_2eNdigits_2eNless__aux___24a3(V0__a,V1__a_27,Vvar__0___24Anonymous__14617) ) ) ) ) ).

fof('$_def_Coq.NArith.Ndigits.eqf',axiom,
    ! [V0__f,V1__g] :
      ( cCoq_2eNArith_2eNdigits_2eeqf___24a2(V0__f,V1__g)
    <=> ! [V2__n] :
          ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__n)
         => happ(V0__f,V2__n) = happ(V1__g,V2__n) ) ) ).

fof('$_def_Coq.PArith.BinPos.Pos.lt',axiom,
    ! [V0__x,V1__y] :
      ( cCoq_2ePArith_2eBinPos_2ePos_2elt___24a2(V0__x,V1__y)
    <=> cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eLt ) ).

fof('$_def_Coq.PArith.BinPosDef.Pos.compare',axiom,
    cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare = cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare__cont___24a1(cCoq_2eInit_2eDatatypes_2eEq) ).

fof('$_def_Coq.PArith.BinPosDef.Pos.divide',axiom,
    ! [V0__p,V1__q] :
      ( cCoq_2ePArith_2eBinPosDef_2ePos_2edivide___24a2(V0__p,V1__q)
    <=> ? [V2__r] :
          ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V2__r)
          & V1__q = cCoq_2ePArith_2eBinPosDef_2ePos_2emul___24a2(V2__r,V0__p) ) ) ).

fof('$_def_Coq.PArith.BinPosDef.Pos.iter',axiom,
    ! [V0__A,V1__f,V3__x,V4__n] :
      ( cType___24t(V0__A)
     => ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V4__n)
       => ( ? [Vvar__0___24Anonymous__19132] :
              ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__19132)
              & V4__n = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__19132)
              & cCoq_2ePArith_2eBinPosDef_2ePos_2eiter___24a4(V0__A,V1__f,V3__x,V4__n) = happ(V1__f,cCoq_2ePArith_2eBinPosDef_2ePos_2eiter___24a4(V0__A,V1__f,cCoq_2ePArith_2eBinPosDef_2ePos_2eiter___24a4(V0__A,V1__f,V3__x,Vvar__0___24Anonymous__19132),Vvar__0___24Anonymous__19132)) )
          | ? [Vvar__0___24Anonymous__19133] :
              ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__19133)
              & V4__n = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__19133)
              & cCoq_2ePArith_2eBinPosDef_2ePos_2eiter___24a4(V0__A,V1__f,V3__x,V4__n) = cCoq_2ePArith_2eBinPosDef_2ePos_2eiter___24a4(V0__A,V1__f,cCoq_2ePArith_2eBinPosDef_2ePos_2eiter___24a4(V0__A,V1__f,V3__x,Vvar__0___24Anonymous__19133),Vvar__0___24Anonymous__19133) )
          | ( V4__n = cCoq_2eNumbers_2eBinNums_2exH
            & cCoq_2ePArith_2eBinPosDef_2ePos_2eiter___24a4(V0__A,V1__f,V3__x,V4__n) = happ(V1__f,V3__x) ) ) ) ) ).

fof('$_def_Coq.PArith.BinPosDef.Pos.iter_op',axiom,
    ! [V0__A,V1__op,V3__p,V4__a] :
      ( cType___24t(V0__A)
     => ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V3__p)
       => ( ? [Vvar__0___24Anonymous__33500] :
              ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__33500)
              & V3__p = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__33500)
              & cCoq_2ePArith_2eBinPosDef_2ePos_2eiter__op___24a4(V0__A,V1__op,V3__p,V4__a) = happ(happ(V1__op,V4__a),cCoq_2ePArith_2eBinPosDef_2ePos_2eiter__op___24a4(V0__A,V1__op,Vvar__0___24Anonymous__33500,happ(happ(V1__op,V4__a),V4__a))) )
          | ? [Vvar__0___24Anonymous__33501] :
              ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__33501)
              & V3__p = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__33501)
              & cCoq_2ePArith_2eBinPosDef_2ePos_2eiter__op___24a4(V0__A,V1__op,V3__p,V4__a) = cCoq_2ePArith_2eBinPosDef_2ePos_2eiter__op___24a4(V0__A,V1__op,Vvar__0___24Anonymous__33501,happ(happ(V1__op,V4__a),V4__a)) )
          | ( V3__p = cCoq_2eNumbers_2eBinNums_2exH
            & cCoq_2ePArith_2eBinPosDef_2ePos_2eiter__op___24a4(V0__A,V1__op,V3__p,V4__a) = V4__a ) ) ) ) ).

fof('$_def_Coq.PArith.BinPosDef.Pos.max',axiom,
    ! [V0__p,V1__p_27] :
      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V0__p)
     => ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__p_27)
       => ( ( cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare___24a2(V0__p,V1__p_27) = cCoq_2eInit_2eDatatypes_2eEq
            & cCoq_2ePArith_2eBinPosDef_2ePos_2emax___24a2(V0__p,V1__p_27) = V1__p_27 )
          | ( cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare___24a2(V0__p,V1__p_27) = cCoq_2eInit_2eDatatypes_2eLt
            & cCoq_2ePArith_2eBinPosDef_2ePos_2emax___24a2(V0__p,V1__p_27) = V1__p_27 )
          | ( cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare___24a2(V0__p,V1__p_27) = cCoq_2eInit_2eDatatypes_2eGt
            & cCoq_2ePArith_2eBinPosDef_2ePos_2emax___24a2(V0__p,V1__p_27) = V0__p ) ) ) ) ).

fof('$_def_Coq.PArith.BinPosDef.Pos.min',axiom,
    ! [V0__p,V1__p_27] :
      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V0__p)
     => ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__p_27)
       => ( ( cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare___24a2(V0__p,V1__p_27) = cCoq_2eInit_2eDatatypes_2eEq
            & cCoq_2ePArith_2eBinPosDef_2ePos_2emin___24a2(V0__p,V1__p_27) = V0__p )
          | ( cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare___24a2(V0__p,V1__p_27) = cCoq_2eInit_2eDatatypes_2eLt
            & cCoq_2ePArith_2eBinPosDef_2ePos_2emin___24a2(V0__p,V1__p_27) = V0__p )
          | ( cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare___24a2(V0__p,V1__p_27) = cCoq_2eInit_2eDatatypes_2eGt
            & cCoq_2ePArith_2eBinPosDef_2ePos_2emin___24a2(V0__p,V1__p_27) = V1__p_27 ) ) ) ) ).

fof('$_def_Coq.PArith.BinPosDef.Pos.succ',axiom,
    ! [V1__x] :
      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__x)
     => ( ? [Vvar__0___24Anonymous__19023] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__19023)
            & V1__x = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__19023)
            & cCoq_2ePArith_2eBinPosDef_2ePos_2esucc___24a1(V1__x) = cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2esucc___24a1(Vvar__0___24Anonymous__19023)) )
        | ? [Vvar__0___24Anonymous__19024] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__19024)
            & V1__x = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__19024)
            & cCoq_2ePArith_2eBinPosDef_2ePos_2esucc___24a1(V1__x) = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__19024) )
        | ( V1__x = cCoq_2eNumbers_2eBinNums_2exH
          & cCoq_2ePArith_2eBinPosDef_2ePos_2esucc___24a1(V1__x) = cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2eNumbers_2eBinNums_2exH) ) ) ) ).

fof('$_def_Coq.QArith.QArith_base.Qden',axiom,
    ! [V0__q] :
      ( cCoq_2eQArith_2eQArith__base_2eQ___24t(V0__q)
     => ? [Vvar__0__Qnum__23149] :
          ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__0__Qnum__23149)
          & ? [Vvar__1__Qden__23150] :
              ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1__Qden__23150)
              & V0__q = cCoq_2eQArith_2eQArith__base_2eQmake___24a2(Vvar__0__Qnum__23149,Vvar__1__Qden__23150)
              & cCoq_2eQArith_2eQArith__base_2eQden___24a1(V0__q) = Vvar__1__Qden__23150 ) ) ) ).

fof('$_def_Coq.QArith.QArith_base.Qnum',axiom,
    ! [V0__q] :
      ( cCoq_2eQArith_2eQArith__base_2eQ___24t(V0__q)
     => ? [Vvar__0__Qnum__23144] :
          ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__0__Qnum__23144)
          & ? [Vvar__1__Qden__23145] :
              ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1__Qden__23145)
              & V0__q = cCoq_2eQArith_2eQArith__base_2eQmake___24a2(Vvar__0__Qnum__23144,Vvar__1__Qden__23145)
              & cCoq_2eQArith_2eQArith__base_2eQnum___24a1(V0__q) = Vvar__0__Qnum__23144 ) ) ) ).

fof('$_def_Coq.Reals.Rdefinitions.IZR',axiom,
    ! [V0__z] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__z)
     => ( ( V0__z = cCoq_2eNumbers_2eBinNums_2eZ0
          & cCoq_2eReals_2eRdefinitions_2eIZR___24a1(V0__z) = cCoq_2eReals_2eRdefinitions_2eR0 )
        | ? [Vvar__0___24Anonymous__14720] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__14720)
            & V0__z = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__14720)
            & cCoq_2eReals_2eRdefinitions_2eIZR___24a1(V0__z) = cCoq_2eReals_2eRdefinitions_2eIPR___24a1(Vvar__0___24Anonymous__14720) )
        | ? [Vvar__0___24Anonymous__14721] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__14721)
            & V0__z = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__14721)
            & cCoq_2eReals_2eRdefinitions_2eIZR___24a1(V0__z) = cCoq_2eReals_2eRdefinitions_2eRopp___24a1(cCoq_2eReals_2eRdefinitions_2eIPR___24a1(Vvar__0___24Anonymous__14721)) ) ) ) ).

fof('$_def_Coq.Reals.Rdefinitions.Rge',axiom,
    ! [V0__r1,V1__r2] :
      ( cCoq_2eReals_2eRdefinitions_2eRge___24a2(V0__r1,V1__r2)
    <=> ( cCoq_2eReals_2eRdefinitions_2eRgt___24a2(V0__r1,V1__r2)
        | V0__r1 = V1__r2 ) ) ).

fof('$_def_Coq.Reals.Rdefinitions.Rgt',axiom,
    ! [V0__r1,V1__r2] :
      ( cCoq_2eReals_2eRdefinitions_2eRgt___24a2(V0__r1,V1__r2)
    <=> cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V1__r2,V0__r1) ) ).

fof('$_def_Coq.Reals.Rdefinitions.Rle',axiom,
    ! [V0__r1,V1__r2] :
      ( cCoq_2eReals_2eRdefinitions_2eRle___24a2(V0__r1,V1__r2)
    <=> ( cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V0__r1,V1__r2)
        | V0__r1 = V1__r2 ) ) ).

fof('$_def_Coq.Relations.Relation_Definitions.antisymmetric',axiom,
    ! [V0__A,V1__R] :
      ( cCoq_2eRelations_2eRelation__Definitions_2eantisymmetric___24a2(V0__A,V1__R)
    <=> ! [V2__x] :
          ( t(V2__x,V0__A)
         => ! [V3__y] :
              ( t(V3__y,V0__A)
             => ( p(happ(happ(V1__R,V2__x),V3__y))
               => ( p(happ(happ(V1__R,V3__y),V2__x))
                 => V2__x = V3__y ) ) ) ) ) ).

fof('$_def_Coq.Relations.Relation_Definitions.relation',axiom,
    ! [V0__A] : cCoq_2eRelations_2eRelation__Definitions_2erelation___24a1(V0__A) = c_24__type__12419___24a1(V0__A) ).

fof('$_def_Coq.Setoids.Setoid.Setoid_Theory',axiom,
    cCoq_2eSetoids_2eSetoid_2eSetoid__Theory = cCoq_2eClasses_2eRelationClasses_2eEquivalence ).

fof('$_def_Coq.Sets.Relations_1.Relation',axiom,
    ! [V0__U] : cCoq_2eSets_2eRelations__1_2eRelation___24a1(V0__U) = c_24__type__12419___24a1(V0__U) ).

fof('$_def_Coq.Structures.OrderedTypeEx.N_as_OT.t',axiom,
    ! [Vvar__33489] :
      ( cCoq_2eStructures_2eOrderedTypeEx_2eN__as__OT_2et___24t(Vvar__33489)
    <=> cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__33489) ) ).

fof('$_def_Coq.Structures.OrderedTypeEx.Nat_as_OT.t',axiom,
    ! [Vvar__33496] :
      ( cCoq_2eStructures_2eOrderedTypeEx_2eNat__as__OT_2et___24t(Vvar__33496)
    <=> cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__33496) ) ).

fof('$_def_Coq.Structures.OrderedTypeEx.PositiveOrderedTypeBits.eq',axiom,
    cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2eeq = c_3d___24a1(cCoq_2eNumbers_2eBinNums_2epositive) ).

fof('$_def_Coq.Structures.OrderedTypeEx.PositiveOrderedTypeBits.t',axiom,
    ! [Vvar__33447] :
      ( cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2et___24t(Vvar__33447)
    <=> cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__33447) ) ).

fof('$_def_Coq.Structures.OrderedTypeEx.Positive_as_OT.t',axiom,
    ! [Vvar__33583] :
      ( cCoq_2eStructures_2eOrderedTypeEx_2ePositive__as__OT_2et___24t(Vvar__33583)
    <=> cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__33583) ) ).

fof('$_def_Coq.Structures.OrderedTypeEx.String_as_OT.t',axiom,
    ! [Vvar__33585] :
      ( cCoq_2eStructures_2eOrderedTypeEx_2eString__as__OT_2et___24t(Vvar__33585)
    <=> cCoq_2eStrings_2eString_2estring___24t(Vvar__33585) ) ).

fof('$_def_Coq.Structures.OrderedTypeEx.Z_as_OT.t',axiom,
    ! [Vvar__33639] :
      ( cCoq_2eStructures_2eOrderedTypeEx_2eZ__as__OT_2et___24t(Vvar__33639)
    <=> cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__33639) ) ).

fof('$_def_Coq.ZArith.BinInt.Z.divide',axiom,
    ! [V0__x,V1__y] :
      ( cCoq_2eZArith_2eBinInt_2eZ_2edivide___24a2(V0__x,V1__y)
    <=> ? [V2__z] :
          ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__z)
          & V1__y = cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V2__z,V0__x) ) ) ).

fof('$_def_Coq.ZArith.BinInt.Z.eqf',axiom,
    ! [V0__f,V1__g] :
      ( cCoq_2eZArith_2eBinInt_2eZ_2eeqf___24a2(V0__f,V1__g)
    <=> ! [V2__n] :
          ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__n)
         => happ(V0__f,V2__n) = happ(V1__g,V2__n) ) ) ).

fof('$_def_Coq.ZArith.BinInt.Z.gt',axiom,
    ! [V0__x,V1__y] :
      ( cCoq_2eZArith_2eBinInt_2eZ_2egt___24a2(V0__x,V1__y)
    <=> cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eGt ) ).

fof('$_def_Coq.ZArith.BinInt.Z.le',axiom,
    ! [V0__x,V1__y] :
      ( cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__x,V1__y)
    <=> cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) != cCoq_2eInit_2eDatatypes_2eGt ) ).

fof('$_def_Coq.ZArith.BinInt.Z.lt',axiom,
    ! [V0__x,V1__y] :
      ( cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__x,V1__y)
    <=> cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eLt ) ).

fof('$_def_Coq.ZArith.BinInt.Zne',axiom,
    ! [V0__x,V1__y] :
      ( cCoq_2eZArith_2eBinInt_2eZne___24a2(V0__x,V1__y)
    <=> V0__x != V1__y ) ).

fof('$_def_Coq.ZArith.BinIntDef.Z.abs',axiom,
    ! [V0__z] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__z)
     => ( ( V0__z = cCoq_2eNumbers_2eBinNums_2eZ0
          & cCoq_2eZArith_2eBinIntDef_2eZ_2eabs___24a1(V0__z) = cCoq_2eNumbers_2eBinNums_2eZ0 )
        | ? [Vvar__0___24Anonymous__19755] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__19755)
            & V0__z = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__19755)
            & cCoq_2eZArith_2eBinIntDef_2eZ_2eabs___24a1(V0__z) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__19755) )
        | ? [Vvar__0___24Anonymous__19756] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__19756)
            & V0__z = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__19756)
            & cCoq_2eZArith_2eBinIntDef_2eZ_2eabs___24a1(V0__z) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__19756) ) ) ) ).

fof('$_def_Coq.ZArith.BinIntDef.Z.add',axiom,
    ! [V0__x,V1__y] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
     => ( ( V0__x = cCoq_2eNumbers_2eBinNums_2eZ0
          & cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__x,V1__y) = V1__y )
        | ? [Vvar__0___24Anonymous__19702] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__19702)
            & ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
             => ( V0__x = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__19702)
                & ( ( V1__y = cCoq_2eNumbers_2eBinNums_2eZ0
                    & cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__x,V1__y) = V0__x )
                  | ? [Vvar__0___24Anonymous__19706] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__19706)
                      & V1__y = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__19706)
                      & cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(Vvar__0___24Anonymous__19702,Vvar__0___24Anonymous__19706)) )
                  | ? [Vvar__0___24Anonymous__19707] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__19707)
                      & V1__y = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__19707)
                      & cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__x,V1__y) = cCoq_2eZArith_2eBinIntDef_2eZ_2epos__sub___24a2(Vvar__0___24Anonymous__19702,Vvar__0___24Anonymous__19707) ) ) ) ) )
        | ? [Vvar__0___24Anonymous__19708] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__19708)
            & ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
             => ( V0__x = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__19708)
                & ( ( V1__y = cCoq_2eNumbers_2eBinNums_2eZ0
                    & cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__x,V1__y) = V0__x )
                  | ? [Vvar__0___24Anonymous__19712] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__19712)
                      & V1__y = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__19712)
                      & cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__x,V1__y) = cCoq_2eZArith_2eBinIntDef_2eZ_2epos__sub___24a2(Vvar__0___24Anonymous__19712,Vvar__0___24Anonymous__19708) )
                  | ? [Vvar__0___24Anonymous__19713] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__19713)
                      & V1__y = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__19713)
                      & cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(Vvar__0___24Anonymous__19708,Vvar__0___24Anonymous__19713)) ) ) ) ) ) ) ) ).

fof('$_def_Coq.ZArith.BinIntDef.Z.div',axiom,
    ! [V0__a,V1__b] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
     => ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__b)
       => ? [Vvar__2___24Anonymous__19769] :
            ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__2___24Anonymous__19769)
            & ? [Vvar__3___24Anonymous__19770] :
                ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__3___24Anonymous__19770)
                & cCoq_2eZArith_2eBinIntDef_2eZ_2ediv__eucl___24a2(V0__a,V1__b) = cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eNumbers_2eBinNums_2eZ,Vvar__2___24Anonymous__19769,Vvar__3___24Anonymous__19770)
                & cCoq_2eZArith_2eBinIntDef_2eZ_2ediv___24a2(V0__a,V1__b) = Vvar__2___24Anonymous__19769 ) ) ) ) ).

fof('$_def_Coq.ZArith.BinIntDef.Z.max',axiom,
    ! [V0__n,V1__m] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
     => ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
       => ( ( cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__n,V1__m) = cCoq_2eInit_2eDatatypes_2eEq
            & cCoq_2eZArith_2eBinIntDef_2eZ_2emax___24a2(V0__n,V1__m) = V0__n )
          | ( cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__n,V1__m) = cCoq_2eInit_2eDatatypes_2eLt
            & cCoq_2eZArith_2eBinIntDef_2eZ_2emax___24a2(V0__n,V1__m) = V1__m )
          | ( cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__n,V1__m) = cCoq_2eInit_2eDatatypes_2eGt
            & cCoq_2eZArith_2eBinIntDef_2eZ_2emax___24a2(V0__n,V1__m) = V0__n ) ) ) ) ).

fof('$_def_Coq.ZArith.BinIntDef.Z.min',axiom,
    ! [V0__n,V1__m] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
     => ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
       => ( ( cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__n,V1__m) = cCoq_2eInit_2eDatatypes_2eEq
            & cCoq_2eZArith_2eBinIntDef_2eZ_2emin___24a2(V0__n,V1__m) = V0__n )
          | ( cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__n,V1__m) = cCoq_2eInit_2eDatatypes_2eLt
            & cCoq_2eZArith_2eBinIntDef_2eZ_2emin___24a2(V0__n,V1__m) = V0__n )
          | ( cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__n,V1__m) = cCoq_2eInit_2eDatatypes_2eGt
            & cCoq_2eZArith_2eBinIntDef_2eZ_2emin___24a2(V0__n,V1__m) = V1__m ) ) ) ) ).

fof('$_def_Coq.ZArith.BinIntDef.Z.modulo',axiom,
    ! [V0__a,V1__b] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
     => ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__b)
       => ? [Vvar__2___24Anonymous__19777] :
            ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__2___24Anonymous__19777)
            & ? [Vvar__3___24Anonymous__19778] :
                ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__3___24Anonymous__19778)
                & cCoq_2eZArith_2eBinIntDef_2eZ_2ediv__eucl___24a2(V0__a,V1__b) = cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eNumbers_2eBinNums_2eZ,Vvar__2___24Anonymous__19777,Vvar__3___24Anonymous__19778)
                & cCoq_2eZArith_2eBinIntDef_2eZ_2emodulo___24a2(V0__a,V1__b) = Vvar__3___24Anonymous__19778 ) ) ) ) ).

fof('$_def_Coq.ZArith.BinIntDef.Z.mul',axiom,
    ! [V0__x,V1__y] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
     => ( ( V0__x = cCoq_2eNumbers_2eBinNums_2eZ0
          & cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZ0 )
        | ? [Vvar__0___24Anonymous__19722] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__19722)
            & ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
             => ( V0__x = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__19722)
                & ( ( V1__y = cCoq_2eNumbers_2eBinNums_2eZ0
                    & cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZ0 )
                  | ? [Vvar__0___24Anonymous__19726] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__19726)
                      & V1__y = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__19726)
                      & cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2emul___24a2(Vvar__0___24Anonymous__19722,Vvar__0___24Anonymous__19726)) )
                  | ? [Vvar__0___24Anonymous__19727] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__19727)
                      & V1__y = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__19727)
                      & cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2emul___24a2(Vvar__0___24Anonymous__19722,Vvar__0___24Anonymous__19727)) ) ) ) ) )
        | ? [Vvar__0___24Anonymous__19728] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__19728)
            & ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
             => ( V0__x = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__19728)
                & ( ( V1__y = cCoq_2eNumbers_2eBinNums_2eZ0
                    & cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZ0 )
                  | ? [Vvar__0___24Anonymous__19732] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__19732)
                      & V1__y = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__19732)
                      & cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2emul___24a2(Vvar__0___24Anonymous__19728,Vvar__0___24Anonymous__19732)) )
                  | ? [Vvar__0___24Anonymous__19733] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__19733)
                      & V1__y = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__19733)
                      & cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2emul___24a2(Vvar__0___24Anonymous__19728,Vvar__0___24Anonymous__19733)) ) ) ) ) ) ) ) ).

fof('$_def_Coq.ZArith.BinIntDef.Z.odd',axiom,
    ! [V0__z] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__z)
     => ( ( V0__z = cCoq_2eNumbers_2eBinNums_2eZ0
          & cCoq_2eZArith_2eBinIntDef_2eZ_2eodd___24a1(V0__z) = cCoq_2eInit_2eDatatypes_2efalse )
        | ? [Vvar__0___24Anonymous__33622] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__33622)
            & ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__33622)
             => ( V0__z = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__33622)
                & ( ? [Vvar__0___24Anonymous__33626] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__33626)
                      & Vvar__0___24Anonymous__33622 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__33626)
                      & cCoq_2eZArith_2eBinIntDef_2eZ_2eodd___24a1(V0__z) = cCoq_2eInit_2eDatatypes_2etrue )
                  | ? [Vvar__0___24Anonymous__33627] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__33627)
                      & Vvar__0___24Anonymous__33622 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__33627)
                      & cCoq_2eZArith_2eBinIntDef_2eZ_2eodd___24a1(V0__z) = cCoq_2eInit_2eDatatypes_2efalse )
                  | ( Vvar__0___24Anonymous__33622 = cCoq_2eNumbers_2eBinNums_2exH
                    & cCoq_2eZArith_2eBinIntDef_2eZ_2eodd___24a1(V0__z) = cCoq_2eInit_2eDatatypes_2etrue ) ) ) ) )
        | ? [Vvar__0___24Anonymous__33628] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__33628)
            & ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__33628)
             => ( V0__z = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__33628)
                & ( ? [Vvar__0___24Anonymous__33632] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__33632)
                      & Vvar__0___24Anonymous__33628 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__33632)
                      & cCoq_2eZArith_2eBinIntDef_2eZ_2eodd___24a1(V0__z) = cCoq_2eInit_2eDatatypes_2etrue )
                  | ? [Vvar__0___24Anonymous__33633] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__33633)
                      & Vvar__0___24Anonymous__33628 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__33633)
                      & cCoq_2eZArith_2eBinIntDef_2eZ_2eodd___24a1(V0__z) = cCoq_2eInit_2eDatatypes_2efalse )
                  | ( Vvar__0___24Anonymous__33628 = cCoq_2eNumbers_2eBinNums_2exH
                    & cCoq_2eZArith_2eBinIntDef_2eZ_2eodd___24a1(V0__z) = cCoq_2eInit_2eDatatypes_2etrue ) ) ) ) ) ) ) ).

fof('$_def_Coq.ZArith.BinIntDef.Z.of_N',axiom,
    ! [V0__n] :
      ( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
     => ( ( V0__n = cCoq_2eNumbers_2eBinNums_2eN0
          & cCoq_2eZArith_2eBinIntDef_2eZ_2eof__N___24a1(V0__n) = cCoq_2eNumbers_2eBinNums_2eZ0 )
        | ? [Vvar__0___24Anonymous__33601] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__33601)
            & V0__n = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__33601)
            & cCoq_2eZArith_2eBinIntDef_2eZ_2eof__N___24a1(V0__n) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__33601) ) ) ) ).

fof('$_def_Coq.ZArith.BinIntDef.Z.opp',axiom,
    ! [V0__x] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
     => ( ( V0__x = cCoq_2eNumbers_2eBinNums_2eZ0
          & cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V0__x) = cCoq_2eNumbers_2eBinNums_2eZ0 )
        | ? [Vvar__0___24Anonymous__19717] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__19717)
            & V0__x = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__19717)
            & cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V0__x) = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__19717) )
        | ? [Vvar__0___24Anonymous__19718] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__19718)
            & V0__x = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__19718)
            & cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V0__x) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__19718) ) ) ) ).

fof('$_def_Coq.ZArith.BinIntDef.Z.pow',axiom,
    ! [V0__x,V1__y] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
     => ( ( V1__y = cCoq_2eNumbers_2eBinNums_2eZ0
          & cCoq_2eZArith_2eBinIntDef_2eZ_2epow___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH) )
        | ? [Vvar__0___24Anonymous__34662] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__34662)
            & V1__y = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__34662)
            & cCoq_2eZArith_2eBinIntDef_2eZ_2epow___24a2(V0__x,V1__y) = cCoq_2eZArith_2eBinIntDef_2eZ_2epow__pos___24a2(V0__x,Vvar__0___24Anonymous__34662) )
        | ? [Vvar__0___24Anonymous__34663] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__34663)
            & V1__y = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__34663)
            & cCoq_2eZArith_2eBinIntDef_2eZ_2epow___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZ0 ) ) ) ).

fof('$_def_Coq.ZArith.BinIntDef.Z.sub',axiom,
    ! [V0__m,V1__n] : cCoq_2eZArith_2eBinIntDef_2eZ_2esub___24a2(V0__m,V1__n) = cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__m,cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V1__n)) ).

fof('$_def_Coq.ZArith.BinIntDef.Z.succ',axiom,
    ! [V0__x] : cCoq_2eZArith_2eBinIntDef_2eZ_2esucc___24a1(V0__x) = cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__x,cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)) ).

fof('$_def_Coq.ZArith.BinIntDef.Z.to_pos',axiom,
    ! [V0__z] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__z)
     => ( ( V0__z = cCoq_2eNumbers_2eBinNums_2eZ0
          & cCoq_2eZArith_2eBinIntDef_2eZ_2eto__pos___24a1(V0__z) = cCoq_2eNumbers_2eBinNums_2exH )
        | ? [Vvar__0___24Anonymous__33604] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__33604)
            & V0__z = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__33604)
            & cCoq_2eZArith_2eBinIntDef_2eZ_2eto__pos___24a1(V0__z) = Vvar__0___24Anonymous__33604 )
        | ? [Vvar__0___24Anonymous__33605] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__33605)
            & V0__z = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__33605)
            & cCoq_2eZArith_2eBinIntDef_2eZ_2eto__pos___24a1(V0__z) = cCoq_2eNumbers_2eBinNums_2exH ) ) ) ).

fof('$_def_Coq.ZArith.Zbool.Zeq_bool',axiom,
    ! [V0__x,V1__y] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
     => ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
       => ( ( cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eEq
            & cCoq_2eZArith_2eZbool_2eZeq__bool___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2etrue )
          | ( cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eLt
            & cCoq_2eZArith_2eZbool_2eZeq__bool___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2efalse )
          | ( cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eGt
            & cCoq_2eZArith_2eZbool_2eZeq__bool___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ).

fof('$_def_Coq.ZArith.Zeven.Zeven',axiom,
    ! [V0__z] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__z)
     => ( ( V0__z = cCoq_2eNumbers_2eBinNums_2eZ0
          & ( cCoq_2eZArith_2eZeven_2eZeven___24a1(V0__z)
          <=> p(c_24True) ) )
        | ? [Vvar__0___24Anonymous__33347] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__33347)
            & ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__33347)
             => ( V0__z = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__33347)
                & ( ? [Vvar__0___24Anonymous__33351] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__33351)
                      & Vvar__0___24Anonymous__33347 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__33351)
                      & ( cCoq_2eZArith_2eZeven_2eZeven___24a1(V0__z)
                      <=> p(c_24False) ) )
                  | ? [Vvar__0___24Anonymous__33352] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__33352)
                      & Vvar__0___24Anonymous__33347 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__33352)
                      & ( cCoq_2eZArith_2eZeven_2eZeven___24a1(V0__z)
                      <=> p(c_24True) ) )
                  | ( Vvar__0___24Anonymous__33347 = cCoq_2eNumbers_2eBinNums_2exH
                    & ( cCoq_2eZArith_2eZeven_2eZeven___24a1(V0__z)
                    <=> p(c_24False) ) ) ) ) ) )
        | ? [Vvar__0___24Anonymous__33353] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__33353)
            & ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__33353)
             => ( V0__z = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__33353)
                & ( ? [Vvar__0___24Anonymous__33357] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__33357)
                      & Vvar__0___24Anonymous__33353 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__33357)
                      & ( cCoq_2eZArith_2eZeven_2eZeven___24a1(V0__z)
                      <=> p(c_24False) ) )
                  | ? [Vvar__0___24Anonymous__33358] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__33358)
                      & Vvar__0___24Anonymous__33353 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__33358)
                      & ( cCoq_2eZArith_2eZeven_2eZeven___24a1(V0__z)
                      <=> p(c_24True) ) )
                  | ( Vvar__0___24Anonymous__33353 = cCoq_2eNumbers_2eBinNums_2exH
                    & ( cCoq_2eZArith_2eZeven_2eZeven___24a1(V0__z)
                    <=> p(c_24False) ) ) ) ) ) ) ) ) ).

fof('$_def_Coq.ZArith.Zeven.Zodd',axiom,
    ! [V0__z] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__z)
     => ( ( V0__z = cCoq_2eNumbers_2eBinNums_2eZ0
          & ( cCoq_2eZArith_2eZeven_2eZodd___24a1(V0__z)
          <=> p(c_24False) ) )
        | ? [Vvar__0___24Anonymous__33359] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__33359)
            & ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__33359)
             => ( V0__z = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__33359)
                & ( ? [Vvar__0___24Anonymous__33363] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__33363)
                      & Vvar__0___24Anonymous__33359 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__33363)
                      & ( cCoq_2eZArith_2eZeven_2eZodd___24a1(V0__z)
                      <=> p(c_24True) ) )
                  | ? [Vvar__0___24Anonymous__33364] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__33364)
                      & Vvar__0___24Anonymous__33359 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__33364)
                      & ( cCoq_2eZArith_2eZeven_2eZodd___24a1(V0__z)
                      <=> p(c_24False) ) )
                  | ( Vvar__0___24Anonymous__33359 = cCoq_2eNumbers_2eBinNums_2exH
                    & ( cCoq_2eZArith_2eZeven_2eZodd___24a1(V0__z)
                    <=> p(c_24True) ) ) ) ) ) )
        | ? [Vvar__0___24Anonymous__33365] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__33365)
            & ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__33365)
             => ( V0__z = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__33365)
                & ( ? [Vvar__0___24Anonymous__33369] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__33369)
                      & Vvar__0___24Anonymous__33365 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__33369)
                      & ( cCoq_2eZArith_2eZeven_2eZodd___24a1(V0__z)
                      <=> p(c_24True) ) )
                  | ? [Vvar__0___24Anonymous__33370] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__33370)
                      & Vvar__0___24Anonymous__33365 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__33370)
                      & ( cCoq_2eZArith_2eZeven_2eZodd___24a1(V0__z)
                      <=> p(c_24False) ) )
                  | ( Vvar__0___24Anonymous__33365 = cCoq_2eNumbers_2eBinNums_2exH
                    & ( cCoq_2eZArith_2eZeven_2eZodd___24a1(V0__z)
                    <=> p(c_24True) ) ) ) ) ) ) ) ) ).

fof('$_def_Coq.ZArith.Zlogarithm.Is_power',axiom,
    ! [V1__p] :
      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__p)
     => ( ? [Vvar__0___24Anonymous__33372] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__33372)
            & V1__p = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__33372)
            & ( cCoq_2eZArith_2eZlogarithm_2eIs__power___24a1(V1__p)
            <=> p(c_24False) ) )
        | ? [Vvar__0___24Anonymous__33373] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__33373)
            & V1__p = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__33373)
            & ( cCoq_2eZArith_2eZlogarithm_2eIs__power___24a1(V1__p)
            <=> cCoq_2eZArith_2eZlogarithm_2eIs__power___24a1(Vvar__0___24Anonymous__33373) ) )
        | ( V1__p = cCoq_2eNumbers_2eBinNums_2exH
          & ( cCoq_2eZArith_2eZlogarithm_2eIs__power___24a1(V1__p)
          <=> p(c_24True) ) ) ) ) ).

fof('$_def_Coq.ZArith.Znat.neq',axiom,
    ! [V0__x,V1__y] :
      ( cCoq_2eZArith_2eZnat_2eneq___24a2(V0__x,V1__y)
    <=> V0__x != V1__y ) ).

fof('$_def_Coq.micromega.Env.Env',axiom,
    ! [V0__D] : cCoq_2emicromega_2eEnv_2eEnv___24a1(V0__D) = c_24__type__19986___24a1(V0__D) ).

fof('$_def_Coq.micromega.Refl.make_conj',axiom,
    ! [V1__A,V2__eval,V3__l] :
      ( cType___24t(V1__A)
     => ( cCoq_2eInit_2eDatatypes_2elist___24t(V1__A,V3__l)
       => ( ( V3__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V1__A)
            & ( cCoq_2emicromega_2eRefl_2emake__conj___24a3(V1__A,V2__eval,V3__l)
            <=> p(c_24True) ) )
          | ? [Vvar__1___24Anonymous__23318] :
              ( t(Vvar__1___24Anonymous__23318,V1__A)
              & ? [Vvar__2___24Anonymous__23319] :
                  ( cCoq_2eInit_2eDatatypes_2elist___24t(V1__A,Vvar__2___24Anonymous__23319)
                  & ( cType___24t(V1__A)
                   => ( cCoq_2eInit_2eDatatypes_2elist___24t(V1__A,Vvar__2___24Anonymous__23319)
                     => ( V3__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V1__A,Vvar__1___24Anonymous__23318,Vvar__2___24Anonymous__23319)
                        & ( ( Vvar__2___24Anonymous__23319 = cCoq_2eInit_2eDatatypes_2enil___24a1(V1__A)
                            & ( cCoq_2emicromega_2eRefl_2emake__conj___24a3(V1__A,V2__eval,V3__l)
                            <=> p(happ(V2__eval,Vvar__1___24Anonymous__23318)) ) )
                          | ? [Vvar__1___24Anonymous__23330] :
                              ( t(Vvar__1___24Anonymous__23330,V1__A)
                              & ? [Vvar__2___24Anonymous__23331] :
                                  ( cCoq_2eInit_2eDatatypes_2elist___24t(V1__A,Vvar__2___24Anonymous__23331)
                                  & Vvar__2___24Anonymous__23319 = cCoq_2eInit_2eDatatypes_2econs___24a3(V1__A,Vvar__1___24Anonymous__23330,Vvar__2___24Anonymous__23331)
                                  & ( cCoq_2emicromega_2eRefl_2emake__conj___24a3(V1__A,V2__eval,V3__l)
                                  <=> ( p(happ(V2__eval,Vvar__1___24Anonymous__23318))
                                      & cCoq_2emicromega_2eRefl_2emake__conj___24a3(V1__A,V2__eval,Vvar__2___24Anonymous__23319) ) ) ) ) ) ) ) ) ) ) ) ) ) ).

fof('$_def_Coq.micromega.RingMicromega.PolEnv',axiom,
    ! [V0__R] : cCoq_2emicromega_2eRingMicromega_2ePolEnv___24a1(V0__R) = cCoq_2emicromega_2eEnv_2eEnv___24a1(V0__R) ).

fof('$_def_Coq.setoid_ring.InitialRing.gen_phiPOS',axiom,
    ! [V0__R,V1__rI,V2__radd,V3__rmul,V5__p] :
      ( cType___24t(V0__R)
     => ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V5__p)
       => ( ? [Vvar__0___24Anonymous__21644] :
              ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__21644)
              & ( cType___24t(V0__R)
               => ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__21644)
                 => ( V5__p = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__21644)
                    & ( ? [Vvar__0___24Anonymous__21648] :
                          ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__21648)
                          & Vvar__0___24Anonymous__21644 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__21648)
                          & cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS___24a5(V0__R,V1__rI,V2__radd,V3__rmul,V5__p) = happ(happ(V2__radd,V1__rI),happ(happ(V3__rmul,happ(happ(V2__radd,V1__rI),V1__rI)),cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS___24a5(V0__R,V1__rI,V2__radd,V3__rmul,Vvar__0___24Anonymous__21644))) )
                      | ? [Vvar__0___24Anonymous__21649] :
                          ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__21649)
                          & Vvar__0___24Anonymous__21644 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__21649)
                          & cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS___24a5(V0__R,V1__rI,V2__radd,V3__rmul,V5__p) = happ(happ(V2__radd,V1__rI),happ(happ(V3__rmul,happ(happ(V2__radd,V1__rI),V1__rI)),cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS___24a5(V0__R,V1__rI,V2__radd,V3__rmul,Vvar__0___24Anonymous__21644))) )
                      | ( Vvar__0___24Anonymous__21644 = cCoq_2eNumbers_2eBinNums_2exH
                        & cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS___24a5(V0__R,V1__rI,V2__radd,V3__rmul,V5__p) = happ(happ(V2__radd,V1__rI),happ(happ(V2__radd,V1__rI),V1__rI)) ) ) ) ) ) )
          | ? [Vvar__0___24Anonymous__21650] :
              ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__21650)
              & ( cType___24t(V0__R)
               => ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__21650)
                 => ( V5__p = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__21650)
                    & ( ? [Vvar__0___24Anonymous__21654] :
                          ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__21654)
                          & Vvar__0___24Anonymous__21650 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__21654)
                          & cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS___24a5(V0__R,V1__rI,V2__radd,V3__rmul,V5__p) = happ(happ(V3__rmul,happ(happ(V2__radd,V1__rI),V1__rI)),cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS___24a5(V0__R,V1__rI,V2__radd,V3__rmul,Vvar__0___24Anonymous__21650)) )
                      | ? [Vvar__0___24Anonymous__21655] :
                          ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__21655)
                          & Vvar__0___24Anonymous__21650 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__21655)
                          & cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS___24a5(V0__R,V1__rI,V2__radd,V3__rmul,V5__p) = happ(happ(V3__rmul,happ(happ(V2__radd,V1__rI),V1__rI)),cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS___24a5(V0__R,V1__rI,V2__radd,V3__rmul,Vvar__0___24Anonymous__21650)) )
                      | ( Vvar__0___24Anonymous__21650 = cCoq_2eNumbers_2eBinNums_2exH
                        & cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS___24a5(V0__R,V1__rI,V2__radd,V3__rmul,V5__p) = happ(happ(V2__radd,V1__rI),V1__rI) ) ) ) ) ) )
          | ( V5__p = cCoq_2eNumbers_2eBinNums_2exH
            & cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS___24a5(V0__R,V1__rI,V2__radd,V3__rmul,V5__p) = V1__rI ) ) ) ) ).

fof('$_def_Coq.setoid_ring.InitialRing.gen_phiPOS1',axiom,
    ! [V0__R,V1__rI,V2__radd,V3__rmul,V5__p] :
      ( cType___24t(V0__R)
     => ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V5__p)
       => ( ? [Vvar__0___24Anonymous__21611] :
              ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__21611)
              & V5__p = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__21611)
              & cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS1___24a5(V0__R,V1__rI,V2__radd,V3__rmul,V5__p) = happ(happ(V2__radd,V1__rI),happ(happ(V3__rmul,happ(happ(V2__radd,V1__rI),V1__rI)),cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS1___24a5(V0__R,V1__rI,V2__radd,V3__rmul,Vvar__0___24Anonymous__21611))) )
          | ? [Vvar__0___24Anonymous__21612] :
              ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__21612)
              & V5__p = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__21612)
              & cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS1___24a5(V0__R,V1__rI,V2__radd,V3__rmul,V5__p) = happ(happ(V3__rmul,happ(happ(V2__radd,V1__rI),V1__rI)),cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS1___24a5(V0__R,V1__rI,V2__radd,V3__rmul,Vvar__0___24Anonymous__21612)) )
          | ( V5__p = cCoq_2eNumbers_2eBinNums_2exH
            & cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS1___24a5(V0__R,V1__rI,V2__radd,V3__rmul,V5__p) = V1__rI ) ) ) ) ).

fof('$_def_Coq.setoid_ring.Ring_tac.ring_subst_niter',axiom,
    cCoq_2esetoid__ring_2eRing__tac_2ering__subst__niter = cCoq_2eInit_2eNat_2emul___24a2(cCoq_2eInit_2eNat_2emul___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO)))))))))),cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO))))))))))),cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO))))))))))) ).

fof('$_def_Coq.setoid_ring.Ring_theory.IDphi',axiom,
    ! [V0__R,V1__x] : cCoq_2esetoid__ring_2eRing__theory_2eIDphi___24a2(V0__R,V1__x) = V1__x ).

fof('$_def_Coq.setoid_ring.Ring_theory.SRopp',axiom,
    ! [V0__R,V1__x] : cCoq_2esetoid__ring_2eRing__theory_2eSRopp___24a2(V0__R,V1__x) = V1__x ).

fof('$_def_Coq.setoid_ring.Ring_theory.pow_pos',axiom,
    ! [V0__R,V1__rmul,V3__x,V4__i] :
      ( cType___24t(V0__R)
     => ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V4__i)
       => ( ? [Vvar__0___24Anonymous__28905] :
              ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__28905)
              & V4__i = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__28905)
              & cCoq_2esetoid__ring_2eRing__theory_2epow__pos___24a4(V0__R,V1__rmul,V3__x,V4__i) = happ(happ(V1__rmul,V3__x),happ(happ(V1__rmul,c_24__let__var__6__p__28906__28909___24a4(V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__28905)),c_24__let__var__6__p__28906__28909___24a4(V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__28905))) )
          | ? [Vvar__0___24Anonymous__28907] :
              ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__28907)
              & V4__i = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__28907)
              & cCoq_2esetoid__ring_2eRing__theory_2epow__pos___24a4(V0__R,V1__rmul,V3__x,V4__i) = happ(happ(V1__rmul,c_24__let__var__6__p__28908__28910___24a4(V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__28907)),c_24__let__var__6__p__28908__28910___24a4(V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__28907)) )
          | ( V4__i = cCoq_2eNumbers_2eBinNums_2exH
            & cCoq_2esetoid__ring_2eRing__theory_2epow__pos___24a4(V0__R,V1__rmul,V3__x,V4__i) = V3__x ) ) ) ) ).

fof('$_def_IntMap.Fset.FSet',axiom,
    ! [Vvar__1903] :
      ( cIntMap_2eFset_2eFSet___24t(Vvar__1903)
    <=> cIntMap_2eMap_2eMap___24t(cCoq_2eInit_2eDatatypes_2eunit,Vvar__1903) ) ).

fof('$_def_IntMap.Fset.FSetDiff',axiom,
    ! [V0__s,V1__s_27] : cIntMap_2eFset_2eFSetDiff___24a2(V0__s,V1__s_27) = cIntMap_2eFset_2eMapDomRestrBy___24a4(cCoq_2eInit_2eDatatypes_2eunit,cCoq_2eInit_2eDatatypes_2eunit,V0__s,V1__s_27) ).

fof('$_def_IntMap.Fset.FSetInter',axiom,
    ! [V0__s,V1__s_27] : cIntMap_2eFset_2eFSetInter___24a2(V0__s,V1__s_27) = cIntMap_2eFset_2eMapDomRestrTo___24a4(cCoq_2eInit_2eDatatypes_2eunit,cCoq_2eInit_2eDatatypes_2eunit,V0__s,V1__s_27) ).

fof('$_def_IntMap.Fset.FSetUnion',axiom,
    ! [V0__s,V1__s_27] : cIntMap_2eFset_2eFSetUnion___24a2(V0__s,V1__s_27) = cIntMap_2eMap_2eMapMerge___24a3(cCoq_2eInit_2eDatatypes_2eunit,V0__s,V1__s_27) ).

fof('$_def_IntMap.Fset.MapDom',axiom,
    ! [V0__A,V2__m] :
      ( cType___24t(V0__A)
     => ( cIntMap_2eMap_2eMap___24t(V0__A,V2__m)
       => ( ( V2__m = cIntMap_2eMap_2eM0___24a1(V0__A)
            & cIntMap_2eFset_2eMapDom___24a2(V0__A,V2__m) = cIntMap_2eMap_2eM0___24a1(cCoq_2eInit_2eDatatypes_2eunit) )
          | ? [Vvar__1___24Anonymous__1908] :
              ( cIntMap_2eMap_2ead___24t(Vvar__1___24Anonymous__1908)
              & ? [Vvar__2___24Anonymous__1909] :
                  ( t(Vvar__2___24Anonymous__1909,V0__A)
                  & V2__m = cIntMap_2eMap_2eM1___24a3(V0__A,Vvar__1___24Anonymous__1908,Vvar__2___24Anonymous__1909)
                  & cIntMap_2eFset_2eMapDom___24a2(V0__A,V2__m) = cIntMap_2eMap_2eM1___24a3(cCoq_2eInit_2eDatatypes_2eunit,Vvar__1___24Anonymous__1908,cCoq_2eInit_2eDatatypes_2ett) ) )
          | ? [Vvar__1___24Anonymous__1912] :
              ( cIntMap_2eMap_2eMap___24t(V0__A,Vvar__1___24Anonymous__1912)
              & ? [Vvar__2___24Anonymous__1913] :
                  ( cIntMap_2eMap_2eMap___24t(V0__A,Vvar__2___24Anonymous__1913)
                  & V2__m = cIntMap_2eMap_2eM2___24a3(V0__A,Vvar__1___24Anonymous__1912,Vvar__2___24Anonymous__1913)
                  & cIntMap_2eFset_2eMapDom___24a2(V0__A,V2__m) = cIntMap_2eMap_2eM2___24a3(cCoq_2eInit_2eDatatypes_2eunit,cIntMap_2eFset_2eMapDom___24a2(V0__A,Vvar__1___24Anonymous__1912),cIntMap_2eFset_2eMapDom___24a2(V0__A,Vvar__2___24Anonymous__1913)) ) ) ) ) ) ).

fof('$_def_IntMap.Fset.MapDomRestrBy',axiom,
    ! [V0__A,V1__B,V3__m] :
      ( cType___24t(V0__A)
     => ( cIntMap_2eMap_2eMap___24t(V0__A,V3__m)
       => ( ( V3__m = cIntMap_2eMap_2eM0___24a1(V0__A)
            & cIntMap_2eFset_2eMapDomRestrBy___24a3(V0__A,V1__B,V3__m) = c_24__lam__1083___24a2(V0__A,V1__B) )
          | ? [Vvar__1___24Anonymous__1187] :
              ( cIntMap_2eMap_2ead___24t(Vvar__1___24Anonymous__1187)
              & ? [Vvar__2___24Anonymous__1188] :
                  ( t(Vvar__2___24Anonymous__1188,V0__A)
                  & V3__m = cIntMap_2eMap_2eM1___24a3(V0__A,Vvar__1___24Anonymous__1187,Vvar__2___24Anonymous__1188)
                  & cIntMap_2eFset_2eMapDomRestrBy___24a3(V0__A,V1__B,V3__m) = c_24__lam__1228___24a4(V0__A,V1__B,V3__m,Vvar__1___24Anonymous__1187) ) )
          | ? [Vvar__1___24Anonymous__1197] :
              ( cIntMap_2eMap_2eMap___24t(V0__A,Vvar__1___24Anonymous__1197)
              & ? [Vvar__2___24Anonymous__1198] :
                  ( cIntMap_2eMap_2eMap___24t(V0__A,Vvar__2___24Anonymous__1198)
                  & V3__m = cIntMap_2eMap_2eM2___24a3(V0__A,Vvar__1___24Anonymous__1197,Vvar__2___24Anonymous__1198)
                  & cIntMap_2eFset_2eMapDomRestrBy___24a3(V0__A,V1__B,V3__m) = c_24__lam__1270___24a5(V0__A,V1__B,V3__m,Vvar__1___24Anonymous__1197,Vvar__2___24Anonymous__1198) ) ) ) ) ) ).

fof('$_def_IntMap.Fset.MapDomRestrTo',axiom,
    ! [V0__A,V1__B,V3__m] :
      ( cType___24t(V0__A)
     => ( cIntMap_2eMap_2eMap___24t(V0__A,V3__m)
       => ( ( V3__m = cIntMap_2eMap_2eM0___24a1(V0__A)
            & cIntMap_2eFset_2eMapDomRestrTo___24a3(V0__A,V1__B,V3__m) = c_24__lam__1083___24a2(V0__A,V1__B) )
          | ? [Vvar__1___24Anonymous__1052] :
              ( cIntMap_2eMap_2ead___24t(Vvar__1___24Anonymous__1052)
              & ? [Vvar__2___24Anonymous__1053] :
                  ( t(Vvar__2___24Anonymous__1053,V0__A)
                  & V3__m = cIntMap_2eMap_2eM1___24a3(V0__A,Vvar__1___24Anonymous__1052,Vvar__2___24Anonymous__1053)
                  & cIntMap_2eFset_2eMapDomRestrTo___24a3(V0__A,V1__B,V3__m) = c_24__lam__1098___24a4(V0__A,V1__B,V3__m,Vvar__1___24Anonymous__1052) ) )
          | ? [Vvar__1___24Anonymous__1062] :
              ( cIntMap_2eMap_2eMap___24t(V0__A,Vvar__1___24Anonymous__1062)
              & ? [Vvar__2___24Anonymous__1063] :
                  ( cIntMap_2eMap_2eMap___24t(V0__A,Vvar__2___24Anonymous__1063)
                  & V3__m = cIntMap_2eMap_2eM2___24a3(V0__A,Vvar__1___24Anonymous__1062,Vvar__2___24Anonymous__1063)
                  & cIntMap_2eFset_2eMapDomRestrTo___24a3(V0__A,V1__B,V3__m) = c_24__lam__1156___24a5(V0__A,V1__B,V3__m,Vvar__1___24Anonymous__1062,Vvar__2___24Anonymous__1063) ) ) ) ) ) ).

fof('$_def_IntMap.Fset.in_FSet',axiom,
    cIntMap_2eFset_2ein__FSet = cIntMap_2eFset_2ein__dom___24a1(cCoq_2eInit_2eDatatypes_2eunit) ).

fof('$_def_IntMap.Fset.in_dom',axiom,
    ! [V0__A,V1__a,V2__m] :
      ( cType___24t(V0__A)
     => ( cIntMap_2eMap_2ead___24t(V1__a)
       => ( cIntMap_2eMap_2eMap___24t(V0__A,V2__m)
         => ( ? [Vvar__1___24Anonymous__1896] :
                ( t(Vvar__1___24Anonymous__1896,V0__A)
                & cIntMap_2eMap_2eMapGet___24a3(V0__A,V2__m,V1__a) = cCoq_2eInit_2eDatatypes_2eSome___24a2(V0__A,Vvar__1___24Anonymous__1896)
                & cIntMap_2eFset_2ein__dom___24a3(V0__A,V1__a,V2__m) = cCoq_2eInit_2eDatatypes_2etrue )
            | ( cIntMap_2eMap_2eMapGet___24a3(V0__A,V2__m,V1__a) = cCoq_2eInit_2eDatatypes_2eNone___24a1(V0__A)
              & cIntMap_2eFset_2ein__dom___24a3(V0__A,V1__a,V2__m) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ) ).

fof('$_def_IntMap.Lsort.ad_monotonic',axiom,
    ! [V0__pf] :
      ( cIntMap_2eLsort_2ead__monotonic___24a1(V0__pf)
    <=> ! [V1__a] :
          ( cIntMap_2eMap_2ead___24t(V1__a)
         => ! [V2__a_27] :
              ( cIntMap_2eMap_2ead___24t(V2__a_27)
             => ( cCoq_2eNArith_2eNdigits_2eNless___24a2(V1__a,V2__a_27) = cCoq_2eInit_2eDatatypes_2etrue
               => cCoq_2eNArith_2eNdigits_2eNless___24a2(happ(V0__pf,V1__a),happ(V0__pf,V2__a_27)) = cCoq_2eInit_2eDatatypes_2etrue ) ) ) ) ).

fof('$_def_IntMap.Lsort.alist_nth_ad',axiom,
    ! [V0__A,V2__n,V3__l] :
      ( cType___24t(V0__A)
     => ( cIntMap_2eMapiter_2ealist___24t(V0__A,V3__l)
       => ( ( V3__l = cCoq_2eInit_2eDatatypes_2enil___24a1(cCoq_2eInit_2eDatatypes_2eprod___24a2(cIntMap_2eMap_2ead,V0__A))
            & cIntMap_2eLsort_2ealist__nth__ad___24a3(V0__A,V2__n,V3__l) = cCoq_2eNumbers_2eBinNums_2eN0 )
          | ? [Vvar__1___24Anonymous__13064] :
              ( cCoq_2eInit_2eDatatypes_2eprod___24t(cIntMap_2eMap_2ead,V0__A,Vvar__1___24Anonymous__13064)
              & ? [Vvar__2___24Anonymous__13065] :
                  ( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eInit_2eDatatypes_2eprod___24a2(cIntMap_2eMap_2ead,V0__A),Vvar__2___24Anonymous__13065)
                  & ( cType___24t(V0__A)
                   => ( cCoq_2eInit_2eDatatypes_2eprod___24t(cIntMap_2eMap_2ead,V0__A,Vvar__1___24Anonymous__13064)
                     => ( V3__l = cCoq_2eInit_2eDatatypes_2econs___24a3(cCoq_2eInit_2eDatatypes_2eprod___24a2(cIntMap_2eMap_2ead,V0__A),Vvar__1___24Anonymous__13064,Vvar__2___24Anonymous__13065)
                        & ? [Vvar__2___24Anonymous__13081] :
                            ( cIntMap_2eMap_2ead___24t(Vvar__2___24Anonymous__13081)
                            & ? [Vvar__3___24Anonymous__13082] :
                                ( t(Vvar__3___24Anonymous__13082,V0__A)
                                & ( cType___24t(V0__A)
                                 => ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__n)
                                   => ( Vvar__1___24Anonymous__13064 = cCoq_2eInit_2eDatatypes_2epair___24a4(cIntMap_2eMap_2ead,V0__A,Vvar__2___24Anonymous__13081,Vvar__3___24Anonymous__13082)
                                      & ( ( V2__n = cCoq_2eInit_2eDatatypes_2eO
                                          & cIntMap_2eLsort_2ealist__nth__ad___24a3(V0__A,V2__n,V3__l) = Vvar__2___24Anonymous__13081 )
                                        | ? [Vvar__0___24Anonymous__13088] :
                                            ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__13088)
                                            & V2__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__13088)
                                            & cIntMap_2eLsort_2ealist__nth__ad___24a3(V0__A,V2__n,V3__l) = cIntMap_2eLsort_2ealist__nth__ad___24a3(V0__A,Vvar__0___24Anonymous__13088,Vvar__2___24Anonymous__13065) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).

fof('$_def_IntMap.Map.MapCard',axiom,
    ! [V0__A,V2__m] :
      ( cType___24t(V0__A)
     => ( cIntMap_2eMap_2eMap___24t(V0__A,V2__m)
       => ( ( V2__m = cIntMap_2eMap_2eM0___24a1(V0__A)
            & cIntMap_2eMap_2eMapCard___24a2(V0__A,V2__m) = cCoq_2eInit_2eDatatypes_2eO )
          | ? [Vvar__1___24Anonymous__727] :
              ( cIntMap_2eMap_2ead___24t(Vvar__1___24Anonymous__727)
              & ? [Vvar__2___24Anonymous__728] :
                  ( t(Vvar__2___24Anonymous__728,V0__A)
                  & V2__m = cIntMap_2eMap_2eM1___24a3(V0__A,Vvar__1___24Anonymous__727,Vvar__2___24Anonymous__728)
                  & cIntMap_2eMap_2eMapCard___24a2(V0__A,V2__m) = cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO) ) )
          | ? [Vvar__1___24Anonymous__731] :
              ( cIntMap_2eMap_2eMap___24t(V0__A,Vvar__1___24Anonymous__731)
              & ? [Vvar__2___24Anonymous__732] :
                  ( cIntMap_2eMap_2eMap___24t(V0__A,Vvar__2___24Anonymous__732)
                  & V2__m = cIntMap_2eMap_2eM2___24a3(V0__A,Vvar__1___24Anonymous__731,Vvar__2___24Anonymous__732)
                  & cIntMap_2eMap_2eMapCard___24a2(V0__A,V2__m) = cCoq_2eInit_2eNat_2eadd___24a2(cIntMap_2eMap_2eMapCard___24a2(V0__A,Vvar__1___24Anonymous__731),cIntMap_2eMap_2eMapCard___24a2(V0__A,Vvar__2___24Anonymous__732)) ) ) ) ) ) ).

fof('$_def_IntMap.Map.MapDelta',axiom,
    ! [V0__A,V2__m] :
      ( cType___24t(V0__A)
     => ( cIntMap_2eMap_2eMap___24t(V0__A,V2__m)
       => ( ( V2__m = cIntMap_2eMap_2eM0___24a1(V0__A)
            & cIntMap_2eMap_2eMapDelta___24a2(V0__A,V2__m) = c_24__lam__319___24a1(V0__A) )
          | ? [Vvar__1___24Anonymous__1424] :
              ( cIntMap_2eMap_2ead___24t(Vvar__1___24Anonymous__1424)
              & ? [Vvar__2___24Anonymous__1425] :
                  ( t(Vvar__2___24Anonymous__1425,V0__A)
                  & V2__m = cIntMap_2eMap_2eM1___24a3(V0__A,Vvar__1___24Anonymous__1424,Vvar__2___24Anonymous__1425)
                  & cIntMap_2eMap_2eMapDelta___24a2(V0__A,V2__m) = c_24__lam__1465___24a3(V0__A,Vvar__1___24Anonymous__1424,Vvar__2___24Anonymous__1425) ) )
          | ? [Vvar__1___24Anonymous__1434] :
              ( cIntMap_2eMap_2eMap___24t(V0__A,Vvar__1___24Anonymous__1434)
              & ? [Vvar__2___24Anonymous__1435] :
                  ( cIntMap_2eMap_2eMap___24t(V0__A,Vvar__2___24Anonymous__1435)
                  & V2__m = cIntMap_2eMap_2eM2___24a3(V0__A,Vvar__1___24Anonymous__1434,Vvar__2___24Anonymous__1435)
                  & cIntMap_2eMap_2eMapDelta___24a2(V0__A,V2__m) = c_24__lam__1515___24a4(V0__A,V2__m,Vvar__1___24Anonymous__1434,Vvar__2___24Anonymous__1435) ) ) ) ) ) ).

fof('$_def_IntMap.Map.MapEmptyp',axiom,
    ! [V0__A,V1__m] :
      ( cType___24t(V0__A)
     => ( cIntMap_2eMap_2eMap___24t(V0__A,V1__m)
       => ( ( V1__m = cIntMap_2eMap_2eM0___24a1(V0__A)
            & cIntMap_2eMap_2eMapEmptyp___24a2(V0__A,V1__m) = cCoq_2eInit_2eDatatypes_2etrue )
          | ? [Vvar__1___24Anonymous__2056] :
              ( cIntMap_2eMap_2ead___24t(Vvar__1___24Anonymous__2056)
              & ? [Vvar__2___24Anonymous__2057] :
                  ( t(Vvar__2___24Anonymous__2057,V0__A)
                  & V1__m = cIntMap_2eMap_2eM1___24a3(V0__A,Vvar__1___24Anonymous__2056,Vvar__2___24Anonymous__2057)
                  & cIntMap_2eMap_2eMapEmptyp___24a2(V0__A,V1__m) = cCoq_2eInit_2eDatatypes_2efalse ) )
          | ? [Vvar__1___24Anonymous__2060] :
              ( cIntMap_2eMap_2eMap___24t(V0__A,Vvar__1___24Anonymous__2060)
              & ? [Vvar__2___24Anonymous__2061] :
                  ( cIntMap_2eMap_2eMap___24t(V0__A,Vvar__2___24Anonymous__2061)
                  & V1__m = cIntMap_2eMap_2eM2___24a3(V0__A,Vvar__1___24Anonymous__2060,Vvar__2___24Anonymous__2061)
                  & cIntMap_2eMap_2eMapEmptyp___24a2(V0__A,V1__m) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ) ).

fof('$_def_IntMap.Map.MapGet',axiom,
    ! [V0__A,V2__m] :
      ( cType___24t(V0__A)
     => ( cIntMap_2eMap_2eMap___24t(V0__A,V2__m)
       => ( ( V2__m = cIntMap_2eMap_2eM0___24a1(V0__A)
            & cIntMap_2eMap_2eMapGet___24a2(V0__A,V2__m) = c_24__lam__128___24a1(V0__A) )
          | ? [Vvar__1___24Anonymous__104] :
              ( cIntMap_2eMap_2ead___24t(Vvar__1___24Anonymous__104)
              & ? [Vvar__2___24Anonymous__105] :
                  ( t(Vvar__2___24Anonymous__105,V0__A)
                  & V2__m = cIntMap_2eMap_2eM1___24a3(V0__A,Vvar__1___24Anonymous__104,Vvar__2___24Anonymous__105)
                  & cIntMap_2eMap_2eMapGet___24a2(V0__A,V2__m) = c_24__lam__136___24a3(V0__A,Vvar__1___24Anonymous__104,Vvar__2___24Anonymous__105) ) )
          | ? [Vvar__1___24Anonymous__112] :
              ( cIntMap_2eMap_2eMap___24t(V0__A,Vvar__1___24Anonymous__112)
              & ? [Vvar__2___24Anonymous__113] :
                  ( cIntMap_2eMap_2eMap___24t(V0__A,Vvar__2___24Anonymous__113)
                  & V2__m = cIntMap_2eMap_2eM2___24a3(V0__A,Vvar__1___24Anonymous__112,Vvar__2___24Anonymous__113)
                  & cIntMap_2eMap_2eMapGet___24a2(V0__A,V2__m) = c_24__lam__163___24a3(V0__A,Vvar__1___24Anonymous__112,Vvar__2___24Anonymous__113) ) ) ) ) ) ).

fof('$_def_IntMap.Map.MapMerge',axiom,
    ! [V0__A,V2__m] :
      ( cType___24t(V0__A)
     => ( cIntMap_2eMap_2eMap___24t(V0__A,V2__m)
       => ( ( V2__m = cIntMap_2eMap_2eM0___24a1(V0__A)
            & cIntMap_2eMap_2eMapMerge___24a2(V0__A,V2__m) = c_24__lam__319___24a1(V0__A) )
          | ? [Vvar__1___24Anonymous__297] :
              ( cIntMap_2eMap_2ead___24t(Vvar__1___24Anonymous__297)
              & ? [Vvar__2___24Anonymous__298] :
                  ( t(Vvar__2___24Anonymous__298,V0__A)
                  & V2__m = cIntMap_2eMap_2eM1___24a3(V0__A,Vvar__1___24Anonymous__297,Vvar__2___24Anonymous__298)
                  & cIntMap_2eMap_2eMapMerge___24a2(V0__A,V2__m) = c_24__lam__323___24a3(V0__A,Vvar__1___24Anonymous__297,Vvar__2___24Anonymous__298) ) )
          | ? [Vvar__1___24Anonymous__303] :
              ( cIntMap_2eMap_2eMap___24t(V0__A,Vvar__1___24Anonymous__303)
              & ? [Vvar__2___24Anonymous__304] :
                  ( cIntMap_2eMap_2eMap___24t(V0__A,Vvar__2___24Anonymous__304)
                  & V2__m = cIntMap_2eMap_2eM2___24a3(V0__A,Vvar__1___24Anonymous__303,Vvar__2___24Anonymous__304)
                  & cIntMap_2eMap_2eMapMerge___24a2(V0__A,V2__m) = c_24__lam__355___24a4(V0__A,V2__m,Vvar__1___24Anonymous__303,Vvar__2___24Anonymous__304) ) ) ) ) ) ).

fof('$_def_IntMap.Map.MapPut',axiom,
    ! [V0__A,V2__m] :
      ( cType___24t(V0__A)
     => ( cIntMap_2eMap_2eMap___24t(V0__A,V2__m)
       => ( ( V2__m = cIntMap_2eMap_2eM0___24a1(V0__A)
            & cIntMap_2eMap_2eMapPut___24a2(V0__A,V2__m) = cIntMap_2eMap_2eM1___24a1(V0__A) )
          | ? [Vvar__1___24Anonymous__179] :
              ( cIntMap_2eMap_2ead___24t(Vvar__1___24Anonymous__179)
              & ? [Vvar__2___24Anonymous__180] :
                  ( t(Vvar__2___24Anonymous__180,V0__A)
                  & V2__m = cIntMap_2eMap_2eM1___24a3(V0__A,Vvar__1___24Anonymous__179,Vvar__2___24Anonymous__180)
                  & cIntMap_2eMap_2eMapPut___24a2(V0__A,V2__m) = c_24__lam__225___24a3(V0__A,Vvar__1___24Anonymous__179,Vvar__2___24Anonymous__180) ) )
          | ? [Vvar__1___24Anonymous__191] :
              ( cIntMap_2eMap_2eMap___24t(V0__A,Vvar__1___24Anonymous__191)
              & ? [Vvar__2___24Anonymous__192] :
                  ( cIntMap_2eMap_2eMap___24t(V0__A,Vvar__2___24Anonymous__192)
                  & V2__m = cIntMap_2eMap_2eM2___24a3(V0__A,Vvar__1___24Anonymous__191,Vvar__2___24Anonymous__192)
                  & cIntMap_2eMap_2eMapPut___24a2(V0__A,V2__m) = c_24__lam__262___24a3(V0__A,Vvar__1___24Anonymous__191,Vvar__2___24Anonymous__192) ) ) ) ) ) ).

fof('$_def_IntMap.Map.MapPut1',axiom,
    ! [V0__A,V2__a,V3__y,V4__a_27,V5__y_27,V6__p] :
      ( cType___24t(V0__A)
     => ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V6__p)
       => ( ? [Vvar__0___24Anonymous__563] :
              ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__563)
              & ( cType___24t(V0__A)
               => ( cIntMap_2eMap_2ead___24t(V2__a)
                 => ( V6__p = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__563)
                    & ( ( cCoq_2eNArith_2eBinNatDef_2eN_2eodd___24a1(V2__a) = cCoq_2eInit_2eDatatypes_2etrue
                        & cIntMap_2eMap_2eMapPut1___24a6(V0__A,V2__a,V3__y,V4__a_27,V5__y_27,V6__p) = cIntMap_2eMap_2eM2___24a3(V0__A,cIntMap_2eMap_2eM1___24a3(V0__A,cCoq_2eNArith_2eBinNatDef_2eN_2ediv2___24a1(V4__a_27),V5__y_27),cIntMap_2eMap_2eM1___24a3(V0__A,cCoq_2eNArith_2eBinNatDef_2eN_2ediv2___24a1(V2__a),V3__y)) )
                      | ( cCoq_2eNArith_2eBinNatDef_2eN_2eodd___24a1(V2__a) = cCoq_2eInit_2eDatatypes_2efalse
                        & cIntMap_2eMap_2eMapPut1___24a6(V0__A,V2__a,V3__y,V4__a_27,V5__y_27,V6__p) = cIntMap_2eMap_2eM2___24a3(V0__A,cIntMap_2eMap_2eM1___24a3(V0__A,cCoq_2eNArith_2eBinNatDef_2eN_2ediv2___24a1(V2__a),V3__y),cIntMap_2eMap_2eM1___24a3(V0__A,cCoq_2eNArith_2eBinNatDef_2eN_2ediv2___24a1(V4__a_27),V5__y_27)) ) ) ) ) ) )
          | ? [Vvar__0___24Anonymous__565] :
              ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__565)
              & V6__p = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__565)
              & cIntMap_2eMap_2eMapPut1___24a6(V0__A,V2__a,V3__y,V4__a_27,V5__y_27,V6__p) = c_24__case__Coq_2eInit_2eDatatypes_2ebool_24577___24a6(V0__A,V2__a,V3__y,V4__a_27,V5__y_27,Vvar__0___24Anonymous__565) )
          | ( cType___24t(V0__A)
           => ( cIntMap_2eMap_2ead___24t(V2__a)
             => ( V6__p = cCoq_2eNumbers_2eBinNums_2exH
                & ( ( cCoq_2eNArith_2eBinNatDef_2eN_2eodd___24a1(V2__a) = cCoq_2eInit_2eDatatypes_2etrue
                    & cIntMap_2eMap_2eMapPut1___24a6(V0__A,V2__a,V3__y,V4__a_27,V5__y_27,V6__p) = cIntMap_2eMap_2eM2___24a3(V0__A,cIntMap_2eMap_2eM1___24a3(V0__A,cCoq_2eNArith_2eBinNatDef_2eN_2ediv2___24a1(V4__a_27),V5__y_27),cIntMap_2eMap_2eM1___24a3(V0__A,cCoq_2eNArith_2eBinNatDef_2eN_2ediv2___24a1(V2__a),V3__y)) )
                  | ( cCoq_2eNArith_2eBinNatDef_2eN_2eodd___24a1(V2__a) = cCoq_2eInit_2eDatatypes_2efalse
                    & cIntMap_2eMap_2eMapPut1___24a6(V0__A,V2__a,V3__y,V4__a_27,V5__y_27,V6__p) = cIntMap_2eMap_2eM2___24a3(V0__A,cIntMap_2eMap_2eM1___24a3(V0__A,cCoq_2eNArith_2eBinNatDef_2eN_2ediv2___24a1(V2__a),V3__y),cIntMap_2eMap_2eM1___24a3(V0__A,cCoq_2eNArith_2eBinNatDef_2eN_2ediv2___24a1(V4__a_27),V5__y_27)) ) ) ) ) ) ) ) ) ).

fof('$_def_IntMap.Map.MapPut_behind',axiom,
    ! [V0__A,V2__m] :
      ( cType___24t(V0__A)
     => ( cIntMap_2eMap_2eMap___24t(V0__A,V2__m)
       => ( ( V2__m = cIntMap_2eMap_2eM0___24a1(V0__A)
            & cIntMap_2eMap_2eMapPut__behind___24a2(V0__A,V2__m) = cIntMap_2eMap_2eM1___24a1(V0__A) )
          | ? [Vvar__1___24Anonymous__599] :
              ( cIntMap_2eMap_2ead___24t(Vvar__1___24Anonymous__599)
              & ? [Vvar__2___24Anonymous__600] :
                  ( t(Vvar__2___24Anonymous__600,V0__A)
                  & V2__m = cIntMap_2eMap_2eM1___24a3(V0__A,Vvar__1___24Anonymous__599,Vvar__2___24Anonymous__600)
                  & cIntMap_2eMap_2eMapPut__behind___24a2(V0__A,V2__m) = c_24__lam__649___24a4(V0__A,V2__m,Vvar__1___24Anonymous__599,Vvar__2___24Anonymous__600) ) )
          | ? [Vvar__1___24Anonymous__611] :
              ( cIntMap_2eMap_2eMap___24t(V0__A,Vvar__1___24Anonymous__611)
              & ? [Vvar__2___24Anonymous__612] :
                  ( cIntMap_2eMap_2eMap___24t(V0__A,Vvar__2___24Anonymous__612)
                  & V2__m = cIntMap_2eMap_2eM2___24a3(V0__A,Vvar__1___24Anonymous__611,Vvar__2___24Anonymous__612)
                  & cIntMap_2eMap_2eMapPut__behind___24a2(V0__A,V2__m) = c_24__lam__686___24a3(V0__A,Vvar__1___24Anonymous__611,Vvar__2___24Anonymous__612) ) ) ) ) ) ).

fof('$_def_IntMap.Map.MapRemove',axiom,
    ! [V0__A,V2__m] :
      ( cType___24t(V0__A)
     => ( cIntMap_2eMap_2eMap___24t(V0__A,V2__m)
       => ( ( V2__m = cIntMap_2eMap_2eM0___24a1(V0__A)
            & cIntMap_2eMap_2eMapRemove___24a2(V0__A,V2__m) = c_24__lam__1398___24a1(V0__A) )
          | ? [Vvar__1___24Anonymous__1382] :
              ( cIntMap_2eMap_2ead___24t(Vvar__1___24Anonymous__1382)
              & ? [Vvar__2___24Anonymous__1383] :
                  ( t(Vvar__2___24Anonymous__1383,V0__A)
                  & V2__m = cIntMap_2eMap_2eM1___24a3(V0__A,Vvar__1___24Anonymous__1382,Vvar__2___24Anonymous__1383)
                  & cIntMap_2eMap_2eMapRemove___24a2(V0__A,V2__m) = c_24__lam__1406___24a3(V0__A,V2__m,Vvar__1___24Anonymous__1382) ) )
          | ? [Vvar__1___24Anonymous__1390] :
              ( cIntMap_2eMap_2eMap___24t(V0__A,Vvar__1___24Anonymous__1390)
              & ? [Vvar__2___24Anonymous__1391] :
                  ( cIntMap_2eMap_2eMap___24t(V0__A,Vvar__2___24Anonymous__1391)
                  & V2__m = cIntMap_2eMap_2eM2___24a3(V0__A,Vvar__1___24Anonymous__1390,Vvar__2___24Anonymous__1391)
                  & cIntMap_2eMap_2eMapRemove___24a2(V0__A,V2__m) = c_24__lam__1414___24a3(V0__A,Vvar__1___24Anonymous__1390,Vvar__2___24Anonymous__1391) ) ) ) ) ) ).

fof('$_def_IntMap.Map.MapSingleton',axiom,
    ! [V0__A] : cIntMap_2eMap_2eMapSingleton___24a1(V0__A) = cIntMap_2eMap_2eM1___24a1(V0__A) ).

fof('$_def_IntMap.Map.Map_rec',axiom,
    ! [V0__A,V1__P] : cIntMap_2eMap_2eMap__rec___24a2(V0__A,V1__P) = cIntMap_2eMap_2eMap__rect___24a2(V0__A,V1__P) ).

fof('$_def_IntMap.Map.Map_rect',axiom,
    ! [V0__A,V1__P,V2__f,V3__f,V4__f,V6__m] :
      ( cType___24t(V0__A)
     => ( c_24__type__476___24t(V0__A,V1__P,V1__P)
       => ( cIntMap_2eMap_2eMap___24t(V0__A,V6__m)
         => ( ( V6__m = cIntMap_2eMap_2eM0___24a1(V0__A)
              & cIntMap_2eMap_2eMap__rect___24a6(V0__A,V1__P,V2__f,V3__f,V4__f,V6__m) = V2__f )
            | ? [Vvar__1___24Anonymous__466] :
                ( cIntMap_2eMap_2ead___24t(Vvar__1___24Anonymous__466)
                & ? [Vvar__2___24Anonymous__467] :
                    ( t(Vvar__2___24Anonymous__467,V0__A)
                    & V6__m = cIntMap_2eMap_2eM1___24a3(V0__A,Vvar__1___24Anonymous__466,Vvar__2___24Anonymous__467)
                    & cIntMap_2eMap_2eMap__rect___24a6(V0__A,V1__P,V2__f,V3__f,V4__f,V6__m) = happ(happ(V3__f,Vvar__1___24Anonymous__466),Vvar__2___24Anonymous__467) ) )
            | ? [Vvar__1___24Anonymous__470] :
                ( cIntMap_2eMap_2eMap___24t(V0__A,Vvar__1___24Anonymous__470)
                & ? [Vvar__2___24Anonymous__471] :
                    ( cIntMap_2eMap_2eMap___24t(V0__A,Vvar__2___24Anonymous__471)
                    & V6__m = cIntMap_2eMap_2eM2___24a3(V0__A,Vvar__1___24Anonymous__470,Vvar__2___24Anonymous__471)
                    & cIntMap_2eMap_2eMap__rect___24a6(V0__A,V1__P,V2__f,V3__f,V4__f,V6__m) = happ(happ(happ(happ(V4__f,Vvar__1___24Anonymous__470),cIntMap_2eMap_2eMap__rect___24a6(V0__A,V1__P,V2__f,V3__f,V4__f,Vvar__1___24Anonymous__470)),Vvar__2___24Anonymous__471),cIntMap_2eMap_2eMap__rect___24a6(V0__A,V1__P,V2__f,V3__f,V4__f,Vvar__2___24Anonymous__471)) ) ) ) ) ) ) ).

fof('$_def_IntMap.Map.ad',axiom,
    ! [Vvar__52] :
      ( cIntMap_2eMap_2ead___24t(Vvar__52)
    <=> cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__52) ) ).

fof('$_def_IntMap.Map.eqm',axiom,
    ! [V0__A,V1__g,V2__g_27] :
      ( cIntMap_2eMap_2eeqm___24a3(V0__A,V1__g,V2__g_27)
    <=> ! [V3__a] :
          ( cIntMap_2eMap_2ead___24t(V3__a)
         => happ(V1__g,V3__a) = happ(V2__g_27,V3__a) ) ) ).

fof('$_def_IntMap.Map.makeM2',axiom,
    ! [V0__A,V1__m,V2__m_27] :
      ( cType___24t(V0__A)
     => ( cIntMap_2eMap_2eMap___24t(V0__A,V1__m)
       => ( ( cType___24t(V0__A)
           => ( cIntMap_2eMap_2eMap___24t(V0__A,V2__m_27)
             => ( V1__m = cIntMap_2eMap_2eM0___24a1(V0__A)
                & ( ( V2__m_27 = cIntMap_2eMap_2eM0___24a1(V0__A)
                    & cIntMap_2eMap_2emakeM2___24a3(V0__A,V1__m,V2__m_27) = cIntMap_2eMap_2eM0___24a1(V0__A) )
                  | ? [Vvar__1___24Anonymous__1340] :
                      ( cIntMap_2eMap_2ead___24t(Vvar__1___24Anonymous__1340)
                      & ? [Vvar__2___24Anonymous__1341] :
                          ( t(Vvar__2___24Anonymous__1341,V0__A)
                          & V2__m_27 = cIntMap_2eMap_2eM1___24a3(V0__A,Vvar__1___24Anonymous__1340,Vvar__2___24Anonymous__1341)
                          & cIntMap_2eMap_2emakeM2___24a3(V0__A,V1__m,V2__m_27) = cIntMap_2eMap_2eM1___24a3(V0__A,cCoq_2eNArith_2eBinNatDef_2eN_2esucc__double___24a1(Vvar__1___24Anonymous__1340),Vvar__2___24Anonymous__1341) ) )
                  | ? [Vvar__1___24Anonymous__1344] :
                      ( cIntMap_2eMap_2eMap___24t(V0__A,Vvar__1___24Anonymous__1344)
                      & ? [Vvar__2___24Anonymous__1345] :
                          ( cIntMap_2eMap_2eMap___24t(V0__A,Vvar__2___24Anonymous__1345)
                          & V2__m_27 = cIntMap_2eMap_2eM2___24a3(V0__A,Vvar__1___24Anonymous__1344,Vvar__2___24Anonymous__1345)
                          & cIntMap_2eMap_2emakeM2___24a3(V0__A,V1__m,V2__m_27) = cIntMap_2eMap_2eM2___24a3(V0__A,V1__m,V2__m_27) ) ) ) ) ) )
          | ? [Vvar__1___24Anonymous__1348] :
              ( cIntMap_2eMap_2ead___24t(Vvar__1___24Anonymous__1348)
              & ? [Vvar__2___24Anonymous__1349] :
                  ( t(Vvar__2___24Anonymous__1349,V0__A)
                  & ( cType___24t(V0__A)
                   => ( cIntMap_2eMap_2eMap___24t(V0__A,V2__m_27)
                     => ( V1__m = cIntMap_2eMap_2eM1___24a3(V0__A,Vvar__1___24Anonymous__1348,Vvar__2___24Anonymous__1349)
                        & ( ( V2__m_27 = cIntMap_2eMap_2eM0___24a1(V0__A)
                            & cIntMap_2eMap_2emakeM2___24a3(V0__A,V1__m,V2__m_27) = cIntMap_2eMap_2eM1___24a3(V0__A,cCoq_2eNArith_2eBinNatDef_2eN_2edouble___24a1(Vvar__1___24Anonymous__1348),Vvar__2___24Anonymous__1349) )
                          | ? [Vvar__1___24Anonymous__1364] :
                              ( cIntMap_2eMap_2ead___24t(Vvar__1___24Anonymous__1364)
                              & ? [Vvar__2___24Anonymous__1365] :
                                  ( t(Vvar__2___24Anonymous__1365,V0__A)
                                  & V2__m_27 = cIntMap_2eMap_2eM1___24a3(V0__A,Vvar__1___24Anonymous__1364,Vvar__2___24Anonymous__1365)
                                  & cIntMap_2eMap_2emakeM2___24a3(V0__A,V1__m,V2__m_27) = cIntMap_2eMap_2eM2___24a3(V0__A,V1__m,V2__m_27) ) )
                          | ? [Vvar__1___24Anonymous__1368] :
                              ( cIntMap_2eMap_2eMap___24t(V0__A,Vvar__1___24Anonymous__1368)
                              & ? [Vvar__2___24Anonymous__1369] :
                                  ( cIntMap_2eMap_2eMap___24t(V0__A,Vvar__2___24Anonymous__1369)
                                  & V2__m_27 = cIntMap_2eMap_2eM2___24a3(V0__A,Vvar__1___24Anonymous__1368,Vvar__2___24Anonymous__1369)
                                  & cIntMap_2eMap_2emakeM2___24a3(V0__A,V1__m,V2__m_27) = cIntMap_2eMap_2eM2___24a3(V0__A,V1__m,V2__m_27) ) ) ) ) ) ) ) )
          | ? [Vvar__1___24Anonymous__1372] :
              ( cIntMap_2eMap_2eMap___24t(V0__A,Vvar__1___24Anonymous__1372)
              & ? [Vvar__2___24Anonymous__1373] :
                  ( cIntMap_2eMap_2eMap___24t(V0__A,Vvar__2___24Anonymous__1373)
                  & V1__m = cIntMap_2eMap_2eM2___24a3(V0__A,Vvar__1___24Anonymous__1372,Vvar__2___24Anonymous__1373)
                  & cIntMap_2eMap_2emakeM2___24a3(V0__A,V1__m,V2__m_27) = cIntMap_2eMap_2eM2___24a3(V0__A,V1__m,V2__m_27) ) ) ) ) ) ).

fof('$_def_IntMap.Map.newMap',axiom,
    ! [V0__A] : cIntMap_2eMap_2enewMap___24a1(V0__A) = cIntMap_2eMap_2eM0___24a1(V0__A) ).

fof('$_def_IntMap.Mapaxioms.eqmap',axiom,
    ! [V0__A,V1__m,V2__m_27] :
      ( cIntMap_2eMapaxioms_2eeqmap___24a3(V0__A,V1__m,V2__m_27)
    <=> cIntMap_2eMap_2eeqm___24a3(V0__A,cIntMap_2eMap_2eMapGet___24a2(V0__A,V1__m),cIntMap_2eMap_2eMapGet___24a2(V0__A,V2__m_27)) ) ).

fof('$_def_IntMap.Mapcanon.MapCanonicalize',axiom,
    ! [V0__A,V2__m] :
      ( cType___24t(V0__A)
     => ( cIntMap_2eMap_2eMap___24t(V0__A,V2__m)
       => ( ( V2__m = cIntMap_2eMap_2eM0___24a1(V0__A)
            & cIntMap_2eMapcanon_2eMapCanonicalize___24a2(V0__A,V2__m) = V2__m )
          | ? [Vvar__1___24Anonymous__2070] :
              ( cIntMap_2eMap_2ead___24t(Vvar__1___24Anonymous__2070)
              & ? [Vvar__2___24Anonymous__2071] :
                  ( t(Vvar__2___24Anonymous__2071,V0__A)
                  & V2__m = cIntMap_2eMap_2eM1___24a3(V0__A,Vvar__1___24Anonymous__2070,Vvar__2___24Anonymous__2071)
                  & cIntMap_2eMapcanon_2eMapCanonicalize___24a2(V0__A,V2__m) = V2__m ) )
          | ? [Vvar__1___24Anonymous__2074] :
              ( cIntMap_2eMap_2eMap___24t(V0__A,Vvar__1___24Anonymous__2074)
              & ? [Vvar__2___24Anonymous__2075] :
                  ( cIntMap_2eMap_2eMap___24t(V0__A,Vvar__2___24Anonymous__2075)
                  & V2__m = cIntMap_2eMap_2eM2___24a3(V0__A,Vvar__1___24Anonymous__2074,Vvar__2___24Anonymous__2075)
                  & cIntMap_2eMapcanon_2eMapCanonicalize___24a2(V0__A,V2__m) = cIntMap_2eMap_2emakeM2___24a3(V0__A,cIntMap_2eMapcanon_2eMapCanonicalize___24a2(V0__A,Vvar__1___24Anonymous__2074),cIntMap_2eMapcanon_2eMapCanonicalize___24a2(V0__A,Vvar__2___24Anonymous__2075)) ) ) ) ) ) ).

fof('$_def_IntMap.Mapiter.MapCollect',axiom,
    ! [V0__A,V1__B,V2__f,V3__m] : cIntMap_2eMapiter_2eMapCollect___24a4(V0__A,V1__B,V2__f,V3__m) = cIntMap_2eMapiter_2eMapCollect1___24a5(V0__A,V1__B,V2__f,c_24__lam__1605___24a2(V0__A,V1__B),V3__m) ).

fof('$_def_IntMap.Mapiter.MapCollect1',axiom,
    ! [V0__A,V1__B,V3__f,V4__pf,V5__m] :
      ( cType___24t(V0__A)
     => ( cType___24t(V1__B)
       => ( cIntMap_2eMap_2eMap___24t(V0__A,V5__m)
         => ( ( V5__m = cIntMap_2eMap_2eM0___24a1(V0__A)
              & cIntMap_2eMapiter_2eMapCollect1___24a5(V0__A,V1__B,V3__f,V4__pf,V5__m) = cIntMap_2eMap_2eM0___24a1(V1__B) )
            | ? [Vvar__1___24Anonymous__2113] :
                ( cIntMap_2eMap_2ead___24t(Vvar__1___24Anonymous__2113)
                & ? [Vvar__2___24Anonymous__2114] :
                    ( t(Vvar__2___24Anonymous__2114,V0__A)
                    & V5__m = cIntMap_2eMap_2eM1___24a3(V0__A,Vvar__1___24Anonymous__2113,Vvar__2___24Anonymous__2114)
                    & cIntMap_2eMapiter_2eMapCollect1___24a5(V0__A,V1__B,V3__f,V4__pf,V5__m) = happ(happ(V3__f,happ(V4__pf,Vvar__1___24Anonymous__2113)),Vvar__2___24Anonymous__2114) ) )
            | ? [Vvar__1___24Anonymous__2117] :
                ( cIntMap_2eMap_2eMap___24t(V0__A,Vvar__1___24Anonymous__2117)
                & ? [Vvar__2___24Anonymous__2118] :
                    ( cIntMap_2eMap_2eMap___24t(V0__A,Vvar__2___24Anonymous__2118)
                    & V5__m = cIntMap_2eMap_2eM2___24a3(V0__A,Vvar__1___24Anonymous__2117,Vvar__2___24Anonymous__2118)
                    & cIntMap_2eMapiter_2eMapCollect1___24a5(V0__A,V1__B,V3__f,V4__pf,V5__m) = cIntMap_2eMap_2eMapMerge___24a3(V1__B,cIntMap_2eMapiter_2eMapCollect1___24a5(V0__A,V1__B,V3__f,c_24__lam__2129___24a3(V0__A,V1__B,V4__pf),Vvar__1___24Anonymous__2117),cIntMap_2eMapiter_2eMapCollect1___24a5(V0__A,V1__B,V3__f,c_24__lam__2135___24a3(V0__A,V1__B,V4__pf),Vvar__2___24Anonymous__2118)) ) ) ) ) ) ) ).

fof('$_def_IntMap.Mapiter.MapFold',axiom,
    ! [V0__A,V1__M,V2__neutral,V3__op,V4__f,V5__m] : cIntMap_2eMapiter_2eMapFold___24a6(V0__A,V1__M,V2__neutral,V3__op,V4__f,V5__m) = cIntMap_2eMapiter_2eMapFold1___24a7(V0__A,V1__M,V2__neutral,V3__op,V4__f,c_24__lam__1605___24a2(V0__A,V1__M),V5__m) ).

fof('$_def_IntMap.Mapiter.MapFold1',axiom,
    ! [V0__A,V1__M,V2__neutral,V3__op,V5__f,V6__pf,V7__m] :
      ( cType___24t(V0__A)
     => ( cType___24t(V1__M)
       => ( cIntMap_2eMap_2eMap___24t(V0__A,V7__m)
         => ( ( V7__m = cIntMap_2eMap_2eM0___24a1(V0__A)
              & cIntMap_2eMapiter_2eMapFold1___24a7(V0__A,V1__M,V2__neutral,V3__op,V5__f,V6__pf,V7__m) = V2__neutral )
            | ? [Vvar__1___24Anonymous__1628] :
                ( cIntMap_2eMap_2ead___24t(Vvar__1___24Anonymous__1628)
                & ? [Vvar__2___24Anonymous__1629] :
                    ( t(Vvar__2___24Anonymous__1629,V0__A)
                    & V7__m = cIntMap_2eMap_2eM1___24a3(V0__A,Vvar__1___24Anonymous__1628,Vvar__2___24Anonymous__1629)
                    & cIntMap_2eMapiter_2eMapFold1___24a7(V0__A,V1__M,V2__neutral,V3__op,V5__f,V6__pf,V7__m) = happ(happ(V5__f,happ(V6__pf,Vvar__1___24Anonymous__1628)),Vvar__2___24Anonymous__1629) ) )
            | ? [Vvar__1___24Anonymous__1632] :
                ( cIntMap_2eMap_2eMap___24t(V0__A,Vvar__1___24Anonymous__1632)
                & ? [Vvar__2___24Anonymous__1633] :
                    ( cIntMap_2eMap_2eMap___24t(V0__A,Vvar__2___24Anonymous__1633)
                    & V7__m = cIntMap_2eMap_2eM2___24a3(V0__A,Vvar__1___24Anonymous__1632,Vvar__2___24Anonymous__1633)
                    & cIntMap_2eMapiter_2eMapFold1___24a7(V0__A,V1__M,V2__neutral,V3__op,V5__f,V6__pf,V7__m) = happ(happ(V3__op,cIntMap_2eMapiter_2eMapFold1___24a7(V0__A,V1__M,V2__neutral,V3__op,V5__f,c_24__lam__1644___24a3(V0__A,V1__M,V6__pf),Vvar__1___24Anonymous__1632)),cIntMap_2eMapiter_2eMapFold1___24a7(V0__A,V1__M,V2__neutral,V3__op,V5__f,c_24__lam__1650___24a3(V0__A,V1__M,V6__pf),Vvar__2___24Anonymous__1633)) ) ) ) ) ) ) ).

fof('$_def_IntMap.Mapiter.MapFold1_state',axiom,
    ! [V0__A,V1__M,V2__neutral,V3__op,V4__State,V5__f,V7__state,V8__pf,V9__m] :
      ( cType___24t(V0__A)
     => ( cType___24t(V1__M)
       => ( cType___24t(V4__State)
         => ( cIntMap_2eMap_2eMap___24t(V0__A,V9__m)
           => ( ( V9__m = cIntMap_2eMap_2eM0___24a1(V0__A)
                & cIntMap_2eMapiter_2eMapFold1__state___24a9(V0__A,V1__M,V2__neutral,V3__op,V4__State,V5__f,V7__state,V8__pf,V9__m) = cCoq_2eInit_2eDatatypes_2epair___24a4(V4__State,V1__M,V7__state,V2__neutral) )
              | ? [Vvar__1___24Anonymous__13849] :
                  ( cIntMap_2eMap_2ead___24t(Vvar__1___24Anonymous__13849)
                  & ? [Vvar__2___24Anonymous__13850] :
                      ( t(Vvar__2___24Anonymous__13850,V0__A)
                      & V9__m = cIntMap_2eMap_2eM1___24a3(V0__A,Vvar__1___24Anonymous__13849,Vvar__2___24Anonymous__13850)
                      & cIntMap_2eMapiter_2eMapFold1__state___24a9(V0__A,V1__M,V2__neutral,V3__op,V4__State,V5__f,V7__state,V8__pf,V9__m) = happ(happ(happ(V5__f,V7__state),happ(V8__pf,Vvar__1___24Anonymous__13849)),Vvar__2___24Anonymous__13850) ) )
              | ? [Vvar__1___24Anonymous__13853] :
                  ( cIntMap_2eMap_2eMap___24t(V0__A,Vvar__1___24Anonymous__13853)
                  & ? [Vvar__2___24Anonymous__13854] :
                      ( cIntMap_2eMap_2eMap___24t(V0__A,Vvar__2___24Anonymous__13854)
                      & ( cType___24t(V0__A)
                       => ( cType___24t(V1__M)
                         => ( t(V2__neutral,V1__M)
                           => ( c_24__type__13901___24t(V0__A,V1__M,V4__State,V3__op)
                             => ( cType___24t(V4__State)
                               => ( c_24__type__13915___24t(V0__A,V1__M,V4__State,V5__f)
                                 => ( t(V7__state,V4__State)
                                   => ( c_24__type__13920___24t(V0__A,V1__M,V4__State,V8__pf)
                                     => ( cIntMap_2eMap_2eMap___24t(V0__A,Vvar__1___24Anonymous__13853)
                                       => ( V9__m = cIntMap_2eMap_2eM2___24a3(V0__A,Vvar__1___24Anonymous__13853,Vvar__2___24Anonymous__13854)
                                          & ? [Vvar__2___24Anonymous__13876] :
                                              ( t(Vvar__2___24Anonymous__13876,V4__State)
                                              & ? [Vvar__3___24Anonymous__13877] :
                                                  ( t(Vvar__3___24Anonymous__13877,V1__M)
                                                  & ( cType___24t(V0__A)
                                                   => ( cType___24t(V1__M)
                                                     => ( t(V2__neutral,V1__M)
                                                       => ( c_24__type__13901___24t(V0__A,V1__M,V4__State,V3__op)
                                                         => ( cType___24t(V4__State)
                                                           => ( c_24__type__13915___24t(V0__A,V1__M,V4__State,V5__f)
                                                             => ( c_24__type__13920___24t(V0__A,V1__M,V4__State,V8__pf)
                                                               => ( cIntMap_2eMap_2eMap___24t(V0__A,Vvar__2___24Anonymous__13854)
                                                                 => ( t(Vvar__2___24Anonymous__13876,V4__State)
                                                                   => ( cIntMap_2eMapiter_2eMapFold1__state___24a9(V0__A,V1__M,V2__neutral,V3__op,V4__State,V5__f,V7__state,c_24__lam__13951___24a4(V0__A,V1__M,V4__State,V8__pf),Vvar__1___24Anonymous__13853) = cCoq_2eInit_2eDatatypes_2epair___24a4(V4__State,V1__M,Vvar__2___24Anonymous__13876,Vvar__3___24Anonymous__13877)
                                                                      & ? [Vvar__2___24Anonymous__13891] :
                                                                          ( t(Vvar__2___24Anonymous__13891,V4__State)
                                                                          & ? [Vvar__3___24Anonymous__13892] :
                                                                              ( t(Vvar__3___24Anonymous__13892,V1__M)
                                                                              & cIntMap_2eMapiter_2eMapFold1__state___24a9(V0__A,V1__M,V2__neutral,V3__op,V4__State,V5__f,Vvar__2___24Anonymous__13876,c_24__lam__13959___24a4(V0__A,V1__M,V4__State,V8__pf),Vvar__2___24Anonymous__13854) = cCoq_2eInit_2eDatatypes_2epair___24a4(V4__State,V1__M,Vvar__2___24Anonymous__13891,Vvar__3___24Anonymous__13892)
                                                                              & cIntMap_2eMapiter_2eMapFold1__state___24a9(V0__A,V1__M,V2__neutral,V3__op,V4__State,V5__f,V7__state,V8__pf,V9__m) = cCoq_2eInit_2eDatatypes_2epair___24a4(V4__State,V1__M,Vvar__2___24Anonymous__13891,happ(happ(V3__op,Vvar__3___24Anonymous__13877),Vvar__3___24Anonymous__13892)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).

fof('$_def_IntMap.Mapiter.MapFold_state',axiom,
    ! [V0__A,V1__M,V2__neutral,V3__op,V4__State,V5__f,V6__state] : cIntMap_2eMapiter_2eMapFold__state___24a7(V0__A,V1__M,V2__neutral,V3__op,V4__State,V5__f,V6__state) = cIntMap_2eMapiter_2eMapFold1__state___24a8(V0__A,V1__M,V2__neutral,V3__op,V4__State,V5__f,V6__state,c_24__lam__14051___24a3(V0__A,V1__M,V4__State)) ).

fof('$_def_IntMap.Mapiter.MapSweep',axiom,
    ! [V0__A,V1__f,V2__m] : cIntMap_2eMapiter_2eMapSweep___24a3(V0__A,V1__f,V2__m) = cIntMap_2eMapiter_2eMapSweep1___24a4(V0__A,V1__f,c_24__lam__13613___24a1(V0__A),V2__m) ).

fof('$_def_IntMap.Mapiter.MapSweep1',axiom,
    ! [V0__A,V1__f,V3__pf,V4__m] :
      ( cType___24t(V0__A)
     => ( cIntMap_2eMap_2eMap___24t(V0__A,V4__m)
       => ( ( V4__m = cIntMap_2eMap_2eM0___24a1(V0__A)
            & cIntMap_2eMapiter_2eMapSweep1___24a4(V0__A,V1__f,V3__pf,V4__m) = cCoq_2eInit_2eDatatypes_2eNone___24a1(cCoq_2eInit_2eDatatypes_2eprod___24a2(cIntMap_2eMap_2ead,V0__A)) )
          | ? [Vvar__1___24Anonymous__13560] :
              ( cIntMap_2eMap_2ead___24t(Vvar__1___24Anonymous__13560)
              & ? [Vvar__2___24Anonymous__13561] :
                  ( t(Vvar__2___24Anonymous__13561,V0__A)
                  & V4__m = cIntMap_2eMap_2eM1___24a3(V0__A,Vvar__1___24Anonymous__13560,Vvar__2___24Anonymous__13561)
                  & cIntMap_2eMapiter_2eMapSweep1___24a4(V0__A,V1__f,V3__pf,V4__m) = cIntMap_2eMapiter_2eMapSweep2___24a4(V0__A,V1__f,happ(V3__pf,Vvar__1___24Anonymous__13560),Vvar__2___24Anonymous__13561) ) )
          | ? [Vvar__1___24Anonymous__13564] :
              ( cIntMap_2eMap_2eMap___24t(V0__A,Vvar__1___24Anonymous__13564)
              & ? [Vvar__2___24Anonymous__13565] :
                  ( cIntMap_2eMap_2eMap___24t(V0__A,Vvar__2___24Anonymous__13565)
                  & ( cType___24t(V0__A)
                   => ( c_24__type__13540___24t(V0__A,V1__f)
                     => ( c_24__type__13176___24t(V0__A,V3__pf)
                       => ( cIntMap_2eMap_2eMap___24t(V0__A,Vvar__1___24Anonymous__13564)
                         => ( V4__m = cIntMap_2eMap_2eM2___24a3(V0__A,Vvar__1___24Anonymous__13564,Vvar__2___24Anonymous__13565)
                            & ( ? [Vvar__1___24Anonymous__13577] :
                                  ( cCoq_2eInit_2eDatatypes_2eprod___24t(cIntMap_2eMap_2ead,V0__A,Vvar__1___24Anonymous__13577)
                                  & cIntMap_2eMapiter_2eMapSweep1___24a4(V0__A,V1__f,c_24__lam__13586___24a2(V0__A,V3__pf),Vvar__1___24Anonymous__13564) = cCoq_2eInit_2eDatatypes_2eSome___24a2(cCoq_2eInit_2eDatatypes_2eprod___24a2(cIntMap_2eMap_2ead,V0__A),Vvar__1___24Anonymous__13577)
                                  & cIntMap_2eMapiter_2eMapSweep1___24a4(V0__A,V1__f,V3__pf,V4__m) = cCoq_2eInit_2eDatatypes_2eSome___24a2(cCoq_2eInit_2eDatatypes_2eprod___24a2(cIntMap_2eMap_2ead,V0__A),Vvar__1___24Anonymous__13577) )
                              | ( cIntMap_2eMapiter_2eMapSweep1___24a4(V0__A,V1__f,c_24__lam__13590___24a2(V0__A,V3__pf),Vvar__1___24Anonymous__13564) = cCoq_2eInit_2eDatatypes_2eNone___24a1(cCoq_2eInit_2eDatatypes_2eprod___24a2(cIntMap_2eMap_2ead,V0__A))
                                & cIntMap_2eMapiter_2eMapSweep1___24a4(V0__A,V1__f,V3__pf,V4__m) = cIntMap_2eMapiter_2eMapSweep1___24a4(V0__A,V1__f,c_24__lam__13594___24a2(V0__A,V3__pf),Vvar__2___24Anonymous__13565) ) ) ) ) ) ) ) ) ) ) ) ) ).

fof('$_def_IntMap.Mapiter.MapSweep2',axiom,
    ! [V0__A,V1__f,V2__a0,V3__y] :
      ( cType___24t(V0__A)
     => ( c_24__type__13540___24t(V0__A,V1__f)
       => ( cIntMap_2eMap_2ead___24t(V2__a0)
         => ( t(V3__y,V0__A)
           => ( ( happ(happ(V1__f,V2__a0),V3__y) = cCoq_2eInit_2eDatatypes_2etrue
                & cIntMap_2eMapiter_2eMapSweep2___24a4(V0__A,V1__f,V2__a0,V3__y) = cCoq_2eInit_2eDatatypes_2eSome___24a2(cCoq_2eInit_2eDatatypes_2eprod___24a2(cIntMap_2eMap_2ead,V0__A),cCoq_2eInit_2eDatatypes_2epair___24a4(cIntMap_2eMap_2ead,V0__A,V2__a0,V3__y)) )
              | ( happ(happ(V1__f,V2__a0),V3__y) = cCoq_2eInit_2eDatatypes_2efalse
                & cIntMap_2eMapiter_2eMapSweep2___24a4(V0__A,V1__f,V2__a0,V3__y) = cCoq_2eInit_2eDatatypes_2eNone___24a1(cCoq_2eInit_2eDatatypes_2eprod___24a2(cIntMap_2eMap_2ead,V0__A)) ) ) ) ) ) ) ).

fof('$_def_IntMap.Mapiter.Map_of_alist',axiom,
    ! [V0__A,V2__l] :
      ( cType___24t(V0__A)
     => ( cIntMap_2eMapiter_2ealist___24t(V0__A,V2__l)
       => ( ( V2__l = cCoq_2eInit_2eDatatypes_2enil___24a1(cCoq_2eInit_2eDatatypes_2eprod___24a2(cIntMap_2eMap_2ead,V0__A))
            & cIntMap_2eMapiter_2eMap__of__alist___24a2(V0__A,V2__l) = cIntMap_2eMap_2eM0___24a1(V0__A) )
          | ? [Vvar__1___24Anonymous__1761] :
              ( cCoq_2eInit_2eDatatypes_2eprod___24t(cIntMap_2eMap_2ead,V0__A,Vvar__1___24Anonymous__1761)
              & ? [Vvar__2___24Anonymous__1762] :
                  ( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eInit_2eDatatypes_2eprod___24a2(cIntMap_2eMap_2ead,V0__A),Vvar__2___24Anonymous__1762)
                  & ( cType___24t(V0__A)
                   => ( cCoq_2eInit_2eDatatypes_2eprod___24t(cIntMap_2eMap_2ead,V0__A,Vvar__1___24Anonymous__1761)
                     => ( V2__l = cCoq_2eInit_2eDatatypes_2econs___24a3(cCoq_2eInit_2eDatatypes_2eprod___24a2(cIntMap_2eMap_2ead,V0__A),Vvar__1___24Anonymous__1761,Vvar__2___24Anonymous__1762)
                        & ? [Vvar__2___24Anonymous__1774] :
                            ( cIntMap_2eMap_2ead___24t(Vvar__2___24Anonymous__1774)
                            & ? [Vvar__3___24Anonymous__1775] :
                                ( t(Vvar__3___24Anonymous__1775,V0__A)
                                & Vvar__1___24Anonymous__1761 = cCoq_2eInit_2eDatatypes_2epair___24a4(cIntMap_2eMap_2ead,V0__A,Vvar__2___24Anonymous__1774,Vvar__3___24Anonymous__1775)
                                & cIntMap_2eMapiter_2eMap__of__alist___24a2(V0__A,V2__l) = cIntMap_2eMap_2eMapPut___24a4(V0__A,cIntMap_2eMapiter_2eMap__of__alist___24a2(V0__A,Vvar__2___24Anonymous__1762),Vvar__2___24Anonymous__1774,Vvar__3___24Anonymous__1775) ) ) ) ) ) ) ) ) ) ) ).

fof('$_def_IntMap.Mapiter.aapp',axiom,
    ! [V0__A] : cIntMap_2eMapiter_2eaapp___24a1(V0__A) = cCoq_2eInit_2eDatatypes_2eapp___24a1(cCoq_2eInit_2eDatatypes_2eprod___24a2(cIntMap_2eMap_2ead,V0__A)) ).

fof('$_def_IntMap.Mapiter.acons',axiom,
    ! [V0__A] : cIntMap_2eMapiter_2eacons___24a1(V0__A) = cCoq_2eInit_2eDatatypes_2econs___24a1(cCoq_2eInit_2eDatatypes_2eprod___24a2(cIntMap_2eMap_2ead,V0__A)) ).

fof('$_def_IntMap.Mapiter.ad_inj',axiom,
    ! [V0__pf] :
      ( cIntMap_2eMapiter_2ead__inj___24a1(V0__pf)
    <=> ! [V1__a0] :
          ( cIntMap_2eMap_2ead___24t(V1__a0)
         => ! [V2__a1] :
              ( cIntMap_2eMap_2ead___24t(V2__a1)
             => ( happ(V0__pf,V1__a0) = happ(V0__pf,V2__a1)
               => V1__a0 = V2__a1 ) ) ) ) ).

fof('$_def_IntMap.Mapiter.alist',axiom,
    ! [V0__A] : cIntMap_2eMapiter_2ealist___24a1(V0__A) = cCoq_2eInit_2eDatatypes_2elist___24a1(cCoq_2eInit_2eDatatypes_2eprod___24a2(cIntMap_2eMap_2ead,V0__A)) ).

fof('$_def_IntMap.Mapiter.alist_of_Map',axiom,
    ! [V0__A] : cIntMap_2eMapiter_2ealist__of__Map___24a1(V0__A) = cIntMap_2eMapiter_2eMapFold___24a5(V0__A,cIntMap_2eMapiter_2ealist___24a1(V0__A),cIntMap_2eMapiter_2eanil___24a1(V0__A),cIntMap_2eMapiter_2eaapp___24a1(V0__A),c_24__lam__2179___24a1(V0__A)) ).

fof('$_def_IntMap.Mapiter.alist_semantics',axiom,
    ! [V0__A,V2__l] :
      ( cType___24t(V0__A)
     => ( cIntMap_2eMapiter_2ealist___24t(V0__A,V2__l)
       => ( ( V2__l = cCoq_2eInit_2eDatatypes_2enil___24a1(cCoq_2eInit_2eDatatypes_2eprod___24a2(cIntMap_2eMap_2ead,V0__A))
            & cIntMap_2eMapiter_2ealist__semantics___24a2(V0__A,V2__l) = c_24__lam__128___24a1(V0__A) )
          | ? [Vvar__1___24Anonymous__2187] :
              ( cCoq_2eInit_2eDatatypes_2eprod___24t(cIntMap_2eMap_2ead,V0__A,Vvar__1___24Anonymous__2187)
              & ? [Vvar__2___24Anonymous__2188] :
                  ( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eInit_2eDatatypes_2eprod___24a2(cIntMap_2eMap_2ead,V0__A),Vvar__2___24Anonymous__2188)
                  & ( cType___24t(V0__A)
                   => ( cCoq_2eInit_2eDatatypes_2eprod___24t(cIntMap_2eMap_2ead,V0__A,Vvar__1___24Anonymous__2187)
                     => ( V2__l = cCoq_2eInit_2eDatatypes_2econs___24a3(cCoq_2eInit_2eDatatypes_2eprod___24a2(cIntMap_2eMap_2ead,V0__A),Vvar__1___24Anonymous__2187,Vvar__2___24Anonymous__2188)
                        & ? [Vvar__2___24Anonymous__2206] :
                            ( cIntMap_2eMap_2ead___24t(Vvar__2___24Anonymous__2206)
                            & ? [Vvar__3___24Anonymous__2207] :
                                ( t(Vvar__3___24Anonymous__2207,V0__A)
                                & Vvar__1___24Anonymous__2187 = cCoq_2eInit_2eDatatypes_2epair___24a4(cIntMap_2eMap_2ead,V0__A,Vvar__2___24Anonymous__2206,Vvar__3___24Anonymous__2207)
                                & cIntMap_2eMapiter_2ealist__semantics___24a2(V0__A,V2__l) = c_24__lam__2223___24a4(V0__A,Vvar__2___24Anonymous__2188,Vvar__2___24Anonymous__2206,Vvar__3___24Anonymous__2207) ) ) ) ) ) ) ) ) ) ) ).

fof('$_def_IntMap.Mapiter.anil',axiom,
    ! [V0__A] : cIntMap_2eMapiter_2eanil___24a1(V0__A) = cCoq_2eInit_2eDatatypes_2enil___24a1(cCoq_2eInit_2eDatatypes_2eprod___24a2(cIntMap_2eMap_2ead,V0__A)) ).

fof('$_def_IntMap.Mapsubset.MapDisjoint',axiom,
    ! [V0__A,V1__B,V2__m,V3__m_27] :
      ( cIntMap_2eMapsubset_2eMapDisjoint___24a4(V0__A,V1__B,V2__m,V3__m_27)
    <=> ! [V4__a] :
          ( cIntMap_2eMap_2ead___24t(V4__a)
         => ( cIntMap_2eFset_2ein__dom___24a3(V0__A,V4__a,V2__m) = cCoq_2eInit_2eDatatypes_2etrue
           => ( cIntMap_2eFset_2ein__dom___24a3(V1__B,V4__a,V3__m_27) = cCoq_2eInit_2eDatatypes_2etrue
             => p(c_24False) ) ) ) ) ).

fof('$_def_IntMap.Mapsubset.MapDisjoint_1',axiom,
    ! [V0__A,V1__B,V2__m,V3__m_27] :
      ( cType___24t(V0__A)
     => ( cType___24t(V1__B)
       => ( cIntMap_2eMap_2eMap___24t(V0__A,V2__m)
         => ( cIntMap_2eMap_2eMap___24t(V1__B,V3__m_27)
           => ( ? [Vvar__1___24Anonymous__14549] :
                  ( cCoq_2eInit_2eDatatypes_2eprod___24t(cIntMap_2eMap_2ead,V0__A,Vvar__1___24Anonymous__14549)
                  & cIntMap_2eMapiter_2eMapSweep___24a3(V0__A,c_24__lam__14558___24a3(V0__A,V1__B,V3__m_27),V2__m) = cCoq_2eInit_2eDatatypes_2eSome___24a2(cCoq_2eInit_2eDatatypes_2eprod___24a2(cIntMap_2eMap_2ead,V0__A),Vvar__1___24Anonymous__14549)
                  & cIntMap_2eMapsubset_2eMapDisjoint__1___24a4(V0__A,V1__B,V2__m,V3__m_27) = cCoq_2eInit_2eDatatypes_2efalse )
              | ( cIntMap_2eMapiter_2eMapSweep___24a3(V0__A,c_24__lam__14558___24a3(V0__A,V1__B,V3__m_27),V2__m) = cCoq_2eInit_2eDatatypes_2eNone___24a1(cCoq_2eInit_2eDatatypes_2eprod___24a2(cIntMap_2eMap_2ead,V0__A))
                & cIntMap_2eMapsubset_2eMapDisjoint__1___24a4(V0__A,V1__B,V2__m,V3__m_27) = cCoq_2eInit_2eDatatypes_2etrue ) ) ) ) ) ) ).

fof('$_def_IntMap.Mapsubset.MapDisjoint_2',axiom,
    ! [V0__A,V1__B,V2__m,V3__m_27] :
      ( cIntMap_2eMapsubset_2eMapDisjoint__2___24a4(V0__A,V1__B,V2__m,V3__m_27)
    <=> cIntMap_2eMapaxioms_2eeqmap___24a3(V0__A,cIntMap_2eFset_2eMapDomRestrTo___24a4(V0__A,V1__B,V2__m,V3__m_27),cIntMap_2eMap_2eM0___24a1(V0__A)) ) ).

fof('$_def_IntMap.Mapsubset.MapSubset',axiom,
    ! [V0__A,V1__B,V2__m,V3__m_27] :
      ( cIntMap_2eMapsubset_2eMapSubset___24a4(V0__A,V1__B,V2__m,V3__m_27)
    <=> ! [V4__a] :
          ( cIntMap_2eMap_2ead___24t(V4__a)
         => ( cIntMap_2eFset_2ein__dom___24a3(V0__A,V4__a,V2__m) = cCoq_2eInit_2eDatatypes_2etrue
           => cIntMap_2eFset_2ein__dom___24a3(V1__B,V4__a,V3__m_27) = cCoq_2eInit_2eDatatypes_2etrue ) ) ) ).

fof('$_def_IntMap.Mapsubset.MapSubset_1',axiom,
    ! [V0__A,V1__B,V2__m,V3__m_27] :
      ( cType___24t(V0__A)
     => ( cType___24t(V1__B)
       => ( cIntMap_2eMap_2eMap___24t(V0__A,V2__m)
         => ( cIntMap_2eMap_2eMap___24t(V1__B,V3__m_27)
           => ( ? [Vvar__1___24Anonymous__14515] :
                  ( cCoq_2eInit_2eDatatypes_2eprod___24t(cIntMap_2eMap_2ead,V0__A,Vvar__1___24Anonymous__14515)
                  & cIntMap_2eMapiter_2eMapSweep___24a3(V0__A,c_24__lam__14524___24a3(V0__A,V1__B,V3__m_27),V2__m) = cCoq_2eInit_2eDatatypes_2eSome___24a2(cCoq_2eInit_2eDatatypes_2eprod___24a2(cIntMap_2eMap_2ead,V0__A),Vvar__1___24Anonymous__14515)
                  & cIntMap_2eMapsubset_2eMapSubset__1___24a4(V0__A,V1__B,V2__m,V3__m_27) = cCoq_2eInit_2eDatatypes_2efalse )
              | ( cIntMap_2eMapiter_2eMapSweep___24a3(V0__A,c_24__lam__14524___24a3(V0__A,V1__B,V3__m_27),V2__m) = cCoq_2eInit_2eDatatypes_2eNone___24a1(cCoq_2eInit_2eDatatypes_2eprod___24a2(cIntMap_2eMap_2ead,V0__A))
                & cIntMap_2eMapsubset_2eMapSubset__1___24a4(V0__A,V1__B,V2__m,V3__m_27) = cCoq_2eInit_2eDatatypes_2etrue ) ) ) ) ) ) ).

fof('$_def_IntMap.Mapsubset.MapSubset_2',axiom,
    ! [V0__A,V1__B,V2__m,V3__m_27] :
      ( cIntMap_2eMapsubset_2eMapSubset__2___24a4(V0__A,V1__B,V2__m,V3__m_27)
    <=> cIntMap_2eMapaxioms_2eeqmap___24a3(V0__A,cIntMap_2eFset_2eMapDomRestrBy___24a4(V0__A,V1__B,V2__m,V3__m_27),cIntMap_2eMap_2eM0___24a1(V0__A)) ) ).

fof('$_discrim_Coq.Bool.Bool.ReflectT$Coq.Bool.Bool.ReflectF',axiom,
    ! [Vvar__0__P__19871,Vvar__1___24Anonymous__19872,Vvar__0__P__19873,Vvar__1___24Anonymous__19874] : cCoq_2eBool_2eBool_2eReflectT___24a1(Vvar__0__P__19871) != cCoq_2eBool_2eBool_2eReflectF___24a1(Vvar__0__P__19873) ).

fof('$_discrim_Coq.FSets.FSetPositive.PositiveSet.Leaf$Coq.FSets.FSetPositive.PositiveSet.Node',axiom,
    ! [Vvar__0___24Anonymous__19224,Vvar__1___24Anonymous__19225,Vvar__2___24Anonymous__19226] : cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eLeaf != cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eNode___24a3(Vvar__0___24Anonymous__19224,Vvar__1___24Anonymous__19225,Vvar__2___24Anonymous__19226) ).

fof('$_discrim_Coq.Init.Byte.x00$Coq.Init.Byte.x01',axiom,
    cCoq_2eInit_2eByte_2ex00 != cCoq_2eInit_2eByte_2ex01 ).

fof('$_discrim_Coq.Init.Datatypes.CompEqT$Coq.Init.Datatypes.CompLtT',axiom,
    ! [Vvar__0__Peq__19951,Vvar__1__Plt__19952,Vvar__2__Pgt__19953,Vvar__3___24Anonymous__19954,Vvar__0__Peq__19955,Vvar__1__Plt__19956,Vvar__2__Pgt__19957,Vvar__3___24Anonymous__19958] : cCoq_2eInit_2eDatatypes_2eCompEqT___24a3(Vvar__0__Peq__19951,Vvar__1__Plt__19952,Vvar__2__Pgt__19953) != cCoq_2eInit_2eDatatypes_2eCompLtT___24a3(Vvar__0__Peq__19955,Vvar__1__Plt__19956,Vvar__2__Pgt__19957) ).

fof('$_discrim_Coq.Init.Datatypes.Eq$Coq.Init.Datatypes.Lt',axiom,
    cCoq_2eInit_2eDatatypes_2eEq != cCoq_2eInit_2eDatatypes_2eLt ).

fof('$_discrim_Coq.Init.Datatypes.O$Coq.Init.Datatypes.S',axiom,
    ! [Vvar__0___24Anonymous__455] : cCoq_2eInit_2eDatatypes_2eO != cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__455) ).

fof('$_discrim_Coq.Init.Datatypes.Some$Coq.Init.Datatypes.None',axiom,
    ! [Vvar__0__A__38,Vvar__1___24Anonymous__39,Vvar__0__A__40] : cCoq_2eInit_2eDatatypes_2eSome___24a2(Vvar__0__A__38,Vvar__1___24Anonymous__39) != cCoq_2eInit_2eDatatypes_2eNone___24a1(Vvar__0__A__40) ).

fof('$_discrim_Coq.Init.Datatypes.inl$Coq.Init.Datatypes.inr',axiom,
    ! [Vvar__0__A__10814,Vvar__1__B__10815,Vvar__2___24Anonymous__10816,Vvar__0__A__10817,Vvar__1__B__10818,Vvar__2___24Anonymous__10819] : cCoq_2eInit_2eDatatypes_2einl___24a3(Vvar__0__A__10814,Vvar__1__B__10815,Vvar__2___24Anonymous__10816) != cCoq_2eInit_2eDatatypes_2einr___24a3(Vvar__0__A__10817,Vvar__1__B__10818,Vvar__2___24Anonymous__10819) ).

fof('$_discrim_Coq.Init.Datatypes.nil$Coq.Init.Datatypes.cons',axiom,
    ! [Vvar__0__A__1036,Vvar__0__A__1037,Vvar__1___24Anonymous__1038,Vvar__2___24Anonymous__1039] : cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__1036) != cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__1037,Vvar__1___24Anonymous__1038,Vvar__2___24Anonymous__1039) ).

fof('$_discrim_Coq.Init.Datatypes.true$Coq.Init.Datatypes.false',axiom,
    cCoq_2eInit_2eDatatypes_2etrue != cCoq_2eInit_2eDatatypes_2efalse ).

fof('$_discrim_Coq.Init.Specif.inleft$Coq.Init.Specif.inright',axiom,
    ! [Vvar__0__A__928,Vvar__1__B__929,Vvar__2___24Anonymous__930,Vvar__0__A__931,Vvar__1__B__932,Vvar__2___24Anonymous__933] : cCoq_2eInit_2eSpecif_2einleft___24a3(Vvar__0__A__928,Vvar__1__B__929,Vvar__2___24Anonymous__930) != cCoq_2eInit_2eSpecif_2einright___24a2(Vvar__0__A__931,Vvar__1__B__932) ).

fof('$_discrim_Coq.Init.Specif.left$Coq.Init.Specif.right',axiom,
    ! [Vvar__0__A__402,Vvar__1__B__403,Vvar__2___24Anonymous__404,Vvar__0__A__405,Vvar__1__B__406,Vvar__2___24Anonymous__407] : cCoq_2eInit_2eSpecif_2eleft___24a2(Vvar__0__A__402,Vvar__1__B__403) != cCoq_2eInit_2eSpecif_2eright___24a2(Vvar__0__A__405,Vvar__1__B__406) ).

fof('$_discrim_Coq.Numbers.BinNums.N0$Coq.Numbers.BinNums.Npos',axiom,
    ! [Vvar__0___24Anonymous__22] : cCoq_2eNumbers_2eBinNums_2eN0 != cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__22) ).

fof('$_discrim_Coq.Numbers.BinNums.Z0$Coq.Numbers.BinNums.Zpos',axiom,
    ! [Vvar__0___24Anonymous__2664] : cCoq_2eNumbers_2eBinNums_2eZ0 != cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__2664) ).

fof('$_discrim_Coq.Numbers.BinNums.xI$Coq.Numbers.BinNums.xO',axiom,
    ! [Vvar__0___24Anonymous__6,Vvar__0___24Anonymous__7] : cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__6) != cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__7) ).

fof('$_discrim_Coq.PArith.BinPos.Pos.PeanoOne$Coq.PArith.BinPos.Pos.PeanoSucc',axiom,
    ! [Vvar__0__p__33576,Vvar__1___24Anonymous__33577] : cCoq_2ePArith_2eBinPos_2ePos_2ePeanoOne != cCoq_2ePArith_2eBinPos_2ePos_2ePeanoSucc___24a2(Vvar__0__p__33576,Vvar__1___24Anonymous__33577) ).

fof('$_discrim_Coq.PArith.BinPosDef.Pos.IsNul$Coq.PArith.BinPosDef.Pos.IsPos',axiom,
    ! [Vvar__0___24Anonymous__19090] : cCoq_2ePArith_2eBinPosDef_2ePos_2eIsNul != cCoq_2ePArith_2eBinPosDef_2ePos_2eIsPos___24a1(Vvar__0___24Anonymous__19090) ).

fof('$_discrim_Coq.Reals.Rfunctions.ZintNull$Coq.Reals.Rfunctions.ZintPos',axiom,
    ! [Vvar__0__x__23414,Vvar__1___24Anonymous__23415,Vvar__0__x__23416,Vvar__1__n__23417,Vvar__2___24Anonymous__23418] : cCoq_2eReals_2eRfunctions_2eZintNull___24a1(Vvar__0__x__23414) != cCoq_2eReals_2eRfunctions_2eZintPos___24a2(Vvar__0__x__23416,Vvar__1__n__23417) ).

fof('$_discrim_Coq.Strings.String.EmptyString$Coq.Strings.String.String',axiom,
    ! [Vvar__0___24Anonymous__32751,Vvar__1___24Anonymous__32752] : cCoq_2eStrings_2eString_2eEmptyString != cCoq_2eStrings_2eString_2eString___24a2(Vvar__0___24Anonymous__32751,Vvar__1___24Anonymous__32752) ).

fof('$_discrim_Coq.Structures.OrderedType.LT$Coq.Structures.OrderedType.EQ',axiom,
    ! [Vvar__0__X__23084,Vvar__1__lt__23085,Vvar__2__eq__23086,Vvar__3__x__23087,Vvar__4__y__23088,Vvar__5___24Anonymous__23089,Vvar__0__X__23090,Vvar__1__lt__23091,Vvar__2__eq__23092,Vvar__3__x__23093,Vvar__4__y__23094,Vvar__5___24Anonymous__23095] : cCoq_2eStructures_2eOrderedType_2eLT___24a5(Vvar__0__X__23084,Vvar__1__lt__23085,Vvar__2__eq__23086,Vvar__3__x__23087,Vvar__4__y__23088) != cCoq_2eStructures_2eOrderedType_2eEQ___24a5(Vvar__0__X__23090,Vvar__1__lt__23091,Vvar__2__eq__23092,Vvar__3__x__23093,Vvar__4__y__23094) ).

fof('$_discrim_Coq.Structures.OrdersTac.OEQ$Coq.Structures.OrdersTac.OLT',axiom,
    cCoq_2eStructures_2eOrdersTac_2eOEQ != cCoq_2eStructures_2eOrdersTac_2eOLT ).

fof('$_discrim_Coq.Vectors.Fin.F1$Coq.Vectors.Fin.FS',axiom,
    ! [Vvar__0__n__21601,Vvar__0__n__21602,Vvar__1___24Anonymous__21603] : cCoq_2eVectors_2eFin_2eF1___24a1(Vvar__0__n__21601) != cCoq_2eVectors_2eFin_2eFS___24a2(Vvar__0__n__21602,Vvar__1___24Anonymous__21603) ).

fof('$_discrim_Coq.Vectors.VectorDef.nil$Coq.Vectors.VectorDef.cons',axiom,
    ! [Vvar__0__A__33211,Vvar__0__A__33212,Vvar__1__h__33213,Vvar__2__n__33214,Vvar__3___24Anonymous__33215] : cCoq_2eVectors_2eVectorDef_2enil___24a1(Vvar__0__A__33211) != cCoq_2eVectors_2eVectorDef_2econs___24a4(Vvar__0__A__33212,Vvar__1__h__33213,Vvar__2__n__33214,Vvar__3___24Anonymous__33215) ).

fof('$_discrim_Coq.micromega.EnvRing.PEc$Coq.micromega.EnvRing.PEX',axiom,
    ! [Vvar__0__C__11122,Vvar__1___24Anonymous__11123,Vvar__0__C__11124,Vvar__1___24Anonymous__11125] : cCoq_2emicromega_2eEnvRing_2ePEc___24a2(Vvar__0__C__11122,Vvar__1___24Anonymous__11123) != cCoq_2emicromega_2eEnvRing_2ePEX___24a2(Vvar__0__C__11124,Vvar__1___24Anonymous__11125) ).

fof('$_discrim_Coq.micromega.EnvRing.Pc$Coq.micromega.EnvRing.Pinj',axiom,
    ! [Vvar__0__C__20012,Vvar__1___24Anonymous__20013,Vvar__0__C__20014,Vvar__1___24Anonymous__20015,Vvar__2___24Anonymous__20016] : cCoq_2emicromega_2eEnvRing_2ePc___24a2(Vvar__0__C__20012,Vvar__1___24Anonymous__20013) != cCoq_2emicromega_2eEnvRing_2ePinj___24a3(Vvar__0__C__20014,Vvar__1___24Anonymous__20015,Vvar__2___24Anonymous__20016) ).

fof('$_discrim_Coq.micromega.EnvRing.mon0$Coq.micromega.EnvRing.zmon',axiom,
    ! [Vvar__0___24Anonymous__20049,Vvar__1___24Anonymous__20050] : cCoq_2emicromega_2eEnvRing_2emon0 != cCoq_2emicromega_2eEnvRing_2ezmon___24a2(Vvar__0___24Anonymous__20049,Vvar__1___24Anonymous__20050) ).

fof('$_discrim_Coq.micromega.RingMicromega.Equal$Coq.micromega.RingMicromega.NonEqual',axiom,
    cCoq_2emicromega_2eRingMicromega_2eEqual != cCoq_2emicromega_2eRingMicromega_2eNonEqual ).

fof('$_discrim_Coq.micromega.RingMicromega.OpEq$Coq.micromega.RingMicromega.OpNEq',axiom,
    cCoq_2emicromega_2eRingMicromega_2eOpEq != cCoq_2emicromega_2eRingMicromega_2eOpNEq ).

fof('$_discrim_Coq.micromega.Tauto.TT$Coq.micromega.Tauto.FF',axiom,
    ! [Vvar__0__TA__33106,Vvar__1__TX__33107,Vvar__2__AA__33108,Vvar__3__AF__33109,Vvar__0__TA__33110,Vvar__1__TX__33111,Vvar__2__AA__33112,Vvar__3__AF__33113] : cCoq_2emicromega_2eTauto_2eTT___24a4(Vvar__0__TA__33106,Vvar__1__TX__33107,Vvar__2__AA__33108,Vvar__3__AF__33109) != cCoq_2emicromega_2eTauto_2eFF___24a4(Vvar__0__TA__33110,Vvar__1__TX__33111,Vvar__2__AA__33112,Vvar__3__AF__33113) ).

fof('$_discrim_Coq.setoid_ring.Field_theory.FEO$Coq.setoid_ring.Field_theory.FEI',axiom,
    ! [Vvar__0__C__11791,Vvar__0__C__11792] : cCoq_2esetoid__ring_2eField__theory_2eFEO___24a1(Vvar__0__C__11791) != cCoq_2esetoid__ring_2eField__theory_2eFEI___24a1(Vvar__0__C__11792) ).

fof('$_discrim_Coq.setoid_ring.Ring_polynom.PEO$Coq.setoid_ring.Ring_polynom.PEI',axiom,
    ! [Vvar__0__C__15463,Vvar__0__C__15464] : cCoq_2esetoid__ring_2eRing__polynom_2ePEO___24a1(Vvar__0__C__15463) != cCoq_2esetoid__ring_2eRing__polynom_2ePEI___24a1(Vvar__0__C__15464) ).

fof('$_discrim_Coq.setoid_ring.Ring_polynom.Pc$Coq.setoid_ring.Ring_polynom.Pinj',axiom,
    ! [Vvar__0__C__15107,Vvar__1___24Anonymous__15108,Vvar__0__C__15109,Vvar__1___24Anonymous__15110,Vvar__2___24Anonymous__15111] : cCoq_2esetoid__ring_2eRing__polynom_2ePc___24a2(Vvar__0__C__15107,Vvar__1___24Anonymous__15108) != cCoq_2esetoid__ring_2eRing__polynom_2ePinj___24a3(Vvar__0__C__15109,Vvar__1___24Anonymous__15110,Vvar__2___24Anonymous__15111) ).

fof('$_discrim_Coq.setoid_ring.Ring_polynom.mon0$Coq.setoid_ring.Ring_polynom.zmon',axiom,
    ! [Vvar__0___24Anonymous__15273,Vvar__1___24Anonymous__15274] : cCoq_2esetoid__ring_2eRing__polynom_2emon0 != cCoq_2esetoid__ring_2eRing__polynom_2ezmon___24a2(Vvar__0___24Anonymous__15273,Vvar__1___24Anonymous__15274) ).

fof('$_discrim_Coq.setoid_ring.Ring_theory.Abstract$Coq.setoid_ring.Ring_theory.Computational',axiom,
    ! [Vvar__0__R__18633,Vvar__1__req__18634,Vvar__2__reqb__18635,Vvar__3___24Anonymous__18636] : cCoq_2esetoid__ring_2eRing__theory_2eAbstract != cCoq_2esetoid__ring_2eRing__theory_2eComputational___24a3(Vvar__0__R__18633,Vvar__1__req__18634,Vvar__2__reqb__18635) ).

fof('$_discrim_IntMap.Map.M0$IntMap.Map.M1',axiom,
    ! [Vvar__0__A__72,Vvar__0__A__73,Vvar__1___24Anonymous__74,Vvar__2___24Anonymous__75] : cIntMap_2eMap_2eM0___24a1(Vvar__0__A__72) != cIntMap_2eMap_2eM1___24a3(Vvar__0__A__73,Vvar__1___24Anonymous__74,Vvar__2___24Anonymous__75) ).

fof('$_fix_33571_v_CANONICAL_0',axiom,
    ! [Vv__CANONICAL__1] :
      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__1)
     => ( ? [Vvar__0___24Anonymous__33572] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__33572)
            & Vv__CANONICAL__1 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__33572)
            & c_24__fix__33571__v__CANONICAL__0___24a1(Vv__CANONICAL__1) = cCoq_2eNumbers_2eBinNums_2exO___24a1(c_24__fix__33571__v__CANONICAL__0___24a1(Vvar__0___24Anonymous__33572)) )
        | ? [Vvar__0___24Anonymous__33573] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__33573)
            & Vv__CANONICAL__1 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__33573)
            & c_24__fix__33571__v__CANONICAL__0___24a1(Vv__CANONICAL__1) = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__33573) )
        | ( Vv__CANONICAL__1 = cCoq_2eNumbers_2eBinNums_2exH
          & c_24__fix__33571__v__CANONICAL__0___24a1(Vv__CANONICAL__1) = cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2eNumbers_2eBinNums_2exH) ) ) ) ).

fof('$_inj_Coq.Bool.Bool.ReflectF',axiom,
    ! [Vvar__0__P__19879,Vvar__0__P__19880,Vvar__1___24Anonymous__19881,Vvar__1___24Anonymous__19882] :
      ( cCoq_2eBool_2eBool_2eReflectF___24a1(Vvar__0__P__19879) = cCoq_2eBool_2eBool_2eReflectF___24a1(Vvar__0__P__19880)
     => ( c_24Proof = c_24Proof
        & Vvar__0__P__19879 = Vvar__0__P__19880 ) ) ).

fof('$_inj_Coq.Bool.Bool.ReflectT',axiom,
    ! [Vvar__0__P__19875,Vvar__0__P__19876,Vvar__1___24Anonymous__19877,Vvar__1___24Anonymous__19878] :
      ( cCoq_2eBool_2eBool_2eReflectT___24a1(Vvar__0__P__19875) = cCoq_2eBool_2eBool_2eReflectT___24a1(Vvar__0__P__19876)
     => ( c_24Proof = c_24Proof
        & Vvar__0__P__19875 = Vvar__0__P__19876 ) ) ).

fof('$_inj_Coq.FSets.FSetPositive.PositiveSet.Node',axiom,
    ! [Vvar__0___24Anonymous__19227,Vvar__0___24Anonymous__19228,Vvar__1___24Anonymous__19229,Vvar__1___24Anonymous__19230,Vvar__2___24Anonymous__19231,Vvar__2___24Anonymous__19232] :
      ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eNode___24a3(Vvar__0___24Anonymous__19227,Vvar__1___24Anonymous__19229,Vvar__2___24Anonymous__19231) = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eNode___24a3(Vvar__0___24Anonymous__19228,Vvar__1___24Anonymous__19230,Vvar__2___24Anonymous__19232)
     => ( Vvar__2___24Anonymous__19231 = Vvar__2___24Anonymous__19232
        & Vvar__1___24Anonymous__19229 = Vvar__1___24Anonymous__19230
        & Vvar__0___24Anonymous__19227 = Vvar__0___24Anonymous__19228 ) ) ).

fof('$_inj_Coq.Init.Datatypes.CompEqT',axiom,
    ! [Vvar__0__Peq__19959,Vvar__0__Peq__19960,Vvar__1__Plt__19961,Vvar__1__Plt__19962,Vvar__2__Pgt__19963,Vvar__2__Pgt__19964,Vvar__3___24Anonymous__19965,Vvar__3___24Anonymous__19966] :
      ( cCoq_2eInit_2eDatatypes_2eCompEqT___24a3(Vvar__0__Peq__19959,Vvar__1__Plt__19961,Vvar__2__Pgt__19963) = cCoq_2eInit_2eDatatypes_2eCompEqT___24a3(Vvar__0__Peq__19960,Vvar__1__Plt__19962,Vvar__2__Pgt__19964)
     => ( c_24Proof = c_24Proof
        & Vvar__2__Pgt__19963 = Vvar__2__Pgt__19964
        & Vvar__1__Plt__19961 = Vvar__1__Plt__19962
        & Vvar__0__Peq__19959 = Vvar__0__Peq__19960 ) ) ).

fof('$_inj_Coq.Init.Datatypes.CompGtT',axiom,
    ! [Vvar__0__Peq__19975,Vvar__0__Peq__19976,Vvar__1__Plt__19977,Vvar__1__Plt__19978,Vvar__2__Pgt__19979,Vvar__2__Pgt__19980,Vvar__3___24Anonymous__19981,Vvar__3___24Anonymous__19982] :
      ( cCoq_2eInit_2eDatatypes_2eCompGtT___24a3(Vvar__0__Peq__19975,Vvar__1__Plt__19977,Vvar__2__Pgt__19979) = cCoq_2eInit_2eDatatypes_2eCompGtT___24a3(Vvar__0__Peq__19976,Vvar__1__Plt__19978,Vvar__2__Pgt__19980)
     => ( c_24Proof = c_24Proof
        & Vvar__2__Pgt__19979 = Vvar__2__Pgt__19980
        & Vvar__1__Plt__19977 = Vvar__1__Plt__19978
        & Vvar__0__Peq__19975 = Vvar__0__Peq__19976 ) ) ).

fof('$_inj_Coq.Init.Datatypes.CompLtT',axiom,
    ! [Vvar__0__Peq__19967,Vvar__0__Peq__19968,Vvar__1__Plt__19969,Vvar__1__Plt__19970,Vvar__2__Pgt__19971,Vvar__2__Pgt__19972,Vvar__3___24Anonymous__19973,Vvar__3___24Anonymous__19974] :
      ( cCoq_2eInit_2eDatatypes_2eCompLtT___24a3(Vvar__0__Peq__19967,Vvar__1__Plt__19969,Vvar__2__Pgt__19971) = cCoq_2eInit_2eDatatypes_2eCompLtT___24a3(Vvar__0__Peq__19968,Vvar__1__Plt__19970,Vvar__2__Pgt__19972)
     => ( c_24Proof = c_24Proof
        & Vvar__2__Pgt__19971 = Vvar__2__Pgt__19972
        & Vvar__1__Plt__19969 = Vvar__1__Plt__19970
        & Vvar__0__Peq__19967 = Vvar__0__Peq__19968 ) ) ).

fof('$_inj_Coq.Init.Datatypes.None',axiom,
    ! [Vvar__0__A__45,Vvar__0__A__46] :
      ( cCoq_2eInit_2eDatatypes_2eNone___24a1(Vvar__0__A__45) = cCoq_2eInit_2eDatatypes_2eNone___24a1(Vvar__0__A__46)
     => Vvar__0__A__45 = Vvar__0__A__46 ) ).

fof('$_inj_Coq.Init.Datatypes.S',axiom,
    ! [Vvar__0___24Anonymous__456,Vvar__0___24Anonymous__457] :
      ( cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__456) = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__457)
     => Vvar__0___24Anonymous__456 = Vvar__0___24Anonymous__457 ) ).

fof('$_inj_Coq.Init.Datatypes.Some',axiom,
    ! [Vvar__0__A__41,Vvar__0__A__42,Vvar__1___24Anonymous__43,Vvar__1___24Anonymous__44] :
      ( cCoq_2eInit_2eDatatypes_2eSome___24a2(Vvar__0__A__41,Vvar__1___24Anonymous__43) = cCoq_2eInit_2eDatatypes_2eSome___24a2(Vvar__0__A__42,Vvar__1___24Anonymous__44)
     => ( Vvar__1___24Anonymous__43 = Vvar__1___24Anonymous__44
        & Vvar__0__A__41 = Vvar__0__A__42 ) ) ).

fof('$_inj_Coq.Init.Datatypes.cons',axiom,
    ! [Vvar__0__A__1042,Vvar__0__A__1043,Vvar__1___24Anonymous__1044,Vvar__1___24Anonymous__1045,Vvar__2___24Anonymous__1046,Vvar__2___24Anonymous__1047] :
      ( cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__1042,Vvar__1___24Anonymous__1044,Vvar__2___24Anonymous__1046) = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__1043,Vvar__1___24Anonymous__1045,Vvar__2___24Anonymous__1047)
     => ( Vvar__2___24Anonymous__1046 = Vvar__2___24Anonymous__1047
        & Vvar__1___24Anonymous__1044 = Vvar__1___24Anonymous__1045
        & Vvar__0__A__1042 = Vvar__0__A__1043 ) ) ).

fof('$_inj_Coq.Init.Datatypes.inl',axiom,
    ! [Vvar__0__A__10820,Vvar__0__A__10821,Vvar__1__B__10822,Vvar__1__B__10823,Vvar__2___24Anonymous__10824,Vvar__2___24Anonymous__10825] :
      ( cCoq_2eInit_2eDatatypes_2einl___24a3(Vvar__0__A__10820,Vvar__1__B__10822,Vvar__2___24Anonymous__10824) = cCoq_2eInit_2eDatatypes_2einl___24a3(Vvar__0__A__10821,Vvar__1__B__10823,Vvar__2___24Anonymous__10825)
     => ( Vvar__2___24Anonymous__10824 = Vvar__2___24Anonymous__10825
        & Vvar__1__B__10822 = Vvar__1__B__10823
        & Vvar__0__A__10820 = Vvar__0__A__10821 ) ) ).

fof('$_inj_Coq.Init.Datatypes.inr',axiom,
    ! [Vvar__0__A__10826,Vvar__0__A__10827,Vvar__1__B__10828,Vvar__1__B__10829,Vvar__2___24Anonymous__10830,Vvar__2___24Anonymous__10831] :
      ( cCoq_2eInit_2eDatatypes_2einr___24a3(Vvar__0__A__10826,Vvar__1__B__10828,Vvar__2___24Anonymous__10830) = cCoq_2eInit_2eDatatypes_2einr___24a3(Vvar__0__A__10827,Vvar__1__B__10829,Vvar__2___24Anonymous__10831)
     => ( Vvar__2___24Anonymous__10830 = Vvar__2___24Anonymous__10831
        & Vvar__1__B__10828 = Vvar__1__B__10829
        & Vvar__0__A__10826 = Vvar__0__A__10827 ) ) ).

fof('$_inj_Coq.Init.Datatypes.nil',axiom,
    ! [Vvar__0__A__1040,Vvar__0__A__1041] :
      ( cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__1040) = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__1041)
     => Vvar__0__A__1040 = Vvar__0__A__1041 ) ).

fof('$_inj_Coq.Init.Datatypes.pair',axiom,
    ! [Vvar__0__A__1022,Vvar__0__A__1023,Vvar__1__B__1024,Vvar__1__B__1025,Vvar__2___24Anonymous__1026,Vvar__2___24Anonymous__1027,Vvar__3___24Anonymous__1028,Vvar__3___24Anonymous__1029] :
      ( cCoq_2eInit_2eDatatypes_2epair___24a4(Vvar__0__A__1022,Vvar__1__B__1024,Vvar__2___24Anonymous__1026,Vvar__3___24Anonymous__1028) = cCoq_2eInit_2eDatatypes_2epair___24a4(Vvar__0__A__1023,Vvar__1__B__1025,Vvar__2___24Anonymous__1027,Vvar__3___24Anonymous__1029)
     => ( Vvar__3___24Anonymous__1028 = Vvar__3___24Anonymous__1029
        & Vvar__2___24Anonymous__1026 = Vvar__2___24Anonymous__1027
        & Vvar__1__B__1024 = Vvar__1__B__1025
        & Vvar__0__A__1022 = Vvar__0__A__1023 ) ) ).

fof('$_inj_Coq.Init.Specif.exist',axiom,
    ! [Vvar__0__A__814,Vvar__0__A__815,Vvar__1__P__816,Vvar__1__P__817,Vvar__2__x__818,Vvar__2__x__819,Vvar__3___24Anonymous__820,Vvar__3___24Anonymous__821] :
      ( cCoq_2eInit_2eSpecif_2eexist___24a3(Vvar__0__A__814,Vvar__1__P__816,Vvar__2__x__818) = cCoq_2eInit_2eSpecif_2eexist___24a3(Vvar__0__A__815,Vvar__1__P__817,Vvar__2__x__819)
     => ( c_24Proof = c_24Proof
        & Vvar__2__x__818 = Vvar__2__x__819
        & Vvar__1__P__816 = Vvar__1__P__817
        & Vvar__0__A__814 = Vvar__0__A__815 ) ) ).

fof('$_inj_Coq.Init.Specif.exist2',axiom,
    ! [Vvar__0__A__32736,Vvar__0__A__32737,Vvar__1__P__32738,Vvar__1__P__32739,Vvar__2__Q__32740,Vvar__2__Q__32741,Vvar__3__x__32742,Vvar__3__x__32743,Vvar__4___24Anonymous__32744,Vvar__4___24Anonymous__32745,Vvar__5___24Anonymous__32746,Vvar__5___24Anonymous__32747] :
      ( cCoq_2eInit_2eSpecif_2eexist2___24a4(Vvar__0__A__32736,Vvar__1__P__32738,Vvar__2__Q__32740,Vvar__3__x__32742) = cCoq_2eInit_2eSpecif_2eexist2___24a4(Vvar__0__A__32737,Vvar__1__P__32739,Vvar__2__Q__32741,Vvar__3__x__32743)
     => ( c_24Proof = c_24Proof
        & c_24Proof = c_24Proof
        & Vvar__3__x__32742 = Vvar__3__x__32743
        & Vvar__2__Q__32740 = Vvar__2__Q__32741
        & Vvar__1__P__32738 = Vvar__1__P__32739
        & Vvar__0__A__32736 = Vvar__0__A__32737 ) ) ).

fof('$_inj_Coq.Init.Specif.existT',axiom,
    ! [Vvar__0__A__18744,Vvar__0__A__18745,Vvar__1__P__18746,Vvar__1__P__18747,Vvar__2__x__18748,Vvar__2__x__18749,Vvar__3___24Anonymous__18750,Vvar__3___24Anonymous__18751] :
      ( cCoq_2eInit_2eSpecif_2eexistT___24a4(Vvar__0__A__18744,Vvar__1__P__18746,Vvar__2__x__18748,Vvar__3___24Anonymous__18750) = cCoq_2eInit_2eSpecif_2eexistT___24a4(Vvar__0__A__18745,Vvar__1__P__18747,Vvar__2__x__18749,Vvar__3___24Anonymous__18751)
     => ( Vvar__3___24Anonymous__18750 = Vvar__3___24Anonymous__18751
        & Vvar__2__x__18748 = Vvar__2__x__18749
        & Vvar__1__P__18746 = Vvar__1__P__18747
        & Vvar__0__A__18744 = Vvar__0__A__18745 ) ) ).

fof('$_inj_Coq.Init.Specif.existT2',axiom,
    ! [Vvar__0__A__18872,Vvar__0__A__18873,Vvar__1__P__18874,Vvar__1__P__18875,Vvar__2__Q__18876,Vvar__2__Q__18877,Vvar__3__x__18878,Vvar__3__x__18879,Vvar__4___24Anonymous__18880,Vvar__4___24Anonymous__18881,Vvar__5___24Anonymous__18882,Vvar__5___24Anonymous__18883] :
      ( cCoq_2eInit_2eSpecif_2eexistT2___24a6(Vvar__0__A__18872,Vvar__1__P__18874,Vvar__2__Q__18876,Vvar__3__x__18878,Vvar__4___24Anonymous__18880,Vvar__5___24Anonymous__18882) = cCoq_2eInit_2eSpecif_2eexistT2___24a6(Vvar__0__A__18873,Vvar__1__P__18875,Vvar__2__Q__18877,Vvar__3__x__18879,Vvar__4___24Anonymous__18881,Vvar__5___24Anonymous__18883)
     => ( Vvar__5___24Anonymous__18882 = Vvar__5___24Anonymous__18883
        & Vvar__4___24Anonymous__18880 = Vvar__4___24Anonymous__18881
        & Vvar__3__x__18878 = Vvar__3__x__18879
        & Vvar__2__Q__18876 = Vvar__2__Q__18877
        & Vvar__1__P__18874 = Vvar__1__P__18875
        & Vvar__0__A__18872 = Vvar__0__A__18873 ) ) ).

fof('$_inj_Coq.Init.Specif.inleft',axiom,
    ! [Vvar__0__A__934,Vvar__0__A__935,Vvar__1__B__936,Vvar__1__B__937,Vvar__2___24Anonymous__938,Vvar__2___24Anonymous__939] :
      ( cCoq_2eInit_2eSpecif_2einleft___24a3(Vvar__0__A__934,Vvar__1__B__936,Vvar__2___24Anonymous__938) = cCoq_2eInit_2eSpecif_2einleft___24a3(Vvar__0__A__935,Vvar__1__B__937,Vvar__2___24Anonymous__939)
     => ( Vvar__2___24Anonymous__938 = Vvar__2___24Anonymous__939
        & Vvar__1__B__936 = Vvar__1__B__937
        & Vvar__0__A__934 = Vvar__0__A__935 ) ) ).

fof('$_inj_Coq.Init.Specif.inright',axiom,
    ! [Vvar__0__A__940,Vvar__0__A__941,Vvar__1__B__942,Vvar__1__B__943,Vvar__2___24Anonymous__944,Vvar__2___24Anonymous__945] :
      ( cCoq_2eInit_2eSpecif_2einright___24a2(Vvar__0__A__940,Vvar__1__B__942) = cCoq_2eInit_2eSpecif_2einright___24a2(Vvar__0__A__941,Vvar__1__B__943)
     => ( c_24Proof = c_24Proof
        & Vvar__1__B__942 = Vvar__1__B__943
        & Vvar__0__A__940 = Vvar__0__A__941 ) ) ).

fof('$_inj_Coq.Init.Specif.left',axiom,
    ! [Vvar__0__A__408,Vvar__0__A__409,Vvar__1__B__410,Vvar__1__B__411,Vvar__2___24Anonymous__412,Vvar__2___24Anonymous__413] :
      ( cCoq_2eInit_2eSpecif_2eleft___24a2(Vvar__0__A__408,Vvar__1__B__410) = cCoq_2eInit_2eSpecif_2eleft___24a2(Vvar__0__A__409,Vvar__1__B__411)
     => ( c_24Proof = c_24Proof
        & Vvar__1__B__410 = Vvar__1__B__411
        & Vvar__0__A__408 = Vvar__0__A__409 ) ) ).

fof('$_inj_Coq.Init.Specif.right',axiom,
    ! [Vvar__0__A__414,Vvar__0__A__415,Vvar__1__B__416,Vvar__1__B__417,Vvar__2___24Anonymous__418,Vvar__2___24Anonymous__419] :
      ( cCoq_2eInit_2eSpecif_2eright___24a2(Vvar__0__A__414,Vvar__1__B__416) = cCoq_2eInit_2eSpecif_2eright___24a2(Vvar__0__A__415,Vvar__1__B__417)
     => ( c_24Proof = c_24Proof
        & Vvar__1__B__416 = Vvar__1__B__417
        & Vvar__0__A__414 = Vvar__0__A__415 ) ) ).

fof('$_inj_Coq.Numbers.BinNums.Npos',axiom,
    ! [Vvar__0___24Anonymous__23,Vvar__0___24Anonymous__24] :
      ( cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__23) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__24)
     => Vvar__0___24Anonymous__23 = Vvar__0___24Anonymous__24 ) ).

fof('$_inj_Coq.Numbers.BinNums.Zneg',axiom,
    ! [Vvar__0___24Anonymous__2667,Vvar__0___24Anonymous__2668] :
      ( cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__2667) = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__2668)
     => Vvar__0___24Anonymous__2667 = Vvar__0___24Anonymous__2668 ) ).

fof('$_inj_Coq.Numbers.BinNums.Zpos',axiom,
    ! [Vvar__0___24Anonymous__2665,Vvar__0___24Anonymous__2666] :
      ( cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__2665) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__2666)
     => Vvar__0___24Anonymous__2665 = Vvar__0___24Anonymous__2666 ) ).

fof('$_inj_Coq.Numbers.BinNums.xI',axiom,
    ! [Vvar__0___24Anonymous__8,Vvar__0___24Anonymous__9] :
      ( cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__8) = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__9)
     => Vvar__0___24Anonymous__8 = Vvar__0___24Anonymous__9 ) ).

fof('$_inj_Coq.Numbers.BinNums.xO',axiom,
    ! [Vvar__0___24Anonymous__10,Vvar__0___24Anonymous__11] :
      ( cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__10) = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__11)
     => Vvar__0___24Anonymous__10 = Vvar__0___24Anonymous__11 ) ).

fof('$_inj_Coq.PArith.BinPos.Pos.PeanoSucc',axiom,
    ! [Vvar__0__p__33578,Vvar__0__p__33579,Vvar__1___24Anonymous__33580,Vvar__1___24Anonymous__33581] :
      ( cCoq_2ePArith_2eBinPos_2ePos_2ePeanoSucc___24a2(Vvar__0__p__33578,Vvar__1___24Anonymous__33580) = cCoq_2ePArith_2eBinPos_2ePos_2ePeanoSucc___24a2(Vvar__0__p__33579,Vvar__1___24Anonymous__33581)
     => ( Vvar__1___24Anonymous__33580 = Vvar__1___24Anonymous__33581
        & Vvar__0__p__33578 = Vvar__0__p__33579 ) ) ).

fof('$_inj_Coq.PArith.BinPosDef.Pos.IsPos',axiom,
    ! [Vvar__0___24Anonymous__19091,Vvar__0___24Anonymous__19092] :
      ( cCoq_2ePArith_2eBinPosDef_2ePos_2eIsPos___24a1(Vvar__0___24Anonymous__19091) = cCoq_2ePArith_2eBinPosDef_2ePos_2eIsPos___24a1(Vvar__0___24Anonymous__19092)
     => Vvar__0___24Anonymous__19091 = Vvar__0___24Anonymous__19092 ) ).

fof('$_inj_Coq.QArith.QArith_base.Qmake',axiom,
    ! [Vvar__0__Qnum__23137,Vvar__0__Qnum__23138,Vvar__1__Qden__23139,Vvar__1__Qden__23140] :
      ( cCoq_2eQArith_2eQArith__base_2eQmake___24a2(Vvar__0__Qnum__23137,Vvar__1__Qden__23139) = cCoq_2eQArith_2eQArith__base_2eQmake___24a2(Vvar__0__Qnum__23138,Vvar__1__Qden__23140)
     => ( Vvar__1__Qden__23139 = Vvar__1__Qden__23140
        & Vvar__0__Qnum__23137 = Vvar__0__Qnum__23138 ) ) ).

fof('$_inj_Coq.Reals.RIneq.mknonzeroreal',axiom,
    ! [Vvar__0__nonzero__23157,Vvar__0__nonzero__23158,Vvar__1__cond__nonzero__23159,Vvar__1__cond__nonzero__23160] :
      ( cCoq_2eReals_2eRIneq_2emknonzeroreal___24a1(Vvar__0__nonzero__23157) = cCoq_2eReals_2eRIneq_2emknonzeroreal___24a1(Vvar__0__nonzero__23158)
     => ( c_24Proof = c_24Proof
        & Vvar__0__nonzero__23157 = Vvar__0__nonzero__23158 ) ) ).

fof('$_inj_Coq.Reals.Rfunctions.ZintNeg',axiom,
    ! [Vvar__0__x__23429,Vvar__0__x__23430,Vvar__1__n__23431,Vvar__1__n__23432,Vvar__2___24Anonymous__23433,Vvar__2___24Anonymous__23434] :
      ( cCoq_2eReals_2eRfunctions_2eZintNeg___24a2(Vvar__0__x__23429,Vvar__1__n__23431) = cCoq_2eReals_2eRfunctions_2eZintNeg___24a2(Vvar__0__x__23430,Vvar__1__n__23432)
     => ( c_24Proof = c_24Proof
        & Vvar__1__n__23431 = Vvar__1__n__23432
        & Vvar__0__x__23429 = Vvar__0__x__23430 ) ) ).

fof('$_inj_Coq.Reals.Rfunctions.ZintNull',axiom,
    ! [Vvar__0__x__23419,Vvar__0__x__23420,Vvar__1___24Anonymous__23421,Vvar__1___24Anonymous__23422] :
      ( cCoq_2eReals_2eRfunctions_2eZintNull___24a1(Vvar__0__x__23419) = cCoq_2eReals_2eRfunctions_2eZintNull___24a1(Vvar__0__x__23420)
     => ( c_24Proof = c_24Proof
        & Vvar__0__x__23419 = Vvar__0__x__23420 ) ) ).

fof('$_inj_Coq.Reals.Rfunctions.ZintPos',axiom,
    ! [Vvar__0__x__23423,Vvar__0__x__23424,Vvar__1__n__23425,Vvar__1__n__23426,Vvar__2___24Anonymous__23427,Vvar__2___24Anonymous__23428] :
      ( cCoq_2eReals_2eRfunctions_2eZintPos___24a2(Vvar__0__x__23423,Vvar__1__n__23425) = cCoq_2eReals_2eRfunctions_2eZintPos___24a2(Vvar__0__x__23424,Vvar__1__n__23426)
     => ( c_24Proof = c_24Proof
        & Vvar__1__n__23425 = Vvar__1__n__23426
        & Vvar__0__x__23423 = Vvar__0__x__23424 ) ) ).

fof('$_inj_Coq.Strings.Ascii.Ascii',axiom,
    ! [Vvar__0___24Anonymous__2394,Vvar__0___24Anonymous__2395,Vvar__1___24Anonymous__2396,Vvar__1___24Anonymous__2397,Vvar__2___24Anonymous__2398,Vvar__2___24Anonymous__2399,Vvar__3___24Anonymous__2400,Vvar__3___24Anonymous__2401,Vvar__4___24Anonymous__2402,Vvar__4___24Anonymous__2403,Vvar__5___24Anonymous__2404,Vvar__5___24Anonymous__2405,Vvar__6___24Anonymous__2406,Vvar__6___24Anonymous__2407,Vvar__7___24Anonymous__2408,Vvar__7___24Anonymous__2409] :
      ( cCoq_2eStrings_2eAscii_2eAscii___24a8(Vvar__0___24Anonymous__2394,Vvar__1___24Anonymous__2396,Vvar__2___24Anonymous__2398,Vvar__3___24Anonymous__2400,Vvar__4___24Anonymous__2402,Vvar__5___24Anonymous__2404,Vvar__6___24Anonymous__2406,Vvar__7___24Anonymous__2408) = cCoq_2eStrings_2eAscii_2eAscii___24a8(Vvar__0___24Anonymous__2395,Vvar__1___24Anonymous__2397,Vvar__2___24Anonymous__2399,Vvar__3___24Anonymous__2401,Vvar__4___24Anonymous__2403,Vvar__5___24Anonymous__2405,Vvar__6___24Anonymous__2407,Vvar__7___24Anonymous__2409)
     => ( Vvar__7___24Anonymous__2408 = Vvar__7___24Anonymous__2409
        & Vvar__6___24Anonymous__2406 = Vvar__6___24Anonymous__2407
        & Vvar__5___24Anonymous__2404 = Vvar__5___24Anonymous__2405
        & Vvar__4___24Anonymous__2402 = Vvar__4___24Anonymous__2403
        & Vvar__3___24Anonymous__2400 = Vvar__3___24Anonymous__2401
        & Vvar__2___24Anonymous__2398 = Vvar__2___24Anonymous__2399
        & Vvar__1___24Anonymous__2396 = Vvar__1___24Anonymous__2397
        & Vvar__0___24Anonymous__2394 = Vvar__0___24Anonymous__2395 ) ) ).

fof('$_inj_Coq.Strings.String.String',axiom,
    ! [Vvar__0___24Anonymous__32753,Vvar__0___24Anonymous__32754,Vvar__1___24Anonymous__32755,Vvar__1___24Anonymous__32756] :
      ( cCoq_2eStrings_2eString_2eString___24a2(Vvar__0___24Anonymous__32753,Vvar__1___24Anonymous__32755) = cCoq_2eStrings_2eString_2eString___24a2(Vvar__0___24Anonymous__32754,Vvar__1___24Anonymous__32756)
     => ( Vvar__1___24Anonymous__32755 = Vvar__1___24Anonymous__32756
        & Vvar__0___24Anonymous__32753 = Vvar__0___24Anonymous__32754 ) ) ).

fof('$_inj_Coq.Structures.OrderedType.EQ',axiom,
    ! [Vvar__0__X__23108,Vvar__0__X__23109,Vvar__1__lt__23110,Vvar__1__lt__23111,Vvar__2__eq__23112,Vvar__2__eq__23113,Vvar__3__x__23114,Vvar__3__x__23115,Vvar__4__y__23116,Vvar__4__y__23117,Vvar__5___24Anonymous__23118,Vvar__5___24Anonymous__23119] :
      ( cCoq_2eStructures_2eOrderedType_2eEQ___24a5(Vvar__0__X__23108,Vvar__1__lt__23110,Vvar__2__eq__23112,Vvar__3__x__23114,Vvar__4__y__23116) = cCoq_2eStructures_2eOrderedType_2eEQ___24a5(Vvar__0__X__23109,Vvar__1__lt__23111,Vvar__2__eq__23113,Vvar__3__x__23115,Vvar__4__y__23117)
     => ( c_24Proof = c_24Proof
        & Vvar__4__y__23116 = Vvar__4__y__23117
        & Vvar__3__x__23114 = Vvar__3__x__23115
        & Vvar__2__eq__23112 = Vvar__2__eq__23113
        & Vvar__1__lt__23110 = Vvar__1__lt__23111
        & Vvar__0__X__23108 = Vvar__0__X__23109 ) ) ).

fof('$_inj_Coq.Structures.OrderedType.GT',axiom,
    ! [Vvar__0__X__23120,Vvar__0__X__23121,Vvar__1__lt__23122,Vvar__1__lt__23123,Vvar__2__eq__23124,Vvar__2__eq__23125,Vvar__3__x__23126,Vvar__3__x__23127,Vvar__4__y__23128,Vvar__4__y__23129,Vvar__5___24Anonymous__23130,Vvar__5___24Anonymous__23131] :
      ( cCoq_2eStructures_2eOrderedType_2eGT___24a5(Vvar__0__X__23120,Vvar__1__lt__23122,Vvar__2__eq__23124,Vvar__3__x__23126,Vvar__4__y__23128) = cCoq_2eStructures_2eOrderedType_2eGT___24a5(Vvar__0__X__23121,Vvar__1__lt__23123,Vvar__2__eq__23125,Vvar__3__x__23127,Vvar__4__y__23129)
     => ( c_24Proof = c_24Proof
        & Vvar__4__y__23128 = Vvar__4__y__23129
        & Vvar__3__x__23126 = Vvar__3__x__23127
        & Vvar__2__eq__23124 = Vvar__2__eq__23125
        & Vvar__1__lt__23122 = Vvar__1__lt__23123
        & Vvar__0__X__23120 = Vvar__0__X__23121 ) ) ).

fof('$_inj_Coq.Structures.OrderedType.LT',axiom,
    ! [Vvar__0__X__23096,Vvar__0__X__23097,Vvar__1__lt__23098,Vvar__1__lt__23099,Vvar__2__eq__23100,Vvar__2__eq__23101,Vvar__3__x__23102,Vvar__3__x__23103,Vvar__4__y__23104,Vvar__4__y__23105,Vvar__5___24Anonymous__23106,Vvar__5___24Anonymous__23107] :
      ( cCoq_2eStructures_2eOrderedType_2eLT___24a5(Vvar__0__X__23096,Vvar__1__lt__23098,Vvar__2__eq__23100,Vvar__3__x__23102,Vvar__4__y__23104) = cCoq_2eStructures_2eOrderedType_2eLT___24a5(Vvar__0__X__23097,Vvar__1__lt__23099,Vvar__2__eq__23101,Vvar__3__x__23103,Vvar__4__y__23105)
     => ( c_24Proof = c_24Proof
        & Vvar__4__y__23104 = Vvar__4__y__23105
        & Vvar__3__x__23102 = Vvar__3__x__23103
        & Vvar__2__eq__23100 = Vvar__2__eq__23101
        & Vvar__1__lt__23098 = Vvar__1__lt__23099
        & Vvar__0__X__23096 = Vvar__0__X__23097 ) ) ).

fof('$_inj_Coq.Vectors.Fin.F1',axiom,
    ! [Vvar__0__n__21604,Vvar__0__n__21605] :
      ( cCoq_2eVectors_2eFin_2eF1___24a1(Vvar__0__n__21604) = cCoq_2eVectors_2eFin_2eF1___24a1(Vvar__0__n__21605)
     => Vvar__0__n__21604 = Vvar__0__n__21605 ) ).

fof('$_inj_Coq.Vectors.Fin.FS',axiom,
    ! [Vvar__0__n__21606,Vvar__0__n__21607,Vvar__1___24Anonymous__21608,Vvar__1___24Anonymous__21609] :
      ( cCoq_2eVectors_2eFin_2eFS___24a2(Vvar__0__n__21606,Vvar__1___24Anonymous__21608) = cCoq_2eVectors_2eFin_2eFS___24a2(Vvar__0__n__21607,Vvar__1___24Anonymous__21609)
     => ( Vvar__1___24Anonymous__21608 = Vvar__1___24Anonymous__21609
        & Vvar__0__n__21606 = Vvar__0__n__21607 ) ) ).

fof('$_inj_Coq.Vectors.VectorDef.cons',axiom,
    ! [Vvar__0__A__33218,Vvar__0__A__33219,Vvar__1__h__33220,Vvar__1__h__33221,Vvar__2__n__33222,Vvar__2__n__33223,Vvar__3___24Anonymous__33224,Vvar__3___24Anonymous__33225] :
      ( cCoq_2eVectors_2eVectorDef_2econs___24a4(Vvar__0__A__33218,Vvar__1__h__33220,Vvar__2__n__33222,Vvar__3___24Anonymous__33224) = cCoq_2eVectors_2eVectorDef_2econs___24a4(Vvar__0__A__33219,Vvar__1__h__33221,Vvar__2__n__33223,Vvar__3___24Anonymous__33225)
     => ( Vvar__3___24Anonymous__33224 = Vvar__3___24Anonymous__33225
        & Vvar__2__n__33222 = Vvar__2__n__33223
        & Vvar__1__h__33220 = Vvar__1__h__33221
        & Vvar__0__A__33218 = Vvar__0__A__33219 ) ) ).

fof('$_inj_Coq.Vectors.VectorDef.nil',axiom,
    ! [Vvar__0__A__33216,Vvar__0__A__33217] :
      ( cCoq_2eVectors_2eVectorDef_2enil___24a1(Vvar__0__A__33216) = cCoq_2eVectors_2eVectorDef_2enil___24a1(Vvar__0__A__33217)
     => Vvar__0__A__33216 = Vvar__0__A__33217 ) ).

fof('$_inj_Coq.ZArith.Znumtheory.Euclid_intro',axiom,
    ! [Vvar__0__a__33385,Vvar__0__a__33386,Vvar__1__b__33387,Vvar__1__b__33388,Vvar__2__u__33389,Vvar__2__u__33390,Vvar__3__v__33391,Vvar__3__v__33392,Vvar__4__d__33393,Vvar__4__d__33394,Vvar__5___24Anonymous__33395,Vvar__5___24Anonymous__33396,Vvar__6___24Anonymous__33397,Vvar__6___24Anonymous__33398] :
      ( cCoq_2eZArith_2eZnumtheory_2eEuclid__intro___24a5(Vvar__0__a__33385,Vvar__1__b__33387,Vvar__2__u__33389,Vvar__3__v__33391,Vvar__4__d__33393) = cCoq_2eZArith_2eZnumtheory_2eEuclid__intro___24a5(Vvar__0__a__33386,Vvar__1__b__33388,Vvar__2__u__33390,Vvar__3__v__33392,Vvar__4__d__33394)
     => ( c_24Proof = c_24Proof
        & c_24Proof = c_24Proof
        & Vvar__4__d__33393 = Vvar__4__d__33394
        & Vvar__3__v__33391 = Vvar__3__v__33392
        & Vvar__2__u__33389 = Vvar__2__u__33390
        & Vvar__1__b__33387 = Vvar__1__b__33388
        & Vvar__0__a__33385 = Vvar__0__a__33386 ) ) ).

fof('$_inj_Coq.ZArith.Zpower.Zdiv_rest_proof',axiom,
    ! [Vvar__0__x__33433,Vvar__0__x__33434,Vvar__1__p__33435,Vvar__1__p__33436,Vvar__2__q__33437,Vvar__2__q__33438,Vvar__3__r__33439,Vvar__3__r__33440,Vvar__4___24Anonymous__33441,Vvar__4___24Anonymous__33442,Vvar__5___24Anonymous__33443,Vvar__5___24Anonymous__33444,Vvar__6___24Anonymous__33445,Vvar__6___24Anonymous__33446] :
      ( cCoq_2eZArith_2eZpower_2eZdiv__rest__proof___24a4(Vvar__0__x__33433,Vvar__1__p__33435,Vvar__2__q__33437,Vvar__3__r__33439) = cCoq_2eZArith_2eZpower_2eZdiv__rest__proof___24a4(Vvar__0__x__33434,Vvar__1__p__33436,Vvar__2__q__33438,Vvar__3__r__33440)
     => ( c_24Proof = c_24Proof
        & c_24Proof = c_24Proof
        & c_24Proof = c_24Proof
        & Vvar__3__r__33439 = Vvar__3__r__33440
        & Vvar__2__q__33437 = Vvar__2__q__33438
        & Vvar__1__p__33435 = Vvar__1__p__33436
        & Vvar__0__x__33433 = Vvar__0__x__33434 ) ) ).

fof('$_inj_Coq.micromega.EnvRing.PEX',axiom,
    ! [Vvar__0__C__11130,Vvar__0__C__11131,Vvar__1___24Anonymous__11132,Vvar__1___24Anonymous__11133] :
      ( cCoq_2emicromega_2eEnvRing_2ePEX___24a2(Vvar__0__C__11130,Vvar__1___24Anonymous__11132) = cCoq_2emicromega_2eEnvRing_2ePEX___24a2(Vvar__0__C__11131,Vvar__1___24Anonymous__11133)
     => ( Vvar__1___24Anonymous__11132 = Vvar__1___24Anonymous__11133
        & Vvar__0__C__11130 = Vvar__0__C__11131 ) ) ).

fof('$_inj_Coq.micromega.EnvRing.PEadd',axiom,
    ! [Vvar__0__C__11134,Vvar__0__C__11135,Vvar__1___24Anonymous__11136,Vvar__1___24Anonymous__11137,Vvar__2___24Anonymous__11138,Vvar__2___24Anonymous__11139] :
      ( cCoq_2emicromega_2eEnvRing_2ePEadd___24a3(Vvar__0__C__11134,Vvar__1___24Anonymous__11136,Vvar__2___24Anonymous__11138) = cCoq_2emicromega_2eEnvRing_2ePEadd___24a3(Vvar__0__C__11135,Vvar__1___24Anonymous__11137,Vvar__2___24Anonymous__11139)
     => ( Vvar__2___24Anonymous__11138 = Vvar__2___24Anonymous__11139
        & Vvar__1___24Anonymous__11136 = Vvar__1___24Anonymous__11137
        & Vvar__0__C__11134 = Vvar__0__C__11135 ) ) ).

fof('$_inj_Coq.micromega.EnvRing.PEc',axiom,
    ! [Vvar__0__C__11126,Vvar__0__C__11127,Vvar__1___24Anonymous__11128,Vvar__1___24Anonymous__11129] :
      ( cCoq_2emicromega_2eEnvRing_2ePEc___24a2(Vvar__0__C__11126,Vvar__1___24Anonymous__11128) = cCoq_2emicromega_2eEnvRing_2ePEc___24a2(Vvar__0__C__11127,Vvar__1___24Anonymous__11129)
     => ( Vvar__1___24Anonymous__11128 = Vvar__1___24Anonymous__11129
        & Vvar__0__C__11126 = Vvar__0__C__11127 ) ) ).

fof('$_inj_Coq.micromega.EnvRing.PEmul',axiom,
    ! [Vvar__0__C__11146,Vvar__0__C__11147,Vvar__1___24Anonymous__11148,Vvar__1___24Anonymous__11149,Vvar__2___24Anonymous__11150,Vvar__2___24Anonymous__11151] :
      ( cCoq_2emicromega_2eEnvRing_2ePEmul___24a3(Vvar__0__C__11146,Vvar__1___24Anonymous__11148,Vvar__2___24Anonymous__11150) = cCoq_2emicromega_2eEnvRing_2ePEmul___24a3(Vvar__0__C__11147,Vvar__1___24Anonymous__11149,Vvar__2___24Anonymous__11151)
     => ( Vvar__2___24Anonymous__11150 = Vvar__2___24Anonymous__11151
        & Vvar__1___24Anonymous__11148 = Vvar__1___24Anonymous__11149
        & Vvar__0__C__11146 = Vvar__0__C__11147 ) ) ).

fof('$_inj_Coq.micromega.EnvRing.PEopp',axiom,
    ! [Vvar__0__C__11152,Vvar__0__C__11153,Vvar__1___24Anonymous__11154,Vvar__1___24Anonymous__11155] :
      ( cCoq_2emicromega_2eEnvRing_2ePEopp___24a2(Vvar__0__C__11152,Vvar__1___24Anonymous__11154) = cCoq_2emicromega_2eEnvRing_2ePEopp___24a2(Vvar__0__C__11153,Vvar__1___24Anonymous__11155)
     => ( Vvar__1___24Anonymous__11154 = Vvar__1___24Anonymous__11155
        & Vvar__0__C__11152 = Vvar__0__C__11153 ) ) ).

fof('$_inj_Coq.micromega.EnvRing.PEpow',axiom,
    ! [Vvar__0__C__11156,Vvar__0__C__11157,Vvar__1___24Anonymous__11158,Vvar__1___24Anonymous__11159,Vvar__2___24Anonymous__11160,Vvar__2___24Anonymous__11161] :
      ( cCoq_2emicromega_2eEnvRing_2ePEpow___24a3(Vvar__0__C__11156,Vvar__1___24Anonymous__11158,Vvar__2___24Anonymous__11160) = cCoq_2emicromega_2eEnvRing_2ePEpow___24a3(Vvar__0__C__11157,Vvar__1___24Anonymous__11159,Vvar__2___24Anonymous__11161)
     => ( Vvar__2___24Anonymous__11160 = Vvar__2___24Anonymous__11161
        & Vvar__1___24Anonymous__11158 = Vvar__1___24Anonymous__11159
        & Vvar__0__C__11156 = Vvar__0__C__11157 ) ) ).

fof('$_inj_Coq.micromega.EnvRing.PEsub',axiom,
    ! [Vvar__0__C__11140,Vvar__0__C__11141,Vvar__1___24Anonymous__11142,Vvar__1___24Anonymous__11143,Vvar__2___24Anonymous__11144,Vvar__2___24Anonymous__11145] :
      ( cCoq_2emicromega_2eEnvRing_2ePEsub___24a3(Vvar__0__C__11140,Vvar__1___24Anonymous__11142,Vvar__2___24Anonymous__11144) = cCoq_2emicromega_2eEnvRing_2ePEsub___24a3(Vvar__0__C__11141,Vvar__1___24Anonymous__11143,Vvar__2___24Anonymous__11145)
     => ( Vvar__2___24Anonymous__11144 = Vvar__2___24Anonymous__11145
        & Vvar__1___24Anonymous__11142 = Vvar__1___24Anonymous__11143
        & Vvar__0__C__11140 = Vvar__0__C__11141 ) ) ).

fof('$_inj_Coq.micromega.EnvRing.PX',axiom,
    ! [Vvar__0__C__20027,Vvar__0__C__20028,Vvar__1___24Anonymous__20029,Vvar__1___24Anonymous__20030,Vvar__2___24Anonymous__20031,Vvar__2___24Anonymous__20032,Vvar__3___24Anonymous__20033,Vvar__3___24Anonymous__20034] :
      ( cCoq_2emicromega_2eEnvRing_2ePX___24a4(Vvar__0__C__20027,Vvar__1___24Anonymous__20029,Vvar__2___24Anonymous__20031,Vvar__3___24Anonymous__20033) = cCoq_2emicromega_2eEnvRing_2ePX___24a4(Vvar__0__C__20028,Vvar__1___24Anonymous__20030,Vvar__2___24Anonymous__20032,Vvar__3___24Anonymous__20034)
     => ( Vvar__3___24Anonymous__20033 = Vvar__3___24Anonymous__20034
        & Vvar__2___24Anonymous__20031 = Vvar__2___24Anonymous__20032
        & Vvar__1___24Anonymous__20029 = Vvar__1___24Anonymous__20030
        & Vvar__0__C__20027 = Vvar__0__C__20028 ) ) ).

fof('$_inj_Coq.micromega.EnvRing.Pc',axiom,
    ! [Vvar__0__C__20017,Vvar__0__C__20018,Vvar__1___24Anonymous__20019,Vvar__1___24Anonymous__20020] :
      ( cCoq_2emicromega_2eEnvRing_2ePc___24a2(Vvar__0__C__20017,Vvar__1___24Anonymous__20019) = cCoq_2emicromega_2eEnvRing_2ePc___24a2(Vvar__0__C__20018,Vvar__1___24Anonymous__20020)
     => ( Vvar__1___24Anonymous__20019 = Vvar__1___24Anonymous__20020
        & Vvar__0__C__20017 = Vvar__0__C__20018 ) ) ).

fof('$_inj_Coq.micromega.EnvRing.Pinj',axiom,
    ! [Vvar__0__C__20021,Vvar__0__C__20022,Vvar__1___24Anonymous__20023,Vvar__1___24Anonymous__20024,Vvar__2___24Anonymous__20025,Vvar__2___24Anonymous__20026] :
      ( cCoq_2emicromega_2eEnvRing_2ePinj___24a3(Vvar__0__C__20021,Vvar__1___24Anonymous__20023,Vvar__2___24Anonymous__20025) = cCoq_2emicromega_2eEnvRing_2ePinj___24a3(Vvar__0__C__20022,Vvar__1___24Anonymous__20024,Vvar__2___24Anonymous__20026)
     => ( Vvar__2___24Anonymous__20025 = Vvar__2___24Anonymous__20026
        & Vvar__1___24Anonymous__20023 = Vvar__1___24Anonymous__20024
        & Vvar__0__C__20021 = Vvar__0__C__20022 ) ) ).

fof('$_inj_Coq.micromega.EnvRing.vmon',axiom,
    ! [Vvar__0___24Anonymous__20055,Vvar__0___24Anonymous__20056,Vvar__1___24Anonymous__20057,Vvar__1___24Anonymous__20058] :
      ( cCoq_2emicromega_2eEnvRing_2evmon___24a2(Vvar__0___24Anonymous__20055,Vvar__1___24Anonymous__20057) = cCoq_2emicromega_2eEnvRing_2evmon___24a2(Vvar__0___24Anonymous__20056,Vvar__1___24Anonymous__20058)
     => ( Vvar__1___24Anonymous__20057 = Vvar__1___24Anonymous__20058
        & Vvar__0___24Anonymous__20055 = Vvar__0___24Anonymous__20056 ) ) ).

fof('$_inj_Coq.micromega.EnvRing.zmon',axiom,
    ! [Vvar__0___24Anonymous__20051,Vvar__0___24Anonymous__20052,Vvar__1___24Anonymous__20053,Vvar__1___24Anonymous__20054] :
      ( cCoq_2emicromega_2eEnvRing_2ezmon___24a2(Vvar__0___24Anonymous__20051,Vvar__1___24Anonymous__20053) = cCoq_2emicromega_2eEnvRing_2ezmon___24a2(Vvar__0___24Anonymous__20052,Vvar__1___24Anonymous__20054)
     => ( Vvar__1___24Anonymous__20053 = Vvar__1___24Anonymous__20054
        & Vvar__0___24Anonymous__20051 = Vvar__0___24Anonymous__20052 ) ) ).

fof('$_inj_Coq.micromega.Tauto.A',axiom,
    ! [Vvar__0__TA__33140,Vvar__0__TA__33141,Vvar__1__TX__33142,Vvar__1__TX__33143,Vvar__2__AA__33144,Vvar__2__AA__33145,Vvar__3__AF__33146,Vvar__3__AF__33147,Vvar__4___24Anonymous__33148,Vvar__4___24Anonymous__33149,Vvar__5___24Anonymous__33150,Vvar__5___24Anonymous__33151] :
      ( cCoq_2emicromega_2eTauto_2eA___24a6(Vvar__0__TA__33140,Vvar__1__TX__33142,Vvar__2__AA__33144,Vvar__3__AF__33146,Vvar__4___24Anonymous__33148,Vvar__5___24Anonymous__33150) = cCoq_2emicromega_2eTauto_2eA___24a6(Vvar__0__TA__33141,Vvar__1__TX__33143,Vvar__2__AA__33145,Vvar__3__AF__33147,Vvar__4___24Anonymous__33149,Vvar__5___24Anonymous__33151)
     => ( Vvar__5___24Anonymous__33150 = Vvar__5___24Anonymous__33151
        & Vvar__4___24Anonymous__33148 = Vvar__4___24Anonymous__33149
        & Vvar__3__AF__33146 = Vvar__3__AF__33147
        & Vvar__2__AA__33144 = Vvar__2__AA__33145
        & Vvar__1__TX__33142 = Vvar__1__TX__33143
        & Vvar__0__TA__33140 = Vvar__0__TA__33141 ) ) ).

fof('$_inj_Coq.micromega.Tauto.Cj',axiom,
    ! [Vvar__0__TA__33152,Vvar__0__TA__33153,Vvar__1__TX__33154,Vvar__1__TX__33155,Vvar__2__AA__33156,Vvar__2__AA__33157,Vvar__3__AF__33158,Vvar__3__AF__33159,Vvar__4___24Anonymous__33160,Vvar__4___24Anonymous__33161,Vvar__5___24Anonymous__33162,Vvar__5___24Anonymous__33163] :
      ( cCoq_2emicromega_2eTauto_2eCj___24a6(Vvar__0__TA__33152,Vvar__1__TX__33154,Vvar__2__AA__33156,Vvar__3__AF__33158,Vvar__4___24Anonymous__33160,Vvar__5___24Anonymous__33162) = cCoq_2emicromega_2eTauto_2eCj___24a6(Vvar__0__TA__33153,Vvar__1__TX__33155,Vvar__2__AA__33157,Vvar__3__AF__33159,Vvar__4___24Anonymous__33161,Vvar__5___24Anonymous__33163)
     => ( Vvar__5___24Anonymous__33162 = Vvar__5___24Anonymous__33163
        & Vvar__4___24Anonymous__33160 = Vvar__4___24Anonymous__33161
        & Vvar__3__AF__33158 = Vvar__3__AF__33159
        & Vvar__2__AA__33156 = Vvar__2__AA__33157
        & Vvar__1__TX__33154 = Vvar__1__TX__33155
        & Vvar__0__TA__33152 = Vvar__0__TA__33153 ) ) ).

fof('$_inj_Coq.micromega.Tauto.D',axiom,
    ! [Vvar__0__TA__33164,Vvar__0__TA__33165,Vvar__1__TX__33166,Vvar__1__TX__33167,Vvar__2__AA__33168,Vvar__2__AA__33169,Vvar__3__AF__33170,Vvar__3__AF__33171,Vvar__4___24Anonymous__33172,Vvar__4___24Anonymous__33173,Vvar__5___24Anonymous__33174,Vvar__5___24Anonymous__33175] :
      ( cCoq_2emicromega_2eTauto_2eD___24a6(Vvar__0__TA__33164,Vvar__1__TX__33166,Vvar__2__AA__33168,Vvar__3__AF__33170,Vvar__4___24Anonymous__33172,Vvar__5___24Anonymous__33174) = cCoq_2emicromega_2eTauto_2eD___24a6(Vvar__0__TA__33165,Vvar__1__TX__33167,Vvar__2__AA__33169,Vvar__3__AF__33171,Vvar__4___24Anonymous__33173,Vvar__5___24Anonymous__33175)
     => ( Vvar__5___24Anonymous__33174 = Vvar__5___24Anonymous__33175
        & Vvar__4___24Anonymous__33172 = Vvar__4___24Anonymous__33173
        & Vvar__3__AF__33170 = Vvar__3__AF__33171
        & Vvar__2__AA__33168 = Vvar__2__AA__33169
        & Vvar__1__TX__33166 = Vvar__1__TX__33167
        & Vvar__0__TA__33164 = Vvar__0__TA__33165 ) ) ).

fof('$_inj_Coq.micromega.Tauto.FF',axiom,
    ! [Vvar__0__TA__33122,Vvar__0__TA__33123,Vvar__1__TX__33124,Vvar__1__TX__33125,Vvar__2__AA__33126,Vvar__2__AA__33127,Vvar__3__AF__33128,Vvar__3__AF__33129] :
      ( cCoq_2emicromega_2eTauto_2eFF___24a4(Vvar__0__TA__33122,Vvar__1__TX__33124,Vvar__2__AA__33126,Vvar__3__AF__33128) = cCoq_2emicromega_2eTauto_2eFF___24a4(Vvar__0__TA__33123,Vvar__1__TX__33125,Vvar__2__AA__33127,Vvar__3__AF__33129)
     => ( Vvar__3__AF__33128 = Vvar__3__AF__33129
        & Vvar__2__AA__33126 = Vvar__2__AA__33127
        & Vvar__1__TX__33124 = Vvar__1__TX__33125
        & Vvar__0__TA__33122 = Vvar__0__TA__33123 ) ) ).

fof('$_inj_Coq.micromega.Tauto.I',axiom,
    ! [Vvar__0__TA__33186,Vvar__0__TA__33187,Vvar__1__TX__33188,Vvar__1__TX__33189,Vvar__2__AA__33190,Vvar__2__AA__33191,Vvar__3__AF__33192,Vvar__3__AF__33193,Vvar__4___24Anonymous__33194,Vvar__4___24Anonymous__33195,Vvar__5___24Anonymous__33196,Vvar__5___24Anonymous__33197,Vvar__6___24Anonymous__33198,Vvar__6___24Anonymous__33199] :
      ( cCoq_2emicromega_2eTauto_2eI___24a7(Vvar__0__TA__33186,Vvar__1__TX__33188,Vvar__2__AA__33190,Vvar__3__AF__33192,Vvar__4___24Anonymous__33194,Vvar__5___24Anonymous__33196,Vvar__6___24Anonymous__33198) = cCoq_2emicromega_2eTauto_2eI___24a7(Vvar__0__TA__33187,Vvar__1__TX__33189,Vvar__2__AA__33191,Vvar__3__AF__33193,Vvar__4___24Anonymous__33195,Vvar__5___24Anonymous__33197,Vvar__6___24Anonymous__33199)
     => ( Vvar__6___24Anonymous__33198 = Vvar__6___24Anonymous__33199
        & Vvar__5___24Anonymous__33196 = Vvar__5___24Anonymous__33197
        & Vvar__4___24Anonymous__33194 = Vvar__4___24Anonymous__33195
        & Vvar__3__AF__33192 = Vvar__3__AF__33193
        & Vvar__2__AA__33190 = Vvar__2__AA__33191
        & Vvar__1__TX__33188 = Vvar__1__TX__33189
        & Vvar__0__TA__33186 = Vvar__0__TA__33187 ) ) ).

fof('$_inj_Coq.micromega.Tauto.N',axiom,
    ! [Vvar__0__TA__33176,Vvar__0__TA__33177,Vvar__1__TX__33178,Vvar__1__TX__33179,Vvar__2__AA__33180,Vvar__2__AA__33181,Vvar__3__AF__33182,Vvar__3__AF__33183,Vvar__4___24Anonymous__33184,Vvar__4___24Anonymous__33185] :
      ( cCoq_2emicromega_2eTauto_2eN___24a5(Vvar__0__TA__33176,Vvar__1__TX__33178,Vvar__2__AA__33180,Vvar__3__AF__33182,Vvar__4___24Anonymous__33184) = cCoq_2emicromega_2eTauto_2eN___24a5(Vvar__0__TA__33177,Vvar__1__TX__33179,Vvar__2__AA__33181,Vvar__3__AF__33183,Vvar__4___24Anonymous__33185)
     => ( Vvar__4___24Anonymous__33184 = Vvar__4___24Anonymous__33185
        & Vvar__3__AF__33182 = Vvar__3__AF__33183
        & Vvar__2__AA__33180 = Vvar__2__AA__33181
        & Vvar__1__TX__33178 = Vvar__1__TX__33179
        & Vvar__0__TA__33176 = Vvar__0__TA__33177 ) ) ).

fof('$_inj_Coq.micromega.Tauto.TT',axiom,
    ! [Vvar__0__TA__33114,Vvar__0__TA__33115,Vvar__1__TX__33116,Vvar__1__TX__33117,Vvar__2__AA__33118,Vvar__2__AA__33119,Vvar__3__AF__33120,Vvar__3__AF__33121] :
      ( cCoq_2emicromega_2eTauto_2eTT___24a4(Vvar__0__TA__33114,Vvar__1__TX__33116,Vvar__2__AA__33118,Vvar__3__AF__33120) = cCoq_2emicromega_2eTauto_2eTT___24a4(Vvar__0__TA__33115,Vvar__1__TX__33117,Vvar__2__AA__33119,Vvar__3__AF__33121)
     => ( Vvar__3__AF__33120 = Vvar__3__AF__33121
        & Vvar__2__AA__33118 = Vvar__2__AA__33119
        & Vvar__1__TX__33116 = Vvar__1__TX__33117
        & Vvar__0__TA__33114 = Vvar__0__TA__33115 ) ) ).

fof('$_inj_Coq.micromega.Tauto.X',axiom,
    ! [Vvar__0__TA__33130,Vvar__0__TA__33131,Vvar__1__TX__33132,Vvar__1__TX__33133,Vvar__2__AA__33134,Vvar__2__AA__33135,Vvar__3__AF__33136,Vvar__3__AF__33137,Vvar__4___24Anonymous__33138,Vvar__4___24Anonymous__33139] :
      ( cCoq_2emicromega_2eTauto_2eX___24a5(Vvar__0__TA__33130,Vvar__1__TX__33132,Vvar__2__AA__33134,Vvar__3__AF__33136,Vvar__4___24Anonymous__33138) = cCoq_2emicromega_2eTauto_2eX___24a5(Vvar__0__TA__33131,Vvar__1__TX__33133,Vvar__2__AA__33135,Vvar__3__AF__33137,Vvar__4___24Anonymous__33139)
     => ( Vvar__4___24Anonymous__33138 = Vvar__4___24Anonymous__33139
        & Vvar__3__AF__33136 = Vvar__3__AF__33137
        & Vvar__2__AA__33134 = Vvar__2__AA__33135
        & Vvar__1__TX__33132 = Vvar__1__TX__33133
        & Vvar__0__TA__33130 = Vvar__0__TA__33131 ) ) ).

fof('$_inj_Coq.setoid_ring.Field_theory.FEI',axiom,
    ! [Vvar__0__C__11795,Vvar__0__C__11796] :
      ( cCoq_2esetoid__ring_2eField__theory_2eFEI___24a1(Vvar__0__C__11795) = cCoq_2esetoid__ring_2eField__theory_2eFEI___24a1(Vvar__0__C__11796)
     => Vvar__0__C__11795 = Vvar__0__C__11796 ) ).

fof('$_inj_Coq.setoid_ring.Field_theory.FEO',axiom,
    ! [Vvar__0__C__11793,Vvar__0__C__11794] :
      ( cCoq_2esetoid__ring_2eField__theory_2eFEO___24a1(Vvar__0__C__11793) = cCoq_2esetoid__ring_2eField__theory_2eFEO___24a1(Vvar__0__C__11794)
     => Vvar__0__C__11793 = Vvar__0__C__11794 ) ).

fof('$_inj_Coq.setoid_ring.Field_theory.FEX',axiom,
    ! [Vvar__0__C__11801,Vvar__0__C__11802,Vvar__1___24Anonymous__11803,Vvar__1___24Anonymous__11804] :
      ( cCoq_2esetoid__ring_2eField__theory_2eFEX___24a2(Vvar__0__C__11801,Vvar__1___24Anonymous__11803) = cCoq_2esetoid__ring_2eField__theory_2eFEX___24a2(Vvar__0__C__11802,Vvar__1___24Anonymous__11804)
     => ( Vvar__1___24Anonymous__11803 = Vvar__1___24Anonymous__11804
        & Vvar__0__C__11801 = Vvar__0__C__11802 ) ) ).

fof('$_inj_Coq.setoid_ring.Field_theory.FEadd',axiom,
    ! [Vvar__0__C__11805,Vvar__0__C__11806,Vvar__1___24Anonymous__11807,Vvar__1___24Anonymous__11808,Vvar__2___24Anonymous__11809,Vvar__2___24Anonymous__11810] :
      ( cCoq_2esetoid__ring_2eField__theory_2eFEadd___24a3(Vvar__0__C__11805,Vvar__1___24Anonymous__11807,Vvar__2___24Anonymous__11809) = cCoq_2esetoid__ring_2eField__theory_2eFEadd___24a3(Vvar__0__C__11806,Vvar__1___24Anonymous__11808,Vvar__2___24Anonymous__11810)
     => ( Vvar__2___24Anonymous__11809 = Vvar__2___24Anonymous__11810
        & Vvar__1___24Anonymous__11807 = Vvar__1___24Anonymous__11808
        & Vvar__0__C__11805 = Vvar__0__C__11806 ) ) ).

fof('$_inj_Coq.setoid_ring.Field_theory.FEc',axiom,
    ! [Vvar__0__C__11797,Vvar__0__C__11798,Vvar__1___24Anonymous__11799,Vvar__1___24Anonymous__11800] :
      ( cCoq_2esetoid__ring_2eField__theory_2eFEc___24a2(Vvar__0__C__11797,Vvar__1___24Anonymous__11799) = cCoq_2esetoid__ring_2eField__theory_2eFEc___24a2(Vvar__0__C__11798,Vvar__1___24Anonymous__11800)
     => ( Vvar__1___24Anonymous__11799 = Vvar__1___24Anonymous__11800
        & Vvar__0__C__11797 = Vvar__0__C__11798 ) ) ).

fof('$_inj_Coq.setoid_ring.Field_theory.FEdiv',axiom,
    ! [Vvar__0__C__11831,Vvar__0__C__11832,Vvar__1___24Anonymous__11833,Vvar__1___24Anonymous__11834,Vvar__2___24Anonymous__11835,Vvar__2___24Anonymous__11836] :
      ( cCoq_2esetoid__ring_2eField__theory_2eFEdiv___24a3(Vvar__0__C__11831,Vvar__1___24Anonymous__11833,Vvar__2___24Anonymous__11835) = cCoq_2esetoid__ring_2eField__theory_2eFEdiv___24a3(Vvar__0__C__11832,Vvar__1___24Anonymous__11834,Vvar__2___24Anonymous__11836)
     => ( Vvar__2___24Anonymous__11835 = Vvar__2___24Anonymous__11836
        & Vvar__1___24Anonymous__11833 = Vvar__1___24Anonymous__11834
        & Vvar__0__C__11831 = Vvar__0__C__11832 ) ) ).

fof('$_inj_Coq.setoid_ring.Field_theory.FEinv',axiom,
    ! [Vvar__0__C__11827,Vvar__0__C__11828,Vvar__1___24Anonymous__11829,Vvar__1___24Anonymous__11830] :
      ( cCoq_2esetoid__ring_2eField__theory_2eFEinv___24a2(Vvar__0__C__11827,Vvar__1___24Anonymous__11829) = cCoq_2esetoid__ring_2eField__theory_2eFEinv___24a2(Vvar__0__C__11828,Vvar__1___24Anonymous__11830)
     => ( Vvar__1___24Anonymous__11829 = Vvar__1___24Anonymous__11830
        & Vvar__0__C__11827 = Vvar__0__C__11828 ) ) ).

fof('$_inj_Coq.setoid_ring.Field_theory.FEmul',axiom,
    ! [Vvar__0__C__11817,Vvar__0__C__11818,Vvar__1___24Anonymous__11819,Vvar__1___24Anonymous__11820,Vvar__2___24Anonymous__11821,Vvar__2___24Anonymous__11822] :
      ( cCoq_2esetoid__ring_2eField__theory_2eFEmul___24a3(Vvar__0__C__11817,Vvar__1___24Anonymous__11819,Vvar__2___24Anonymous__11821) = cCoq_2esetoid__ring_2eField__theory_2eFEmul___24a3(Vvar__0__C__11818,Vvar__1___24Anonymous__11820,Vvar__2___24Anonymous__11822)
     => ( Vvar__2___24Anonymous__11821 = Vvar__2___24Anonymous__11822
        & Vvar__1___24Anonymous__11819 = Vvar__1___24Anonymous__11820
        & Vvar__0__C__11817 = Vvar__0__C__11818 ) ) ).

fof('$_inj_Coq.setoid_ring.Field_theory.FEopp',axiom,
    ! [Vvar__0__C__11823,Vvar__0__C__11824,Vvar__1___24Anonymous__11825,Vvar__1___24Anonymous__11826] :
      ( cCoq_2esetoid__ring_2eField__theory_2eFEopp___24a2(Vvar__0__C__11823,Vvar__1___24Anonymous__11825) = cCoq_2esetoid__ring_2eField__theory_2eFEopp___24a2(Vvar__0__C__11824,Vvar__1___24Anonymous__11826)
     => ( Vvar__1___24Anonymous__11825 = Vvar__1___24Anonymous__11826
        & Vvar__0__C__11823 = Vvar__0__C__11824 ) ) ).

fof('$_inj_Coq.setoid_ring.Field_theory.FEpow',axiom,
    ! [Vvar__0__C__11837,Vvar__0__C__11838,Vvar__1___24Anonymous__11839,Vvar__1___24Anonymous__11840,Vvar__2___24Anonymous__11841,Vvar__2___24Anonymous__11842] :
      ( cCoq_2esetoid__ring_2eField__theory_2eFEpow___24a3(Vvar__0__C__11837,Vvar__1___24Anonymous__11839,Vvar__2___24Anonymous__11841) = cCoq_2esetoid__ring_2eField__theory_2eFEpow___24a3(Vvar__0__C__11838,Vvar__1___24Anonymous__11840,Vvar__2___24Anonymous__11842)
     => ( Vvar__2___24Anonymous__11841 = Vvar__2___24Anonymous__11842
        & Vvar__1___24Anonymous__11839 = Vvar__1___24Anonymous__11840
        & Vvar__0__C__11837 = Vvar__0__C__11838 ) ) ).

fof('$_inj_Coq.setoid_ring.Field_theory.FEsub',axiom,
    ! [Vvar__0__C__11811,Vvar__0__C__11812,Vvar__1___24Anonymous__11813,Vvar__1___24Anonymous__11814,Vvar__2___24Anonymous__11815,Vvar__2___24Anonymous__11816] :
      ( cCoq_2esetoid__ring_2eField__theory_2eFEsub___24a3(Vvar__0__C__11811,Vvar__1___24Anonymous__11813,Vvar__2___24Anonymous__11815) = cCoq_2esetoid__ring_2eField__theory_2eFEsub___24a3(Vvar__0__C__11812,Vvar__1___24Anonymous__11814,Vvar__2___24Anonymous__11816)
     => ( Vvar__2___24Anonymous__11815 = Vvar__2___24Anonymous__11816
        & Vvar__1___24Anonymous__11813 = Vvar__1___24Anonymous__11814
        & Vvar__0__C__11811 = Vvar__0__C__11812 ) ) ).

fof('$_inj_Coq.setoid_ring.Field_theory.mk_linear',axiom,
    ! [Vvar__0__C__12140,Vvar__0__C__12141,Vvar__1__num__12142,Vvar__1__num__12143,Vvar__2__denum__12144,Vvar__2__denum__12145,Vvar__3__condition__12146,Vvar__3__condition__12147] :
      ( cCoq_2esetoid__ring_2eField__theory_2emk__linear___24a4(Vvar__0__C__12140,Vvar__1__num__12142,Vvar__2__denum__12144,Vvar__3__condition__12146) = cCoq_2esetoid__ring_2eField__theory_2emk__linear___24a4(Vvar__0__C__12141,Vvar__1__num__12143,Vvar__2__denum__12145,Vvar__3__condition__12147)
     => ( Vvar__3__condition__12146 = Vvar__3__condition__12147
        & Vvar__2__denum__12144 = Vvar__2__denum__12145
        & Vvar__1__num__12142 = Vvar__1__num__12143
        & Vvar__0__C__12140 = Vvar__0__C__12141 ) ) ).

fof('$_inj_Coq.setoid_ring.Ring_polynom.PEI',axiom,
    ! [Vvar__0__C__15467,Vvar__0__C__15468] :
      ( cCoq_2esetoid__ring_2eRing__polynom_2ePEI___24a1(Vvar__0__C__15467) = cCoq_2esetoid__ring_2eRing__polynom_2ePEI___24a1(Vvar__0__C__15468)
     => Vvar__0__C__15467 = Vvar__0__C__15468 ) ).

fof('$_inj_Coq.setoid_ring.Ring_polynom.PEO',axiom,
    ! [Vvar__0__C__15465,Vvar__0__C__15466] :
      ( cCoq_2esetoid__ring_2eRing__polynom_2ePEO___24a1(Vvar__0__C__15465) = cCoq_2esetoid__ring_2eRing__polynom_2ePEO___24a1(Vvar__0__C__15466)
     => Vvar__0__C__15465 = Vvar__0__C__15466 ) ).

fof('$_inj_Coq.setoid_ring.Ring_polynom.PEX',axiom,
    ! [Vvar__0__C__15473,Vvar__0__C__15474,Vvar__1___24Anonymous__15475,Vvar__1___24Anonymous__15476] :
      ( cCoq_2esetoid__ring_2eRing__polynom_2ePEX___24a2(Vvar__0__C__15473,Vvar__1___24Anonymous__15475) = cCoq_2esetoid__ring_2eRing__polynom_2ePEX___24a2(Vvar__0__C__15474,Vvar__1___24Anonymous__15476)
     => ( Vvar__1___24Anonymous__15475 = Vvar__1___24Anonymous__15476
        & Vvar__0__C__15473 = Vvar__0__C__15474 ) ) ).

fof('$_inj_Coq.setoid_ring.Ring_polynom.PEadd',axiom,
    ! [Vvar__0__C__15477,Vvar__0__C__15478,Vvar__1___24Anonymous__15479,Vvar__1___24Anonymous__15480,Vvar__2___24Anonymous__15481,Vvar__2___24Anonymous__15482] :
      ( cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(Vvar__0__C__15477,Vvar__1___24Anonymous__15479,Vvar__2___24Anonymous__15481) = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(Vvar__0__C__15478,Vvar__1___24Anonymous__15480,Vvar__2___24Anonymous__15482)
     => ( Vvar__2___24Anonymous__15481 = Vvar__2___24Anonymous__15482
        & Vvar__1___24Anonymous__15479 = Vvar__1___24Anonymous__15480
        & Vvar__0__C__15477 = Vvar__0__C__15478 ) ) ).

fof('$_inj_Coq.setoid_ring.Ring_polynom.PEc',axiom,
    ! [Vvar__0__C__15469,Vvar__0__C__15470,Vvar__1___24Anonymous__15471,Vvar__1___24Anonymous__15472] :
      ( cCoq_2esetoid__ring_2eRing__polynom_2ePEc___24a2(Vvar__0__C__15469,Vvar__1___24Anonymous__15471) = cCoq_2esetoid__ring_2eRing__polynom_2ePEc___24a2(Vvar__0__C__15470,Vvar__1___24Anonymous__15472)
     => ( Vvar__1___24Anonymous__15471 = Vvar__1___24Anonymous__15472
        & Vvar__0__C__15469 = Vvar__0__C__15470 ) ) ).

fof('$_inj_Coq.setoid_ring.Ring_polynom.PEmul',axiom,
    ! [Vvar__0__C__15489,Vvar__0__C__15490,Vvar__1___24Anonymous__15491,Vvar__1___24Anonymous__15492,Vvar__2___24Anonymous__15493,Vvar__2___24Anonymous__15494] :
      ( cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(Vvar__0__C__15489,Vvar__1___24Anonymous__15491,Vvar__2___24Anonymous__15493) = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(Vvar__0__C__15490,Vvar__1___24Anonymous__15492,Vvar__2___24Anonymous__15494)
     => ( Vvar__2___24Anonymous__15493 = Vvar__2___24Anonymous__15494
        & Vvar__1___24Anonymous__15491 = Vvar__1___24Anonymous__15492
        & Vvar__0__C__15489 = Vvar__0__C__15490 ) ) ).

fof('$_inj_Coq.setoid_ring.Ring_polynom.PEopp',axiom,
    ! [Vvar__0__C__15495,Vvar__0__C__15496,Vvar__1___24Anonymous__15497,Vvar__1___24Anonymous__15498] :
      ( cCoq_2esetoid__ring_2eRing__polynom_2ePEopp___24a2(Vvar__0__C__15495,Vvar__1___24Anonymous__15497) = cCoq_2esetoid__ring_2eRing__polynom_2ePEopp___24a2(Vvar__0__C__15496,Vvar__1___24Anonymous__15498)
     => ( Vvar__1___24Anonymous__15497 = Vvar__1___24Anonymous__15498
        & Vvar__0__C__15495 = Vvar__0__C__15496 ) ) ).

fof('$_inj_Coq.setoid_ring.Ring_polynom.PEpow',axiom,
    ! [Vvar__0__C__15499,Vvar__0__C__15500,Vvar__1___24Anonymous__15501,Vvar__1___24Anonymous__15502,Vvar__2___24Anonymous__15503,Vvar__2___24Anonymous__15504] :
      ( cCoq_2esetoid__ring_2eRing__polynom_2ePEpow___24a3(Vvar__0__C__15499,Vvar__1___24Anonymous__15501,Vvar__2___24Anonymous__15503) = cCoq_2esetoid__ring_2eRing__polynom_2ePEpow___24a3(Vvar__0__C__15500,Vvar__1___24Anonymous__15502,Vvar__2___24Anonymous__15504)
     => ( Vvar__2___24Anonymous__15503 = Vvar__2___24Anonymous__15504
        & Vvar__1___24Anonymous__15501 = Vvar__1___24Anonymous__15502
        & Vvar__0__C__15499 = Vvar__0__C__15500 ) ) ).

fof('$_inj_Coq.setoid_ring.Ring_polynom.PEsub',axiom,
    ! [Vvar__0__C__15483,Vvar__0__C__15484,Vvar__1___24Anonymous__15485,Vvar__1___24Anonymous__15486,Vvar__2___24Anonymous__15487,Vvar__2___24Anonymous__15488] :
      ( cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(Vvar__0__C__15483,Vvar__1___24Anonymous__15485,Vvar__2___24Anonymous__15487) = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(Vvar__0__C__15484,Vvar__1___24Anonymous__15486,Vvar__2___24Anonymous__15488)
     => ( Vvar__2___24Anonymous__15487 = Vvar__2___24Anonymous__15488
        & Vvar__1___24Anonymous__15485 = Vvar__1___24Anonymous__15486
        & Vvar__0__C__15483 = Vvar__0__C__15484 ) ) ).

fof('$_inj_Coq.setoid_ring.Ring_polynom.PX',axiom,
    ! [Vvar__0__C__15122,Vvar__0__C__15123,Vvar__1___24Anonymous__15124,Vvar__1___24Anonymous__15125,Vvar__2___24Anonymous__15126,Vvar__2___24Anonymous__15127,Vvar__3___24Anonymous__15128,Vvar__3___24Anonymous__15129] :
      ( cCoq_2esetoid__ring_2eRing__polynom_2ePX___24a4(Vvar__0__C__15122,Vvar__1___24Anonymous__15124,Vvar__2___24Anonymous__15126,Vvar__3___24Anonymous__15128) = cCoq_2esetoid__ring_2eRing__polynom_2ePX___24a4(Vvar__0__C__15123,Vvar__1___24Anonymous__15125,Vvar__2___24Anonymous__15127,Vvar__3___24Anonymous__15129)
     => ( Vvar__3___24Anonymous__15128 = Vvar__3___24Anonymous__15129
        & Vvar__2___24Anonymous__15126 = Vvar__2___24Anonymous__15127
        & Vvar__1___24Anonymous__15124 = Vvar__1___24Anonymous__15125
        & Vvar__0__C__15122 = Vvar__0__C__15123 ) ) ).

fof('$_inj_Coq.setoid_ring.Ring_polynom.Pc',axiom,
    ! [Vvar__0__C__15112,Vvar__0__C__15113,Vvar__1___24Anonymous__15114,Vvar__1___24Anonymous__15115] :
      ( cCoq_2esetoid__ring_2eRing__polynom_2ePc___24a2(Vvar__0__C__15112,Vvar__1___24Anonymous__15114) = cCoq_2esetoid__ring_2eRing__polynom_2ePc___24a2(Vvar__0__C__15113,Vvar__1___24Anonymous__15115)
     => ( Vvar__1___24Anonymous__15114 = Vvar__1___24Anonymous__15115
        & Vvar__0__C__15112 = Vvar__0__C__15113 ) ) ).

fof('$_inj_Coq.setoid_ring.Ring_polynom.Pinj',axiom,
    ! [Vvar__0__C__15116,Vvar__0__C__15117,Vvar__1___24Anonymous__15118,Vvar__1___24Anonymous__15119,Vvar__2___24Anonymous__15120,Vvar__2___24Anonymous__15121] :
      ( cCoq_2esetoid__ring_2eRing__polynom_2ePinj___24a3(Vvar__0__C__15116,Vvar__1___24Anonymous__15118,Vvar__2___24Anonymous__15120) = cCoq_2esetoid__ring_2eRing__polynom_2ePinj___24a3(Vvar__0__C__15117,Vvar__1___24Anonymous__15119,Vvar__2___24Anonymous__15121)
     => ( Vvar__2___24Anonymous__15120 = Vvar__2___24Anonymous__15121
        & Vvar__1___24Anonymous__15118 = Vvar__1___24Anonymous__15119
        & Vvar__0__C__15116 = Vvar__0__C__15117 ) ) ).

fof('$_inj_Coq.setoid_ring.Ring_polynom.vmon',axiom,
    ! [Vvar__0___24Anonymous__15279,Vvar__0___24Anonymous__15280,Vvar__1___24Anonymous__15281,Vvar__1___24Anonymous__15282] :
      ( cCoq_2esetoid__ring_2eRing__polynom_2evmon___24a2(Vvar__0___24Anonymous__15279,Vvar__1___24Anonymous__15281) = cCoq_2esetoid__ring_2eRing__polynom_2evmon___24a2(Vvar__0___24Anonymous__15280,Vvar__1___24Anonymous__15282)
     => ( Vvar__1___24Anonymous__15281 = Vvar__1___24Anonymous__15282
        & Vvar__0___24Anonymous__15279 = Vvar__0___24Anonymous__15280 ) ) ).

fof('$_inj_Coq.setoid_ring.Ring_polynom.zmon',axiom,
    ! [Vvar__0___24Anonymous__15275,Vvar__0___24Anonymous__15276,Vvar__1___24Anonymous__15277,Vvar__1___24Anonymous__15278] :
      ( cCoq_2esetoid__ring_2eRing__polynom_2ezmon___24a2(Vvar__0___24Anonymous__15275,Vvar__1___24Anonymous__15277) = cCoq_2esetoid__ring_2eRing__polynom_2ezmon___24a2(Vvar__0___24Anonymous__15276,Vvar__1___24Anonymous__15278)
     => ( Vvar__1___24Anonymous__15277 = Vvar__1___24Anonymous__15278
        & Vvar__0___24Anonymous__15275 = Vvar__0___24Anonymous__15276 ) ) ).

fof('$_inj_Coq.setoid_ring.Ring_theory.Computational',axiom,
    ! [Vvar__0__R__18637,Vvar__0__R__18638,Vvar__1__req__18639,Vvar__1__req__18640,Vvar__2__reqb__18641,Vvar__2__reqb__18642,Vvar__3___24Anonymous__18643,Vvar__3___24Anonymous__18644] :
      ( cCoq_2esetoid__ring_2eRing__theory_2eComputational___24a3(Vvar__0__R__18637,Vvar__1__req__18639,Vvar__2__reqb__18641) = cCoq_2esetoid__ring_2eRing__theory_2eComputational___24a3(Vvar__0__R__18638,Vvar__1__req__18640,Vvar__2__reqb__18642)
     => ( c_24Proof = c_24Proof
        & Vvar__2__reqb__18641 = Vvar__2__reqb__18642
        & Vvar__1__req__18639 = Vvar__1__req__18640
        & Vvar__0__R__18637 = Vvar__0__R__18638 ) ) ).

fof('$_inj_Coq.setoid_ring.Ring_theory.Morphism',axiom,
    ! [Vvar__0__R__18645,Vvar__0__R__18646,Vvar__1__rO__18647,Vvar__1__rO__18648,Vvar__2__rI__18649,Vvar__2__rI__18650,Vvar__3__radd__18651,Vvar__3__radd__18652,Vvar__4__rmul__18653,Vvar__4__rmul__18654,Vvar__5__rsub__18655,Vvar__5__rsub__18656,Vvar__6__ropp__18657,Vvar__6__ropp__18658,Vvar__7__req__18659,Vvar__7__req__18660,Vvar__8__C__18661,Vvar__8__C__18662,Vvar__9__cO__18663,Vvar__9__cO__18664,Vvar__10__cI__18665,Vvar__10__cI__18666,Vvar__11__cadd__18667,Vvar__11__cadd__18668,Vvar__12__cmul__18669,Vvar__12__cmul__18670,Vvar__13__csub__18671,Vvar__13__csub__18672,Vvar__14__copp__18673,Vvar__14__copp__18674,Vvar__15__ceqb__18675,Vvar__15__ceqb__18676,Vvar__16__phi__18677,Vvar__16__phi__18678,Vvar__17___24Anonymous__18679,Vvar__17___24Anonymous__18680] :
      ( cCoq_2esetoid__ring_2eRing__theory_2eMorphism___24a17(Vvar__0__R__18645,Vvar__1__rO__18647,Vvar__2__rI__18649,Vvar__3__radd__18651,Vvar__4__rmul__18653,Vvar__5__rsub__18655,Vvar__6__ropp__18657,Vvar__7__req__18659,Vvar__8__C__18661,Vvar__9__cO__18663,Vvar__10__cI__18665,Vvar__11__cadd__18667,Vvar__12__cmul__18669,Vvar__13__csub__18671,Vvar__14__copp__18673,Vvar__15__ceqb__18675,Vvar__16__phi__18677) = cCoq_2esetoid__ring_2eRing__theory_2eMorphism___24a17(Vvar__0__R__18646,Vvar__1__rO__18648,Vvar__2__rI__18650,Vvar__3__radd__18652,Vvar__4__rmul__18654,Vvar__5__rsub__18656,Vvar__6__ropp__18658,Vvar__7__req__18660,Vvar__8__C__18662,Vvar__9__cO__18664,Vvar__10__cI__18666,Vvar__11__cadd__18668,Vvar__12__cmul__18670,Vvar__13__csub__18672,Vvar__14__copp__18674,Vvar__15__ceqb__18676,Vvar__16__phi__18678)
     => ( c_24Proof = c_24Proof
        & Vvar__16__phi__18677 = Vvar__16__phi__18678
        & Vvar__15__ceqb__18675 = Vvar__15__ceqb__18676
        & Vvar__14__copp__18673 = Vvar__14__copp__18674
        & Vvar__13__csub__18671 = Vvar__13__csub__18672
        & Vvar__12__cmul__18669 = Vvar__12__cmul__18670
        & Vvar__11__cadd__18667 = Vvar__11__cadd__18668
        & Vvar__10__cI__18665 = Vvar__10__cI__18666
        & Vvar__9__cO__18663 = Vvar__9__cO__18664
        & Vvar__8__C__18661 = Vvar__8__C__18662
        & Vvar__7__req__18659 = Vvar__7__req__18660
        & Vvar__6__ropp__18657 = Vvar__6__ropp__18658
        & Vvar__5__rsub__18655 = Vvar__5__rsub__18656
        & Vvar__4__rmul__18653 = Vvar__4__rmul__18654
        & Vvar__3__radd__18651 = Vvar__3__radd__18652
        & Vvar__2__rI__18649 = Vvar__2__rI__18650
        & Vvar__1__rO__18647 = Vvar__1__rO__18648
        & Vvar__0__R__18645 = Vvar__0__R__18646 ) ) ).

fof('$_inj_IntMap.Map.M0',axiom,
    ! [Vvar__0__A__76,Vvar__0__A__77] :
      ( cIntMap_2eMap_2eM0___24a1(Vvar__0__A__76) = cIntMap_2eMap_2eM0___24a1(Vvar__0__A__77)
     => Vvar__0__A__76 = Vvar__0__A__77 ) ).

fof('$_inj_IntMap.Map.M1',axiom,
    ! [Vvar__0__A__78,Vvar__0__A__79,Vvar__1___24Anonymous__80,Vvar__1___24Anonymous__81,Vvar__2___24Anonymous__82,Vvar__2___24Anonymous__83] :
      ( cIntMap_2eMap_2eM1___24a3(Vvar__0__A__78,Vvar__1___24Anonymous__80,Vvar__2___24Anonymous__82) = cIntMap_2eMap_2eM1___24a3(Vvar__0__A__79,Vvar__1___24Anonymous__81,Vvar__2___24Anonymous__83)
     => ( Vvar__2___24Anonymous__82 = Vvar__2___24Anonymous__83
        & Vvar__1___24Anonymous__80 = Vvar__1___24Anonymous__81
        & Vvar__0__A__78 = Vvar__0__A__79 ) ) ).

fof('$_inj_IntMap.Map.M2',axiom,
    ! [Vvar__0__A__84,Vvar__0__A__85,Vvar__1___24Anonymous__86,Vvar__1___24Anonymous__87,Vvar__2___24Anonymous__88,Vvar__2___24Anonymous__89] :
      ( cIntMap_2eMap_2eM2___24a3(Vvar__0__A__84,Vvar__1___24Anonymous__86,Vvar__2___24Anonymous__88) = cIntMap_2eMap_2eM2___24a3(Vvar__0__A__85,Vvar__1___24Anonymous__87,Vvar__2___24Anonymous__89)
     => ( Vvar__2___24Anonymous__88 = Vvar__2___24Anonymous__89
        & Vvar__1___24Anonymous__86 = Vvar__1___24Anonymous__87
        & Vvar__0__A__84 = Vvar__0__A__85 ) ) ).

fof('$_inversion_Coq.Arith.Even.even',axiom,
    ! [Vvar__0___24Anonymous__20102] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__20102)
     => ( cCoq_2eArith_2eEven_2eeven___24a1(Vvar__0___24Anonymous__20102)
       => ( Vvar__0___24Anonymous__20102 = cCoq_2eInit_2eDatatypes_2eO
          | ? [Vvar__0__n__20104] :
              ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0__n__20104)
              & cCoq_2eArith_2eEven_2eodd___24a1(Vvar__0__n__20104)
              & Vvar__0___24Anonymous__20102 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0__n__20104) ) ) ) ) ).

fof('$_inversion_Coq.Arith.Even.odd',axiom,
    ! [Vvar__0___24Anonymous__20106] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__20106)
     => ( cCoq_2eArith_2eEven_2eodd___24a1(Vvar__0___24Anonymous__20106)
       => ? [Vvar__0__n__20108] :
            ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0__n__20108)
            & cCoq_2eArith_2eEven_2eeven___24a1(Vvar__0__n__20108)
            & Vvar__0___24Anonymous__20106 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0__n__20108) ) ) ) ).

fof('$_inversion_Coq.Bool.Bool.reflect',axiom,
    ! [Vvar__0__P__19861,Vvar__1___24Anonymous__19862,VX19863] :
      ( cProp___24t(Vvar__0__P__19861)
     => ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__1___24Anonymous__19862)
       => ( cCoq_2eBool_2eBool_2ereflect___24t(Vvar__0__P__19861,Vvar__1___24Anonymous__19862,VX19863)
         => ( ( p(Vvar__0__P__19861)
              & Vvar__1___24Anonymous__19862 = cCoq_2eInit_2eDatatypes_2etrue
              & VX19863 = cCoq_2eBool_2eBool_2eReflectT___24a1(Vvar__0__P__19861) )
            | ( ~ p(Vvar__0__P__19861)
              & Vvar__1___24Anonymous__19862 = cCoq_2eInit_2eDatatypes_2efalse
              & VX19863 = cCoq_2eBool_2eBool_2eReflectF___24a1(Vvar__0__P__19861) ) ) ) ) ) ).

fof('$_inversion_Coq.FSets.FSetPositive.PositiveSet.tree',axiom,
    ! [VX19220] :
      ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree___24t(VX19220)
     => ( VX19220 = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eLeaf
        | ? [Vvar__0___24Anonymous__19221] :
            ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree___24t(Vvar__0___24Anonymous__19221)
            & ? [Vvar__1___24Anonymous__19222] :
                ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__1___24Anonymous__19222)
                & ? [Vvar__2___24Anonymous__19223] :
                    ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree___24t(Vvar__2___24Anonymous__19223)
                    & VX19220 = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eNode___24a3(Vvar__0___24Anonymous__19221,Vvar__1___24Anonymous__19222,Vvar__2___24Anonymous__19223) ) ) ) ) ) ).

fof('$_inversion_Coq.Init.Byte.byte',axiom,
    ! [VX2694] :
      ( cCoq_2eInit_2eByte_2ebyte___24t(VX2694)
     => ( VX2694 = cCoq_2eInit_2eByte_2ex00
        | VX2694 = cCoq_2eInit_2eByte_2ex01
        | VX2694 = cCoq_2eInit_2eByte_2ex02
        | VX2694 = cCoq_2eInit_2eByte_2ex03
        | VX2694 = cCoq_2eInit_2eByte_2ex04
        | VX2694 = cCoq_2eInit_2eByte_2ex05
        | VX2694 = cCoq_2eInit_2eByte_2ex06
        | VX2694 = cCoq_2eInit_2eByte_2ex07
        | VX2694 = cCoq_2eInit_2eByte_2ex08
        | VX2694 = cCoq_2eInit_2eByte_2ex09
        | VX2694 = cCoq_2eInit_2eByte_2ex0a
        | VX2694 = cCoq_2eInit_2eByte_2ex0b
        | VX2694 = cCoq_2eInit_2eByte_2ex0c
        | VX2694 = cCoq_2eInit_2eByte_2ex0d
        | VX2694 = cCoq_2eInit_2eByte_2ex0e
        | VX2694 = cCoq_2eInit_2eByte_2ex0f
        | VX2694 = cCoq_2eInit_2eByte_2ex10
        | VX2694 = cCoq_2eInit_2eByte_2ex11
        | VX2694 = cCoq_2eInit_2eByte_2ex12
        | VX2694 = cCoq_2eInit_2eByte_2ex13
        | VX2694 = cCoq_2eInit_2eByte_2ex14
        | VX2694 = cCoq_2eInit_2eByte_2ex15
        | VX2694 = cCoq_2eInit_2eByte_2ex16
        | VX2694 = cCoq_2eInit_2eByte_2ex17
        | VX2694 = cCoq_2eInit_2eByte_2ex18
        | VX2694 = cCoq_2eInit_2eByte_2ex19
        | VX2694 = cCoq_2eInit_2eByte_2ex1a
        | VX2694 = cCoq_2eInit_2eByte_2ex1b
        | VX2694 = cCoq_2eInit_2eByte_2ex1c
        | VX2694 = cCoq_2eInit_2eByte_2ex1d
        | VX2694 = cCoq_2eInit_2eByte_2ex1e
        | VX2694 = cCoq_2eInit_2eByte_2ex1f
        | VX2694 = cCoq_2eInit_2eByte_2ex20
        | VX2694 = cCoq_2eInit_2eByte_2ex21
        | VX2694 = cCoq_2eInit_2eByte_2ex22
        | VX2694 = cCoq_2eInit_2eByte_2ex23
        | VX2694 = cCoq_2eInit_2eByte_2ex24
        | VX2694 = cCoq_2eInit_2eByte_2ex25
        | VX2694 = cCoq_2eInit_2eByte_2ex26
        | VX2694 = cCoq_2eInit_2eByte_2ex27
        | VX2694 = cCoq_2eInit_2eByte_2ex28
        | VX2694 = cCoq_2eInit_2eByte_2ex29
        | VX2694 = cCoq_2eInit_2eByte_2ex2a
        | VX2694 = cCoq_2eInit_2eByte_2ex2b
        | VX2694 = cCoq_2eInit_2eByte_2ex2c
        | VX2694 = cCoq_2eInit_2eByte_2ex2d
        | VX2694 = cCoq_2eInit_2eByte_2ex2e
        | VX2694 = cCoq_2eInit_2eByte_2ex2f
        | VX2694 = cCoq_2eInit_2eByte_2ex30
        | VX2694 = cCoq_2eInit_2eByte_2ex31
        | VX2694 = cCoq_2eInit_2eByte_2ex32
        | VX2694 = cCoq_2eInit_2eByte_2ex33
        | VX2694 = cCoq_2eInit_2eByte_2ex34
        | VX2694 = cCoq_2eInit_2eByte_2ex35
        | VX2694 = cCoq_2eInit_2eByte_2ex36
        | VX2694 = cCoq_2eInit_2eByte_2ex37
        | VX2694 = cCoq_2eInit_2eByte_2ex38
        | VX2694 = cCoq_2eInit_2eByte_2ex39
        | VX2694 = cCoq_2eInit_2eByte_2ex3a
        | VX2694 = cCoq_2eInit_2eByte_2ex3b
        | VX2694 = cCoq_2eInit_2eByte_2ex3c
        | VX2694 = cCoq_2eInit_2eByte_2ex3d
        | VX2694 = cCoq_2eInit_2eByte_2ex3e
        | VX2694 = cCoq_2eInit_2eByte_2ex3f
        | VX2694 = cCoq_2eInit_2eByte_2ex40
        | VX2694 = cCoq_2eInit_2eByte_2ex41
        | VX2694 = cCoq_2eInit_2eByte_2ex42
        | VX2694 = cCoq_2eInit_2eByte_2ex43
        | VX2694 = cCoq_2eInit_2eByte_2ex44
        | VX2694 = cCoq_2eInit_2eByte_2ex45
        | VX2694 = cCoq_2eInit_2eByte_2ex46
        | VX2694 = cCoq_2eInit_2eByte_2ex47
        | VX2694 = cCoq_2eInit_2eByte_2ex48
        | VX2694 = cCoq_2eInit_2eByte_2ex49
        | VX2694 = cCoq_2eInit_2eByte_2ex4a
        | VX2694 = cCoq_2eInit_2eByte_2ex4b
        | VX2694 = cCoq_2eInit_2eByte_2ex4c
        | VX2694 = cCoq_2eInit_2eByte_2ex4d
        | VX2694 = cCoq_2eInit_2eByte_2ex4e
        | VX2694 = cCoq_2eInit_2eByte_2ex4f
        | VX2694 = cCoq_2eInit_2eByte_2ex50
        | VX2694 = cCoq_2eInit_2eByte_2ex51
        | VX2694 = cCoq_2eInit_2eByte_2ex52
        | VX2694 = cCoq_2eInit_2eByte_2ex53
        | VX2694 = cCoq_2eInit_2eByte_2ex54
        | VX2694 = cCoq_2eInit_2eByte_2ex55
        | VX2694 = cCoq_2eInit_2eByte_2ex56
        | VX2694 = cCoq_2eInit_2eByte_2ex57
        | VX2694 = cCoq_2eInit_2eByte_2ex58
        | VX2694 = cCoq_2eInit_2eByte_2ex59
        | VX2694 = cCoq_2eInit_2eByte_2ex5a
        | VX2694 = cCoq_2eInit_2eByte_2ex5b
        | VX2694 = cCoq_2eInit_2eByte_2ex5c
        | VX2694 = cCoq_2eInit_2eByte_2ex5d
        | VX2694 = cCoq_2eInit_2eByte_2ex5e
        | VX2694 = cCoq_2eInit_2eByte_2ex5f
        | VX2694 = cCoq_2eInit_2eByte_2ex60
        | VX2694 = cCoq_2eInit_2eByte_2ex61
        | VX2694 = cCoq_2eInit_2eByte_2ex62
        | VX2694 = cCoq_2eInit_2eByte_2ex63
        | VX2694 = cCoq_2eInit_2eByte_2ex64
        | VX2694 = cCoq_2eInit_2eByte_2ex65
        | VX2694 = cCoq_2eInit_2eByte_2ex66
        | VX2694 = cCoq_2eInit_2eByte_2ex67
        | VX2694 = cCoq_2eInit_2eByte_2ex68
        | VX2694 = cCoq_2eInit_2eByte_2ex69
        | VX2694 = cCoq_2eInit_2eByte_2ex6a
        | VX2694 = cCoq_2eInit_2eByte_2ex6b
        | VX2694 = cCoq_2eInit_2eByte_2ex6c
        | VX2694 = cCoq_2eInit_2eByte_2ex6d
        | VX2694 = cCoq_2eInit_2eByte_2ex6e
        | VX2694 = cCoq_2eInit_2eByte_2ex6f
        | VX2694 = cCoq_2eInit_2eByte_2ex70
        | VX2694 = cCoq_2eInit_2eByte_2ex71
        | VX2694 = cCoq_2eInit_2eByte_2ex72
        | VX2694 = cCoq_2eInit_2eByte_2ex73
        | VX2694 = cCoq_2eInit_2eByte_2ex74
        | VX2694 = cCoq_2eInit_2eByte_2ex75
        | VX2694 = cCoq_2eInit_2eByte_2ex76
        | VX2694 = cCoq_2eInit_2eByte_2ex77
        | VX2694 = cCoq_2eInit_2eByte_2ex78
        | VX2694 = cCoq_2eInit_2eByte_2ex79
        | VX2694 = cCoq_2eInit_2eByte_2ex7a
        | VX2694 = cCoq_2eInit_2eByte_2ex7b
        | VX2694 = cCoq_2eInit_2eByte_2ex7c
        | VX2694 = cCoq_2eInit_2eByte_2ex7d
        | VX2694 = cCoq_2eInit_2eByte_2ex7e
        | VX2694 = cCoq_2eInit_2eByte_2ex7f
        | VX2694 = cCoq_2eInit_2eByte_2ex80
        | VX2694 = cCoq_2eInit_2eByte_2ex81
        | VX2694 = cCoq_2eInit_2eByte_2ex82
        | VX2694 = cCoq_2eInit_2eByte_2ex83
        | VX2694 = cCoq_2eInit_2eByte_2ex84
        | VX2694 = cCoq_2eInit_2eByte_2ex85
        | VX2694 = cCoq_2eInit_2eByte_2ex86
        | VX2694 = cCoq_2eInit_2eByte_2ex87
        | VX2694 = cCoq_2eInit_2eByte_2ex88
        | VX2694 = cCoq_2eInit_2eByte_2ex89
        | VX2694 = cCoq_2eInit_2eByte_2ex8a
        | VX2694 = cCoq_2eInit_2eByte_2ex8b
        | VX2694 = cCoq_2eInit_2eByte_2ex8c
        | VX2694 = cCoq_2eInit_2eByte_2ex8d
        | VX2694 = cCoq_2eInit_2eByte_2ex8e
        | VX2694 = cCoq_2eInit_2eByte_2ex8f
        | VX2694 = cCoq_2eInit_2eByte_2ex90
        | VX2694 = cCoq_2eInit_2eByte_2ex91
        | VX2694 = cCoq_2eInit_2eByte_2ex92
        | VX2694 = cCoq_2eInit_2eByte_2ex93
        | VX2694 = cCoq_2eInit_2eByte_2ex94
        | VX2694 = cCoq_2eInit_2eByte_2ex95
        | VX2694 = cCoq_2eInit_2eByte_2ex96
        | VX2694 = cCoq_2eInit_2eByte_2ex97
        | VX2694 = cCoq_2eInit_2eByte_2ex98
        | VX2694 = cCoq_2eInit_2eByte_2ex99
        | VX2694 = cCoq_2eInit_2eByte_2ex9a
        | VX2694 = cCoq_2eInit_2eByte_2ex9b
        | VX2694 = cCoq_2eInit_2eByte_2ex9c
        | VX2694 = cCoq_2eInit_2eByte_2ex9d
        | VX2694 = cCoq_2eInit_2eByte_2ex9e
        | VX2694 = cCoq_2eInit_2eByte_2ex9f
        | VX2694 = cCoq_2eInit_2eByte_2exa0
        | VX2694 = cCoq_2eInit_2eByte_2exa1
        | VX2694 = cCoq_2eInit_2eByte_2exa2
        | VX2694 = cCoq_2eInit_2eByte_2exa3
        | VX2694 = cCoq_2eInit_2eByte_2exa4
        | VX2694 = cCoq_2eInit_2eByte_2exa5
        | VX2694 = cCoq_2eInit_2eByte_2exa6
        | VX2694 = cCoq_2eInit_2eByte_2exa7
        | VX2694 = cCoq_2eInit_2eByte_2exa8
        | VX2694 = cCoq_2eInit_2eByte_2exa9
        | VX2694 = cCoq_2eInit_2eByte_2exaa
        | VX2694 = cCoq_2eInit_2eByte_2exab
        | VX2694 = cCoq_2eInit_2eByte_2exac
        | VX2694 = cCoq_2eInit_2eByte_2exad
        | VX2694 = cCoq_2eInit_2eByte_2exae
        | VX2694 = cCoq_2eInit_2eByte_2exaf
        | VX2694 = cCoq_2eInit_2eByte_2exb0
        | VX2694 = cCoq_2eInit_2eByte_2exb1
        | VX2694 = cCoq_2eInit_2eByte_2exb2
        | VX2694 = cCoq_2eInit_2eByte_2exb3
        | VX2694 = cCoq_2eInit_2eByte_2exb4
        | VX2694 = cCoq_2eInit_2eByte_2exb5
        | VX2694 = cCoq_2eInit_2eByte_2exb6
        | VX2694 = cCoq_2eInit_2eByte_2exb7
        | VX2694 = cCoq_2eInit_2eByte_2exb8
        | VX2694 = cCoq_2eInit_2eByte_2exb9
        | VX2694 = cCoq_2eInit_2eByte_2exba
        | VX2694 = cCoq_2eInit_2eByte_2exbb
        | VX2694 = cCoq_2eInit_2eByte_2exbc
        | VX2694 = cCoq_2eInit_2eByte_2exbd
        | VX2694 = cCoq_2eInit_2eByte_2exbe
        | VX2694 = cCoq_2eInit_2eByte_2exbf
        | VX2694 = cCoq_2eInit_2eByte_2exc0
        | VX2694 = cCoq_2eInit_2eByte_2exc1
        | VX2694 = cCoq_2eInit_2eByte_2exc2
        | VX2694 = cCoq_2eInit_2eByte_2exc3
        | VX2694 = cCoq_2eInit_2eByte_2exc4
        | VX2694 = cCoq_2eInit_2eByte_2exc5
        | VX2694 = cCoq_2eInit_2eByte_2exc6
        | VX2694 = cCoq_2eInit_2eByte_2exc7
        | VX2694 = cCoq_2eInit_2eByte_2exc8
        | VX2694 = cCoq_2eInit_2eByte_2exc9
        | VX2694 = cCoq_2eInit_2eByte_2exca
        | VX2694 = cCoq_2eInit_2eByte_2excb
        | VX2694 = cCoq_2eInit_2eByte_2excc
        | VX2694 = cCoq_2eInit_2eByte_2excd
        | VX2694 = cCoq_2eInit_2eByte_2exce
        | VX2694 = cCoq_2eInit_2eByte_2excf
        | VX2694 = cCoq_2eInit_2eByte_2exd0
        | VX2694 = cCoq_2eInit_2eByte_2exd1
        | VX2694 = cCoq_2eInit_2eByte_2exd2
        | VX2694 = cCoq_2eInit_2eByte_2exd3
        | VX2694 = cCoq_2eInit_2eByte_2exd4
        | VX2694 = cCoq_2eInit_2eByte_2exd5
        | VX2694 = cCoq_2eInit_2eByte_2exd6
        | VX2694 = cCoq_2eInit_2eByte_2exd7
        | VX2694 = cCoq_2eInit_2eByte_2exd8
        | VX2694 = cCoq_2eInit_2eByte_2exd9
        | VX2694 = cCoq_2eInit_2eByte_2exda
        | VX2694 = cCoq_2eInit_2eByte_2exdb
        | VX2694 = cCoq_2eInit_2eByte_2exdc
        | VX2694 = cCoq_2eInit_2eByte_2exdd
        | VX2694 = cCoq_2eInit_2eByte_2exde
        | VX2694 = cCoq_2eInit_2eByte_2exdf
        | VX2694 = cCoq_2eInit_2eByte_2exe0
        | VX2694 = cCoq_2eInit_2eByte_2exe1
        | VX2694 = cCoq_2eInit_2eByte_2exe2
        | VX2694 = cCoq_2eInit_2eByte_2exe3
        | VX2694 = cCoq_2eInit_2eByte_2exe4
        | VX2694 = cCoq_2eInit_2eByte_2exe5
        | VX2694 = cCoq_2eInit_2eByte_2exe6
        | VX2694 = cCoq_2eInit_2eByte_2exe7
        | VX2694 = cCoq_2eInit_2eByte_2exe8
        | VX2694 = cCoq_2eInit_2eByte_2exe9
        | VX2694 = cCoq_2eInit_2eByte_2exea
        | VX2694 = cCoq_2eInit_2eByte_2exeb
        | VX2694 = cCoq_2eInit_2eByte_2exec
        | VX2694 = cCoq_2eInit_2eByte_2exed
        | VX2694 = cCoq_2eInit_2eByte_2exee
        | VX2694 = cCoq_2eInit_2eByte_2exef
        | VX2694 = cCoq_2eInit_2eByte_2exf0
        | VX2694 = cCoq_2eInit_2eByte_2exf1
        | VX2694 = cCoq_2eInit_2eByte_2exf2
        | VX2694 = cCoq_2eInit_2eByte_2exf3
        | VX2694 = cCoq_2eInit_2eByte_2exf4
        | VX2694 = cCoq_2eInit_2eByte_2exf5
        | VX2694 = cCoq_2eInit_2eByte_2exf6
        | VX2694 = cCoq_2eInit_2eByte_2exf7
        | VX2694 = cCoq_2eInit_2eByte_2exf8
        | VX2694 = cCoq_2eInit_2eByte_2exf9
        | VX2694 = cCoq_2eInit_2eByte_2exfa
        | VX2694 = cCoq_2eInit_2eByte_2exfb
        | VX2694 = cCoq_2eInit_2eByte_2exfc
        | VX2694 = cCoq_2eInit_2eByte_2exfd
        | VX2694 = cCoq_2eInit_2eByte_2exfe
        | VX2694 = cCoq_2eInit_2eByte_2exff ) ) ).

fof('$_inversion_Coq.Init.Datatypes.CompareSpec',axiom,
    ! [Vvar__0__Peq__19893,Vvar__1__Plt__19894,Vvar__2__Pgt__19895,Vvar__3___24Anonymous__19896] :
      ( cProp___24t(Vvar__0__Peq__19893)
     => ( cProp___24t(Vvar__1__Plt__19894)
       => ( cProp___24t(Vvar__2__Pgt__19895)
         => ( cCoq_2eInit_2eDatatypes_2ecomparison___24t(Vvar__3___24Anonymous__19896)
           => ( cCoq_2eInit_2eDatatypes_2eCompareSpec___24a4(Vvar__0__Peq__19893,Vvar__1__Plt__19894,Vvar__2__Pgt__19895,Vvar__3___24Anonymous__19896)
             => ( ( p(Vvar__0__Peq__19893)
                  & Vvar__3___24Anonymous__19896 = cCoq_2eInit_2eDatatypes_2eEq )
                | ( p(Vvar__1__Plt__19894)
                  & Vvar__3___24Anonymous__19896 = cCoq_2eInit_2eDatatypes_2eLt )
                | ( p(Vvar__2__Pgt__19895)
                  & Vvar__3___24Anonymous__19896 = cCoq_2eInit_2eDatatypes_2eGt ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.Init.Datatypes.CompareSpecT',axiom,
    ! [Vvar__0__Peq__19910,Vvar__1__Plt__19911,Vvar__2__Pgt__19912,Vvar__3___24Anonymous__19913,VX19914] :
      ( cProp___24t(Vvar__0__Peq__19910)
     => ( cProp___24t(Vvar__1__Plt__19911)
       => ( cProp___24t(Vvar__2__Pgt__19912)
         => ( cCoq_2eInit_2eDatatypes_2ecomparison___24t(Vvar__3___24Anonymous__19913)
           => ( cCoq_2eInit_2eDatatypes_2eCompareSpecT___24t(Vvar__0__Peq__19910,Vvar__1__Plt__19911,Vvar__2__Pgt__19912,Vvar__3___24Anonymous__19913,VX19914)
             => ( ( p(Vvar__0__Peq__19910)
                  & Vvar__3___24Anonymous__19913 = cCoq_2eInit_2eDatatypes_2eEq
                  & VX19914 = cCoq_2eInit_2eDatatypes_2eCompEqT___24a3(Vvar__0__Peq__19910,Vvar__1__Plt__19911,Vvar__2__Pgt__19912) )
                | ( p(Vvar__1__Plt__19911)
                  & Vvar__3___24Anonymous__19913 = cCoq_2eInit_2eDatatypes_2eLt
                  & VX19914 = cCoq_2eInit_2eDatatypes_2eCompLtT___24a3(Vvar__0__Peq__19910,Vvar__1__Plt__19911,Vvar__2__Pgt__19912) )
                | ( p(Vvar__2__Pgt__19912)
                  & Vvar__3___24Anonymous__19913 = cCoq_2eInit_2eDatatypes_2eGt
                  & VX19914 = cCoq_2eInit_2eDatatypes_2eCompGtT___24a3(Vvar__0__Peq__19910,Vvar__1__Plt__19911,Vvar__2__Pgt__19912) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.Init.Datatypes.bool',axiom,
    ! [VX30] :
      ( cCoq_2eInit_2eDatatypes_2ebool___24t(VX30)
     => ( VX30 = cCoq_2eInit_2eDatatypes_2etrue
        | VX30 = cCoq_2eInit_2eDatatypes_2efalse ) ) ).

fof('$_inversion_Coq.Init.Datatypes.comparison',axiom,
    ! [VX10987] :
      ( cCoq_2eInit_2eDatatypes_2ecomparison___24t(VX10987)
     => ( VX10987 = cCoq_2eInit_2eDatatypes_2eEq
        | VX10987 = cCoq_2eInit_2eDatatypes_2eLt
        | VX10987 = cCoq_2eInit_2eDatatypes_2eGt ) ) ).

fof('$_inversion_Coq.Init.Datatypes.list',axiom,
    ! [Vvar__0__A__1030,VX1031] :
      ( cType___24t(Vvar__0__A__1030)
     => ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__1030,VX1031)
       => ( VX1031 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__1030)
          | ? [Vvar__1___24Anonymous__1034] :
              ( t(Vvar__1___24Anonymous__1034,Vvar__0__A__1030)
              & ? [Vvar__2___24Anonymous__1035] :
                  ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__1030,Vvar__2___24Anonymous__1035)
                  & VX1031 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__1030,Vvar__1___24Anonymous__1034,Vvar__2___24Anonymous__1035) ) ) ) ) ) ).

fof('$_inversion_Coq.Init.Datatypes.nat',axiom,
    ! [VX453] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(VX453)
     => ( VX453 = cCoq_2eInit_2eDatatypes_2eO
        | ? [Vvar__0___24Anonymous__454] :
            ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__454)
            & VX453 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__454) ) ) ) ).

fof('$_inversion_Coq.Init.Datatypes.option',axiom,
    ! [Vvar__0__A__31,VX32] :
      ( cType___24t(Vvar__0__A__31)
     => ( cCoq_2eInit_2eDatatypes_2eoption___24t(Vvar__0__A__31,VX32)
       => ( ? [Vvar__1___24Anonymous__34] :
              ( t(Vvar__1___24Anonymous__34,Vvar__0__A__31)
              & VX32 = cCoq_2eInit_2eDatatypes_2eSome___24a2(Vvar__0__A__31,Vvar__1___24Anonymous__34) )
          | VX32 = cCoq_2eInit_2eDatatypes_2eNone___24a1(Vvar__0__A__31) ) ) ) ).

fof('$_inversion_Coq.Init.Datatypes.prod',axiom,
    ! [Vvar__0__A__1012,Vvar__1__B__1013,VX1014] :
      ( cType___24t(Vvar__0__A__1012)
     => ( cType___24t(Vvar__1__B__1013)
       => ( cCoq_2eInit_2eDatatypes_2eprod___24t(Vvar__0__A__1012,Vvar__1__B__1013,VX1014)
         => ? [Vvar__2___24Anonymous__1017] :
              ( t(Vvar__2___24Anonymous__1017,Vvar__0__A__1012)
              & ? [Vvar__3___24Anonymous__1018] :
                  ( t(Vvar__3___24Anonymous__1018,Vvar__1__B__1013)
                  & VX1014 = cCoq_2eInit_2eDatatypes_2epair___24a4(Vvar__0__A__1012,Vvar__1__B__1013,Vvar__2___24Anonymous__1017,Vvar__3___24Anonymous__1018) ) ) ) ) ) ).

fof('$_inversion_Coq.Init.Datatypes.sum',axiom,
    ! [Vvar__0__A__10804,Vvar__1__B__10805,VX10806] :
      ( cType___24t(Vvar__0__A__10804)
     => ( cType___24t(Vvar__1__B__10805)
       => ( cCoq_2eInit_2eDatatypes_2esum___24t(Vvar__0__A__10804,Vvar__1__B__10805,VX10806)
         => ( ? [Vvar__2___24Anonymous__10809] :
                ( t(Vvar__2___24Anonymous__10809,Vvar__0__A__10804)
                & VX10806 = cCoq_2eInit_2eDatatypes_2einl___24a3(Vvar__0__A__10804,Vvar__1__B__10805,Vvar__2___24Anonymous__10809) )
            | ? [Vvar__2___24Anonymous__10812] :
                ( t(Vvar__2___24Anonymous__10812,Vvar__1__B__10805)
                & VX10806 = cCoq_2eInit_2eDatatypes_2einr___24a3(Vvar__0__A__10804,Vvar__1__B__10805,Vvar__2___24Anonymous__10812) ) ) ) ) ) ).

fof('$_inversion_Coq.Init.Datatypes.unit',axiom,
    ! [VX1824] :
      ( cCoq_2eInit_2eDatatypes_2eunit___24t(VX1824)
     => VX1824 = cCoq_2eInit_2eDatatypes_2ett ) ).

fof('$_inversion_Coq.Init.Peano.le',axiom,
    ! [Vvar__0__n__1788,Vvar__1___24Anonymous__1789] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0__n__1788)
     => ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__1___24Anonymous__1789)
       => ( cCoq_2eInit_2ePeano_2ele___24a2(Vvar__0__n__1788,Vvar__1___24Anonymous__1789)
         => ( Vvar__1___24Anonymous__1789 = Vvar__0__n__1788
            | ? [Vvar__1__m__1793] :
                ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__1__m__1793)
                & cCoq_2eInit_2ePeano_2ele___24a2(Vvar__0__n__1788,Vvar__1__m__1793)
                & Vvar__1___24Anonymous__1789 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__1__m__1793) ) ) ) ) ) ).

fof('$_inversion_Coq.Init.Specif.sig',axiom,
    ! [Vvar__0__A__791,Vvar__1__P__792,VX795] :
      ( cType___24t(Vvar__0__A__791)
     => ( c_24__type__805___24t(Vvar__0__A__791,Vvar__1__P__792,Vvar__1__P__792)
       => ( cCoq_2eInit_2eSpecif_2esig___24t(Vvar__0__A__791,Vvar__1__P__792,VX795)
         => ? [Vvar__2__x__800] :
              ( t(Vvar__2__x__800,Vvar__0__A__791)
              & p(happ(Vvar__1__P__792,Vvar__2__x__800))
              & VX795 = cCoq_2eInit_2eSpecif_2eexist___24a3(Vvar__0__A__791,Vvar__1__P__792,Vvar__2__x__800) ) ) ) ) ).

fof('$_inversion_Coq.Init.Specif.sig2',axiom,
    ! [Vvar__0__A__32692,Vvar__1__P__32693,Vvar__2__Q__32696,VX32699] :
      ( cType___24t(Vvar__0__A__32692)
     => ( c_24__type__32716___24t(Vvar__0__A__32692,Vvar__1__P__32693,Vvar__2__Q__32696,Vvar__1__P__32693)
       => ( c_24__type__32724___24t(Vvar__0__A__32692,Vvar__1__P__32693,Vvar__2__Q__32696,Vvar__2__Q__32696)
         => ( cCoq_2eInit_2eSpecif_2esig2___24t(Vvar__0__A__32692,Vvar__1__P__32693,Vvar__2__Q__32696,VX32699)
           => ? [Vvar__3__x__32707] :
                ( t(Vvar__3__x__32707,Vvar__0__A__32692)
                & p(happ(Vvar__1__P__32693,Vvar__3__x__32707))
                & p(happ(Vvar__2__Q__32696,Vvar__3__x__32707))
                & VX32699 = cCoq_2eInit_2eSpecif_2eexist2___24a4(Vvar__0__A__32692,Vvar__1__P__32693,Vvar__2__Q__32696,Vvar__3__x__32707) ) ) ) ) ) ).

fof('$_inversion_Coq.Init.Specif.sigT',axiom,
    ! [Vvar__0__A__18723,Vvar__1__P__18724,VX18727] :
      ( cType___24t(Vvar__0__A__18723)
     => ( c_24__type__18737___24t(Vvar__0__A__18723,Vvar__1__P__18724,Vvar__1__P__18724)
       => ( cCoq_2eInit_2eSpecif_2esigT___24t(Vvar__0__A__18723,Vvar__1__P__18724,VX18727)
         => ? [Vvar__2__x__18732] :
              ( t(Vvar__2__x__18732,Vvar__0__A__18723)
              & ? [Vvar__3___24Anonymous__18733] :
                  ( t(Vvar__3___24Anonymous__18733,happ(Vvar__1__P__18724,Vvar__2__x__18732))
                  & VX18727 = cCoq_2eInit_2eSpecif_2eexistT___24a4(Vvar__0__A__18723,Vvar__1__P__18724,Vvar__2__x__18732,Vvar__3___24Anonymous__18733) ) ) ) ) ) ).

fof('$_inversion_Coq.Init.Specif.sigT2',axiom,
    ! [Vvar__0__A__18828,Vvar__1__P__18829,Vvar__2__Q__18832,VX18835] :
      ( cType___24t(Vvar__0__A__18828)
     => ( c_24__type__18852___24t(Vvar__0__A__18828,Vvar__1__P__18829,Vvar__2__Q__18832,Vvar__1__P__18829)
       => ( c_24__type__18860___24t(Vvar__0__A__18828,Vvar__1__P__18829,Vvar__2__Q__18832,Vvar__2__Q__18832)
         => ( cCoq_2eInit_2eSpecif_2esigT2___24t(Vvar__0__A__18828,Vvar__1__P__18829,Vvar__2__Q__18832,VX18835)
           => ? [Vvar__3__x__18843] :
                ( t(Vvar__3__x__18843,Vvar__0__A__18828)
                & ? [Vvar__4___24Anonymous__18844] :
                    ( t(Vvar__4___24Anonymous__18844,happ(Vvar__1__P__18829,Vvar__3__x__18843))
                    & ? [Vvar__5___24Anonymous__18845] :
                        ( t(Vvar__5___24Anonymous__18845,happ(Vvar__2__Q__18832,Vvar__3__x__18843))
                        & VX18835 = cCoq_2eInit_2eSpecif_2eexistT2___24a6(Vvar__0__A__18828,Vvar__1__P__18829,Vvar__2__Q__18832,Vvar__3__x__18843,Vvar__4___24Anonymous__18844,Vvar__5___24Anonymous__18845) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.Init.Specif.sumbool',axiom,
    ! [Vvar__0__A__390,Vvar__1__B__391,VX392] :
      ( cProp___24t(Vvar__0__A__390)
     => ( cProp___24t(Vvar__1__B__391)
       => ( cCoq_2eInit_2eSpecif_2esumbool___24t(Vvar__0__A__390,Vvar__1__B__391,VX392)
         => ( ( p(Vvar__0__A__390)
              & VX392 = cCoq_2eInit_2eSpecif_2eleft___24a2(Vvar__0__A__390,Vvar__1__B__391) )
            | ( p(Vvar__1__B__391)
              & VX392 = cCoq_2eInit_2eSpecif_2eright___24a2(Vvar__0__A__390,Vvar__1__B__391) ) ) ) ) ) ).

fof('$_inversion_Coq.Init.Specif.sumor',axiom,
    ! [Vvar__0__A__916,Vvar__1__B__917,VX918] :
      ( cType___24t(Vvar__0__A__916)
     => ( cProp___24t(Vvar__1__B__917)
       => ( cCoq_2eInit_2eSpecif_2esumor___24t(Vvar__0__A__916,Vvar__1__B__917,VX918)
         => ( ? [Vvar__2___24Anonymous__921] :
                ( t(Vvar__2___24Anonymous__921,Vvar__0__A__916)
                & VX918 = cCoq_2eInit_2eSpecif_2einleft___24a3(Vvar__0__A__916,Vvar__1__B__917,Vvar__2___24Anonymous__921) )
            | ( p(Vvar__1__B__917)
              & VX918 = cCoq_2eInit_2eSpecif_2einright___24a2(Vvar__0__A__916,Vvar__1__B__917) ) ) ) ) ) ).

fof('$_inversion_Coq.Init.Wf.Acc',axiom,
    ! [Vvar__0__A__33226,Vvar__1__R__33227,Vvar__2__x__33232] :
      ( cType___24t(Vvar__0__A__33226)
     => ( c_24__type__33261___24t(Vvar__0__A__33226,Vvar__1__R__33227,Vvar__2__x__33232,Vvar__1__R__33227)
       => ( t(Vvar__2__x__33232,Vvar__0__A__33226)
         => ( cCoq_2eInit_2eWf_2eAcc___24a3(Vvar__0__A__33226,Vvar__1__R__33227,Vvar__2__x__33232)
           => ( ! [Vvar__var__var__var__var__3__y__33242__33244__33246__33248__33250] :
                  ( t(Vvar__var__var__var__var__3__y__33242__33244__33246__33248__33250,Vvar__0__A__33226)
                 => ( p(happ(happ(Vvar__1__R__33227,Vvar__var__var__var__var__3__y__33242__33244__33246__33248__33250),Vvar__2__x__33232))
                   => cCoq_2eInit_2eWf_2eAcc___24a3(Vvar__0__A__33226,Vvar__1__R__33227,Vvar__var__var__var__var__3__y__33242__33244__33246__33248__33250) ) )
              & p(c_24True) ) ) ) ) ) ).

fof('$_inversion_Coq.Lists.List.NoDup',axiom,
    ! [Vvar__0__A__21715,Vvar__1___24Anonymous__21716] :
      ( cType___24t(Vvar__0__A__21715)
     => ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__21715,Vvar__1___24Anonymous__21716)
       => ( cCoq_2eLists_2eList_2eNoDup___24a2(Vvar__0__A__21715,Vvar__1___24Anonymous__21716)
         => ( Vvar__1___24Anonymous__21716 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__21715)
            | ? [Vvar__1__x__21720] :
                ( t(Vvar__1__x__21720,Vvar__0__A__21715)
                & ? [Vvar__2__l__21721] :
                    ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__21715,Vvar__2__l__21721)
                    & ~ cCoq_2eLists_2eList_2eIn___24a3(Vvar__0__A__21715,Vvar__1__x__21720,Vvar__2__l__21721)
                    & cCoq_2eLists_2eList_2eNoDup___24a2(Vvar__0__A__21715,Vvar__2__l__21721)
                    & Vvar__1___24Anonymous__21716 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__21715,Vvar__1__x__21720,Vvar__2__l__21721) ) ) ) ) ) ) ).

fof('$_inversion_Coq.Lists.SetoidList.InA',axiom,
    ! [Vvar__0__A__32438,Vvar__1__eqA__32439,Vvar__2__x__32444,Vvar__3___24Anonymous__32445] :
      ( cType___24t(Vvar__0__A__32438)
     => ( c_24__type__32478___24t(Vvar__0__A__32438,Vvar__1__eqA__32439,Vvar__2__x__32444,Vvar__3___24Anonymous__32445,Vvar__1__eqA__32439)
       => ( t(Vvar__2__x__32444,Vvar__0__A__32438)
         => ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__32438,Vvar__3___24Anonymous__32445)
           => ( cCoq_2eLists_2eSetoidList_2eInA___24a4(Vvar__0__A__32438,Vvar__1__eqA__32439,Vvar__2__x__32444,Vvar__3___24Anonymous__32445)
             => ( ? [Vvar__3__y__32454] :
                    ( t(Vvar__3__y__32454,Vvar__0__A__32438)
                    & ? [Vvar__4__l__32455] :
                        ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__32438,Vvar__4__l__32455)
                        & p(happ(happ(Vvar__1__eqA__32439,Vvar__2__x__32444),Vvar__3__y__32454))
                        & Vvar__3___24Anonymous__32445 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__32438,Vvar__3__y__32454,Vvar__4__l__32455) ) )
                | ? [Vvar__3__y__32464] :
                    ( t(Vvar__3__y__32464,Vvar__0__A__32438)
                    & ? [Vvar__4__l__32465] :
                        ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__32438,Vvar__4__l__32465)
                        & cCoq_2eLists_2eSetoidList_2eInA___24a4(Vvar__0__A__32438,Vvar__1__eqA__32439,Vvar__2__x__32444,Vvar__4__l__32465)
                        & Vvar__3___24Anonymous__32445 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__32438,Vvar__3__y__32464,Vvar__4__l__32465) ) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.Lists.SetoidList.NoDupA',axiom,
    ! [Vvar__0__A__32480,Vvar__1__eqA__32481,Vvar__2___24Anonymous__32486] :
      ( cType___24t(Vvar__0__A__32480)
     => ( c_24__type__32513___24t(Vvar__0__A__32480,Vvar__1__eqA__32481,Vvar__2___24Anonymous__32486,Vvar__1__eqA__32481)
       => ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__32480,Vvar__2___24Anonymous__32486)
         => ( cCoq_2eLists_2eSetoidList_2eNoDupA___24a3(Vvar__0__A__32480,Vvar__1__eqA__32481,Vvar__2___24Anonymous__32486)
           => ( Vvar__2___24Anonymous__32486 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__32480)
              | ? [Vvar__2__x__32500] :
                  ( t(Vvar__2__x__32500,Vvar__0__A__32480)
                  & ? [Vvar__3__l__32501] :
                      ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__32480,Vvar__3__l__32501)
                      & ~ cCoq_2eLists_2eSetoidList_2eInA___24a4(Vvar__0__A__32480,Vvar__1__eqA__32481,Vvar__2__x__32500,Vvar__3__l__32501)
                      & cCoq_2eLists_2eSetoidList_2eNoDupA___24a3(Vvar__0__A__32480,Vvar__1__eqA__32481,Vvar__3__l__32501)
                      & Vvar__2___24Anonymous__32486 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__32480,Vvar__2__x__32500,Vvar__3__l__32501) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.Logic.EqdepFacts.eq_dep',axiom,
    ! [Vvar__0__U__11383,Vvar__1__P__11384,Vvar__2__p__11387,Vvar__3__x__11388,Vvar__4__q__11389,Vvar__5___24Anonymous__11390] :
      ( cType___24t(Vvar__0__U__11383)
     => ( c_24__type__11405___24t(Vvar__0__U__11383,Vvar__1__P__11384,Vvar__2__p__11387,Vvar__3__x__11388,Vvar__4__q__11389,Vvar__5___24Anonymous__11390,Vvar__1__P__11384)
       => ( t(Vvar__2__p__11387,Vvar__0__U__11383)
         => ( t(Vvar__3__x__11388,happ(Vvar__1__P__11384,Vvar__2__p__11387))
           => ( t(Vvar__4__q__11389,Vvar__0__U__11383)
             => ( t(Vvar__5___24Anonymous__11390,happ(Vvar__1__P__11384,Vvar__4__q__11389))
               => ( cCoq_2eLogic_2eEqdepFacts_2eeq__dep___24a6(Vvar__0__U__11383,Vvar__1__P__11384,Vvar__2__p__11387,Vvar__3__x__11388,Vvar__4__q__11389,Vvar__5___24Anonymous__11390)
                 => ( Vvar__5___24Anonymous__11390 = Vvar__3__x__11388
                    & Vvar__4__q__11389 = Vvar__2__p__11387 ) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.Logic.EqdepFacts.eq_dep1',axiom,
    ! [Vvar__0__U__20066,Vvar__1__P__20067,Vvar__2__p__20070,Vvar__3__x__20071,Vvar__4__q__20072,Vvar__5__y__20073] :
      ( cType___24t(Vvar__0__U__20066)
     => ( c_24__type__20092___24t(Vvar__0__U__20066,Vvar__1__P__20067,Vvar__2__p__20070,Vvar__3__x__20071,Vvar__4__q__20072,Vvar__5__y__20073,Vvar__1__P__20067)
       => ( t(Vvar__2__p__20070,Vvar__0__U__20066)
         => ( t(Vvar__3__x__20071,happ(Vvar__1__P__20067,Vvar__2__p__20070))
           => ( t(Vvar__4__q__20072,Vvar__0__U__20066)
             => ( t(Vvar__5__y__20073,happ(Vvar__1__P__20067,Vvar__4__q__20072))
               => ( cCoq_2eLogic_2eEqdepFacts_2eeq__dep1___24a6(Vvar__0__U__20066,Vvar__1__P__20067,Vvar__2__p__20070,Vvar__3__x__20071,Vvar__4__q__20072,Vvar__5__y__20073)
                 => ( Vvar__4__q__20072 = Vvar__2__p__20070
                    & Vvar__3__x__20071 = cCoq_2eInit_2eLogic_2eeq__rect___24a5(Vvar__0__U__20066,Vvar__4__q__20072,Vvar__1__P__20067,Vvar__5__y__20073,Vvar__2__p__20070)
                    & p(c_24True) ) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.Numbers.BinNums.N',axiom,
    ! [VX20] :
      ( cCoq_2eNumbers_2eBinNums_2eN___24t(VX20)
     => ( VX20 = cCoq_2eNumbers_2eBinNums_2eN0
        | ? [Vvar__0___24Anonymous__21] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__21)
            & VX20 = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__21) ) ) ) ).

fof('$_inversion_Coq.Numbers.BinNums.Z',axiom,
    ! [VX2658] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(VX2658)
     => ( VX2658 = cCoq_2eNumbers_2eBinNums_2eZ0
        | ? [Vvar__0___24Anonymous__2659] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__2659)
            & VX2658 = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__2659) )
        | ? [Vvar__0___24Anonymous__2660] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__2660)
            & VX2658 = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__2660) ) ) ) ).

fof('$_inversion_Coq.Numbers.BinNums.positive',axiom,
    ! [VX1] :
      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(VX1)
     => ( ? [Vvar__0___24Anonymous__2] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__2)
            & VX1 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__2) )
        | ? [Vvar__0___24Anonymous__3] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__3)
            & VX1 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__3) )
        | VX1 = cCoq_2eNumbers_2eBinNums_2exH ) ) ).

fof('$_inversion_Coq.PArith.BinPos.Pos.PeanoView',axiom,
    ! [Vvar__0___24Anonymous__33517,VX33518] :
      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__33517)
     => ( cCoq_2ePArith_2eBinPos_2ePos_2ePeanoView___24t(Vvar__0___24Anonymous__33517,VX33518)
       => ( ( Vvar__0___24Anonymous__33517 = cCoq_2eNumbers_2eBinNums_2exH
            & VX33518 = cCoq_2ePArith_2eBinPos_2ePos_2ePeanoOne )
          | ? [Vvar__0__p__33519] :
              ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0__p__33519)
              & ? [Vvar__1___24Anonymous__33520] :
                  ( cCoq_2ePArith_2eBinPos_2ePos_2ePeanoView___24t(Vvar__0__p__33519,Vvar__1___24Anonymous__33520)
                  & Vvar__0___24Anonymous__33517 = c_24__case__Coq_2eNumbers_2eBinNums_2epositive_2433555___24a2(Vvar__0___24Anonymous__33517,Vvar__0__p__33519)
                  & VX33518 = cCoq_2ePArith_2eBinPos_2ePos_2ePeanoSucc___24a2(Vvar__0__p__33519,Vvar__1___24Anonymous__33520) ) ) ) ) ) ).

fof('$_inversion_Coq.PArith.BinPos.Pos.SubMaskSpec',axiom,
    ! [Vvar__0__p__19199,Vvar__1__q__19200,Vvar__2___24Anonymous__19201] :
      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0__p__19199)
     => ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1__q__19200)
       => ( cCoq_2ePArith_2eBinPosDef_2ePos_2emask___24t(Vvar__2___24Anonymous__19201)
         => ( cCoq_2ePArith_2eBinPos_2ePos_2eSubMaskSpec___24a3(Vvar__0__p__19199,Vvar__1__q__19200,Vvar__2___24Anonymous__19201)
           => ( ( Vvar__0__p__19199 = Vvar__1__q__19200
                & Vvar__2___24Anonymous__19201 = cCoq_2ePArith_2eBinPosDef_2ePos_2eIsNul )
              | ? [Vvar__2__r__19208] :
                  ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2__r__19208)
                  & cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(Vvar__1__q__19200,Vvar__2__r__19208) = Vvar__0__p__19199
                  & Vvar__2___24Anonymous__19201 = cCoq_2ePArith_2eBinPosDef_2ePos_2eIsPos___24a1(Vvar__2__r__19208) )
              | ? [Vvar__2__r__19212] :
                  ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2__r__19212)
                  & cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(Vvar__0__p__19199,Vvar__2__r__19212) = Vvar__1__q__19200
                  & Vvar__2___24Anonymous__19201 = cCoq_2ePArith_2eBinPosDef_2ePos_2eIsNeg ) ) ) ) ) ) ).

fof('$_inversion_Coq.PArith.BinPosDef.Pos.mask',axiom,
    ! [VX19087] :
      ( cCoq_2ePArith_2eBinPosDef_2ePos_2emask___24t(VX19087)
     => ( VX19087 = cCoq_2ePArith_2eBinPosDef_2ePos_2eIsNul
        | ? [Vvar__0___24Anonymous__19088] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__19088)
            & VX19087 = cCoq_2ePArith_2eBinPosDef_2ePos_2eIsPos___24a1(Vvar__0___24Anonymous__19088) )
        | VX19087 = cCoq_2ePArith_2eBinPosDef_2ePos_2eIsNeg ) ) ).

fof('$_inversion_Coq.QArith.QArith_base.Q',axiom,
    ! [VX23134] :
      ( cCoq_2eQArith_2eQArith__base_2eQ___24t(VX23134)
     => ? [Vvar__0__Qnum__23135] :
          ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__0__Qnum__23135)
          & ? [Vvar__1__Qden__23136] :
              ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1__Qden__23136)
              & VX23134 = cCoq_2eQArith_2eQArith__base_2eQmake___24a2(Vvar__0__Qnum__23135,Vvar__1__Qden__23136) ) ) ) ).

fof('$_inversion_Coq.Reals.RIneq.nonzeroreal',axiom,
    ! [VX23154] :
      ( cCoq_2eReals_2eRIneq_2enonzeroreal___24t(VX23154)
     => ? [Vvar__0__nonzero__23155] :
          ( cCoq_2eReals_2eRdefinitions_2eR___24t(Vvar__0__nonzero__23155)
          & Vvar__0__nonzero__23155 != cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)
          & VX23154 = cCoq_2eReals_2eRIneq_2emknonzeroreal___24a1(Vvar__0__nonzero__23155) ) ) ).

fof('$_inversion_Coq.Reals.Rfunctions.Z_spec',axiom,
    ! [Vvar__0__x__23346,Vvar__1___24Anonymous__23347,VX23348] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__0__x__23346)
     => ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__1___24Anonymous__23347)
       => ( cCoq_2eReals_2eRfunctions_2eZ__spec___24t(Vvar__0__x__23346,Vvar__1___24Anonymous__23347,VX23348)
         => ( ( Vvar__0__x__23346 = cCoq_2eNumbers_2eBinNums_2eZ0
              & Vvar__1___24Anonymous__23347 = cCoq_2eNumbers_2eBinNums_2eZ0
              & VX23348 = cCoq_2eReals_2eRfunctions_2eZintNull___24a1(Vvar__0__x__23346) )
            | ? [Vvar__1__n__23352] :
                ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__1__n__23352)
                & Vvar__0__x__23346 = cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat___24a1(Vvar__1__n__23352)
                & Vvar__1___24Anonymous__23347 = c_24__case__Coq_2eInit_2eDatatypes_2enat_2423372___24a3(Vvar__0__x__23346,Vvar__1___24Anonymous__23347,Vvar__1__n__23352)
                & VX23348 = cCoq_2eReals_2eRfunctions_2eZintPos___24a2(Vvar__0__x__23346,Vvar__1__n__23352) )
            | ? [Vvar__1__n__23357] :
                ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__1__n__23357)
                & Vvar__0__x__23346 = cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat___24a1(Vvar__1__n__23357))
                & Vvar__1___24Anonymous__23347 = c_24__case__Coq_2eNumbers_2eBinNums_2eZ_2423389___24a3(Vvar__0__x__23346,Vvar__1___24Anonymous__23347,Vvar__1__n__23357)
                & VX23348 = cCoq_2eReals_2eRfunctions_2eZintNeg___24a2(Vvar__0__x__23346,Vvar__1__n__23357) ) ) ) ) ) ).

fof('$_inversion_Coq.Strings.Ascii.ascii',axiom,
    ! [VX2385] :
      ( cCoq_2eStrings_2eAscii_2eascii___24t(VX2385)
     => ? [Vvar__0___24Anonymous__2386] :
          ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__0___24Anonymous__2386)
          & ? [Vvar__1___24Anonymous__2387] :
              ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__1___24Anonymous__2387)
              & ? [Vvar__2___24Anonymous__2388] :
                  ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__2___24Anonymous__2388)
                  & ? [Vvar__3___24Anonymous__2389] :
                      ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__3___24Anonymous__2389)
                      & ? [Vvar__4___24Anonymous__2390] :
                          ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__4___24Anonymous__2390)
                          & ? [Vvar__5___24Anonymous__2391] :
                              ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__5___24Anonymous__2391)
                              & ? [Vvar__6___24Anonymous__2392] :
                                  ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__6___24Anonymous__2392)
                                  & ? [Vvar__7___24Anonymous__2393] :
                                      ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__7___24Anonymous__2393)
                                      & VX2385 = cCoq_2eStrings_2eAscii_2eAscii___24a8(Vvar__0___24Anonymous__2386,Vvar__1___24Anonymous__2387,Vvar__2___24Anonymous__2388,Vvar__3___24Anonymous__2389,Vvar__4___24Anonymous__2390,Vvar__5___24Anonymous__2391,Vvar__6___24Anonymous__2392,Vvar__7___24Anonymous__2393) ) ) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.Strings.String.string',axiom,
    ! [VX32748] :
      ( cCoq_2eStrings_2eString_2estring___24t(VX32748)
     => ( VX32748 = cCoq_2eStrings_2eString_2eEmptyString
        | ? [Vvar__0___24Anonymous__32749] :
            ( cCoq_2eStrings_2eAscii_2eascii___24t(Vvar__0___24Anonymous__32749)
            & ? [Vvar__1___24Anonymous__32750] :
                ( cCoq_2eStrings_2eString_2estring___24t(Vvar__1___24Anonymous__32750)
                & VX32748 = cCoq_2eStrings_2eString_2eString___24a2(Vvar__0___24Anonymous__32749,Vvar__1___24Anonymous__32750) ) ) ) ) ).

fof('$_inversion_Coq.Structures.OrderedType.Compare',axiom,
    ! [Vvar__0__X__22940,Vvar__1__lt__22941,Vvar__2__eq__22946,Vvar__3__x__22951,Vvar__4__y__22952,VX22953] :
      ( cType___24t(Vvar__0__X__22940)
     => ( c_24__type__23013___24t(Vvar__0__X__22940,Vvar__1__lt__22941,Vvar__2__eq__22946,Vvar__3__x__22951,Vvar__4__y__22952,Vvar__1__lt__22941)
       => ( c_24__type__23032___24t(Vvar__0__X__22940,Vvar__1__lt__22941,Vvar__2__eq__22946,Vvar__3__x__22951,Vvar__4__y__22952,Vvar__2__eq__22946)
         => ( t(Vvar__3__x__22951,Vvar__0__X__22940)
           => ( t(Vvar__4__y__22952,Vvar__0__X__22940)
             => ( cCoq_2eStructures_2eOrderedType_2eCompare___24t(Vvar__0__X__22940,Vvar__1__lt__22941,Vvar__2__eq__22946,Vvar__3__x__22951,Vvar__4__y__22952,VX22953)
               => ( ( p(happ(happ(Vvar__1__lt__22941,Vvar__3__x__22951),Vvar__4__y__22952))
                    & VX22953 = cCoq_2eStructures_2eOrderedType_2eLT___24a5(Vvar__0__X__22940,Vvar__1__lt__22941,Vvar__2__eq__22946,Vvar__3__x__22951,Vvar__4__y__22952) )
                  | ( p(happ(happ(Vvar__2__eq__22946,Vvar__3__x__22951),Vvar__4__y__22952))
                    & VX22953 = cCoq_2eStructures_2eOrderedType_2eEQ___24a5(Vvar__0__X__22940,Vvar__1__lt__22941,Vvar__2__eq__22946,Vvar__3__x__22951,Vvar__4__y__22952) )
                  | ( p(happ(happ(Vvar__1__lt__22941,Vvar__4__y__22952),Vvar__3__x__22951))
                    & VX22953 = cCoq_2eStructures_2eOrderedType_2eGT___24a5(Vvar__0__X__22940,Vvar__1__lt__22941,Vvar__2__eq__22946,Vvar__3__x__22951,Vvar__4__y__22952) ) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.Structures.OrdersTac.ord',axiom,
    ! [VX23132] :
      ( cCoq_2eStructures_2eOrdersTac_2eord___24t(VX23132)
     => ( VX23132 = cCoq_2eStructures_2eOrdersTac_2eOEQ
        | VX23132 = cCoq_2eStructures_2eOrdersTac_2eOLT
        | VX23132 = cCoq_2eStructures_2eOrdersTac_2eOLE ) ) ).

fof('$_inversion_Coq.Vectors.Fin.t',axiom,
    ! [Vvar__0___24Anonymous__21596,VX21597] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__21596)
     => ( cCoq_2eVectors_2eFin_2et___24t(Vvar__0___24Anonymous__21596,VX21597)
       => ( ? [Vvar__0__n__21598] :
              ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0__n__21598)
              & Vvar__0___24Anonymous__21596 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0__n__21598)
              & VX21597 = cCoq_2eVectors_2eFin_2eF1___24a1(Vvar__0__n__21598) )
          | ? [Vvar__0__n__21599] :
              ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0__n__21599)
              & ? [Vvar__1___24Anonymous__21600] :
                  ( cCoq_2eVectors_2eFin_2et___24t(Vvar__0__n__21599,Vvar__1___24Anonymous__21600)
                  & Vvar__0___24Anonymous__21596 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0__n__21599)
                  & VX21597 = cCoq_2eVectors_2eFin_2eFS___24a2(Vvar__0__n__21599,Vvar__1___24Anonymous__21600) ) ) ) ) ) ).

fof('$_inversion_Coq.Vectors.VectorDef.t',axiom,
    ! [Vvar__0__A__33200,Vvar__1___24Anonymous__33201,VX33202] :
      ( cType___24t(Vvar__0__A__33200)
     => ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__1___24Anonymous__33201)
       => ( cCoq_2eVectors_2eVectorDef_2et___24t(Vvar__0__A__33200,Vvar__1___24Anonymous__33201,VX33202)
         => ( ( Vvar__1___24Anonymous__33201 = cCoq_2eInit_2eDatatypes_2eO
              & VX33202 = cCoq_2eVectors_2eVectorDef_2enil___24a1(Vvar__0__A__33200) )
            | ? [Vvar__1__h__33205] :
                ( t(Vvar__1__h__33205,Vvar__0__A__33200)
                & ? [Vvar__2__n__33206] :
                    ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__2__n__33206)
                    & ? [Vvar__3___24Anonymous__33207] :
                        ( cCoq_2eVectors_2eVectorDef_2et___24t(Vvar__0__A__33200,Vvar__2__n__33206,Vvar__3___24Anonymous__33207)
                        & Vvar__1___24Anonymous__33201 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__2__n__33206)
                        & VX33202 = cCoq_2eVectors_2eVectorDef_2econs___24a4(Vvar__0__A__33200,Vvar__1__h__33205,Vvar__2__n__33206,Vvar__3___24Anonymous__33207) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.ZArith.Znumtheory.Bezout',axiom,
    ! [Vvar__0__a__33399,Vvar__1__b__33400,Vvar__2__d__33401] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__0__a__33399)
     => ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__1__b__33400)
       => ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__2__d__33401)
         => ( cCoq_2eZArith_2eZnumtheory_2eBezout___24a3(Vvar__0__a__33399,Vvar__1__b__33400,Vvar__2__d__33401)
           => ? [Vvar__3__u__33406] :
                ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__3__u__33406)
                & ? [Vvar__4__v__33407] :
                    ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__4__v__33407)
                    & cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(Vvar__3__u__33406,Vvar__0__a__33399),cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(Vvar__4__v__33407,Vvar__1__b__33400)) = Vvar__2__d__33401
                    & p(c_24True) ) ) ) ) ) ) ).

fof('$_inversion_Coq.ZArith.Znumtheory.Euclid',axiom,
    ! [Vvar__0__a__33374,Vvar__1__b__33375,VX33376] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__0__a__33374)
     => ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__1__b__33375)
       => ( cCoq_2eZArith_2eZnumtheory_2eEuclid___24t(Vvar__0__a__33374,Vvar__1__b__33375,VX33376)
         => ? [Vvar__2__u__33379] :
              ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__2__u__33379)
              & ? [Vvar__3__v__33380] :
                  ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__3__v__33380)
                  & ? [Vvar__4__d__33381] :
                      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__4__d__33381)
                      & cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(Vvar__2__u__33379,Vvar__0__a__33374),cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(Vvar__3__v__33380,Vvar__1__b__33375)) = Vvar__4__d__33381
                      & cCoq_2eZArith_2eZnumtheory_2eZis__gcd___24a3(Vvar__0__a__33374,Vvar__1__b__33375,Vvar__4__d__33381)
                      & VX33376 = cCoq_2eZArith_2eZnumtheory_2eEuclid__intro___24a5(Vvar__0__a__33374,Vvar__1__b__33375,Vvar__2__u__33379,Vvar__3__v__33380,Vvar__4__d__33381) ) ) ) ) ) ) ).

fof('$_inversion_Coq.ZArith.Znumtheory.Zis_gcd',axiom,
    ! [Vvar__0__a__18936,Vvar__1__b__18937,Vvar__2__g__18938] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__0__a__18936)
     => ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__1__b__18937)
       => ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__2__g__18938)
         => ( cCoq_2eZArith_2eZnumtheory_2eZis__gcd___24a3(Vvar__0__a__18936,Vvar__1__b__18937,Vvar__2__g__18938)
           => ( cCoq_2eZArith_2eBinInt_2eZ_2edivide___24a2(Vvar__2__g__18938,Vvar__0__a__18936)
              & cCoq_2eZArith_2eBinInt_2eZ_2edivide___24a2(Vvar__2__g__18938,Vvar__1__b__18937)
              & ! [Vvar__var__var__var__var__5__x__18946__18949__18952__18955__18958] :
                  ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__var__var__var__var__5__x__18946__18949__18952__18955__18958)
                 => ( cCoq_2eZArith_2eBinInt_2eZ_2edivide___24a2(Vvar__var__var__var__var__5__x__18946__18949__18952__18955__18958,Vvar__0__a__18936)
                   => ( cCoq_2eZArith_2eBinInt_2eZ_2edivide___24a2(Vvar__var__var__var__var__5__x__18946__18949__18952__18955__18958,Vvar__1__b__18937)
                     => cCoq_2eZArith_2eBinInt_2eZ_2edivide___24a2(Vvar__var__var__var__var__5__x__18946__18949__18952__18955__18958,Vvar__2__g__18938) ) ) )
              & p(c_24True) ) ) ) ) ) ).

fof('$_inversion_Coq.ZArith.Znumtheory.prime',axiom,
    ! [Vvar__0__p__18965] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__0__p__18965)
     => ( cCoq_2eZArith_2eZnumtheory_2eprime___24a1(Vvar__0__p__18965)
       => ( cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH),Vvar__0__p__18965)
          & ! [Vvar__var__var__2__n__18970__18972__18974] :
              ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__var__var__2__n__18970__18972__18974)
             => ( ( cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH),Vvar__var__var__2__n__18970__18972__18974)
                  & cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(Vvar__var__var__2__n__18970__18972__18974,Vvar__0__p__18965) )
               => cCoq_2eZArith_2eZnumtheory_2erel__prime___24a2(Vvar__var__var__2__n__18970__18972__18974,Vvar__0__p__18965) ) )
          & p(c_24True) ) ) ) ).

fof('$_inversion_Coq.ZArith.Zpower.Zdiv_rest_proofs',axiom,
    ! [Vvar__0__x__33409,Vvar__1__p__33410,VX33411] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__0__x__33409)
     => ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1__p__33410)
       => ( cCoq_2eZArith_2eZpower_2eZdiv__rest__proofs___24t(Vvar__0__x__33409,Vvar__1__p__33410,VX33411)
         => ? [Vvar__2__q__33414] :
              ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__2__q__33414)
              & ? [Vvar__3__r__33415] :
                  ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__3__r__33415)
                  & Vvar__0__x__33409 = cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(Vvar__2__q__33414,cCoq_2eZArith_2eZpower_2etwo__power__pos___24a1(Vvar__1__p__33410)),Vvar__3__r__33415)
                  & cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,Vvar__3__r__33415)
                  & cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(Vvar__3__r__33415,cCoq_2eZArith_2eZpower_2etwo__power__pos___24a1(Vvar__1__p__33410))
                  & VX33411 = cCoq_2eZArith_2eZpower_2eZdiv__rest__proof___24a4(Vvar__0__x__33409,Vvar__1__p__33410,Vvar__2__q__33414,Vvar__3__r__33415) ) ) ) ) ) ).

fof('$_inversion_Coq.micromega.EnvRing.Mon',axiom,
    ! [VX20038] :
      ( cCoq_2emicromega_2eEnvRing_2eMon___24t(VX20038)
     => ( VX20038 = cCoq_2emicromega_2eEnvRing_2emon0
        | ? [Vvar__0___24Anonymous__20039] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__20039)
            & ? [Vvar__1___24Anonymous__20040] :
                ( cCoq_2emicromega_2eEnvRing_2eMon___24t(Vvar__1___24Anonymous__20040)
                & VX20038 = cCoq_2emicromega_2eEnvRing_2ezmon___24a2(Vvar__0___24Anonymous__20039,Vvar__1___24Anonymous__20040) ) )
        | ? [Vvar__0___24Anonymous__20041] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__20041)
            & ? [Vvar__1___24Anonymous__20042] :
                ( cCoq_2emicromega_2eEnvRing_2eMon___24t(Vvar__1___24Anonymous__20042)
                & VX20038 = cCoq_2emicromega_2eEnvRing_2evmon___24a2(Vvar__0___24Anonymous__20041,Vvar__1___24Anonymous__20042) ) ) ) ) ).

fof('$_inversion_Coq.micromega.EnvRing.PExpr',axiom,
    ! [Vvar__0__C__10998,VX10999] :
      ( cType___24t(Vvar__0__C__10998)
     => ( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__C__10998,VX10999)
       => ( ? [Vvar__1___24Anonymous__11001] :
              ( t(Vvar__1___24Anonymous__11001,Vvar__0__C__10998)
              & VX10999 = cCoq_2emicromega_2eEnvRing_2ePEc___24a2(Vvar__0__C__10998,Vvar__1___24Anonymous__11001) )
          | ? [Vvar__1___24Anonymous__11003] :
              ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__11003)
              & VX10999 = cCoq_2emicromega_2eEnvRing_2ePEX___24a2(Vvar__0__C__10998,Vvar__1___24Anonymous__11003) )
          | ? [Vvar__1___24Anonymous__11005] :
              ( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__C__10998,Vvar__1___24Anonymous__11005)
              & ? [Vvar__2___24Anonymous__11006] :
                  ( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__C__10998,Vvar__2___24Anonymous__11006)
                  & VX10999 = cCoq_2emicromega_2eEnvRing_2ePEadd___24a3(Vvar__0__C__10998,Vvar__1___24Anonymous__11005,Vvar__2___24Anonymous__11006) ) )
          | ? [Vvar__1___24Anonymous__11008] :
              ( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__C__10998,Vvar__1___24Anonymous__11008)
              & ? [Vvar__2___24Anonymous__11009] :
                  ( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__C__10998,Vvar__2___24Anonymous__11009)
                  & VX10999 = cCoq_2emicromega_2eEnvRing_2ePEsub___24a3(Vvar__0__C__10998,Vvar__1___24Anonymous__11008,Vvar__2___24Anonymous__11009) ) )
          | ? [Vvar__1___24Anonymous__11011] :
              ( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__C__10998,Vvar__1___24Anonymous__11011)
              & ? [Vvar__2___24Anonymous__11012] :
                  ( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__C__10998,Vvar__2___24Anonymous__11012)
                  & VX10999 = cCoq_2emicromega_2eEnvRing_2ePEmul___24a3(Vvar__0__C__10998,Vvar__1___24Anonymous__11011,Vvar__2___24Anonymous__11012) ) )
          | ? [Vvar__1___24Anonymous__11014] :
              ( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__C__10998,Vvar__1___24Anonymous__11014)
              & VX10999 = cCoq_2emicromega_2eEnvRing_2ePEopp___24a2(Vvar__0__C__10998,Vvar__1___24Anonymous__11014) )
          | ? [Vvar__1___24Anonymous__11016] :
              ( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__C__10998,Vvar__1___24Anonymous__11016)
              & ? [Vvar__2___24Anonymous__11017] :
                  ( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__2___24Anonymous__11017)
                  & VX10999 = cCoq_2emicromega_2eEnvRing_2ePEpow___24a3(Vvar__0__C__10998,Vvar__1___24Anonymous__11016,Vvar__2___24Anonymous__11017) ) ) ) ) ) ).

fof('$_inversion_Coq.micromega.EnvRing.Pol',axiom,
    ! [Vvar__0__C__19988,VX19989] :
      ( cType___24t(Vvar__0__C__19988)
     => ( cCoq_2emicromega_2eEnvRing_2ePol___24t(Vvar__0__C__19988,VX19989)
       => ( ? [Vvar__1___24Anonymous__19991] :
              ( t(Vvar__1___24Anonymous__19991,Vvar__0__C__19988)
              & VX19989 = cCoq_2emicromega_2eEnvRing_2ePc___24a2(Vvar__0__C__19988,Vvar__1___24Anonymous__19991) )
          | ? [Vvar__1___24Anonymous__19993] :
              ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__19993)
              & ? [Vvar__2___24Anonymous__19994] :
                  ( cCoq_2emicromega_2eEnvRing_2ePol___24t(Vvar__0__C__19988,Vvar__2___24Anonymous__19994)
                  & VX19989 = cCoq_2emicromega_2eEnvRing_2ePinj___24a3(Vvar__0__C__19988,Vvar__1___24Anonymous__19993,Vvar__2___24Anonymous__19994) ) )
          | ? [Vvar__1___24Anonymous__19996] :
              ( cCoq_2emicromega_2eEnvRing_2ePol___24t(Vvar__0__C__19988,Vvar__1___24Anonymous__19996)
              & ? [Vvar__2___24Anonymous__19997] :
                  ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2___24Anonymous__19997)
                  & ? [Vvar__3___24Anonymous__19998] :
                      ( cCoq_2emicromega_2eEnvRing_2ePol___24t(Vvar__0__C__19988,Vvar__3___24Anonymous__19998)
                      & VX19989 = cCoq_2emicromega_2eEnvRing_2ePX___24a4(Vvar__0__C__19988,Vvar__1___24Anonymous__19996,Vvar__2___24Anonymous__19997,Vvar__3___24Anonymous__19998) ) ) ) ) ) ) ).

fof('$_inversion_Coq.micromega.RingMicromega.Op1',axiom,
    ! [VX28728] :
      ( cCoq_2emicromega_2eRingMicromega_2eOp1___24t(VX28728)
     => ( VX28728 = cCoq_2emicromega_2eRingMicromega_2eEqual
        | VX28728 = cCoq_2emicromega_2eRingMicromega_2eNonEqual
        | VX28728 = cCoq_2emicromega_2eRingMicromega_2eStrict
        | VX28728 = cCoq_2emicromega_2eRingMicromega_2eNonStrict ) ) ).

fof('$_inversion_Coq.micromega.RingMicromega.Op2',axiom,
    ! [VX28875] :
      ( cCoq_2emicromega_2eRingMicromega_2eOp2___24t(VX28875)
     => ( VX28875 = cCoq_2emicromega_2eRingMicromega_2eOpEq
        | VX28875 = cCoq_2emicromega_2eRingMicromega_2eOpNEq
        | VX28875 = cCoq_2emicromega_2eRingMicromega_2eOpLe
        | VX28875 = cCoq_2emicromega_2eRingMicromega_2eOpGe
        | VX28875 = cCoq_2emicromega_2eRingMicromega_2eOpLt
        | VX28875 = cCoq_2emicromega_2eRingMicromega_2eOpGt ) ) ).

fof('$_inversion_Coq.micromega.RingMicromega.SORaddon',axiom,
    ! [Vvar__0__R__23435,Vvar__1__rO__23436,Vvar__2__rI__23437,Vvar__3__rplus__23438,Vvar__4__rtimes__23443,Vvar__5__rminus__23448,Vvar__6__ropp__23453,Vvar__7__req__23456,Vvar__8__rle__23461,Vvar__9__C__23466,Vvar__10__cO__23467,Vvar__11__cI__23468,Vvar__12__cplus__23469,Vvar__13__ctimes__23474,Vvar__14__cminus__23479,Vvar__15__copp__23484,Vvar__16__ceqb__23487,Vvar__17__cleb__23492,Vvar__18__phi__23497,Vvar__19__E__23500,Vvar__20__pow__phi__23501,Vvar__21__rpow__23504] :
      ( cType___24t(Vvar__0__R__23435)
     => ( t(Vvar__1__rO__23436,Vvar__0__R__23435)
       => ( t(Vvar__2__rI__23437,Vvar__0__R__23435)
         => ( c_24__type__23968___24t(Vvar__0__R__23435,Vvar__1__rO__23436,Vvar__2__rI__23437,Vvar__3__rplus__23438,Vvar__4__rtimes__23443,Vvar__5__rminus__23448,Vvar__6__ropp__23453,Vvar__7__req__23456,Vvar__8__rle__23461,Vvar__9__C__23466,Vvar__10__cO__23467,Vvar__11__cI__23468,Vvar__12__cplus__23469,Vvar__13__ctimes__23474,Vvar__14__cminus__23479,Vvar__15__copp__23484,Vvar__16__ceqb__23487,Vvar__17__cleb__23492,Vvar__18__phi__23497,Vvar__19__E__23500,Vvar__20__pow__phi__23501,Vvar__21__rpow__23504,Vvar__3__rplus__23438)
           => ( c_24__type__24314___24t(Vvar__0__R__23435,Vvar__1__rO__23436,Vvar__2__rI__23437,Vvar__3__rplus__23438,Vvar__4__rtimes__23443,Vvar__5__rminus__23448,Vvar__6__ropp__23453,Vvar__7__req__23456,Vvar__8__rle__23461,Vvar__9__C__23466,Vvar__10__cO__23467,Vvar__11__cI__23468,Vvar__12__cplus__23469,Vvar__13__ctimes__23474,Vvar__14__cminus__23479,Vvar__15__copp__23484,Vvar__16__ceqb__23487,Vvar__17__cleb__23492,Vvar__18__phi__23497,Vvar__19__E__23500,Vvar__20__pow__phi__23501,Vvar__21__rpow__23504,Vvar__4__rtimes__23443)
             => ( c_24__type__24660___24t(Vvar__0__R__23435,Vvar__1__rO__23436,Vvar__2__rI__23437,Vvar__3__rplus__23438,Vvar__4__rtimes__23443,Vvar__5__rminus__23448,Vvar__6__ropp__23453,Vvar__7__req__23456,Vvar__8__rle__23461,Vvar__9__C__23466,Vvar__10__cO__23467,Vvar__11__cI__23468,Vvar__12__cplus__23469,Vvar__13__ctimes__23474,Vvar__14__cminus__23479,Vvar__15__copp__23484,Vvar__16__ceqb__23487,Vvar__17__cleb__23492,Vvar__18__phi__23497,Vvar__19__E__23500,Vvar__20__pow__phi__23501,Vvar__21__rpow__23504,Vvar__5__rminus__23448)
               => ( c_24__type__24983___24t(Vvar__0__R__23435,Vvar__1__rO__23436,Vvar__2__rI__23437,Vvar__3__rplus__23438,Vvar__4__rtimes__23443,Vvar__5__rminus__23448,Vvar__6__ropp__23453,Vvar__7__req__23456,Vvar__8__rle__23461,Vvar__9__C__23466,Vvar__10__cO__23467,Vvar__11__cI__23468,Vvar__12__cplus__23469,Vvar__13__ctimes__23474,Vvar__14__cminus__23479,Vvar__15__copp__23484,Vvar__16__ceqb__23487,Vvar__17__cleb__23492,Vvar__18__phi__23497,Vvar__19__E__23500,Vvar__20__pow__phi__23501,Vvar__21__rpow__23504,Vvar__6__ropp__23453)
                 => ( c_24__type__25329___24t(Vvar__0__R__23435,Vvar__1__rO__23436,Vvar__2__rI__23437,Vvar__3__rplus__23438,Vvar__4__rtimes__23443,Vvar__5__rminus__23448,Vvar__6__ropp__23453,Vvar__7__req__23456,Vvar__8__rle__23461,Vvar__9__C__23466,Vvar__10__cO__23467,Vvar__11__cI__23468,Vvar__12__cplus__23469,Vvar__13__ctimes__23474,Vvar__14__cminus__23479,Vvar__15__copp__23484,Vvar__16__ceqb__23487,Vvar__17__cleb__23492,Vvar__18__phi__23497,Vvar__19__E__23500,Vvar__20__pow__phi__23501,Vvar__21__rpow__23504,Vvar__7__req__23456)
                   => ( c_24__type__25675___24t(Vvar__0__R__23435,Vvar__1__rO__23436,Vvar__2__rI__23437,Vvar__3__rplus__23438,Vvar__4__rtimes__23443,Vvar__5__rminus__23448,Vvar__6__ropp__23453,Vvar__7__req__23456,Vvar__8__rle__23461,Vvar__9__C__23466,Vvar__10__cO__23467,Vvar__11__cI__23468,Vvar__12__cplus__23469,Vvar__13__ctimes__23474,Vvar__14__cminus__23479,Vvar__15__copp__23484,Vvar__16__ceqb__23487,Vvar__17__cleb__23492,Vvar__18__phi__23497,Vvar__19__E__23500,Vvar__20__pow__phi__23501,Vvar__21__rpow__23504,Vvar__8__rle__23461)
                     => ( cType___24t(Vvar__9__C__23466)
                       => ( t(Vvar__10__cO__23467,Vvar__9__C__23466)
                         => ( t(Vvar__11__cI__23468,Vvar__9__C__23466)
                           => ( c_24__type__26021___24t(Vvar__0__R__23435,Vvar__1__rO__23436,Vvar__2__rI__23437,Vvar__3__rplus__23438,Vvar__4__rtimes__23443,Vvar__5__rminus__23448,Vvar__6__ropp__23453,Vvar__7__req__23456,Vvar__8__rle__23461,Vvar__9__C__23466,Vvar__10__cO__23467,Vvar__11__cI__23468,Vvar__12__cplus__23469,Vvar__13__ctimes__23474,Vvar__14__cminus__23479,Vvar__15__copp__23484,Vvar__16__ceqb__23487,Vvar__17__cleb__23492,Vvar__18__phi__23497,Vvar__19__E__23500,Vvar__20__pow__phi__23501,Vvar__21__rpow__23504,Vvar__12__cplus__23469)
                             => ( c_24__type__26367___24t(Vvar__0__R__23435,Vvar__1__rO__23436,Vvar__2__rI__23437,Vvar__3__rplus__23438,Vvar__4__rtimes__23443,Vvar__5__rminus__23448,Vvar__6__ropp__23453,Vvar__7__req__23456,Vvar__8__rle__23461,Vvar__9__C__23466,Vvar__10__cO__23467,Vvar__11__cI__23468,Vvar__12__cplus__23469,Vvar__13__ctimes__23474,Vvar__14__cminus__23479,Vvar__15__copp__23484,Vvar__16__ceqb__23487,Vvar__17__cleb__23492,Vvar__18__phi__23497,Vvar__19__E__23500,Vvar__20__pow__phi__23501,Vvar__21__rpow__23504,Vvar__13__ctimes__23474)
                               => ( c_24__type__26713___24t(Vvar__0__R__23435,Vvar__1__rO__23436,Vvar__2__rI__23437,Vvar__3__rplus__23438,Vvar__4__rtimes__23443,Vvar__5__rminus__23448,Vvar__6__ropp__23453,Vvar__7__req__23456,Vvar__8__rle__23461,Vvar__9__C__23466,Vvar__10__cO__23467,Vvar__11__cI__23468,Vvar__12__cplus__23469,Vvar__13__ctimes__23474,Vvar__14__cminus__23479,Vvar__15__copp__23484,Vvar__16__ceqb__23487,Vvar__17__cleb__23492,Vvar__18__phi__23497,Vvar__19__E__23500,Vvar__20__pow__phi__23501,Vvar__21__rpow__23504,Vvar__14__cminus__23479)
                                 => ( c_24__type__27036___24t(Vvar__0__R__23435,Vvar__1__rO__23436,Vvar__2__rI__23437,Vvar__3__rplus__23438,Vvar__4__rtimes__23443,Vvar__5__rminus__23448,Vvar__6__ropp__23453,Vvar__7__req__23456,Vvar__8__rle__23461,Vvar__9__C__23466,Vvar__10__cO__23467,Vvar__11__cI__23468,Vvar__12__cplus__23469,Vvar__13__ctimes__23474,Vvar__14__cminus__23479,Vvar__15__copp__23484,Vvar__16__ceqb__23487,Vvar__17__cleb__23492,Vvar__18__phi__23497,Vvar__19__E__23500,Vvar__20__pow__phi__23501,Vvar__21__rpow__23504,Vvar__15__copp__23484)
                                   => ( c_24__type__27382___24t(Vvar__0__R__23435,Vvar__1__rO__23436,Vvar__2__rI__23437,Vvar__3__rplus__23438,Vvar__4__rtimes__23443,Vvar__5__rminus__23448,Vvar__6__ropp__23453,Vvar__7__req__23456,Vvar__8__rle__23461,Vvar__9__C__23466,Vvar__10__cO__23467,Vvar__11__cI__23468,Vvar__12__cplus__23469,Vvar__13__ctimes__23474,Vvar__14__cminus__23479,Vvar__15__copp__23484,Vvar__16__ceqb__23487,Vvar__17__cleb__23492,Vvar__18__phi__23497,Vvar__19__E__23500,Vvar__20__pow__phi__23501,Vvar__21__rpow__23504,Vvar__16__ceqb__23487)
                                     => ( c_24__type__27728___24t(Vvar__0__R__23435,Vvar__1__rO__23436,Vvar__2__rI__23437,Vvar__3__rplus__23438,Vvar__4__rtimes__23443,Vvar__5__rminus__23448,Vvar__6__ropp__23453,Vvar__7__req__23456,Vvar__8__rle__23461,Vvar__9__C__23466,Vvar__10__cO__23467,Vvar__11__cI__23468,Vvar__12__cplus__23469,Vvar__13__ctimes__23474,Vvar__14__cminus__23479,Vvar__15__copp__23484,Vvar__16__ceqb__23487,Vvar__17__cleb__23492,Vvar__18__phi__23497,Vvar__19__E__23500,Vvar__20__pow__phi__23501,Vvar__21__rpow__23504,Vvar__17__cleb__23492)
                                       => ( c_24__type__28051___24t(Vvar__0__R__23435,Vvar__1__rO__23436,Vvar__2__rI__23437,Vvar__3__rplus__23438,Vvar__4__rtimes__23443,Vvar__5__rminus__23448,Vvar__6__ropp__23453,Vvar__7__req__23456,Vvar__8__rle__23461,Vvar__9__C__23466,Vvar__10__cO__23467,Vvar__11__cI__23468,Vvar__12__cplus__23469,Vvar__13__ctimes__23474,Vvar__14__cminus__23479,Vvar__15__copp__23484,Vvar__16__ceqb__23487,Vvar__17__cleb__23492,Vvar__18__phi__23497,Vvar__19__E__23500,Vvar__20__pow__phi__23501,Vvar__21__rpow__23504,Vvar__18__phi__23497)
                                         => ( cType___24t(Vvar__19__E__23500)
                                           => ( c_24__type__28374___24t(Vvar__0__R__23435,Vvar__1__rO__23436,Vvar__2__rI__23437,Vvar__3__rplus__23438,Vvar__4__rtimes__23443,Vvar__5__rminus__23448,Vvar__6__ropp__23453,Vvar__7__req__23456,Vvar__8__rle__23461,Vvar__9__C__23466,Vvar__10__cO__23467,Vvar__11__cI__23468,Vvar__12__cplus__23469,Vvar__13__ctimes__23474,Vvar__14__cminus__23479,Vvar__15__copp__23484,Vvar__16__ceqb__23487,Vvar__17__cleb__23492,Vvar__18__phi__23497,Vvar__19__E__23500,Vvar__20__pow__phi__23501,Vvar__21__rpow__23504,Vvar__20__pow__phi__23501)
                                             => ( c_24__type__28720___24t(Vvar__0__R__23435,Vvar__1__rO__23436,Vvar__2__rI__23437,Vvar__3__rplus__23438,Vvar__4__rtimes__23443,Vvar__5__rminus__23448,Vvar__6__ropp__23453,Vvar__7__req__23456,Vvar__8__rle__23461,Vvar__9__C__23466,Vvar__10__cO__23467,Vvar__11__cI__23468,Vvar__12__cplus__23469,Vvar__13__ctimes__23474,Vvar__14__cminus__23479,Vvar__15__copp__23484,Vvar__16__ceqb__23487,Vvar__17__cleb__23492,Vvar__18__phi__23497,Vvar__19__E__23500,Vvar__20__pow__phi__23501,Vvar__21__rpow__23504,Vvar__21__rpow__23504)
                                               => ( cCoq_2emicromega_2eRingMicromega_2eSORaddon___24a22(Vvar__0__R__23435,Vvar__1__rO__23436,Vvar__2__rI__23437,Vvar__3__rplus__23438,Vvar__4__rtimes__23443,Vvar__5__rminus__23448,Vvar__6__ropp__23453,Vvar__7__req__23456,Vvar__8__rle__23461,Vvar__9__C__23466,Vvar__10__cO__23467,Vvar__11__cI__23468,Vvar__12__cplus__23469,Vvar__13__ctimes__23474,Vvar__14__cminus__23479,Vvar__15__copp__23484,Vvar__16__ceqb__23487,Vvar__17__cleb__23492,Vvar__18__phi__23497,Vvar__19__E__23500,Vvar__20__pow__phi__23501,Vvar__21__rpow__23504)
                                                 => ( cCoq_2esetoid__ring_2eRing__theory_2ering__morph___24a17(Vvar__0__R__23435,Vvar__1__rO__23436,Vvar__2__rI__23437,Vvar__3__rplus__23438,Vvar__4__rtimes__23443,Vvar__5__rminus__23448,Vvar__6__ropp__23453,Vvar__7__req__23456,Vvar__9__C__23466,Vvar__10__cO__23467,Vvar__11__cI__23468,Vvar__12__cplus__23469,Vvar__13__ctimes__23474,Vvar__14__cminus__23479,Vvar__15__copp__23484,Vvar__16__ceqb__23487,Vvar__18__phi__23497)
                                                    & cCoq_2esetoid__ring_2eRing__theory_2epower__theory___24a7(Vvar__0__R__23435,Vvar__2__rI__23437,Vvar__4__rtimes__23443,Vvar__7__req__23456,Vvar__19__E__23500,Vvar__20__pow__phi__23501,Vvar__21__rpow__23504)
                                                    & ! [Vvar__var__var__var__var__var__24__x__23587__23590__23600__23603__23606__23609] :
                                                        ( t(Vvar__var__var__var__var__var__24__x__23587__23590__23600__23603__23606__23609,Vvar__9__C__23466)
                                                       => ! [Vvar__var__var__var__var__var__25__y__23588__23591__23601__23604__23607__23610] :
                                                            ( t(Vvar__var__var__var__var__var__25__y__23588__23591__23601__23604__23607__23610,Vvar__9__C__23466)
                                                           => ( happ(happ(Vvar__16__ceqb__23487,Vvar__var__var__var__var__var__24__x__23587__23590__23600__23603__23606__23609),Vvar__var__var__var__var__var__25__y__23588__23591__23601__23604__23607__23610) = cCoq_2eInit_2eDatatypes_2efalse
                                                             => ~ p(happ(happ(Vvar__7__req__23456,happ(Vvar__18__phi__23497,Vvar__var__var__var__var__var__24__x__23587__23590__23600__23603__23606__23609)),happ(Vvar__18__phi__23497,Vvar__var__var__var__var__var__25__y__23588__23591__23601__23604__23607__23610))) ) ) )
                                                    & ! [Vvar__var__var__var__var__var__25__x__23594__23597__23612__23615__23618__23621] :
                                                        ( t(Vvar__var__var__var__var__var__25__x__23594__23597__23612__23615__23618__23621,Vvar__9__C__23466)
                                                       => ! [Vvar__var__var__var__var__var__26__y__23595__23598__23613__23616__23619__23622] :
                                                            ( t(Vvar__var__var__var__var__var__26__y__23595__23598__23613__23616__23619__23622,Vvar__9__C__23466)
                                                           => ( happ(happ(Vvar__17__cleb__23492,Vvar__var__var__var__var__var__25__x__23594__23597__23612__23615__23618__23621),Vvar__var__var__var__var__var__26__y__23595__23598__23613__23616__23619__23622) = cCoq_2eInit_2eDatatypes_2etrue
                                                             => p(happ(happ(Vvar__8__rle__23461,happ(Vvar__18__phi__23497,Vvar__var__var__var__var__var__25__x__23594__23597__23612__23615__23618__23621)),happ(Vvar__18__phi__23497,Vvar__var__var__var__var__var__26__y__23595__23598__23613__23616__23619__23622))) ) ) )
                                                    & p(c_24True) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.micromega.Tauto.GFormula',axiom,
    ! [Vvar__0__TA__32757,Vvar__1__TX__32758,Vvar__2__AA__32759,Vvar__3__AF__32760,VX32761] :
      ( cType___24t(Vvar__0__TA__32757)
     => ( cType___24t(Vvar__1__TX__32758)
       => ( cType___24t(Vvar__2__AA__32759)
         => ( cType___24t(Vvar__3__AF__32760)
           => ( cCoq_2emicromega_2eTauto_2eGFormula___24t(Vvar__0__TA__32757,Vvar__1__TX__32758,Vvar__2__AA__32759,Vvar__3__AF__32760,VX32761)
             => ( VX32761 = cCoq_2emicromega_2eTauto_2eTT___24a4(Vvar__0__TA__32757,Vvar__1__TX__32758,Vvar__2__AA__32759,Vvar__3__AF__32760)
                | VX32761 = cCoq_2emicromega_2eTauto_2eFF___24a4(Vvar__0__TA__32757,Vvar__1__TX__32758,Vvar__2__AA__32759,Vvar__3__AF__32760)
                | ? [Vvar__4___24Anonymous__32774] :
                    ( t(Vvar__4___24Anonymous__32774,Vvar__1__TX__32758)
                    & VX32761 = cCoq_2emicromega_2eTauto_2eX___24a5(Vvar__0__TA__32757,Vvar__1__TX__32758,Vvar__2__AA__32759,Vvar__3__AF__32760,Vvar__4___24Anonymous__32774) )
                | ? [Vvar__4___24Anonymous__32779] :
                    ( t(Vvar__4___24Anonymous__32779,Vvar__0__TA__32757)
                    & ? [Vvar__5___24Anonymous__32780] :
                        ( t(Vvar__5___24Anonymous__32780,Vvar__2__AA__32759)
                        & VX32761 = cCoq_2emicromega_2eTauto_2eA___24a6(Vvar__0__TA__32757,Vvar__1__TX__32758,Vvar__2__AA__32759,Vvar__3__AF__32760,Vvar__4___24Anonymous__32779,Vvar__5___24Anonymous__32780) ) )
                | ? [Vvar__4___24Anonymous__32785] :
                    ( cCoq_2emicromega_2eTauto_2eGFormula___24t(Vvar__0__TA__32757,Vvar__1__TX__32758,Vvar__2__AA__32759,Vvar__3__AF__32760,Vvar__4___24Anonymous__32785)
                    & ? [Vvar__5___24Anonymous__32786] :
                        ( cCoq_2emicromega_2eTauto_2eGFormula___24t(Vvar__0__TA__32757,Vvar__1__TX__32758,Vvar__2__AA__32759,Vvar__3__AF__32760,Vvar__5___24Anonymous__32786)
                        & VX32761 = cCoq_2emicromega_2eTauto_2eCj___24a6(Vvar__0__TA__32757,Vvar__1__TX__32758,Vvar__2__AA__32759,Vvar__3__AF__32760,Vvar__4___24Anonymous__32785,Vvar__5___24Anonymous__32786) ) )
                | ? [Vvar__4___24Anonymous__32791] :
                    ( cCoq_2emicromega_2eTauto_2eGFormula___24t(Vvar__0__TA__32757,Vvar__1__TX__32758,Vvar__2__AA__32759,Vvar__3__AF__32760,Vvar__4___24Anonymous__32791)
                    & ? [Vvar__5___24Anonymous__32792] :
                        ( cCoq_2emicromega_2eTauto_2eGFormula___24t(Vvar__0__TA__32757,Vvar__1__TX__32758,Vvar__2__AA__32759,Vvar__3__AF__32760,Vvar__5___24Anonymous__32792)
                        & VX32761 = cCoq_2emicromega_2eTauto_2eD___24a6(Vvar__0__TA__32757,Vvar__1__TX__32758,Vvar__2__AA__32759,Vvar__3__AF__32760,Vvar__4___24Anonymous__32791,Vvar__5___24Anonymous__32792) ) )
                | ? [Vvar__4___24Anonymous__32797] :
                    ( cCoq_2emicromega_2eTauto_2eGFormula___24t(Vvar__0__TA__32757,Vvar__1__TX__32758,Vvar__2__AA__32759,Vvar__3__AF__32760,Vvar__4___24Anonymous__32797)
                    & VX32761 = cCoq_2emicromega_2eTauto_2eN___24a5(Vvar__0__TA__32757,Vvar__1__TX__32758,Vvar__2__AA__32759,Vvar__3__AF__32760,Vvar__4___24Anonymous__32797) )
                | ? [Vvar__4___24Anonymous__32802] :
                    ( cCoq_2emicromega_2eTauto_2eGFormula___24t(Vvar__0__TA__32757,Vvar__1__TX__32758,Vvar__2__AA__32759,Vvar__3__AF__32760,Vvar__4___24Anonymous__32802)
                    & ? [Vvar__5___24Anonymous__32803] :
                        ( cCoq_2eInit_2eDatatypes_2eoption___24t(Vvar__3__AF__32760,Vvar__5___24Anonymous__32803)
                        & ? [Vvar__6___24Anonymous__32804] :
                            ( cCoq_2emicromega_2eTauto_2eGFormula___24t(Vvar__0__TA__32757,Vvar__1__TX__32758,Vvar__2__AA__32759,Vvar__3__AF__32760,Vvar__6___24Anonymous__32804)
                            & VX32761 = cCoq_2emicromega_2eTauto_2eI___24a7(Vvar__0__TA__32757,Vvar__1__TX__32758,Vvar__2__AA__32759,Vvar__3__AF__32760,Vvar__4___24Anonymous__32802,Vvar__5___24Anonymous__32803,Vvar__6___24Anonymous__32804) ) ) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.micromega.ZMicromega.Vars.Facts.MP.Dec.FSetDecideAuxiliary.FSet_elt_Prop',axiom,
    ! [Vvar__0___24Anonymous__33449] :
      ( cProp___24t(Vvar__0___24Anonymous__33449)
     => ( cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__elt__Prop___24a1(Vvar__0___24Anonymous__33449)
       => ( ? [Vvar__0__S__33451] :
              ( cType___24t(Vvar__0__S__33451)
              & ? [Vvar__1__x__33452] :
                  ( t(Vvar__1__x__33452,Vvar__0__S__33451)
                  & ? [Vvar__2__y__33453] :
                      ( t(Vvar__2__y__33453,Vvar__0__S__33451)
                      & Vvar__0___24Anonymous__33449 = c_24__prop__33473___24a4(Vvar__0___24Anonymous__33449,Vvar__0__S__33451,Vvar__1__x__33452,Vvar__2__y__33453) ) ) )
          | ? [Vvar__0__x__33454] :
              ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0__x__33454)
              & ? [Vvar__1__y__33455] :
                  ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1__y__33455)
                  & Vvar__0___24Anonymous__33449 = c_24__prop__33474___24a3(Vvar__0___24Anonymous__33449,Vvar__0__x__33454,Vvar__1__y__33455) ) )
          | ? [Vvar__0__x__33456] :
              ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(Vvar__0__x__33456)
              & ? [Vvar__1__s__33457] :
                  ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(Vvar__1__s__33457)
                  & Vvar__0___24Anonymous__33449 = c_24__prop__33475___24a3(Vvar__0___24Anonymous__33449,Vvar__0__x__33456,Vvar__1__s__33457) ) )
          | Vvar__0___24Anonymous__33449 = c_24True
          | Vvar__0___24Anonymous__33449 = c_24False
          | ? [Vvar__0__P__33458] :
              ( cProp___24t(Vvar__0__P__33458)
              & ? [Vvar__1__Q__33459] :
                  ( cProp___24t(Vvar__1__Q__33459)
                  & cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__elt__Prop___24a1(Vvar__0__P__33458)
                  & cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__elt__Prop___24a1(Vvar__1__Q__33459)
                  & Vvar__0___24Anonymous__33449 = c_24__prop__33476___24a3(Vvar__0___24Anonymous__33449,Vvar__0__P__33458,Vvar__1__Q__33459) ) )
          | ? [Vvar__0__P__33462] :
              ( cProp___24t(Vvar__0__P__33462)
              & ? [Vvar__1__Q__33463] :
                  ( cProp___24t(Vvar__1__Q__33463)
                  & cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__elt__Prop___24a1(Vvar__0__P__33462)
                  & cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__elt__Prop___24a1(Vvar__1__Q__33463)
                  & Vvar__0___24Anonymous__33449 = c_24__prop__33477___24a3(Vvar__0___24Anonymous__33449,Vvar__0__P__33462,Vvar__1__Q__33463) ) )
          | ? [Vvar__0__P__33466] :
              ( cProp___24t(Vvar__0__P__33466)
              & ? [Vvar__1__Q__33467] :
                  ( cProp___24t(Vvar__1__Q__33467)
                  & cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__elt__Prop___24a1(Vvar__0__P__33466)
                  & cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__elt__Prop___24a1(Vvar__1__Q__33467)
                  & Vvar__0___24Anonymous__33449 = c_24__prop__33478___24a3(Vvar__0___24Anonymous__33449,Vvar__0__P__33466,Vvar__1__Q__33467) ) )
          | ? [Vvar__0__P__33471] :
              ( cProp___24t(Vvar__0__P__33471)
              & cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__elt__Prop___24a1(Vvar__0__P__33471)
              & Vvar__0___24Anonymous__33449 = c_24__prop__33479___24a2(Vvar__0___24Anonymous__33449,Vvar__0__P__33471) ) ) ) ) ).

fof('$_inversion_Coq.micromega.ZMicromega.is_diff_env_elt',axiom,
    ! [Vvar__0__fr__33308,Vvar__1__env__33309,Vvar__2__env_27__33312,Vvar__3__x__33315] :
      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0__fr__33308)
     => ( c_24__type__33336___24t(Vvar__0__fr__33308,Vvar__1__env__33309,Vvar__2__env_27__33312,Vvar__3__x__33315,Vvar__1__env__33309)
       => ( c_24__type__33345___24t(Vvar__0__fr__33308,Vvar__1__env__33309,Vvar__2__env_27__33312,Vvar__3__x__33315,Vvar__2__env_27__33312)
         => ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__3__x__33315)
           => ( cCoq_2emicromega_2eZMicromega_2eis__diff__env__elt___24a4(Vvar__0__fr__33308,Vvar__1__env__33309,Vvar__2__env_27__33312,Vvar__3__x__33315)
             => ( happ(Vvar__1__env__33309,Vvar__3__x__33315) = happ(Vvar__2__env_27__33312,Vvar__3__x__33315)
                & happ(Vvar__1__env__33309,Vvar__3__x__33315) = cCoq_2eZArith_2eBinIntDef_2eZ_2esub___24a2(happ(Vvar__2__env_27__33312,cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(Vvar__0__fr__33308,Vvar__3__x__33315))),happ(Vvar__2__env_27__33312,cCoq_2eNumbers_2eBinNums_2exI___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(Vvar__0__fr__33308,Vvar__3__x__33315))))
                & cCoq_2eZArith_2eBinInt_2eZ_2ege___24a2(happ(Vvar__2__env_27__33312,cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(Vvar__0__fr__33308,Vvar__3__x__33315))),cCoq_2eNumbers_2eBinNums_2eZ0)
                & cCoq_2eZArith_2eBinInt_2eZ_2ege___24a2(happ(Vvar__2__env_27__33312,cCoq_2eNumbers_2eBinNums_2exI___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(Vvar__0__fr__33308,Vvar__3__x__33315))),cCoq_2eNumbers_2eBinNums_2eZ0)
                & p(c_24True) ) ) ) ) ) ) ).

fof('$_inversion_Coq.setoid_ring.Field_theory.FExpr',axiom,
    ! [Vvar__0__C__11516,VX11517] :
      ( cType___24t(Vvar__0__C__11516)
     => ( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__11516,VX11517)
       => ( VX11517 = cCoq_2esetoid__ring_2eField__theory_2eFEO___24a1(Vvar__0__C__11516)
          | VX11517 = cCoq_2esetoid__ring_2eField__theory_2eFEI___24a1(Vvar__0__C__11516)
          | ? [Vvar__1___24Anonymous__11521] :
              ( t(Vvar__1___24Anonymous__11521,Vvar__0__C__11516)
              & VX11517 = cCoq_2esetoid__ring_2eField__theory_2eFEc___24a2(Vvar__0__C__11516,Vvar__1___24Anonymous__11521) )
          | ? [Vvar__1___24Anonymous__11523] :
              ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__11523)
              & VX11517 = cCoq_2esetoid__ring_2eField__theory_2eFEX___24a2(Vvar__0__C__11516,Vvar__1___24Anonymous__11523) )
          | ? [Vvar__1___24Anonymous__11525] :
              ( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__11516,Vvar__1___24Anonymous__11525)
              & ? [Vvar__2___24Anonymous__11526] :
                  ( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__11516,Vvar__2___24Anonymous__11526)
                  & VX11517 = cCoq_2esetoid__ring_2eField__theory_2eFEadd___24a3(Vvar__0__C__11516,Vvar__1___24Anonymous__11525,Vvar__2___24Anonymous__11526) ) )
          | ? [Vvar__1___24Anonymous__11528] :
              ( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__11516,Vvar__1___24Anonymous__11528)
              & ? [Vvar__2___24Anonymous__11529] :
                  ( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__11516,Vvar__2___24Anonymous__11529)
                  & VX11517 = cCoq_2esetoid__ring_2eField__theory_2eFEsub___24a3(Vvar__0__C__11516,Vvar__1___24Anonymous__11528,Vvar__2___24Anonymous__11529) ) )
          | ? [Vvar__1___24Anonymous__11531] :
              ( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__11516,Vvar__1___24Anonymous__11531)
              & ? [Vvar__2___24Anonymous__11532] :
                  ( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__11516,Vvar__2___24Anonymous__11532)
                  & VX11517 = cCoq_2esetoid__ring_2eField__theory_2eFEmul___24a3(Vvar__0__C__11516,Vvar__1___24Anonymous__11531,Vvar__2___24Anonymous__11532) ) )
          | ? [Vvar__1___24Anonymous__11534] :
              ( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__11516,Vvar__1___24Anonymous__11534)
              & VX11517 = cCoq_2esetoid__ring_2eField__theory_2eFEopp___24a2(Vvar__0__C__11516,Vvar__1___24Anonymous__11534) )
          | ? [Vvar__1___24Anonymous__11536] :
              ( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__11516,Vvar__1___24Anonymous__11536)
              & VX11517 = cCoq_2esetoid__ring_2eField__theory_2eFEinv___24a2(Vvar__0__C__11516,Vvar__1___24Anonymous__11536) )
          | ? [Vvar__1___24Anonymous__11538] :
              ( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__11516,Vvar__1___24Anonymous__11538)
              & ? [Vvar__2___24Anonymous__11539] :
                  ( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__11516,Vvar__2___24Anonymous__11539)
                  & VX11517 = cCoq_2esetoid__ring_2eField__theory_2eFEdiv___24a3(Vvar__0__C__11516,Vvar__1___24Anonymous__11538,Vvar__2___24Anonymous__11539) ) )
          | ? [Vvar__1___24Anonymous__11541] :
              ( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__11516,Vvar__1___24Anonymous__11541)
              & ? [Vvar__2___24Anonymous__11542] :
                  ( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__2___24Anonymous__11542)
                  & VX11517 = cCoq_2esetoid__ring_2eField__theory_2eFEpow___24a3(Vvar__0__C__11516,Vvar__1___24Anonymous__11541,Vvar__2___24Anonymous__11542) ) ) ) ) ) ).

fof('$_inversion_Coq.setoid_ring.Field_theory.almost_field_theory',axiom,
    ! [Vvar__0__R__20110,Vvar__1__rO__20111,Vvar__2__rI__20112,Vvar__3__radd__20113,Vvar__4__rmul__20118,Vvar__5__rsub__20123,Vvar__6__ropp__20128,Vvar__7__rdiv__20131,Vvar__8__rinv__20136,Vvar__9__req__20139] :
      ( cType___24t(Vvar__0__R__20110)
     => ( t(Vvar__1__rO__20111,Vvar__0__R__20110)
       => ( t(Vvar__2__rI__20112,Vvar__0__R__20110)
         => ( c_24__type__20304___24t(Vvar__0__R__20110,Vvar__1__rO__20111,Vvar__2__rI__20112,Vvar__3__radd__20113,Vvar__4__rmul__20118,Vvar__5__rsub__20123,Vvar__6__ropp__20128,Vvar__7__rdiv__20131,Vvar__8__rinv__20136,Vvar__9__req__20139,Vvar__3__radd__20113)
           => ( c_24__type__20397___24t(Vvar__0__R__20110,Vvar__1__rO__20111,Vvar__2__rI__20112,Vvar__3__radd__20113,Vvar__4__rmul__20118,Vvar__5__rsub__20123,Vvar__6__ropp__20128,Vvar__7__rdiv__20131,Vvar__8__rinv__20136,Vvar__9__req__20139,Vvar__4__rmul__20118)
             => ( c_24__type__20490___24t(Vvar__0__R__20110,Vvar__1__rO__20111,Vvar__2__rI__20112,Vvar__3__radd__20113,Vvar__4__rmul__20118,Vvar__5__rsub__20123,Vvar__6__ropp__20128,Vvar__7__rdiv__20131,Vvar__8__rinv__20136,Vvar__9__req__20139,Vvar__5__rsub__20123)
               => ( c_24__type__20572___24t(Vvar__0__R__20110,Vvar__1__rO__20111,Vvar__2__rI__20112,Vvar__3__radd__20113,Vvar__4__rmul__20118,Vvar__5__rsub__20123,Vvar__6__ropp__20128,Vvar__7__rdiv__20131,Vvar__8__rinv__20136,Vvar__9__req__20139,Vvar__6__ropp__20128)
                 => ( c_24__type__20665___24t(Vvar__0__R__20110,Vvar__1__rO__20111,Vvar__2__rI__20112,Vvar__3__radd__20113,Vvar__4__rmul__20118,Vvar__5__rsub__20123,Vvar__6__ropp__20128,Vvar__7__rdiv__20131,Vvar__8__rinv__20136,Vvar__9__req__20139,Vvar__7__rdiv__20131)
                   => ( c_24__type__20747___24t(Vvar__0__R__20110,Vvar__1__rO__20111,Vvar__2__rI__20112,Vvar__3__radd__20113,Vvar__4__rmul__20118,Vvar__5__rsub__20123,Vvar__6__ropp__20128,Vvar__7__rdiv__20131,Vvar__8__rinv__20136,Vvar__9__req__20139,Vvar__8__rinv__20136)
                     => ( c_24__type__20840___24t(Vvar__0__R__20110,Vvar__1__rO__20111,Vvar__2__rI__20112,Vvar__3__radd__20113,Vvar__4__rmul__20118,Vvar__5__rsub__20123,Vvar__6__ropp__20128,Vvar__7__rdiv__20131,Vvar__8__rinv__20136,Vvar__9__req__20139,Vvar__9__req__20139)
                       => ( cCoq_2esetoid__ring_2eField__theory_2ealmost__field__theory___24a10(Vvar__0__R__20110,Vvar__1__rO__20111,Vvar__2__rI__20112,Vvar__3__radd__20113,Vvar__4__rmul__20118,Vvar__5__rsub__20123,Vvar__6__ropp__20128,Vvar__7__rdiv__20131,Vvar__8__rinv__20136,Vvar__9__req__20139)
                         => ( cCoq_2esetoid__ring_2eRing__theory_2ealmost__ring__theory___24a8(Vvar__0__R__20110,Vvar__1__rO__20111,Vvar__2__rI__20112,Vvar__3__radd__20113,Vvar__4__rmul__20118,Vvar__5__rsub__20123,Vvar__6__ropp__20128,Vvar__9__req__20139)
                            & ~ p(happ(happ(Vvar__9__req__20139,Vvar__2__rI__20112),Vvar__1__rO__20111))
                            & ! [Vvar__var__var__var__var__var__var__12__p__20182__20184__20191__20193__20195__20197__20199] :
                                ( t(Vvar__var__var__var__var__var__var__12__p__20182__20184__20191__20193__20195__20197__20199,Vvar__0__R__20110)
                               => ! [Vvar__var__var__var__var__var__var__13__q__20183__20185__20192__20194__20196__20198__20200] :
                                    ( t(Vvar__var__var__var__var__var__var__13__q__20183__20185__20192__20194__20196__20198__20200,Vvar__0__R__20110)
                                   => p(happ(happ(Vvar__9__req__20139,happ(happ(Vvar__7__rdiv__20131,Vvar__var__var__var__var__var__var__12__p__20182__20184__20191__20193__20195__20197__20199),Vvar__var__var__var__var__var__var__13__q__20183__20185__20192__20194__20196__20198__20200)),happ(happ(Vvar__4__rmul__20118,Vvar__var__var__var__var__var__var__12__p__20182__20184__20191__20193__20195__20197__20199),happ(Vvar__8__rinv__20136,Vvar__var__var__var__var__var__var__13__q__20183__20185__20192__20194__20196__20198__20200)))) ) )
                            & ! [Vvar__var__var__var__var__var__var__var__13__p__20187__20189__20201__20203__20205__20207__20209__20211] :
                                ( t(Vvar__var__var__var__var__var__var__var__13__p__20187__20189__20201__20203__20205__20207__20209__20211,Vvar__0__R__20110)
                               => ( ~ p(happ(happ(Vvar__9__req__20139,Vvar__var__var__var__var__var__var__var__13__p__20187__20189__20201__20203__20205__20207__20209__20211),Vvar__1__rO__20111))
                                 => p(happ(happ(Vvar__9__req__20139,happ(happ(Vvar__4__rmul__20118,happ(Vvar__8__rinv__20136,Vvar__var__var__var__var__var__var__var__13__p__20187__20189__20201__20203__20205__20207__20209__20211)),Vvar__var__var__var__var__var__var__var__13__p__20187__20189__20201__20203__20205__20207__20209__20211)),Vvar__2__rI__20112)) ) )
                            & p(c_24True) ) ) ) ) ) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.setoid_ring.Field_theory.field_theory',axiom,
    ! [Vvar__0__R__20860,Vvar__1__rO__20861,Vvar__2__rI__20862,Vvar__3__radd__20863,Vvar__4__rmul__20868,Vvar__5__rsub__20873,Vvar__6__ropp__20878,Vvar__7__rdiv__20881,Vvar__8__rinv__20886,Vvar__9__req__20889] :
      ( cType___24t(Vvar__0__R__20860)
     => ( t(Vvar__1__rO__20861,Vvar__0__R__20860)
       => ( t(Vvar__2__rI__20862,Vvar__0__R__20860)
         => ( c_24__type__21054___24t(Vvar__0__R__20860,Vvar__1__rO__20861,Vvar__2__rI__20862,Vvar__3__radd__20863,Vvar__4__rmul__20868,Vvar__5__rsub__20873,Vvar__6__ropp__20878,Vvar__7__rdiv__20881,Vvar__8__rinv__20886,Vvar__9__req__20889,Vvar__3__radd__20863)
           => ( c_24__type__21147___24t(Vvar__0__R__20860,Vvar__1__rO__20861,Vvar__2__rI__20862,Vvar__3__radd__20863,Vvar__4__rmul__20868,Vvar__5__rsub__20873,Vvar__6__ropp__20878,Vvar__7__rdiv__20881,Vvar__8__rinv__20886,Vvar__9__req__20889,Vvar__4__rmul__20868)
             => ( c_24__type__21240___24t(Vvar__0__R__20860,Vvar__1__rO__20861,Vvar__2__rI__20862,Vvar__3__radd__20863,Vvar__4__rmul__20868,Vvar__5__rsub__20873,Vvar__6__ropp__20878,Vvar__7__rdiv__20881,Vvar__8__rinv__20886,Vvar__9__req__20889,Vvar__5__rsub__20873)
               => ( c_24__type__21322___24t(Vvar__0__R__20860,Vvar__1__rO__20861,Vvar__2__rI__20862,Vvar__3__radd__20863,Vvar__4__rmul__20868,Vvar__5__rsub__20873,Vvar__6__ropp__20878,Vvar__7__rdiv__20881,Vvar__8__rinv__20886,Vvar__9__req__20889,Vvar__6__ropp__20878)
                 => ( c_24__type__21415___24t(Vvar__0__R__20860,Vvar__1__rO__20861,Vvar__2__rI__20862,Vvar__3__radd__20863,Vvar__4__rmul__20868,Vvar__5__rsub__20873,Vvar__6__ropp__20878,Vvar__7__rdiv__20881,Vvar__8__rinv__20886,Vvar__9__req__20889,Vvar__7__rdiv__20881)
                   => ( c_24__type__21497___24t(Vvar__0__R__20860,Vvar__1__rO__20861,Vvar__2__rI__20862,Vvar__3__radd__20863,Vvar__4__rmul__20868,Vvar__5__rsub__20873,Vvar__6__ropp__20878,Vvar__7__rdiv__20881,Vvar__8__rinv__20886,Vvar__9__req__20889,Vvar__8__rinv__20886)
                     => ( c_24__type__21590___24t(Vvar__0__R__20860,Vvar__1__rO__20861,Vvar__2__rI__20862,Vvar__3__radd__20863,Vvar__4__rmul__20868,Vvar__5__rsub__20873,Vvar__6__ropp__20878,Vvar__7__rdiv__20881,Vvar__8__rinv__20886,Vvar__9__req__20889,Vvar__9__req__20889)
                       => ( cCoq_2esetoid__ring_2eField__theory_2efield__theory___24a10(Vvar__0__R__20860,Vvar__1__rO__20861,Vvar__2__rI__20862,Vvar__3__radd__20863,Vvar__4__rmul__20868,Vvar__5__rsub__20873,Vvar__6__ropp__20878,Vvar__7__rdiv__20881,Vvar__8__rinv__20886,Vvar__9__req__20889)
                         => ( cCoq_2esetoid__ring_2eRing__theory_2ering__theory___24a8(Vvar__0__R__20860,Vvar__1__rO__20861,Vvar__2__rI__20862,Vvar__3__radd__20863,Vvar__4__rmul__20868,Vvar__5__rsub__20873,Vvar__6__ropp__20878,Vvar__9__req__20889)
                            & ~ p(happ(happ(Vvar__9__req__20889,Vvar__2__rI__20862),Vvar__1__rO__20861))
                            & ! [Vvar__var__var__var__var__var__var__12__p__20932__20934__20941__20943__20945__20947__20949] :
                                ( t(Vvar__var__var__var__var__var__var__12__p__20932__20934__20941__20943__20945__20947__20949,Vvar__0__R__20860)
                               => ! [Vvar__var__var__var__var__var__var__13__q__20933__20935__20942__20944__20946__20948__20950] :
                                    ( t(Vvar__var__var__var__var__var__var__13__q__20933__20935__20942__20944__20946__20948__20950,Vvar__0__R__20860)
                                   => p(happ(happ(Vvar__9__req__20889,happ(happ(Vvar__7__rdiv__20881,Vvar__var__var__var__var__var__var__12__p__20932__20934__20941__20943__20945__20947__20949),Vvar__var__var__var__var__var__var__13__q__20933__20935__20942__20944__20946__20948__20950)),happ(happ(Vvar__4__rmul__20868,Vvar__var__var__var__var__var__var__12__p__20932__20934__20941__20943__20945__20947__20949),happ(Vvar__8__rinv__20886,Vvar__var__var__var__var__var__var__13__q__20933__20935__20942__20944__20946__20948__20950)))) ) )
                            & ! [Vvar__var__var__var__var__var__var__var__13__p__20937__20939__20951__20953__20955__20957__20959__20961] :
                                ( t(Vvar__var__var__var__var__var__var__var__13__p__20937__20939__20951__20953__20955__20957__20959__20961,Vvar__0__R__20860)
                               => ( ~ p(happ(happ(Vvar__9__req__20889,Vvar__var__var__var__var__var__var__var__13__p__20937__20939__20951__20953__20955__20957__20959__20961),Vvar__1__rO__20861))
                                 => p(happ(happ(Vvar__9__req__20889,happ(happ(Vvar__4__rmul__20868,happ(Vvar__8__rinv__20886,Vvar__var__var__var__var__var__var__var__13__p__20937__20939__20951__20953__20955__20957__20959__20961)),Vvar__var__var__var__var__var__var__var__13__p__20937__20939__20951__20953__20955__20957__20959__20961)),Vvar__2__rI__20862)) ) )
                            & p(c_24True) ) ) ) ) ) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.setoid_ring.Field_theory.linear',axiom,
    ! [Vvar__0__C__12134,VX12135] :
      ( cType___24t(Vvar__0__C__12134)
     => ( cCoq_2esetoid__ring_2eField__theory_2elinear___24t(Vvar__0__C__12134,VX12135)
       => ? [Vvar__1__num__12137] :
            ( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__12134,Vvar__1__num__12137)
            & ? [Vvar__2__denum__12138] :
                ( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__12134,Vvar__2__denum__12138)
                & ? [Vvar__3__condition__12139] :
                    ( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(Vvar__0__C__12134),Vvar__3__condition__12139)
                    & VX12135 = cCoq_2esetoid__ring_2eField__theory_2emk__linear___24a4(Vvar__0__C__12134,Vvar__1__num__12137,Vvar__2__denum__12138,Vvar__3__condition__12139) ) ) ) ) ) ).

fof('$_inversion_Coq.setoid_ring.Ring_polynom.Mon',axiom,
    ! [VX15262] :
      ( cCoq_2esetoid__ring_2eRing__polynom_2eMon___24t(VX15262)
     => ( VX15262 = cCoq_2esetoid__ring_2eRing__polynom_2emon0
        | ? [Vvar__0___24Anonymous__15263] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__15263)
            & ? [Vvar__1___24Anonymous__15264] :
                ( cCoq_2esetoid__ring_2eRing__polynom_2eMon___24t(Vvar__1___24Anonymous__15264)
                & VX15262 = cCoq_2esetoid__ring_2eRing__polynom_2ezmon___24a2(Vvar__0___24Anonymous__15263,Vvar__1___24Anonymous__15264) ) )
        | ? [Vvar__0___24Anonymous__15265] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__15265)
            & ? [Vvar__1___24Anonymous__15266] :
                ( cCoq_2esetoid__ring_2eRing__polynom_2eMon___24t(Vvar__1___24Anonymous__15266)
                & VX15262 = cCoq_2esetoid__ring_2eRing__polynom_2evmon___24a2(Vvar__0___24Anonymous__15265,Vvar__1___24Anonymous__15266) ) ) ) ) ).

fof('$_inversion_Coq.setoid_ring.Ring_polynom.PExpr',axiom,
    ! [Vvar__0__C__15283,VX15284] :
      ( cType___24t(Vvar__0__C__15283)
     => ( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__15283,VX15284)
       => ( VX15284 = cCoq_2esetoid__ring_2eRing__polynom_2ePEO___24a1(Vvar__0__C__15283)
          | VX15284 = cCoq_2esetoid__ring_2eRing__polynom_2ePEI___24a1(Vvar__0__C__15283)
          | ? [Vvar__1___24Anonymous__15288] :
              ( t(Vvar__1___24Anonymous__15288,Vvar__0__C__15283)
              & VX15284 = cCoq_2esetoid__ring_2eRing__polynom_2ePEc___24a2(Vvar__0__C__15283,Vvar__1___24Anonymous__15288) )
          | ? [Vvar__1___24Anonymous__15290] :
              ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__15290)
              & VX15284 = cCoq_2esetoid__ring_2eRing__polynom_2ePEX___24a2(Vvar__0__C__15283,Vvar__1___24Anonymous__15290) )
          | ? [Vvar__1___24Anonymous__15292] :
              ( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__15283,Vvar__1___24Anonymous__15292)
              & ? [Vvar__2___24Anonymous__15293] :
                  ( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__15283,Vvar__2___24Anonymous__15293)
                  & VX15284 = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(Vvar__0__C__15283,Vvar__1___24Anonymous__15292,Vvar__2___24Anonymous__15293) ) )
          | ? [Vvar__1___24Anonymous__15295] :
              ( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__15283,Vvar__1___24Anonymous__15295)
              & ? [Vvar__2___24Anonymous__15296] :
                  ( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__15283,Vvar__2___24Anonymous__15296)
                  & VX15284 = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(Vvar__0__C__15283,Vvar__1___24Anonymous__15295,Vvar__2___24Anonymous__15296) ) )
          | ? [Vvar__1___24Anonymous__15298] :
              ( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__15283,Vvar__1___24Anonymous__15298)
              & ? [Vvar__2___24Anonymous__15299] :
                  ( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__15283,Vvar__2___24Anonymous__15299)
                  & VX15284 = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(Vvar__0__C__15283,Vvar__1___24Anonymous__15298,Vvar__2___24Anonymous__15299) ) )
          | ? [Vvar__1___24Anonymous__15301] :
              ( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__15283,Vvar__1___24Anonymous__15301)
              & VX15284 = cCoq_2esetoid__ring_2eRing__polynom_2ePEopp___24a2(Vvar__0__C__15283,Vvar__1___24Anonymous__15301) )
          | ? [Vvar__1___24Anonymous__15303] :
              ( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__15283,Vvar__1___24Anonymous__15303)
              & ? [Vvar__2___24Anonymous__15304] :
                  ( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__2___24Anonymous__15304)
                  & VX15284 = cCoq_2esetoid__ring_2eRing__polynom_2ePEpow___24a3(Vvar__0__C__15283,Vvar__1___24Anonymous__15303,Vvar__2___24Anonymous__15304) ) ) ) ) ) ).

fof('$_inversion_Coq.setoid_ring.Ring_polynom.Pol',axiom,
    ! [Vvar__0__C__15083,VX15084] :
      ( cType___24t(Vvar__0__C__15083)
     => ( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vvar__0__C__15083,VX15084)
       => ( ? [Vvar__1___24Anonymous__15086] :
              ( t(Vvar__1___24Anonymous__15086,Vvar__0__C__15083)
              & VX15084 = cCoq_2esetoid__ring_2eRing__polynom_2ePc___24a2(Vvar__0__C__15083,Vvar__1___24Anonymous__15086) )
          | ? [Vvar__1___24Anonymous__15088] :
              ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__15088)
              & ? [Vvar__2___24Anonymous__15089] :
                  ( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vvar__0__C__15083,Vvar__2___24Anonymous__15089)
                  & VX15084 = cCoq_2esetoid__ring_2eRing__polynom_2ePinj___24a3(Vvar__0__C__15083,Vvar__1___24Anonymous__15088,Vvar__2___24Anonymous__15089) ) )
          | ? [Vvar__1___24Anonymous__15091] :
              ( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vvar__0__C__15083,Vvar__1___24Anonymous__15091)
              & ? [Vvar__2___24Anonymous__15092] :
                  ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2___24Anonymous__15092)
                  & ? [Vvar__3___24Anonymous__15093] :
                      ( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vvar__0__C__15083,Vvar__3___24Anonymous__15093)
                      & VX15084 = cCoq_2esetoid__ring_2eRing__polynom_2ePX___24a4(Vvar__0__C__15083,Vvar__1___24Anonymous__15091,Vvar__2___24Anonymous__15092,Vvar__3___24Anonymous__15093) ) ) ) ) ) ) ).

fof('$_inversion_Coq.setoid_ring.Ring_theory.almost_ring_theory',axiom,
    ! [Vvar__0__R__29210,Vvar__1__rO__29211,Vvar__2__rI__29212,Vvar__3__radd__29213,Vvar__4__rmul__29218,Vvar__5__rsub__29223,Vvar__6__ropp__29228,Vvar__7__req__29231] :
      ( cType___24t(Vvar__0__R__29210)
     => ( t(Vvar__1__rO__29211,Vvar__0__R__29210)
       => ( t(Vvar__2__rI__29212,Vvar__0__R__29210)
         => ( c_24__type__29459___24t(Vvar__0__R__29210,Vvar__1__rO__29211,Vvar__2__rI__29212,Vvar__3__radd__29213,Vvar__4__rmul__29218,Vvar__5__rsub__29223,Vvar__6__ropp__29228,Vvar__7__req__29231,Vvar__3__radd__29213)
           => ( c_24__type__29522___24t(Vvar__0__R__29210,Vvar__1__rO__29211,Vvar__2__rI__29212,Vvar__3__radd__29213,Vvar__4__rmul__29218,Vvar__5__rsub__29223,Vvar__6__ropp__29228,Vvar__7__req__29231,Vvar__4__rmul__29218)
             => ( c_24__type__29585___24t(Vvar__0__R__29210,Vvar__1__rO__29211,Vvar__2__rI__29212,Vvar__3__radd__29213,Vvar__4__rmul__29218,Vvar__5__rsub__29223,Vvar__6__ropp__29228,Vvar__7__req__29231,Vvar__5__rsub__29223)
               => ( c_24__type__29639___24t(Vvar__0__R__29210,Vvar__1__rO__29211,Vvar__2__rI__29212,Vvar__3__radd__29213,Vvar__4__rmul__29218,Vvar__5__rsub__29223,Vvar__6__ropp__29228,Vvar__7__req__29231,Vvar__6__ropp__29228)
                 => ( c_24__type__29702___24t(Vvar__0__R__29210,Vvar__1__rO__29211,Vvar__2__rI__29212,Vvar__3__radd__29213,Vvar__4__rmul__29218,Vvar__5__rsub__29223,Vvar__6__ropp__29228,Vvar__7__req__29231,Vvar__7__req__29231)
                   => ( cCoq_2esetoid__ring_2eRing__theory_2ealmost__ring__theory___24a8(Vvar__0__R__29210,Vvar__1__rO__29211,Vvar__2__rI__29212,Vvar__3__radd__29213,Vvar__4__rmul__29218,Vvar__5__rsub__29223,Vvar__6__ropp__29228,Vvar__7__req__29231)
                     => ( ! [Vvar__var__var__var__var__var__8__x__29264__29265__29318__29319__29320__29321] :
                            ( t(Vvar__var__var__var__var__var__8__x__29264__29265__29318__29319__29320__29321,Vvar__0__R__29210)
                           => p(happ(happ(Vvar__7__req__29231,happ(happ(Vvar__3__radd__29213,Vvar__1__rO__29211),Vvar__var__var__var__var__var__8__x__29264__29265__29318__29319__29320__29321)),Vvar__var__var__var__var__var__8__x__29264__29265__29318__29319__29320__29321)) )
                        & ! [Vvar__var__var__var__var__9__x__29267__29269__29322__29324__29326] :
                            ( t(Vvar__var__var__var__var__9__x__29267__29269__29322__29324__29326,Vvar__0__R__29210)
                           => ! [Vvar__var__var__var__var__10__y__29268__29270__29323__29325__29327] :
                                ( t(Vvar__var__var__var__var__10__y__29268__29270__29323__29325__29327,Vvar__0__R__29210)
                               => p(happ(happ(Vvar__7__req__29231,happ(happ(Vvar__3__radd__29213,Vvar__var__var__var__var__9__x__29267__29269__29322__29324__29326),Vvar__var__var__var__var__10__y__29268__29270__29323__29325__29327)),happ(happ(Vvar__3__radd__29213,Vvar__var__var__var__var__10__y__29268__29270__29323__29325__29327),Vvar__var__var__var__var__9__x__29267__29269__29322__29324__29326))) ) )
                        & ! [Vvar__var__var__var__var__10__x__29272__29275__29328__29331__29334] :
                            ( t(Vvar__var__var__var__var__10__x__29272__29275__29328__29331__29334,Vvar__0__R__29210)
                           => ! [Vvar__var__var__var__var__11__y__29273__29276__29329__29332__29335] :
                                ( t(Vvar__var__var__var__var__11__y__29273__29276__29329__29332__29335,Vvar__0__R__29210)
                               => ! [Vvar__var__var__var__var__12__z__29274__29277__29330__29333__29336] :
                                    ( t(Vvar__var__var__var__var__12__z__29274__29277__29330__29333__29336,Vvar__0__R__29210)
                                   => p(happ(happ(Vvar__7__req__29231,happ(happ(Vvar__3__radd__29213,Vvar__var__var__var__var__10__x__29272__29275__29328__29331__29334),happ(happ(Vvar__3__radd__29213,Vvar__var__var__var__var__11__y__29273__29276__29329__29332__29335),Vvar__var__var__var__var__12__z__29274__29277__29330__29333__29336))),happ(happ(Vvar__3__radd__29213,happ(happ(Vvar__3__radd__29213,Vvar__var__var__var__var__10__x__29272__29275__29328__29331__29334),Vvar__var__var__var__var__11__y__29273__29276__29329__29332__29335)),Vvar__var__var__var__var__12__z__29274__29277__29330__29333__29336))) ) ) )
                        & ! [Vvar__var__var__var__var__var__11__x__29279__29280__29337__29338__29339__29340] :
                            ( t(Vvar__var__var__var__var__var__11__x__29279__29280__29337__29338__29339__29340,Vvar__0__R__29210)
                           => p(happ(happ(Vvar__7__req__29231,happ(happ(Vvar__4__rmul__29218,Vvar__2__rI__29212),Vvar__var__var__var__var__var__11__x__29279__29280__29337__29338__29339__29340)),Vvar__var__var__var__var__var__11__x__29279__29280__29337__29338__29339__29340)) )
                        & ! [Vvar__var__var__var__var__var__12__x__29282__29283__29341__29342__29343__29344] :
                            ( t(Vvar__var__var__var__var__var__12__x__29282__29283__29341__29342__29343__29344,Vvar__0__R__29210)
                           => p(happ(happ(Vvar__7__req__29231,happ(happ(Vvar__4__rmul__29218,Vvar__1__rO__29211),Vvar__var__var__var__var__var__12__x__29282__29283__29341__29342__29343__29344)),Vvar__1__rO__29211)) )
                        & ! [Vvar__var__var__var__var__13__x__29285__29287__29345__29347__29349] :
                            ( t(Vvar__var__var__var__var__13__x__29285__29287__29345__29347__29349,Vvar__0__R__29210)
                           => ! [Vvar__var__var__var__var__14__y__29286__29288__29346__29348__29350] :
                                ( t(Vvar__var__var__var__var__14__y__29286__29288__29346__29348__29350,Vvar__0__R__29210)
                               => p(happ(happ(Vvar__7__req__29231,happ(happ(Vvar__4__rmul__29218,Vvar__var__var__var__var__13__x__29285__29287__29345__29347__29349),Vvar__var__var__var__var__14__y__29286__29288__29346__29348__29350)),happ(happ(Vvar__4__rmul__29218,Vvar__var__var__var__var__14__y__29286__29288__29346__29348__29350),Vvar__var__var__var__var__13__x__29285__29287__29345__29347__29349))) ) )
                        & ! [Vvar__var__var__var__var__14__x__29290__29293__29351__29354__29357] :
                            ( t(Vvar__var__var__var__var__14__x__29290__29293__29351__29354__29357,Vvar__0__R__29210)
                           => ! [Vvar__var__var__var__var__15__y__29291__29294__29352__29355__29358] :
                                ( t(Vvar__var__var__var__var__15__y__29291__29294__29352__29355__29358,Vvar__0__R__29210)
                               => ! [Vvar__var__var__var__var__16__z__29292__29295__29353__29356__29359] :
                                    ( t(Vvar__var__var__var__var__16__z__29292__29295__29353__29356__29359,Vvar__0__R__29210)
                                   => p(happ(happ(Vvar__7__req__29231,happ(happ(Vvar__4__rmul__29218,Vvar__var__var__var__var__14__x__29290__29293__29351__29354__29357),happ(happ(Vvar__4__rmul__29218,Vvar__var__var__var__var__15__y__29291__29294__29352__29355__29358),Vvar__var__var__var__var__16__z__29292__29295__29353__29356__29359))),happ(happ(Vvar__4__rmul__29218,happ(happ(Vvar__4__rmul__29218,Vvar__var__var__var__var__14__x__29290__29293__29351__29354__29357),Vvar__var__var__var__var__15__y__29291__29294__29352__29355__29358)),Vvar__var__var__var__var__16__z__29292__29295__29353__29356__29359))) ) ) )
                        & ! [Vvar__var__var__var__var__var__15__x__29297__29300__29360__29363__29366__29369] :
                            ( t(Vvar__var__var__var__var__var__15__x__29297__29300__29360__29363__29366__29369,Vvar__0__R__29210)
                           => ! [Vvar__var__var__var__var__var__16__y__29298__29301__29361__29364__29367__29370] :
                                ( t(Vvar__var__var__var__var__var__16__y__29298__29301__29361__29364__29367__29370,Vvar__0__R__29210)
                               => ! [Vvar__var__var__var__var__var__17__z__29299__29302__29362__29365__29368__29371] :
                                    ( t(Vvar__var__var__var__var__var__17__z__29299__29302__29362__29365__29368__29371,Vvar__0__R__29210)
                                   => p(happ(happ(Vvar__7__req__29231,happ(happ(Vvar__4__rmul__29218,happ(happ(Vvar__3__radd__29213,Vvar__var__var__var__var__var__15__x__29297__29300__29360__29363__29366__29369),Vvar__var__var__var__var__var__16__y__29298__29301__29361__29364__29367__29370)),Vvar__var__var__var__var__var__17__z__29299__29302__29362__29365__29368__29371)),happ(happ(Vvar__3__radd__29213,happ(happ(Vvar__4__rmul__29218,Vvar__var__var__var__var__var__15__x__29297__29300__29360__29363__29366__29369),Vvar__var__var__var__var__var__17__z__29299__29302__29362__29365__29368__29371)),happ(happ(Vvar__4__rmul__29218,Vvar__var__var__var__var__var__16__y__29298__29301__29361__29364__29367__29370),Vvar__var__var__var__var__var__17__z__29299__29302__29362__29365__29368__29371)))) ) ) )
                        & ! [Vvar__var__var__var__var__var__16__x__29304__29306__29372__29374__29376__29378] :
                            ( t(Vvar__var__var__var__var__var__16__x__29304__29306__29372__29374__29376__29378,Vvar__0__R__29210)
                           => ! [Vvar__var__var__var__var__var__17__y__29305__29307__29373__29375__29377__29379] :
                                ( t(Vvar__var__var__var__var__var__17__y__29305__29307__29373__29375__29377__29379,Vvar__0__R__29210)
                               => p(happ(happ(Vvar__7__req__29231,happ(Vvar__6__ropp__29228,happ(happ(Vvar__4__rmul__29218,Vvar__var__var__var__var__var__16__x__29304__29306__29372__29374__29376__29378),Vvar__var__var__var__var__var__17__y__29305__29307__29373__29375__29377__29379))),happ(happ(Vvar__4__rmul__29218,happ(Vvar__6__ropp__29228,Vvar__var__var__var__var__var__16__x__29304__29306__29372__29374__29376__29378)),Vvar__var__var__var__var__var__17__y__29305__29307__29373__29375__29377__29379))) ) )
                        & ! [Vvar__var__var__var__var__var__17__x__29309__29311__29380__29382__29384__29386] :
                            ( t(Vvar__var__var__var__var__var__17__x__29309__29311__29380__29382__29384__29386,Vvar__0__R__29210)
                           => ! [Vvar__var__var__var__var__var__18__y__29310__29312__29381__29383__29385__29387] :
                                ( t(Vvar__var__var__var__var__var__18__y__29310__29312__29381__29383__29385__29387,Vvar__0__R__29210)
                               => p(happ(happ(Vvar__7__req__29231,happ(Vvar__6__ropp__29228,happ(happ(Vvar__3__radd__29213,Vvar__var__var__var__var__var__17__x__29309__29311__29380__29382__29384__29386),Vvar__var__var__var__var__var__18__y__29310__29312__29381__29383__29385__29387))),happ(happ(Vvar__3__radd__29213,happ(Vvar__6__ropp__29228,Vvar__var__var__var__var__var__17__x__29309__29311__29380__29382__29384__29386)),happ(Vvar__6__ropp__29228,Vvar__var__var__var__var__var__18__y__29310__29312__29381__29383__29385__29387)))) ) )
                        & ! [Vvar__var__var__var__var__var__var__18__x__29314__29316__29388__29390__29392__29394__29396] :
                            ( t(Vvar__var__var__var__var__var__var__18__x__29314__29316__29388__29390__29392__29394__29396,Vvar__0__R__29210)
                           => ! [Vvar__var__var__var__var__var__var__19__y__29315__29317__29389__29391__29393__29395__29397] :
                                ( t(Vvar__var__var__var__var__var__var__19__y__29315__29317__29389__29391__29393__29395__29397,Vvar__0__R__29210)
                               => p(happ(happ(Vvar__7__req__29231,happ(happ(Vvar__5__rsub__29223,Vvar__var__var__var__var__var__var__18__x__29314__29316__29388__29390__29392__29394__29396),Vvar__var__var__var__var__var__var__19__y__29315__29317__29389__29391__29393__29395__29397)),happ(happ(Vvar__3__radd__29213,Vvar__var__var__var__var__var__var__18__x__29314__29316__29388__29390__29392__29394__29396),happ(Vvar__6__ropp__29228,Vvar__var__var__var__var__var__var__19__y__29315__29317__29389__29391__29393__29395__29397)))) ) )
                        & p(c_24True) ) ) ) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.setoid_ring.Ring_theory.power_theory',axiom,
    ! [Vvar__0__R__32204,Vvar__1__rI__32205,Vvar__2__rmul__32206,Vvar__3__req__32211,Vvar__4__Cpow__32216,Vvar__5__Cp__phi__32217,Vvar__6__rpow__32220] :
      ( cType___24t(Vvar__0__R__32204)
     => ( t(Vvar__1__rI__32205,Vvar__0__R__32204)
       => ( c_24__type__32306___24t(Vvar__0__R__32204,Vvar__1__rI__32205,Vvar__2__rmul__32206,Vvar__3__req__32211,Vvar__4__Cpow__32216,Vvar__5__Cp__phi__32217,Vvar__6__rpow__32220,Vvar__2__rmul__32206)
         => ( c_24__type__32350___24t(Vvar__0__R__32204,Vvar__1__rI__32205,Vvar__2__rmul__32206,Vvar__3__req__32211,Vvar__4__Cpow__32216,Vvar__5__Cp__phi__32217,Vvar__6__rpow__32220,Vvar__3__req__32211)
           => ( cType___24t(Vvar__4__Cpow__32216)
             => ( c_24__type__32386___24t(Vvar__0__R__32204,Vvar__1__rI__32205,Vvar__2__rmul__32206,Vvar__3__req__32211,Vvar__4__Cpow__32216,Vvar__5__Cp__phi__32217,Vvar__6__rpow__32220,Vvar__5__Cp__phi__32217)
               => ( c_24__type__32430___24t(Vvar__0__R__32204,Vvar__1__rI__32205,Vvar__2__rmul__32206,Vvar__3__req__32211,Vvar__4__Cpow__32216,Vvar__5__Cp__phi__32217,Vvar__6__rpow__32220,Vvar__6__rpow__32220)
                 => ( cCoq_2esetoid__ring_2eRing__theory_2epower__theory___24a7(Vvar__0__R__32204,Vvar__1__rI__32205,Vvar__2__rmul__32206,Vvar__3__req__32211,Vvar__4__Cpow__32216,Vvar__5__Cp__phi__32217,Vvar__6__rpow__32220)
                   => ( ! [Vvar__var__var__var__var__var__var__var__7__r__32248__32250__32252__32254__32256__32258__32260__32262] :
                          ( t(Vvar__var__var__var__var__var__var__var__7__r__32248__32250__32252__32254__32256__32258__32260__32262,Vvar__0__R__32204)
                         => ! [Vvar__var__var__var__var__var__var__var__8__n__32249__32251__32253__32255__32257__32259__32261__32263] :
                              ( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__var__var__var__var__var__var__var__8__n__32249__32251__32253__32255__32257__32259__32261__32263)
                             => p(happ(happ(Vvar__3__req__32211,happ(happ(Vvar__6__rpow__32220,Vvar__var__var__var__var__var__var__var__7__r__32248__32250__32252__32254__32256__32258__32260__32262),happ(Vvar__5__Cp__phi__32217,Vvar__var__var__var__var__var__var__var__8__n__32249__32251__32253__32255__32257__32259__32261__32263))),cCoq_2esetoid__ring_2eRing__theory_2epow__N___24a5(Vvar__0__R__32204,Vvar__1__rI__32205,Vvar__2__rmul__32206,Vvar__var__var__var__var__var__var__var__7__r__32248__32250__32252__32254__32256__32258__32260__32262,Vvar__var__var__var__var__var__var__var__8__n__32249__32251__32253__32255__32257__32259__32261__32263))) ) )
                      & p(c_24True) ) ) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.setoid_ring.Ring_theory.ring_eq_ext',axiom,
    ! [Vvar__0__R__30461,Vvar__1__radd__30462,Vvar__2__rmul__30467,Vvar__3__ropp__30472,Vvar__4__req__30475] :
      ( cType___24t(Vvar__0__R__30461)
     => ( c_24__type__30566___24t(Vvar__0__R__30461,Vvar__1__radd__30462,Vvar__2__rmul__30467,Vvar__3__ropp__30472,Vvar__4__req__30475,Vvar__1__radd__30462)
       => ( c_24__type__30596___24t(Vvar__0__R__30461,Vvar__1__radd__30462,Vvar__2__rmul__30467,Vvar__3__ropp__30472,Vvar__4__req__30475,Vvar__2__rmul__30467)
         => ( c_24__type__30620___24t(Vvar__0__R__30461,Vvar__1__radd__30462,Vvar__2__rmul__30467,Vvar__3__ropp__30472,Vvar__4__req__30475,Vvar__3__ropp__30472)
           => ( c_24__type__30650___24t(Vvar__0__R__30461,Vvar__1__radd__30462,Vvar__2__rmul__30467,Vvar__3__ropp__30472,Vvar__4__req__30475,Vvar__4__req__30475)
             => ( cCoq_2esetoid__ring_2eRing__theory_2ering__eq__ext___24a5(Vvar__0__R__30461,Vvar__1__radd__30462,Vvar__2__rmul__30467,Vvar__3__ropp__30472,Vvar__4__req__30475)
               => ( cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__30680___24a5(Vvar__0__R__30461,Vvar__1__radd__30462,Vvar__2__rmul__30467,Vvar__3__ropp__30472,Vvar__4__req__30475),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(Vvar__0__R__30461,c_24__type__30704___24a5(Vvar__0__R__30461,Vvar__1__radd__30462,Vvar__2__rmul__30467,Vvar__3__ropp__30472,Vvar__4__req__30475),Vvar__4__req__30475,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(Vvar__0__R__30461,Vvar__0__R__30461,Vvar__4__req__30475,Vvar__4__req__30475)),Vvar__1__radd__30462)
                  & cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__30737___24a5(Vvar__0__R__30461,Vvar__1__radd__30462,Vvar__2__rmul__30467,Vvar__3__ropp__30472,Vvar__4__req__30475),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(Vvar__0__R__30461,c_24__type__30761___24a5(Vvar__0__R__30461,Vvar__1__radd__30462,Vvar__2__rmul__30467,Vvar__3__ropp__30472,Vvar__4__req__30475),Vvar__4__req__30475,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(Vvar__0__R__30461,Vvar__0__R__30461,Vvar__4__req__30475,Vvar__4__req__30475)),Vvar__2__rmul__30467)
                  & cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__30788___24a5(Vvar__0__R__30461,Vvar__1__radd__30462,Vvar__2__rmul__30467,Vvar__3__ropp__30472,Vvar__4__req__30475),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(Vvar__0__R__30461,Vvar__0__R__30461,Vvar__4__req__30475,Vvar__4__req__30475),Vvar__3__ropp__30472)
                  & p(c_24True) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.setoid_ring.Ring_theory.ring_kind',axiom,
    ! [VX18472] :
      ( cCoq_2esetoid__ring_2eRing__theory_2ering__kind___24t(VX18472)
     => ( VX18472 = cCoq_2esetoid__ring_2eRing__theory_2eAbstract
        | ? [Vvar__0__R__18473] :
            ( cType___24t(Vvar__0__R__18473)
            & ? [Vvar__1__req__18474] :
                ( c_24__type__12419___24t(Vvar__0__R__18473,Vvar__1__req__18474)
                & ? [Vvar__2__reqb__18479] :
                    ( c_24__type__12649___24t(Vvar__0__R__18473,Vvar__2__reqb__18479)
                    & ! [Vvar__var__3__x__18485__18488] :
                        ( t(Vvar__var__3__x__18485__18488,Vvar__0__R__18473)
                       => ! [Vvar__var__4__y__18486__18489] :
                            ( t(Vvar__var__4__y__18486__18489,Vvar__0__R__18473)
                           => ( happ(happ(Vvar__2__reqb__18479,Vvar__var__3__x__18485__18488),Vvar__var__4__y__18486__18489) = cCoq_2eInit_2eDatatypes_2etrue
                             => p(happ(happ(Vvar__1__req__18474,Vvar__var__3__x__18485__18488),Vvar__var__4__y__18486__18489)) ) ) )
                    & VX18472 = cCoq_2esetoid__ring_2eRing__theory_2eComputational___24a3(Vvar__0__R__18473,Vvar__1__req__18474,Vvar__2__reqb__18479) ) ) )
        | ? [Vvar__0__R__18491] :
            ( cType___24t(Vvar__0__R__18491)
            & ? [Vvar__1__rO__18492] :
                ( t(Vvar__1__rO__18492,Vvar__0__R__18491)
                & ? [Vvar__2__rI__18493] :
                    ( t(Vvar__2__rI__18493,Vvar__0__R__18491)
                    & ? [Vvar__3__radd__18494] :
                        ( c_24__type__1698___24t(Vvar__0__R__18491,Vvar__3__radd__18494)
                        & ? [Vvar__4__rmul__18499] :
                            ( c_24__type__1698___24t(Vvar__0__R__18491,Vvar__4__rmul__18499)
                            & ? [Vvar__5__rsub__18504] :
                                ( c_24__type__1698___24t(Vvar__0__R__18491,Vvar__5__rsub__18504)
                                & ? [Vvar__6__ropp__18509] :
                                    ( c_24__type__11363___24t(Vvar__0__R__18491,Vvar__6__ropp__18509)
                                    & ? [Vvar__7__req__18512] :
                                        ( c_24__type__12419___24t(Vvar__0__R__18491,Vvar__7__req__18512)
                                        & ? [Vvar__8__C__18517] :
                                            ( cType___24t(Vvar__8__C__18517)
                                            & ? [Vvar__9__cO__18518] :
                                                ( t(Vvar__9__cO__18518,Vvar__8__C__18517)
                                                & ? [Vvar__10__cI__18519] :
                                                    ( t(Vvar__10__cI__18519,Vvar__8__C__18517)
                                                    & ? [Vvar__11__cadd__18520] :
                                                        ( c_24__type__18415___24t(Vvar__0__R__18491,Vvar__8__C__18517,Vvar__11__cadd__18520)
                                                        & ? [Vvar__12__cmul__18525] :
                                                            ( c_24__type__18415___24t(Vvar__0__R__18491,Vvar__8__C__18517,Vvar__12__cmul__18525)
                                                            & ? [Vvar__13__csub__18530] :
                                                                ( c_24__type__18415___24t(Vvar__0__R__18491,Vvar__8__C__18517,Vvar__13__csub__18530)
                                                                & ? [Vvar__14__copp__18535] :
                                                                    ( c_24__type__18429___24t(Vvar__0__R__18491,Vvar__8__C__18517,Vvar__14__copp__18535)
                                                                    & ? [Vvar__15__ceqb__18538] :
                                                                        ( c_24__type__18436___24t(Vvar__0__R__18491,Vvar__8__C__18517,Vvar__15__ceqb__18538)
                                                                        & ? [Vvar__16__phi__18543] :
                                                                            ( c_24__type__11367___24t(Vvar__0__R__18491,Vvar__8__C__18517,Vvar__16__phi__18543)
                                                                            & cCoq_2esetoid__ring_2eRing__theory_2ering__morph___24a17(Vvar__0__R__18491,Vvar__1__rO__18492,Vvar__2__rI__18493,Vvar__3__radd__18494,Vvar__4__rmul__18499,Vvar__5__rsub__18504,Vvar__6__ropp__18509,Vvar__7__req__18512,Vvar__8__C__18517,Vvar__9__cO__18518,Vvar__10__cI__18519,Vvar__11__cadd__18520,Vvar__12__cmul__18525,Vvar__13__csub__18530,Vvar__14__copp__18535,Vvar__15__ceqb__18538,Vvar__16__phi__18543)
                                                                            & VX18472 = cCoq_2esetoid__ring_2eRing__theory_2eMorphism___24a17(Vvar__0__R__18491,Vvar__1__rO__18492,Vvar__2__rI__18493,Vvar__3__radd__18494,Vvar__4__rmul__18499,Vvar__5__rsub__18504,Vvar__6__ropp__18509,Vvar__7__req__18512,Vvar__8__C__18517,Vvar__9__cO__18518,Vvar__10__cI__18519,Vvar__11__cadd__18520,Vvar__12__cmul__18525,Vvar__13__csub__18530,Vvar__14__copp__18535,Vvar__15__ceqb__18538,Vvar__16__phi__18543) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.setoid_ring.Ring_theory.ring_morph',axiom,
    ! [Vvar__0__R__15913,Vvar__1__rO__15914,Vvar__2__rI__15915,Vvar__3__radd__15916,Vvar__4__rmul__15921,Vvar__5__rsub__15926,Vvar__6__ropp__15931,Vvar__7__req__15934,Vvar__8__C__15939,Vvar__9__cO__15940,Vvar__10__cI__15941,Vvar__11__cadd__15942,Vvar__12__cmul__15947,Vvar__13__csub__15952,Vvar__14__copp__15957,Vvar__15__ceqb__15960,Vvar__16__phi__15965] :
      ( cType___24t(Vvar__0__R__15913)
     => ( t(Vvar__1__rO__15914,Vvar__0__R__15913)
       => ( t(Vvar__2__rI__15915,Vvar__0__R__15913)
         => ( c_24__type__16309___24t(Vvar__0__R__15913,Vvar__1__rO__15914,Vvar__2__rI__15915,Vvar__3__radd__15916,Vvar__4__rmul__15921,Vvar__5__rsub__15926,Vvar__6__ropp__15931,Vvar__7__req__15934,Vvar__8__C__15939,Vvar__9__cO__15940,Vvar__10__cI__15941,Vvar__11__cadd__15942,Vvar__12__cmul__15947,Vvar__13__csub__15952,Vvar__14__copp__15957,Vvar__15__ceqb__15960,Vvar__16__phi__15965,Vvar__3__radd__15916)
           => ( c_24__type__16522___24t(Vvar__0__R__15913,Vvar__1__rO__15914,Vvar__2__rI__15915,Vvar__3__radd__15916,Vvar__4__rmul__15921,Vvar__5__rsub__15926,Vvar__6__ropp__15931,Vvar__7__req__15934,Vvar__8__C__15939,Vvar__9__cO__15940,Vvar__10__cI__15941,Vvar__11__cadd__15942,Vvar__12__cmul__15947,Vvar__13__csub__15952,Vvar__14__copp__15957,Vvar__15__ceqb__15960,Vvar__16__phi__15965,Vvar__4__rmul__15921)
             => ( c_24__type__16735___24t(Vvar__0__R__15913,Vvar__1__rO__15914,Vvar__2__rI__15915,Vvar__3__radd__15916,Vvar__4__rmul__15921,Vvar__5__rsub__15926,Vvar__6__ropp__15931,Vvar__7__req__15934,Vvar__8__C__15939,Vvar__9__cO__15940,Vvar__10__cI__15941,Vvar__11__cadd__15942,Vvar__12__cmul__15947,Vvar__13__csub__15952,Vvar__14__copp__15957,Vvar__15__ceqb__15960,Vvar__16__phi__15965,Vvar__5__rsub__15926)
               => ( c_24__type__16930___24t(Vvar__0__R__15913,Vvar__1__rO__15914,Vvar__2__rI__15915,Vvar__3__radd__15916,Vvar__4__rmul__15921,Vvar__5__rsub__15926,Vvar__6__ropp__15931,Vvar__7__req__15934,Vvar__8__C__15939,Vvar__9__cO__15940,Vvar__10__cI__15941,Vvar__11__cadd__15942,Vvar__12__cmul__15947,Vvar__13__csub__15952,Vvar__14__copp__15957,Vvar__15__ceqb__15960,Vvar__16__phi__15965,Vvar__6__ropp__15931)
                 => ( c_24__type__17143___24t(Vvar__0__R__15913,Vvar__1__rO__15914,Vvar__2__rI__15915,Vvar__3__radd__15916,Vvar__4__rmul__15921,Vvar__5__rsub__15926,Vvar__6__ropp__15931,Vvar__7__req__15934,Vvar__8__C__15939,Vvar__9__cO__15940,Vvar__10__cI__15941,Vvar__11__cadd__15942,Vvar__12__cmul__15947,Vvar__13__csub__15952,Vvar__14__copp__15957,Vvar__15__ceqb__15960,Vvar__16__phi__15965,Vvar__7__req__15934)
                   => ( cType___24t(Vvar__8__C__15939)
                     => ( t(Vvar__9__cO__15940,Vvar__8__C__15939)
                       => ( t(Vvar__10__cI__15941,Vvar__8__C__15939)
                         => ( c_24__type__17356___24t(Vvar__0__R__15913,Vvar__1__rO__15914,Vvar__2__rI__15915,Vvar__3__radd__15916,Vvar__4__rmul__15921,Vvar__5__rsub__15926,Vvar__6__ropp__15931,Vvar__7__req__15934,Vvar__8__C__15939,Vvar__9__cO__15940,Vvar__10__cI__15941,Vvar__11__cadd__15942,Vvar__12__cmul__15947,Vvar__13__csub__15952,Vvar__14__copp__15957,Vvar__15__ceqb__15960,Vvar__16__phi__15965,Vvar__11__cadd__15942)
                           => ( c_24__type__17569___24t(Vvar__0__R__15913,Vvar__1__rO__15914,Vvar__2__rI__15915,Vvar__3__radd__15916,Vvar__4__rmul__15921,Vvar__5__rsub__15926,Vvar__6__ropp__15931,Vvar__7__req__15934,Vvar__8__C__15939,Vvar__9__cO__15940,Vvar__10__cI__15941,Vvar__11__cadd__15942,Vvar__12__cmul__15947,Vvar__13__csub__15952,Vvar__14__copp__15957,Vvar__15__ceqb__15960,Vvar__16__phi__15965,Vvar__12__cmul__15947)
                             => ( c_24__type__17782___24t(Vvar__0__R__15913,Vvar__1__rO__15914,Vvar__2__rI__15915,Vvar__3__radd__15916,Vvar__4__rmul__15921,Vvar__5__rsub__15926,Vvar__6__ropp__15931,Vvar__7__req__15934,Vvar__8__C__15939,Vvar__9__cO__15940,Vvar__10__cI__15941,Vvar__11__cadd__15942,Vvar__12__cmul__15947,Vvar__13__csub__15952,Vvar__14__copp__15957,Vvar__15__ceqb__15960,Vvar__16__phi__15965,Vvar__13__csub__15952)
                               => ( c_24__type__17977___24t(Vvar__0__R__15913,Vvar__1__rO__15914,Vvar__2__rI__15915,Vvar__3__radd__15916,Vvar__4__rmul__15921,Vvar__5__rsub__15926,Vvar__6__ropp__15931,Vvar__7__req__15934,Vvar__8__C__15939,Vvar__9__cO__15940,Vvar__10__cI__15941,Vvar__11__cadd__15942,Vvar__12__cmul__15947,Vvar__13__csub__15952,Vvar__14__copp__15957,Vvar__15__ceqb__15960,Vvar__16__phi__15965,Vvar__14__copp__15957)
                                 => ( c_24__type__18190___24t(Vvar__0__R__15913,Vvar__1__rO__15914,Vvar__2__rI__15915,Vvar__3__radd__15916,Vvar__4__rmul__15921,Vvar__5__rsub__15926,Vvar__6__ropp__15931,Vvar__7__req__15934,Vvar__8__C__15939,Vvar__9__cO__15940,Vvar__10__cI__15941,Vvar__11__cadd__15942,Vvar__12__cmul__15947,Vvar__13__csub__15952,Vvar__14__copp__15957,Vvar__15__ceqb__15960,Vvar__16__phi__15965,Vvar__15__ceqb__15960)
                                   => ( c_24__type__18385___24t(Vvar__0__R__15913,Vvar__1__rO__15914,Vvar__2__rI__15915,Vvar__3__radd__15916,Vvar__4__rmul__15921,Vvar__5__rsub__15926,Vvar__6__ropp__15931,Vvar__7__req__15934,Vvar__8__C__15939,Vvar__9__cO__15940,Vvar__10__cI__15941,Vvar__11__cadd__15942,Vvar__12__cmul__15947,Vvar__13__csub__15952,Vvar__14__copp__15957,Vvar__15__ceqb__15960,Vvar__16__phi__15965,Vvar__16__phi__15965)
                                     => ( cCoq_2esetoid__ring_2eRing__theory_2ering__morph___24a17(Vvar__0__R__15913,Vvar__1__rO__15914,Vvar__2__rI__15915,Vvar__3__radd__15916,Vvar__4__rmul__15921,Vvar__5__rsub__15926,Vvar__6__ropp__15931,Vvar__7__req__15934,Vvar__8__C__15939,Vvar__9__cO__15940,Vvar__10__cI__15941,Vvar__11__cadd__15942,Vvar__12__cmul__15947,Vvar__13__csub__15952,Vvar__14__copp__15957,Vvar__15__ceqb__15960,Vvar__16__phi__15965)
                                       => ( p(happ(happ(Vvar__7__req__15934,happ(Vvar__16__phi__15965,Vvar__9__cO__15940)),Vvar__1__rO__15914))
                                          & p(happ(happ(Vvar__7__req__15934,happ(Vvar__16__phi__15965,Vvar__10__cI__15941)),Vvar__2__rI__15915))
                                          & ! [Vvar__var__var__var__var__var__var__19__x__16027__16029__16051__16053__16055__16057__16059] :
                                              ( t(Vvar__var__var__var__var__var__var__19__x__16027__16029__16051__16053__16055__16057__16059,Vvar__8__C__15939)
                                             => ! [Vvar__var__var__var__var__var__var__20__y__16028__16030__16052__16054__16056__16058__16060] :
                                                  ( t(Vvar__var__var__var__var__var__var__20__y__16028__16030__16052__16054__16056__16058__16060,Vvar__8__C__15939)
                                                 => p(happ(happ(Vvar__7__req__15934,happ(Vvar__16__phi__15965,happ(happ(Vvar__11__cadd__15942,Vvar__var__var__var__var__var__var__19__x__16027__16029__16051__16053__16055__16057__16059),Vvar__var__var__var__var__var__var__20__y__16028__16030__16052__16054__16056__16058__16060))),happ(happ(Vvar__3__radd__15916,happ(Vvar__16__phi__15965,Vvar__var__var__var__var__var__var__19__x__16027__16029__16051__16053__16055__16057__16059)),happ(Vvar__16__phi__15965,Vvar__var__var__var__var__var__var__20__y__16028__16030__16052__16054__16056__16058__16060)))) ) )
                                          & ! [Vvar__var__var__var__var__var__var__20__x__16032__16034__16061__16063__16065__16067__16069] :
                                              ( t(Vvar__var__var__var__var__var__var__20__x__16032__16034__16061__16063__16065__16067__16069,Vvar__8__C__15939)
                                             => ! [Vvar__var__var__var__var__var__var__21__y__16033__16035__16062__16064__16066__16068__16070] :
                                                  ( t(Vvar__var__var__var__var__var__var__21__y__16033__16035__16062__16064__16066__16068__16070,Vvar__8__C__15939)
                                                 => p(happ(happ(Vvar__7__req__15934,happ(Vvar__16__phi__15965,happ(happ(Vvar__13__csub__15952,Vvar__var__var__var__var__var__var__20__x__16032__16034__16061__16063__16065__16067__16069),Vvar__var__var__var__var__var__var__21__y__16033__16035__16062__16064__16066__16068__16070))),happ(happ(Vvar__5__rsub__15926,happ(Vvar__16__phi__15965,Vvar__var__var__var__var__var__var__20__x__16032__16034__16061__16063__16065__16067__16069)),happ(Vvar__16__phi__15965,Vvar__var__var__var__var__var__var__21__y__16033__16035__16062__16064__16066__16068__16070)))) ) )
                                          & ! [Vvar__var__var__var__var__var__var__21__x__16037__16039__16071__16073__16075__16077__16079] :
                                              ( t(Vvar__var__var__var__var__var__var__21__x__16037__16039__16071__16073__16075__16077__16079,Vvar__8__C__15939)
                                             => ! [Vvar__var__var__var__var__var__var__22__y__16038__16040__16072__16074__16076__16078__16080] :
                                                  ( t(Vvar__var__var__var__var__var__var__22__y__16038__16040__16072__16074__16076__16078__16080,Vvar__8__C__15939)
                                                 => p(happ(happ(Vvar__7__req__15934,happ(Vvar__16__phi__15965,happ(happ(Vvar__12__cmul__15947,Vvar__var__var__var__var__var__var__21__x__16037__16039__16071__16073__16075__16077__16079),Vvar__var__var__var__var__var__var__22__y__16038__16040__16072__16074__16076__16078__16080))),happ(happ(Vvar__4__rmul__15921,happ(Vvar__16__phi__15965,Vvar__var__var__var__var__var__var__21__x__16037__16039__16071__16073__16075__16077__16079)),happ(Vvar__16__phi__15965,Vvar__var__var__var__var__var__var__22__y__16038__16040__16072__16074__16076__16078__16080)))) ) )
                                          & ! [Vvar__var__var__var__var__var__var__22__x__16042__16043__16081__16082__16083__16084__16085] :
                                              ( t(Vvar__var__var__var__var__var__var__22__x__16042__16043__16081__16082__16083__16084__16085,Vvar__8__C__15939)
                                             => p(happ(happ(Vvar__7__req__15934,happ(Vvar__16__phi__15965,happ(Vvar__14__copp__15957,Vvar__var__var__var__var__var__var__22__x__16042__16043__16081__16082__16083__16084__16085))),happ(Vvar__6__ropp__15931,happ(Vvar__16__phi__15965,Vvar__var__var__var__var__var__var__22__x__16042__16043__16081__16082__16083__16084__16085)))) )
                                          & ! [Vvar__var__var__var__var__var__23__x__16045__16048__16086__16089__16092__16095] :
                                              ( t(Vvar__var__var__var__var__var__23__x__16045__16048__16086__16089__16092__16095,Vvar__8__C__15939)
                                             => ! [Vvar__var__var__var__var__var__24__y__16046__16049__16087__16090__16093__16096] :
                                                  ( t(Vvar__var__var__var__var__var__24__y__16046__16049__16087__16090__16093__16096,Vvar__8__C__15939)
                                                 => ( happ(happ(Vvar__15__ceqb__15960,Vvar__var__var__var__var__var__23__x__16045__16048__16086__16089__16092__16095),Vvar__var__var__var__var__var__24__y__16046__16049__16087__16090__16093__16096) = cCoq_2eInit_2eDatatypes_2etrue
                                                   => p(happ(happ(Vvar__7__req__15934,happ(Vvar__16__phi__15965,Vvar__var__var__var__var__var__23__x__16045__16048__16086__16089__16092__16095)),happ(Vvar__16__phi__15965,Vvar__var__var__var__var__var__24__y__16046__16049__16087__16090__16093__16096))) ) ) )
                                          & p(c_24True) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.setoid_ring.Ring_theory.ring_theory',axiom,
    ! [Vvar__0__R__29752,Vvar__1__rO__29753,Vvar__2__rI__29754,Vvar__3__radd__29755,Vvar__4__rmul__29760,Vvar__5__rsub__29765,Vvar__6__ropp__29770,Vvar__7__req__29773] :
      ( cType___24t(Vvar__0__R__29752)
     => ( t(Vvar__1__rO__29753,Vvar__0__R__29752)
       => ( t(Vvar__2__rI__29754,Vvar__0__R__29752)
         => ( c_24__type__29976___24t(Vvar__0__R__29752,Vvar__1__rO__29753,Vvar__2__rI__29754,Vvar__3__radd__29755,Vvar__4__rmul__29760,Vvar__5__rsub__29765,Vvar__6__ropp__29770,Vvar__7__req__29773,Vvar__3__radd__29755)
           => ( c_24__type__30039___24t(Vvar__0__R__29752,Vvar__1__rO__29753,Vvar__2__rI__29754,Vvar__3__radd__29755,Vvar__4__rmul__29760,Vvar__5__rsub__29765,Vvar__6__ropp__29770,Vvar__7__req__29773,Vvar__4__rmul__29760)
             => ( c_24__type__30102___24t(Vvar__0__R__29752,Vvar__1__rO__29753,Vvar__2__rI__29754,Vvar__3__radd__29755,Vvar__4__rmul__29760,Vvar__5__rsub__29765,Vvar__6__ropp__29770,Vvar__7__req__29773,Vvar__5__rsub__29765)
               => ( c_24__type__30156___24t(Vvar__0__R__29752,Vvar__1__rO__29753,Vvar__2__rI__29754,Vvar__3__radd__29755,Vvar__4__rmul__29760,Vvar__5__rsub__29765,Vvar__6__ropp__29770,Vvar__7__req__29773,Vvar__6__ropp__29770)
                 => ( c_24__type__30219___24t(Vvar__0__R__29752,Vvar__1__rO__29753,Vvar__2__rI__29754,Vvar__3__radd__29755,Vvar__4__rmul__29760,Vvar__5__rsub__29765,Vvar__6__ropp__29770,Vvar__7__req__29773,Vvar__7__req__29773)
                   => ( cCoq_2esetoid__ring_2eRing__theory_2ering__theory___24a8(Vvar__0__R__29752,Vvar__1__rO__29753,Vvar__2__rI__29754,Vvar__3__radd__29755,Vvar__4__rmul__29760,Vvar__5__rsub__29765,Vvar__6__ropp__29770,Vvar__7__req__29773)
                     => ( ! [Vvar__var__var__var__var__var__8__x__29806__29807__29850__29851__29852__29853] :
                            ( t(Vvar__var__var__var__var__var__8__x__29806__29807__29850__29851__29852__29853,Vvar__0__R__29752)
                           => p(happ(happ(Vvar__7__req__29773,happ(happ(Vvar__3__radd__29755,Vvar__1__rO__29753),Vvar__var__var__var__var__var__8__x__29806__29807__29850__29851__29852__29853)),Vvar__var__var__var__var__var__8__x__29806__29807__29850__29851__29852__29853)) )
                        & ! [Vvar__var__var__var__var__9__x__29809__29811__29854__29856__29858] :
                            ( t(Vvar__var__var__var__var__9__x__29809__29811__29854__29856__29858,Vvar__0__R__29752)
                           => ! [Vvar__var__var__var__var__10__y__29810__29812__29855__29857__29859] :
                                ( t(Vvar__var__var__var__var__10__y__29810__29812__29855__29857__29859,Vvar__0__R__29752)
                               => p(happ(happ(Vvar__7__req__29773,happ(happ(Vvar__3__radd__29755,Vvar__var__var__var__var__9__x__29809__29811__29854__29856__29858),Vvar__var__var__var__var__10__y__29810__29812__29855__29857__29859)),happ(happ(Vvar__3__radd__29755,Vvar__var__var__var__var__10__y__29810__29812__29855__29857__29859),Vvar__var__var__var__var__9__x__29809__29811__29854__29856__29858))) ) )
                        & ! [Vvar__var__var__var__var__10__x__29814__29817__29860__29863__29866] :
                            ( t(Vvar__var__var__var__var__10__x__29814__29817__29860__29863__29866,Vvar__0__R__29752)
                           => ! [Vvar__var__var__var__var__11__y__29815__29818__29861__29864__29867] :
                                ( t(Vvar__var__var__var__var__11__y__29815__29818__29861__29864__29867,Vvar__0__R__29752)
                               => ! [Vvar__var__var__var__var__12__z__29816__29819__29862__29865__29868] :
                                    ( t(Vvar__var__var__var__var__12__z__29816__29819__29862__29865__29868,Vvar__0__R__29752)
                                   => p(happ(happ(Vvar__7__req__29773,happ(happ(Vvar__3__radd__29755,Vvar__var__var__var__var__10__x__29814__29817__29860__29863__29866),happ(happ(Vvar__3__radd__29755,Vvar__var__var__var__var__11__y__29815__29818__29861__29864__29867),Vvar__var__var__var__var__12__z__29816__29819__29862__29865__29868))),happ(happ(Vvar__3__radd__29755,happ(happ(Vvar__3__radd__29755,Vvar__var__var__var__var__10__x__29814__29817__29860__29863__29866),Vvar__var__var__var__var__11__y__29815__29818__29861__29864__29867)),Vvar__var__var__var__var__12__z__29816__29819__29862__29865__29868))) ) ) )
                        & ! [Vvar__var__var__var__var__var__11__x__29821__29822__29869__29870__29871__29872] :
                            ( t(Vvar__var__var__var__var__var__11__x__29821__29822__29869__29870__29871__29872,Vvar__0__R__29752)
                           => p(happ(happ(Vvar__7__req__29773,happ(happ(Vvar__4__rmul__29760,Vvar__2__rI__29754),Vvar__var__var__var__var__var__11__x__29821__29822__29869__29870__29871__29872)),Vvar__var__var__var__var__var__11__x__29821__29822__29869__29870__29871__29872)) )
                        & ! [Vvar__var__var__var__var__12__x__29824__29826__29873__29875__29877] :
                            ( t(Vvar__var__var__var__var__12__x__29824__29826__29873__29875__29877,Vvar__0__R__29752)
                           => ! [Vvar__var__var__var__var__13__y__29825__29827__29874__29876__29878] :
                                ( t(Vvar__var__var__var__var__13__y__29825__29827__29874__29876__29878,Vvar__0__R__29752)
                               => p(happ(happ(Vvar__7__req__29773,happ(happ(Vvar__4__rmul__29760,Vvar__var__var__var__var__12__x__29824__29826__29873__29875__29877),Vvar__var__var__var__var__13__y__29825__29827__29874__29876__29878)),happ(happ(Vvar__4__rmul__29760,Vvar__var__var__var__var__13__y__29825__29827__29874__29876__29878),Vvar__var__var__var__var__12__x__29824__29826__29873__29875__29877))) ) )
                        & ! [Vvar__var__var__var__var__13__x__29829__29832__29879__29882__29885] :
                            ( t(Vvar__var__var__var__var__13__x__29829__29832__29879__29882__29885,Vvar__0__R__29752)
                           => ! [Vvar__var__var__var__var__14__y__29830__29833__29880__29883__29886] :
                                ( t(Vvar__var__var__var__var__14__y__29830__29833__29880__29883__29886,Vvar__0__R__29752)
                               => ! [Vvar__var__var__var__var__15__z__29831__29834__29881__29884__29887] :
                                    ( t(Vvar__var__var__var__var__15__z__29831__29834__29881__29884__29887,Vvar__0__R__29752)
                                   => p(happ(happ(Vvar__7__req__29773,happ(happ(Vvar__4__rmul__29760,Vvar__var__var__var__var__13__x__29829__29832__29879__29882__29885),happ(happ(Vvar__4__rmul__29760,Vvar__var__var__var__var__14__y__29830__29833__29880__29883__29886),Vvar__var__var__var__var__15__z__29831__29834__29881__29884__29887))),happ(happ(Vvar__4__rmul__29760,happ(happ(Vvar__4__rmul__29760,Vvar__var__var__var__var__13__x__29829__29832__29879__29882__29885),Vvar__var__var__var__var__14__y__29830__29833__29880__29883__29886)),Vvar__var__var__var__var__15__z__29831__29834__29881__29884__29887))) ) ) )
                        & ! [Vvar__var__var__var__var__var__14__x__29836__29839__29888__29891__29894__29897] :
                            ( t(Vvar__var__var__var__var__var__14__x__29836__29839__29888__29891__29894__29897,Vvar__0__R__29752)
                           => ! [Vvar__var__var__var__var__var__15__y__29837__29840__29889__29892__29895__29898] :
                                ( t(Vvar__var__var__var__var__var__15__y__29837__29840__29889__29892__29895__29898,Vvar__0__R__29752)
                               => ! [Vvar__var__var__var__var__var__16__z__29838__29841__29890__29893__29896__29899] :
                                    ( t(Vvar__var__var__var__var__var__16__z__29838__29841__29890__29893__29896__29899,Vvar__0__R__29752)
                                   => p(happ(happ(Vvar__7__req__29773,happ(happ(Vvar__4__rmul__29760,happ(happ(Vvar__3__radd__29755,Vvar__var__var__var__var__var__14__x__29836__29839__29888__29891__29894__29897),Vvar__var__var__var__var__var__15__y__29837__29840__29889__29892__29895__29898)),Vvar__var__var__var__var__var__16__z__29838__29841__29890__29893__29896__29899)),happ(happ(Vvar__3__radd__29755,happ(happ(Vvar__4__rmul__29760,Vvar__var__var__var__var__var__14__x__29836__29839__29888__29891__29894__29897),Vvar__var__var__var__var__var__16__z__29838__29841__29890__29893__29896__29899)),happ(happ(Vvar__4__rmul__29760,Vvar__var__var__var__var__var__15__y__29837__29840__29889__29892__29895__29898),Vvar__var__var__var__var__var__16__z__29838__29841__29890__29893__29896__29899)))) ) ) )
                        & ! [Vvar__var__var__var__var__var__var__15__x__29843__29845__29900__29902__29904__29906__29908] :
                            ( t(Vvar__var__var__var__var__var__var__15__x__29843__29845__29900__29902__29904__29906__29908,Vvar__0__R__29752)
                           => ! [Vvar__var__var__var__var__var__var__16__y__29844__29846__29901__29903__29905__29907__29909] :
                                ( t(Vvar__var__var__var__var__var__var__16__y__29844__29846__29901__29903__29905__29907__29909,Vvar__0__R__29752)
                               => p(happ(happ(Vvar__7__req__29773,happ(happ(Vvar__5__rsub__29765,Vvar__var__var__var__var__var__var__15__x__29843__29845__29900__29902__29904__29906__29908),Vvar__var__var__var__var__var__var__16__y__29844__29846__29901__29903__29905__29907__29909)),happ(happ(Vvar__3__radd__29755,Vvar__var__var__var__var__var__var__15__x__29843__29845__29900__29902__29904__29906__29908),happ(Vvar__6__ropp__29770,Vvar__var__var__var__var__var__var__16__y__29844__29846__29901__29903__29905__29907__29909)))) ) )
                        & ! [Vvar__var__var__var__var__var__var__16__x__29848__29849__29910__29911__29912__29913__29914] :
                            ( t(Vvar__var__var__var__var__var__var__16__x__29848__29849__29910__29911__29912__29913__29914,Vvar__0__R__29752)
                           => p(happ(happ(Vvar__7__req__29773,happ(happ(Vvar__3__radd__29755,Vvar__var__var__var__var__var__var__16__x__29848__29849__29910__29911__29912__29913__29914),happ(Vvar__6__ropp__29770,Vvar__var__var__var__var__var__var__16__x__29848__29849__29910__29911__29912__29913__29914))),Vvar__1__rO__29753)) )
                        & p(c_24True) ) ) ) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.setoid_ring.Ring_theory.semi_morph',axiom,
    ! [Vvar__0__R__30791,Vvar__1__rO__30792,Vvar__2__rI__30793,Vvar__3__radd__30794,Vvar__4__rmul__30799,Vvar__5__req__30804,Vvar__6__C__30809,Vvar__7__cO__30810,Vvar__8__cI__30811,Vvar__9__cadd__30812,Vvar__10__cmul__30817,Vvar__11__ceqb__30822,Vvar__12__phi__30827] :
      ( cType___24t(Vvar__0__R__30791)
     => ( t(Vvar__1__rO__30792,Vvar__0__R__30791)
       => ( t(Vvar__2__rI__30793,Vvar__0__R__30791)
         => ( c_24__type__31044___24t(Vvar__0__R__30791,Vvar__1__rO__30792,Vvar__2__rI__30793,Vvar__3__radd__30794,Vvar__4__rmul__30799,Vvar__5__req__30804,Vvar__6__C__30809,Vvar__7__cO__30810,Vvar__8__cI__30811,Vvar__9__cadd__30812,Vvar__10__cmul__30817,Vvar__11__ceqb__30822,Vvar__12__phi__30827,Vvar__3__radd__30794)
           => ( c_24__type__31169___24t(Vvar__0__R__30791,Vvar__1__rO__30792,Vvar__2__rI__30793,Vvar__3__radd__30794,Vvar__4__rmul__30799,Vvar__5__req__30804,Vvar__6__C__30809,Vvar__7__cO__30810,Vvar__8__cI__30811,Vvar__9__cadd__30812,Vvar__10__cmul__30817,Vvar__11__ceqb__30822,Vvar__12__phi__30827,Vvar__4__rmul__30799)
             => ( c_24__type__31294___24t(Vvar__0__R__30791,Vvar__1__rO__30792,Vvar__2__rI__30793,Vvar__3__radd__30794,Vvar__4__rmul__30799,Vvar__5__req__30804,Vvar__6__C__30809,Vvar__7__cO__30810,Vvar__8__cI__30811,Vvar__9__cadd__30812,Vvar__10__cmul__30817,Vvar__11__ceqb__30822,Vvar__12__phi__30827,Vvar__5__req__30804)
               => ( cType___24t(Vvar__6__C__30809)
                 => ( t(Vvar__7__cO__30810,Vvar__6__C__30809)
                   => ( t(Vvar__8__cI__30811,Vvar__6__C__30809)
                     => ( c_24__type__31419___24t(Vvar__0__R__30791,Vvar__1__rO__30792,Vvar__2__rI__30793,Vvar__3__radd__30794,Vvar__4__rmul__30799,Vvar__5__req__30804,Vvar__6__C__30809,Vvar__7__cO__30810,Vvar__8__cI__30811,Vvar__9__cadd__30812,Vvar__10__cmul__30817,Vvar__11__ceqb__30822,Vvar__12__phi__30827,Vvar__9__cadd__30812)
                       => ( c_24__type__31544___24t(Vvar__0__R__30791,Vvar__1__rO__30792,Vvar__2__rI__30793,Vvar__3__radd__30794,Vvar__4__rmul__30799,Vvar__5__req__30804,Vvar__6__C__30809,Vvar__7__cO__30810,Vvar__8__cI__30811,Vvar__9__cadd__30812,Vvar__10__cmul__30817,Vvar__11__ceqb__30822,Vvar__12__phi__30827,Vvar__10__cmul__30817)
                         => ( c_24__type__31669___24t(Vvar__0__R__30791,Vvar__1__rO__30792,Vvar__2__rI__30793,Vvar__3__radd__30794,Vvar__4__rmul__30799,Vvar__5__req__30804,Vvar__6__C__30809,Vvar__7__cO__30810,Vvar__8__cI__30811,Vvar__9__cadd__30812,Vvar__10__cmul__30817,Vvar__11__ceqb__30822,Vvar__12__phi__30827,Vvar__11__ceqb__30822)
                           => ( c_24__type__31780___24t(Vvar__0__R__30791,Vvar__1__rO__30792,Vvar__2__rI__30793,Vvar__3__radd__30794,Vvar__4__rmul__30799,Vvar__5__req__30804,Vvar__6__C__30809,Vvar__7__cO__30810,Vvar__8__cI__30811,Vvar__9__cadd__30812,Vvar__10__cmul__30817,Vvar__11__ceqb__30822,Vvar__12__phi__30827,Vvar__12__phi__30827)
                             => ( cCoq_2esetoid__ring_2eRing__theory_2esemi__morph___24a13(Vvar__0__R__30791,Vvar__1__rO__30792,Vvar__2__rI__30793,Vvar__3__radd__30794,Vvar__4__rmul__30799,Vvar__5__req__30804,Vvar__6__C__30809,Vvar__7__cO__30810,Vvar__8__cI__30811,Vvar__9__cadd__30812,Vvar__10__cmul__30817,Vvar__11__ceqb__30822,Vvar__12__phi__30827)
                               => ( p(happ(happ(Vvar__5__req__30804,happ(Vvar__12__phi__30827,Vvar__7__cO__30810)),Vvar__1__rO__30792))
                                  & p(happ(happ(Vvar__5__req__30804,happ(Vvar__12__phi__30827,Vvar__8__cI__30811)),Vvar__2__rI__30793))
                                  & ! [Vvar__var__var__var__var__var__var__15__x__30873__30875__30889__30891__30893__30895__30897] :
                                      ( t(Vvar__var__var__var__var__var__var__15__x__30873__30875__30889__30891__30893__30895__30897,Vvar__6__C__30809)
                                     => ! [Vvar__var__var__var__var__var__var__16__y__30874__30876__30890__30892__30894__30896__30898] :
                                          ( t(Vvar__var__var__var__var__var__var__16__y__30874__30876__30890__30892__30894__30896__30898,Vvar__6__C__30809)
                                         => p(happ(happ(Vvar__5__req__30804,happ(Vvar__12__phi__30827,happ(happ(Vvar__9__cadd__30812,Vvar__var__var__var__var__var__var__15__x__30873__30875__30889__30891__30893__30895__30897),Vvar__var__var__var__var__var__var__16__y__30874__30876__30890__30892__30894__30896__30898))),happ(happ(Vvar__3__radd__30794,happ(Vvar__12__phi__30827,Vvar__var__var__var__var__var__var__15__x__30873__30875__30889__30891__30893__30895__30897)),happ(Vvar__12__phi__30827,Vvar__var__var__var__var__var__var__16__y__30874__30876__30890__30892__30894__30896__30898)))) ) )
                                  & ! [Vvar__var__var__var__var__var__var__16__x__30878__30880__30899__30901__30903__30905__30907] :
                                      ( t(Vvar__var__var__var__var__var__var__16__x__30878__30880__30899__30901__30903__30905__30907,Vvar__6__C__30809)
                                     => ! [Vvar__var__var__var__var__var__var__17__y__30879__30881__30900__30902__30904__30906__30908] :
                                          ( t(Vvar__var__var__var__var__var__var__17__y__30879__30881__30900__30902__30904__30906__30908,Vvar__6__C__30809)
                                         => p(happ(happ(Vvar__5__req__30804,happ(Vvar__12__phi__30827,happ(happ(Vvar__10__cmul__30817,Vvar__var__var__var__var__var__var__16__x__30878__30880__30899__30901__30903__30905__30907),Vvar__var__var__var__var__var__var__17__y__30879__30881__30900__30902__30904__30906__30908))),happ(happ(Vvar__4__rmul__30799,happ(Vvar__12__phi__30827,Vvar__var__var__var__var__var__var__16__x__30878__30880__30899__30901__30903__30905__30907)),happ(Vvar__12__phi__30827,Vvar__var__var__var__var__var__var__17__y__30879__30881__30900__30902__30904__30906__30908)))) ) )
                                  & ! [Vvar__var__var__var__var__var__17__x__30883__30886__30909__30912__30915__30918] :
                                      ( t(Vvar__var__var__var__var__var__17__x__30883__30886__30909__30912__30915__30918,Vvar__6__C__30809)
                                     => ! [Vvar__var__var__var__var__var__18__y__30884__30887__30910__30913__30916__30919] :
                                          ( t(Vvar__var__var__var__var__var__18__y__30884__30887__30910__30913__30916__30919,Vvar__6__C__30809)
                                         => ( happ(happ(Vvar__11__ceqb__30822,Vvar__var__var__var__var__var__17__x__30883__30886__30909__30912__30915__30918),Vvar__var__var__var__var__var__18__y__30884__30887__30910__30913__30916__30919) = cCoq_2eInit_2eDatatypes_2etrue
                                           => p(happ(happ(Vvar__5__req__30804,happ(Vvar__12__phi__30827,Vvar__var__var__var__var__var__17__x__30883__30886__30909__30912__30915__30918)),happ(Vvar__12__phi__30827,Vvar__var__var__var__var__var__18__y__30884__30887__30910__30913__30916__30919))) ) ) )
                                  & p(c_24True) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.setoid_ring.Ring_theory.sring_eq_ext',axiom,
    ! [Vvar__0__R__30239,Vvar__1__radd__30240,Vvar__2__rmul__30245,Vvar__3__req__30250] :
      ( cType___24t(Vvar__0__R__30239)
     => ( c_24__type__30325___24t(Vvar__0__R__30239,Vvar__1__radd__30240,Vvar__2__rmul__30245,Vvar__3__req__30250,Vvar__1__radd__30240)
       => ( c_24__type__30348___24t(Vvar__0__R__30239,Vvar__1__radd__30240,Vvar__2__rmul__30245,Vvar__3__req__30250,Vvar__2__rmul__30245)
         => ( c_24__type__30371___24t(Vvar__0__R__30239,Vvar__1__radd__30240,Vvar__2__rmul__30245,Vvar__3__req__30250,Vvar__3__req__30250)
           => ( cCoq_2esetoid__ring_2eRing__theory_2esring__eq__ext___24a4(Vvar__0__R__30239,Vvar__1__radd__30240,Vvar__2__rmul__30245,Vvar__3__req__30250)
             => ( cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__30394___24a4(Vvar__0__R__30239,Vvar__1__radd__30240,Vvar__2__rmul__30245,Vvar__3__req__30250),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(Vvar__0__R__30239,c_24__type__30412___24a4(Vvar__0__R__30239,Vvar__1__radd__30240,Vvar__2__rmul__30245,Vvar__3__req__30250),Vvar__3__req__30250,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(Vvar__0__R__30239,Vvar__0__R__30239,Vvar__3__req__30250,Vvar__3__req__30250)),Vvar__1__radd__30240)
                & cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__30438___24a4(Vvar__0__R__30239,Vvar__1__radd__30240,Vvar__2__rmul__30245,Vvar__3__req__30250),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(Vvar__0__R__30239,c_24__type__30456___24a4(Vvar__0__R__30239,Vvar__1__radd__30240,Vvar__2__rmul__30245,Vvar__3__req__30250),Vvar__3__req__30250,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(Vvar__0__R__30239,Vvar__0__R__30239,Vvar__3__req__30250,Vvar__3__req__30250)),Vvar__2__rmul__30245)
                & p(c_24True) ) ) ) ) ) ) ).

fof('$_inversion_IntMap.Map.Map',axiom,
    ! [Vvar__0__A__53,VX54] :
      ( cType___24t(Vvar__0__A__53)
     => ( cIntMap_2eMap_2eMap___24t(Vvar__0__A__53,VX54)
       => ( VX54 = cIntMap_2eMap_2eM0___24a1(Vvar__0__A__53)
          | ? [Vvar__1___24Anonymous__57] :
              ( cIntMap_2eMap_2ead___24t(Vvar__1___24Anonymous__57)
              & ? [Vvar__2___24Anonymous__58] :
                  ( t(Vvar__2___24Anonymous__58,Vvar__0__A__53)
                  & VX54 = cIntMap_2eMap_2eM1___24a3(Vvar__0__A__53,Vvar__1___24Anonymous__57,Vvar__2___24Anonymous__58) ) )
          | ? [Vvar__1___24Anonymous__60] :
              ( cIntMap_2eMap_2eMap___24t(Vvar__0__A__53,Vvar__1___24Anonymous__60)
              & ? [Vvar__2___24Anonymous__61] :
                  ( cIntMap_2eMap_2eMap___24t(Vvar__0__A__53,Vvar__2___24Anonymous__61)
                  & VX54 = cIntMap_2eMap_2eM2___24a3(Vvar__0__A__53,Vvar__1___24Anonymous__60,Vvar__2___24Anonymous__61) ) ) ) ) ) ).

fof('$_inversion_IntMap.Mapcanon.mapcanon',axiom,
    ! [Vvar__0__A__1537,Vvar__1___24Anonymous__1538] :
      ( cType___24t(Vvar__0__A__1537)
     => ( cIntMap_2eMap_2eMap___24t(Vvar__0__A__1537,Vvar__1___24Anonymous__1538)
       => ( cIntMap_2eMapcanon_2emapcanon___24a2(Vvar__0__A__1537,Vvar__1___24Anonymous__1538)
         => ( Vvar__1___24Anonymous__1538 = cIntMap_2eMap_2eM0___24a1(Vvar__0__A__1537)
            | ? [Vvar__1__a__1542] :
                ( cIntMap_2eMap_2ead___24t(Vvar__1__a__1542)
                & ? [Vvar__2__y__1543] :
                    ( t(Vvar__2__y__1543,Vvar__0__A__1537)
                    & Vvar__1___24Anonymous__1538 = cIntMap_2eMap_2eM1___24a3(Vvar__0__A__1537,Vvar__1__a__1542,Vvar__2__y__1543) ) )
            | ? [Vvar__1__m1__1545] :
                ( cIntMap_2eMap_2eMap___24t(Vvar__0__A__1537,Vvar__1__m1__1545)
                & ? [Vvar__2__m2__1546] :
                    ( cIntMap_2eMap_2eMap___24t(Vvar__0__A__1537,Vvar__2__m2__1546)
                    & cIntMap_2eMapcanon_2emapcanon___24a2(Vvar__0__A__1537,Vvar__1__m1__1545)
                    & cIntMap_2eMapcanon_2emapcanon___24a2(Vvar__0__A__1537,Vvar__2__m2__1546)
                    & cCoq_2eInit_2ePeano_2ele___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO)),cIntMap_2eMap_2eMapCard___24a2(Vvar__0__A__1537,cIntMap_2eMap_2eM2___24a3(Vvar__0__A__1537,Vvar__1__m1__1545,Vvar__2__m2__1546)))
                    & Vvar__1___24Anonymous__1538 = cIntMap_2eMap_2eM2___24a3(Vvar__0__A__1537,Vvar__1__m1__1545,Vvar__2__m2__1546) ) ) ) ) ) ) ).

fof('$_lam_1083',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] : c_24__lam__1083___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = cIntMap_2eMap_2eM0___24a1(Vv__CANONICAL__0) ).

fof('$_lam_1098',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4] :
      ( cType___24t(Vv__CANONICAL__0)
     => ( cType___24t(Vv__CANONICAL__1)
       => ( cIntMap_2eMap_2ead___24t(Vv__CANONICAL__3)
         => ( cIntMap_2eMap_2eMap___24t(Vv__CANONICAL__1,Vv__CANONICAL__4)
           => ( ? [Vvar__1___24Anonymous__1101] :
                  ( t(Vvar__1___24Anonymous__1101,Vv__CANONICAL__1)
                  & cIntMap_2eMap_2eMapGet___24a3(Vv__CANONICAL__1,Vv__CANONICAL__4,Vv__CANONICAL__3) = cCoq_2eInit_2eDatatypes_2eSome___24a2(Vv__CANONICAL__1,Vvar__1___24Anonymous__1101)
                  & c_24__lam__1098___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4) = Vv__CANONICAL__2 )
              | ( cIntMap_2eMap_2eMapGet___24a3(Vv__CANONICAL__1,Vv__CANONICAL__4,Vv__CANONICAL__3) = cCoq_2eInit_2eDatatypes_2eNone___24a1(Vv__CANONICAL__1)
                & c_24__lam__1098___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4) = cIntMap_2eMap_2eM0___24a1(Vv__CANONICAL__0) ) ) ) ) ) ) ).

fof('$_lam_1156',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5] :
      ( cType___24t(Vv__CANONICAL__0)
     => ( cType___24t(Vv__CANONICAL__1)
       => ( cIntMap_2eMap_2eMap___24t(Vv__CANONICAL__1,Vv__CANONICAL__5)
         => ( ( Vv__CANONICAL__5 = cIntMap_2eMap_2eM0___24a1(Vv__CANONICAL__1)
              & c_24__lam__1156___24a6(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5) = cIntMap_2eMap_2eM0___24a1(Vv__CANONICAL__0) )
            | ? [Vvar__1___24Anonymous__1160] :
                ( cIntMap_2eMap_2ead___24t(Vvar__1___24Anonymous__1160)
                & ? [Vvar__2___24Anonymous__1161] :
                    ( t(Vvar__2___24Anonymous__1161,Vv__CANONICAL__1)
                    & ( cType___24t(Vv__CANONICAL__0)
                     => ( cType___24t(Vv__CANONICAL__1)
                       => ( cIntMap_2eMap_2eMap___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
                         => ( cIntMap_2eMap_2ead___24t(Vvar__1___24Anonymous__1160)
                           => ( Vv__CANONICAL__5 = cIntMap_2eMap_2eM1___24a3(Vv__CANONICAL__1,Vvar__1___24Anonymous__1160,Vvar__2___24Anonymous__1161)
                              & ( ? [Vvar__1___24Anonymous__1169] :
                                    ( t(Vvar__1___24Anonymous__1169,Vv__CANONICAL__0)
                                    & cIntMap_2eMap_2eMapGet___24a3(Vv__CANONICAL__0,Vv__CANONICAL__2,Vvar__1___24Anonymous__1160) = cCoq_2eInit_2eDatatypes_2eSome___24a2(Vv__CANONICAL__0,Vvar__1___24Anonymous__1169)
                                    & c_24__lam__1156___24a6(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5) = cIntMap_2eMap_2eM1___24a3(Vv__CANONICAL__0,Vvar__1___24Anonymous__1160,Vvar__1___24Anonymous__1169) )
                                | ( cIntMap_2eMap_2eMapGet___24a3(Vv__CANONICAL__0,Vv__CANONICAL__2,Vvar__1___24Anonymous__1160) = cCoq_2eInit_2eDatatypes_2eNone___24a1(Vv__CANONICAL__0)
                                  & c_24__lam__1156___24a6(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5) = cIntMap_2eMap_2eM0___24a1(Vv__CANONICAL__0) ) ) ) ) ) ) ) ) )
            | ? [Vvar__1___24Anonymous__1172] :
                ( cIntMap_2eMap_2eMap___24t(Vv__CANONICAL__1,Vvar__1___24Anonymous__1172)
                & ? [Vvar__2___24Anonymous__1173] :
                    ( cIntMap_2eMap_2eMap___24t(Vv__CANONICAL__1,Vvar__2___24Anonymous__1173)
                    & Vv__CANONICAL__5 = cIntMap_2eMap_2eM2___24a3(Vv__CANONICAL__1,Vvar__1___24Anonymous__1172,Vvar__2___24Anonymous__1173)
                    & c_24__lam__1156___24a6(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5) = cIntMap_2eMap_2emakeM2___24a3(Vv__CANONICAL__0,cIntMap_2eFset_2eMapDomRestrTo___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__3,Vvar__1___24Anonymous__1172),cIntMap_2eFset_2eMapDomRestrTo___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__4,Vvar__2___24Anonymous__1173)) ) ) ) ) ) ) ).

fof('$_lam_1228',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4] :
      ( cType___24t(Vv__CANONICAL__0)
     => ( cType___24t(Vv__CANONICAL__1)
       => ( cIntMap_2eMap_2ead___24t(Vv__CANONICAL__3)
         => ( cIntMap_2eMap_2eMap___24t(Vv__CANONICAL__1,Vv__CANONICAL__4)
           => ( ? [Vvar__1___24Anonymous__1231] :
                  ( t(Vvar__1___24Anonymous__1231,Vv__CANONICAL__1)
                  & cIntMap_2eMap_2eMapGet___24a3(Vv__CANONICAL__1,Vv__CANONICAL__4,Vv__CANONICAL__3) = cCoq_2eInit_2eDatatypes_2eSome___24a2(Vv__CANONICAL__1,Vvar__1___24Anonymous__1231)
                  & c_24__lam__1228___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4) = cIntMap_2eMap_2eM0___24a1(Vv__CANONICAL__0) )
              | ( cIntMap_2eMap_2eMapGet___24a3(Vv__CANONICAL__1,Vv__CANONICAL__4,Vv__CANONICAL__3) = cCoq_2eInit_2eDatatypes_2eNone___24a1(Vv__CANONICAL__1)
                & c_24__lam__1228___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4) = Vv__CANONICAL__2 ) ) ) ) ) ) ).

fof('$_lam_1270',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5] :
      ( cType___24t(Vv__CANONICAL__0)
     => ( cType___24t(Vv__CANONICAL__1)
       => ( cIntMap_2eMap_2eMap___24t(Vv__CANONICAL__1,Vv__CANONICAL__5)
         => ( ( Vv__CANONICAL__5 = cIntMap_2eMap_2eM0___24a1(Vv__CANONICAL__1)
              & c_24__lam__1270___24a6(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5) = Vv__CANONICAL__2 )
            | ? [Vvar__1___24Anonymous__1274] :
                ( cIntMap_2eMap_2ead___24t(Vvar__1___24Anonymous__1274)
                & ? [Vvar__2___24Anonymous__1275] :
                    ( t(Vvar__2___24Anonymous__1275,Vv__CANONICAL__1)
                    & Vv__CANONICAL__5 = cIntMap_2eMap_2eM1___24a3(Vv__CANONICAL__1,Vvar__1___24Anonymous__1274,Vvar__2___24Anonymous__1275)
                    & c_24__lam__1270___24a6(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5) = cIntMap_2eMap_2eMapRemove___24a3(Vv__CANONICAL__0,Vv__CANONICAL__2,Vvar__1___24Anonymous__1274) ) )
            | ? [Vvar__1___24Anonymous__1278] :
                ( cIntMap_2eMap_2eMap___24t(Vv__CANONICAL__1,Vvar__1___24Anonymous__1278)
                & ? [Vvar__2___24Anonymous__1279] :
                    ( cIntMap_2eMap_2eMap___24t(Vv__CANONICAL__1,Vvar__2___24Anonymous__1279)
                    & Vv__CANONICAL__5 = cIntMap_2eMap_2eM2___24a3(Vv__CANONICAL__1,Vvar__1___24Anonymous__1278,Vvar__2___24Anonymous__1279)
                    & c_24__lam__1270___24a6(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5) = cIntMap_2eMap_2emakeM2___24a3(Vv__CANONICAL__0,cIntMap_2eFset_2eMapDomRestrBy___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__3,Vvar__1___24Anonymous__1278),cIntMap_2eFset_2eMapDomRestrBy___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__4,Vvar__2___24Anonymous__1279)) ) ) ) ) ) ) ).

fof('$_lam_128',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1] : c_24__lam__128___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = cCoq_2eInit_2eDatatypes_2eNone___24a1(Vv__CANONICAL__0) ).

fof('$_lam_13198',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1] : c_24__lam__13198___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = happ(Vv__CANONICAL__0,cCoq_2eNArith_2eBinNatDef_2eN_2edouble___24a1(Vv__CANONICAL__1)) ).

fof('$_lam_13200',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1] : c_24__lam__13200___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = happ(Vv__CANONICAL__0,cCoq_2eNArith_2eBinNatDef_2eN_2esucc__double___24a1(Vv__CANONICAL__1)) ).

fof('$_lam_13247',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] : c_24__lam__13247___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = cIntMap_2eMap_2eMapGet___24a3(Vv__CANONICAL__0,cIntMap_2eMap_2eM2___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2),cCoq_2eNArith_2eBinNatDef_2eN_2edouble___24a1(Vv__CANONICAL__3)) ).

fof('$_lam_13256',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] : c_24__lam__13256___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = cIntMap_2eMap_2eMapGet___24a3(Vv__CANONICAL__0,cIntMap_2eMap_2eM2___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2),cCoq_2eNArith_2eBinNatDef_2eN_2esucc__double___24a1(Vv__CANONICAL__3)) ).

fof('$_lam_13275',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] :
      ( cType___24t(Vv__CANONICAL__0)
     => ( cIntMap_2eMap_2ead___24t(Vv__CANONICAL__3)
       => ( ( cCoq_2eNArith_2eBinNatDef_2eN_2eodd___24a1(Vv__CANONICAL__3) = cCoq_2eInit_2eDatatypes_2etrue
            & c_24__lam__13275___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = cIntMap_2eMap_2eMapGet___24a3(Vv__CANONICAL__0,Vv__CANONICAL__2,cCoq_2eNArith_2eBinNatDef_2eN_2ediv2___24a1(Vv__CANONICAL__3)) )
          | ( cCoq_2eNArith_2eBinNatDef_2eN_2eodd___24a1(Vv__CANONICAL__3) = cCoq_2eInit_2eDatatypes_2efalse
            & c_24__lam__13275___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = cIntMap_2eMap_2eMapGet___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,cCoq_2eNArith_2eBinNatDef_2eN_2ediv2___24a1(Vv__CANONICAL__3)) ) ) ) ) ).

fof('$_lam_13367',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] :
      ( c_24__lam__13367___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
    <=> cIntMap_2eMap_2eMapCard___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = cCoq_2eInit_2eDatatypes_2eS___24a1(Vv__CANONICAL__2) ) ).

fof('$_lam_13414',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] : c_24__lam__13414___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO) ).

fof('$_lam_13536',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] :
      ( c_24__lam__13536___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
    <=> cIntMap_2eFset_2ein__dom___24a3(Vv__CANONICAL__0,Vv__CANONICAL__2,Vv__CANONICAL__1) = cCoq_2eInit_2eDatatypes_2etrue ) ).

fof('$_lam_13586',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] : c_24__lam__13586___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = happ(Vv__CANONICAL__1,cCoq_2eNArith_2eBinNatDef_2eN_2edouble___24a1(Vv__CANONICAL__2)) ).

fof('$_lam_13590',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] : c_24__lam__13590___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = happ(Vv__CANONICAL__1,cCoq_2eNArith_2eBinNatDef_2eN_2edouble___24a1(Vv__CANONICAL__2)) ).

fof('$_lam_13594',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] : c_24__lam__13594___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = happ(Vv__CANONICAL__1,cCoq_2eNArith_2eBinNatDef_2eN_2esucc__double___24a1(Vv__CANONICAL__2)) ).

fof('$_lam_136',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] :
      ( cType___24t(Vv__CANONICAL__0)
     => ( cIntMap_2eMap_2ead___24t(Vv__CANONICAL__1)
       => ( cIntMap_2eMap_2ead___24t(Vv__CANONICAL__3)
         => ( ( cCoq_2eNArith_2eBinNatDef_2eN_2eeqb___24a2(Vv__CANONICAL__1,Vv__CANONICAL__3) = cCoq_2eInit_2eDatatypes_2etrue
              & c_24__lam__136___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = cCoq_2eInit_2eDatatypes_2eSome___24a2(Vv__CANONICAL__0,Vv__CANONICAL__2) )
            | ( cCoq_2eNArith_2eBinNatDef_2eN_2eeqb___24a2(Vv__CANONICAL__1,Vv__CANONICAL__3) = cCoq_2eInit_2eDatatypes_2efalse
              & c_24__lam__136___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = cCoq_2eInit_2eDatatypes_2eNone___24a1(Vv__CANONICAL__0) ) ) ) ) ) ).

fof('$_lam_13613',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1] : c_24__lam__13613___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = Vv__CANONICAL__1 ).

fof('$_lam_13951',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4] : c_24__lam__13951___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4) = happ(Vv__CANONICAL__3,cCoq_2eNArith_2eBinNatDef_2eN_2edouble___24a1(Vv__CANONICAL__4)) ).

fof('$_lam_13959',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4] : c_24__lam__13959___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4) = happ(Vv__CANONICAL__3,cCoq_2eNArith_2eBinNatDef_2eN_2esucc__double___24a1(Vv__CANONICAL__4)) ).

fof('$_lam_1398',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1] : c_24__lam__1398___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = cIntMap_2eMap_2eM0___24a1(Vv__CANONICAL__0) ).

fof('$_lam_14051',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] : c_24__lam__14051___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = Vv__CANONICAL__3 ).

fof('$_lam_1406',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] :
      ( cType___24t(Vv__CANONICAL__0)
     => ( cIntMap_2eMap_2ead___24t(Vv__CANONICAL__2)
       => ( cIntMap_2eMap_2ead___24t(Vv__CANONICAL__3)
         => ( ( cCoq_2eNArith_2eBinNatDef_2eN_2eeqb___24a2(Vv__CANONICAL__2,Vv__CANONICAL__3) = cCoq_2eInit_2eDatatypes_2etrue
              & c_24__lam__1406___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = cIntMap_2eMap_2eM0___24a1(Vv__CANONICAL__0) )
            | ( cCoq_2eNArith_2eBinNatDef_2eN_2eeqb___24a2(Vv__CANONICAL__2,Vv__CANONICAL__3) = cCoq_2eInit_2eDatatypes_2efalse
              & c_24__lam__1406___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = Vv__CANONICAL__1 ) ) ) ) ) ).

fof('$_lam_1414',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] :
      ( cType___24t(Vv__CANONICAL__0)
     => ( cIntMap_2eMap_2ead___24t(Vv__CANONICAL__3)
       => ( ( cCoq_2eNArith_2eBinNatDef_2eN_2eodd___24a1(Vv__CANONICAL__3) = cCoq_2eInit_2eDatatypes_2etrue
            & c_24__lam__1414___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = cIntMap_2eMap_2emakeM2___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,cIntMap_2eMap_2eMapRemove___24a3(Vv__CANONICAL__0,Vv__CANONICAL__2,cCoq_2eNArith_2eBinNatDef_2eN_2ediv2___24a1(Vv__CANONICAL__3))) )
          | ( cCoq_2eNArith_2eBinNatDef_2eN_2eodd___24a1(Vv__CANONICAL__3) = cCoq_2eInit_2eDatatypes_2efalse
            & c_24__lam__1414___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = cIntMap_2eMap_2emakeM2___24a3(Vv__CANONICAL__0,cIntMap_2eMap_2eMapRemove___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,cCoq_2eNArith_2eBinNatDef_2eN_2ediv2___24a1(Vv__CANONICAL__3)),Vv__CANONICAL__2) ) ) ) ) ).

fof('$_lam_14287',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5] :
      ( cType___24t(Vv__CANONICAL__0)
     => ( cType___24t(Vv__CANONICAL__1)
       => ( cCoq_2eInit_2eDatatypes_2eprod___24t(cIntMap_2eMap_2ead,Vv__CANONICAL__0,Vv__CANONICAL__4)
         => ? [Vvar__2___24Anonymous__14292] :
              ( cIntMap_2eMap_2ead___24t(Vvar__2___24Anonymous__14292)
              & ? [Vvar__3___24Anonymous__14293] :
                  ( t(Vvar__3___24Anonymous__14293,Vv__CANONICAL__0)
                  & Vv__CANONICAL__4 = cCoq_2eInit_2eDatatypes_2epair___24a4(cIntMap_2eMap_2ead,Vv__CANONICAL__0,Vvar__2___24Anonymous__14292,Vvar__3___24Anonymous__14293)
                  & c_24__lam__14287___24a6(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5) = happ(happ(Vv__CANONICAL__2,happ(happ(Vv__CANONICAL__3,Vvar__2___24Anonymous__14292),Vvar__3___24Anonymous__14293)),Vv__CANONICAL__5) ) ) ) ) ) ).

fof('$_lam_14333',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5] :
      ( cType___24t(Vv__CANONICAL__0)
     => ( cType___24t(Vv__CANONICAL__1)
       => ( cCoq_2eInit_2eDatatypes_2eprod___24t(cIntMap_2eMap_2ead,Vv__CANONICAL__0,Vv__CANONICAL__4)
         => ? [Vvar__2___24Anonymous__14338] :
              ( cIntMap_2eMap_2ead___24t(Vvar__2___24Anonymous__14338)
              & ? [Vvar__3___24Anonymous__14339] :
                  ( t(Vvar__3___24Anonymous__14339,Vv__CANONICAL__0)
                  & Vv__CANONICAL__4 = cCoq_2eInit_2eDatatypes_2epair___24a4(cIntMap_2eMap_2ead,Vv__CANONICAL__0,Vvar__2___24Anonymous__14338,Vvar__3___24Anonymous__14339)
                  & c_24__lam__14333___24a6(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5) = happ(happ(Vv__CANONICAL__2,happ(happ(Vv__CANONICAL__3,Vvar__2___24Anonymous__14338),Vvar__3___24Anonymous__14339)),Vv__CANONICAL__5) ) ) ) ) ) ).

fof('$_lam_14379',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5] :
      ( cType___24t(Vv__CANONICAL__0)
     => ( cType___24t(Vv__CANONICAL__1)
       => ( cCoq_2eInit_2eDatatypes_2eprod___24t(cIntMap_2eMap_2ead,Vv__CANONICAL__0,Vv__CANONICAL__4)
         => ? [Vvar__2___24Anonymous__14384] :
              ( cIntMap_2eMap_2ead___24t(Vvar__2___24Anonymous__14384)
              & ? [Vvar__3___24Anonymous__14385] :
                  ( t(Vvar__3___24Anonymous__14385,Vv__CANONICAL__0)
                  & Vv__CANONICAL__4 = cCoq_2eInit_2eDatatypes_2epair___24a4(cIntMap_2eMap_2ead,Vv__CANONICAL__0,Vvar__2___24Anonymous__14384,Vvar__3___24Anonymous__14385)
                  & c_24__lam__14379___24a6(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5) = happ(happ(Vv__CANONICAL__2,happ(happ(Vv__CANONICAL__3,Vvar__2___24Anonymous__14384),Vvar__3___24Anonymous__14385)),Vv__CANONICAL__5) ) ) ) ) ) ).

fof('$_lam_14505',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5] :
      ( cType___24t(Vv__CANONICAL__0)
     => ( cType___24t(Vv__CANONICAL__1)
       => ( cCoq_2eInit_2eDatatypes_2eprod___24t(cIntMap_2eMap_2ead,Vv__CANONICAL__0,Vv__CANONICAL__4)
         => ? [Vvar__2___24Anonymous__14510] :
              ( cIntMap_2eMap_2ead___24t(Vvar__2___24Anonymous__14510)
              & ? [Vvar__3___24Anonymous__14511] :
                  ( t(Vvar__3___24Anonymous__14511,Vv__CANONICAL__0)
                  & Vv__CANONICAL__4 = cCoq_2eInit_2eDatatypes_2epair___24a4(cIntMap_2eMap_2ead,Vv__CANONICAL__0,Vvar__2___24Anonymous__14510,Vvar__3___24Anonymous__14511)
                  & c_24__lam__14505___24a6(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5) = happ(happ(Vv__CANONICAL__2,happ(happ(Vv__CANONICAL__3,Vvar__2___24Anonymous__14510),Vvar__3___24Anonymous__14511)),Vv__CANONICAL__5) ) ) ) ) ) ).

fof('$_lam_14524',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4] : c_24__lam__14524___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4) = cCoq_2eInit_2eDatatypes_2enegb___24a1(cIntMap_2eFset_2ein__dom___24a3(Vv__CANONICAL__1,Vv__CANONICAL__3,Vv__CANONICAL__2)) ).

fof('$_lam_14558',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4] : c_24__lam__14558___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4) = cIntMap_2eFset_2ein__dom___24a3(Vv__CANONICAL__1,Vv__CANONICAL__3,Vv__CANONICAL__2) ).

fof('$_lam_14614',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1] :
      ( c_24__lam__14614___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1)
    <=> Vv__CANONICAL__0 = cCoq_2eNArith_2eBinNatDef_2eN_2edouble___24a1(Vv__CANONICAL__1) ) ).

fof('$_lam_14616',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1] :
      ( c_24__lam__14616___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1)
    <=> Vv__CANONICAL__0 = cCoq_2eNArith_2eBinNatDef_2eN_2esucc__double___24a1(Vv__CANONICAL__1) ) ).

fof('$_lam_1465',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] :
      ( cType___24t(Vv__CANONICAL__0)
     => ( cIntMap_2eMap_2ead___24t(Vv__CANONICAL__1)
       => ( cIntMap_2eMap_2eMap___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
         => ( ? [Vvar__1___24Anonymous__1468] :
                ( t(Vvar__1___24Anonymous__1468,Vv__CANONICAL__0)
                & cIntMap_2eMap_2eMapGet___24a3(Vv__CANONICAL__0,Vv__CANONICAL__3,Vv__CANONICAL__1) = cCoq_2eInit_2eDatatypes_2eSome___24a2(Vv__CANONICAL__0,Vvar__1___24Anonymous__1468)
                & c_24__lam__1465___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = cIntMap_2eMap_2eMapRemove___24a3(Vv__CANONICAL__0,Vv__CANONICAL__3,Vv__CANONICAL__1) )
            | ( cIntMap_2eMap_2eMapGet___24a3(Vv__CANONICAL__0,Vv__CANONICAL__3,Vv__CANONICAL__1) = cCoq_2eInit_2eDatatypes_2eNone___24a1(Vv__CANONICAL__0)
              & c_24__lam__1465___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = cIntMap_2eMap_2eMapPut___24a4(Vv__CANONICAL__0,Vv__CANONICAL__3,Vv__CANONICAL__1,Vv__CANONICAL__2) ) ) ) ) ) ).

fof('$_lam_1515',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4] :
      ( cType___24t(Vv__CANONICAL__0)
     => ( cIntMap_2eMap_2eMap___24t(Vv__CANONICAL__0,Vv__CANONICAL__4)
       => ( ( Vv__CANONICAL__4 = cIntMap_2eMap_2eM0___24a1(Vv__CANONICAL__0)
            & c_24__lam__1515___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4) = Vv__CANONICAL__1 )
          | ? [Vvar__1___24Anonymous__1519] :
              ( cIntMap_2eMap_2ead___24t(Vvar__1___24Anonymous__1519)
              & ? [Vvar__2___24Anonymous__1520] :
                  ( t(Vvar__2___24Anonymous__1520,Vv__CANONICAL__0)
                  & ( cType___24t(Vv__CANONICAL__0)
                   => ( cIntMap_2eMap_2eMap___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
                     => ( cIntMap_2eMap_2ead___24t(Vvar__1___24Anonymous__1519)
                       => ( Vv__CANONICAL__4 = cIntMap_2eMap_2eM1___24a3(Vv__CANONICAL__0,Vvar__1___24Anonymous__1519,Vvar__2___24Anonymous__1520)
                          & ( ? [Vvar__1___24Anonymous__1528] :
                                ( t(Vvar__1___24Anonymous__1528,Vv__CANONICAL__0)
                                & cIntMap_2eMap_2eMapGet___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__1___24Anonymous__1519) = cCoq_2eInit_2eDatatypes_2eSome___24a2(Vv__CANONICAL__0,Vvar__1___24Anonymous__1528)
                                & c_24__lam__1515___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4) = cIntMap_2eMap_2eMapRemove___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__1___24Anonymous__1519) )
                            | ( cIntMap_2eMap_2eMapGet___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__1___24Anonymous__1519) = cCoq_2eInit_2eDatatypes_2eNone___24a1(Vv__CANONICAL__0)
                              & c_24__lam__1515___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4) = cIntMap_2eMap_2eMapPut___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__1___24Anonymous__1519,Vvar__2___24Anonymous__1520) ) ) ) ) ) ) ) )
          | ? [Vvar__1___24Anonymous__1531] :
              ( cIntMap_2eMap_2eMap___24t(Vv__CANONICAL__0,Vvar__1___24Anonymous__1531)
              & ? [Vvar__2___24Anonymous__1532] :
                  ( cIntMap_2eMap_2eMap___24t(Vv__CANONICAL__0,Vvar__2___24Anonymous__1532)
                  & Vv__CANONICAL__4 = cIntMap_2eMap_2eM2___24a3(Vv__CANONICAL__0,Vvar__1___24Anonymous__1531,Vvar__2___24Anonymous__1532)
                  & c_24__lam__1515___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4) = cIntMap_2eMap_2emakeM2___24a3(Vv__CANONICAL__0,cIntMap_2eMap_2eMapDelta___24a3(Vv__CANONICAL__0,Vv__CANONICAL__2,Vvar__1___24Anonymous__1531),cIntMap_2eMap_2eMapDelta___24a3(Vv__CANONICAL__0,Vv__CANONICAL__3,Vvar__2___24Anonymous__1532)) ) ) ) ) ) ).

fof('$_lam_1605',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] : c_24__lam__1605___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = Vv__CANONICAL__2 ).

fof('$_lam_163',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] :
      ( cType___24t(Vv__CANONICAL__0)
     => ( cIntMap_2eMap_2ead___24t(Vv__CANONICAL__3)
       => ( ( Vv__CANONICAL__3 = cCoq_2eNumbers_2eBinNums_2eN0
            & c_24__lam__163___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = cIntMap_2eMap_2eMapGet___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,cCoq_2eNumbers_2eBinNums_2eN0) )
          | ? [Vvar__0___24Anonymous__164] :
              ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__164)
              & ( cType___24t(Vv__CANONICAL__0)
               => ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__164)
                 => ( Vv__CANONICAL__3 = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__164)
                    & ( ? [Vvar__0___24Anonymous__168] :
                          ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__168)
                          & Vvar__0___24Anonymous__164 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__168)
                          & c_24__lam__163___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = cIntMap_2eMap_2eMapGet___24a3(Vv__CANONICAL__0,Vv__CANONICAL__2,cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__168)) )
                      | ? [Vvar__0___24Anonymous__169] :
                          ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__169)
                          & Vvar__0___24Anonymous__164 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__169)
                          & c_24__lam__163___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = cIntMap_2eMap_2eMapGet___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__169)) )
                      | ( Vvar__0___24Anonymous__164 = cCoq_2eNumbers_2eBinNums_2exH
                        & c_24__lam__163___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = cIntMap_2eMap_2eMapGet___24a3(Vv__CANONICAL__0,Vv__CANONICAL__2,cCoq_2eNumbers_2eBinNums_2eN0) ) ) ) ) ) ) ) ) ) ).

fof('$_lam_1644',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] : c_24__lam__1644___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = happ(Vv__CANONICAL__2,cCoq_2eNArith_2eBinNatDef_2eN_2edouble___24a1(Vv__CANONICAL__3)) ).

fof('$_lam_1650',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] : c_24__lam__1650___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = happ(Vv__CANONICAL__2,cCoq_2eNArith_2eBinNatDef_2eN_2esucc__double___24a1(Vv__CANONICAL__3)) ).

fof('$_lam_1870',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4] :
      ( cType___24t(Vv__CANONICAL__0)
     => ( cType___24t(Vv__CANONICAL__1)
       => ( cIntMap_2eMap_2eMap___24t(Vv__CANONICAL__1,Vv__CANONICAL__3)
         => ( cIntMap_2eMap_2ead___24t(Vv__CANONICAL__4)
           => ( ? [Vvar__1___24Anonymous__1873] :
                  ( t(Vvar__1___24Anonymous__1873,Vv__CANONICAL__1)
                  & cIntMap_2eMap_2eMapGet___24a3(Vv__CANONICAL__1,Vv__CANONICAL__3,Vv__CANONICAL__4) = cCoq_2eInit_2eDatatypes_2eSome___24a2(Vv__CANONICAL__1,Vvar__1___24Anonymous__1873)
                  & c_24__lam__1870___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4) = cIntMap_2eMap_2eMapGet___24a3(Vv__CANONICAL__0,Vv__CANONICAL__2,Vv__CANONICAL__4) )
              | ( cIntMap_2eMap_2eMapGet___24a3(Vv__CANONICAL__1,Vv__CANONICAL__3,Vv__CANONICAL__4) = cCoq_2eInit_2eDatatypes_2eNone___24a1(Vv__CANONICAL__1)
                & c_24__lam__1870___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4) = cCoq_2eInit_2eDatatypes_2eNone___24a1(Vv__CANONICAL__0) ) ) ) ) ) ) ).

fof('$_lam_1889',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4] :
      ( cType___24t(Vv__CANONICAL__0)
     => ( cType___24t(Vv__CANONICAL__1)
       => ( cIntMap_2eMap_2eMap___24t(Vv__CANONICAL__1,Vv__CANONICAL__3)
         => ( cIntMap_2eMap_2ead___24t(Vv__CANONICAL__4)
           => ( ? [Vvar__1___24Anonymous__1892] :
                  ( t(Vvar__1___24Anonymous__1892,Vv__CANONICAL__1)
                  & cIntMap_2eMap_2eMapGet___24a3(Vv__CANONICAL__1,Vv__CANONICAL__3,Vv__CANONICAL__4) = cCoq_2eInit_2eDatatypes_2eSome___24a2(Vv__CANONICAL__1,Vvar__1___24Anonymous__1892)
                  & c_24__lam__1889___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4) = cCoq_2eInit_2eDatatypes_2eNone___24a1(Vv__CANONICAL__0) )
              | ( cIntMap_2eMap_2eMapGet___24a3(Vv__CANONICAL__1,Vv__CANONICAL__3,Vv__CANONICAL__4) = cCoq_2eInit_2eDatatypes_2eNone___24a1(Vv__CANONICAL__1)
                & c_24__lam__1889___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4) = cIntMap_2eMap_2eMapGet___24a3(Vv__CANONICAL__0,Vv__CANONICAL__2,Vv__CANONICAL__4) ) ) ) ) ) ) ).

fof('$_lam_1973',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] :
      ( c_24__lam__1973___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
    <=> Vv__CANONICAL__1 = cCoq_2eInit_2eDatatypes_2eSome___24a2(Vv__CANONICAL__0,Vv__CANONICAL__2) ) ).

fof('$_lam_2008',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] :
      ( cType___24t(Vv__CANONICAL__0)
     => ( cIntMap_2eMap_2ead___24t(Vv__CANONICAL__2)
       => ( cIntMap_2eMap_2ead___24t(Vv__CANONICAL__3)
         => ( ( cCoq_2eNArith_2eBinNatDef_2eN_2eeqb___24a2(Vv__CANONICAL__2,Vv__CANONICAL__3) = cCoq_2eInit_2eDatatypes_2etrue
              & c_24__lam__2008___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = cCoq_2eInit_2eDatatypes_2eNone___24a1(Vv__CANONICAL__0) )
            | ( cCoq_2eNArith_2eBinNatDef_2eN_2eeqb___24a2(Vv__CANONICAL__2,Vv__CANONICAL__3) = cCoq_2eInit_2eDatatypes_2efalse
              & c_24__lam__2008___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = cIntMap_2eMap_2eMapGet___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__3) ) ) ) ) ) ).

fof('$_lam_2038',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] :
      ( cType___24t(Vv__CANONICAL__0)
     => ( cIntMap_2eMap_2eMap___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
       => ( cIntMap_2eMap_2ead___24t(Vv__CANONICAL__3)
         => ( ? [Vvar__1___24Anonymous__2041] :
                ( t(Vvar__1___24Anonymous__2041,Vv__CANONICAL__0)
                & ( cType___24t(Vv__CANONICAL__0)
                 => ( cIntMap_2eMap_2eMap___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
                   => ( cIntMap_2eMap_2ead___24t(Vv__CANONICAL__3)
                     => ( cIntMap_2eMap_2eMapGet___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__3) = cCoq_2eInit_2eDatatypes_2eSome___24a2(Vv__CANONICAL__0,Vvar__1___24Anonymous__2041)
                        & ( ? [Vvar__1___24Anonymous__2046] :
                              ( t(Vvar__1___24Anonymous__2046,Vv__CANONICAL__0)
                              & cIntMap_2eMap_2eMapGet___24a3(Vv__CANONICAL__0,Vv__CANONICAL__2,Vv__CANONICAL__3) = cCoq_2eInit_2eDatatypes_2eSome___24a2(Vv__CANONICAL__0,Vvar__1___24Anonymous__2046)
                              & c_24__lam__2038___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = cCoq_2eInit_2eDatatypes_2eNone___24a1(Vv__CANONICAL__0) )
                          | ( cIntMap_2eMap_2eMapGet___24a3(Vv__CANONICAL__0,Vv__CANONICAL__2,Vv__CANONICAL__3) = cCoq_2eInit_2eDatatypes_2eNone___24a1(Vv__CANONICAL__0)
                            & c_24__lam__2038___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = cCoq_2eInit_2eDatatypes_2eSome___24a2(Vv__CANONICAL__0,Vvar__1___24Anonymous__2041) ) ) ) ) ) ) )
            | ( cType___24t(Vv__CANONICAL__0)
             => ( cIntMap_2eMap_2eMap___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
               => ( cIntMap_2eMap_2ead___24t(Vv__CANONICAL__3)
                 => ( cIntMap_2eMap_2eMapGet___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__3) = cCoq_2eInit_2eDatatypes_2eNone___24a1(Vv__CANONICAL__0)
                    & ( ? [Vvar__1___24Anonymous__2051] :
                          ( t(Vvar__1___24Anonymous__2051,Vv__CANONICAL__0)
                          & cIntMap_2eMap_2eMapGet___24a3(Vv__CANONICAL__0,Vv__CANONICAL__2,Vv__CANONICAL__3) = cCoq_2eInit_2eDatatypes_2eSome___24a2(Vv__CANONICAL__0,Vvar__1___24Anonymous__2051)
                          & c_24__lam__2038___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = cCoq_2eInit_2eDatatypes_2eSome___24a2(Vv__CANONICAL__0,Vvar__1___24Anonymous__2051) )
                      | ( cIntMap_2eMap_2eMapGet___24a3(Vv__CANONICAL__0,Vv__CANONICAL__2,Vv__CANONICAL__3) = cCoq_2eInit_2eDatatypes_2eNone___24a1(Vv__CANONICAL__0)
                        & c_24__lam__2038___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = cCoq_2eInit_2eDatatypes_2eNone___24a1(Vv__CANONICAL__0) ) ) ) ) ) ) ) ) ) ) ).

fof('$_lam_2087',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] :
      ( c_24__lam__2087___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
    <=> ( cIntMap_2eMapaxioms_2eeqmap___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
        & cIntMap_2eMapcanon_2emapcanon___24a2(Vv__CANONICAL__0,Vv__CANONICAL__2) ) ) ).

fof('$_lam_2108',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] :
      ( c_24__lam__2108___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3)
    <=> cIntMap_2eMap_2eMapGet___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = cCoq_2eInit_2eDatatypes_2eSome___24a2(Vv__CANONICAL__0,Vv__CANONICAL__3) ) ).

fof('$_lam_2129',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] : c_24__lam__2129___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = happ(Vv__CANONICAL__2,cCoq_2eNArith_2eBinNatDef_2eN_2edouble___24a1(Vv__CANONICAL__3)) ).

fof('$_lam_2135',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] : c_24__lam__2135___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = happ(Vv__CANONICAL__2,cCoq_2eNArith_2eBinNatDef_2eN_2esucc__double___24a1(Vv__CANONICAL__3)) ).

fof('$_lam_2179',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] : c_24__lam__2179___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = cIntMap_2eMapiter_2eacons___24a3(Vv__CANONICAL__0,cCoq_2eInit_2eDatatypes_2epair___24a4(cIntMap_2eMap_2ead,Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2),cIntMap_2eMapiter_2eanil___24a1(Vv__CANONICAL__0)) ).

fof('$_lam_2223',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4] :
      ( cType___24t(Vv__CANONICAL__0)
     => ( cIntMap_2eMap_2ead___24t(Vv__CANONICAL__2)
       => ( cIntMap_2eMap_2ead___24t(Vv__CANONICAL__4)
         => ( ( cCoq_2eNArith_2eBinNatDef_2eN_2eeqb___24a2(Vv__CANONICAL__2,Vv__CANONICAL__4) = cCoq_2eInit_2eDatatypes_2etrue
              & c_24__lam__2223___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4) = cCoq_2eInit_2eDatatypes_2eSome___24a2(Vv__CANONICAL__0,Vv__CANONICAL__3) )
            | ( cCoq_2eNArith_2eBinNatDef_2eN_2eeqb___24a2(Vv__CANONICAL__2,Vv__CANONICAL__4) = cCoq_2eInit_2eDatatypes_2efalse
              & c_24__lam__2223___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4) = cIntMap_2eMapiter_2ealist__semantics___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__4) ) ) ) ) ) ).

fof('$_lam_225',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4] :
      ( cType___24t(Vv__CANONICAL__0)
     => ( cIntMap_2eMap_2ead___24t(Vv__CANONICAL__1)
       => ( cIntMap_2eMap_2ead___24t(Vv__CANONICAL__3)
         => ( ( cCoq_2eNArith_2eBinNatDef_2eN_2elxor___24a2(Vv__CANONICAL__1,Vv__CANONICAL__3) = cCoq_2eNumbers_2eBinNums_2eN0
              & c_24__lam__225___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4) = cIntMap_2eMap_2eM1___24a3(Vv__CANONICAL__0,Vv__CANONICAL__3,Vv__CANONICAL__4) )
            | ? [Vvar__0___24Anonymous__226] :
                ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__226)
                & cCoq_2eNArith_2eBinNatDef_2eN_2elxor___24a2(Vv__CANONICAL__1,Vv__CANONICAL__3) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__226)
                & c_24__lam__225___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4) = cIntMap_2eMap_2eMapPut1___24a6(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__0___24Anonymous__226) ) ) ) ) ) ).

fof('$_lam_262',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4] :
      ( cType___24t(Vv__CANONICAL__0)
     => ( cIntMap_2eMap_2ead___24t(Vv__CANONICAL__3)
       => ( ( Vv__CANONICAL__3 = cCoq_2eNumbers_2eBinNums_2eN0
            & c_24__lam__262___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4) = cIntMap_2eMap_2eM2___24a3(Vv__CANONICAL__0,cIntMap_2eMap_2eMapPut___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,cCoq_2eNumbers_2eBinNums_2eN0,Vv__CANONICAL__4),Vv__CANONICAL__2) )
          | ? [Vvar__0___24Anonymous__263] :
              ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__263)
              & ( cType___24t(Vv__CANONICAL__0)
               => ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__263)
                 => ( Vv__CANONICAL__3 = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__263)
                    & ( ? [Vvar__0___24Anonymous__267] :
                          ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__267)
                          & Vvar__0___24Anonymous__263 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__267)
                          & c_24__lam__262___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4) = cIntMap_2eMap_2eM2___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,cIntMap_2eMap_2eMapPut___24a4(Vv__CANONICAL__0,Vv__CANONICAL__2,cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__267),Vv__CANONICAL__4)) )
                      | ? [Vvar__0___24Anonymous__268] :
                          ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__268)
                          & Vvar__0___24Anonymous__263 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__268)
                          & c_24__lam__262___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4) = cIntMap_2eMap_2eM2___24a3(Vv__CANONICAL__0,cIntMap_2eMap_2eMapPut___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__268),Vv__CANONICAL__4),Vv__CANONICAL__2) )
                      | ( Vvar__0___24Anonymous__263 = cCoq_2eNumbers_2eBinNums_2exH
                        & c_24__lam__262___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4) = cIntMap_2eMap_2eM2___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,cIntMap_2eMap_2eMapPut___24a4(Vv__CANONICAL__0,Vv__CANONICAL__2,cCoq_2eNumbers_2eBinNums_2eN0,Vv__CANONICAL__4)) ) ) ) ) ) ) ) ) ) ).

fof('$_lam_292',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4] :
      ( cType___24t(Vv__CANONICAL__0)
     => ( cIntMap_2eMap_2ead___24t(Vv__CANONICAL__2)
       => ( cIntMap_2eMap_2ead___24t(Vv__CANONICAL__4)
         => ( ( cCoq_2eNArith_2eBinNatDef_2eN_2eeqb___24a2(Vv__CANONICAL__2,Vv__CANONICAL__4) = cCoq_2eInit_2eDatatypes_2etrue
              & c_24__lam__292___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4) = cCoq_2eInit_2eDatatypes_2eSome___24a2(Vv__CANONICAL__0,Vv__CANONICAL__3) )
            | ( cCoq_2eNArith_2eBinNatDef_2eN_2eeqb___24a2(Vv__CANONICAL__2,Vv__CANONICAL__4) = cCoq_2eInit_2eDatatypes_2efalse
              & c_24__lam__292___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4) = cIntMap_2eMap_2eMapGet___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__4) ) ) ) ) ) ).

fof('$_lam_319',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1] : c_24__lam__319___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = Vv__CANONICAL__1 ).

fof('$_lam_323',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] : c_24__lam__323___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = cIntMap_2eMap_2eMapPut__behind___24a4(Vv__CANONICAL__0,Vv__CANONICAL__3,Vv__CANONICAL__1,Vv__CANONICAL__2) ).

fof('$_lam_355',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4] :
      ( cType___24t(Vv__CANONICAL__0)
     => ( cIntMap_2eMap_2eMap___24t(Vv__CANONICAL__0,Vv__CANONICAL__4)
       => ( ( Vv__CANONICAL__4 = cIntMap_2eMap_2eM0___24a1(Vv__CANONICAL__0)
            & c_24__lam__355___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4) = Vv__CANONICAL__1 )
          | ? [Vvar__1___24Anonymous__359] :
              ( cIntMap_2eMap_2ead___24t(Vvar__1___24Anonymous__359)
              & ? [Vvar__2___24Anonymous__360] :
                  ( t(Vvar__2___24Anonymous__360,Vv__CANONICAL__0)
                  & Vv__CANONICAL__4 = cIntMap_2eMap_2eM1___24a3(Vv__CANONICAL__0,Vvar__1___24Anonymous__359,Vvar__2___24Anonymous__360)
                  & c_24__lam__355___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4) = cIntMap_2eMap_2eMapPut___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__1___24Anonymous__359,Vvar__2___24Anonymous__360) ) )
          | ? [Vvar__1___24Anonymous__363] :
              ( cIntMap_2eMap_2eMap___24t(Vv__CANONICAL__0,Vvar__1___24Anonymous__363)
              & ? [Vvar__2___24Anonymous__364] :
                  ( cIntMap_2eMap_2eMap___24t(Vv__CANONICAL__0,Vvar__2___24Anonymous__364)
                  & Vv__CANONICAL__4 = cIntMap_2eMap_2eM2___24a3(Vv__CANONICAL__0,Vvar__1___24Anonymous__363,Vvar__2___24Anonymous__364)
                  & c_24__lam__355___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4) = cIntMap_2eMap_2eM2___24a3(Vv__CANONICAL__0,cIntMap_2eMap_2eMapMerge___24a3(Vv__CANONICAL__0,Vv__CANONICAL__2,Vvar__1___24Anonymous__363),cIntMap_2eMap_2eMapMerge___24a3(Vv__CANONICAL__0,Vv__CANONICAL__3,Vvar__2___24Anonymous__364)) ) ) ) ) ) ).

fof('$_lam_36687',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] : c_24__lam__36687___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = Vv__CANONICAL__1 ).

fof('$_lam_36722',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4] :
      ( c_24__lam__36722___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4)
    <=> happ(Vv__CANONICAL__2,Vv__CANONICAL__3) = happ(Vv__CANONICAL__2,Vv__CANONICAL__4) ) ).

fof('$_lam_380',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] :
      ( cType___24t(Vv__CANONICAL__0)
     => ( cIntMap_2eMap_2eMap___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
       => ( cIntMap_2eMap_2ead___24t(Vv__CANONICAL__3)
         => ( ? [Vvar__1___24Anonymous__383] :
                ( t(Vvar__1___24Anonymous__383,Vv__CANONICAL__0)
                & cIntMap_2eMap_2eMapGet___24a3(Vv__CANONICAL__0,Vv__CANONICAL__2,Vv__CANONICAL__3) = cCoq_2eInit_2eDatatypes_2eSome___24a2(Vv__CANONICAL__0,Vvar__1___24Anonymous__383)
                & c_24__lam__380___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = cCoq_2eInit_2eDatatypes_2eSome___24a2(Vv__CANONICAL__0,Vvar__1___24Anonymous__383) )
            | ( cIntMap_2eMap_2eMapGet___24a3(Vv__CANONICAL__0,Vv__CANONICAL__2,Vv__CANONICAL__3) = cCoq_2eInit_2eDatatypes_2eNone___24a1(Vv__CANONICAL__0)
              & c_24__lam__380___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = cIntMap_2eMap_2eMapGet___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__3) ) ) ) ) ) ).

fof('$_lam_649',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5] :
      ( cType___24t(Vv__CANONICAL__0)
     => ( cIntMap_2eMap_2ead___24t(Vv__CANONICAL__2)
       => ( cIntMap_2eMap_2ead___24t(Vv__CANONICAL__4)
         => ( ( cCoq_2eNArith_2eBinNatDef_2eN_2elxor___24a2(Vv__CANONICAL__2,Vv__CANONICAL__4) = cCoq_2eNumbers_2eBinNums_2eN0
              & c_24__lam__649___24a6(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5) = Vv__CANONICAL__1 )
            | ? [Vvar__0___24Anonymous__650] :
                ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__650)
                & cCoq_2eNArith_2eBinNatDef_2eN_2elxor___24a2(Vv__CANONICAL__2,Vv__CANONICAL__4) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__650)
                & c_24__lam__649___24a6(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5) = cIntMap_2eMap_2eMapPut1___24a6(Vv__CANONICAL__0,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__0___24Anonymous__650) ) ) ) ) ) ).

fof('$_lam_686',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4] :
      ( cType___24t(Vv__CANONICAL__0)
     => ( cIntMap_2eMap_2ead___24t(Vv__CANONICAL__3)
       => ( ( Vv__CANONICAL__3 = cCoq_2eNumbers_2eBinNums_2eN0
            & c_24__lam__686___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4) = cIntMap_2eMap_2eM2___24a3(Vv__CANONICAL__0,cIntMap_2eMap_2eMapPut__behind___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,cCoq_2eNumbers_2eBinNums_2eN0,Vv__CANONICAL__4),Vv__CANONICAL__2) )
          | ? [Vvar__0___24Anonymous__687] :
              ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__687)
              & ( cType___24t(Vv__CANONICAL__0)
               => ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__687)
                 => ( Vv__CANONICAL__3 = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__687)
                    & ( ? [Vvar__0___24Anonymous__691] :
                          ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__691)
                          & Vvar__0___24Anonymous__687 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__691)
                          & c_24__lam__686___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4) = cIntMap_2eMap_2eM2___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,cIntMap_2eMap_2eMapPut__behind___24a4(Vv__CANONICAL__0,Vv__CANONICAL__2,cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__691),Vv__CANONICAL__4)) )
                      | ? [Vvar__0___24Anonymous__692] :
                          ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__692)
                          & Vvar__0___24Anonymous__687 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__692)
                          & c_24__lam__686___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4) = cIntMap_2eMap_2eM2___24a3(Vv__CANONICAL__0,cIntMap_2eMap_2eMapPut__behind___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__692),Vv__CANONICAL__4),Vv__CANONICAL__2) )
                      | ( Vvar__0___24Anonymous__687 = cCoq_2eNumbers_2eBinNums_2exH
                        & c_24__lam__686___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4) = cIntMap_2eMap_2eM2___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,cIntMap_2eMap_2eMapPut__behind___24a4(Vv__CANONICAL__0,Vv__CANONICAL__2,cCoq_2eNumbers_2eBinNums_2eN0,Vv__CANONICAL__4)) ) ) ) ) ) ) ) ) ) ).

fof('$_lam_718',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4] :
      ( cType___24t(Vv__CANONICAL__0)
     => ( cIntMap_2eMap_2eMap___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
       => ( cIntMap_2eMap_2ead___24t(Vv__CANONICAL__4)
         => ( ? [Vvar__1___24Anonymous__721] :
                ( t(Vvar__1___24Anonymous__721,Vv__CANONICAL__0)
                & cIntMap_2eMap_2eMapGet___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__4) = cCoq_2eInit_2eDatatypes_2eSome___24a2(Vv__CANONICAL__0,Vvar__1___24Anonymous__721)
                & c_24__lam__718___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4) = cCoq_2eInit_2eDatatypes_2eSome___24a2(Vv__CANONICAL__0,Vvar__1___24Anonymous__721) )
            | ( cType___24t(Vv__CANONICAL__0)
             => ( cIntMap_2eMap_2ead___24t(Vv__CANONICAL__2)
               => ( cIntMap_2eMap_2ead___24t(Vv__CANONICAL__4)
                 => ( cIntMap_2eMap_2eMapGet___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__4) = cCoq_2eInit_2eDatatypes_2eNone___24a1(Vv__CANONICAL__0)
                    & ( ( cCoq_2eNArith_2eBinNatDef_2eN_2eeqb___24a2(Vv__CANONICAL__2,Vv__CANONICAL__4) = cCoq_2eInit_2eDatatypes_2etrue
                        & c_24__lam__718___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4) = cCoq_2eInit_2eDatatypes_2eSome___24a2(Vv__CANONICAL__0,Vv__CANONICAL__3) )
                      | ( cCoq_2eNArith_2eBinNatDef_2eN_2eeqb___24a2(Vv__CANONICAL__2,Vv__CANONICAL__4) = cCoq_2eInit_2eDatatypes_2efalse
                        & c_24__lam__718___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4) = cCoq_2eInit_2eDatatypes_2eNone___24a1(Vv__CANONICAL__0) ) ) ) ) ) ) ) ) ) ) ).

fof('$_prop_13465',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__5,Vv__CANONICAL__6] :
      ( p(c_24__prop__13465___24a3(Vv__CANONICAL__0,Vv__CANONICAL__5,Vv__CANONICAL__6))
    <=> Vv__CANONICAL__6 = Vv__CANONICAL__5 ) ).

fof('$_prop_13466',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__5,Vv__CANONICAL__6] :
      ( p(c_24__prop__13466___24a3(Vv__CANONICAL__0,Vv__CANONICAL__5,Vv__CANONICAL__6))
    <=> Vv__CANONICAL__6 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vv__CANONICAL__5) ) ).

fof('$_prop_13505',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__4,Vv__CANONICAL__5] :
      ( p(c_24__prop__13505___24a3(Vv__CANONICAL__0,Vv__CANONICAL__4,Vv__CANONICAL__5))
    <=> Vv__CANONICAL__4 = Vv__CANONICAL__5 ) ).

fof('$_prop_13506',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__4,Vv__CANONICAL__5] :
      ( p(c_24__prop__13506___24a3(Vv__CANONICAL__0,Vv__CANONICAL__4,Vv__CANONICAL__5))
    <=> Vv__CANONICAL__4 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vv__CANONICAL__5) ) ).

fof('$_prop_1812',axiom,
    ( p(c_24__prop__1812)
  <=> cCoq_2eInit_2eDatatypes_2etrue = cCoq_2eInit_2eDatatypes_2etrue ) ).

fof('$_prop_1813',axiom,
    ! [V1__b2] :
      ( p(c_24__prop__1813___24a1(V1__b2))
    <=> V1__b2 = cCoq_2eInit_2eDatatypes_2etrue ) ).

fof('$_prop_1815',axiom,
    ! [V1__b2] :
      ( p(c_24__prop__1815___24a1(V1__b2))
    <=> cCoq_2eInit_2eDatatypes_2efalse = cCoq_2eInit_2eDatatypes_2etrue ) ).

fof('$_prop_1816',axiom,
    ! [V1__b2] :
      ( p(c_24__prop__1816___24a1(V1__b2))
    <=> V1__b2 = cCoq_2eInit_2eDatatypes_2etrue ) ).

fof('$_prop_1822',axiom,
    ! [Vv__CANONICAL__0] :
      ( p(c_24__prop__1822___24a1(Vv__CANONICAL__0))
    <=> Vv__CANONICAL__0 = cCoq_2eInit_2eDatatypes_2etrue ) ).

fof('$_prop_1823',axiom,
    ! [Vv__CANONICAL__1] :
      ( p(c_24__prop__1823___24a1(Vv__CANONICAL__1))
    <=> Vv__CANONICAL__1 = cCoq_2eInit_2eDatatypes_2etrue ) ).

fof('$_prop_1974',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1] :
      ( p(c_24__prop__1974___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1))
    <=> Vv__CANONICAL__1 = cCoq_2eInit_2eDatatypes_2eNone___24a1(Vv__CANONICAL__0) ) ).

fof('$_prop_19859',axiom,
    ! [V0__n,V1__m] :
      ( p(c_24__prop__19859___24a2(V0__n,V1__m))
    <=> V0__n = V1__m ) ).

fof('$_prop_33473',axiom,
    ! [Vvar__0___24Anonymous__33449,Vvar__0__S__33451,Vvar__1__x__33452,Vvar__2__y__33453] :
      ( p(c_24__prop__33473___24a4(Vvar__0___24Anonymous__33449,Vvar__0__S__33451,Vvar__1__x__33452,Vvar__2__y__33453))
    <=> Vvar__1__x__33452 = Vvar__2__y__33453 ) ).

fof('$_prop_33474',axiom,
    ! [Vvar__0___24Anonymous__33449,Vvar__0__x__33454,Vvar__1__y__33455] :
      ( p(c_24__prop__33474___24a3(Vvar__0___24Anonymous__33449,Vvar__0__x__33454,Vvar__1__y__33455))
    <=> Vvar__0__x__33454 = Vvar__1__y__33455 ) ).

fof('$_prop_33475',axiom,
    ! [Vvar__0___24Anonymous__33449,Vvar__0__x__33456,Vvar__1__s__33457] :
      ( p(c_24__prop__33475___24a3(Vvar__0___24Anonymous__33449,Vvar__0__x__33456,Vvar__1__s__33457))
    <=> cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2emem___24a2(Vvar__0__x__33456,Vvar__1__s__33457) = cCoq_2eInit_2eDatatypes_2etrue ) ).

fof('$_prop_33476',axiom,
    ! [Vvar__0___24Anonymous__33449,Vvar__0__P__33458,Vvar__1__Q__33459] :
      ( p(c_24__prop__33476___24a3(Vvar__0___24Anonymous__33449,Vvar__0__P__33458,Vvar__1__Q__33459))
    <=> ( p(Vvar__0__P__33458)
        & p(Vvar__1__Q__33459) ) ) ).

fof('$_prop_33477',axiom,
    ! [Vvar__0___24Anonymous__33449,Vvar__0__P__33462,Vvar__1__Q__33463] :
      ( p(c_24__prop__33477___24a3(Vvar__0___24Anonymous__33449,Vvar__0__P__33462,Vvar__1__Q__33463))
    <=> ( p(Vvar__0__P__33462)
        | p(Vvar__1__Q__33463) ) ) ).

fof('$_prop_33478',axiom,
    ! [Vvar__0___24Anonymous__33449,Vvar__0__P__33466,Vvar__1__Q__33467] :
      ( p(c_24__prop__33478___24a3(Vvar__0___24Anonymous__33449,Vvar__0__P__33466,Vvar__1__Q__33467))
    <=> ( p(Vvar__0__P__33466)
       => p(Vvar__1__Q__33467) ) ) ).

fof('$_prop_33479',axiom,
    ! [Vvar__0___24Anonymous__33449,Vvar__0__P__33471] :
      ( p(c_24__prop__33479___24a2(Vvar__0___24Anonymous__33449,Vvar__0__P__33471))
    <=> ~ p(Vvar__0__P__33471) ) ).

fof('$_prop_36754',axiom,
    ! [V0__S,V1__x,V2__y] :
      ( p(c_24__prop__36754___24a3(V0__S,V1__x,V2__y))
    <=> V1__x = V2__y ) ).

fof('$_prop_36755',axiom,
    ! [V0__x,V1__y] :
      ( p(c_24__prop__36755___24a2(V0__x,V1__y))
    <=> V0__x = V1__y ) ).

fof('$_prop_36756',axiom,
    ! [V0__n,V1__m] :
      ( p(c_24__prop__36756___24a2(V0__n,V1__m))
    <=> V0__n = V1__m ) ).

fof('$_prop_36758',axiom,
    ! [V0__n,V1__m] :
      ( p(c_24__prop__36758___24a2(V0__n,V1__m))
    <=> V0__n = V1__m ) ).

fof('$_prop_426',axiom,
    ( p(c_24__prop__426)
  <=> cCoq_2eInit_2eDatatypes_2etrue = cCoq_2eInit_2eDatatypes_2etrue ) ).

fof('$_prop_427',axiom,
    ( p(c_24__prop__427)
  <=> cCoq_2eInit_2eDatatypes_2etrue = cCoq_2eInit_2eDatatypes_2efalse ) ).

fof('$_prop_428',axiom,
    ( p(c_24__prop__428)
  <=> cCoq_2eInit_2eDatatypes_2efalse = cCoq_2eInit_2eDatatypes_2etrue ) ).

fof('$_prop_429',axiom,
    ( p(c_24__prop__429)
  <=> cCoq_2eInit_2eDatatypes_2efalse = cCoq_2eInit_2eDatatypes_2efalse ) ).

fof('$_prop_432',axiom,
    ! [Vv__CANONICAL__0] :
      ( p(c_24__prop__432___24a1(Vv__CANONICAL__0))
    <=> Vv__CANONICAL__0 = cCoq_2eInit_2eDatatypes_2etrue ) ).

fof('$_prop_433',axiom,
    ! [Vv__CANONICAL__0] :
      ( p(c_24__prop__433___24a1(Vv__CANONICAL__0))
    <=> Vv__CANONICAL__0 = cCoq_2eInit_2eDatatypes_2efalse ) ).

fof('$_prop_784',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__5,Vv__CANONICAL__6] :
      ( p(c_24__prop__784___24a3(Vv__CANONICAL__0,Vv__CANONICAL__5,Vv__CANONICAL__6))
    <=> Vv__CANONICAL__6 = Vv__CANONICAL__5 ) ).

fof('$_prop_785',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__5,Vv__CANONICAL__6] :
      ( p(c_24__prop__785___24a3(Vv__CANONICAL__0,Vv__CANONICAL__5,Vv__CANONICAL__6))
    <=> Vv__CANONICAL__6 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vv__CANONICAL__5) ) ).

fof('$_type_1020',axiom,
    ! [Vvar__1021] :
      ( c_24__type__1020___24t(Vvar__1021)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cType___24t(Vv__CANONICAL__1)
             => cType___24t(happ(happ(Vvar__1021,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_10770',axiom,
    ! [Vvar__10771] :
      ( c_24__type__10770___24t(Vvar__10771)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eInit_2eDatatypes_2eunit___24t(Vv__CANONICAL__0)
         => cProp___24t(happ(Vvar__10771,Vv__CANONICAL__0)) ) ) ).

fof('$_type_10772',axiom,
    ! [Vvar__10773] :
      ( c_24__type__10772___24t(Vvar__10773)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__0)
         => cProp___24t(happ(Vvar__10773,Vv__CANONICAL__0)) ) ) ).

fof('$_type_10793',axiom,
    ! [Vvar__10794] :
      ( c_24__type__10793___24t(Vvar__10794)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
         => cType___24t(happ(Vvar__10794,Vv__CANONICAL__0)) ) ) ).

fof('$_type_10800',axiom,
    ! [Vvar__10801] :
      ( c_24__type__10800___24t(Vvar__10801)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
         => cProp___24t(happ(Vvar__10801,Vv__CANONICAL__0)) ) ) ).

fof('$_type_10849',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__10850] :
      ( c_24__type__10849___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__10850)
    <=> ! [Vv__CANONICAL__3] :
          ( cCoq_2eInit_2eDatatypes_2eprod___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__3)
         => cType___24t(happ(Vvar__10850,Vv__CANONICAL__3)) ) ) ).

fof('$_type_10870',axiom,
    ! [Vvar__10871] :
      ( c_24__type__10870___24t(Vvar__10871)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cType___24t(Vv__CANONICAL__1)
             => ! [Vv__CANONICAL__2] :
                  ( c_24__type__10874___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
                 => ! [Vv__CANONICAL__3] :
                      ( c_24__type__10885___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3)
                     => ! [Vv__CANONICAL__4] :
                          ( cCoq_2eInit_2eDatatypes_2eprod___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__4)
                         => t(happ(happ(happ(happ(happ(Vvar__10871,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),happ(Vv__CANONICAL__2,Vv__CANONICAL__4)) ) ) ) ) ) ) ).

fof('$_type_10874',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__10875] :
      ( c_24__type__10874___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__10875)
    <=> ! [Vv__CANONICAL__2] :
          ( cCoq_2eInit_2eDatatypes_2eprod___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
         => cType___24t(happ(Vvar__10875,Vv__CANONICAL__2)) ) ) ).

fof('$_type_10885',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__10886] :
      ( c_24__type__10885___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__10886)
    <=> ! [Vv__CANONICAL__3] :
          ( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__4] :
              ( t(Vv__CANONICAL__4,Vv__CANONICAL__1)
             => t(happ(happ(Vvar__10886,Vv__CANONICAL__3),Vv__CANONICAL__4),happ(Vv__CANONICAL__2,cCoq_2eInit_2eDatatypes_2epair___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__3,Vv__CANONICAL__4))) ) ) ) ).

fof('$_type_10897',axiom,
    ! [Vvar__10898] :
      ( c_24__type__10897___24t(Vvar__10898)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cType___24t(Vv__CANONICAL__1)
             => ! [Vv__CANONICAL__2] :
                  ( cCoq_2eInit_2eDatatypes_2eprod___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
                 => t(happ(happ(happ(Vvar__10898,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__0) ) ) ) ) ).

fof('$_type_10909',axiom,
    ! [Vvar__10910] :
      ( c_24__type__10909___24t(Vvar__10910)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cType___24t(Vv__CANONICAL__1)
             => ! [Vv__CANONICAL__2] :
                  ( cCoq_2eInit_2eDatatypes_2eprod___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
                 => t(happ(happ(happ(Vvar__10910,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__1) ) ) ) ) ).

fof('$_type_10911',axiom,
    ! [Vvar__10912] :
      ( c_24__type__10911___24t(Vvar__10912)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,happ(Vvar__10912,Vv__CANONICAL__0)) ) ) ).

fof('$_type_10973',axiom,
    ! [Vvar__10974] :
      ( c_24__type__10973___24t(Vvar__10974)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
             => cCoq_2eInit_2eDatatypes_2enat___24t(happ(happ(Vvar__10974,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_10985',axiom,
    ! [Vvar__10986] :
      ( c_24__type__10985___24t(Vvar__10986)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
             => ! [Vv__CANONICAL__2] :
                  ( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
                 => cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,happ(happ(happ(Vvar__10986,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).

fof('$_type_11363',axiom,
    ! [Vv__CANONICAL__0,Vvar__11364] :
      ( c_24__type__11363___24t(Vv__CANONICAL__0,Vvar__11364)
    <=> ! [Vv__CANONICAL__1] :
          ( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
         => t(happ(Vvar__11364,Vv__CANONICAL__1),Vv__CANONICAL__0) ) ) ).

fof('$_type_11367',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__11368] :
      ( c_24__type__11367___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__11368)
    <=> ! [Vv__CANONICAL__2] :
          ( t(Vv__CANONICAL__2,Vv__CANONICAL__1)
         => t(happ(Vvar__11368,Vv__CANONICAL__2),Vv__CANONICAL__0) ) ) ).

fof('$_type_11405',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__11406] :
      ( c_24__type__11405___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__11406)
    <=> ! [Vv__CANONICAL__6] :
          ( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
         => cType___24t(happ(Vvar__11406,Vv__CANONICAL__6)) ) ) ).

fof('$_type_11408',axiom,
    ! [Vv__CANONICAL__0,Vvar__11409] :
      ( c_24__type__11408___24t(Vv__CANONICAL__0,Vvar__11409)
    <=> ! [Vv__CANONICAL__1] :
          ( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
         => cType___24t(happ(Vvar__11409,Vv__CANONICAL__1)) ) ) ).

fof('$_type_11418',axiom,
    ! [Vvar__11419] :
      ( c_24__type__11418___24t(Vvar__11419)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
             => ! [Vv__CANONICAL__2] :
                  ( c_24__type__11408___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
                 => ! [Vv__CANONICAL__3] :
                      ( t(Vv__CANONICAL__3,happ(Vv__CANONICAL__2,Vv__CANONICAL__1))
                     => cProp___24t(happ(happ(happ(happ(Vvar__11419,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).

fof('$_type_11426',axiom,
    ! [Vvar__11427] :
      ( c_24__type__11426___24t(Vvar__11427)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
             => ! [Vv__CANONICAL__2] :
                  ( c_24__type__11430___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
                 => cProp___24t(happ(happ(happ(Vvar__11427,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).

fof('$_type_11430',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__11431] :
      ( c_24__type__11430___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__11431)
    <=> ( Vv__CANONICAL__1 = Vv__CANONICAL__1
       => cProp___24t(Vvar__11431) ) ) ).

fof('$_type_1181',axiom,
    ! [Vvar__1182] :
      ( c_24__type__1181___24t(Vvar__1182)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cType___24t(Vv__CANONICAL__1)
             => ! [Vv__CANONICAL__2] :
                  ( cIntMap_2eMap_2eMap___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
                 => ! [Vv__CANONICAL__3] :
                      ( cIntMap_2eMap_2eMap___24t(Vv__CANONICAL__1,Vv__CANONICAL__3)
                     => cIntMap_2eMap_2eMap___24t(Vv__CANONICAL__0,happ(happ(happ(happ(Vvar__1182,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).

fof('$_type_12',axiom,
    ! [Vvar__13] :
      ( c_24__type__12___24t(Vvar__13)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__0)
         => cCoq_2eNumbers_2eBinNums_2epositive___24t(happ(Vvar__13,Vv__CANONICAL__0)) ) ) ).

fof('$_type_12419',axiom,
    ! [Vv__CANONICAL__0,Vvar__12420] :
      ( c_24__type__12419___24t(Vv__CANONICAL__0,Vvar__12420)
    <=> ! [Vv__CANONICAL__1] :
          ( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__2] :
              ( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
             => cProp___24t(happ(happ(Vvar__12420,Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ).

fof('$_type_12649',axiom,
    ! [Vv__CANONICAL__0,Vvar__12650] :
      ( c_24__type__12649___24t(Vv__CANONICAL__0,Vvar__12650)
    <=> ! [Vv__CANONICAL__1] :
          ( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__2] :
              ( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
             => cCoq_2eInit_2eDatatypes_2ebool___24t(happ(happ(Vvar__12650,Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ).

fof('$_type_12824',axiom,
    ! [Vvar__12825] :
      ( c_24__type__12824___24t(Vvar__12825)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cIntMap_2eMap_2eMap___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
             => ! [Vv__CANONICAL__2] :
                  ( cIntMap_2eMap_2ead___24t(Vv__CANONICAL__2)
                 => ( cIntMap_2eFset_2ein__dom___24a3(Vv__CANONICAL__0,Vv__CANONICAL__2,Vv__CANONICAL__1) = cCoq_2eInit_2eDatatypes_2etrue
                   => cCoq_2eInit_2eSpecif_2esig___24t(Vv__CANONICAL__0,c_24__lam__2108___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2),happ(happ(happ(Vvar__12825,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ) ).

fof('$_type_12830',axiom,
    ! [Vvar__12831] :
      ( c_24__type__12830___24t(Vvar__12831)
    <=> ! [Vv__CANONICAL__0] :
          ( cIntMap_2eMap_2ead___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cIntMap_2eFset_2eFSet___24t(Vv__CANONICAL__1)
             => cCoq_2eInit_2eDatatypes_2ebool___24t(happ(happ(Vvar__12831,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_12842',axiom,
    ! [Vvar__12843] :
      ( c_24__type__12842___24t(Vvar__12843)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cIntMap_2eMap_2eMap___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
             => ! [Vv__CANONICAL__2] :
                  ( cIntMap_2eMap_2ead___24t(Vv__CANONICAL__2)
                 => ( cIntMap_2eFset_2ein__FSet___24a2(Vv__CANONICAL__2,cIntMap_2eFset_2eMapDom___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1)) = cCoq_2eInit_2eDatatypes_2etrue
                   => cCoq_2eInit_2eSpecif_2esig___24t(Vv__CANONICAL__0,c_24__lam__2108___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2),happ(happ(happ(Vvar__12843,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ) ).

fof('$_type_12935',axiom,
    ! [Vvar__12936] :
      ( c_24__type__12935___24t(Vvar__12936)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cType___24t(Vv__CANONICAL__1)
             => ! [Vv__CANONICAL__2] :
                  ( c_24__type__12942___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
                 => ! [Vv__CANONICAL__3] :
                      ( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__1,Vv__CANONICAL__3)
                     => ! [Vv__CANONICAL__4] :
                          ( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
                         => t(happ(happ(happ(happ(happ(Vvar__12936,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__0) ) ) ) ) ) ) ).

fof('$_type_12942',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__12943] :
      ( c_24__type__12942___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__12943)
    <=> ! [Vv__CANONICAL__2] :
          ( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__3] :
              ( t(Vv__CANONICAL__3,Vv__CANONICAL__1)
             => t(happ(happ(Vvar__12943,Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_12966',axiom,
    ! [Vvar__12967] :
      ( c_24__type__12966___24t(Vvar__12967)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cType___24t(Vv__CANONICAL__1)
             => ! [Vv__CANONICAL__2] :
                  ( c_24__type__12973___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
                 => ! [Vv__CANONICAL__3] :
                      ( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
                     => ! [Vv__CANONICAL__4] :
                          ( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__1,Vv__CANONICAL__4)
                         => t(happ(happ(happ(happ(happ(Vvar__12967,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__0) ) ) ) ) ) ) ).

fof('$_type_12973',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__12974] :
      ( c_24__type__12973___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__12974)
    <=> ! [Vv__CANONICAL__2] :
          ( t(Vv__CANONICAL__2,Vv__CANONICAL__1)
         => ! [Vv__CANONICAL__3] :
              ( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
             => t(happ(happ(Vvar__12974,Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_13092',axiom,
    ! [Vvar__13093] :
      ( c_24__type__13092___24t(Vvar__13093)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
             => ! [Vv__CANONICAL__2] :
                  ( cIntMap_2eMapiter_2ealist___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
                 => cIntMap_2eMap_2ead___24t(happ(happ(happ(Vvar__13093,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).

fof('$_type_13176',axiom,
    ! [Vv__CANONICAL__0,Vvar__13177] :
      ( c_24__type__13176___24t(Vv__CANONICAL__0,Vvar__13177)
    <=> ! [Vv__CANONICAL__1] :
          ( cIntMap_2eMap_2ead___24t(Vv__CANONICAL__1)
         => cIntMap_2eMap_2ead___24t(happ(Vvar__13177,Vv__CANONICAL__1)) ) ) ).

fof('$_type_13189',axiom,
    ! [Vvar__13190] :
      ( c_24__type__13189___24t(Vvar__13190)
    <=> ! [Vv__CANONICAL__0] :
          ( c_24__type__13191___24t(Vv__CANONICAL__0)
         => cProp___24t(happ(Vvar__13190,Vv__CANONICAL__0)) ) ) ).

fof('$_type_13191',axiom,
    ! [Vvar__13192] :
      ( c_24__type__13191___24t(Vvar__13192)
    <=> ! [Vv__CANONICAL__0] :
          ( cIntMap_2eMap_2ead___24t(Vv__CANONICAL__0)
         => cIntMap_2eMap_2ead___24t(happ(Vvar__13192,Vv__CANONICAL__0)) ) ) ).

fof('$_type_13363',axiom,
    ! [Vvar__13364] :
      ( c_24__type__13363___24t(Vvar__13364)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cIntMap_2eMap_2eMap___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
             => ! [Vv__CANONICAL__2] :
                  ( cIntMap_2eMap_2ead___24t(Vv__CANONICAL__2)
                 => ! [Vv__CANONICAL__3] :
                      ( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
                     => ( cIntMap_2eMap_2eMapGet___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = cCoq_2eInit_2eDatatypes_2eSome___24a2(Vv__CANONICAL__0,Vv__CANONICAL__3)
                       => cCoq_2eInit_2eSpecif_2esig___24t(cCoq_2eInit_2eDatatypes_2enat,c_24__lam__13367___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1),happ(happ(happ(happ(Vvar__13364,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ) ).

fof('$_type_13463',axiom,
    ! [Vvar__13464] :
      ( c_24__type__13463___24t(Vvar__13464)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cIntMap_2eMap_2eMap___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
             => ! [Vv__CANONICAL__2] :
                  ( cIntMap_2eMap_2eMap___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
                 => ! [Vv__CANONICAL__3] :
                      ( cIntMap_2eMap_2ead___24t(Vv__CANONICAL__3)
                     => ! [Vv__CANONICAL__4] :
                          ( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
                         => ! [Vv__CANONICAL__5] :
                              ( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__5)
                             => ! [Vv__CANONICAL__6] :
                                  ( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__6)
                                 => ( Vv__CANONICAL__2 = cIntMap_2eMap_2eMapPut__behind___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__3,Vv__CANONICAL__4)
                                   => ( Vv__CANONICAL__5 = cIntMap_2eMap_2eMapCard___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1)
                                     => ( Vv__CANONICAL__6 = cIntMap_2eMap_2eMapCard___24a2(Vv__CANONICAL__0,Vv__CANONICAL__2)
                                       => cCoq_2eInit_2eSpecif_2esumbool___24t(c_24__prop__13465___24a3(Vv__CANONICAL__0,Vv__CANONICAL__5,Vv__CANONICAL__6),c_24__prop__13466___24a3(Vv__CANONICAL__0,Vv__CANONICAL__5,Vv__CANONICAL__6),happ(happ(happ(happ(happ(happ(happ(Vvar__13464,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__6)) ) ) ) ) ) ) ) ) ) ) ) ).

fof('$_type_13503',axiom,
    ! [Vvar__13504] :
      ( c_24__type__13503___24t(Vvar__13504)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cIntMap_2eMap_2eMap___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
             => ! [Vv__CANONICAL__2] :
                  ( cIntMap_2eMap_2eMap___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
                 => ! [Vv__CANONICAL__3] :
                      ( cIntMap_2eMap_2ead___24t(Vv__CANONICAL__3)
                     => ! [Vv__CANONICAL__4] :
                          ( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__4)
                         => ! [Vv__CANONICAL__5] :
                              ( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__5)
                             => ( Vv__CANONICAL__2 = cIntMap_2eMap_2eMapRemove___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__3)
                               => ( Vv__CANONICAL__4 = cIntMap_2eMap_2eMapCard___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1)
                                 => ( Vv__CANONICAL__5 = cIntMap_2eMap_2eMapCard___24a2(Vv__CANONICAL__0,Vv__CANONICAL__2)
                                   => cCoq_2eInit_2eSpecif_2esumbool___24t(c_24__prop__13505___24a3(Vv__CANONICAL__0,Vv__CANONICAL__4,Vv__CANONICAL__5),c_24__prop__13506___24a3(Vv__CANONICAL__0,Vv__CANONICAL__4,Vv__CANONICAL__5),happ(happ(happ(happ(happ(happ(Vvar__13504,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5)) ) ) ) ) ) ) ) ) ) ) ).

fof('$_type_13532',axiom,
    ! [Vvar__13533] :
      ( c_24__type__13532___24t(Vvar__13533)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cIntMap_2eMap_2eMap___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
             => ! [Vv__CANONICAL__2] :
                  ( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__2)
                 => ( cIntMap_2eMap_2eMapCard___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = cCoq_2eInit_2eDatatypes_2eS___24a1(Vv__CANONICAL__2)
                   => cCoq_2eInit_2eSpecif_2esig___24t(cIntMap_2eMap_2ead,c_24__lam__13536___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1),happ(happ(happ(Vvar__13533,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ) ).

fof('$_type_13540',axiom,
    ! [Vv__CANONICAL__0,Vvar__13541] :
      ( c_24__type__13540___24t(Vv__CANONICAL__0,Vvar__13541)
    <=> ! [Vv__CANONICAL__1] :
          ( cIntMap_2eMap_2ead___24t(Vv__CANONICAL__1)
         => ! [Vv__CANONICAL__2] :
              ( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
             => cCoq_2eInit_2eDatatypes_2ebool___24t(happ(happ(Vvar__13541,Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ).

fof('$_type_13551',axiom,
    ! [Vvar__13552] :
      ( c_24__type__13551___24t(Vvar__13552)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( c_24__type__13540___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
             => ! [Vv__CANONICAL__2] :
                  ( cIntMap_2eMap_2ead___24t(Vv__CANONICAL__2)
                 => ! [Vv__CANONICAL__3] :
                      ( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
                     => cCoq_2eInit_2eDatatypes_2eoption___24t(cCoq_2eInit_2eDatatypes_2eprod___24a2(cIntMap_2eMap_2ead,Vv__CANONICAL__0),happ(happ(happ(happ(Vvar__13552,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).

fof('$_type_13606',axiom,
    ! [Vvar__13607] :
      ( c_24__type__13606___24t(Vvar__13607)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( c_24__type__13540___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
             => ! [Vv__CANONICAL__2] :
                  ( c_24__type__13176___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
                 => ! [Vv__CANONICAL__3] :
                      ( cIntMap_2eMap_2eMap___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
                     => cCoq_2eInit_2eDatatypes_2eoption___24t(cCoq_2eInit_2eDatatypes_2eprod___24a2(cIntMap_2eMap_2ead,Vv__CANONICAL__0),happ(happ(happ(happ(Vvar__13607,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).

fof('$_type_13620',axiom,
    ! [Vvar__13621] :
      ( c_24__type__13620___24t(Vvar__13621)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( c_24__type__13540___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
             => ! [Vv__CANONICAL__2] :
                  ( cIntMap_2eMap_2eMap___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
                 => cCoq_2eInit_2eDatatypes_2eoption___24t(cCoq_2eInit_2eDatatypes_2eprod___24a2(cIntMap_2eMap_2ead,Vv__CANONICAL__0),happ(happ(happ(Vvar__13621,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).

fof('$_type_13901',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__13902] :
      ( c_24__type__13901___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__13902)
    <=> ! [Vv__CANONICAL__3] :
          ( t(Vv__CANONICAL__3,Vv__CANONICAL__1)
         => ! [Vv__CANONICAL__4] :
              ( t(Vv__CANONICAL__4,Vv__CANONICAL__1)
             => t(happ(happ(Vvar__13902,Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__1) ) ) ) ).

fof('$_type_13915',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__13916] :
      ( c_24__type__13915___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__13916)
    <=> ! [Vv__CANONICAL__3] :
          ( t(Vv__CANONICAL__3,Vv__CANONICAL__2)
         => ! [Vv__CANONICAL__4] :
              ( cIntMap_2eMap_2ead___24t(Vv__CANONICAL__4)
             => ! [Vv__CANONICAL__5] :
                  ( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
                 => cCoq_2eInit_2eDatatypes_2eprod___24t(Vv__CANONICAL__2,Vv__CANONICAL__1,happ(happ(happ(Vvar__13916,Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5)) ) ) ) ) ).

fof('$_type_13920',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__13921] :
      ( c_24__type__13920___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__13921)
    <=> ! [Vv__CANONICAL__3] :
          ( cIntMap_2eMap_2ead___24t(Vv__CANONICAL__3)
         => cIntMap_2eMap_2ead___24t(happ(Vvar__13921,Vv__CANONICAL__3)) ) ) ).

fof('$_type_14',axiom,
    ! [Vvar__15] :
      ( c_24__type__14___24t(Vvar__15)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__0)
         => cProp___24t(happ(Vvar__15,Vv__CANONICAL__0)) ) ) ).

fof('$_type_14028',axiom,
    ! [Vvar__14029] :
      ( c_24__type__14028___24t(Vvar__14029)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cType___24t(Vv__CANONICAL__1)
             => ! [Vv__CANONICAL__2] :
                  ( t(Vv__CANONICAL__2,Vv__CANONICAL__1)
                 => ! [Vv__CANONICAL__3] :
                      ( c_24__type__1698___24t(Vv__CANONICAL__1,Vv__CANONICAL__3)
                     => ! [Vv__CANONICAL__4] :
                          ( cType___24t(Vv__CANONICAL__4)
                         => ! [Vv__CANONICAL__5] :
                              ( c_24__type__13915___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__4,Vv__CANONICAL__5)
                             => ! [Vv__CANONICAL__6] :
                                  ( t(Vv__CANONICAL__6,Vv__CANONICAL__4)
                                 => ! [Vv__CANONICAL__7] :
                                      ( c_24__type__13920___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__4,Vv__CANONICAL__7)
                                     => ! [Vv__CANONICAL__8] :
                                          ( cIntMap_2eMap_2eMap___24t(Vv__CANONICAL__0,Vv__CANONICAL__8)
                                         => cCoq_2eInit_2eDatatypes_2eprod___24t(Vv__CANONICAL__4,Vv__CANONICAL__1,happ(happ(happ(happ(happ(happ(happ(happ(happ(Vvar__14029,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__6),Vv__CANONICAL__7),Vv__CANONICAL__8)) ) ) ) ) ) ) ) ) ) ) ).

fof('$_type_14105',axiom,
    ! [Vvar__14106] :
      ( c_24__type__14105___24t(Vvar__14106)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cType___24t(Vv__CANONICAL__1)
             => ! [Vv__CANONICAL__2] :
                  ( t(Vv__CANONICAL__2,Vv__CANONICAL__1)
                 => ! [Vv__CANONICAL__3] :
                      ( c_24__type__1698___24t(Vv__CANONICAL__1,Vv__CANONICAL__3)
                     => ! [Vv__CANONICAL__4] :
                          ( cType___24t(Vv__CANONICAL__4)
                         => ! [Vv__CANONICAL__5] :
                              ( c_24__type__13915___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__4,Vv__CANONICAL__5)
                             => ! [Vv__CANONICAL__6] :
                                  ( t(Vv__CANONICAL__6,Vv__CANONICAL__4)
                                 => ! [Vv__CANONICAL__7] :
                                      ( cIntMap_2eMap_2eMap___24t(Vv__CANONICAL__0,Vv__CANONICAL__7)
                                     => cCoq_2eInit_2eDatatypes_2eprod___24t(Vv__CANONICAL__4,Vv__CANONICAL__1,happ(happ(happ(happ(happ(happ(happ(happ(Vvar__14106,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__6),Vv__CANONICAL__7)) ) ) ) ) ) ) ) ) ) ).

fof('$_type_14144',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__14145] :
      ( c_24__type__14144___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__14145)
    <=> ! [Vv__CANONICAL__3] :
          ( cIntMap_2eMap_2ead___24t(Vv__CANONICAL__3)
         => ! [Vv__CANONICAL__4] :
              ( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
             => t(happ(happ(Vvar__14145,Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__1) ) ) ) ).

fof('$_type_14177',axiom,
    ! [Vvar__14178] :
      ( c_24__type__14177___24t(Vvar__14178)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eInit_2eDatatypes_2eprod___24a2(cIntMap_2eMap_2ead,Vv__CANONICAL__0),happ(Vvar__14178,Vv__CANONICAL__0)) ) ) ).

fof('$_type_1418',axiom,
    ! [Vvar__1419] :
      ( c_24__type__1418___24t(Vvar__1419)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cIntMap_2eMap_2eMap___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
             => ! [Vv__CANONICAL__2] :
                  ( cIntMap_2eMap_2ead___24t(Vv__CANONICAL__2)
                 => cIntMap_2eMap_2eMap___24t(Vv__CANONICAL__0,happ(happ(happ(Vvar__1419,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).

fof('$_type_14182',axiom,
    ! [Vvar__14183] :
      ( c_24__type__14182___24t(Vvar__14183)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cCoq_2eInit_2eDatatypes_2eprod___24t(cIntMap_2eMap_2ead,Vv__CANONICAL__0,Vv__CANONICAL__1)
             => ! [Vv__CANONICAL__2] :
                  ( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eInit_2eDatatypes_2eprod___24a2(cIntMap_2eMap_2ead,Vv__CANONICAL__0),Vv__CANONICAL__2)
                 => cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eInit_2eDatatypes_2eprod___24a2(cIntMap_2eMap_2ead,Vv__CANONICAL__0),happ(happ(happ(Vvar__14183,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).

fof('$_type_14538',axiom,
    ! [Vvar__14539] :
      ( c_24__type__14538___24t(Vvar__14539)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cType___24t(Vv__CANONICAL__1)
             => ! [Vv__CANONICAL__2] :
                  ( cIntMap_2eMap_2eMap___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
                 => ! [Vv__CANONICAL__3] :
                      ( cIntMap_2eMap_2eMap___24t(Vv__CANONICAL__1,Vv__CANONICAL__3)
                     => cCoq_2eInit_2eDatatypes_2ebool___24t(happ(happ(happ(happ(Vvar__14539,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).

fof('$_type_14593',axiom,
    ! [Vvar__14594] :
      ( c_24__type__14593___24t(Vvar__14594)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
         => cCoq_2eInit_2eDatatypes_2ebool___24t(happ(Vvar__14594,Vv__CANONICAL__0)) ) ) ).

fof('$_type_14607',axiom,
    ! [Vvar__14608] :
      ( c_24__type__14607___24t(Vvar__14608)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
             => cCoq_2eInit_2eDatatypes_2ebool___24t(happ(happ(Vvar__14608,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_14611',axiom,
    ! [Vvar__14612] :
      ( c_24__type__14611___24t(Vvar__14612)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__0)
         => cCoq_2eInit_2eDatatypes_2esum___24t(cCoq_2eInit_2eSpecif_2esig___24a2(cCoq_2eNumbers_2eBinNums_2eN,c_24__lam__14614___24a1(Vv__CANONICAL__0)),cCoq_2eInit_2eSpecif_2esig___24a2(cCoq_2eNumbers_2eBinNums_2eN,c_24__lam__14616___24a1(Vv__CANONICAL__0)),happ(Vvar__14612,Vv__CANONICAL__0)) ) ) ).

fof('$_type_14619',axiom,
    ! [Vvar__14620] :
      ( c_24__type__14619___24t(Vvar__14620)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
         => cProp___24t(happ(Vvar__14620,Vv__CANONICAL__0)) ) ) ).

fof('$_type_14713',axiom,
    ! [Vvar__14714] :
      ( c_24__type__14713___24t(Vvar__14714)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__1)
             => cCoq_2eReals_2eRdefinitions_2eR___24t(happ(happ(Vvar__14714,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_14716',axiom,
    ! [Vvar__14717] :
      ( c_24__type__14716___24t(Vvar__14717)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__0)
         => cCoq_2eReals_2eRdefinitions_2eR___24t(happ(Vvar__14717,Vv__CANONICAL__0)) ) ) ).

fof('$_type_14722',axiom,
    ! [Vvar__14723] :
      ( c_24__type__14722___24t(Vvar__14723)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
         => cCoq_2eReals_2eRdefinitions_2eR___24t(happ(Vvar__14723,Vv__CANONICAL__0)) ) ) ).

fof('$_type_15506',axiom,
    ! [Vvar__15507] :
      ( c_24__type__15506___24t(Vvar__15507)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
             => cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vv__CANONICAL__0,happ(happ(Vvar__15507,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_15511',axiom,
    ! [Vvar__15512] :
      ( c_24__type__15511___24t(Vvar__15512)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
             => ! [Vv__CANONICAL__2] :
                  ( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
                 => cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vv__CANONICAL__0,happ(happ(happ(Vvar__15512,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).

fof('$_type_1563',axiom,
    ! [Vv__CANONICAL__0,Vvar__1564] :
      ( c_24__type__1563___24t(Vv__CANONICAL__0,Vvar__1564)
    <=> ! [Vv__CANONICAL__1] :
          ( cIntMap_2eMap_2eMap___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
         => ! [Vv__CANONICAL__2] :
              ( cIntMap_2eMap_2eMap___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
             => cIntMap_2eMap_2eMap___24t(Vv__CANONICAL__0,happ(happ(Vvar__1564,Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ).

fof('$_type_1574',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__1575] :
      ( c_24__type__1574___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__1575)
    <=> ! [Vv__CANONICAL__2] :
          ( cIntMap_2eMap_2ead___24t(Vv__CANONICAL__2)
         => ! [Vv__CANONICAL__3] :
              ( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
             => cIntMap_2eMap_2eMap___24t(Vv__CANONICAL__1,happ(happ(Vvar__1575,Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ).

fof('$_type_1580',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__1581] :
      ( c_24__type__1580___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__1581)
    <=> ! [Vv__CANONICAL__2] :
          ( cIntMap_2eMap_2ead___24t(Vv__CANONICAL__2)
         => cIntMap_2eMap_2ead___24t(happ(Vvar__1581,Vv__CANONICAL__2)) ) ) ).

fof('$_type_1617',axiom,
    ! [Vvar__1618] :
      ( c_24__type__1617___24t(Vvar__1618)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cType___24t(Vv__CANONICAL__1)
             => ! [Vv__CANONICAL__2] :
                  ( c_24__type__1574___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
                 => ! [Vv__CANONICAL__3] :
                      ( cIntMap_2eMap_2eMap___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
                     => cIntMap_2eMap_2eMap___24t(Vv__CANONICAL__1,happ(happ(happ(happ(Vvar__1618,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).

fof('$_type_16309',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__16310] :
      ( c_24__type__16309___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__16310)
    <=> ! [Vv__CANONICAL__17] :
          ( t(Vv__CANONICAL__17,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__18] :
              ( t(Vv__CANONICAL__18,Vv__CANONICAL__0)
             => t(happ(happ(Vvar__16310,Vv__CANONICAL__17),Vv__CANONICAL__18),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_16522',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__16523] :
      ( c_24__type__16522___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__16523)
    <=> ! [Vv__CANONICAL__17] :
          ( t(Vv__CANONICAL__17,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__18] :
              ( t(Vv__CANONICAL__18,Vv__CANONICAL__0)
             => t(happ(happ(Vvar__16523,Vv__CANONICAL__17),Vv__CANONICAL__18),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_16735',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__16736] :
      ( c_24__type__16735___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__16736)
    <=> ! [Vv__CANONICAL__17] :
          ( t(Vv__CANONICAL__17,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__18] :
              ( t(Vv__CANONICAL__18,Vv__CANONICAL__0)
             => t(happ(happ(Vvar__16736,Vv__CANONICAL__17),Vv__CANONICAL__18),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_1693',axiom,
    ! [Vvar__1694] :
      ( c_24__type__1693___24t(Vvar__1694)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cType___24t(Vv__CANONICAL__1)
             => ! [Vv__CANONICAL__2] :
                  ( t(Vv__CANONICAL__2,Vv__CANONICAL__1)
                 => ! [Vv__CANONICAL__3] :
                      ( c_24__type__1698___24t(Vv__CANONICAL__1,Vv__CANONICAL__3)
                     => ! [Vv__CANONICAL__4] :
                          ( c_24__type__1705___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__4)
                         => ! [Vv__CANONICAL__5] :
                              ( c_24__type__1580___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__5)
                             => ! [Vv__CANONICAL__6] :
                                  ( cIntMap_2eMap_2eMap___24t(Vv__CANONICAL__0,Vv__CANONICAL__6)
                                 => t(happ(happ(happ(happ(happ(happ(happ(Vvar__1694,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__6),Vv__CANONICAL__1) ) ) ) ) ) ) ) ) ).

fof('$_type_16930',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__16931] :
      ( c_24__type__16930___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__16931)
    <=> ! [Vv__CANONICAL__17] :
          ( t(Vv__CANONICAL__17,Vv__CANONICAL__0)
         => t(happ(Vvar__16931,Vv__CANONICAL__17),Vv__CANONICAL__0) ) ) ).

fof('$_type_1698',axiom,
    ! [Vv__CANONICAL__0,Vvar__1699] :
      ( c_24__type__1698___24t(Vv__CANONICAL__0,Vvar__1699)
    <=> ! [Vv__CANONICAL__1] :
          ( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__2] :
              ( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
             => t(happ(happ(Vvar__1699,Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_1705',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__1706] :
      ( c_24__type__1705___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__1706)
    <=> ! [Vv__CANONICAL__2] :
          ( cIntMap_2eMap_2ead___24t(Vv__CANONICAL__2)
         => ! [Vv__CANONICAL__3] :
              ( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
             => t(happ(happ(Vvar__1706,Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__1) ) ) ) ).

fof('$_type_17143',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__17144] :
      ( c_24__type__17143___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__17144)
    <=> ! [Vv__CANONICAL__17] :
          ( t(Vv__CANONICAL__17,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__18] :
              ( t(Vv__CANONICAL__18,Vv__CANONICAL__0)
             => cProp___24t(happ(happ(Vvar__17144,Vv__CANONICAL__17),Vv__CANONICAL__18)) ) ) ) ).

fof('$_type_173',axiom,
    ! [Vvar__174] :
      ( c_24__type__173___24t(Vvar__174)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cIntMap_2eMap_2eMap___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
             => ! [Vv__CANONICAL__2] :
                  ( cIntMap_2eMap_2ead___24t(Vv__CANONICAL__2)
                 => cCoq_2eInit_2eDatatypes_2eoption___24t(Vv__CANONICAL__0,happ(happ(happ(Vvar__174,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).

fof('$_type_17356',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__17357] :
      ( c_24__type__17356___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__17357)
    <=> ! [Vv__CANONICAL__17] :
          ( t(Vv__CANONICAL__17,Vv__CANONICAL__8)
         => ! [Vv__CANONICAL__18] :
              ( t(Vv__CANONICAL__18,Vv__CANONICAL__8)
             => t(happ(happ(Vvar__17357,Vv__CANONICAL__17),Vv__CANONICAL__18),Vv__CANONICAL__8) ) ) ) ).

fof('$_type_1742',axiom,
    ! [Vvar__1743] :
      ( c_24__type__1742___24t(Vvar__1743)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cType___24t(Vv__CANONICAL__1)
             => ! [Vv__CANONICAL__2] :
                  ( t(Vv__CANONICAL__2,Vv__CANONICAL__1)
                 => ! [Vv__CANONICAL__3] :
                      ( c_24__type__1698___24t(Vv__CANONICAL__1,Vv__CANONICAL__3)
                     => ! [Vv__CANONICAL__4] :
                          ( c_24__type__1705___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__4)
                         => ! [Vv__CANONICAL__5] :
                              ( cIntMap_2eMap_2eMap___24t(Vv__CANONICAL__0,Vv__CANONICAL__5)
                             => t(happ(happ(happ(happ(happ(happ(Vvar__1743,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__1) ) ) ) ) ) ) ) ).

fof('$_type_17569',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__17570] :
      ( c_24__type__17569___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__17570)
    <=> ! [Vv__CANONICAL__17] :
          ( t(Vv__CANONICAL__17,Vv__CANONICAL__8)
         => ! [Vv__CANONICAL__18] :
              ( t(Vv__CANONICAL__18,Vv__CANONICAL__8)
             => t(happ(happ(Vvar__17570,Vv__CANONICAL__17),Vv__CANONICAL__18),Vv__CANONICAL__8) ) ) ) ).

fof('$_type_1778',axiom,
    ! [Vvar__1779] :
      ( c_24__type__1778___24t(Vvar__1779)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cIntMap_2eMapiter_2ealist___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
             => cIntMap_2eMap_2eMap___24t(Vv__CANONICAL__0,happ(happ(Vvar__1779,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_17782',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__17783] :
      ( c_24__type__17782___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__17783)
    <=> ! [Vv__CANONICAL__17] :
          ( t(Vv__CANONICAL__17,Vv__CANONICAL__8)
         => ! [Vv__CANONICAL__18] :
              ( t(Vv__CANONICAL__18,Vv__CANONICAL__8)
             => t(happ(happ(Vvar__17783,Vv__CANONICAL__17),Vv__CANONICAL__18),Vv__CANONICAL__8) ) ) ) ).

fof('$_type_1786',axiom,
    ! [Vvar__1787] :
      ( c_24__type__1786___24t(Vvar__1787)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cType___24t(Vv__CANONICAL__1)
             => ! [Vv__CANONICAL__2] :
                  ( cIntMap_2eMap_2eMap___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
                 => ! [Vv__CANONICAL__3] :
                      ( cIntMap_2eMap_2eMap___24t(Vv__CANONICAL__1,Vv__CANONICAL__3)
                     => cProp___24t(happ(happ(happ(happ(Vvar__1787,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).

fof('$_type_17977',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__17978] :
      ( c_24__type__17977___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__17978)
    <=> ! [Vv__CANONICAL__17] :
          ( t(Vv__CANONICAL__17,Vv__CANONICAL__8)
         => t(happ(Vvar__17978,Vv__CANONICAL__17),Vv__CANONICAL__8) ) ) ).

fof('$_type_1799',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__1800] :
      ( c_24__type__1799___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__1800)
    <=> ! [Vv__CANONICAL__2] :
          ( cCoq_2eInit_2eSpecif_2esig___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
         => cProp___24t(happ(Vvar__1800,Vv__CANONICAL__2)) ) ) ).

fof('$_type_1805',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__1806] :
      ( c_24__type__1805___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__1806)
    <=> ! [Vv__CANONICAL__2] :
          ( cCoq_2eInit_2eSpecif_2esumor___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
         => cProp___24t(happ(Vvar__1806,Vv__CANONICAL__2)) ) ) ).

fof('$_type_18190',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__18191] :
      ( c_24__type__18190___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__18191)
    <=> ! [Vv__CANONICAL__17] :
          ( t(Vv__CANONICAL__17,Vv__CANONICAL__8)
         => ! [Vv__CANONICAL__18] :
              ( t(Vv__CANONICAL__18,Vv__CANONICAL__8)
             => cCoq_2eInit_2eDatatypes_2ebool___24t(happ(happ(Vvar__18191,Vv__CANONICAL__17),Vv__CANONICAL__18)) ) ) ) ).

fof('$_type_1820',axiom,
    ! [Vvar__1821] :
      ( c_24__type__1820___24t(Vvar__1821)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__1)
             => ( cCoq_2eInit_2eDatatypes_2eorb___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = cCoq_2eInit_2eDatatypes_2etrue
               => cCoq_2eInit_2eSpecif_2esumbool___24t(c_24__prop__1822___24a1(Vv__CANONICAL__0),c_24__prop__1823___24a1(Vv__CANONICAL__1),happ(happ(Vvar__1821,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ) ).

fof('$_type_1826',axiom,
    ! [Vvar__1827] :
      ( c_24__type__1826___24t(Vvar__1827)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__1)
             => cCoq_2eInit_2eDatatypes_2ebool___24t(happ(happ(Vvar__1827,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_1829',axiom,
    ! [Vvar__1830] :
      ( c_24__type__1829___24t(Vvar__1830)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__0)
         => cCoq_2eInit_2eDatatypes_2ebool___24t(happ(Vvar__1830,Vv__CANONICAL__0)) ) ) ).

fof('$_type_1837',axiom,
    ! [Vvar__1838] :
      ( c_24__type__1837___24t(Vvar__1838)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cType___24t(Vv__CANONICAL__1)
             => ! [Vv__CANONICAL__2] :
                  ( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
                 => ! [Vv__CANONICAL__3] :
                      ( t(Vv__CANONICAL__3,Vv__CANONICAL__1)
                     => cCoq_2eInit_2eDatatypes_2eprod___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,happ(happ(happ(happ(Vvar__1838,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).

fof('$_type_18385',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__18386] :
      ( c_24__type__18385___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__18386)
    <=> ! [Vv__CANONICAL__17] :
          ( t(Vv__CANONICAL__17,Vv__CANONICAL__8)
         => t(happ(Vvar__18386,Vv__CANONICAL__17),Vv__CANONICAL__0) ) ) ).

fof('$_type_1841',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__1842] :
      ( c_24__type__1841___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__1842)
    <=> ! [Vv__CANONICAL__2] :
          ( cCoq_2eInit_2eDatatypes_2eprod___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
         => cProp___24t(happ(Vvar__1842,Vv__CANONICAL__2)) ) ) ).

fof('$_type_18415',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__18416] :
      ( c_24__type__18415___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__18416)
    <=> ! [Vv__CANONICAL__2] :
          ( t(Vv__CANONICAL__2,Vv__CANONICAL__1)
         => ! [Vv__CANONICAL__3] :
              ( t(Vv__CANONICAL__3,Vv__CANONICAL__1)
             => t(happ(happ(Vvar__18416,Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__1) ) ) ) ).

fof('$_type_18429',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__18430] :
      ( c_24__type__18429___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__18430)
    <=> ! [Vv__CANONICAL__2] :
          ( t(Vv__CANONICAL__2,Vv__CANONICAL__1)
         => t(happ(Vvar__18430,Vv__CANONICAL__2),Vv__CANONICAL__1) ) ) ).

fof('$_type_18436',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__18437] :
      ( c_24__type__18436___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__18437)
    <=> ! [Vv__CANONICAL__2] :
          ( t(Vv__CANONICAL__2,Vv__CANONICAL__1)
         => ! [Vv__CANONICAL__3] :
              ( t(Vv__CANONICAL__3,Vv__CANONICAL__1)
             => cCoq_2eInit_2eDatatypes_2ebool___24t(happ(happ(Vvar__18437,Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ).

fof('$_type_18451',axiom,
    ! [Vvar__18452] :
      ( c_24__type__18451___24t(Vvar__18452)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
             => t(happ(happ(Vvar__18452,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_1848',axiom,
    ! [Vvar__1849] :
      ( c_24__type__1848___24t(Vvar__1849)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
             => ! [Vv__CANONICAL__2] :
                  ( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
                 => cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,happ(happ(happ(Vvar__1849,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).

fof('$_type_1851',axiom,
    ! [Vv__CANONICAL__0,Vvar__1852] :
      ( c_24__type__1851___24t(Vv__CANONICAL__0,Vvar__1852)
    <=> ! [Vv__CANONICAL__1] :
          ( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
         => cProp___24t(happ(Vvar__1852,Vv__CANONICAL__1)) ) ) ).

fof('$_type_18737',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__18738] :
      ( c_24__type__18737___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__18738)
    <=> ! [Vv__CANONICAL__2] :
          ( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
         => cType___24t(happ(Vvar__18738,Vv__CANONICAL__2)) ) ) ).

fof('$_type_18741',axiom,
    ! [Vvar__18742] :
      ( c_24__type__18741___24t(Vvar__18742)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( c_24__type__11408___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
             => cType___24t(happ(happ(Vvar__18742,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_18759',axiom,
    ! [Vvar__18760] :
      ( c_24__type__18759___24t(Vvar__18760)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( c_24__type__11408___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
             => ! [Vv__CANONICAL__2] :
                  ( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
                 => ! [Vv__CANONICAL__3] :
                      ( t(Vv__CANONICAL__3,happ(Vv__CANONICAL__1,Vv__CANONICAL__2))
                     => cCoq_2eInit_2eSpecif_2esigT___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,happ(happ(happ(happ(Vvar__18760,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).

fof('$_type_18778',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__18779] :
      ( c_24__type__18778___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__18779)
    <=> ! [Vv__CANONICAL__3] :
          ( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
         => cType___24t(happ(Vvar__18779,Vv__CANONICAL__3)) ) ) ).

fof('$_type_18786',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__18787] :
      ( c_24__type__18786___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__18787)
    <=> ! [Vv__CANONICAL__3] :
          ( cCoq_2eInit_2eSpecif_2esigT___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__3)
         => cType___24t(happ(Vvar__18787,Vv__CANONICAL__3)) ) ) ).

fof('$_type_18808',axiom,
    ! [Vvar__18809] :
      ( c_24__type__18808___24t(Vvar__18809)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( c_24__type__11408___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
             => ! [Vv__CANONICAL__2] :
                  ( c_24__type__18814___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
                 => ! [Vv__CANONICAL__3] :
                      ( c_24__type__18826___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3)
                     => ! [Vv__CANONICAL__4] :
                          ( cCoq_2eInit_2eSpecif_2esigT___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__4)
                         => t(happ(happ(happ(happ(happ(Vvar__18809,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),happ(Vv__CANONICAL__2,Vv__CANONICAL__4)) ) ) ) ) ) ) ).

fof('$_type_18814',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__18815] :
      ( c_24__type__18814___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__18815)
    <=> ! [Vv__CANONICAL__2] :
          ( cCoq_2eInit_2eSpecif_2esigT___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
         => cType___24t(happ(Vvar__18815,Vv__CANONICAL__2)) ) ) ).

fof('$_type_18826',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__18827] :
      ( c_24__type__18826___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__18827)
    <=> ! [Vv__CANONICAL__3] :
          ( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__4] :
              ( t(Vv__CANONICAL__4,happ(Vv__CANONICAL__1,Vv__CANONICAL__3))
             => t(happ(happ(Vvar__18827,Vv__CANONICAL__3),Vv__CANONICAL__4),happ(Vv__CANONICAL__2,cCoq_2eInit_2eSpecif_2eexistT___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__3,Vv__CANONICAL__4))) ) ) ) ).

fof('$_type_18852',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__18853] :
      ( c_24__type__18852___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__18853)
    <=> ! [Vv__CANONICAL__3] :
          ( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
         => cType___24t(happ(Vvar__18853,Vv__CANONICAL__3)) ) ) ).

fof('$_type_18860',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__18861] :
      ( c_24__type__18860___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__18861)
    <=> ! [Vv__CANONICAL__3] :
          ( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
         => cType___24t(happ(Vvar__18861,Vv__CANONICAL__3)) ) ) ).

fof('$_type_18868',axiom,
    ! [Vvar__18869] :
      ( c_24__type__18868___24t(Vvar__18869)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( c_24__type__11408___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
             => ! [Vv__CANONICAL__2] :
                  ( c_24__type__11408___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
                 => cType___24t(happ(happ(happ(Vvar__18869,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).

fof('$_type_18934',axiom,
    ! [Vvar__18935] :
      ( c_24__type__18934___24t(Vvar__18935)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__1)
             => cCoq_2eInit_2eDatatypes_2ebool___24t(happ(happ(Vvar__18935,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_19006',axiom,
    ! [Vvar__19007] :
      ( c_24__type__19006___24t(Vvar__19007)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__0)
         => cCoq_2eInit_2eDatatypes_2enat___24t(happ(Vvar__19007,Vv__CANONICAL__0)) ) ) ).

fof('$_type_19009',axiom,
    ! [Vvar__19010] :
      ( c_24__type__19009___24t(Vvar__19010)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__1)
             => cProp___24t(happ(happ(Vvar__19010,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_1901',axiom,
    ! [Vvar__1902] :
      ( c_24__type__1901___24t(Vvar__1902)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cIntMap_2eMap_2ead___24t(Vv__CANONICAL__1)
             => ! [Vv__CANONICAL__2] :
                  ( cIntMap_2eMap_2eMap___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
                 => cCoq_2eInit_2eDatatypes_2ebool___24t(happ(happ(happ(Vvar__1902,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).

fof('$_type_19055',axiom,
    ! [Vvar__19056] :
      ( c_24__type__19055___24t(Vvar__19056)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__1)
             => cCoq_2eNumbers_2eBinNums_2epositive___24t(happ(happ(Vvar__19056,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_19093',axiom,
    ! [Vvar__19094] :
      ( c_24__type__19093___24t(Vvar__19094)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__0)
         => cCoq_2ePArith_2eBinPosDef_2ePos_2emask___24t(happ(Vvar__19094,Vv__CANONICAL__0)) ) ) ).

fof('$_type_19141',axiom,
    ! [Vvar__19142] :
      ( c_24__type__19141___24t(Vvar__19142)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( c_24__type__11363___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
             => ! [Vv__CANONICAL__2] :
                  ( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
                 => ! [Vv__CANONICAL__3] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__3)
                     => t(happ(happ(happ(happ(Vvar__19142,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__0) ) ) ) ) ) ).

fof('$_type_1916',axiom,
    ! [Vvar__1917] :
      ( c_24__type__1916___24t(Vvar__1917)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cIntMap_2eMap_2eMap___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
             => cIntMap_2eFset_2eFSet___24t(happ(happ(Vvar__1917,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_19168',axiom,
    ! [Vvar__19169] :
      ( c_24__type__19168___24t(Vvar__19169)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__1)
             => cCoq_2eInit_2eDatatypes_2ecomparison___24t(happ(happ(Vvar__19169,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_19184',axiom,
    ! [Vvar__19185] :
      ( c_24__type__19184___24t(Vvar__19185)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__1)
             => cProp___24t(happ(happ(Vvar__19185,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_19189',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__19190] :
      ( c_24__type__19189___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__19190)
    <=> ! [Vv__CANONICAL__2] :
          ( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
         => t(happ(Vvar__19190,Vv__CANONICAL__2),Vv__CANONICAL__1) ) ) ).

fof('$_type_1919',axiom,
    ! [Vvar__1920] :
      ( c_24__type__1919___24t(Vvar__1920)
    <=> ! [Vv__CANONICAL__0] :
          ( cIntMap_2eFset_2eFSet___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cIntMap_2eFset_2eFSet___24t(Vv__CANONICAL__1)
             => cIntMap_2eFset_2eFSet___24t(happ(happ(Vvar__1920,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_19236',axiom,
    ! [Vvar__19237] :
      ( c_24__type__19236___24t(Vvar__19237)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__1)
             => ! [Vv__CANONICAL__2] :
                  ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree___24t(Vv__CANONICAL__2)
                 => cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree___24t(happ(happ(happ(Vvar__19237,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).

fof('$_type_19382',axiom,
    ! [Vvar__19383] :
      ( c_24__type__19382___24t(Vvar__19383)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(Vv__CANONICAL__1)
             => cProp___24t(happ(happ(Vvar__19383,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_1969',axiom,
    ! [Vvar__1970] :
      ( c_24__type__1969___24t(Vvar__1970)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cCoq_2eInit_2eDatatypes_2eoption___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
             => cCoq_2eInit_2eSpecif_2esumor___24t(cCoq_2eInit_2eSpecif_2esig___24a2(Vv__CANONICAL__0,c_24__lam__1973___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1)),c_24__prop__1974___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1),happ(happ(Vvar__1970,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_19715',axiom,
    ! [Vvar__19716] :
      ( c_24__type__19715___24t(Vvar__19716)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__1)
             => cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(happ(Vvar__19716,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_19719',axiom,
    ! [Vvar__19720] :
      ( c_24__type__19719___24t(Vvar__19720)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
         => cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(Vvar__19720,Vv__CANONICAL__0)) ) ) ).

fof('$_type_1984',axiom,
    ! [Vvar__1985] :
      ( c_24__type__1984___24t(Vvar__1985)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( c_24__type__1987___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
             => ! [Vv__CANONICAL__2] :
                  ( c_24__type__1987___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
                 => cProp___24t(happ(happ(happ(Vvar__1985,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).

fof('$_type_19869',axiom,
    ! [Vvar__19870] :
      ( c_24__type__19869___24t(Vvar__19870)
    <=> ! [Vv__CANONICAL__0] :
          ( cProp___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__1)
             => cType___24t(happ(happ(Vvar__19870,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_1987',axiom,
    ! [Vv__CANONICAL__0,Vvar__1988] :
      ( c_24__type__1987___24t(Vv__CANONICAL__0,Vvar__1988)
    <=> ! [Vv__CANONICAL__1] :
          ( cIntMap_2eMap_2ead___24t(Vv__CANONICAL__1)
         => cCoq_2eInit_2eDatatypes_2eoption___24t(Vv__CANONICAL__0,happ(Vvar__1988,Vv__CANONICAL__1)) ) ) ).

fof('$_type_19933',axiom,
    ! [Vvar__19934] :
      ( c_24__type__19933___24t(Vvar__19934)
    <=> ! [Vv__CANONICAL__0] :
          ( cProp___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cProp___24t(Vv__CANONICAL__1)
             => ! [Vv__CANONICAL__2] :
                  ( cProp___24t(Vv__CANONICAL__2)
                 => ! [Vv__CANONICAL__3] :
                      ( cCoq_2eInit_2eDatatypes_2ecomparison___24t(Vv__CANONICAL__3)
                     => cType___24t(happ(happ(happ(happ(Vvar__19934,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).

fof('$_type_19983',axiom,
    ! [Vvar__19984] :
      ( c_24__type__19983___24t(Vvar__19984)
    <=> ! [Vv__CANONICAL__0] :
          ( cProp___24t(Vv__CANONICAL__0)
         => cProp___24t(happ(Vvar__19984,Vv__CANONICAL__0)) ) ) ).

fof('$_type_19986',axiom,
    ! [Vv__CANONICAL__0,Vvar__19987] :
      ( c_24__type__19986___24t(Vv__CANONICAL__0,Vvar__19987)
    <=> ! [Vv__CANONICAL__1] :
          ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__1)
         => t(happ(Vvar__19987,Vv__CANONICAL__1),Vv__CANONICAL__0) ) ) ).

fof('$_type_20092',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__20093] :
      ( c_24__type__20092___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__20093)
    <=> ! [Vv__CANONICAL__6] :
          ( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
         => cType___24t(happ(Vvar__20093,Vv__CANONICAL__6)) ) ) ).

fof('$_type_20100',axiom,
    ! [Vvar__20101] :
      ( c_24__type__20100___24t(Vvar__20101)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
             => ! [Vv__CANONICAL__2] :
                  ( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
                 => ( Vv__CANONICAL__1 = Vv__CANONICAL__2
                   => cProp___24t(happ(happ(happ(Vvar__20101,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ) ).

fof('$_type_20304',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__20305] :
      ( c_24__type__20304___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__20305)
    <=> ! [Vv__CANONICAL__10] :
          ( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__11] :
              ( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
             => t(happ(happ(Vvar__20305,Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_20397',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__20398] :
      ( c_24__type__20397___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__20398)
    <=> ! [Vv__CANONICAL__10] :
          ( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__11] :
              ( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
             => t(happ(happ(Vvar__20398,Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_20490',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__20491] :
      ( c_24__type__20490___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__20491)
    <=> ! [Vv__CANONICAL__10] :
          ( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__11] :
              ( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
             => t(happ(happ(Vvar__20491,Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_20572',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__20573] :
      ( c_24__type__20572___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__20573)
    <=> ! [Vv__CANONICAL__10] :
          ( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
         => t(happ(Vvar__20573,Vv__CANONICAL__10),Vv__CANONICAL__0) ) ) ).

fof('$_type_2064',axiom,
    ! [Vvar__2065] :
      ( c_24__type__2064___24t(Vvar__2065)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cIntMap_2eMap_2eMap___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
             => cCoq_2eInit_2eDatatypes_2ebool___24t(happ(happ(Vvar__2065,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_20665',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__20666] :
      ( c_24__type__20665___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__20666)
    <=> ! [Vv__CANONICAL__10] :
          ( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__11] :
              ( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
             => t(happ(happ(Vvar__20666,Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_20747',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__20748] :
      ( c_24__type__20747___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__20748)
    <=> ! [Vv__CANONICAL__10] :
          ( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
         => t(happ(Vvar__20748,Vv__CANONICAL__10),Vv__CANONICAL__0) ) ) ).

fof('$_type_2078',axiom,
    ! [Vvar__2079] :
      ( c_24__type__2078___24t(Vvar__2079)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cIntMap_2eMap_2eMap___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
             => cIntMap_2eMap_2eMap___24t(Vv__CANONICAL__0,happ(happ(Vvar__2079,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_2083',axiom,
    ! [Vvar__2084] :
      ( c_24__type__2083___24t(Vvar__2084)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cIntMap_2eMap_2eMap___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
             => cCoq_2eInit_2eSpecif_2esig___24t(cIntMap_2eMap_2eMap___24a1(Vv__CANONICAL__0),c_24__lam__2087___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1),happ(happ(Vvar__2084,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_20840',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__20841] :
      ( c_24__type__20840___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__20841)
    <=> ! [Vv__CANONICAL__10] :
          ( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__11] :
              ( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
             => cProp___24t(happ(happ(Vvar__20841,Vv__CANONICAL__10),Vv__CANONICAL__11)) ) ) ) ).

fof('$_type_21054',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__21055] :
      ( c_24__type__21054___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__21055)
    <=> ! [Vv__CANONICAL__10] :
          ( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__11] :
              ( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
             => t(happ(happ(Vvar__21055,Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_21147',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__21148] :
      ( c_24__type__21147___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__21148)
    <=> ! [Vv__CANONICAL__10] :
          ( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__11] :
              ( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
             => t(happ(happ(Vvar__21148,Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_21240',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__21241] :
      ( c_24__type__21240___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__21241)
    <=> ! [Vv__CANONICAL__10] :
          ( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__11] :
              ( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
             => t(happ(happ(Vvar__21241,Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_21322',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__21323] :
      ( c_24__type__21322___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__21323)
    <=> ! [Vv__CANONICAL__10] :
          ( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
         => t(happ(Vvar__21323,Vv__CANONICAL__10),Vv__CANONICAL__0) ) ) ).

fof('$_type_21415',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__21416] :
      ( c_24__type__21415___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__21416)
    <=> ! [Vv__CANONICAL__10] :
          ( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__11] :
              ( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
             => t(happ(happ(Vvar__21416,Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_21497',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__21498] :
      ( c_24__type__21497___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__21498)
    <=> ! [Vv__CANONICAL__10] :
          ( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
         => t(happ(Vvar__21498,Vv__CANONICAL__10),Vv__CANONICAL__0) ) ) ).

fof('$_type_2154',axiom,
    ! [Vvar__2155] :
      ( c_24__type__2154___24t(Vvar__2155)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cType___24t(Vv__CANONICAL__1)
             => ! [Vv__CANONICAL__2] :
                  ( c_24__type__1574___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
                 => ! [Vv__CANONICAL__3] :
                      ( c_24__type__1580___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__3)
                     => ! [Vv__CANONICAL__4] :
                          ( cIntMap_2eMap_2eMap___24t(Vv__CANONICAL__0,Vv__CANONICAL__4)
                         => cIntMap_2eMap_2eMap___24t(Vv__CANONICAL__1,happ(happ(happ(happ(happ(Vvar__2155,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ) ) ) ).

fof('$_type_21590',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__21591] :
      ( c_24__type__21590___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__21591)
    <=> ! [Vv__CANONICAL__10] :
          ( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__11] :
              ( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
             => cProp___24t(happ(happ(Vvar__21591,Vv__CANONICAL__10),Vv__CANONICAL__11)) ) ) ) ).

fof('$_type_21635',axiom,
    ! [Vvar__21636] :
      ( c_24__type__21635___24t(Vvar__21636)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
             => ! [Vv__CANONICAL__2] :
                  ( c_24__type__1698___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
                 => ! [Vv__CANONICAL__3] :
                      ( c_24__type__1698___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
                     => ! [Vv__CANONICAL__4] :
                          ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__4)
                         => t(happ(happ(happ(happ(happ(Vvar__21636,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__0) ) ) ) ) ) ) ).

fof('$_type_21699',axiom,
    ! [Vvar__21700] :
      ( c_24__type__21699___24t(Vvar__21700)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
             => ! [Vv__CANONICAL__2] :
                  ( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
                 => cProp___24t(happ(happ(happ(Vvar__21700,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).

fof('$_type_2174',axiom,
    ! [Vvar__2175] :
      ( c_24__type__2174___24t(Vvar__2175)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eInit_2eDatatypes_2eprod___24a2(cIntMap_2eMap_2ead,Vv__CANONICAL__0),Vv__CANONICAL__1)
             => ! [Vv__CANONICAL__2] :
                  ( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eInit_2eDatatypes_2eprod___24a2(cIntMap_2eMap_2ead,Vv__CANONICAL__0),Vv__CANONICAL__2)
                 => cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eInit_2eDatatypes_2eprod___24a2(cIntMap_2eMap_2ead,Vv__CANONICAL__0),happ(happ(happ(Vvar__2175,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).

fof('$_type_2181',axiom,
    ! [Vvar__2182] :
      ( c_24__type__2181___24t(Vvar__2182)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cIntMap_2eMap_2eMap___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
             => cIntMap_2eMapiter_2ealist___24t(Vv__CANONICAL__0,happ(happ(Vvar__2182,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_21860',axiom,
    ! [Vvar__21861] :
      ( c_24__type__21860___24t(Vvar__21861)
    <=> ! [Vv__CANONICAL__0] :
          ( c_24__type__14593___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( c_24__type__14593___24t(Vv__CANONICAL__1)
             => cProp___24t(happ(happ(Vvar__21861,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_2227',axiom,
    ! [Vvar__2228] :
      ( c_24__type__2227___24t(Vvar__2228)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cIntMap_2eMapiter_2ealist___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
             => ! [Vv__CANONICAL__2] :
                  ( cIntMap_2eMap_2ead___24t(Vv__CANONICAL__2)
                 => cCoq_2eInit_2eDatatypes_2eoption___24t(Vv__CANONICAL__0,happ(happ(happ(Vvar__2228,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).

fof('$_type_2249',axiom,
    ! [Vvar__2250] :
      ( c_24__type__2249___24t(Vvar__2250)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
             => cProp___24t(happ(happ(Vvar__2250,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_2258',axiom,
    ! [Vvar__2259] :
      ( c_24__type__2258___24t(Vvar__2259)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( c_24__type__812___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
             => ! [Vv__CANONICAL__2] :
                  ( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
                 => ( p(happ(Vv__CANONICAL__1,Vv__CANONICAL__2))
                   => cCoq_2eInit_2eSpecif_2esig___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,happ(happ(happ(Vvar__2259,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ) ).

fof('$_type_2277',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__2278] :
      ( c_24__type__2277___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__2278)
    <=> ! [Vv__CANONICAL__3] :
          ( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
         => cProp___24t(happ(Vvar__2278,Vv__CANONICAL__3)) ) ) ).

fof('$_type_2285',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__2286] :
      ( c_24__type__2285___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__2286)
    <=> ! [Vv__CANONICAL__3] :
          ( cCoq_2eInit_2eSpecif_2esig___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__3)
         => cType___24t(happ(Vvar__2286,Vv__CANONICAL__3)) ) ) ).

fof('$_type_23013',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__23014] :
      ( c_24__type__23013___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__23014)
    <=> ! [Vv__CANONICAL__5] :
          ( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__6] :
              ( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
             => cProp___24t(happ(happ(Vvar__23014,Vv__CANONICAL__5),Vv__CANONICAL__6)) ) ) ) ).

fof('$_type_23032',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__23033] :
      ( c_24__type__23032___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__23033)
    <=> ! [Vv__CANONICAL__5] :
          ( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__6] :
              ( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
             => cProp___24t(happ(happ(Vvar__23033,Vv__CANONICAL__5),Vv__CANONICAL__6)) ) ) ) ).

fof('$_type_23052',axiom,
    ! [Vvar__23053] :
      ( c_24__type__23052___24t(Vvar__23053)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( c_24__type__12419___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
             => ! [Vv__CANONICAL__2] :
                  ( c_24__type__12419___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
                 => ! [Vv__CANONICAL__3] :
                      ( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
                     => ! [Vv__CANONICAL__4] :
                          ( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
                         => cType___24t(happ(happ(happ(happ(happ(Vvar__23053,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ) ) ) ).

fof('$_type_23142',axiom,
    ! [Vvar__23143] :
      ( c_24__type__23142___24t(Vvar__23143)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__1)
             => cCoq_2eQArith_2eQArith__base_2eQ___24t(happ(happ(Vvar__23143,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_23147',axiom,
    ! [Vvar__23148] :
      ( c_24__type__23147___24t(Vvar__23148)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eQArith_2eQArith__base_2eQ___24t(Vv__CANONICAL__0)
         => cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(Vvar__23148,Vv__CANONICAL__0)) ) ) ).

fof('$_type_23152',axiom,
    ! [Vvar__23153] :
      ( c_24__type__23152___24t(Vvar__23153)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eQArith_2eQArith__base_2eQ___24t(Vv__CANONICAL__0)
         => cCoq_2eNumbers_2eBinNums_2epositive___24t(happ(Vvar__23153,Vv__CANONICAL__0)) ) ) ).

fof('$_type_2320',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__2321] :
      ( c_24__type__2320___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__2321)
    <=> ! [Vv__CANONICAL__3] :
          ( cCoq_2eInit_2eSpecif_2esumbool___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__3)
         => cType___24t(happ(Vvar__2321,Vv__CANONICAL__3)) ) ) ).

fof('$_type_23307',axiom,
    ! [Vvar__23308] :
      ( c_24__type__23307___24t(Vvar__23308)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__1)
             => cProp___24t(happ(happ(Vvar__23308,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_23309',axiom,
    ! [Vvar__23310] :
      ( c_24__type__23309___24t(Vvar__23310)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__0)
         => cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(Vvar__23310,Vv__CANONICAL__0)) ) ) ).

fof('$_type_23337',axiom,
    ! [Vvar__23338] :
      ( c_24__type__23337___24t(Vvar__23338)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( c_24__type__812___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
             => ! [Vv__CANONICAL__2] :
                  ( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
                 => cProp___24t(happ(happ(happ(Vvar__23338,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).

fof('$_type_23401',axiom,
    ! [Vvar__23402] :
      ( c_24__type__23401___24t(Vvar__23402)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__1)
             => cType___24t(happ(happ(Vvar__23402,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_2359',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__2360] :
      ( c_24__type__2359___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__2360)
    <=> ! [Vv__CANONICAL__3] :
          ( cCoq_2eInit_2eSpecif_2esumor___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__3)
         => cType___24t(happ(Vvar__2360,Vv__CANONICAL__3)) ) ) ).

fof('$_type_23968',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__23969] :
      ( c_24__type__23968___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__23969)
    <=> ! [Vv__CANONICAL__22] :
          ( t(Vv__CANONICAL__22,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__23] :
              ( t(Vv__CANONICAL__23,Vv__CANONICAL__0)
             => t(happ(happ(Vvar__23969,Vv__CANONICAL__22),Vv__CANONICAL__23),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_24314',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__24315] :
      ( c_24__type__24314___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__24315)
    <=> ! [Vv__CANONICAL__22] :
          ( t(Vv__CANONICAL__22,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__23] :
              ( t(Vv__CANONICAL__23,Vv__CANONICAL__0)
             => t(happ(happ(Vvar__24315,Vv__CANONICAL__22),Vv__CANONICAL__23),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_2438',axiom,
    ! [Vvar__2439] :
      ( c_24__type__2438___24t(Vvar__2439)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__1)
             => ! [Vv__CANONICAL__2] :
                  ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__2)
                 => ! [Vv__CANONICAL__3] :
                      ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__3)
                     => ! [Vv__CANONICAL__4] :
                          ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__4)
                         => ! [Vv__CANONICAL__5] :
                              ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__5)
                             => ! [Vv__CANONICAL__6] :
                                  ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__6)
                                 => ! [Vv__CANONICAL__7] :
                                      ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__7)
                                     => cCoq_2eStrings_2eAscii_2eascii___24t(happ(happ(happ(happ(happ(happ(happ(happ(Vvar__2439,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__6),Vv__CANONICAL__7)) ) ) ) ) ) ) ) ) ) ).

fof('$_type_24660',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__24661] :
      ( c_24__type__24660___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__24661)
    <=> ! [Vv__CANONICAL__22] :
          ( t(Vv__CANONICAL__22,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__23] :
              ( t(Vv__CANONICAL__23,Vv__CANONICAL__0)
             => t(happ(happ(Vvar__24661,Vv__CANONICAL__22),Vv__CANONICAL__23),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_24983',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__24984] :
      ( c_24__type__24983___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__24984)
    <=> ! [Vv__CANONICAL__22] :
          ( t(Vv__CANONICAL__22,Vv__CANONICAL__0)
         => t(happ(Vvar__24984,Vv__CANONICAL__22),Vv__CANONICAL__0) ) ) ).

fof('$_type_25',axiom,
    ! [Vvar__26] :
      ( c_24__type__25___24t(Vvar__26)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__0)
         => cCoq_2eNumbers_2eBinNums_2eN___24t(happ(Vvar__26,Vv__CANONICAL__0)) ) ) ).

fof('$_type_25329',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__25330] :
      ( c_24__type__25329___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__25330)
    <=> ! [Vv__CANONICAL__22] :
          ( t(Vv__CANONICAL__22,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__23] :
              ( t(Vv__CANONICAL__23,Vv__CANONICAL__0)
             => cProp___24t(happ(happ(Vvar__25330,Vv__CANONICAL__22),Vv__CANONICAL__23)) ) ) ) ).

fof('$_type_25675',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__25676] :
      ( c_24__type__25675___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__25676)
    <=> ! [Vv__CANONICAL__22] :
          ( t(Vv__CANONICAL__22,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__23] :
              ( t(Vv__CANONICAL__23,Vv__CANONICAL__0)
             => cProp___24t(happ(happ(Vvar__25676,Vv__CANONICAL__22),Vv__CANONICAL__23)) ) ) ) ).

fof('$_type_26021',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__26022] :
      ( c_24__type__26021___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__26022)
    <=> ! [Vv__CANONICAL__22] :
          ( t(Vv__CANONICAL__22,Vv__CANONICAL__9)
         => ! [Vv__CANONICAL__23] :
              ( t(Vv__CANONICAL__23,Vv__CANONICAL__9)
             => t(happ(happ(Vvar__26022,Vv__CANONICAL__22),Vv__CANONICAL__23),Vv__CANONICAL__9) ) ) ) ).

fof('$_type_26367',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__26368] :
      ( c_24__type__26367___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__26368)
    <=> ! [Vv__CANONICAL__22] :
          ( t(Vv__CANONICAL__22,Vv__CANONICAL__9)
         => ! [Vv__CANONICAL__23] :
              ( t(Vv__CANONICAL__23,Vv__CANONICAL__9)
             => t(happ(happ(Vvar__26368,Vv__CANONICAL__22),Vv__CANONICAL__23),Vv__CANONICAL__9) ) ) ) ).

fof('$_type_2656',axiom,
    ! [Vvar__2657] :
      ( c_24__type__2656___24t(Vvar__2657)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__1)
             => cProp___24t(happ(happ(Vvar__2657,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_2669',axiom,
    ! [Vvar__2670] :
      ( c_24__type__2669___24t(Vvar__2670)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__0)
         => cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(Vvar__2670,Vv__CANONICAL__0)) ) ) ).

fof('$_type_26713',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__26714] :
      ( c_24__type__26713___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__26714)
    <=> ! [Vv__CANONICAL__22] :
          ( t(Vv__CANONICAL__22,Vv__CANONICAL__9)
         => ! [Vv__CANONICAL__23] :
              ( t(Vv__CANONICAL__23,Vv__CANONICAL__9)
             => t(happ(happ(Vvar__26714,Vv__CANONICAL__22),Vv__CANONICAL__23),Vv__CANONICAL__9) ) ) ) ).

fof('$_type_27',axiom,
    ! [Vvar__28] :
      ( c_24__type__27___24t(Vvar__28)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__0)
         => cProp___24t(happ(Vvar__28,Vv__CANONICAL__0)) ) ) ).

fof('$_type_27036',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__27037] :
      ( c_24__type__27036___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__27037)
    <=> ! [Vv__CANONICAL__22] :
          ( t(Vv__CANONICAL__22,Vv__CANONICAL__9)
         => t(happ(Vvar__27037,Vv__CANONICAL__22),Vv__CANONICAL__9) ) ) ).

fof('$_type_27382',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__27383] :
      ( c_24__type__27382___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__27383)
    <=> ! [Vv__CANONICAL__22] :
          ( t(Vv__CANONICAL__22,Vv__CANONICAL__9)
         => ! [Vv__CANONICAL__23] :
              ( t(Vv__CANONICAL__23,Vv__CANONICAL__9)
             => cCoq_2eInit_2eDatatypes_2ebool___24t(happ(happ(Vvar__27383,Vv__CANONICAL__22),Vv__CANONICAL__23)) ) ) ) ).

fof('$_type_275',axiom,
    ! [Vvar__276] :
      ( c_24__type__275___24t(Vvar__276)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cIntMap_2eMap_2eMap___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
             => ! [Vv__CANONICAL__2] :
                  ( cIntMap_2eMap_2ead___24t(Vv__CANONICAL__2)
                 => ! [Vv__CANONICAL__3] :
                      ( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
                     => cIntMap_2eMap_2eMap___24t(Vv__CANONICAL__0,happ(happ(happ(happ(Vvar__276,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).

fof('$_type_27728',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__27729] :
      ( c_24__type__27728___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__27729)
    <=> ! [Vv__CANONICAL__22] :
          ( t(Vv__CANONICAL__22,Vv__CANONICAL__9)
         => ! [Vv__CANONICAL__23] :
              ( t(Vv__CANONICAL__23,Vv__CANONICAL__9)
             => cCoq_2eInit_2eDatatypes_2ebool___24t(happ(happ(Vvar__27729,Vv__CANONICAL__22),Vv__CANONICAL__23)) ) ) ) ).

fof('$_type_28051',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__28052] :
      ( c_24__type__28051___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__28052)
    <=> ! [Vv__CANONICAL__22] :
          ( t(Vv__CANONICAL__22,Vv__CANONICAL__9)
         => t(happ(Vvar__28052,Vv__CANONICAL__22),Vv__CANONICAL__0) ) ) ).

fof('$_type_28374',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__28375] :
      ( c_24__type__28374___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__28375)
    <=> ! [Vv__CANONICAL__22] :
          ( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__22)
         => t(happ(Vvar__28375,Vv__CANONICAL__22),Vv__CANONICAL__19) ) ) ).

fof('$_type_28720',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__28721] :
      ( c_24__type__28720___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__28721)
    <=> ! [Vv__CANONICAL__22] :
          ( t(Vv__CANONICAL__22,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__23] :
              ( t(Vv__CANONICAL__23,Vv__CANONICAL__19)
             => t(happ(happ(Vvar__28721,Vv__CANONICAL__22),Vv__CANONICAL__23),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_28893',axiom,
    ! [Vvar__28894] :
      ( c_24__type__28893___24t(Vvar__28894)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__1)
             => cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vv__CANONICAL__0,happ(happ(Vvar__28894,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_28902',axiom,
    ! [Vvar__28903] :
      ( c_24__type__28902___24t(Vvar__28903)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
             => cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vv__CANONICAL__0,happ(happ(Vvar__28903,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_28920',axiom,
    ! [Vvar__28921] :
      ( c_24__type__28920___24t(Vvar__28921)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( c_24__type__1698___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
             => ! [Vv__CANONICAL__2] :
                  ( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
                 => ! [Vv__CANONICAL__3] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__3)
                     => t(happ(happ(happ(happ(Vvar__28921,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__0) ) ) ) ) ) ).

fof('$_type_29459',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__29460] :
      ( c_24__type__29459___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__29460)
    <=> ! [Vv__CANONICAL__8] :
          ( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__9] :
              ( t(Vv__CANONICAL__9,Vv__CANONICAL__0)
             => t(happ(happ(Vvar__29460,Vv__CANONICAL__8),Vv__CANONICAL__9),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_29522',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__29523] :
      ( c_24__type__29522___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__29523)
    <=> ! [Vv__CANONICAL__8] :
          ( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__9] :
              ( t(Vv__CANONICAL__9,Vv__CANONICAL__0)
             => t(happ(happ(Vvar__29523,Vv__CANONICAL__8),Vv__CANONICAL__9),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_29585',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__29586] :
      ( c_24__type__29585___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__29586)
    <=> ! [Vv__CANONICAL__8] :
          ( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__9] :
              ( t(Vv__CANONICAL__9,Vv__CANONICAL__0)
             => t(happ(happ(Vvar__29586,Vv__CANONICAL__8),Vv__CANONICAL__9),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_29639',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__29640] :
      ( c_24__type__29639___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__29640)
    <=> ! [Vv__CANONICAL__8] :
          ( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
         => t(happ(Vvar__29640,Vv__CANONICAL__8),Vv__CANONICAL__0) ) ) ).

fof('$_type_29702',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__29703] :
      ( c_24__type__29702___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__29703)
    <=> ! [Vv__CANONICAL__8] :
          ( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__9] :
              ( t(Vv__CANONICAL__9,Vv__CANONICAL__0)
             => cProp___24t(happ(happ(Vvar__29703,Vv__CANONICAL__8),Vv__CANONICAL__9)) ) ) ) ).

fof('$_type_29976',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__29977] :
      ( c_24__type__29976___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__29977)
    <=> ! [Vv__CANONICAL__8] :
          ( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__9] :
              ( t(Vv__CANONICAL__9,Vv__CANONICAL__0)
             => t(happ(happ(Vvar__29977,Vv__CANONICAL__8),Vv__CANONICAL__9),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_30039',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__30040] :
      ( c_24__type__30039___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__30040)
    <=> ! [Vv__CANONICAL__8] :
          ( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__9] :
              ( t(Vv__CANONICAL__9,Vv__CANONICAL__0)
             => t(happ(happ(Vvar__30040,Vv__CANONICAL__8),Vv__CANONICAL__9),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_30102',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__30103] :
      ( c_24__type__30102___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__30103)
    <=> ! [Vv__CANONICAL__8] :
          ( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__9] :
              ( t(Vv__CANONICAL__9,Vv__CANONICAL__0)
             => t(happ(happ(Vvar__30103,Vv__CANONICAL__8),Vv__CANONICAL__9),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_30156',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__30157] :
      ( c_24__type__30156___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__30157)
    <=> ! [Vv__CANONICAL__8] :
          ( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
         => t(happ(Vvar__30157,Vv__CANONICAL__8),Vv__CANONICAL__0) ) ) ).

fof('$_type_30219',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__30220] :
      ( c_24__type__30219___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__30220)
    <=> ! [Vv__CANONICAL__8] :
          ( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__9] :
              ( t(Vv__CANONICAL__9,Vv__CANONICAL__0)
             => cProp___24t(happ(happ(Vvar__30220,Vv__CANONICAL__8),Vv__CANONICAL__9)) ) ) ) ).

fof('$_type_30325',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__30326] :
      ( c_24__type__30325___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__30326)
    <=> ! [Vv__CANONICAL__4] :
          ( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__5] :
              ( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
             => t(happ(happ(Vvar__30326,Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_30348',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__30349] :
      ( c_24__type__30348___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__30349)
    <=> ! [Vv__CANONICAL__4] :
          ( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__5] :
              ( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
             => t(happ(happ(Vvar__30349,Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_30371',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__30372] :
      ( c_24__type__30371___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__30372)
    <=> ! [Vv__CANONICAL__4] :
          ( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__5] :
              ( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
             => cProp___24t(happ(happ(Vvar__30372,Vv__CANONICAL__4),Vv__CANONICAL__5)) ) ) ) ).

fof('$_type_30394',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__30395] :
      ( c_24__type__30394___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__30395)
    <=> ! [Vv__CANONICAL__4] :
          ( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__5] :
              ( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
             => t(happ(happ(Vvar__30395,Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_30412',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__30413] :
      ( c_24__type__30412___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__30413)
    <=> ! [Vv__CANONICAL__4] :
          ( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
         => t(happ(Vvar__30413,Vv__CANONICAL__4),Vv__CANONICAL__0) ) ) ).

fof('$_type_30438',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__30439] :
      ( c_24__type__30438___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__30439)
    <=> ! [Vv__CANONICAL__4] :
          ( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__5] :
              ( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
             => t(happ(happ(Vvar__30439,Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_30456',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__30457] :
      ( c_24__type__30456___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__30457)
    <=> ! [Vv__CANONICAL__4] :
          ( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
         => t(happ(Vvar__30457,Vv__CANONICAL__4),Vv__CANONICAL__0) ) ) ).

fof('$_type_30566',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__30567] :
      ( c_24__type__30566___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__30567)
    <=> ! [Vv__CANONICAL__5] :
          ( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__6] :
              ( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
             => t(happ(happ(Vvar__30567,Vv__CANONICAL__5),Vv__CANONICAL__6),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_30596',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__30597] :
      ( c_24__type__30596___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__30597)
    <=> ! [Vv__CANONICAL__5] :
          ( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__6] :
              ( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
             => t(happ(happ(Vvar__30597,Vv__CANONICAL__5),Vv__CANONICAL__6),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_30620',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__30621] :
      ( c_24__type__30620___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__30621)
    <=> ! [Vv__CANONICAL__5] :
          ( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
         => t(happ(Vvar__30621,Vv__CANONICAL__5),Vv__CANONICAL__0) ) ) ).

fof('$_type_30650',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__30651] :
      ( c_24__type__30650___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__30651)
    <=> ! [Vv__CANONICAL__5] :
          ( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__6] :
              ( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
             => cProp___24t(happ(happ(Vvar__30651,Vv__CANONICAL__5),Vv__CANONICAL__6)) ) ) ) ).

fof('$_type_30680',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__30681] :
      ( c_24__type__30680___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__30681)
    <=> ! [Vv__CANONICAL__5] :
          ( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__6] :
              ( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
             => t(happ(happ(Vvar__30681,Vv__CANONICAL__5),Vv__CANONICAL__6),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_30704',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__30705] :
      ( c_24__type__30704___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__30705)
    <=> ! [Vv__CANONICAL__5] :
          ( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
         => t(happ(Vvar__30705,Vv__CANONICAL__5),Vv__CANONICAL__0) ) ) ).

fof('$_type_30737',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__30738] :
      ( c_24__type__30737___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__30738)
    <=> ! [Vv__CANONICAL__5] :
          ( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__6] :
              ( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
             => t(happ(happ(Vvar__30738,Vv__CANONICAL__5),Vv__CANONICAL__6),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_30761',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__30762] :
      ( c_24__type__30761___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__30762)
    <=> ! [Vv__CANONICAL__5] :
          ( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
         => t(happ(Vvar__30762,Vv__CANONICAL__5),Vv__CANONICAL__0) ) ) ).

fof('$_type_30788',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__30789] :
      ( c_24__type__30788___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__30789)
    <=> ! [Vv__CANONICAL__5] :
          ( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
         => t(happ(Vvar__30789,Vv__CANONICAL__5),Vv__CANONICAL__0) ) ) ).

fof('$_type_31044',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vvar__31045] :
      ( c_24__type__31044___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vvar__31045)
    <=> ! [Vv__CANONICAL__13] :
          ( t(Vv__CANONICAL__13,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__14] :
              ( t(Vv__CANONICAL__14,Vv__CANONICAL__0)
             => t(happ(happ(Vvar__31045,Vv__CANONICAL__13),Vv__CANONICAL__14),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_31169',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vvar__31170] :
      ( c_24__type__31169___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vvar__31170)
    <=> ! [Vv__CANONICAL__13] :
          ( t(Vv__CANONICAL__13,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__14] :
              ( t(Vv__CANONICAL__14,Vv__CANONICAL__0)
             => t(happ(happ(Vvar__31170,Vv__CANONICAL__13),Vv__CANONICAL__14),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_31294',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vvar__31295] :
      ( c_24__type__31294___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vvar__31295)
    <=> ! [Vv__CANONICAL__13] :
          ( t(Vv__CANONICAL__13,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__14] :
              ( t(Vv__CANONICAL__14,Vv__CANONICAL__0)
             => cProp___24t(happ(happ(Vvar__31295,Vv__CANONICAL__13),Vv__CANONICAL__14)) ) ) ) ).

fof('$_type_31419',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vvar__31420] :
      ( c_24__type__31419___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vvar__31420)
    <=> ! [Vv__CANONICAL__13] :
          ( t(Vv__CANONICAL__13,Vv__CANONICAL__6)
         => ! [Vv__CANONICAL__14] :
              ( t(Vv__CANONICAL__14,Vv__CANONICAL__6)
             => t(happ(happ(Vvar__31420,Vv__CANONICAL__13),Vv__CANONICAL__14),Vv__CANONICAL__6) ) ) ) ).

fof('$_type_31544',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vvar__31545] :
      ( c_24__type__31544___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vvar__31545)
    <=> ! [Vv__CANONICAL__13] :
          ( t(Vv__CANONICAL__13,Vv__CANONICAL__6)
         => ! [Vv__CANONICAL__14] :
              ( t(Vv__CANONICAL__14,Vv__CANONICAL__6)
             => t(happ(happ(Vvar__31545,Vv__CANONICAL__13),Vv__CANONICAL__14),Vv__CANONICAL__6) ) ) ) ).

fof('$_type_31669',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vvar__31670] :
      ( c_24__type__31669___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vvar__31670)
    <=> ! [Vv__CANONICAL__13] :
          ( t(Vv__CANONICAL__13,Vv__CANONICAL__6)
         => ! [Vv__CANONICAL__14] :
              ( t(Vv__CANONICAL__14,Vv__CANONICAL__6)
             => cCoq_2eInit_2eDatatypes_2ebool___24t(happ(happ(Vvar__31670,Vv__CANONICAL__13),Vv__CANONICAL__14)) ) ) ) ).

fof('$_type_31780',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vvar__31781] :
      ( c_24__type__31780___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vvar__31781)
    <=> ! [Vv__CANONICAL__13] :
          ( t(Vv__CANONICAL__13,Vv__CANONICAL__6)
         => t(happ(Vvar__31781,Vv__CANONICAL__13),Vv__CANONICAL__0) ) ) ).

fof('$_type_32306',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__32307] :
      ( c_24__type__32306___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__32307)
    <=> ! [Vv__CANONICAL__7] :
          ( t(Vv__CANONICAL__7,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__8] :
              ( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
             => t(happ(happ(Vvar__32307,Vv__CANONICAL__7),Vv__CANONICAL__8),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_32350',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__32351] :
      ( c_24__type__32350___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__32351)
    <=> ! [Vv__CANONICAL__7] :
          ( t(Vv__CANONICAL__7,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__8] :
              ( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
             => cProp___24t(happ(happ(Vvar__32351,Vv__CANONICAL__7),Vv__CANONICAL__8)) ) ) ) ).

fof('$_type_32386',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__32387] :
      ( c_24__type__32386___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__32387)
    <=> ! [Vv__CANONICAL__7] :
          ( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__7)
         => t(happ(Vvar__32387,Vv__CANONICAL__7),Vv__CANONICAL__4) ) ) ).

fof('$_type_32430',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__32431] :
      ( c_24__type__32430___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__32431)
    <=> ! [Vv__CANONICAL__7] :
          ( t(Vv__CANONICAL__7,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__8] :
              ( t(Vv__CANONICAL__8,Vv__CANONICAL__4)
             => t(happ(happ(Vvar__32431,Vv__CANONICAL__7),Vv__CANONICAL__8),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_32436',axiom,
    ! [Vvar__32437] :
      ( c_24__type__32436___24t(Vvar__32437)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
             => cProp___24t(happ(happ(Vvar__32437,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_32478',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__32479] :
      ( c_24__type__32478___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__32479)
    <=> ! [Vv__CANONICAL__4] :
          ( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__5] :
              ( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
             => cProp___24t(happ(happ(Vvar__32479,Vv__CANONICAL__4),Vv__CANONICAL__5)) ) ) ) ).

fof('$_type_32513',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__32514] :
      ( c_24__type__32513___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__32514)
    <=> ! [Vv__CANONICAL__3] :
          ( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__4] :
              ( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
             => cProp___24t(happ(happ(Vvar__32514,Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ).

fof('$_type_32716',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__32717] :
      ( c_24__type__32716___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__32717)
    <=> ! [Vv__CANONICAL__3] :
          ( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
         => cProp___24t(happ(Vvar__32717,Vv__CANONICAL__3)) ) ) ).

fof('$_type_32724',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__32725] :
      ( c_24__type__32724___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__32725)
    <=> ! [Vv__CANONICAL__3] :
          ( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
         => cProp___24t(happ(Vvar__32725,Vv__CANONICAL__3)) ) ) ).

fof('$_type_32732',axiom,
    ! [Vvar__32733] :
      ( c_24__type__32732___24t(Vvar__32733)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( c_24__type__812___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
             => ! [Vv__CANONICAL__2] :
                  ( c_24__type__812___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
                 => cType___24t(happ(happ(happ(Vvar__32733,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).

fof('$_type_32811',axiom,
    ! [Vvar__32812] :
      ( c_24__type__32811___24t(Vvar__32812)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cType___24t(Vv__CANONICAL__1)
             => ! [Vv__CANONICAL__2] :
                  ( cType___24t(Vv__CANONICAL__2)
                 => ! [Vv__CANONICAL__3] :
                      ( cType___24t(Vv__CANONICAL__3)
                     => cType___24t(happ(happ(happ(happ(Vvar__32812,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).

fof('$_type_33209',axiom,
    ! [Vvar__33210] :
      ( c_24__type__33209___24t(Vvar__33210)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
             => cType___24t(happ(happ(Vvar__33210,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_33261',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__33262] :
      ( c_24__type__33261___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__33262)
    <=> ! [Vv__CANONICAL__3] :
          ( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__4] :
              ( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
             => cProp___24t(happ(happ(Vvar__33262,Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ).

fof('$_type_33336',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__33337] :
      ( c_24__type__33336___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__33337)
    <=> ! [Vv__CANONICAL__4] :
          ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__4)
         => cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(Vvar__33337,Vv__CANONICAL__4)) ) ) ).

fof('$_type_33345',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__33346] :
      ( c_24__type__33345___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__33346)
    <=> ! [Vv__CANONICAL__4] :
          ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__4)
         => cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(Vvar__33346,Vv__CANONICAL__4)) ) ) ).

fof('$_type_33431',axiom,
    ! [Vvar__33432] :
      ( c_24__type__33431___24t(Vvar__33432)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__1)
             => cType___24t(happ(happ(Vvar__33432,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_33487',axiom,
    ! [Vvar__33488] :
      ( c_24__type__33487___24t(Vvar__33488)
    <=> ! [Vv__CANONICAL__0] :
          ( c_24__type__451___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( c_24__type__451___24t(Vv__CANONICAL__1)
             => cProp___24t(happ(happ(Vvar__33488,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_33511',axiom,
    ! [Vvar__33512] :
      ( c_24__type__33511___24t(Vvar__33512)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( c_24__type__1698___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
             => ! [Vv__CANONICAL__2] :
                  ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__2)
                 => ! [Vv__CANONICAL__3] :
                      ( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
                     => t(happ(happ(happ(happ(Vvar__33512,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__0) ) ) ) ) ) ).

fof('$_type_33574',axiom,
    ! [Vvar__33575] :
      ( c_24__type__33574___24t(Vvar__33575)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__0)
         => cType___24t(happ(Vvar__33575,Vv__CANONICAL__0)) ) ) ).

fof('$_type_33602',axiom,
    ! [Vvar__33603] :
      ( c_24__type__33602___24t(Vvar__33603)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__0)
         => cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(Vvar__33603,Vv__CANONICAL__0)) ) ) ).

fof('$_type_33606',axiom,
    ! [Vvar__33607] :
      ( c_24__type__33606___24t(Vvar__33607)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
         => cCoq_2eNumbers_2eBinNums_2epositive___24t(happ(Vvar__33607,Vv__CANONICAL__0)) ) ) ).

fof('$_type_33620',axiom,
    ! [Vvar__33621] :
      ( c_24__type__33620___24t(Vvar__33621)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
         => cCoq_2eInit_2eDatatypes_2ebool___24t(happ(Vvar__33621,Vv__CANONICAL__0)) ) ) ).

fof('$_type_33637',axiom,
    ! [Vvar__33638] :
      ( c_24__type__33637___24t(Vvar__33638)
    <=> ! [Vv__CANONICAL__0] :
          ( c_24__type__33620___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( c_24__type__33620___24t(Vv__CANONICAL__1)
             => cProp___24t(happ(happ(Vvar__33638,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_36',axiom,
    ! [Vvar__37] :
      ( c_24__type__36___24t(Vvar__37)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => cType___24t(happ(Vvar__37,Vv__CANONICAL__0)) ) ) ).

fof('$_type_36642',axiom,
    ! [Vvar__36643] :
      ( c_24__type__36642___24t(Vvar__36643)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__1)
             => cProp___24t(happ(happ(Vvar__36643,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_36678',axiom,
    ! [Vvar__36679] :
      ( c_24__type__36678___24t(Vvar__36679)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( c_24__type__11408___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
             => ! [Vv__CANONICAL__2] :
                  ( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
                 => ! [Vv__CANONICAL__3] :
                      ( t(Vv__CANONICAL__3,happ(Vv__CANONICAL__1,Vv__CANONICAL__2))
                     => cProp___24t(happ(happ(happ(happ(Vvar__36679,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).

fof('$_type_36683',axiom,
    ! [Vvar__36684] :
      ( c_24__type__36683___24t(Vvar__36684)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => cProp___24t(happ(Vvar__36684,Vv__CANONICAL__0)) ) ) ).

fof('$_type_36702',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__36703] :
      ( c_24__type__36702___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__36703)
    <=> ! [Vv__CANONICAL__5] :
          ( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__6] :
              ( t(Vv__CANONICAL__6,happ(Vv__CANONICAL__1,Vv__CANONICAL__5))
             => t(happ(happ(Vvar__36703,Vv__CANONICAL__5),Vv__CANONICAL__6),Vv__CANONICAL__2) ) ) ) ).

fof('$_type_36708',axiom,
    ! [Vv__CANONICAL__0,Vvar__36709] :
      ( c_24__type__36708___24t(Vv__CANONICAL__0,Vvar__36709)
    <=> ! [Vv__CANONICAL__1] :
          ( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
         => t(happ(Vvar__36709,Vv__CANONICAL__1),Vv__CANONICAL__0) ) ) ).

fof('$_type_388',axiom,
    ! [Vvar__389] :
      ( c_24__type__388___24t(Vvar__389)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cIntMap_2eMap_2eMap___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
             => ! [Vv__CANONICAL__2] :
                  ( cIntMap_2eMap_2eMap___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
                 => cProp___24t(happ(happ(happ(Vvar__389,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).

fof('$_type_400',axiom,
    ! [Vvar__401] :
      ( c_24__type__400___24t(Vvar__401)
    <=> ! [Vv__CANONICAL__0] :
          ( cProp___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cProp___24t(Vv__CANONICAL__1)
             => cType___24t(happ(happ(Vvar__401,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_422',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__423] :
      ( c_24__type__422___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__423)
    <=> ! [Vv__CANONICAL__2] :
          ( cCoq_2eInit_2eSpecif_2esumbool___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
         => cProp___24t(happ(Vvar__423,Vv__CANONICAL__2)) ) ) ).

fof('$_type_430',axiom,
    ! [Vvar__431] :
      ( c_24__type__430___24t(Vvar__431)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__0)
         => cCoq_2eInit_2eSpecif_2esumbool___24t(c_24__prop__432___24a1(Vv__CANONICAL__0),c_24__prop__433___24a1(Vv__CANONICAL__0),happ(Vvar__431,Vv__CANONICAL__0)) ) ) ).

fof('$_type_441',axiom,
    ! [Vvar__442] :
      ( c_24__type__441___24t(Vvar__442)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__1)
             => cCoq_2eInit_2eDatatypes_2ebool___24t(happ(happ(Vvar__442,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_449',axiom,
    ! [Vvar__450] :
      ( c_24__type__449___24t(Vvar__450)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__0)
         => cCoq_2eNumbers_2eBinNums_2eN___24t(happ(Vvar__450,Vv__CANONICAL__0)) ) ) ).

fof('$_type_451',axiom,
    ! [Vvar__452] :
      ( c_24__type__451___24t(Vvar__452)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__0)
         => cCoq_2eInit_2eDatatypes_2ebool___24t(happ(Vvar__452,Vv__CANONICAL__0)) ) ) ).

fof('$_type_458',axiom,
    ! [Vvar__459] :
      ( c_24__type__458___24t(Vvar__459)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
         => cCoq_2eInit_2eDatatypes_2enat___24t(happ(Vvar__459,Vv__CANONICAL__0)) ) ) ).

fof('$_type_460',axiom,
    ! [Vvar__461] :
      ( c_24__type__460___24t(Vvar__461)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => cIntMap_2eMap_2eMap___24t(Vv__CANONICAL__0,happ(Vvar__461,Vv__CANONICAL__0)) ) ) ).

fof('$_type_476',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__477] :
      ( c_24__type__476___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__477)
    <=> ! [Vv__CANONICAL__2] :
          ( cIntMap_2eMap_2eMap___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
         => cType___24t(happ(Vvar__477,Vv__CANONICAL__2)) ) ) ).

fof('$_type_48',axiom,
    ! [Vvar__49] :
      ( c_24__type__48___24t(Vvar__49)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
             => cCoq_2eInit_2eDatatypes_2eoption___24t(Vv__CANONICAL__0,happ(happ(Vvar__49,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_50',axiom,
    ! [Vvar__51] :
      ( c_24__type__50___24t(Vvar__51)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => cCoq_2eInit_2eDatatypes_2eoption___24t(Vv__CANONICAL__0,happ(Vvar__51,Vv__CANONICAL__0)) ) ) ).

fof('$_type_523',axiom,
    ! [Vvar__524] :
      ( c_24__type__523___24t(Vvar__524)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( c_24__type__526___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
             => ! [Vv__CANONICAL__2] :
                  ( t(Vv__CANONICAL__2,happ(Vv__CANONICAL__1,cIntMap_2eMap_2eM0___24a1(Vv__CANONICAL__0)))
                 => ! [Vv__CANONICAL__3] :
                      ( c_24__type__534___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__3)
                     => ! [Vv__CANONICAL__4] :
                          ( c_24__type__551___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__4)
                         => ! [Vv__CANONICAL__5] :
                              ( cIntMap_2eMap_2eMap___24t(Vv__CANONICAL__0,Vv__CANONICAL__5)
                             => t(happ(happ(happ(happ(happ(happ(Vvar__524,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5),happ(Vv__CANONICAL__1,Vv__CANONICAL__5)) ) ) ) ) ) ) ) ).

fof('$_type_526',axiom,
    ! [Vv__CANONICAL__0,Vvar__527] :
      ( c_24__type__526___24t(Vv__CANONICAL__0,Vvar__527)
    <=> ! [Vv__CANONICAL__1] :
          ( cIntMap_2eMap_2eMap___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
         => cType___24t(happ(Vvar__527,Vv__CANONICAL__1)) ) ) ).

fof('$_type_534',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__535] :
      ( c_24__type__534___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__535)
    <=> ! [Vv__CANONICAL__2] :
          ( cIntMap_2eMap_2ead___24t(Vv__CANONICAL__2)
         => ! [Vv__CANONICAL__3] :
              ( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
             => t(happ(happ(Vvar__535,Vv__CANONICAL__2),Vv__CANONICAL__3),happ(Vv__CANONICAL__1,cIntMap_2eMap_2eM1___24a3(Vv__CANONICAL__0,Vv__CANONICAL__2,Vv__CANONICAL__3))) ) ) ) ).

fof('$_type_551',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__552] :
      ( c_24__type__551___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__552)
    <=> ! [Vv__CANONICAL__2] :
          ( cIntMap_2eMap_2eMap___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
         => ! [Vv__CANONICAL__3] :
              ( t(Vv__CANONICAL__3,happ(Vv__CANONICAL__1,Vv__CANONICAL__2))
             => ! [Vv__CANONICAL__4] :
                  ( cIntMap_2eMap_2eMap___24t(Vv__CANONICAL__0,Vv__CANONICAL__4)
                 => ! [Vv__CANONICAL__5] :
                      ( t(Vv__CANONICAL__5,happ(Vv__CANONICAL__1,Vv__CANONICAL__4))
                     => t(happ(happ(happ(happ(Vvar__552,Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5),happ(Vv__CANONICAL__1,cIntMap_2eMap_2eM2___24a3(Vv__CANONICAL__0,Vv__CANONICAL__2,Vv__CANONICAL__4))) ) ) ) ) ) ).

fof('$_type_554',axiom,
    ! [Vv__CANONICAL__0,Vvar__555] :
      ( c_24__type__554___24t(Vv__CANONICAL__0,Vvar__555)
    <=> ! [Vv__CANONICAL__1] :
          ( cIntMap_2eMap_2eMap___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
         => cProp___24t(happ(Vvar__555,Vv__CANONICAL__1)) ) ) ).

fof('$_type_593',axiom,
    ! [Vvar__594] :
      ( c_24__type__593___24t(Vvar__594)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cIntMap_2eMap_2ead___24t(Vv__CANONICAL__1)
             => ! [Vv__CANONICAL__2] :
                  ( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
                 => ! [Vv__CANONICAL__3] :
                      ( cIntMap_2eMap_2ead___24t(Vv__CANONICAL__3)
                     => ! [Vv__CANONICAL__4] :
                          ( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
                         => ! [Vv__CANONICAL__5] :
                              ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__5)
                             => cIntMap_2eMap_2eMap___24t(Vv__CANONICAL__0,happ(happ(happ(happ(happ(happ(Vvar__594,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5)) ) ) ) ) ) ) ) ).

fof('$_type_735',axiom,
    ! [Vvar__736] :
      ( c_24__type__735___24t(Vvar__736)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cIntMap_2eMap_2eMap___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
             => cCoq_2eInit_2eDatatypes_2enat___24t(happ(happ(Vvar__736,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_782',axiom,
    ! [Vvar__783] :
      ( c_24__type__782___24t(Vvar__783)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cIntMap_2eMap_2eMap___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
             => ! [Vv__CANONICAL__2] :
                  ( cIntMap_2eMap_2eMap___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
                 => ! [Vv__CANONICAL__3] :
                      ( cIntMap_2eMap_2ead___24t(Vv__CANONICAL__3)
                     => ! [Vv__CANONICAL__4] :
                          ( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
                         => ! [Vv__CANONICAL__5] :
                              ( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__5)
                             => ! [Vv__CANONICAL__6] :
                                  ( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__6)
                                 => ( Vv__CANONICAL__2 = cIntMap_2eMap_2eMapPut___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__3,Vv__CANONICAL__4)
                                   => ( Vv__CANONICAL__5 = cIntMap_2eMap_2eMapCard___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1)
                                     => ( Vv__CANONICAL__6 = cIntMap_2eMap_2eMapCard___24a2(Vv__CANONICAL__0,Vv__CANONICAL__2)
                                       => cCoq_2eInit_2eSpecif_2esumbool___24t(c_24__prop__784___24a3(Vv__CANONICAL__0,Vv__CANONICAL__5,Vv__CANONICAL__6),c_24__prop__785___24a3(Vv__CANONICAL__0,Vv__CANONICAL__5,Vv__CANONICAL__6),happ(happ(happ(happ(happ(happ(happ(Vvar__783,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__6)) ) ) ) ) ) ) ) ) ) ) ) ).

fof('$_type_789',axiom,
    ! [Vvar__790] :
      ( c_24__type__789___24t(Vvar__790)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
             => cCoq_2eInit_2eDatatypes_2enat___24t(happ(happ(Vvar__790,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_805',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__806] :
      ( c_24__type__805___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__806)
    <=> ! [Vv__CANONICAL__2] :
          ( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
         => cProp___24t(happ(Vvar__806,Vv__CANONICAL__2)) ) ) ).

fof('$_type_809',axiom,
    ! [Vvar__810] :
      ( c_24__type__809___24t(Vvar__810)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( c_24__type__812___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
             => cType___24t(happ(happ(Vvar__810,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_812',axiom,
    ! [Vv__CANONICAL__0,Vvar__813] :
      ( c_24__type__812___24t(Vv__CANONICAL__0,Vvar__813)
    <=> ! [Vv__CANONICAL__1] :
          ( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
         => cProp___24t(happ(Vvar__813,Vv__CANONICAL__1)) ) ) ).

fof('$_type_842',axiom,
    ! [Vvar__843] :
      ( c_24__type__842___24t(Vvar__843)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( c_24__type__812___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
             => ! [Vv__CANONICAL__2] :
                  ( c_24__type__848___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
                 => ! [Vv__CANONICAL__3] :
                      ( c_24__type__860___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3)
                     => ! [Vv__CANONICAL__4] :
                          ( cCoq_2eInit_2eSpecif_2esig___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__4)
                         => t(happ(happ(happ(happ(happ(Vvar__843,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),happ(Vv__CANONICAL__2,Vv__CANONICAL__4)) ) ) ) ) ) ) ).

fof('$_type_848',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__849] :
      ( c_24__type__848___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__849)
    <=> ! [Vv__CANONICAL__2] :
          ( cCoq_2eInit_2eSpecif_2esig___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
         => cType___24t(happ(Vvar__849,Vv__CANONICAL__2)) ) ) ).

fof('$_type_860',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__861] :
      ( c_24__type__860___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__861)
    <=> ! [Vv__CANONICAL__3] :
          ( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
         => ( p(happ(Vv__CANONICAL__1,Vv__CANONICAL__3))
           => t(happ(Vvar__861,Vv__CANONICAL__3),happ(Vv__CANONICAL__2,cCoq_2eInit_2eSpecif_2eexist___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__3))) ) ) ) ).

fof('$_type_865',axiom,
    ! [Vvar__866] :
      ( c_24__type__865___24t(Vvar__866)
    <=> ! [Vv__CANONICAL__0] :
          ( cProp___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cProp___24t(Vv__CANONICAL__1)
             => ( p(Vv__CANONICAL__0)
               => cCoq_2eInit_2eSpecif_2esumbool___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,happ(happ(Vvar__866,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ) ).

fof('$_type_870',axiom,
    ! [Vvar__871] :
      ( c_24__type__870___24t(Vvar__871)
    <=> ! [Vv__CANONICAL__0] :
          ( cProp___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cProp___24t(Vv__CANONICAL__1)
             => ( p(Vv__CANONICAL__1)
               => cCoq_2eInit_2eSpecif_2esumbool___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,happ(happ(Vvar__871,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ) ).

fof('$_type_896',axiom,
    ! [Vvar__897] :
      ( c_24__type__896___24t(Vvar__897)
    <=> ! [Vv__CANONICAL__0] :
          ( cProp___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cProp___24t(Vv__CANONICAL__1)
             => ! [Vv__CANONICAL__2] :
                  ( c_24__type__900___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
                 => ! [Vv__CANONICAL__3] :
                      ( c_24__type__907___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3)
                     => ! [Vv__CANONICAL__4] :
                          ( c_24__type__914___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__4)
                         => ! [Vv__CANONICAL__5] :
                              ( cCoq_2eInit_2eSpecif_2esumbool___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__5)
                             => t(happ(happ(happ(happ(happ(happ(Vvar__897,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5),happ(Vv__CANONICAL__2,Vv__CANONICAL__5)) ) ) ) ) ) ) ) ).

fof('$_type_900',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__901] :
      ( c_24__type__900___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__901)
    <=> ! [Vv__CANONICAL__2] :
          ( cCoq_2eInit_2eSpecif_2esumbool___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
         => cType___24t(happ(Vvar__901,Vv__CANONICAL__2)) ) ) ).

fof('$_type_907',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__908] :
      ( c_24__type__907___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__908)
    <=> ( p(Vv__CANONICAL__0)
       => t(Vvar__908,happ(Vv__CANONICAL__2,cCoq_2eInit_2eSpecif_2eleft___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1))) ) ) ).

fof('$_type_914',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__915] :
      ( c_24__type__914___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__915)
    <=> ( p(Vv__CANONICAL__1)
       => t(Vvar__915,happ(Vv__CANONICAL__2,cCoq_2eInit_2eSpecif_2eright___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1))) ) ) ).

fof('$_type_926',axiom,
    ! [Vvar__927] :
      ( c_24__type__926___24t(Vvar__927)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cProp___24t(Vv__CANONICAL__1)
             => cType___24t(happ(happ(Vvar__927,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_93',axiom,
    ! [Vvar__94] :
      ( c_24__type__93___24t(Vvar__94)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cIntMap_2eMap_2ead___24t(Vv__CANONICAL__1)
             => ! [Vv__CANONICAL__2] :
                  ( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
                 => cIntMap_2eMap_2eMap___24t(Vv__CANONICAL__0,happ(happ(happ(Vvar__94,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).

fof('$_type_970',axiom,
    ! [Vvar__971] :
      ( c_24__type__970___24t(Vvar__971)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cProp___24t(Vv__CANONICAL__1)
             => ! [Vv__CANONICAL__2] :
                  ( c_24__type__974___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
                 => ! [Vv__CANONICAL__3] :
                      ( c_24__type__981___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3)
                     => ! [Vv__CANONICAL__4] :
                          ( c_24__type__988___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__4)
                         => ! [Vv__CANONICAL__5] :
                              ( cCoq_2eInit_2eSpecif_2esumor___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__5)
                             => t(happ(happ(happ(happ(happ(happ(Vvar__971,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5),happ(Vv__CANONICAL__2,Vv__CANONICAL__5)) ) ) ) ) ) ) ) ).

fof('$_type_974',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__975] :
      ( c_24__type__974___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__975)
    <=> ! [Vv__CANONICAL__2] :
          ( cCoq_2eInit_2eSpecif_2esumor___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
         => cType___24t(happ(Vvar__975,Vv__CANONICAL__2)) ) ) ).

fof('$_type_98',axiom,
    ! [Vvar__99] :
      ( c_24__type__98___24t(Vvar__99)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cIntMap_2eMap_2eMap___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
             => ! [Vv__CANONICAL__2] :
                  ( cIntMap_2eMap_2eMap___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
                 => cIntMap_2eMap_2eMap___24t(Vv__CANONICAL__0,happ(happ(happ(Vvar__99,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).

fof('$_type_981',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__982] :
      ( c_24__type__981___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__982)
    <=> ! [Vv__CANONICAL__3] :
          ( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
         => t(happ(Vvar__982,Vv__CANONICAL__3),happ(Vv__CANONICAL__2,cCoq_2eInit_2eSpecif_2einleft___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__3))) ) ) ).

fof('$_type_988',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__989] :
      ( c_24__type__988___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__989)
    <=> ( p(Vv__CANONICAL__1)
       => t(Vvar__989,happ(Vv__CANONICAL__2,cCoq_2eInit_2eSpecif_2einright___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1))) ) ) ).

fof('$_type_995',axiom,
    ! [Vvar__996] :
      ( c_24__type__995___24t(Vvar__996)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__1)
             => cCoq_2eNumbers_2eBinNums_2eN___24t(happ(happ(Vvar__996,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_typeof_A',axiom,
    cType___24t(cA) ).

fof('$_typeof_B',axiom,
    cType___24t(cB) ).

fof('$_typeof_C',axiom,
    cType___24t(cC) ).

fof('$_typeof_Coq.Arith.EqNat.eq_nat',axiom,
    c_24__type__2249___24t(cCoq_2eArith_2eEqNat_2eeq__nat) ).

fof('$_typeof_Coq.Arith.PeanoNat.Nat.divide',axiom,
    c_24__type__2249___24t(cCoq_2eArith_2ePeanoNat_2eNat_2edivide) ).

fof('$_typeof_Coq.Arith.PeanoNat.Nat.eqf',axiom,
    c_24__type__21860___24t(cCoq_2eArith_2ePeanoNat_2eNat_2eeqf) ).

fof('$_typeof_Coq.Arith.PeanoNat.Nat.le_alt',axiom,
    c_24__type__2249___24t(cCoq_2eArith_2ePeanoNat_2eNat_2ele__alt) ).

fof('$_typeof_Coq.Bool.Bool.Is_true',axiom,
    c_24__type__10772___24t(cCoq_2eBool_2eBool_2eIs__true) ).

fof('$_typeof_Coq.Bool.Bool.eqb',axiom,
    c_24__type__1826___24t(cCoq_2eBool_2eBool_2eeqb) ).

fof('$_typeof_Coq.Bool.Bool.leb',axiom,
    c_24__type__36642___24t(cCoq_2eBool_2eBool_2eleb) ).

fof('$_typeof_Coq.Bool.Bool.orb_true_elim',axiom,
    c_24__type__1820___24t(cCoq_2eBool_2eBool_2eorb__true__elim) ).

fof('$_typeof_Coq.Bool.Bool.reflect',axiom,
    c_24__type__19869___24t(cCoq_2eBool_2eBool_2ereflect) ).

fof('$_typeof_Coq.Bool.Sumbool.sumbool_of_bool',axiom,
    c_24__type__430___24t(cCoq_2eBool_2eSumbool_2esumbool__of__bool) ).

fof('$_typeof_Coq.FSets.FSetPositive.PositiveSet.In',axiom,
    c_24__type__19382___24t(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eIn) ).

fof('$_typeof_Coq.FSets.FSetPositive.PositiveSet.Leaf',axiom,
    cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree___24t(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eLeaf) ).

fof('$_typeof_Coq.FSets.FSetPositive.PositiveSet.Node',axiom,
    c_24__type__19236___24t(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eNode) ).

fof('$_typeof_Coq.FSets.FSetPositive.PositiveSet.elt',axiom,
    cType___24t(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt) ).

fof('$_typeof_Coq.FSets.FSetPositive.PositiveSet.t',axiom,
    cType___24t(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et) ).

fof('$_typeof_Coq.FSets.FSetPositive.PositiveSet.tree',axiom,
    cType___24t(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree) ).

fof('$_typeof_Coq.Init.Byte.byte',axiom,
    cType___24t(cCoq_2eInit_2eByte_2ebyte) ).

fof('$_typeof_Coq.Init.Byte.x00',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex00) ).

fof('$_typeof_Coq.Init.Byte.x01',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex01) ).

fof('$_typeof_Coq.Init.Byte.x02',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex02) ).

fof('$_typeof_Coq.Init.Byte.x03',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex03) ).

fof('$_typeof_Coq.Init.Byte.x04',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex04) ).

fof('$_typeof_Coq.Init.Byte.x05',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex05) ).

fof('$_typeof_Coq.Init.Byte.x06',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex06) ).

fof('$_typeof_Coq.Init.Byte.x07',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex07) ).

fof('$_typeof_Coq.Init.Byte.x08',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex08) ).

fof('$_typeof_Coq.Init.Byte.x09',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex09) ).

fof('$_typeof_Coq.Init.Byte.x0a',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex0a) ).

fof('$_typeof_Coq.Init.Byte.x0b',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex0b) ).

fof('$_typeof_Coq.Init.Byte.x0c',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex0c) ).

fof('$_typeof_Coq.Init.Byte.x0d',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex0d) ).

fof('$_typeof_Coq.Init.Byte.x0e',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex0e) ).

fof('$_typeof_Coq.Init.Byte.x0f',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex0f) ).

fof('$_typeof_Coq.Init.Byte.x10',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex10) ).

fof('$_typeof_Coq.Init.Byte.x11',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex11) ).

fof('$_typeof_Coq.Init.Byte.x12',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex12) ).

fof('$_typeof_Coq.Init.Byte.x13',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex13) ).

fof('$_typeof_Coq.Init.Byte.x14',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex14) ).

fof('$_typeof_Coq.Init.Byte.x15',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex15) ).

fof('$_typeof_Coq.Init.Byte.x16',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex16) ).

fof('$_typeof_Coq.Init.Byte.x17',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex17) ).

fof('$_typeof_Coq.Init.Byte.x18',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex18) ).

fof('$_typeof_Coq.Init.Byte.x19',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex19) ).

fof('$_typeof_Coq.Init.Byte.x1a',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex1a) ).

fof('$_typeof_Coq.Init.Byte.x1b',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex1b) ).

fof('$_typeof_Coq.Init.Byte.x1c',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex1c) ).

fof('$_typeof_Coq.Init.Byte.x1d',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex1d) ).

fof('$_typeof_Coq.Init.Byte.x1e',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex1e) ).

fof('$_typeof_Coq.Init.Byte.x1f',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex1f) ).

fof('$_typeof_Coq.Init.Byte.x20',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex20) ).

fof('$_typeof_Coq.Init.Byte.x21',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex21) ).

fof('$_typeof_Coq.Init.Byte.x22',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex22) ).

fof('$_typeof_Coq.Init.Byte.x23',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex23) ).

fof('$_typeof_Coq.Init.Byte.x24',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex24) ).

fof('$_typeof_Coq.Init.Byte.x25',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex25) ).

fof('$_typeof_Coq.Init.Byte.x26',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex26) ).

fof('$_typeof_Coq.Init.Byte.x27',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex27) ).

fof('$_typeof_Coq.Init.Byte.x28',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex28) ).

fof('$_typeof_Coq.Init.Byte.x29',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex29) ).

fof('$_typeof_Coq.Init.Byte.x2a',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex2a) ).

fof('$_typeof_Coq.Init.Byte.x2b',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex2b) ).

fof('$_typeof_Coq.Init.Byte.x2c',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex2c) ).

fof('$_typeof_Coq.Init.Byte.x2d',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex2d) ).

fof('$_typeof_Coq.Init.Byte.x2e',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex2e) ).

fof('$_typeof_Coq.Init.Byte.x2f',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex2f) ).

fof('$_typeof_Coq.Init.Byte.x30',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex30) ).

fof('$_typeof_Coq.Init.Byte.x31',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex31) ).

fof('$_typeof_Coq.Init.Byte.x32',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex32) ).

fof('$_typeof_Coq.Init.Byte.x33',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex33) ).

fof('$_typeof_Coq.Init.Byte.x34',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex34) ).

fof('$_typeof_Coq.Init.Byte.x35',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex35) ).

fof('$_typeof_Coq.Init.Byte.x36',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex36) ).

fof('$_typeof_Coq.Init.Byte.x37',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex37) ).

fof('$_typeof_Coq.Init.Byte.x38',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex38) ).

fof('$_typeof_Coq.Init.Byte.x39',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex39) ).

fof('$_typeof_Coq.Init.Byte.x3a',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex3a) ).

fof('$_typeof_Coq.Init.Byte.x3b',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex3b) ).

fof('$_typeof_Coq.Init.Byte.x3c',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex3c) ).

fof('$_typeof_Coq.Init.Byte.x3d',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex3d) ).

fof('$_typeof_Coq.Init.Byte.x3e',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex3e) ).

fof('$_typeof_Coq.Init.Byte.x3f',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex3f) ).

fof('$_typeof_Coq.Init.Byte.x40',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex40) ).

fof('$_typeof_Coq.Init.Byte.x41',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex41) ).

fof('$_typeof_Coq.Init.Byte.x42',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex42) ).

fof('$_typeof_Coq.Init.Byte.x43',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex43) ).

fof('$_typeof_Coq.Init.Byte.x44',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex44) ).

fof('$_typeof_Coq.Init.Byte.x45',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex45) ).

fof('$_typeof_Coq.Init.Byte.x46',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex46) ).

fof('$_typeof_Coq.Init.Byte.x47',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex47) ).

fof('$_typeof_Coq.Init.Byte.x48',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex48) ).

fof('$_typeof_Coq.Init.Byte.x49',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex49) ).

fof('$_typeof_Coq.Init.Byte.x4a',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex4a) ).

fof('$_typeof_Coq.Init.Byte.x4b',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex4b) ).

fof('$_typeof_Coq.Init.Byte.x4c',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex4c) ).

fof('$_typeof_Coq.Init.Byte.x4d',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex4d) ).

fof('$_typeof_Coq.Init.Byte.x4e',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex4e) ).

fof('$_typeof_Coq.Init.Byte.x4f',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex4f) ).

fof('$_typeof_Coq.Init.Byte.x50',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex50) ).

fof('$_typeof_Coq.Init.Byte.x51',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex51) ).

fof('$_typeof_Coq.Init.Byte.x52',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex52) ).

fof('$_typeof_Coq.Init.Byte.x53',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex53) ).

fof('$_typeof_Coq.Init.Byte.x54',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex54) ).

fof('$_typeof_Coq.Init.Byte.x55',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex55) ).

fof('$_typeof_Coq.Init.Byte.x56',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex56) ).

fof('$_typeof_Coq.Init.Byte.x57',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex57) ).

fof('$_typeof_Coq.Init.Byte.x58',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex58) ).

fof('$_typeof_Coq.Init.Byte.x59',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex59) ).

fof('$_typeof_Coq.Init.Byte.x5a',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex5a) ).

fof('$_typeof_Coq.Init.Byte.x5b',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex5b) ).

fof('$_typeof_Coq.Init.Byte.x5c',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex5c) ).

fof('$_typeof_Coq.Init.Byte.x5d',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex5d) ).

fof('$_typeof_Coq.Init.Byte.x5e',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex5e) ).

fof('$_typeof_Coq.Init.Byte.x5f',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex5f) ).

fof('$_typeof_Coq.Init.Byte.x60',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex60) ).

fof('$_typeof_Coq.Init.Byte.x61',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex61) ).

fof('$_typeof_Coq.Init.Byte.x62',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex62) ).

fof('$_typeof_Coq.Init.Byte.x63',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex63) ).

fof('$_typeof_Coq.Init.Byte.x64',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex64) ).

fof('$_typeof_Coq.Init.Byte.x65',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex65) ).

fof('$_typeof_Coq.Init.Byte.x66',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex66) ).

fof('$_typeof_Coq.Init.Byte.x67',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex67) ).

fof('$_typeof_Coq.Init.Byte.x68',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex68) ).

fof('$_typeof_Coq.Init.Byte.x69',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex69) ).

fof('$_typeof_Coq.Init.Byte.x6a',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex6a) ).

fof('$_typeof_Coq.Init.Byte.x6b',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex6b) ).

fof('$_typeof_Coq.Init.Byte.x6c',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex6c) ).

fof('$_typeof_Coq.Init.Byte.x6d',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex6d) ).

fof('$_typeof_Coq.Init.Byte.x6e',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex6e) ).

fof('$_typeof_Coq.Init.Byte.x6f',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex6f) ).

fof('$_typeof_Coq.Init.Byte.x70',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex70) ).

fof('$_typeof_Coq.Init.Byte.x71',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex71) ).

fof('$_typeof_Coq.Init.Byte.x72',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex72) ).

fof('$_typeof_Coq.Init.Byte.x73',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex73) ).

fof('$_typeof_Coq.Init.Byte.x74',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex74) ).

fof('$_typeof_Coq.Init.Byte.x75',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex75) ).

fof('$_typeof_Coq.Init.Byte.x76',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex76) ).

fof('$_typeof_Coq.Init.Byte.x77',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex77) ).

fof('$_typeof_Coq.Init.Byte.x78',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex78) ).

fof('$_typeof_Coq.Init.Byte.x79',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex79) ).

fof('$_typeof_Coq.Init.Byte.x7a',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex7a) ).

fof('$_typeof_Coq.Init.Byte.x7b',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex7b) ).

fof('$_typeof_Coq.Init.Byte.x7c',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex7c) ).

fof('$_typeof_Coq.Init.Byte.x7d',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex7d) ).

fof('$_typeof_Coq.Init.Byte.x7e',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex7e) ).

fof('$_typeof_Coq.Init.Byte.x7f',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex7f) ).

fof('$_typeof_Coq.Init.Byte.x80',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex80) ).

fof('$_typeof_Coq.Init.Byte.x81',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex81) ).

fof('$_typeof_Coq.Init.Byte.x82',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex82) ).

fof('$_typeof_Coq.Init.Byte.x83',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex83) ).

fof('$_typeof_Coq.Init.Byte.x84',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex84) ).

fof('$_typeof_Coq.Init.Byte.x85',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex85) ).

fof('$_typeof_Coq.Init.Byte.x86',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex86) ).

fof('$_typeof_Coq.Init.Byte.x87',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex87) ).

fof('$_typeof_Coq.Init.Byte.x88',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex88) ).

fof('$_typeof_Coq.Init.Byte.x89',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex89) ).

fof('$_typeof_Coq.Init.Byte.x8a',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex8a) ).

fof('$_typeof_Coq.Init.Byte.x8b',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex8b) ).

fof('$_typeof_Coq.Init.Byte.x8c',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex8c) ).

fof('$_typeof_Coq.Init.Byte.x8d',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex8d) ).

fof('$_typeof_Coq.Init.Byte.x8e',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex8e) ).

fof('$_typeof_Coq.Init.Byte.x8f',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex8f) ).

fof('$_typeof_Coq.Init.Byte.x90',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex90) ).

fof('$_typeof_Coq.Init.Byte.x91',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex91) ).

fof('$_typeof_Coq.Init.Byte.x92',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex92) ).

fof('$_typeof_Coq.Init.Byte.x93',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex93) ).

fof('$_typeof_Coq.Init.Byte.x94',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex94) ).

fof('$_typeof_Coq.Init.Byte.x95',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex95) ).

fof('$_typeof_Coq.Init.Byte.x96',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex96) ).

fof('$_typeof_Coq.Init.Byte.x97',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex97) ).

fof('$_typeof_Coq.Init.Byte.x98',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex98) ).

fof('$_typeof_Coq.Init.Byte.x99',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex99) ).

fof('$_typeof_Coq.Init.Byte.x9a',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex9a) ).

fof('$_typeof_Coq.Init.Byte.x9b',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex9b) ).

fof('$_typeof_Coq.Init.Byte.x9c',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex9c) ).

fof('$_typeof_Coq.Init.Byte.x9d',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex9d) ).

fof('$_typeof_Coq.Init.Byte.x9e',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex9e) ).

fof('$_typeof_Coq.Init.Byte.x9f',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex9f) ).

fof('$_typeof_Coq.Init.Byte.xa0',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exa0) ).

fof('$_typeof_Coq.Init.Byte.xa1',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exa1) ).

fof('$_typeof_Coq.Init.Byte.xa2',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exa2) ).

fof('$_typeof_Coq.Init.Byte.xa3',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exa3) ).

fof('$_typeof_Coq.Init.Byte.xa4',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exa4) ).

fof('$_typeof_Coq.Init.Byte.xa5',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exa5) ).

fof('$_typeof_Coq.Init.Byte.xa6',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exa6) ).

fof('$_typeof_Coq.Init.Byte.xa7',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exa7) ).

fof('$_typeof_Coq.Init.Byte.xa8',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exa8) ).

fof('$_typeof_Coq.Init.Byte.xa9',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exa9) ).

fof('$_typeof_Coq.Init.Byte.xaa',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exaa) ).

fof('$_typeof_Coq.Init.Byte.xab',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exab) ).

fof('$_typeof_Coq.Init.Byte.xac',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exac) ).

fof('$_typeof_Coq.Init.Byte.xad',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exad) ).

fof('$_typeof_Coq.Init.Byte.xae',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exae) ).

fof('$_typeof_Coq.Init.Byte.xaf',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exaf) ).

fof('$_typeof_Coq.Init.Byte.xb0',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exb0) ).

fof('$_typeof_Coq.Init.Byte.xb1',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exb1) ).

fof('$_typeof_Coq.Init.Byte.xb2',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exb2) ).

fof('$_typeof_Coq.Init.Byte.xb3',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exb3) ).

fof('$_typeof_Coq.Init.Byte.xb4',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exb4) ).

fof('$_typeof_Coq.Init.Byte.xb5',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exb5) ).

fof('$_typeof_Coq.Init.Byte.xb6',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exb6) ).

fof('$_typeof_Coq.Init.Byte.xb7',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exb7) ).

fof('$_typeof_Coq.Init.Byte.xb8',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exb8) ).

fof('$_typeof_Coq.Init.Byte.xb9',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exb9) ).

fof('$_typeof_Coq.Init.Byte.xba',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exba) ).

fof('$_typeof_Coq.Init.Byte.xbb',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exbb) ).

fof('$_typeof_Coq.Init.Byte.xbc',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exbc) ).

fof('$_typeof_Coq.Init.Byte.xbd',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exbd) ).

fof('$_typeof_Coq.Init.Byte.xbe',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exbe) ).

fof('$_typeof_Coq.Init.Byte.xbf',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exbf) ).

fof('$_typeof_Coq.Init.Byte.xc0',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exc0) ).

fof('$_typeof_Coq.Init.Byte.xc1',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exc1) ).

fof('$_typeof_Coq.Init.Byte.xc2',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exc2) ).

fof('$_typeof_Coq.Init.Byte.xc3',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exc3) ).

fof('$_typeof_Coq.Init.Byte.xc4',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exc4) ).

fof('$_typeof_Coq.Init.Byte.xc5',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exc5) ).

fof('$_typeof_Coq.Init.Byte.xc6',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exc6) ).

fof('$_typeof_Coq.Init.Byte.xc7',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exc7) ).

fof('$_typeof_Coq.Init.Byte.xc8',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exc8) ).

fof('$_typeof_Coq.Init.Byte.xc9',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exc9) ).

fof('$_typeof_Coq.Init.Byte.xca',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exca) ).

fof('$_typeof_Coq.Init.Byte.xcb',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2excb) ).

fof('$_typeof_Coq.Init.Byte.xcc',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2excc) ).

fof('$_typeof_Coq.Init.Byte.xcd',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2excd) ).

fof('$_typeof_Coq.Init.Byte.xce',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exce) ).

fof('$_typeof_Coq.Init.Byte.xcf',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2excf) ).

fof('$_typeof_Coq.Init.Byte.xd0',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exd0) ).

fof('$_typeof_Coq.Init.Byte.xd1',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exd1) ).

fof('$_typeof_Coq.Init.Byte.xd2',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exd2) ).

fof('$_typeof_Coq.Init.Byte.xd3',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exd3) ).

fof('$_typeof_Coq.Init.Byte.xd4',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exd4) ).

fof('$_typeof_Coq.Init.Byte.xd5',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exd5) ).

fof('$_typeof_Coq.Init.Byte.xd6',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exd6) ).

fof('$_typeof_Coq.Init.Byte.xd7',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exd7) ).

fof('$_typeof_Coq.Init.Byte.xd8',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exd8) ).

fof('$_typeof_Coq.Init.Byte.xd9',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exd9) ).

fof('$_typeof_Coq.Init.Byte.xda',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exda) ).

fof('$_typeof_Coq.Init.Byte.xdb',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exdb) ).

fof('$_typeof_Coq.Init.Byte.xdc',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exdc) ).

fof('$_typeof_Coq.Init.Byte.xdd',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exdd) ).

fof('$_typeof_Coq.Init.Byte.xde',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exde) ).

fof('$_typeof_Coq.Init.Byte.xdf',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exdf) ).

fof('$_typeof_Coq.Init.Byte.xe0',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exe0) ).

fof('$_typeof_Coq.Init.Byte.xe1',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exe1) ).

fof('$_typeof_Coq.Init.Byte.xe2',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exe2) ).

fof('$_typeof_Coq.Init.Byte.xe3',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exe3) ).

fof('$_typeof_Coq.Init.Byte.xe4',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exe4) ).

fof('$_typeof_Coq.Init.Byte.xe5',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exe5) ).

fof('$_typeof_Coq.Init.Byte.xe6',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exe6) ).

fof('$_typeof_Coq.Init.Byte.xe7',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exe7) ).

fof('$_typeof_Coq.Init.Byte.xe8',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exe8) ).

fof('$_typeof_Coq.Init.Byte.xe9',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exe9) ).

fof('$_typeof_Coq.Init.Byte.xea',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exea) ).

fof('$_typeof_Coq.Init.Byte.xeb',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exeb) ).

fof('$_typeof_Coq.Init.Byte.xec',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exec) ).

fof('$_typeof_Coq.Init.Byte.xed',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exed) ).

fof('$_typeof_Coq.Init.Byte.xee',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exee) ).

fof('$_typeof_Coq.Init.Byte.xef',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exef) ).

fof('$_typeof_Coq.Init.Byte.xf0',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exf0) ).

fof('$_typeof_Coq.Init.Byte.xf1',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exf1) ).

fof('$_typeof_Coq.Init.Byte.xf2',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exf2) ).

fof('$_typeof_Coq.Init.Byte.xf3',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exf3) ).

fof('$_typeof_Coq.Init.Byte.xf4',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exf4) ).

fof('$_typeof_Coq.Init.Byte.xf5',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exf5) ).

fof('$_typeof_Coq.Init.Byte.xf6',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exf6) ).

fof('$_typeof_Coq.Init.Byte.xf7',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exf7) ).

fof('$_typeof_Coq.Init.Byte.xf8',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exf8) ).

fof('$_typeof_Coq.Init.Byte.xf9',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exf9) ).

fof('$_typeof_Coq.Init.Byte.xfa',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exfa) ).

fof('$_typeof_Coq.Init.Byte.xfb',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exfb) ).

fof('$_typeof_Coq.Init.Byte.xfc',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exfc) ).

fof('$_typeof_Coq.Init.Byte.xfd',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exfd) ).

fof('$_typeof_Coq.Init.Byte.xfe',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exfe) ).

fof('$_typeof_Coq.Init.Byte.xff',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exff) ).

fof('$_typeof_Coq.Init.Datatypes.CompareSpecT',axiom,
    c_24__type__19933___24t(cCoq_2eInit_2eDatatypes_2eCompareSpecT) ).

fof('$_typeof_Coq.Init.Datatypes.Eq',axiom,
    cCoq_2eInit_2eDatatypes_2ecomparison___24t(cCoq_2eInit_2eDatatypes_2eEq) ).

fof('$_typeof_Coq.Init.Datatypes.Gt',axiom,
    cCoq_2eInit_2eDatatypes_2ecomparison___24t(cCoq_2eInit_2eDatatypes_2eGt) ).

fof('$_typeof_Coq.Init.Datatypes.IDProp',axiom,
    cProp___24t(cCoq_2eInit_2eDatatypes_2eIDProp) ).

fof('$_typeof_Coq.Init.Datatypes.Lt',axiom,
    cCoq_2eInit_2eDatatypes_2ecomparison___24t(cCoq_2eInit_2eDatatypes_2eLt) ).

fof('$_typeof_Coq.Init.Datatypes.None',axiom,
    c_24__type__50___24t(cCoq_2eInit_2eDatatypes_2eNone) ).

fof('$_typeof_Coq.Init.Datatypes.O',axiom,
    cCoq_2eInit_2eDatatypes_2enat___24t(cCoq_2eInit_2eDatatypes_2eO) ).

fof('$_typeof_Coq.Init.Datatypes.S',axiom,
    c_24__type__458___24t(cCoq_2eInit_2eDatatypes_2eS) ).

fof('$_typeof_Coq.Init.Datatypes.Some',axiom,
    c_24__type__48___24t(cCoq_2eInit_2eDatatypes_2eSome) ).

fof('$_typeof_Coq.Init.Datatypes.andb',axiom,
    c_24__type__1826___24t(cCoq_2eInit_2eDatatypes_2eandb) ).

fof('$_typeof_Coq.Init.Datatypes.app',axiom,
    c_24__type__10985___24t(cCoq_2eInit_2eDatatypes_2eapp) ).

fof('$_typeof_Coq.Init.Datatypes.bool',axiom,
    cType___24t(cCoq_2eInit_2eDatatypes_2ebool) ).

fof('$_typeof_Coq.Init.Datatypes.comparison',axiom,
    cType___24t(cCoq_2eInit_2eDatatypes_2ecomparison) ).

fof('$_typeof_Coq.Init.Datatypes.cons',axiom,
    c_24__type__1848___24t(cCoq_2eInit_2eDatatypes_2econs) ).

fof('$_typeof_Coq.Init.Datatypes.false',axiom,
    cCoq_2eInit_2eDatatypes_2ebool___24t(cCoq_2eInit_2eDatatypes_2efalse) ).

fof('$_typeof_Coq.Init.Datatypes.fst',axiom,
    c_24__type__10897___24t(cCoq_2eInit_2eDatatypes_2efst) ).

fof('$_typeof_Coq.Init.Datatypes.is_true',axiom,
    c_24__type__10772___24t(cCoq_2eInit_2eDatatypes_2eis__true) ).

fof('$_typeof_Coq.Init.Datatypes.length',axiom,
    c_24__type__10973___24t(cCoq_2eInit_2eDatatypes_2elength) ).

fof('$_typeof_Coq.Init.Datatypes.list',axiom,
    c_24__type__36___24t(cCoq_2eInit_2eDatatypes_2elist) ).

fof('$_typeof_Coq.Init.Datatypes.nat',axiom,
    cType___24t(cCoq_2eInit_2eDatatypes_2enat) ).

fof('$_typeof_Coq.Init.Datatypes.negb',axiom,
    c_24__type__1829___24t(cCoq_2eInit_2eDatatypes_2enegb) ).

fof('$_typeof_Coq.Init.Datatypes.nil',axiom,
    c_24__type__10911___24t(cCoq_2eInit_2eDatatypes_2enil) ).

fof('$_typeof_Coq.Init.Datatypes.option',axiom,
    c_24__type__36___24t(cCoq_2eInit_2eDatatypes_2eoption) ).

fof('$_typeof_Coq.Init.Datatypes.orb',axiom,
    c_24__type__1826___24t(cCoq_2eInit_2eDatatypes_2eorb) ).

fof('$_typeof_Coq.Init.Datatypes.pair',axiom,
    c_24__type__1837___24t(cCoq_2eInit_2eDatatypes_2epair) ).

fof('$_typeof_Coq.Init.Datatypes.prod',axiom,
    c_24__type__1020___24t(cCoq_2eInit_2eDatatypes_2eprod) ).

fof('$_typeof_Coq.Init.Datatypes.prod_rect',axiom,
    c_24__type__10870___24t(cCoq_2eInit_2eDatatypes_2eprod__rect) ).

fof('$_typeof_Coq.Init.Datatypes.snd',axiom,
    c_24__type__10909___24t(cCoq_2eInit_2eDatatypes_2esnd) ).

fof('$_typeof_Coq.Init.Datatypes.sum',axiom,
    c_24__type__1020___24t(cCoq_2eInit_2eDatatypes_2esum) ).

fof('$_typeof_Coq.Init.Datatypes.true',axiom,
    cCoq_2eInit_2eDatatypes_2ebool___24t(cCoq_2eInit_2eDatatypes_2etrue) ).

fof('$_typeof_Coq.Init.Datatypes.tt',axiom,
    cCoq_2eInit_2eDatatypes_2eunit___24t(cCoq_2eInit_2eDatatypes_2ett) ).

fof('$_typeof_Coq.Init.Datatypes.unit',axiom,
    cType___24t(cCoq_2eInit_2eDatatypes_2eunit) ).

fof('$_typeof_Coq.Init.Datatypes.xorb',axiom,
    c_24__type__1826___24t(cCoq_2eInit_2eDatatypes_2exorb) ).

fof('$_typeof_Coq.Init.Nat.add',axiom,
    c_24__type__789___24t(cCoq_2eInit_2eNat_2eadd) ).

fof('$_typeof_Coq.Init.Nat.div2',axiom,
    c_24__type__458___24t(cCoq_2eInit_2eNat_2ediv2) ).

fof('$_typeof_Coq.Init.Nat.double',axiom,
    c_24__type__458___24t(cCoq_2eInit_2eNat_2edouble) ).

fof('$_typeof_Coq.Init.Nat.eqb',axiom,
    c_24__type__14607___24t(cCoq_2eInit_2eNat_2eeqb) ).

fof('$_typeof_Coq.Init.Nat.even',axiom,
    c_24__type__14593___24t(cCoq_2eInit_2eNat_2eeven) ).

fof('$_typeof_Coq.Init.Nat.max',axiom,
    c_24__type__789___24t(cCoq_2eInit_2eNat_2emax) ).

fof('$_typeof_Coq.Init.Nat.min',axiom,
    c_24__type__789___24t(cCoq_2eInit_2eNat_2emin) ).

fof('$_typeof_Coq.Init.Nat.mul',axiom,
    c_24__type__789___24t(cCoq_2eInit_2eNat_2emul) ).

fof('$_typeof_Coq.Init.Nat.pow',axiom,
    c_24__type__789___24t(cCoq_2eInit_2eNat_2epow) ).

fof('$_typeof_Coq.Init.Nat.pred',axiom,
    c_24__type__458___24t(cCoq_2eInit_2eNat_2epred) ).

fof('$_typeof_Coq.Init.Nat.sub',axiom,
    c_24__type__789___24t(cCoq_2eInit_2eNat_2esub) ).

fof('$_typeof_Coq.Init.Nat.testbit',axiom,
    c_24__type__14607___24t(cCoq_2eInit_2eNat_2etestbit) ).

fof('$_typeof_Coq.Init.Peano.ge',axiom,
    c_24__type__2249___24t(cCoq_2eInit_2ePeano_2ege) ).

fof('$_typeof_Coq.Init.Peano.gt',axiom,
    c_24__type__2249___24t(cCoq_2eInit_2ePeano_2egt) ).

fof('$_typeof_Coq.Init.Peano.lt',axiom,
    c_24__type__2249___24t(cCoq_2eInit_2ePeano_2elt) ).

fof('$_typeof_Coq.Init.Specif.exist',axiom,
    c_24__type__2258___24t(cCoq_2eInit_2eSpecif_2eexist) ).

fof('$_typeof_Coq.Init.Specif.existT',axiom,
    c_24__type__18759___24t(cCoq_2eInit_2eSpecif_2eexistT) ).

fof('$_typeof_Coq.Init.Specif.left',axiom,
    c_24__type__865___24t(cCoq_2eInit_2eSpecif_2eleft) ).

fof('$_typeof_Coq.Init.Specif.right',axiom,
    c_24__type__870___24t(cCoq_2eInit_2eSpecif_2eright) ).

fof('$_typeof_Coq.Init.Specif.sig',axiom,
    c_24__type__809___24t(cCoq_2eInit_2eSpecif_2esig) ).

fof('$_typeof_Coq.Init.Specif.sig2',axiom,
    c_24__type__32732___24t(cCoq_2eInit_2eSpecif_2esig2) ).

fof('$_typeof_Coq.Init.Specif.sigT',axiom,
    c_24__type__18741___24t(cCoq_2eInit_2eSpecif_2esigT) ).

fof('$_typeof_Coq.Init.Specif.sigT2',axiom,
    c_24__type__18868___24t(cCoq_2eInit_2eSpecif_2esigT2) ).

fof('$_typeof_Coq.Init.Specif.sigT_rect',axiom,
    c_24__type__18808___24t(cCoq_2eInit_2eSpecif_2esigT__rect) ).

fof('$_typeof_Coq.Init.Specif.sig_rec',axiom,
    c_24__type__842___24t(cCoq_2eInit_2eSpecif_2esig__rec) ).

fof('$_typeof_Coq.Init.Specif.sig_rect',axiom,
    c_24__type__842___24t(cCoq_2eInit_2eSpecif_2esig__rect) ).

fof('$_typeof_Coq.Init.Specif.sumbool',axiom,
    c_24__type__400___24t(cCoq_2eInit_2eSpecif_2esumbool) ).

fof('$_typeof_Coq.Init.Specif.sumbool_rec',axiom,
    c_24__type__896___24t(cCoq_2eInit_2eSpecif_2esumbool__rec) ).

fof('$_typeof_Coq.Init.Specif.sumbool_rect',axiom,
    c_24__type__896___24t(cCoq_2eInit_2eSpecif_2esumbool__rect) ).

fof('$_typeof_Coq.Init.Specif.sumor',axiom,
    c_24__type__926___24t(cCoq_2eInit_2eSpecif_2esumor) ).

fof('$_typeof_Coq.Init.Specif.sumor_rec',axiom,
    c_24__type__970___24t(cCoq_2eInit_2eSpecif_2esumor__rec) ).

fof('$_typeof_Coq.Init.Specif.sumor_rect',axiom,
    c_24__type__970___24t(cCoq_2eInit_2eSpecif_2esumor__rect) ).

fof('$_typeof_Coq.Lists.List.In',axiom,
    c_24__type__21699___24t(cCoq_2eLists_2eList_2eIn) ).

fof('$_typeof_Coq.Lists.List.fold_left',axiom,
    c_24__type__12935___24t(cCoq_2eLists_2eList_2efold__left) ).

fof('$_typeof_Coq.Lists.List.fold_right',axiom,
    c_24__type__12966___24t(cCoq_2eLists_2eList_2efold__right) ).

fof('$_typeof_Coq.Logic.Decidable.decidable',axiom,
    c_24__type__19983___24t(cCoq_2eLogic_2eDecidable_2edecidable) ).

fof('$_typeof_Coq.Logic.EqdepFacts.Eq_dep_eq_on',axiom,
    c_24__type__36678___24t(cCoq_2eLogic_2eEqdepFacts_2eEq__dep__eq__on) ).

fof('$_typeof_Coq.Logic.EqdepFacts.Eq_rect_eq_on',axiom,
    c_24__type__11418___24t(cCoq_2eLogic_2eEqdepFacts_2eEq__rect__eq__on) ).

fof('$_typeof_Coq.Logic.EqdepFacts.Streicher_K_',axiom,
    c_24__type__36683___24t(cCoq_2eLogic_2eEqdepFacts_2eStreicher__K__) ).

fof('$_typeof_Coq.Logic.EqdepFacts.Streicher_K_on_',axiom,
    c_24__type__11426___24t(cCoq_2eLogic_2eEqdepFacts_2eStreicher__K__on__) ).

fof('$_typeof_Coq.Logic.EqdepFacts.UIP_on_',axiom,
    c_24__type__20100___24t(cCoq_2eLogic_2eEqdepFacts_2eUIP__on__) ).

fof('$_typeof_Coq.NArith.BinNat.N.divide',axiom,
    c_24__type__19009___24t(cCoq_2eNArith_2eBinNat_2eN_2edivide) ).

fof('$_typeof_Coq.NArith.BinNat.N.eqf',axiom,
    c_24__type__33487___24t(cCoq_2eNArith_2eBinNat_2eN_2eeqf) ).

fof('$_typeof_Coq.NArith.BinNat.N.le',axiom,
    c_24__type__19009___24t(cCoq_2eNArith_2eBinNat_2eN_2ele) ).

fof('$_typeof_Coq.NArith.BinNat.N.lt',axiom,
    c_24__type__19009___24t(cCoq_2eNArith_2eBinNat_2eN_2elt) ).

fof('$_typeof_Coq.NArith.BinNatDef.N.add',axiom,
    c_24__type__995___24t(cCoq_2eNArith_2eBinNatDef_2eN_2eadd) ).

fof('$_typeof_Coq.NArith.BinNatDef.N.div2',axiom,
    c_24__type__449___24t(cCoq_2eNArith_2eBinNatDef_2eN_2ediv2) ).

fof('$_typeof_Coq.NArith.BinNatDef.N.double',axiom,
    c_24__type__449___24t(cCoq_2eNArith_2eBinNatDef_2eN_2edouble) ).

fof('$_typeof_Coq.NArith.BinNatDef.N.eqb',axiom,
    c_24__type__441___24t(cCoq_2eNArith_2eBinNatDef_2eN_2eeqb) ).

fof('$_typeof_Coq.NArith.BinNatDef.N.lxor',axiom,
    c_24__type__995___24t(cCoq_2eNArith_2eBinNatDef_2eN_2elxor) ).

fof('$_typeof_Coq.NArith.BinNatDef.N.max',axiom,
    c_24__type__995___24t(cCoq_2eNArith_2eBinNatDef_2eN_2emax) ).

fof('$_typeof_Coq.NArith.BinNatDef.N.min',axiom,
    c_24__type__995___24t(cCoq_2eNArith_2eBinNatDef_2eN_2emin) ).

fof('$_typeof_Coq.NArith.BinNatDef.N.mul',axiom,
    c_24__type__995___24t(cCoq_2eNArith_2eBinNatDef_2eN_2emul) ).

fof('$_typeof_Coq.NArith.BinNatDef.N.odd',axiom,
    c_24__type__451___24t(cCoq_2eNArith_2eBinNatDef_2eN_2eodd) ).

fof('$_typeof_Coq.NArith.BinNatDef.N.pred',axiom,
    c_24__type__449___24t(cCoq_2eNArith_2eBinNatDef_2eN_2epred) ).

fof('$_typeof_Coq.NArith.BinNatDef.N.succ',axiom,
    c_24__type__449___24t(cCoq_2eNArith_2eBinNatDef_2eN_2esucc) ).

fof('$_typeof_Coq.NArith.BinNatDef.N.succ_double',axiom,
    c_24__type__449___24t(cCoq_2eNArith_2eBinNatDef_2eN_2esucc__double) ).

fof('$_typeof_Coq.NArith.BinNatDef.N.testbit',axiom,
    c_24__type__441___24t(cCoq_2eNArith_2eBinNatDef_2eN_2etestbit) ).

fof('$_typeof_Coq.NArith.BinNatDef.N.to_nat',axiom,
    c_24__type__19006___24t(cCoq_2eNArith_2eBinNatDef_2eN_2eto__nat) ).

fof('$_typeof_Coq.NArith.Ndec.Ndouble_or_double_plus_un',axiom,
    c_24__type__14611___24t(cCoq_2eNArith_2eNdec_2eNdouble__or__double__plus__un) ).

fof('$_typeof_Coq.NArith.Ndigits.Nless',axiom,
    c_24__type__441___24t(cCoq_2eNArith_2eNdigits_2eNless) ).

fof('$_typeof_Coq.NArith.Ndigits.eqf',axiom,
    c_24__type__21860___24t(cCoq_2eNArith_2eNdigits_2eeqf) ).

fof('$_typeof_Coq.Numbers.BinNums.N',axiom,
    cType___24t(cCoq_2eNumbers_2eBinNums_2eN) ).

fof('$_typeof_Coq.Numbers.BinNums.N0',axiom,
    cCoq_2eNumbers_2eBinNums_2eN___24t(cCoq_2eNumbers_2eBinNums_2eN0) ).

fof('$_typeof_Coq.Numbers.BinNums.Npos',axiom,
    c_24__type__25___24t(cCoq_2eNumbers_2eBinNums_2eNpos) ).

fof('$_typeof_Coq.Numbers.BinNums.Z',axiom,
    cType___24t(cCoq_2eNumbers_2eBinNums_2eZ) ).

fof('$_typeof_Coq.Numbers.BinNums.Z0',axiom,
    cCoq_2eNumbers_2eBinNums_2eZ___24t(cCoq_2eNumbers_2eBinNums_2eZ0) ).

fof('$_typeof_Coq.Numbers.BinNums.Zneg',axiom,
    c_24__type__2669___24t(cCoq_2eNumbers_2eBinNums_2eZneg) ).

fof('$_typeof_Coq.Numbers.BinNums.Zpos',axiom,
    c_24__type__2669___24t(cCoq_2eNumbers_2eBinNums_2eZpos) ).

fof('$_typeof_Coq.Numbers.BinNums.positive',axiom,
    cType___24t(cCoq_2eNumbers_2eBinNums_2epositive) ).

fof('$_typeof_Coq.Numbers.BinNums.xH',axiom,
    cCoq_2eNumbers_2eBinNums_2epositive___24t(cCoq_2eNumbers_2eBinNums_2exH) ).

fof('$_typeof_Coq.Numbers.BinNums.xI',axiom,
    c_24__type__12___24t(cCoq_2eNumbers_2eBinNums_2exI) ).

fof('$_typeof_Coq.Numbers.BinNums.xO',axiom,
    c_24__type__12___24t(cCoq_2eNumbers_2eBinNums_2exO) ).

fof('$_typeof_Coq.PArith.BinPos.Pos.PeanoView',axiom,
    c_24__type__33574___24t(cCoq_2ePArith_2eBinPos_2ePos_2ePeanoView) ).

fof('$_typeof_Coq.PArith.BinPos.Pos.lt',axiom,
    c_24__type__19184___24t(cCoq_2ePArith_2eBinPos_2ePos_2elt) ).

fof('$_typeof_Coq.PArith.BinPosDef.Pos.IsNeg',axiom,
    cCoq_2ePArith_2eBinPosDef_2ePos_2emask___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2eIsNeg) ).

fof('$_typeof_Coq.PArith.BinPosDef.Pos.IsNul',axiom,
    cCoq_2ePArith_2eBinPosDef_2ePos_2emask___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2eIsNul) ).

fof('$_typeof_Coq.PArith.BinPosDef.Pos.IsPos',axiom,
    c_24__type__19093___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2eIsPos) ).

fof('$_typeof_Coq.PArith.BinPosDef.Pos.compare',axiom,
    c_24__type__19168___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare) ).

fof('$_typeof_Coq.PArith.BinPosDef.Pos.divide',axiom,
    c_24__type__19184___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2edivide) ).

fof('$_typeof_Coq.PArith.BinPosDef.Pos.iter',axiom,
    c_24__type__19141___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2eiter) ).

fof('$_typeof_Coq.PArith.BinPosDef.Pos.iter_op',axiom,
    c_24__type__33511___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2eiter__op) ).

fof('$_typeof_Coq.PArith.BinPosDef.Pos.mask',axiom,
    cType___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2emask) ).

fof('$_typeof_Coq.PArith.BinPosDef.Pos.max',axiom,
    c_24__type__19055___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2emax) ).

fof('$_typeof_Coq.PArith.BinPosDef.Pos.min',axiom,
    c_24__type__19055___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2emin) ).

fof('$_typeof_Coq.PArith.BinPosDef.Pos.succ',axiom,
    c_24__type__12___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2esucc) ).

fof('$_typeof_Coq.QArith.QArith_base.Q',axiom,
    cType___24t(cCoq_2eQArith_2eQArith__base_2eQ) ).

fof('$_typeof_Coq.QArith.QArith_base.Qden',axiom,
    c_24__type__23152___24t(cCoq_2eQArith_2eQArith__base_2eQden) ).

fof('$_typeof_Coq.QArith.QArith_base.Qmake',axiom,
    c_24__type__23142___24t(cCoq_2eQArith_2eQArith__base_2eQmake) ).

fof('$_typeof_Coq.QArith.QArith_base.Qnum',axiom,
    c_24__type__23147___24t(cCoq_2eQArith_2eQArith__base_2eQnum) ).

fof('$_typeof_Coq.Reals.RIneq.nonzeroreal',axiom,
    cType___24t(cCoq_2eReals_2eRIneq_2enonzeroreal) ).

fof('$_typeof_Coq.Reals.Rdefinitions.IZR',axiom,
    c_24__type__14722___24t(cCoq_2eReals_2eRdefinitions_2eIZR) ).

fof('$_typeof_Coq.Reals.Rdefinitions.R',axiom,
    cType___24t(cCoq_2eReals_2eRdefinitions_2eR) ).

fof('$_typeof_Coq.Reals.Rdefinitions.R0',axiom,
    cCoq_2eReals_2eRdefinitions_2eR___24t(cCoq_2eReals_2eRdefinitions_2eR0) ).

fof('$_typeof_Coq.Reals.Rdefinitions.Rge',axiom,
    c_24__type__23307___24t(cCoq_2eReals_2eRdefinitions_2eRge) ).

fof('$_typeof_Coq.Reals.Rdefinitions.Rgt',axiom,
    c_24__type__23307___24t(cCoq_2eReals_2eRdefinitions_2eRgt) ).

fof('$_typeof_Coq.Reals.Rdefinitions.Rinv',axiom,
    c_24__type__14716___24t(cCoq_2eReals_2eRdefinitions_2eRinv) ).

fof('$_typeof_Coq.Reals.Rdefinitions.Rle',axiom,
    c_24__type__23307___24t(cCoq_2eReals_2eRdefinitions_2eRle) ).

fof('$_typeof_Coq.Reals.Rdefinitions.Rlt',axiom,
    c_24__type__23307___24t(cCoq_2eReals_2eRdefinitions_2eRlt) ).

fof('$_typeof_Coq.Reals.Rdefinitions.Rmult',axiom,
    c_24__type__14713___24t(cCoq_2eReals_2eRdefinitions_2eRmult) ).

fof('$_typeof_Coq.Reals.Rdefinitions.Ropp',axiom,
    c_24__type__14716___24t(cCoq_2eReals_2eRdefinitions_2eRopp) ).

fof('$_typeof_Coq.Reals.Rdefinitions.Rplus',axiom,
    c_24__type__14713___24t(cCoq_2eReals_2eRdefinitions_2eRplus) ).

fof('$_typeof_Coq.Reals.Rdefinitions.up',axiom,
    c_24__type__23309___24t(cCoq_2eReals_2eRdefinitions_2eup) ).

fof('$_typeof_Coq.Reals.Rfunctions.Z_spec',axiom,
    c_24__type__23401___24t(cCoq_2eReals_2eRfunctions_2eZ__spec) ).

fof('$_typeof_Coq.Relations.Relation_Definitions.antisymmetric',axiom,
    c_24__type__32436___24t(cCoq_2eRelations_2eRelation__Definitions_2eantisymmetric) ).

fof('$_typeof_Coq.Relations.Relation_Definitions.relation',axiom,
    c_24__type__36___24t(cCoq_2eRelations_2eRelation__Definitions_2erelation) ).

fof('$_typeof_Coq.Setoids.Setoid.Setoid_Theory',axiom,
    c_24__type__32436___24t(cCoq_2eSetoids_2eSetoid_2eSetoid__Theory) ).

fof('$_typeof_Coq.Sets.Relations_1.Relation',axiom,
    c_24__type__36___24t(cCoq_2eSets_2eRelations__1_2eRelation) ).

fof('$_typeof_Coq.Strings.Ascii.Ascii',axiom,
    c_24__type__2438___24t(cCoq_2eStrings_2eAscii_2eAscii) ).

fof('$_typeof_Coq.Strings.Ascii.ascii',axiom,
    cType___24t(cCoq_2eStrings_2eAscii_2eascii) ).

fof('$_typeof_Coq.Strings.String.EmptyString',axiom,
    cCoq_2eStrings_2eString_2estring___24t(cCoq_2eStrings_2eString_2eEmptyString) ).

fof('$_typeof_Coq.Strings.String.string',axiom,
    cType___24t(cCoq_2eStrings_2eString_2estring) ).

fof('$_typeof_Coq.Structures.OrderedType.Compare',axiom,
    c_24__type__23052___24t(cCoq_2eStructures_2eOrderedType_2eCompare) ).

fof('$_typeof_Coq.Structures.OrderedTypeEx.N_as_OT.t',axiom,
    cType___24t(cCoq_2eStructures_2eOrderedTypeEx_2eN__as__OT_2et) ).

fof('$_typeof_Coq.Structures.OrderedTypeEx.Nat_as_OT.t',axiom,
    cType___24t(cCoq_2eStructures_2eOrderedTypeEx_2eNat__as__OT_2et) ).

fof('$_typeof_Coq.Structures.OrderedTypeEx.PositiveOrderedTypeBits.eq',axiom,
    c_24__type__19184___24t(cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2eeq) ).

fof('$_typeof_Coq.Structures.OrderedTypeEx.PositiveOrderedTypeBits.t',axiom,
    cType___24t(cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2et) ).

fof('$_typeof_Coq.Structures.OrderedTypeEx.Positive_as_OT.t',axiom,
    cType___24t(cCoq_2eStructures_2eOrderedTypeEx_2ePositive__as__OT_2et) ).

fof('$_typeof_Coq.Structures.OrderedTypeEx.String_as_OT.t',axiom,
    cType___24t(cCoq_2eStructures_2eOrderedTypeEx_2eString__as__OT_2et) ).

fof('$_typeof_Coq.Structures.OrderedTypeEx.Z_as_OT.t',axiom,
    cType___24t(cCoq_2eStructures_2eOrderedTypeEx_2eZ__as__OT_2et) ).

fof('$_typeof_Coq.Structures.OrdersTac.OEQ',axiom,
    cCoq_2eStructures_2eOrdersTac_2eord___24t(cCoq_2eStructures_2eOrdersTac_2eOEQ) ).

fof('$_typeof_Coq.Structures.OrdersTac.ord',axiom,
    cType___24t(cCoq_2eStructures_2eOrdersTac_2eord) ).

fof('$_typeof_Coq.Vectors.Fin.t',axiom,
    c_24__type__10793___24t(cCoq_2eVectors_2eFin_2et) ).

fof('$_typeof_Coq.Vectors.VectorDef.t',axiom,
    c_24__type__33209___24t(cCoq_2eVectors_2eVectorDef_2et) ).

fof('$_typeof_Coq.ZArith.BinInt.Z.divide',axiom,
    c_24__type__2656___24t(cCoq_2eZArith_2eBinInt_2eZ_2edivide) ).

fof('$_typeof_Coq.ZArith.BinInt.Z.eqf',axiom,
    c_24__type__33637___24t(cCoq_2eZArith_2eBinInt_2eZ_2eeqf) ).

fof('$_typeof_Coq.ZArith.BinInt.Z.gt',axiom,
    c_24__type__2656___24t(cCoq_2eZArith_2eBinInt_2eZ_2egt) ).

fof('$_typeof_Coq.ZArith.BinInt.Z.le',axiom,
    c_24__type__2656___24t(cCoq_2eZArith_2eBinInt_2eZ_2ele) ).

fof('$_typeof_Coq.ZArith.BinInt.Z.lt',axiom,
    c_24__type__2656___24t(cCoq_2eZArith_2eBinInt_2eZ_2elt) ).

fof('$_typeof_Coq.ZArith.BinInt.Zne',axiom,
    c_24__type__2656___24t(cCoq_2eZArith_2eBinInt_2eZne) ).

fof('$_typeof_Coq.ZArith.BinIntDef.Z.abs',axiom,
    c_24__type__19719___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2eabs) ).

fof('$_typeof_Coq.ZArith.BinIntDef.Z.add',axiom,
    c_24__type__19715___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2eadd) ).

fof('$_typeof_Coq.ZArith.BinIntDef.Z.div',axiom,
    c_24__type__19715___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2ediv) ).

fof('$_typeof_Coq.ZArith.BinIntDef.Z.max',axiom,
    c_24__type__19715___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2emax) ).

fof('$_typeof_Coq.ZArith.BinIntDef.Z.min',axiom,
    c_24__type__19715___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2emin) ).

fof('$_typeof_Coq.ZArith.BinIntDef.Z.modulo',axiom,
    c_24__type__19715___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2emodulo) ).

fof('$_typeof_Coq.ZArith.BinIntDef.Z.mul',axiom,
    c_24__type__19715___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2emul) ).

fof('$_typeof_Coq.ZArith.BinIntDef.Z.odd',axiom,
    c_24__type__33620___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2eodd) ).

fof('$_typeof_Coq.ZArith.BinIntDef.Z.of_N',axiom,
    c_24__type__33602___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2eof__N) ).

fof('$_typeof_Coq.ZArith.BinIntDef.Z.opp',axiom,
    c_24__type__19719___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2eopp) ).

fof('$_typeof_Coq.ZArith.BinIntDef.Z.pow',axiom,
    c_24__type__19715___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2epow) ).

fof('$_typeof_Coq.ZArith.BinIntDef.Z.sub',axiom,
    c_24__type__19715___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2esub) ).

fof('$_typeof_Coq.ZArith.BinIntDef.Z.succ',axiom,
    c_24__type__19719___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2esucc) ).

fof('$_typeof_Coq.ZArith.BinIntDef.Z.to_pos',axiom,
    c_24__type__33606___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2eto__pos) ).

fof('$_typeof_Coq.ZArith.Zbool.Zeq_bool',axiom,
    c_24__type__18934___24t(cCoq_2eZArith_2eZbool_2eZeq__bool) ).

fof('$_typeof_Coq.ZArith.Zeven.Zeven',axiom,
    c_24__type__14619___24t(cCoq_2eZArith_2eZeven_2eZeven) ).

fof('$_typeof_Coq.ZArith.Zeven.Zodd',axiom,
    c_24__type__14619___24t(cCoq_2eZArith_2eZeven_2eZodd) ).

fof('$_typeof_Coq.ZArith.Zlogarithm.Is_power',axiom,
    c_24__type__14___24t(cCoq_2eZArith_2eZlogarithm_2eIs__power) ).

fof('$_typeof_Coq.ZArith.Znat.neq',axiom,
    c_24__type__2249___24t(cCoq_2eZArith_2eZnat_2eneq) ).

fof('$_typeof_Coq.ZArith.Znumtheory.Euclid',axiom,
    c_24__type__23401___24t(cCoq_2eZArith_2eZnumtheory_2eEuclid) ).

fof('$_typeof_Coq.ZArith.Zpower.Zdiv_rest_proofs',axiom,
    c_24__type__33431___24t(cCoq_2eZArith_2eZpower_2eZdiv__rest__proofs) ).

fof('$_typeof_Coq.micromega.Env.Env',axiom,
    c_24__type__36___24t(cCoq_2emicromega_2eEnv_2eEnv) ).

fof('$_typeof_Coq.micromega.EnvRing.Mon',axiom,
    cType___24t(cCoq_2emicromega_2eEnvRing_2eMon) ).

fof('$_typeof_Coq.micromega.EnvRing.PExpr',axiom,
    c_24__type__36___24t(cCoq_2emicromega_2eEnvRing_2ePExpr) ).

fof('$_typeof_Coq.micromega.EnvRing.Pol',axiom,
    c_24__type__36___24t(cCoq_2emicromega_2eEnvRing_2ePol) ).

fof('$_typeof_Coq.micromega.Refl.make_conj',axiom,
    c_24__type__23337___24t(cCoq_2emicromega_2eRefl_2emake__conj) ).

fof('$_typeof_Coq.micromega.RingMicromega.Op1',axiom,
    cType___24t(cCoq_2emicromega_2eRingMicromega_2eOp1) ).

fof('$_typeof_Coq.micromega.RingMicromega.Op2',axiom,
    cType___24t(cCoq_2emicromega_2eRingMicromega_2eOp2) ).

fof('$_typeof_Coq.micromega.RingMicromega.PolEnv',axiom,
    c_24__type__36___24t(cCoq_2emicromega_2eRingMicromega_2ePolEnv) ).

fof('$_typeof_Coq.micromega.Tauto.GFormula',axiom,
    c_24__type__32811___24t(cCoq_2emicromega_2eTauto_2eGFormula) ).

fof('$_typeof_Coq.setoid_ring.Field_theory.FExpr',axiom,
    c_24__type__36___24t(cCoq_2esetoid__ring_2eField__theory_2eFExpr) ).

fof('$_typeof_Coq.setoid_ring.Field_theory.linear',axiom,
    c_24__type__36___24t(cCoq_2esetoid__ring_2eField__theory_2elinear) ).

fof('$_typeof_Coq.setoid_ring.InitialRing.gen_phiPOS',axiom,
    c_24__type__21635___24t(cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS) ).

fof('$_typeof_Coq.setoid_ring.InitialRing.gen_phiPOS1',axiom,
    c_24__type__21635___24t(cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS1) ).

fof('$_typeof_Coq.setoid_ring.Ring_polynom.Mon',axiom,
    cType___24t(cCoq_2esetoid__ring_2eRing__polynom_2eMon) ).

fof('$_typeof_Coq.setoid_ring.Ring_polynom.PEX',axiom,
    c_24__type__28893___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePEX) ).

fof('$_typeof_Coq.setoid_ring.Ring_polynom.PEadd',axiom,
    c_24__type__15511___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePEadd) ).

fof('$_typeof_Coq.setoid_ring.Ring_polynom.PEc',axiom,
    c_24__type__15506___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePEc) ).

fof('$_typeof_Coq.setoid_ring.Ring_polynom.PEmul',axiom,
    c_24__type__15511___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePEmul) ).

fof('$_typeof_Coq.setoid_ring.Ring_polynom.PEopp',axiom,
    c_24__type__28902___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePEopp) ).

fof('$_typeof_Coq.setoid_ring.Ring_polynom.PEsub',axiom,
    c_24__type__15511___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePEsub) ).

fof('$_typeof_Coq.setoid_ring.Ring_polynom.PExpr',axiom,
    c_24__type__36___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr) ).

fof('$_typeof_Coq.setoid_ring.Ring_polynom.Pol',axiom,
    c_24__type__36___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePol) ).

fof('$_typeof_Coq.setoid_ring.Ring_tac.ring_subst_niter',axiom,
    cCoq_2eInit_2eDatatypes_2enat___24t(cCoq_2esetoid__ring_2eRing__tac_2ering__subst__niter) ).

fof('$_typeof_Coq.setoid_ring.Ring_theory.IDphi',axiom,
    c_24__type__18451___24t(cCoq_2esetoid__ring_2eRing__theory_2eIDphi) ).

fof('$_typeof_Coq.setoid_ring.Ring_theory.SRopp',axiom,
    c_24__type__18451___24t(cCoq_2esetoid__ring_2eRing__theory_2eSRopp) ).

fof('$_typeof_Coq.setoid_ring.Ring_theory.pow_pos',axiom,
    c_24__type__28920___24t(cCoq_2esetoid__ring_2eRing__theory_2epow__pos) ).

fof('$_typeof_Coq.setoid_ring.Ring_theory.ring_kind',axiom,
    cType___24t(cCoq_2esetoid__ring_2eRing__theory_2ering__kind) ).

fof('$_typeof_IntMap.Fset.FSet',axiom,
    cType___24t(cIntMap_2eFset_2eFSet) ).

fof('$_typeof_IntMap.Fset.FSetDiff',axiom,
    c_24__type__1919___24t(cIntMap_2eFset_2eFSetDiff) ).

fof('$_typeof_IntMap.Fset.FSetInter',axiom,
    c_24__type__1919___24t(cIntMap_2eFset_2eFSetInter) ).

fof('$_typeof_IntMap.Fset.FSetUnion',axiom,
    c_24__type__1919___24t(cIntMap_2eFset_2eFSetUnion) ).

fof('$_typeof_IntMap.Fset.MapDom',axiom,
    c_24__type__1916___24t(cIntMap_2eFset_2eMapDom) ).

fof('$_typeof_IntMap.Fset.MapDomRestrBy',axiom,
    c_24__type__1181___24t(cIntMap_2eFset_2eMapDomRestrBy) ).

fof('$_typeof_IntMap.Fset.MapDomRestrTo',axiom,
    c_24__type__1181___24t(cIntMap_2eFset_2eMapDomRestrTo) ).

fof('$_typeof_IntMap.Fset.MapDom_semantics_2',axiom,
    c_24__type__12842___24t(cIntMap_2eFset_2eMapDom__semantics__2) ).

fof('$_typeof_IntMap.Fset.in_FSet',axiom,
    c_24__type__12830___24t(cIntMap_2eFset_2ein__FSet) ).

fof('$_typeof_IntMap.Fset.in_dom',axiom,
    c_24__type__1901___24t(cIntMap_2eFset_2ein__dom) ).

fof('$_typeof_IntMap.Fset.in_dom_some',axiom,
    c_24__type__12824___24t(cIntMap_2eFset_2ein__dom__some) ).

fof('$_typeof_IntMap.Lsort.ad_monotonic',axiom,
    c_24__type__13189___24t(cIntMap_2eLsort_2ead__monotonic) ).

fof('$_typeof_IntMap.Lsort.alist_nth_ad',axiom,
    c_24__type__13092___24t(cIntMap_2eLsort_2ealist__nth__ad) ).

fof('$_typeof_IntMap.Map.M0',axiom,
    c_24__type__460___24t(cIntMap_2eMap_2eM0) ).

fof('$_typeof_IntMap.Map.M1',axiom,
    c_24__type__93___24t(cIntMap_2eMap_2eM1) ).

fof('$_typeof_IntMap.Map.M2',axiom,
    c_24__type__98___24t(cIntMap_2eMap_2eM2) ).

fof('$_typeof_IntMap.Map.Map',axiom,
    c_24__type__36___24t(cIntMap_2eMap_2eMap) ).

fof('$_typeof_IntMap.Map.MapCard',axiom,
    c_24__type__735___24t(cIntMap_2eMap_2eMapCard) ).

fof('$_typeof_IntMap.Map.MapDelta',axiom,
    c_24__type__98___24t(cIntMap_2eMap_2eMapDelta) ).

fof('$_typeof_IntMap.Map.MapEmptyp',axiom,
    c_24__type__2064___24t(cIntMap_2eMap_2eMapEmptyp) ).

fof('$_typeof_IntMap.Map.MapGet',axiom,
    c_24__type__173___24t(cIntMap_2eMap_2eMapGet) ).

fof('$_typeof_IntMap.Map.MapMerge',axiom,
    c_24__type__98___24t(cIntMap_2eMap_2eMapMerge) ).

fof('$_typeof_IntMap.Map.MapPut',axiom,
    c_24__type__275___24t(cIntMap_2eMap_2eMapPut) ).

fof('$_typeof_IntMap.Map.MapPut1',axiom,
    c_24__type__593___24t(cIntMap_2eMap_2eMapPut1) ).

fof('$_typeof_IntMap.Map.MapPut_behind',axiom,
    c_24__type__275___24t(cIntMap_2eMap_2eMapPut__behind) ).

fof('$_typeof_IntMap.Map.MapRemove',axiom,
    c_24__type__1418___24t(cIntMap_2eMap_2eMapRemove) ).

fof('$_typeof_IntMap.Map.MapSingleton',axiom,
    c_24__type__93___24t(cIntMap_2eMap_2eMapSingleton) ).

fof('$_typeof_IntMap.Map.Map_rec',axiom,
    c_24__type__523___24t(cIntMap_2eMap_2eMap__rec) ).

fof('$_typeof_IntMap.Map.Map_rect',axiom,
    c_24__type__523___24t(cIntMap_2eMap_2eMap__rect) ).

fof('$_typeof_IntMap.Map.ad',axiom,
    cType___24t(cIntMap_2eMap_2ead) ).

fof('$_typeof_IntMap.Map.eqm',axiom,
    c_24__type__1984___24t(cIntMap_2eMap_2eeqm) ).

fof('$_typeof_IntMap.Map.makeM2',axiom,
    c_24__type__98___24t(cIntMap_2eMap_2emakeM2) ).

fof('$_typeof_IntMap.Map.newMap',axiom,
    c_24__type__460___24t(cIntMap_2eMap_2enewMap) ).

fof('$_typeof_IntMap.Map.option_sum',axiom,
    c_24__type__1969___24t(cIntMap_2eMap_2eoption__sum) ).

fof('$_typeof_IntMap.Mapaxioms.eqmap',axiom,
    c_24__type__388___24t(cIntMap_2eMapaxioms_2eeqmap) ).

fof('$_typeof_IntMap.Mapcanon.MapCanonicalize',axiom,
    c_24__type__2078___24t(cIntMap_2eMapcanon_2eMapCanonicalize) ).

fof('$_typeof_IntMap.Mapcanon.mapcanon_exists',axiom,
    c_24__type__2083___24t(cIntMap_2eMapcanon_2emapcanon__exists) ).

fof('$_typeof_IntMap.Mapcard.MapCard_Put_behind_sum',axiom,
    c_24__type__13463___24t(cIntMap_2eMapcard_2eMapCard__Put__behind__sum) ).

fof('$_typeof_IntMap.Mapcard.MapCard_Put_sum',axiom,
    c_24__type__782___24t(cIntMap_2eMapcard_2eMapCard__Put__sum) ).

fof('$_typeof_IntMap.Mapcard.MapCard_Remove_sum',axiom,
    c_24__type__13503___24t(cIntMap_2eMapcard_2eMapCard__Remove__sum) ).

fof('$_typeof_IntMap.Mapcard.MapCard_is_Sn',axiom,
    c_24__type__13532___24t(cIntMap_2eMapcard_2eMapCard__is__Sn) ).

fof('$_typeof_IntMap.Mapcard.MapCard_is_not_O',axiom,
    c_24__type__13363___24t(cIntMap_2eMapcard_2eMapCard__is__not__O) ).

fof('$_typeof_IntMap.Mapiter.MapCollect',axiom,
    c_24__type__1617___24t(cIntMap_2eMapiter_2eMapCollect) ).

fof('$_typeof_IntMap.Mapiter.MapCollect1',axiom,
    c_24__type__2154___24t(cIntMap_2eMapiter_2eMapCollect1) ).

fof('$_typeof_IntMap.Mapiter.MapFold',axiom,
    c_24__type__1742___24t(cIntMap_2eMapiter_2eMapFold) ).

fof('$_typeof_IntMap.Mapiter.MapFold1',axiom,
    c_24__type__1693___24t(cIntMap_2eMapiter_2eMapFold1) ).

fof('$_typeof_IntMap.Mapiter.MapFold1_state',axiom,
    c_24__type__14028___24t(cIntMap_2eMapiter_2eMapFold1__state) ).

fof('$_typeof_IntMap.Mapiter.MapFold_state',axiom,
    c_24__type__14105___24t(cIntMap_2eMapiter_2eMapFold__state) ).

fof('$_typeof_IntMap.Mapiter.MapSweep',axiom,
    c_24__type__13620___24t(cIntMap_2eMapiter_2eMapSweep) ).

fof('$_typeof_IntMap.Mapiter.MapSweep1',axiom,
    c_24__type__13606___24t(cIntMap_2eMapiter_2eMapSweep1) ).

fof('$_typeof_IntMap.Mapiter.MapSweep2',axiom,
    c_24__type__13551___24t(cIntMap_2eMapiter_2eMapSweep2) ).

fof('$_typeof_IntMap.Mapiter.Map_of_alist',axiom,
    c_24__type__1778___24t(cIntMap_2eMapiter_2eMap__of__alist) ).

fof('$_typeof_IntMap.Mapiter.aapp',axiom,
    c_24__type__2174___24t(cIntMap_2eMapiter_2eaapp) ).

fof('$_typeof_IntMap.Mapiter.acons',axiom,
    c_24__type__14182___24t(cIntMap_2eMapiter_2eacons) ).

fof('$_typeof_IntMap.Mapiter.ad_inj',axiom,
    c_24__type__13189___24t(cIntMap_2eMapiter_2ead__inj) ).

fof('$_typeof_IntMap.Mapiter.alist',axiom,
    c_24__type__36___24t(cIntMap_2eMapiter_2ealist) ).

fof('$_typeof_IntMap.Mapiter.alist_of_Map',axiom,
    c_24__type__2181___24t(cIntMap_2eMapiter_2ealist__of__Map) ).

fof('$_typeof_IntMap.Mapiter.alist_semantics',axiom,
    c_24__type__2227___24t(cIntMap_2eMapiter_2ealist__semantics) ).

fof('$_typeof_IntMap.Mapiter.anil',axiom,
    c_24__type__14177___24t(cIntMap_2eMapiter_2eanil) ).

fof('$_typeof_IntMap.Mapsubset.MapDisjoint',axiom,
    c_24__type__1786___24t(cIntMap_2eMapsubset_2eMapDisjoint) ).

fof('$_typeof_IntMap.Mapsubset.MapDisjoint_1',axiom,
    c_24__type__14538___24t(cIntMap_2eMapsubset_2eMapDisjoint__1) ).

fof('$_typeof_IntMap.Mapsubset.MapDisjoint_2',axiom,
    c_24__type__1786___24t(cIntMap_2eMapsubset_2eMapDisjoint__2) ).

fof('$_typeof_IntMap.Mapsubset.MapSubset',axiom,
    c_24__type__1786___24t(cIntMap_2eMapsubset_2eMapSubset) ).

fof('$_typeof_IntMap.Mapsubset.MapSubset_1',axiom,
    c_24__type__14538___24t(cIntMap_2eMapsubset_2eMapSubset__1) ).

fof('$_typeof_IntMap.Mapsubset.MapSubset_2',axiom,
    c_24__type__1786___24t(cIntMap_2eMapsubset_2eMapSubset__2) ).

fof('Coq.Arith.Le.le_S_n',axiom,
    ! [V0__n] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
     => ! [V1__m] :
          ( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
         => ( cCoq_2eInit_2ePeano_2ele___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(V0__n),cCoq_2eInit_2eDatatypes_2eS___24a1(V1__m))
           => cCoq_2eInit_2ePeano_2ele___24a2(V0__n,V1__m) ) ) ) ).

fof('Coq.Arith.Le.le_n_S',axiom,
    ! [V0__n] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
     => ! [V1__m] :
          ( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
         => ( cCoq_2eInit_2ePeano_2ele___24a2(V0__n,V1__m)
           => cCoq_2eInit_2ePeano_2ele___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(V0__n),cCoq_2eInit_2eDatatypes_2eS___24a1(V1__m)) ) ) ) ).

fof('Coq.Arith.Lt.le_lt_or_eq',axiom,
    ! [V0__n] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
     => ! [V1__m] :
          ( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
         => ( cCoq_2eInit_2ePeano_2ele___24a2(V0__n,V1__m)
           => ( cCoq_2eInit_2ePeano_2elt___24a2(V0__n,V1__m)
              | V0__n = V1__m ) ) ) ) ).

fof('Coq.Arith.PeanoNat.Nat.Private_OrderTac.Tac.eq_neq',axiom,
    ! [V0__x] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)
     => ! [V1__y] :
          ( cCoq_2eInit_2eDatatypes_2enat___24t(V1__y)
         => ! [V2__z] :
              ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__z)
             => ( V0__x = V1__y
               => ( V1__y != V2__z
                 => V0__x != V2__z ) ) ) ) ) ).

fof('Coq.Arith.PeanoNat.Nat.Private_OrderTac.Tac.eq_refl',axiom,
    ! [V0__x] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)
     => V0__x = V0__x ) ).

fof('Coq.Arith.PeanoNat.Nat.Private_OrderTac.Tac.eq_sym',axiom,
    ! [V0__x] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)
     => ! [V1__y] :
          ( cCoq_2eInit_2eDatatypes_2enat___24t(V1__y)
         => ( V0__x = V1__y
           => V1__y = V0__x ) ) ) ).

fof('Coq.Arith.PeanoNat.Nat.Private_OrderTac.Tac.le_antisym',axiom,
    ! [V0__x] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)
     => ! [V1__y] :
          ( cCoq_2eInit_2eDatatypes_2enat___24t(V1__y)
         => ( cCoq_2eInit_2ePeano_2ele___24a2(V0__x,V1__y)
           => ( cCoq_2eInit_2ePeano_2ele___24a2(V1__y,V0__x)
             => V0__x = V1__y ) ) ) ) ).

fof('Coq.Arith.PeanoNat.Nat.Private_OrderTac.Tac.le_refl',axiom,
    ! [V0__x] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)
     => cCoq_2eInit_2ePeano_2ele___24a2(V0__x,V0__x) ) ).

fof('Coq.Arith.PeanoNat.Nat.Private_OrderTac.Tac.lt_irrefl',axiom,
    ! [V0__x] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)
     => ~ cCoq_2eInit_2ePeano_2elt___24a2(V0__x,V0__x) ) ).

fof('Coq.Arith.PeanoNat.Nat.Private_OrderTac.Tac.neq_eq',axiom,
    ! [V0__x] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)
     => ! [V1__y] :
          ( cCoq_2eInit_2eDatatypes_2enat___24t(V1__y)
         => ! [V2__z] :
              ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__z)
             => ( V0__x != V1__y
               => ( V1__y = V2__z
                 => V0__x != V2__z ) ) ) ) ) ).

fof('Coq.Arith.PeanoNat.Nat.Private_OrderTac.Tac.not_neq_eq',axiom,
    ! [V0__x] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)
     => ! [V1__y] :
          ( cCoq_2eInit_2eDatatypes_2enat___24t(V1__y)
         => ( ~ ( V0__x != V1__y )
           => V0__x = V1__y ) ) ) ).

fof('Coq.Arith.PeanoNat.Nat.Private_Tac.eq_neq',axiom,
    ! [V0__x] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)
     => ! [V1__y] :
          ( cCoq_2eInit_2eDatatypes_2enat___24t(V1__y)
         => ! [V2__z] :
              ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__z)
             => ( V0__x = V1__y
               => ( V1__y != V2__z
                 => V0__x != V2__z ) ) ) ) ) ).

fof('Coq.Arith.PeanoNat.Nat.Private_Tac.eq_refl',axiom,
    ! [V0__x] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)
     => V0__x = V0__x ) ).

fof('Coq.Arith.PeanoNat.Nat.Private_Tac.eq_sym',axiom,
    ! [V0__x] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)
     => ! [V1__y] :
          ( cCoq_2eInit_2eDatatypes_2enat___24t(V1__y)
         => ( V0__x = V1__y
           => V1__y = V0__x ) ) ) ).

fof('Coq.Arith.PeanoNat.Nat.Private_Tac.le_antisym',axiom,
    ! [V0__x] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)
     => ! [V1__y] :
          ( cCoq_2eInit_2eDatatypes_2enat___24t(V1__y)
         => ( cCoq_2eInit_2ePeano_2ele___24a2(V0__x,V1__y)
           => ( cCoq_2eInit_2ePeano_2ele___24a2(V1__y,V0__x)
             => V0__x = V1__y ) ) ) ) ).

fof('Coq.Arith.PeanoNat.Nat.Private_Tac.neq_eq',axiom,
    ! [V0__x] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)
     => ! [V1__y] :
          ( cCoq_2eInit_2eDatatypes_2enat___24t(V1__y)
         => ! [V2__z] :
              ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__z)
             => ( V0__x != V1__y
               => ( V1__y = V2__z
                 => V0__x != V2__z ) ) ) ) ) ).

fof('Coq.Arith.PeanoNat.Nat.Private_Tac.neq_sym',axiom,
    ! [V0__x] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)
     => ! [V1__y] :
          ( cCoq_2eInit_2eDatatypes_2enat___24t(V1__y)
         => ( V0__x != V1__y
           => V1__y != V0__x ) ) ) ).

fof('Coq.Arith.PeanoNat.Nat.Private_Tac.not_neq_eq',axiom,
    ! [V0__x] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)
     => ! [V1__y] :
          ( cCoq_2eInit_2eDatatypes_2enat___24t(V1__y)
         => ( ~ ( V0__x != V1__y )
           => V0__x = V1__y ) ) ) ).

fof('Coq.Arith.PeanoNat.Nat.add_0_l',axiom,
    ! [V0__n] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
     => cCoq_2eInit_2eNat_2eadd___24a2(cCoq_2eInit_2eDatatypes_2eO,V0__n) = V0__n ) ).

fof('Coq.Arith.PeanoNat.Nat.add_0_r',axiom,
    ! [V0__n] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
     => cCoq_2eInit_2eNat_2eadd___24a2(V0__n,cCoq_2eInit_2eDatatypes_2eO) = V0__n ) ).

fof('Coq.Arith.PeanoNat.Nat.add_comm',axiom,
    ! [V0__n] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
     => ! [V1__m] :
          ( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
         => cCoq_2eInit_2eNat_2eadd___24a2(V0__n,V1__m) = cCoq_2eInit_2eNat_2eadd___24a2(V1__m,V0__n) ) ) ).

fof('Coq.Arith.PeanoNat.Nat.add_shuffle1',axiom,
    ! [V0__n] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
     => ! [V1__m] :
          ( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
         => ! [V2__p] :
              ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__p)
             => ! [V3__q] :
                  ( cCoq_2eInit_2eDatatypes_2enat___24t(V3__q)
                 => cCoq_2eInit_2eNat_2eadd___24a2(cCoq_2eInit_2eNat_2eadd___24a2(V0__n,V1__m),cCoq_2eInit_2eNat_2eadd___24a2(V2__p,V3__q)) = cCoq_2eInit_2eNat_2eadd___24a2(cCoq_2eInit_2eNat_2eadd___24a2(V0__n,V2__p),cCoq_2eInit_2eNat_2eadd___24a2(V1__m,V3__q)) ) ) ) ) ).

fof('Coq.Arith.PeanoNat.Nat.eq_decidable',axiom,
    ! [V0__n] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
     => ! [V1__m] :
          ( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
         => cCoq_2eLogic_2eDecidable_2edecidable___24a1(c_24__prop__36758___24a2(V0__n,V1__m)) ) ) ).

fof('Coq.Arith.PeanoNat.Nat.eq_equiv',axiom,
    cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(cCoq_2eInit_2eDatatypes_2enat,c_3d___24a1(cCoq_2eInit_2eDatatypes_2enat)) ).

fof('Coq.Arith.PeanoNat.Nat.eq_stepl',axiom,
    ! [V0__x] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)
     => ! [V1__y] :
          ( cCoq_2eInit_2eDatatypes_2enat___24t(V1__y)
         => ! [V2__z] :
              ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__z)
             => ( V0__x = V1__y
               => ( V0__x = V2__z
                 => V2__z = V1__y ) ) ) ) ) ).

fof('Coq.Arith.PeanoNat.Nat.eq_sym_iff',axiom,
    ! [V0__x] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)
     => ! [V1__y] :
          ( cCoq_2eInit_2eDatatypes_2enat___24t(V1__y)
         => ( V0__x = V1__y
          <=> V1__y = V0__x ) ) ) ).

fof('Coq.Arith.PeanoNat.Nat.le_0_l',axiom,
    ! [V0__n] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
     => cCoq_2eInit_2ePeano_2ele___24a2(cCoq_2eInit_2eDatatypes_2eO,V0__n) ) ).

fof('Coq.Arith.PeanoNat.Nat.le_antisymm',axiom,
    ! [V0__n] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
     => ! [V1__m] :
          ( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
         => ( cCoq_2eInit_2ePeano_2ele___24a2(V0__n,V1__m)
           => ( cCoq_2eInit_2ePeano_2ele___24a2(V1__m,V0__n)
             => V0__n = V1__m ) ) ) ) ).

fof('Coq.Arith.PeanoNat.Nat.le_gt_cases',axiom,
    ! [V0__n] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
     => ! [V1__m] :
          ( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
         => ( cCoq_2eInit_2ePeano_2ele___24a2(V0__n,V1__m)
            | cCoq_2eInit_2ePeano_2elt___24a2(V1__m,V0__n) ) ) ) ).

fof('Coq.Arith.PeanoNat.Nat.le_succ_diag_r',axiom,
    ! [V0__n] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
     => cCoq_2eInit_2ePeano_2ele___24a2(V0__n,cCoq_2eInit_2eDatatypes_2eS___24a1(V0__n)) ) ).

fof('Coq.Arith.PeanoNat.Nat.le_trans',axiom,
    ! [V0__n] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
     => ! [V1__m] :
          ( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
         => ! [V2__p] :
              ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__p)
             => ( cCoq_2eInit_2ePeano_2ele___24a2(V0__n,V1__m)
               => ( cCoq_2eInit_2ePeano_2ele___24a2(V1__m,V2__p)
                 => cCoq_2eInit_2ePeano_2ele___24a2(V0__n,V2__p) ) ) ) ) ) ).

fof('Coq.Arith.PeanoNat.Nat.lt_eq_cases',axiom,
    ! [V0__n] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
     => ! [V1__m] :
          ( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
         => ( cCoq_2eInit_2ePeano_2ele___24a2(V0__n,V1__m)
          <=> ( cCoq_2eInit_2ePeano_2elt___24a2(V0__n,V1__m)
              | V0__n = V1__m ) ) ) ) ).

fof('Coq.Arith.PeanoNat.Nat.lt_neq',axiom,
    ! [V0__n] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
     => ! [V1__m] :
          ( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
         => ( cCoq_2eInit_2ePeano_2elt___24a2(V0__n,V1__m)
           => V0__n != V1__m ) ) ) ).

fof('Coq.Arith.PeanoNat.Nat.lt_trichotomy',axiom,
    ! [V0__n] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
     => ! [V1__m] :
          ( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
         => ( cCoq_2eInit_2ePeano_2elt___24a2(V0__n,V1__m)
            | V0__n = V1__m
            | cCoq_2eInit_2ePeano_2elt___24a2(V1__m,V0__n) ) ) ) ).

fof('Coq.Arith.PeanoNat.Nat.mul_comm',axiom,
    ! [V0__n] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
     => ! [V1__m] :
          ( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
         => cCoq_2eInit_2eNat_2emul___24a2(V0__n,V1__m) = cCoq_2eInit_2eNat_2emul___24a2(V1__m,V0__n) ) ) ).

fof('Coq.Arith.PeanoNat.Nat.neq_0',axiom,
    ~ ! [V0__n] :
        ( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
       => V0__n = cCoq_2eInit_2eDatatypes_2eO ) ).

fof('Coq.Arith.PeanoNat.Nat.neq_sym',axiom,
    ! [V0__n] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
     => ! [V1__m] :
          ( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
         => ( V0__n != V1__m
           => V1__m != V0__n ) ) ) ).

fof('Coq.Arith.PeanoNat.Nat.nle_succ_0',axiom,
    ! [V0__n] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
     => ~ cCoq_2eInit_2ePeano_2ele___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(V0__n),cCoq_2eInit_2eDatatypes_2eO) ) ).

fof('Coq.Arith.PeanoNat.Nat.one_succ',axiom,
    cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO) = cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO) ).

fof('Coq.Arith.Plus.le_plus_l',axiom,
    ! [V0__n] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
     => ! [V1__m] :
          ( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
         => cCoq_2eInit_2ePeano_2ele___24a2(V0__n,cCoq_2eInit_2eNat_2eadd___24a2(V0__n,V1__m)) ) ) ).

fof('Coq.Arith.Plus.le_plus_r',axiom,
    ! [V0__n] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
     => ! [V1__m] :
          ( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
         => cCoq_2eInit_2ePeano_2ele___24a2(V1__m,cCoq_2eInit_2eNat_2eadd___24a2(V0__n,V1__m)) ) ) ).

fof('Coq.Arith.Plus.plus_Snm_nSm',axiom,
    ! [V0__n] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
     => ! [V1__m] :
          ( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
         => cCoq_2eInit_2eNat_2eadd___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(V0__n),V1__m) = cCoq_2eInit_2eNat_2eadd___24a2(V0__n,cCoq_2eInit_2eDatatypes_2eS___24a1(V1__m)) ) ) ).

fof('Coq.Arith.Plus.plus_assoc_reverse',axiom,
    ! [V0__n] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
     => ! [V1__m] :
          ( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
         => ! [V2__p] :
              ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__p)
             => cCoq_2eInit_2eNat_2eadd___24a2(cCoq_2eInit_2eNat_2eadd___24a2(V0__n,V1__m),V2__p) = cCoq_2eInit_2eNat_2eadd___24a2(V0__n,cCoq_2eInit_2eNat_2eadd___24a2(V1__m,V2__p)) ) ) ) ).

fof('Coq.Arith.Plus.plus_is_O',axiom,
    ! [V0__n] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
     => ! [V1__m] :
          ( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
         => ( cCoq_2eInit_2eNat_2eadd___24a2(V0__n,V1__m) = cCoq_2eInit_2eDatatypes_2eO
           => ( V0__n = cCoq_2eInit_2eDatatypes_2eO
              & V1__m = cCoq_2eInit_2eDatatypes_2eO ) ) ) ) ).

fof('Coq.Arith.Plus.plus_le_compat',axiom,
    ! [V0__n] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
     => ! [V1__m] :
          ( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
         => ! [V2__p] :
              ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__p)
             => ! [V3__q] :
                  ( cCoq_2eInit_2eDatatypes_2enat___24t(V3__q)
                 => ( cCoq_2eInit_2ePeano_2ele___24a2(V0__n,V1__m)
                   => ( cCoq_2eInit_2ePeano_2ele___24a2(V2__p,V3__q)
                     => cCoq_2eInit_2ePeano_2ele___24a2(cCoq_2eInit_2eNat_2eadd___24a2(V0__n,V2__p),cCoq_2eInit_2eNat_2eadd___24a2(V1__m,V3__q)) ) ) ) ) ) ) ).

fof('Coq.Arith.Plus.plus_le_compat_l',axiom,
    ! [V0__n] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
     => ! [V1__m] :
          ( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
         => ! [V2__p] :
              ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__p)
             => ( cCoq_2eInit_2ePeano_2ele___24a2(V0__n,V1__m)
               => cCoq_2eInit_2ePeano_2ele___24a2(cCoq_2eInit_2eNat_2eadd___24a2(V2__p,V0__n),cCoq_2eInit_2eNat_2eadd___24a2(V2__p,V1__m)) ) ) ) ) ).

fof('Coq.Arith.Plus.plus_le_compat_r',axiom,
    ! [V0__n] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
     => ! [V1__m] :
          ( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
         => ! [V2__p] :
              ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__p)
             => ( cCoq_2eInit_2ePeano_2ele___24a2(V0__n,V1__m)
               => cCoq_2eInit_2ePeano_2ele___24a2(cCoq_2eInit_2eNat_2eadd___24a2(V0__n,V2__p),cCoq_2eInit_2eNat_2eadd___24a2(V1__m,V2__p)) ) ) ) ) ).

fof('Coq.Arith.Plus.plus_le_reg_l',axiom,
    ! [V0__n] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
     => ! [V1__m] :
          ( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
         => ! [V2__p] :
              ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__p)
             => ( cCoq_2eInit_2ePeano_2ele___24a2(cCoq_2eInit_2eNat_2eadd___24a2(V2__p,V0__n),cCoq_2eInit_2eNat_2eadd___24a2(V2__p,V1__m))
               => cCoq_2eInit_2ePeano_2ele___24a2(V0__n,V1__m) ) ) ) ) ).

fof('Coq.Arith.Plus.plus_reg_l',axiom,
    ! [V0__n] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
     => ! [V1__m] :
          ( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
         => ! [V2__p] :
              ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__p)
             => ( cCoq_2eInit_2eNat_2eadd___24a2(V2__p,V0__n) = cCoq_2eInit_2eNat_2eadd___24a2(V2__p,V1__m)
               => V0__n = V1__m ) ) ) ) ).

fof('Coq.Bool.Bool.absurd_eq_bool',axiom,
    ! [V0__b] :
      ( cCoq_2eInit_2eDatatypes_2ebool___24t(V0__b)
     => ! [V1__b_27] :
          ( cCoq_2eInit_2eDatatypes_2ebool___24t(V1__b_27)
         => ( p(c_24False)
           => V0__b = V1__b_27 ) ) ) ).

fof('Coq.Bool.Bool.absurd_eq_true',axiom,
    ! [V0__b] :
      ( cCoq_2eInit_2eDatatypes_2ebool___24t(V0__b)
     => ( p(c_24False)
       => V0__b = cCoq_2eInit_2eDatatypes_2etrue ) ) ).

fof('Coq.Bool.Bool.andb_false_r',axiom,
    ! [V0__b] :
      ( cCoq_2eInit_2eDatatypes_2ebool___24t(V0__b)
     => cCoq_2eInit_2eDatatypes_2eandb___24a2(V0__b,cCoq_2eInit_2eDatatypes_2efalse) = cCoq_2eInit_2eDatatypes_2efalse ) ).

fof('Coq.Bool.Bool.andb_if',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__a] :
          ( t(V1__a,V0__A)
         => ! [V2__a_27] :
              ( t(V2__a_27,V0__A)
             => ! [V3__b] :
                  ( cCoq_2eInit_2eDatatypes_2ebool___24t(V3__b)
                 => ! [V4__b_27] :
                      ( cCoq_2eInit_2eDatatypes_2ebool___24t(V4__b_27)
                     => c_24__case__Coq_2eInit_2eDatatypes_2ebool_2436649___24a5(V0__A,V1__a,V2__a_27,V3__b,V4__b_27) = c_24__case__Coq_2eInit_2eDatatypes_2ebool_2436660___24a5(V0__A,V1__a,V2__a_27,V3__b,V4__b_27) ) ) ) ) ) ).

fof('Coq.Bool.Bool.andb_true_r',axiom,
    ! [V0__b] :
      ( cCoq_2eInit_2eDatatypes_2ebool___24t(V0__b)
     => cCoq_2eInit_2eDatatypes_2eandb___24a2(V0__b,cCoq_2eInit_2eDatatypes_2etrue) = V0__b ) ).

fof('Coq.Bool.Bool.eq_true_iff_eq',axiom,
    ! [V0__b1] :
      ( cCoq_2eInit_2eDatatypes_2ebool___24t(V0__b1)
     => ! [V1__b2] :
          ( cCoq_2eInit_2eDatatypes_2ebool___24t(V1__b2)
         => ( ( V0__b1 = cCoq_2eInit_2eDatatypes_2etrue
            <=> V1__b2 = cCoq_2eInit_2eDatatypes_2etrue )
           => V0__b1 = V1__b2 ) ) ) ).

fof('Coq.Bool.Bool.if_negb',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__b] :
          ( cCoq_2eInit_2eDatatypes_2ebool___24t(V1__b)
         => ! [V2__x] :
              ( t(V2__x,V0__A)
             => ! [V3__y] :
                  ( t(V3__y,V0__A)
                 => c_24__case__Coq_2eInit_2eDatatypes_2ebool_242675___24a4(V0__A,V1__b,V2__x,V3__y) = c_24__case__Coq_2eInit_2eDatatypes_2ebool_242680___24a4(V0__A,V1__b,V2__x,V3__y) ) ) ) ) ).

fof('Coq.Bool.Bool.negb_if',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__a] :
          ( t(V1__a,V0__A)
         => ! [V2__a_27] :
              ( t(V2__a_27,V0__A)
             => ! [V3__b] :
                  ( cCoq_2eInit_2eDatatypes_2ebool___24t(V3__b)
                 => c_24__case__Coq_2eInit_2eDatatypes_2ebool_2436665___24a4(V0__A,V1__a,V2__a_27,V3__b) = c_24__case__Coq_2eInit_2eDatatypes_2ebool_2436670___24a4(V0__A,V1__a,V2__a_27,V3__b) ) ) ) ) ).

fof('Coq.Bool.Bool.negb_involutive_reverse',axiom,
    ! [V0__b] :
      ( cCoq_2eInit_2eDatatypes_2ebool___24t(V0__b)
     => V0__b = cCoq_2eInit_2eDatatypes_2enegb___24a1(cCoq_2eInit_2eDatatypes_2enegb___24a1(V0__b)) ) ).

fof('Coq.Bool.Bool.orb_false_l',axiom,
    ! [V0__b] :
      ( cCoq_2eInit_2eDatatypes_2ebool___24t(V0__b)
     => cCoq_2eInit_2eDatatypes_2eorb___24a2(cCoq_2eInit_2eDatatypes_2efalse,V0__b) = V0__b ) ).

fof('Coq.Bool.Bool.orb_false_r',axiom,
    ! [V0__b] :
      ( cCoq_2eInit_2eDatatypes_2ebool___24t(V0__b)
     => cCoq_2eInit_2eDatatypes_2eorb___24a2(V0__b,cCoq_2eInit_2eDatatypes_2efalse) = V0__b ) ).

fof('Coq.Bool.Bool.orb_true_l',axiom,
    ! [V0__b] :
      ( cCoq_2eInit_2eDatatypes_2ebool___24t(V0__b)
     => cCoq_2eInit_2eDatatypes_2eorb___24a2(cCoq_2eInit_2eDatatypes_2etrue,V0__b) = cCoq_2eInit_2eDatatypes_2etrue ) ).

fof('Coq.Bool.Bool.orb_true_r',axiom,
    ! [V0__b] :
      ( cCoq_2eInit_2eDatatypes_2ebool___24t(V0__b)
     => cCoq_2eInit_2eDatatypes_2eorb___24a2(V0__b,cCoq_2eInit_2eDatatypes_2etrue) = cCoq_2eInit_2eDatatypes_2etrue ) ).

fof('Coq.Bool.Bool.trans_eq_bool',axiom,
    ! [V0__x] :
      ( cCoq_2eInit_2eDatatypes_2ebool___24t(V0__x)
     => ! [V1__y] :
          ( cCoq_2eInit_2eDatatypes_2ebool___24t(V1__y)
         => ! [V2__z] :
              ( cCoq_2eInit_2eDatatypes_2ebool___24t(V2__z)
             => ( V0__x = V1__y
               => ( V1__y = V2__z
                 => V0__x = V2__z ) ) ) ) ) ).

fof('Coq.Init.Datatypes.andb_prop',axiom,
    ! [V0__a] :
      ( cCoq_2eInit_2eDatatypes_2ebool___24t(V0__a)
     => ! [V1__b] :
          ( cCoq_2eInit_2eDatatypes_2ebool___24t(V1__b)
         => ( cCoq_2eInit_2eDatatypes_2eandb___24a2(V0__a,V1__b) = cCoq_2eInit_2eDatatypes_2etrue
           => ( V0__a = cCoq_2eInit_2eDatatypes_2etrue
              & V1__b = cCoq_2eInit_2eDatatypes_2etrue ) ) ) ) ).

fof('Coq.Init.Datatypes.bool_ind',axiom,
    ! [V0__P] :
      ( c_24__type__10772___24t(V0__P)
     => ( p(happ(V0__P,cCoq_2eInit_2eDatatypes_2etrue))
       => ( p(happ(V0__P,cCoq_2eInit_2eDatatypes_2efalse))
         => ! [V3__b] :
              ( cCoq_2eInit_2eDatatypes_2ebool___24t(V3__b)
             => p(happ(V0__P,V3__b)) ) ) ) ) ).

fof('Coq.Init.Datatypes.list_ind',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__P] :
          ( c_24__type__1851___24t(V0__A,V1__P)
         => ( p(happ(V1__P,cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)))
           => ( ! [V3__a] :
                  ( t(V3__a,V0__A)
                 => ! [V4__l] :
                      ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V4__l)
                     => ( p(happ(V1__P,V4__l))
                       => p(happ(V1__P,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V3__a,V4__l))) ) ) )
             => ! [V4__l] :
                  ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V4__l)
                 => p(happ(V1__P,V4__l)) ) ) ) ) ) ).

fof('Coq.Init.Datatypes.nat_ind',axiom,
    ! [V0__P] :
      ( c_24__type__10800___24t(V0__P)
     => ( p(happ(V0__P,cCoq_2eInit_2eDatatypes_2eO))
       => ( ! [V2__n] :
              ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__n)
             => ( p(happ(V0__P,V2__n))
               => p(happ(V0__P,cCoq_2eInit_2eDatatypes_2eS___24a1(V2__n))) ) )
         => ! [V3__n] :
              ( cCoq_2eInit_2eDatatypes_2enat___24t(V3__n)
             => p(happ(V0__P,V3__n)) ) ) ) ) ).

fof('Coq.Init.Datatypes.prod_ind',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__B] :
          ( cType___24t(V1__B)
         => ! [V2__P] :
              ( c_24__type__1841___24t(V0__A,V1__B,V2__P)
             => ( ! [V3__a] :
                    ( t(V3__a,V0__A)
                   => ! [V4__b] :
                        ( t(V4__b,V1__B)
                       => p(happ(V2__P,cCoq_2eInit_2eDatatypes_2epair___24a4(V0__A,V1__B,V3__a,V4__b))) ) )
               => ! [V4__p] :
                    ( cCoq_2eInit_2eDatatypes_2eprod___24t(V0__A,V1__B,V4__p)
                   => p(happ(V2__P,V4__p)) ) ) ) ) ) ).

fof('Coq.Init.Datatypes.unit_ind',axiom,
    ! [V0__P] :
      ( c_24__type__10770___24t(V0__P)
     => ( p(happ(V0__P,cCoq_2eInit_2eDatatypes_2ett))
       => ! [V2__u] :
            ( cCoq_2eInit_2eDatatypes_2eunit___24t(V2__u)
           => p(happ(V0__P,V2__u)) ) ) ) ).

fof('Coq.Init.Peano.f_equal_nat',axiom,
    ! [V0__B] :
      ( cType___24t(V0__B)
     => ! [V1__f] :
          ( c_24__type__36708___24t(V0__B,V1__f)
         => ! [V2__x] :
              ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__x)
             => ! [V3__y] :
                  ( cCoq_2eInit_2eDatatypes_2enat___24t(V3__y)
                 => ( V2__x = V3__y
                   => happ(V1__f,V2__x) = happ(V1__f,V3__y) ) ) ) ) ) ).

fof('Coq.Init.Peano.le_n',axiom,
    ! [V0__n] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
     => cCoq_2eInit_2ePeano_2ele___24a2(V0__n,V0__n) ) ).

fof('Coq.Init.Peano.plus_n_O',axiom,
    ! [V0__n] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
     => V0__n = cCoq_2eInit_2eNat_2eadd___24a2(V0__n,cCoq_2eInit_2eDatatypes_2eO) ) ).

fof('Coq.Init.Specif.sig_ind',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__P] :
          ( c_24__type__812___24t(V0__A,V1__P)
         => ! [V2__P] :
              ( c_24__type__1799___24t(V0__A,V1__P,V2__P)
             => ( ! [V3__x] :
                    ( t(V3__x,V0__A)
                   => ( p(happ(V1__P,V3__x))
                     => p(happ(V2__P,cCoq_2eInit_2eSpecif_2eexist___24a3(V0__A,V1__P,V3__x))) ) )
               => ! [V4__s] :
                    ( cCoq_2eInit_2eSpecif_2esig___24t(V0__A,V1__P,V4__s)
                   => p(happ(V2__P,V4__s)) ) ) ) ) ) ).

fof('Coq.Init.Specif.sumbool_ind',axiom,
    ! [V0__A] :
      ( cProp___24t(V0__A)
     => ! [V1__B] :
          ( cProp___24t(V1__B)
         => ! [V2__P] :
              ( c_24__type__422___24t(V0__A,V1__B,V2__P)
             => ( ( p(V0__A)
                 => p(happ(V2__P,cCoq_2eInit_2eSpecif_2eleft___24a2(V0__A,V1__B))) )
               => ( ( p(V1__B)
                   => p(happ(V2__P,cCoq_2eInit_2eSpecif_2eright___24a2(V0__A,V1__B))) )
                 => ! [V5__s] :
                      ( cCoq_2eInit_2eSpecif_2esumbool___24t(V0__A,V1__B,V5__s)
                     => p(happ(V2__P,V5__s)) ) ) ) ) ) ) ).

fof('Coq.Init.Specif.sumor_ind',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__B] :
          ( cProp___24t(V1__B)
         => ! [V2__P] :
              ( c_24__type__1805___24t(V0__A,V1__B,V2__P)
             => ( ! [V3__a] :
                    ( t(V3__a,V0__A)
                   => p(happ(V2__P,cCoq_2eInit_2eSpecif_2einleft___24a3(V0__A,V1__B,V3__a))) )
               => ( ( p(V1__B)
                   => p(happ(V2__P,cCoq_2eInit_2eSpecif_2einright___24a2(V0__A,V1__B))) )
                 => ! [V5__s] :
                      ( cCoq_2eInit_2eSpecif_2esumor___24t(V0__A,V1__B,V5__s)
                     => p(happ(V2__P,V5__s)) ) ) ) ) ) ) ).

fof('Coq.Logic.Decidable.dec_not_not',axiom,
    ! [V0__P] :
      ( cProp___24t(V0__P)
     => ( cCoq_2eLogic_2eDecidable_2edecidable___24a1(V0__P)
       => ( ( ~ p(V0__P)
           => p(c_24False) )
         => p(V0__P) ) ) ) ).

fof('Coq.Logic.EqdepFacts.eq_dep_non_dep',axiom,
    ! [V0__U] :
      ( cType___24t(V0__U)
     => ! [V1__P] :
          ( cType___24t(V1__P)
         => ! [V2__p] :
              ( t(V2__p,V0__U)
             => ! [V3__q] :
                  ( t(V3__q,V0__U)
                 => ! [V4__x] :
                      ( t(V4__x,V1__P)
                     => ! [V5__y] :
                          ( t(V5__y,V1__P)
                         => ( cCoq_2eLogic_2eEqdepFacts_2eeq__dep___24a6(V0__U,c_24__lam__36687___24a2(V0__U,V1__P),V2__p,V4__x,V3__q,V5__y)
                           => V4__x = V5__y ) ) ) ) ) ) ) ).

fof('Coq.Logic.EqdepFacts.f_eq_dep_non_dep',axiom,
    ! [V0__U] :
      ( cType___24t(V0__U)
     => ! [V1__P] :
          ( c_24__type__11408___24t(V0__U,V1__P)
         => ! [V2__R] :
              ( cType___24t(V2__R)
             => ! [V3__p] :
                  ( t(V3__p,V0__U)
                 => ! [V4__q] :
                      ( t(V4__q,V0__U)
                     => ! [V5__x] :
                          ( t(V5__x,happ(V1__P,V3__p))
                         => ! [V6__y] :
                              ( t(V6__y,happ(V1__P,V4__q))
                             => ! [V7__f] :
                                  ( c_24__type__36702___24t(V0__U,V1__P,V2__R,V3__p,V4__q,V7__f)
                                 => ( cCoq_2eLogic_2eEqdepFacts_2eeq__dep___24a6(V0__U,V1__P,V3__p,V5__x,V4__q,V6__y)
                                   => happ(happ(V7__f,V3__p),V5__x) = happ(happ(V7__f,V4__q),V6__y) ) ) ) ) ) ) ) ) ) ).

fof('Coq.Logic.EqdepFacts.internal_eq_sym_internal',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__x] :
          ( t(V1__x,V0__A)
         => ! [V2__y] :
              ( t(V2__y,V0__A)
             => ( V1__x = V2__y
               => V2__y = V1__x ) ) ) ) ).

fof('Coq.Logic.Eqdep_dec.eq_proofs_unicity',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ( ! [V1__x] :
            ( t(V1__x,V0__A)
           => ! [V2__y] :
                ( t(V2__y,V0__A)
               => ( V1__x = V2__y
                  | V1__x != V2__y ) ) )
       => ! [V2__x] :
            ( t(V2__x,V0__A)
           => ! [V3__y] :
                ( t(V3__y,V0__A)
               => ( V2__x = V3__y
                 => ( V2__x = V3__y
                   => c_24Proof = c_24Proof ) ) ) ) ) ) ).

fof('Coq.Logic.Eqdep_dec.eq_proofs_unicity_on',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__x] :
          ( t(V1__x,V0__A)
         => ( ! [V2__y] :
                ( t(V2__y,V0__A)
               => ( V1__x = V2__y
                  | V1__x != V2__y ) )
           => ! [V3__y] :
                ( t(V3__y,V0__A)
               => ( V1__x = V3__y
                 => ( V1__x = V3__y
                   => c_24Proof = c_24Proof ) ) ) ) ) ) ).

fof('Coq.NArith.BinNat.N.Private_OrderTac.Tac.eq_neq',axiom,
    ! [V0__x] :
      ( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__x)
     => ! [V1__y] :
          ( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__y)
         => ! [V2__z] :
              ( cCoq_2eNumbers_2eBinNums_2eN___24t(V2__z)
             => ( V0__x = V1__y
               => ( V1__y != V2__z
                 => V0__x != V2__z ) ) ) ) ) ).

fof('Coq.NArith.BinNat.N.Private_OrderTac.Tac.eq_refl',axiom,
    ! [V0__x] :
      ( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__x)
     => V0__x = V0__x ) ).

fof('Coq.NArith.BinNat.N.Private_OrderTac.Tac.eq_sym',axiom,
    ! [V0__x] :
      ( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__x)
     => ! [V1__y] :
          ( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__y)
         => ( V0__x = V1__y
           => V1__y = V0__x ) ) ) ).

fof('Coq.NArith.BinNat.N.Private_OrderTac.Tac.le_antisym',axiom,
    ! [V0__x] :
      ( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__x)
     => ! [V1__y] :
          ( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__y)
         => ( cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(V0__x,V1__y)
           => ( cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(V1__y,V0__x)
             => V0__x = V1__y ) ) ) ) ).

fof('Coq.NArith.BinNat.N.Private_OrderTac.Tac.le_refl',axiom,
    ! [V0__x] :
      ( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__x)
     => cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(V0__x,V0__x) ) ).

fof('Coq.NArith.BinNat.N.Private_OrderTac.Tac.lt_irrefl',axiom,
    ! [V0__x] :
      ( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__x)
     => ~ cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V0__x,V0__x) ) ).

fof('Coq.NArith.BinNat.N.Private_OrderTac.Tac.neq_eq',axiom,
    ! [V0__x] :
      ( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__x)
     => ! [V1__y] :
          ( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__y)
         => ! [V2__z] :
              ( cCoq_2eNumbers_2eBinNums_2eN___24t(V2__z)
             => ( V0__x != V1__y
               => ( V1__y = V2__z
                 => V0__x != V2__z ) ) ) ) ) ).

fof('Coq.NArith.BinNat.N.Private_OrderTac.Tac.not_neq_eq',axiom,
    ! [V0__x] :
      ( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__x)
     => ! [V1__y] :
          ( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__y)
         => ( ~ ( V0__x != V1__y )
           => V0__x = V1__y ) ) ) ).

fof('Coq.NArith.BinNat.N.Private_Tac.eq_neq',axiom,
    ! [V0__x] :
      ( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__x)
     => ! [V1__y] :
          ( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__y)
         => ! [V2__z] :
              ( cCoq_2eNumbers_2eBinNums_2eN___24t(V2__z)
             => ( V0__x = V1__y
               => ( V1__y != V2__z
                 => V0__x != V2__z ) ) ) ) ) ).

fof('Coq.NArith.BinNat.N.Private_Tac.eq_refl',axiom,
    ! [V0__x] :
      ( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__x)
     => V0__x = V0__x ) ).

fof('Coq.NArith.BinNat.N.Private_Tac.eq_sym',axiom,
    ! [V0__x] :
      ( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__x)
     => ! [V1__y] :
          ( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__y)
         => ( V0__x = V1__y
           => V1__y = V0__x ) ) ) ).

fof('Coq.NArith.BinNat.N.Private_Tac.le_antisym',axiom,
    ! [V0__x] :
      ( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__x)
     => ! [V1__y] :
          ( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__y)
         => ( cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(V0__x,V1__y)
           => ( cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(V1__y,V0__x)
             => V0__x = V1__y ) ) ) ) ).

fof('Coq.NArith.BinNat.N.Private_Tac.neq_eq',axiom,
    ! [V0__x] :
      ( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__x)
     => ! [V1__y] :
          ( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__y)
         => ! [V2__z] :
              ( cCoq_2eNumbers_2eBinNums_2eN___24t(V2__z)
             => ( V0__x != V1__y
               => ( V1__y = V2__z
                 => V0__x != V2__z ) ) ) ) ) ).

fof('Coq.NArith.BinNat.N.Private_Tac.neq_sym',axiom,
    ! [V0__x] :
      ( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__x)
     => ! [V1__y] :
          ( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__y)
         => ( V0__x != V1__y
           => V1__y != V0__x ) ) ) ).

fof('Coq.NArith.BinNat.N.add_0_l',axiom,
    ! [V0__n] :
      ( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
     => cCoq_2eNArith_2eBinNatDef_2eN_2eadd___24a2(cCoq_2eNumbers_2eBinNums_2eN0,V0__n) = V0__n ) ).

fof('Coq.NArith.BinNat.N.add_0_r',axiom,
    ! [V0__n] :
      ( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
     => cCoq_2eNArith_2eBinNatDef_2eN_2eadd___24a2(V0__n,cCoq_2eNumbers_2eBinNums_2eN0) = V0__n ) ).

fof('Coq.NArith.BinNat.N.div2_double',axiom,
    ! [V0__n] :
      ( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
     => cCoq_2eNArith_2eBinNatDef_2eN_2ediv2___24a1(cCoq_2eNArith_2eBinNatDef_2eN_2edouble___24a1(V0__n)) = V0__n ) ).

fof('Coq.NArith.BinNat.N.div2_succ_double',axiom,
    ! [V0__n] :
      ( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
     => cCoq_2eNArith_2eBinNatDef_2eN_2ediv2___24a1(cCoq_2eNArith_2eBinNatDef_2eN_2esucc__double___24a1(V0__n)) = V0__n ) ).

fof('Coq.NArith.BinNat.N.eq_decidable',axiom,
    ! [V0__n] :
      ( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
     => ! [V1__m] :
          ( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
         => cCoq_2eLogic_2eDecidable_2edecidable___24a1(c_24__prop__36756___24a2(V0__n,V1__m)) ) ) ).

fof('Coq.NArith.BinNat.N.eq_equiv',axiom,
    cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(cCoq_2eNumbers_2eBinNums_2eN,c_3d___24a1(cCoq_2eNumbers_2eBinNums_2eN)) ).

fof('Coq.NArith.BinNat.N.eq_stepl',axiom,
    ! [V0__x] :
      ( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__x)
     => ! [V1__y] :
          ( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__y)
         => ! [V2__z] :
              ( cCoq_2eNumbers_2eBinNums_2eN___24t(V2__z)
             => ( V0__x = V1__y
               => ( V0__x = V2__z
                 => V2__z = V1__y ) ) ) ) ) ).

fof('Coq.NArith.BinNat.N.eq_sym_iff',axiom,
    ! [V0__x] :
      ( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__x)
     => ! [V1__y] :
          ( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__y)
         => ( V0__x = V1__y
          <=> V1__y = V0__x ) ) ) ).

fof('Coq.NArith.BinNat.N.eqb_refl',axiom,
    ! [V0__x] :
      ( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__x)
     => cCoq_2eNArith_2eBinNatDef_2eN_2eeqb___24a2(V0__x,V0__x) = cCoq_2eInit_2eDatatypes_2etrue ) ).

fof('Coq.NArith.BinNat.N.eqb_sym',axiom,
    ! [V0__x] :
      ( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__x)
     => ! [V1__y] :
          ( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__y)
         => cCoq_2eNArith_2eBinNatDef_2eN_2eeqb___24a2(V0__x,V1__y) = cCoq_2eNArith_2eBinNatDef_2eN_2eeqb___24a2(V1__y,V0__x) ) ) ).

fof('Coq.NArith.BinNat.N.le_0_l',axiom,
    ! [V0__n] :
      ( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
     => cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eN0,V0__n) ) ).

fof('Coq.NArith.BinNat.N.le_antisymm',axiom,
    ! [V0__n] :
      ( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
     => ! [V1__m] :
          ( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
         => ( cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(V0__n,V1__m)
           => ( cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(V1__m,V0__n)
             => V0__n = V1__m ) ) ) ) ).

fof('Coq.NArith.BinNat.N.lt_trichotomy',axiom,
    ! [V0__n] :
      ( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
     => ! [V1__m] :
          ( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
         => ( cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V0__n,V1__m)
            | V0__n = V1__m
            | cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V1__m,V0__n) ) ) ) ).

fof('Coq.NArith.BinNat.N.lxor_eq',axiom,
    ! [V0__a] :
      ( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__a)
     => ! [V1__a_27] :
          ( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__a_27)
         => ( cCoq_2eNArith_2eBinNatDef_2eN_2elxor___24a2(V0__a,V1__a_27) = cCoq_2eNumbers_2eBinNums_2eN0
           => V0__a = V1__a_27 ) ) ) ).

fof('Coq.NArith.BinNat.N.lxor_nilpotent',axiom,
    ! [V0__a] :
      ( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__a)
     => cCoq_2eNArith_2eBinNatDef_2eN_2elxor___24a2(V0__a,V0__a) = cCoq_2eNumbers_2eBinNums_2eN0 ) ).

fof('Coq.NArith.BinNat.N.mul_comm',axiom,
    ! [V0__n] :
      ( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
     => ! [V1__m] :
          ( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
         => cCoq_2eNArith_2eBinNatDef_2eN_2emul___24a2(V0__n,V1__m) = cCoq_2eNArith_2eBinNatDef_2eN_2emul___24a2(V1__m,V0__n) ) ) ).

fof('Coq.NArith.Ndec.Nbit0_neq',axiom,
    ! [V0__a] :
      ( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__a)
     => ! [V1__a_27] :
          ( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__a_27)
         => ( cCoq_2eNArith_2eBinNatDef_2eN_2eodd___24a1(V0__a) = cCoq_2eInit_2eDatatypes_2efalse
           => ( cCoq_2eNArith_2eBinNatDef_2eN_2eodd___24a1(V1__a_27) = cCoq_2eInit_2eDatatypes_2etrue
             => cCoq_2eNArith_2eBinNatDef_2eN_2eeqb___24a2(V0__a,V1__a_27) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ).

fof('Coq.NArith.Ndec.Ndiv2_eq',axiom,
    ! [V0__a] :
      ( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__a)
     => ! [V1__a_27] :
          ( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__a_27)
         => ( cCoq_2eNArith_2eBinNatDef_2eN_2eeqb___24a2(V0__a,V1__a_27) = cCoq_2eInit_2eDatatypes_2etrue
           => cCoq_2eNArith_2eBinNatDef_2eN_2eeqb___24a2(cCoq_2eNArith_2eBinNatDef_2eN_2ediv2___24a1(V0__a),cCoq_2eNArith_2eBinNatDef_2eN_2ediv2___24a1(V1__a_27)) = cCoq_2eInit_2eDatatypes_2etrue ) ) ) ).

fof('Coq.NArith.Ndec.Neqb_complete',axiom,
    ! [V0__n] :
      ( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
     => ! [V1__n_27] :
          ( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__n_27)
         => ( cCoq_2eNArith_2eBinNatDef_2eN_2eeqb___24a2(V0__n,V1__n_27) = cCoq_2eInit_2eDatatypes_2etrue
           => V0__n = V1__n_27 ) ) ) ).

fof('Coq.NArith.Ndec.Nxor_eq_false',axiom,
    ! [V0__n] :
      ( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
     => ! [V1__n_27] :
          ( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__n_27)
         => ! [V2__p] :
              ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V2__p)
             => ( cCoq_2eNArith_2eBinNatDef_2eN_2elxor___24a2(V0__n,V1__n_27) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(V2__p)
               => cCoq_2eNArith_2eBinNatDef_2eN_2eeqb___24a2(V0__n,V1__n_27) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ).

fof('Coq.NArith.Ndigits.Ndiv2_double',axiom,
    ! [V0__n] :
      ( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
     => ( cCoq_2eNArith_2eNdigits_2eNeven___24a1(V0__n)
       => cCoq_2eNArith_2eBinNatDef_2eN_2edouble___24a1(cCoq_2eNArith_2eBinNatDef_2eN_2ediv2___24a1(V0__n)) = V0__n ) ) ).

fof('Coq.NArith.Ndigits.Ndiv2_double_plus_one',axiom,
    ! [V0__n] :
      ( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
     => ( cCoq_2eNArith_2eNdigits_2eNodd___24a1(V0__n)
       => cCoq_2eNArith_2eBinNatDef_2eN_2esucc__double___24a1(cCoq_2eNArith_2eBinNatDef_2eN_2ediv2___24a1(V0__n)) = V0__n ) ) ).

fof('Coq.NArith.Ndigits.Ndouble_bit0',axiom,
    ! [V0__n] :
      ( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
     => cCoq_2eNArith_2eBinNatDef_2eN_2eodd___24a1(cCoq_2eNArith_2eBinNatDef_2eN_2edouble___24a1(V0__n)) = cCoq_2eInit_2eDatatypes_2efalse ) ).

fof('Coq.NArith.Ndigits.Ndouble_plus_one_bit0',axiom,
    ! [V0__n] :
      ( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
     => cCoq_2eNArith_2eBinNatDef_2eN_2eodd___24a1(cCoq_2eNArith_2eBinNatDef_2eN_2esucc__double___24a1(V0__n)) = cCoq_2eInit_2eDatatypes_2etrue ) ).

fof('Coq.NArith.Ndigits.Nless_def_3',axiom,
    ! [V0__a] :
      ( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__a)
     => ! [V1__a_27] :
          ( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__a_27)
         => cCoq_2eNArith_2eNdigits_2eNless___24a2(cCoq_2eNArith_2eBinNatDef_2eN_2edouble___24a1(V0__a),cCoq_2eNArith_2eBinNatDef_2eN_2esucc__double___24a1(V1__a_27)) = cCoq_2eInit_2eDatatypes_2etrue ) ) ).

fof('Coq.Numbers.BinNums.N_ind',axiom,
    ! [V0__P] :
      ( c_24__type__27___24t(V0__P)
     => ( p(happ(V0__P,cCoq_2eNumbers_2eBinNums_2eN0))
       => ( ! [V2__p] :
              ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V2__p)
             => p(happ(V0__P,cCoq_2eNumbers_2eBinNums_2eNpos___24a1(V2__p))) )
         => ! [V3__n] :
              ( cCoq_2eNumbers_2eBinNums_2eN___24t(V3__n)
             => p(happ(V0__P,V3__n)) ) ) ) ) ).

fof('Coq.Numbers.BinNums.positive_ind',axiom,
    ! [V0__P] :
      ( c_24__type__14___24t(V0__P)
     => ( ! [V1__p] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__p)
           => ( p(happ(V0__P,V1__p))
             => p(happ(V0__P,cCoq_2eNumbers_2eBinNums_2exI___24a1(V1__p))) ) )
       => ( ! [V2__p] :
              ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V2__p)
             => ( p(happ(V0__P,V2__p))
               => p(happ(V0__P,cCoq_2eNumbers_2eBinNums_2exO___24a1(V2__p))) ) )
         => ( p(happ(V0__P,cCoq_2eNumbers_2eBinNums_2exH))
           => ! [V4__p] :
                ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V4__p)
               => p(happ(V0__P,V4__p)) ) ) ) ) ) ).

fof('Coq.PArith.BinPos.Pos.Private_Tac.eq_neq',axiom,
    ! [V0__x] :
      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V0__x)
     => ! [V1__y] :
          ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__y)
         => ! [V2__z] :
              ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V2__z)
             => ( V0__x = V1__y
               => ( V1__y != V2__z
                 => V0__x != V2__z ) ) ) ) ) ).

fof('Coq.PArith.BinPos.Pos.Private_Tac.eq_refl',axiom,
    ! [V0__x] :
      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V0__x)
     => V0__x = V0__x ) ).

fof('Coq.PArith.BinPos.Pos.Private_Tac.eq_sym',axiom,
    ! [V0__x] :
      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V0__x)
     => ! [V1__y] :
          ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__y)
         => ( V0__x = V1__y
           => V1__y = V0__x ) ) ) ).

fof('Coq.PArith.BinPos.Pos.Private_Tac.le_antisym',axiom,
    ! [V0__x] :
      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V0__x)
     => ! [V1__y] :
          ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__y)
         => ( cCoq_2ePArith_2eBinPos_2ePos_2ele___24a2(V0__x,V1__y)
           => ( cCoq_2ePArith_2eBinPos_2ePos_2ele___24a2(V1__y,V0__x)
             => V0__x = V1__y ) ) ) ) ).

fof('Coq.PArith.BinPos.Pos.le_antisym',axiom,
    ! [V0__p] :
      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V0__p)
     => ! [V1__q] :
          ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__q)
         => ( cCoq_2ePArith_2eBinPos_2ePos_2ele___24a2(V0__p,V1__q)
           => ( cCoq_2ePArith_2eBinPos_2ePos_2ele___24a2(V1__q,V0__p)
             => V0__p = V1__q ) ) ) ) ).

fof('Coq.PArith.BinPos.Pos.lt_total',axiom,
    ! [V0__p] :
      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V0__p)
     => ! [V1__q] :
          ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__q)
         => ( cCoq_2ePArith_2eBinPos_2ePos_2elt___24a2(V0__p,V1__q)
            | V0__p = V1__q
            | cCoq_2ePArith_2eBinPos_2ePos_2elt___24a2(V1__q,V0__p) ) ) ) ).

fof('Coq.Reals.RIneq.Req_dec',axiom,
    ! [V0__r1] :
      ( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
     => ! [V1__r2] :
          ( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
         => ( V0__r1 = V1__r2
            | V0__r1 != V1__r2 ) ) ) ).

fof('Coq.Reals.RIneq.Rle_antisym',axiom,
    ! [V0__r1] :
      ( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
     => ! [V1__r2] :
          ( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
         => ( cCoq_2eReals_2eRdefinitions_2eRle___24a2(V0__r1,V1__r2)
           => ( cCoq_2eReals_2eRdefinitions_2eRle___24a2(V1__r2,V0__r1)
             => V0__r1 = V1__r2 ) ) ) ) ).

fof('Coq.Relations.Relations.inverse_image_of_eq',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__B] :
          ( cType___24t(V1__B)
         => ! [V2__f] :
              ( c_24__type__19189___24t(V0__A,V1__B,V2__f)
             => cCoq_2eRelations_2eRelation__Definitions_2eequivalence___24a2(V0__A,c_24__lam__36722___24a3(V0__A,V1__B,V2__f)) ) ) ) ).

fof('Coq.ZArith.BinInt.Z.Private_OrderTac.Tac.eq_neq',axiom,
    ! [V0__x] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
     => ! [V1__y] :
          ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
         => ! [V2__z] :
              ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__z)
             => ( V0__x = V1__y
               => ( V1__y != V2__z
                 => V0__x != V2__z ) ) ) ) ) ).

fof('Coq.ZArith.BinInt.Z.Private_OrderTac.Tac.eq_refl',axiom,
    ! [V0__x] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
     => V0__x = V0__x ) ).

fof('Coq.ZArith.BinInt.Z.Private_OrderTac.Tac.eq_sym',axiom,
    ! [V0__x] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
     => ! [V1__y] :
          ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
         => ( V0__x = V1__y
           => V1__y = V0__x ) ) ) ).

fof('Coq.ZArith.BinInt.Z.Private_OrderTac.Tac.le_antisym',axiom,
    ! [V0__x] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
     => ! [V1__y] :
          ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
         => ( cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__x,V1__y)
           => ( cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V1__y,V0__x)
             => V0__x = V1__y ) ) ) ) ).

fof('Coq.ZArith.BinInt.Z.Private_OrderTac.Tac.le_refl',axiom,
    ! [V0__x] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
     => cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__x,V0__x) ) ).

fof('Coq.ZArith.BinInt.Z.Private_OrderTac.Tac.lt_irrefl',axiom,
    ! [V0__x] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
     => ~ cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__x,V0__x) ) ).

fof('Coq.ZArith.BinInt.Z.Private_OrderTac.Tac.neq_eq',axiom,
    ! [V0__x] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
     => ! [V1__y] :
          ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
         => ! [V2__z] :
              ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__z)
             => ( V0__x != V1__y
               => ( V1__y = V2__z
                 => V0__x != V2__z ) ) ) ) ) ).

fof('Coq.ZArith.BinInt.Z.Private_OrderTac.Tac.neq_sym',axiom,
    ! [V0__x] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
     => ! [V1__y] :
          ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
         => ( V0__x != V1__y
           => V1__y != V0__x ) ) ) ).

fof('Coq.ZArith.BinInt.Z.Private_OrderTac.Tac.not_ge_lt',axiom,
    ! [V0__x] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
     => ! [V1__y] :
          ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
         => ( ~ cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V1__y,V0__x)
           => cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__x,V1__y) ) ) ) ).

fof('Coq.ZArith.BinInt.Z.Private_OrderTac.Tac.not_gt_le',axiom,
    ! [V0__x] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
     => ! [V1__y] :
          ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
         => ( ~ cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V1__y,V0__x)
           => cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__x,V1__y) ) ) ) ).

fof('Coq.ZArith.BinInt.Z.Private_OrderTac.Tac.not_neq_eq',axiom,
    ! [V0__x] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
     => ! [V1__y] :
          ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
         => ( ~ ( V0__x != V1__y )
           => V0__x = V1__y ) ) ) ).

fof('Coq.ZArith.BinInt.Z.Private_Tac.eq_neq',axiom,
    ! [V0__x] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
     => ! [V1__y] :
          ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
         => ! [V2__z] :
              ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__z)
             => ( V0__x = V1__y
               => ( V1__y != V2__z
                 => V0__x != V2__z ) ) ) ) ) ).

fof('Coq.ZArith.BinInt.Z.Private_Tac.eq_refl',axiom,
    ! [V0__x] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
     => V0__x = V0__x ) ).

fof('Coq.ZArith.BinInt.Z.Private_Tac.eq_sym',axiom,
    ! [V0__x] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
     => ! [V1__y] :
          ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
         => ( V0__x = V1__y
           => V1__y = V0__x ) ) ) ).

fof('Coq.ZArith.BinInt.Z.Private_Tac.le_antisym',axiom,
    ! [V0__x] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
     => ! [V1__y] :
          ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
         => ( cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__x,V1__y)
           => ( cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V1__y,V0__x)
             => V0__x = V1__y ) ) ) ) ).

fof('Coq.ZArith.BinInt.Z.Private_Tac.le_refl',axiom,
    ! [V0__x] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
     => cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__x,V0__x) ) ).

fof('Coq.ZArith.BinInt.Z.Private_Tac.lt_irrefl',axiom,
    ! [V0__x] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
     => ~ cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__x,V0__x) ) ).

fof('Coq.ZArith.BinInt.Z.Private_Tac.neq_eq',axiom,
    ! [V0__x] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
     => ! [V1__y] :
          ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
         => ! [V2__z] :
              ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__z)
             => ( V0__x != V1__y
               => ( V1__y = V2__z
                 => V0__x != V2__z ) ) ) ) ) ).

fof('Coq.ZArith.BinInt.Z.Private_Tac.neq_sym',axiom,
    ! [V0__x] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
     => ! [V1__y] :
          ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
         => ( V0__x != V1__y
           => V1__y != V0__x ) ) ) ).

fof('Coq.ZArith.BinInt.Z.Private_Tac.not_neq_eq',axiom,
    ! [V0__x] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
     => ! [V1__y] :
          ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
         => ( ~ ( V0__x != V1__y )
           => V0__x = V1__y ) ) ) ).

fof('Coq.ZArith.BinInt.Z.add_0_l',axiom,
    ! [V0__n] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
     => cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V0__n) = V0__n ) ).

fof('Coq.ZArith.BinInt.Z.add_0_r',axiom,
    ! [V0__n] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
     => cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__n,cCoq_2eNumbers_2eBinNums_2eZ0) = V0__n ) ).

fof('Coq.ZArith.BinInt.Z.add_cancel_l',axiom,
    ! [V0__n] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
     => ! [V1__m] :
          ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
         => ! [V2__p] :
              ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__p)
             => ( cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V2__p,V0__n) = cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V2__p,V1__m)
              <=> V0__n = V1__m ) ) ) ) ).

fof('Coq.ZArith.BinInt.Z.add_cancel_r',axiom,
    ! [V0__n] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
     => ! [V1__m] :
          ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
         => ! [V2__p] :
              ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__p)
             => ( cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__n,V2__p) = cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V1__m,V2__p)
              <=> V0__n = V1__m ) ) ) ) ).

fof('Coq.ZArith.BinInt.Z.add_comm',axiom,
    ! [V0__n] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
     => ! [V1__m] :
          ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
         => cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__n,V1__m) = cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V1__m,V0__n) ) ) ).

fof('Coq.ZArith.BinInt.Z.eq_decidable',axiom,
    ! [V0__n] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
     => ! [V1__m] :
          ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
         => cCoq_2eLogic_2eDecidable_2edecidable___24a1(c_24__prop__19859___24a2(V0__n,V1__m)) ) ) ).

fof('Coq.ZArith.BinInt.Z.eq_equiv',axiom,
    cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(cCoq_2eNumbers_2eBinNums_2eZ,c_3d___24a1(cCoq_2eNumbers_2eBinNums_2eZ)) ).

fof('Coq.ZArith.BinInt.Z.eq_stepl',axiom,
    ! [V0__x] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
     => ! [V1__y] :
          ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
         => ! [V2__z] :
              ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__z)
             => ( V0__x = V1__y
               => ( V0__x = V2__z
                 => V2__z = V1__y ) ) ) ) ) ).

fof('Coq.ZArith.BinInt.Z.eq_sym_iff',axiom,
    ! [V0__x] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
     => ! [V1__y] :
          ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
         => ( V0__x = V1__y
          <=> V1__y = V0__x ) ) ) ).

fof('Coq.ZArith.BinInt.Z.le_antisymm',axiom,
    ! [V0__n] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
     => ! [V1__m] :
          ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
         => ( cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__n,V1__m)
           => ( cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V1__m,V0__n)
             => V0__n = V1__m ) ) ) ) ).

fof('Coq.ZArith.BinInt.Z.le_ge_cases',axiom,
    ! [V0__n] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
     => ! [V1__m] :
          ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
         => ( cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__n,V1__m)
            | cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V1__m,V0__n) ) ) ) ).

fof('Coq.ZArith.BinInt.Z.le_gt_cases',axiom,
    ! [V0__n] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
     => ! [V1__m] :
          ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
         => ( cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__n,V1__m)
            | cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V1__m,V0__n) ) ) ) ).

fof('Coq.ZArith.BinInt.Z.le_refl',axiom,
    ! [V0__n] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
     => cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__n,V0__n) ) ).

fof('Coq.ZArith.BinInt.Z.lt_eq_cases',axiom,
    ! [V0__n] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
     => ! [V1__m] :
          ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
         => ( cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__n,V1__m)
          <=> ( cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__n,V1__m)
              | V0__n = V1__m ) ) ) ) ).

fof('Coq.ZArith.BinInt.Z.lt_neq',axiom,
    ! [V0__n] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
     => ! [V1__m] :
          ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
         => ( cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__n,V1__m)
           => V0__n != V1__m ) ) ) ).

fof('Coq.ZArith.BinInt.Z.lt_total',axiom,
    ! [V0__n] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
     => ! [V1__m] :
          ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
         => ( cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__n,V1__m)
            | V0__n = V1__m
            | cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V1__m,V0__n) ) ) ) ).

fof('Coq.ZArith.BinInt.Z.lt_trichotomy',axiom,
    ! [V0__n] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
     => ! [V1__m] :
          ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
         => ( cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__n,V1__m)
            | V0__n = V1__m
            | cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V1__m,V0__n) ) ) ) ).

fof('Coq.ZArith.BinInt.Z.mul_1_l',axiom,
    ! [V0__n] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
     => cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH),V0__n) = V0__n ) ).

fof('Coq.ZArith.BinInt.Z.mul_1_r',axiom,
    ! [V0__n] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
     => cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n,cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)) = V0__n ) ).

fof('Coq.ZArith.BinInt.Z.mul_comm',axiom,
    ! [V0__n] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
     => ! [V1__m] :
          ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
         => cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n,V1__m) = cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__m,V0__n) ) ) ).

fof('Coq.micromega.ZMicromega.Vars.Facts.MP.Dec.FSetDecideAuxiliary.dec_eq',axiom,
    ! [V0__x] :
      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V0__x)
     => ! [V1__y] :
          ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__y)
         => cCoq_2eLogic_2eDecidable_2edecidable___24a1(c_24__prop__36755___24a2(V0__x,V1__y)) ) ) ).

fof('Coq.micromega.ZMicromega.Vars.Facts.MP.Dec.FSetDecideAuxiliary.eq_Prop',axiom,
    ! [V0__S] :
      ( cType___24t(V0__S)
     => ! [V1__x] :
          ( t(V1__x,V0__S)
         => ! [V2__y] :
              ( t(V2__y,V0__S)
             => cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__elt__Prop___24a1(c_24__prop__36754___24a3(V0__S,V1__x,V2__y)) ) ) ) ).

fof('Coq.micromega.ZMicromega.Vars.Facts.MP.Dec.FSetDecideAuxiliary.eq_refl_iff',axiom,
    ! [V0__x] :
      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V0__x)
     => ( V0__x = V0__x
      <=> p(c_24True) ) ) ).

fof('Coq.omega.OmegaLemmas.new_var',axiom,
    ! [V0__x] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
     => ? [V1__y] :
          ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
          & V0__x = V1__y ) ) ).

fof('Coq.setoid_ring.Ring_theory.Eq_ext',axiom,
    ! [V0__R] :
      ( cType___24t(V0__R)
     => ! [V1__radd] :
          ( c_24__type__1698___24t(V0__R,V1__radd)
         => ! [V2__rmul] :
              ( c_24__type__1698___24t(V0__R,V2__rmul)
             => ! [V3__ropp] :
                  ( c_24__type__11363___24t(V0__R,V3__ropp)
                 => cCoq_2esetoid__ring_2eRing__theory_2ering__eq__ext___24a5(V0__R,V1__radd,V2__rmul,V3__ropp,c_3d___24a1(V0__R)) ) ) ) ) ).

fof('Coq.setoid_ring.Ring_theory.Eqsth',axiom,
    ! [V0__R] :
      ( cType___24t(V0__R)
     => cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(V0__R,c_3d___24a1(V0__R)) ) ).

fof('IntMap.Fset.MapDomRestrBy_semantics',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__B] :
          ( cType___24t(V1__B)
         => ! [V2__m] :
              ( cIntMap_2eMap_2eMap___24t(V0__A,V2__m)
             => ! [V3__m_27] :
                  ( cIntMap_2eMap_2eMap___24t(V1__B,V3__m_27)
                 => cIntMap_2eMap_2eeqm___24a3(V0__A,cIntMap_2eMap_2eMapGet___24a2(V0__A,cIntMap_2eFset_2eMapDomRestrBy___24a4(V0__A,V1__B,V2__m,V3__m_27)),c_24__lam__1889___24a4(V0__A,V1__B,V2__m,V3__m_27)) ) ) ) ) ).

fof('IntMap.Fset.MapDomRestrTo_semantics',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__B] :
          ( cType___24t(V1__B)
         => ! [V2__m] :
              ( cIntMap_2eMap_2eMap___24t(V0__A,V2__m)
             => ! [V3__m_27] :
                  ( cIntMap_2eMap_2eMap___24t(V1__B,V3__m_27)
                 => cIntMap_2eMap_2eeqm___24a3(V0__A,cIntMap_2eMap_2eMapGet___24a2(V0__A,cIntMap_2eFset_2eMapDomRestrTo___24a4(V0__A,V1__B,V2__m,V3__m_27)),c_24__lam__1870___24a4(V0__A,V1__B,V2__m,V3__m_27)) ) ) ) ) ).

fof('IntMap.Fset.MapDom_Dom',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__m] :
          ( cIntMap_2eMap_2eMap___24t(V0__A,V1__m)
         => ! [V2__a] :
              ( cIntMap_2eMap_2ead___24t(V2__a)
             => cIntMap_2eFset_2ein__dom___24a3(V0__A,V2__a,V1__m) = cIntMap_2eFset_2ein__FSet___24a2(V2__a,cIntMap_2eFset_2eMapDom___24a2(V0__A,V1__m)) ) ) ) ).

fof('IntMap.Fset.MapDom_semantics_1',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__m] :
          ( cIntMap_2eMap_2eMap___24t(V0__A,V1__m)
         => ! [V2__a] :
              ( cIntMap_2eMap_2ead___24t(V2__a)
             => ! [V3__y] :
                  ( t(V3__y,V0__A)
                 => ( cIntMap_2eMap_2eMapGet___24a3(V0__A,V1__m,V2__a) = cCoq_2eInit_2eDatatypes_2eSome___24a2(V0__A,V3__y)
                   => cIntMap_2eFset_2ein__FSet___24a2(V2__a,cIntMap_2eFset_2eMapDom___24a2(V0__A,V1__m)) = cCoq_2eInit_2eDatatypes_2etrue ) ) ) ) ) ).

fof('IntMap.Fset.MapDom_semantics_4',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__m] :
          ( cIntMap_2eMap_2eMap___24t(V0__A,V1__m)
         => ! [V2__a] :
              ( cIntMap_2eMap_2ead___24t(V2__a)
             => ( cIntMap_2eFset_2ein__FSet___24a2(V2__a,cIntMap_2eFset_2eMapDom___24a2(V0__A,V1__m)) = cCoq_2eInit_2eDatatypes_2efalse
               => cIntMap_2eMap_2eMapGet___24a3(V0__A,V1__m,V2__a) = cCoq_2eInit_2eDatatypes_2eNone___24a1(V0__A) ) ) ) ) ).

fof('IntMap.Fset.in_dom_M1_1',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__a] :
          ( cIntMap_2eMap_2ead___24t(V1__a)
         => ! [V2__y] :
              ( t(V2__y,V0__A)
             => cIntMap_2eFset_2ein__dom___24a3(V0__A,V1__a,cIntMap_2eMap_2eM1___24a3(V0__A,V1__a,V2__y)) = cCoq_2eInit_2eDatatypes_2etrue ) ) ) ).

fof('IntMap.Fset.in_dom_M1_2',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__a] :
          ( cIntMap_2eMap_2ead___24t(V1__a)
         => ! [V2__a0] :
              ( cIntMap_2eMap_2ead___24t(V2__a0)
             => ! [V3__y] :
                  ( t(V3__y,V0__A)
                 => ( cIntMap_2eFset_2ein__dom___24a3(V0__A,V2__a0,cIntMap_2eMap_2eM1___24a3(V0__A,V1__a,V3__y)) = cCoq_2eInit_2eDatatypes_2etrue
                   => V1__a = V2__a0 ) ) ) ) ) ).

fof('IntMap.Fset.in_dom_delta',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__m] :
          ( cIntMap_2eMap_2eMap___24t(V0__A,V1__m)
         => ! [V2__m_27] :
              ( cIntMap_2eMap_2eMap___24t(V0__A,V2__m_27)
             => ! [V3__a] :
                  ( cIntMap_2eMap_2ead___24t(V3__a)
                 => cIntMap_2eFset_2ein__dom___24a3(V0__A,V3__a,cIntMap_2eMap_2eMapDelta___24a3(V0__A,V1__m,V2__m_27)) = cCoq_2eInit_2eDatatypes_2exorb___24a2(cIntMap_2eFset_2ein__dom___24a3(V0__A,V3__a,V1__m),cIntMap_2eFset_2ein__dom___24a3(V0__A,V3__a,V2__m_27)) ) ) ) ) ).

fof('IntMap.Fset.in_dom_merge',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__m] :
          ( cIntMap_2eMap_2eMap___24t(V0__A,V1__m)
         => ! [V2__m_27] :
              ( cIntMap_2eMap_2eMap___24t(V0__A,V2__m_27)
             => ! [V3__a] :
                  ( cIntMap_2eMap_2ead___24t(V3__a)
                 => cIntMap_2eFset_2ein__dom___24a3(V0__A,V3__a,cIntMap_2eMap_2eMapMerge___24a3(V0__A,V1__m,V2__m_27)) = cCoq_2eInit_2eDatatypes_2eorb___24a2(cIntMap_2eFset_2ein__dom___24a3(V0__A,V3__a,V1__m),cIntMap_2eFset_2ein__dom___24a3(V0__A,V3__a,V2__m_27)) ) ) ) ) ).

fof('IntMap.Fset.in_dom_none',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__m] :
          ( cIntMap_2eMap_2eMap___24t(V0__A,V1__m)
         => ! [V2__a] :
              ( cIntMap_2eMap_2ead___24t(V2__a)
             => ( cIntMap_2eFset_2ein__dom___24a3(V0__A,V2__a,V1__m) = cCoq_2eInit_2eDatatypes_2efalse
               => cIntMap_2eMap_2eMapGet___24a3(V0__A,V1__m,V2__a) = cCoq_2eInit_2eDatatypes_2eNone___24a1(V0__A) ) ) ) ) ).

fof('IntMap.Fset.in_dom_put',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__m] :
          ( cIntMap_2eMap_2eMap___24t(V0__A,V1__m)
         => ! [V2__a0] :
              ( cIntMap_2eMap_2ead___24t(V2__a0)
             => ! [V3__y0] :
                  ( t(V3__y0,V0__A)
                 => ! [V4__a] :
                      ( cIntMap_2eMap_2ead___24t(V4__a)
                     => cIntMap_2eFset_2ein__dom___24a3(V0__A,V4__a,cIntMap_2eMap_2eMapPut___24a4(V0__A,V1__m,V2__a0,V3__y0)) = cCoq_2eInit_2eDatatypes_2eorb___24a2(cCoq_2eNArith_2eBinNatDef_2eN_2eeqb___24a2(V4__a,V2__a0),cIntMap_2eFset_2ein__dom___24a3(V0__A,V4__a,V1__m)) ) ) ) ) ) ).

fof('IntMap.Fset.in_dom_put_behind',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__m] :
          ( cIntMap_2eMap_2eMap___24t(V0__A,V1__m)
         => ! [V2__a0] :
              ( cIntMap_2eMap_2ead___24t(V2__a0)
             => ! [V3__y0] :
                  ( t(V3__y0,V0__A)
                 => ! [V4__a] :
                      ( cIntMap_2eMap_2ead___24t(V4__a)
                     => cIntMap_2eFset_2ein__dom___24a3(V0__A,V4__a,cIntMap_2eMap_2eMapPut__behind___24a4(V0__A,V1__m,V2__a0,V3__y0)) = cCoq_2eInit_2eDatatypes_2eorb___24a2(cCoq_2eNArith_2eBinNatDef_2eN_2eeqb___24a2(V4__a,V2__a0),cIntMap_2eFset_2ein__dom___24a3(V0__A,V4__a,V1__m)) ) ) ) ) ) ).

fof('IntMap.Fset.in_dom_remove',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__m] :
          ( cIntMap_2eMap_2eMap___24t(V0__A,V1__m)
         => ! [V2__a0] :
              ( cIntMap_2eMap_2ead___24t(V2__a0)
             => ! [V3__a] :
                  ( cIntMap_2eMap_2ead___24t(V3__a)
                 => cIntMap_2eFset_2ein__dom___24a3(V0__A,V3__a,cIntMap_2eMap_2eMapRemove___24a3(V0__A,V1__m,V2__a0)) = cCoq_2eInit_2eDatatypes_2eandb___24a2(cCoq_2eInit_2eDatatypes_2enegb___24a1(cCoq_2eNArith_2eBinNatDef_2eN_2eeqb___24a2(V3__a,V2__a0)),cIntMap_2eFset_2ein__dom___24a3(V0__A,V3__a,V1__m)) ) ) ) ) ).

fof('IntMap.Fset.in_dom_restrby',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__B] :
          ( cType___24t(V1__B)
         => ! [V2__m] :
              ( cIntMap_2eMap_2eMap___24t(V0__A,V2__m)
             => ! [V3__m_27] :
                  ( cIntMap_2eMap_2eMap___24t(V1__B,V3__m_27)
                 => ! [V4__a] :
                      ( cIntMap_2eMap_2ead___24t(V4__a)
                     => cIntMap_2eFset_2ein__dom___24a3(V0__A,V4__a,cIntMap_2eFset_2eMapDomRestrBy___24a4(V0__A,V1__B,V2__m,V3__m_27)) = cCoq_2eInit_2eDatatypes_2eandb___24a2(cIntMap_2eFset_2ein__dom___24a3(V0__A,V4__a,V2__m),cCoq_2eInit_2eDatatypes_2enegb___24a1(cIntMap_2eFset_2ein__dom___24a3(V1__B,V4__a,V3__m_27))) ) ) ) ) ) ).

fof('IntMap.Fset.in_dom_restrto',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__B] :
          ( cType___24t(V1__B)
         => ! [V2__m] :
              ( cIntMap_2eMap_2eMap___24t(V0__A,V2__m)
             => ! [V3__m_27] :
                  ( cIntMap_2eMap_2eMap___24t(V1__B,V3__m_27)
                 => ! [V4__a] :
                      ( cIntMap_2eMap_2ead___24t(V4__a)
                     => cIntMap_2eFset_2ein__dom___24a3(V0__A,V4__a,cIntMap_2eFset_2eMapDomRestrTo___24a4(V0__A,V1__B,V2__m,V3__m_27)) = cCoq_2eInit_2eDatatypes_2eandb___24a2(cIntMap_2eFset_2ein__dom___24a3(V0__A,V4__a,V2__m),cIntMap_2eFset_2ein__dom___24a3(V1__B,V4__a,V3__m_27)) ) ) ) ) ) ).

fof('IntMap.Lsort.ad_comp_double_monotonic',axiom,
    ! [V0__pf] :
      ( c_24__type__13191___24t(V0__pf)
     => ( cIntMap_2eLsort_2ead__monotonic___24a1(V0__pf)
       => cIntMap_2eLsort_2ead__monotonic___24a1(c_24__lam__13198___24a1(V0__pf)) ) ) ).

fof('IntMap.Lsort.ad_comp_double_plus_un_monotonic',axiom,
    ! [V0__pf] :
      ( c_24__type__13191___24t(V0__pf)
     => ( cIntMap_2eLsort_2ead__monotonic___24a1(V0__pf)
       => cIntMap_2eLsort_2ead__monotonic___24a1(c_24__lam__13200___24a1(V0__pf)) ) ) ).

fof('IntMap.Lsort.alist_canonical',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__l] :
          ( cIntMap_2eMapiter_2ealist___24t(V0__A,V1__l)
         => ! [V2__l_27] :
              ( cIntMap_2eMapiter_2ealist___24t(V0__A,V2__l_27)
             => ( cIntMap_2eMap_2eeqm___24a3(V0__A,cIntMap_2eMapiter_2ealist__semantics___24a2(V0__A,V1__l),cIntMap_2eMapiter_2ealist__semantics___24a2(V0__A,V2__l_27))
               => ( cIntMap_2eLsort_2ealist__sorted__2___24a2(V0__A,V1__l)
                 => ( cIntMap_2eLsort_2ealist__sorted__2___24a2(V0__A,V2__l_27)
                   => V1__l = V2__l_27 ) ) ) ) ) ) ).

fof('IntMap.Lsort.alist_of_Map_sorts',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__m] :
          ( cIntMap_2eMap_2eMap___24t(V0__A,V1__m)
         => cIntMap_2eLsort_2ealist__sorted___24a2(V0__A,cIntMap_2eMapiter_2ealist__of__Map___24a2(V0__A,V1__m)) = cCoq_2eInit_2eDatatypes_2etrue ) ) ).

fof('IntMap.Lsort.alist_of_Map_sorts1',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__m] :
          ( cIntMap_2eMap_2eMap___24t(V0__A,V1__m)
         => cIntMap_2eLsort_2ealist__sorted__1___24a2(V0__A,cIntMap_2eMapiter_2ealist__of__Map___24a2(V0__A,V1__m)) ) ) ).

fof('IntMap.Lsort.alist_of_Map_sorts2',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__m] :
          ( cIntMap_2eMap_2eMap___24t(V0__A,V1__m)
         => cIntMap_2eLsort_2ealist__sorted__2___24a2(V0__A,cIntMap_2eMapiter_2ealist__of__Map___24a2(V0__A,V1__m)) ) ) ).

fof('IntMap.Lsort.alist_sorted_1_imp_2',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__l] :
          ( cIntMap_2eMapiter_2ealist___24t(V0__A,V1__l)
         => ( cIntMap_2eLsort_2ealist__sorted__1___24a2(V0__A,V1__l)
           => cIntMap_2eLsort_2ealist__sorted__2___24a2(V0__A,V1__l) ) ) ) ).

fof('IntMap.Lsort.alist_sorted_imp_1',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__l] :
          ( cIntMap_2eMapiter_2ealist___24t(V0__A,V1__l)
         => ( cIntMap_2eLsort_2ealist__sorted___24a2(V0__A,V1__l) = cCoq_2eInit_2eDatatypes_2etrue
           => cIntMap_2eLsort_2ealist__sorted__1___24a2(V0__A,V1__l) ) ) ) ).

fof('IntMap.Map.M1_semantics_1',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__a] :
          ( cIntMap_2eMap_2ead___24t(V1__a)
         => ! [V2__y] :
              ( t(V2__y,V0__A)
             => cIntMap_2eMap_2eMapGet___24a3(V0__A,cIntMap_2eMap_2eM1___24a3(V0__A,V1__a,V2__y),V1__a) = cCoq_2eInit_2eDatatypes_2eSome___24a2(V0__A,V2__y) ) ) ) ).

fof('IntMap.Map.M1_semantics_2',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__a] :
          ( cIntMap_2eMap_2ead___24t(V1__a)
         => ! [V2__a_27] :
              ( cIntMap_2eMap_2ead___24t(V2__a_27)
             => ! [V3__y] :
                  ( t(V3__y,V0__A)
                 => ( cCoq_2eNArith_2eBinNatDef_2eN_2eeqb___24a2(V1__a,V2__a_27) = cCoq_2eInit_2eDatatypes_2efalse
                   => cIntMap_2eMap_2eMapGet___24a3(V0__A,cIntMap_2eMap_2eM1___24a3(V0__A,V1__a,V3__y),V2__a_27) = cCoq_2eInit_2eDatatypes_2eNone___24a1(V0__A) ) ) ) ) ) ).

fof('IntMap.Map.Map2_semantics_1',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__m] :
          ( cIntMap_2eMap_2eMap___24t(V0__A,V1__m)
         => ! [V2__m_27] :
              ( cIntMap_2eMap_2eMap___24t(V0__A,V2__m_27)
             => cIntMap_2eMap_2eeqm___24a3(V0__A,cIntMap_2eMap_2eMapGet___24a2(V0__A,V1__m),c_24__lam__13247___24a3(V0__A,V1__m,V2__m_27)) ) ) ) ).

fof('IntMap.Map.Map2_semantics_2',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__m] :
          ( cIntMap_2eMap_2eMap___24t(V0__A,V1__m)
         => ! [V2__m_27] :
              ( cIntMap_2eMap_2eMap___24t(V0__A,V2__m_27)
             => cIntMap_2eMap_2eeqm___24a3(V0__A,cIntMap_2eMap_2eMapGet___24a2(V0__A,V2__m_27),c_24__lam__13256___24a3(V0__A,V1__m,V2__m_27)) ) ) ) ).

fof('IntMap.Map.Map2_semantics_3',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__m] :
          ( cIntMap_2eMap_2eMap___24t(V0__A,V1__m)
         => ! [V2__m_27] :
              ( cIntMap_2eMap_2eMap___24t(V0__A,V2__m_27)
             => cIntMap_2eMap_2eeqm___24a3(V0__A,cIntMap_2eMap_2eMapGet___24a2(V0__A,cIntMap_2eMap_2eM2___24a3(V0__A,V1__m,V2__m_27)),c_24__lam__13275___24a3(V0__A,V1__m,V2__m_27)) ) ) ) ).

fof('IntMap.Map.MapDelta_semantics',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__m] :
          ( cIntMap_2eMap_2eMap___24t(V0__A,V1__m)
         => ! [V2__m_27] :
              ( cIntMap_2eMap_2eMap___24t(V0__A,V2__m_27)
             => cIntMap_2eMap_2eeqm___24a3(V0__A,cIntMap_2eMap_2eMapGet___24a2(V0__A,cIntMap_2eMap_2eMapDelta___24a3(V0__A,V1__m,V2__m_27)),c_24__lam__2038___24a3(V0__A,V1__m,V2__m_27)) ) ) ) ).

fof('IntMap.Map.MapDelta_semantics_1',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__m] :
          ( cIntMap_2eMap_2eMap___24t(V0__A,V1__m)
         => ! [V2__m_27] :
              ( cIntMap_2eMap_2eMap___24t(V0__A,V2__m_27)
             => ! [V3__a] :
                  ( cIntMap_2eMap_2ead___24t(V3__a)
                 => ( cIntMap_2eMap_2eMapGet___24a3(V0__A,V1__m,V3__a) = cCoq_2eInit_2eDatatypes_2eNone___24a1(V0__A)
                   => ( cIntMap_2eMap_2eMapGet___24a3(V0__A,V2__m_27,V3__a) = cCoq_2eInit_2eDatatypes_2eNone___24a1(V0__A)
                     => cIntMap_2eMap_2eMapGet___24a3(V0__A,cIntMap_2eMap_2eMapDelta___24a3(V0__A,V1__m,V2__m_27),V3__a) = cCoq_2eInit_2eDatatypes_2eNone___24a1(V0__A) ) ) ) ) ) ) ).

fof('IntMap.Map.MapDelta_semantics_comm',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__m] :
          ( cIntMap_2eMap_2eMap___24t(V0__A,V1__m)
         => ! [V2__m_27] :
              ( cIntMap_2eMap_2eMap___24t(V0__A,V2__m_27)
             => cIntMap_2eMap_2eeqm___24a3(V0__A,cIntMap_2eMap_2eMapGet___24a2(V0__A,cIntMap_2eMap_2eMapDelta___24a3(V0__A,V1__m,V2__m_27)),cIntMap_2eMap_2eMapGet___24a2(V0__A,cIntMap_2eMap_2eMapDelta___24a3(V0__A,V2__m_27,V1__m))) ) ) ) ).

fof('IntMap.Map.MapEmptyp_complete',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__m] :
          ( cIntMap_2eMap_2eMap___24t(V0__A,V1__m)
         => ( cIntMap_2eMap_2eMapEmptyp___24a2(V0__A,V1__m) = cCoq_2eInit_2eDatatypes_2etrue
           => V1__m = cIntMap_2eMap_2eM0___24a1(V0__A) ) ) ) ).

fof('IntMap.Map.MapGet_M2_bit_0',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__m] :
          ( cIntMap_2eMap_2eMap___24t(V0__A,V1__m)
         => ! [V2__m_27] :
              ( cIntMap_2eMap_2eMap___24t(V0__A,V2__m_27)
             => ! [V3__m_27_27] :
                  ( cIntMap_2eMap_2eMap___24t(V0__A,V3__m_27_27)
                 => ! [V4__a] :
                      ( cIntMap_2eMap_2ead___24t(V4__a)
                     => c_24__case__Coq_2eInit_2eDatatypes_2ebool_2413267___24a5(V0__A,V1__m,V2__m_27,V3__m_27_27,V4__a) = cIntMap_2eMap_2eMapGet___24a3(V0__A,V1__m,cCoq_2eNArith_2eBinNatDef_2eN_2ediv2___24a1(V4__a)) ) ) ) ) ) ).

fof('IntMap.Map.MapGet_M2_bit_0_0',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__a] :
          ( cIntMap_2eMap_2ead___24t(V1__a)
         => ( cCoq_2eNArith_2eBinNatDef_2eN_2eodd___24a1(V1__a) = cCoq_2eInit_2eDatatypes_2efalse
           => ! [V3__m] :
                ( cIntMap_2eMap_2eMap___24t(V0__A,V3__m)
               => ! [V4__m_27] :
                    ( cIntMap_2eMap_2eMap___24t(V0__A,V4__m_27)
                   => cIntMap_2eMap_2eMapGet___24a3(V0__A,cIntMap_2eMap_2eM2___24a3(V0__A,V3__m,V4__m_27),V1__a) = cIntMap_2eMap_2eMapGet___24a3(V0__A,V3__m,cCoq_2eNArith_2eBinNatDef_2eN_2ediv2___24a1(V1__a)) ) ) ) ) ) ).

fof('IntMap.Map.MapGet_M2_bit_0_1',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__a] :
          ( cIntMap_2eMap_2ead___24t(V1__a)
         => ( cCoq_2eNArith_2eBinNatDef_2eN_2eodd___24a1(V1__a) = cCoq_2eInit_2eDatatypes_2etrue
           => ! [V3__m] :
                ( cIntMap_2eMap_2eMap___24t(V0__A,V3__m)
               => ! [V4__m_27] :
                    ( cIntMap_2eMap_2eMap___24t(V0__A,V4__m_27)
                   => cIntMap_2eMap_2eMapGet___24a3(V0__A,cIntMap_2eMap_2eM2___24a3(V0__A,V3__m,V4__m_27),V1__a) = cIntMap_2eMap_2eMapGet___24a3(V0__A,V4__m_27,cCoq_2eNArith_2eBinNatDef_2eN_2ediv2___24a1(V1__a)) ) ) ) ) ) ).

fof('IntMap.Map.MapGet_M2_bit_0_2',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__m] :
          ( cIntMap_2eMap_2eMap___24t(V0__A,V1__m)
         => ! [V2__m_27] :
              ( cIntMap_2eMap_2eMap___24t(V0__A,V2__m_27)
             => ! [V3__m_27_27] :
                  ( cIntMap_2eMap_2eMap___24t(V0__A,V3__m_27_27)
                 => ! [V4__a] :
                      ( cIntMap_2eMap_2ead___24t(V4__a)
                     => cIntMap_2eMap_2eMapGet___24a3(V0__A,c_24__case__Coq_2eInit_2eDatatypes_2ebool_2413309___24a5(V0__A,V1__m,V2__m_27,V3__m_27_27,V4__a),V4__a) = cIntMap_2eMap_2eMapGet___24a3(V0__A,V2__m_27,cCoq_2eNArith_2eBinNatDef_2eN_2ediv2___24a1(V4__a)) ) ) ) ) ) ).

fof('IntMap.Map.MapGet_M2_bit_0_if',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__m] :
          ( cIntMap_2eMap_2eMap___24t(V0__A,V1__m)
         => ! [V2__m_27] :
              ( cIntMap_2eMap_2eMap___24t(V0__A,V2__m_27)
             => ! [V3__a] :
                  ( cIntMap_2eMap_2ead___24t(V3__a)
                 => cIntMap_2eMap_2eMapGet___24a3(V0__A,cIntMap_2eMap_2eM2___24a3(V0__A,V1__m,V2__m_27),V3__a) = c_24__case__Coq_2eInit_2eDatatypes_2ebool_241994___24a4(V0__A,V1__m,V2__m_27,V3__a) ) ) ) ) ).

fof('IntMap.Map.MapGet_if_commute',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__b] :
          ( cCoq_2eInit_2eDatatypes_2ebool___24t(V1__b)
         => ! [V2__m] :
              ( cIntMap_2eMap_2eMap___24t(V0__A,V2__m)
             => ! [V3__m_27] :
                  ( cIntMap_2eMap_2eMap___24t(V0__A,V3__m_27)
                 => ! [V4__a] :
                      ( cIntMap_2eMap_2ead___24t(V4__a)
                     => cIntMap_2eMap_2eMapGet___24a3(V0__A,c_24__case__Coq_2eInit_2eDatatypes_2ebool_2413293___24a4(V0__A,V1__b,V2__m,V3__m_27),V4__a) = c_24__case__Coq_2eInit_2eDatatypes_2ebool_2413299___24a5(V0__A,V1__b,V2__m,V3__m_27,V4__a) ) ) ) ) ) ).

fof('IntMap.Map.MapGet_if_same',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__m] :
          ( cIntMap_2eMap_2eMap___24t(V0__A,V1__m)
         => ! [V2__b] :
              ( cCoq_2eInit_2eDatatypes_2ebool___24t(V2__b)
             => ! [V3__a] :
                  ( cIntMap_2eMap_2ead___24t(V3__a)
                 => cIntMap_2eMap_2eMapGet___24a3(V0__A,c_24__case__Coq_2eInit_2eDatatypes_2ebool_2413303___24a3(V0__A,V1__m,V2__b),V3__a) = cIntMap_2eMap_2eMapGet___24a3(V0__A,V1__m,V3__a) ) ) ) ) ).

fof('IntMap.Map.MapMerge_semantics',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__m] :
          ( cIntMap_2eMap_2eMap___24t(V0__A,V1__m)
         => ! [V2__m_27] :
              ( cIntMap_2eMap_2eMap___24t(V0__A,V2__m_27)
             => cIntMap_2eMap_2eeqm___24a3(V0__A,cIntMap_2eMap_2eMapGet___24a2(V0__A,cIntMap_2eMap_2eMapMerge___24a3(V0__A,V1__m,V2__m_27)),c_24__lam__380___24a3(V0__A,V1__m,V2__m_27)) ) ) ) ).

fof('IntMap.Map.MapPut_behind_new',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__m] :
          ( cIntMap_2eMap_2eMap___24t(V0__A,V1__m)
         => ! [V2__a] :
              ( cIntMap_2eMap_2ead___24t(V2__a)
             => ! [V3__y] :
                  ( t(V3__y,V0__A)
                 => cIntMap_2eMap_2eMapGet___24a3(V0__A,cIntMap_2eMap_2eMapPut__behind___24a4(V0__A,V1__m,V2__a,V3__y),V2__a) = c_24__case__Coq_2eInit_2eDatatypes_2eoption_2413336___24a4(V0__A,V1__m,V2__a,V3__y) ) ) ) ) ).

fof('IntMap.Map.MapPut_behind_semantics',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__m] :
          ( cIntMap_2eMap_2eMap___24t(V0__A,V1__m)
         => ! [V2__a] :
              ( cIntMap_2eMap_2ead___24t(V2__a)
             => ! [V3__y] :
                  ( t(V3__y,V0__A)
                 => cIntMap_2eMap_2eeqm___24a3(V0__A,cIntMap_2eMap_2eMapGet___24a2(V0__A,cIntMap_2eMap_2eMapPut__behind___24a4(V0__A,V1__m,V2__a,V3__y)),c_24__lam__718___24a4(V0__A,V1__m,V2__a,V3__y)) ) ) ) ) ).

fof('IntMap.Map.MapPut_behind_semantics_3_1',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__m] :
          ( cIntMap_2eMap_2eMap___24t(V0__A,V1__m)
         => ! [V2__m_27] :
              ( cIntMap_2eMap_2eMap___24t(V0__A,V2__m_27)
             => ! [V3__a] :
                  ( cIntMap_2eMap_2ead___24t(V3__a)
                 => ! [V4__y] :
                      ( t(V4__y,V0__A)
                     => cIntMap_2eMap_2eMapPut__behind___24a4(V0__A,cIntMap_2eMap_2eM2___24a3(V0__A,V1__m,V2__m_27),V3__a,V4__y) = c_24__case__Coq_2eInit_2eDatatypes_2ebool_242000___24a5(V0__A,V1__m,V2__m_27,V3__a,V4__y) ) ) ) ) ) ).

fof('IntMap.Map.MapPut_semantics',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__m] :
          ( cIntMap_2eMap_2eMap___24t(V0__A,V1__m)
         => ! [V2__a] :
              ( cIntMap_2eMap_2ead___24t(V2__a)
             => ! [V3__y] :
                  ( t(V3__y,V0__A)
                 => cIntMap_2eMap_2eeqm___24a3(V0__A,cIntMap_2eMap_2eMapGet___24a2(V0__A,cIntMap_2eMap_2eMapPut___24a4(V0__A,V1__m,V2__a,V3__y)),c_24__lam__292___24a4(V0__A,V1__m,V2__a,V3__y)) ) ) ) ) ).

fof('IntMap.Map.MapPut_semantics_3_1',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__m] :
          ( cIntMap_2eMap_2eMap___24t(V0__A,V1__m)
         => ! [V2__m_27] :
              ( cIntMap_2eMap_2eMap___24t(V0__A,V2__m_27)
             => ! [V3__a] :
                  ( cIntMap_2eMap_2ead___24t(V3__a)
                 => ! [V4__y] :
                      ( t(V4__y,V0__A)
                     => cIntMap_2eMap_2eMapPut___24a4(V0__A,cIntMap_2eMap_2eM2___24a3(V0__A,V1__m,V2__m_27),V3__a,V4__y) = c_24__case__Coq_2eInit_2eDatatypes_2ebool_24282___24a5(V0__A,V1__m,V2__m_27,V3__a,V4__y) ) ) ) ) ) ).

fof('IntMap.Map.MapRemove_semantics',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__m] :
          ( cIntMap_2eMap_2eMap___24t(V0__A,V1__m)
         => ! [V2__a] :
              ( cIntMap_2eMap_2ead___24t(V2__a)
             => cIntMap_2eMap_2eeqm___24a3(V0__A,cIntMap_2eMap_2eMapGet___24a2(V0__A,cIntMap_2eMap_2eMapRemove___24a3(V0__A,V1__m,V2__a)),c_24__lam__2008___24a3(V0__A,V1__m,V2__a)) ) ) ) ).

fof('IntMap.Map.Map_ind',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__P] :
          ( c_24__type__554___24t(V0__A,V1__P)
         => ( p(happ(V1__P,cIntMap_2eMap_2eM0___24a1(V0__A)))
           => ( ! [V3__a] :
                  ( cIntMap_2eMap_2ead___24t(V3__a)
                 => ! [V4__a] :
                      ( t(V4__a,V0__A)
                     => p(happ(V1__P,cIntMap_2eMap_2eM1___24a3(V0__A,V3__a,V4__a))) ) )
             => ( ! [V4__m] :
                    ( cIntMap_2eMap_2eMap___24t(V0__A,V4__m)
                   => ( p(happ(V1__P,V4__m))
                     => ! [V6__m] :
                          ( cIntMap_2eMap_2eMap___24t(V0__A,V6__m)
                         => ( p(happ(V1__P,V6__m))
                           => p(happ(V1__P,cIntMap_2eMap_2eM2___24a3(V0__A,V4__m,V6__m))) ) ) ) )
               => ! [V5__m] :
                    ( cIntMap_2eMap_2eMap___24t(V0__A,V5__m)
                   => p(happ(V1__P,V5__m)) ) ) ) ) ) ) ).

fof('IntMap.Map.makeM2_M2',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__m] :
          ( cIntMap_2eMap_2eMap___24t(V0__A,V1__m)
         => ! [V2__m_27] :
              ( cIntMap_2eMap_2eMap___24t(V0__A,V2__m_27)
             => cIntMap_2eMap_2eeqm___24a3(V0__A,cIntMap_2eMap_2eMapGet___24a2(V0__A,cIntMap_2eMap_2emakeM2___24a3(V0__A,V1__m,V2__m_27)),cIntMap_2eMap_2eMapGet___24a2(V0__A,cIntMap_2eMap_2eM2___24a3(V0__A,V1__m,V2__m_27))) ) ) ) ).

fof('IntMap.Mapaxioms.MapDelta_as_DomRestrBy',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__m] :
          ( cIntMap_2eMap_2eMap___24t(V0__A,V1__m)
         => ! [V2__m_27] :
              ( cIntMap_2eMap_2eMap___24t(V0__A,V2__m_27)
             => cIntMap_2eMapaxioms_2eeqmap___24a3(V0__A,cIntMap_2eMap_2eMapDelta___24a3(V0__A,V1__m,V2__m_27),cIntMap_2eFset_2eMapDomRestrBy___24a4(V0__A,V0__A,cIntMap_2eMap_2eMapMerge___24a3(V0__A,V1__m,V2__m_27),cIntMap_2eFset_2eMapDomRestrTo___24a4(V0__A,V0__A,V1__m,V2__m_27))) ) ) ) ).

fof('IntMap.Mapaxioms.MapDelta_as_DomRestrBy_2',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__m] :
          ( cIntMap_2eMap_2eMap___24t(V0__A,V1__m)
         => ! [V2__m_27] :
              ( cIntMap_2eMap_2eMap___24t(V0__A,V2__m_27)
             => cIntMap_2eMapaxioms_2eeqmap___24a3(V0__A,cIntMap_2eMap_2eMapDelta___24a3(V0__A,V1__m,V2__m_27),cIntMap_2eFset_2eMapDomRestrBy___24a4(V0__A,V0__A,cIntMap_2eMap_2eMapMerge___24a3(V0__A,V1__m,V2__m_27),cIntMap_2eFset_2eMapDomRestrTo___24a4(V0__A,V0__A,V2__m_27,V1__m))) ) ) ) ).

fof('IntMap.Mapaxioms.MapDelta_as_Merge',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__m] :
          ( cIntMap_2eMap_2eMap___24t(V0__A,V1__m)
         => ! [V2__m_27] :
              ( cIntMap_2eMap_2eMap___24t(V0__A,V2__m_27)
             => cIntMap_2eMapaxioms_2eeqmap___24a3(V0__A,cIntMap_2eMap_2eMapDelta___24a3(V0__A,V1__m,V2__m_27),cIntMap_2eMap_2eMapMerge___24a3(V0__A,cIntMap_2eFset_2eMapDomRestrBy___24a4(V0__A,V0__A,V1__m,V2__m_27),cIntMap_2eFset_2eMapDomRestrBy___24a4(V0__A,V0__A,V2__m_27,V1__m))) ) ) ) ).

fof('IntMap.Mapaxioms.MapDelta_empty_m',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__m] :
          ( cIntMap_2eMap_2eMap___24t(V0__A,V1__m)
         => cIntMap_2eMapaxioms_2eeqmap___24a3(V0__A,cIntMap_2eMap_2eMapDelta___24a3(V0__A,cIntMap_2eMap_2eM0___24a1(V0__A),V1__m),V1__m) ) ) ).

fof('IntMap.Mapaxioms.MapDelta_empty_m_1',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__m] :
          ( cIntMap_2eMap_2eMap___24t(V0__A,V1__m)
         => cIntMap_2eMap_2eMapDelta___24a3(V0__A,cIntMap_2eMap_2eM0___24a1(V0__A),V1__m) = V1__m ) ) ).

fof('IntMap.Mapaxioms.MapDelta_ext',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__m1] :
          ( cIntMap_2eMap_2eMap___24t(V0__A,V1__m1)
         => ! [V2__m2] :
              ( cIntMap_2eMap_2eMap___24t(V0__A,V2__m2)
             => ! [V3__m_271] :
                  ( cIntMap_2eMap_2eMap___24t(V0__A,V3__m_271)
                 => ! [V4__m_272] :
                      ( cIntMap_2eMap_2eMap___24t(V0__A,V4__m_272)
                     => ( cIntMap_2eMapaxioms_2eeqmap___24a3(V0__A,V1__m1,V3__m_271)
                       => ( cIntMap_2eMapaxioms_2eeqmap___24a3(V0__A,V2__m2,V4__m_272)
                         => cIntMap_2eMapaxioms_2eeqmap___24a3(V0__A,cIntMap_2eMap_2eMapDelta___24a3(V0__A,V1__m1,V2__m2),cIntMap_2eMap_2eMapDelta___24a3(V0__A,V3__m_271,V4__m_272)) ) ) ) ) ) ) ) ).

fof('IntMap.Mapaxioms.MapDelta_ext_l',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__m1] :
          ( cIntMap_2eMap_2eMap___24t(V0__A,V1__m1)
         => ! [V2__m_271] :
              ( cIntMap_2eMap_2eMap___24t(V0__A,V2__m_271)
             => ! [V3__m2] :
                  ( cIntMap_2eMap_2eMap___24t(V0__A,V3__m2)
                 => ( cIntMap_2eMapaxioms_2eeqmap___24a3(V0__A,V1__m1,V2__m_271)
                   => cIntMap_2eMapaxioms_2eeqmap___24a3(V0__A,cIntMap_2eMap_2eMapDelta___24a3(V0__A,V1__m1,V3__m2),cIntMap_2eMap_2eMapDelta___24a3(V0__A,V2__m_271,V3__m2)) ) ) ) ) ) ).

fof('IntMap.Mapaxioms.MapDelta_ext_r',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__m1] :
          ( cIntMap_2eMap_2eMap___24t(V0__A,V1__m1)
         => ! [V2__m2] :
              ( cIntMap_2eMap_2eMap___24t(V0__A,V2__m2)
             => ! [V3__m_272] :
                  ( cIntMap_2eMap_2eMap___24t(V0__A,V3__m_272)
                 => ( cIntMap_2eMapaxioms_2eeqmap___24a3(V0__A,V2__m2,V3__m_272)
                   => cIntMap_2eMapaxioms_2eeqmap___24a3(V0__A,cIntMap_2eMap_2eMapDelta___24a3(V0__A,V1__m1,V2__m2),cIntMap_2eMap_2eMapDelta___24a3(V0__A,V1__m1,V3__m_272)) ) ) ) ) ) ).

fof('IntMap.Mapaxioms.MapDelta_m_empty',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__m] :
          ( cIntMap_2eMap_2eMap___24t(V0__A,V1__m)
         => cIntMap_2eMapaxioms_2eeqmap___24a3(V0__A,cIntMap_2eMap_2eMapDelta___24a3(V0__A,V1__m,cIntMap_2eMap_2eM0___24a1(V0__A)),V1__m) ) ) ).

fof('IntMap.Mapaxioms.MapDelta_m_empty_1',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__m] :
          ( cIntMap_2eMap_2eMap___24t(V0__A,V1__m)
         => cIntMap_2eMap_2eMapDelta___24a3(V0__A,V1__m,cIntMap_2eMap_2eM0___24a1(V0__A)) = V1__m ) ) ).

fof('IntMap.Mapaxioms.MapDelta_nilpotent',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__m] :
          ( cIntMap_2eMap_2eMap___24t(V0__A,V1__m)
         => cIntMap_2eMapaxioms_2eeqmap___24a3(V0__A,cIntMap_2eMap_2eMapDelta___24a3(V0__A,V1__m,V1__m),cIntMap_2eMap_2eM0___24a1(V0__A)) ) ) ).

fof('IntMap.Mapaxioms.MapDelta_sym',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__m] :
          ( cIntMap_2eMap_2eMap___24t(V0__A,V1__m)
         => ! [V2__m_27] :
              ( cIntMap_2eMap_2eMap___24t(V0__A,V2__m_27)
             => cIntMap_2eMapaxioms_2eeqmap___24a3(V0__A,cIntMap_2eMap_2eMapDelta___24a3(V0__A,V1__m,V2__m_27),cIntMap_2eMap_2eMapDelta___24a3(V0__A,V2__m_27,V1__m)) ) ) ) ).

fof('IntMap.Mapaxioms.MapDomRestrBy_By',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__B] :
          ( cType___24t(V1__B)
         => ! [V2__m] :
              ( cIntMap_2eMap_2eMap___24t(V0__A,V2__m)
             => ! [V3__m_27] :
                  ( cIntMap_2eMap_2eMap___24t(V1__B,V3__m_27)
                 => ! [V4__m_27_27] :
                      ( cIntMap_2eMap_2eMap___24t(V1__B,V4__m_27_27)
                     => cIntMap_2eMapaxioms_2eeqmap___24a3(V0__A,cIntMap_2eFset_2eMapDomRestrBy___24a4(V0__A,V1__B,cIntMap_2eFset_2eMapDomRestrBy___24a4(V0__A,V1__B,V2__m,V3__m_27),V4__m_27_27),cIntMap_2eFset_2eMapDomRestrBy___24a4(V0__A,V1__B,V2__m,cIntMap_2eMap_2eMapMerge___24a3(V1__B,V3__m_27,V4__m_27_27))) ) ) ) ) ) ).

fof('IntMap.Mapaxioms.MapDomRestrBy_By_comm',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__B] :
          ( cType___24t(V1__B)
         => ! [V2__C] :
              ( cType___24t(V2__C)
             => ! [V3__m] :
                  ( cIntMap_2eMap_2eMap___24t(V0__A,V3__m)
                 => ! [V4__m_27] :
                      ( cIntMap_2eMap_2eMap___24t(V1__B,V4__m_27)
                     => ! [V5__m_27_27] :
                          ( cIntMap_2eMap_2eMap___24t(V2__C,V5__m_27_27)
                         => cIntMap_2eMapaxioms_2eeqmap___24a3(V0__A,cIntMap_2eFset_2eMapDomRestrBy___24a4(V0__A,V2__C,cIntMap_2eFset_2eMapDomRestrBy___24a4(V0__A,V1__B,V3__m,V4__m_27),V5__m_27_27),cIntMap_2eFset_2eMapDomRestrBy___24a4(V0__A,V1__B,cIntMap_2eFset_2eMapDomRestrBy___24a4(V0__A,V2__C,V3__m,V5__m_27_27),V4__m_27)) ) ) ) ) ) ) ).

fof('IntMap.Mapaxioms.MapDomRestrBy_Dom',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__B] :
          ( cType___24t(V1__B)
         => ! [V2__m] :
              ( cIntMap_2eMap_2eMap___24t(V0__A,V2__m)
             => ! [V3__m_27] :
                  ( cIntMap_2eMap_2eMap___24t(V1__B,V3__m_27)
                 => cIntMap_2eMapaxioms_2eeqmap___24a3(V0__A,cIntMap_2eFset_2eMapDomRestrBy___24a4(V0__A,V1__B,V2__m,V3__m_27),cIntMap_2eFset_2eMapDomRestrBy___24a4(V0__A,cCoq_2eInit_2eDatatypes_2eunit,V2__m,cIntMap_2eFset_2eMapDom___24a2(V1__B,V3__m_27))) ) ) ) ) ).

fof('IntMap.Mapaxioms.MapDomRestrBy_To',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__B] :
          ( cType___24t(V1__B)
         => ! [V2__C] :
              ( cType___24t(V2__C)
             => ! [V3__m] :
                  ( cIntMap_2eMap_2eMap___24t(V0__A,V3__m)
                 => ! [V4__m_27] :
                      ( cIntMap_2eMap_2eMap___24t(V1__B,V4__m_27)
                     => ! [V5__m_27_27] :
                          ( cIntMap_2eMap_2eMap___24t(V2__C,V5__m_27_27)
                         => cIntMap_2eMapaxioms_2eeqmap___24a3(V0__A,cIntMap_2eFset_2eMapDomRestrBy___24a4(V0__A,V2__C,cIntMap_2eFset_2eMapDomRestrTo___24a4(V0__A,V1__B,V3__m,V4__m_27),V5__m_27_27),cIntMap_2eFset_2eMapDomRestrTo___24a4(V0__A,V1__B,V3__m,cIntMap_2eFset_2eMapDomRestrBy___24a4(V1__B,V2__C,V4__m_27,V5__m_27_27))) ) ) ) ) ) ) ).

fof('IntMap.Mapaxioms.MapDomRestrBy_To_comm',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__B] :
          ( cType___24t(V1__B)
         => ! [V2__C] :
              ( cType___24t(V2__C)
             => ! [V3__m] :
                  ( cIntMap_2eMap_2eMap___24t(V0__A,V3__m)
                 => ! [V4__m_27] :
                      ( cIntMap_2eMap_2eMap___24t(V1__B,V4__m_27)
                     => ! [V5__m_27_27] :
                          ( cIntMap_2eMap_2eMap___24t(V2__C,V5__m_27_27)
                         => cIntMap_2eMapaxioms_2eeqmap___24a3(V0__A,cIntMap_2eFset_2eMapDomRestrBy___24a4(V0__A,V2__C,cIntMap_2eFset_2eMapDomRestrTo___24a4(V0__A,V1__B,V3__m,V4__m_27),V5__m_27_27),cIntMap_2eFset_2eMapDomRestrTo___24a4(V0__A,V1__B,cIntMap_2eFset_2eMapDomRestrBy___24a4(V0__A,V2__C,V3__m,V5__m_27_27),V4__m_27)) ) ) ) ) ) ) ).

fof('IntMap.Mapaxioms.MapDomRestrBy_empty_m',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__B] :
          ( cType___24t(V1__B)
         => ! [V2__m] :
              ( cIntMap_2eMap_2eMap___24t(V1__B,V2__m)
             => cIntMap_2eMapaxioms_2eeqmap___24a3(V0__A,cIntMap_2eFset_2eMapDomRestrBy___24a4(V0__A,V1__B,cIntMap_2eMap_2eM0___24a1(V0__A),V2__m),cIntMap_2eMap_2eM0___24a1(V0__A)) ) ) ) ).

fof('IntMap.Mapaxioms.MapDomRestrBy_empty_m_1',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__B] :
          ( cType___24t(V1__B)
         => ! [V2__m] :
              ( cIntMap_2eMap_2eMap___24t(V1__B,V2__m)
             => cIntMap_2eFset_2eMapDomRestrBy___24a4(V0__A,V1__B,cIntMap_2eMap_2eM0___24a1(V0__A),V2__m) = cIntMap_2eMap_2eM0___24a1(V0__A) ) ) ) ).

fof('IntMap.Mapaxioms.MapDomRestrBy_ext',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__B] :
          ( cType___24t(V1__B)
         => ! [V2__m1] :
              ( cIntMap_2eMap_2eMap___24t(V0__A,V2__m1)
             => ! [V3__m2] :
                  ( cIntMap_2eMap_2eMap___24t(V1__B,V3__m2)
                 => ! [V4__m_271] :
                      ( cIntMap_2eMap_2eMap___24t(V0__A,V4__m_271)
                     => ! [V5__m_272] :
                          ( cIntMap_2eMap_2eMap___24t(V1__B,V5__m_272)
                         => ( cIntMap_2eMapaxioms_2eeqmap___24a3(V0__A,V2__m1,V4__m_271)
                           => ( cIntMap_2eMapaxioms_2eeqmap___24a3(V1__B,V3__m2,V5__m_272)
                             => cIntMap_2eMapaxioms_2eeqmap___24a3(V0__A,cIntMap_2eFset_2eMapDomRestrBy___24a4(V0__A,V1__B,V2__m1,V3__m2),cIntMap_2eFset_2eMapDomRestrBy___24a4(V0__A,V1__B,V4__m_271,V5__m_272)) ) ) ) ) ) ) ) ) ).

fof('IntMap.Mapaxioms.MapDomRestrBy_ext_l',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__B] :
          ( cType___24t(V1__B)
         => ! [V2__m1] :
              ( cIntMap_2eMap_2eMap___24t(V0__A,V2__m1)
             => ! [V3__m2] :
                  ( cIntMap_2eMap_2eMap___24t(V1__B,V3__m2)
                 => ! [V4__m_271] :
                      ( cIntMap_2eMap_2eMap___24t(V0__A,V4__m_271)
                     => ( cIntMap_2eMapaxioms_2eeqmap___24a3(V0__A,V2__m1,V4__m_271)
                       => cIntMap_2eMapaxioms_2eeqmap___24a3(V0__A,cIntMap_2eFset_2eMapDomRestrBy___24a4(V0__A,V1__B,V2__m1,V3__m2),cIntMap_2eFset_2eMapDomRestrBy___24a4(V0__A,V1__B,V4__m_271,V3__m2)) ) ) ) ) ) ) ).

fof('IntMap.Mapaxioms.MapDomRestrBy_ext_r',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__B] :
          ( cType___24t(V1__B)
         => ! [V2__m1] :
              ( cIntMap_2eMap_2eMap___24t(V0__A,V2__m1)
             => ! [V3__m2] :
                  ( cIntMap_2eMap_2eMap___24t(V1__B,V3__m2)
                 => ! [V4__m_272] :
                      ( cIntMap_2eMap_2eMap___24t(V1__B,V4__m_272)
                     => ( cIntMap_2eMapaxioms_2eeqmap___24a3(V1__B,V3__m2,V4__m_272)
                       => cIntMap_2eMapaxioms_2eeqmap___24a3(V0__A,cIntMap_2eFset_2eMapDomRestrBy___24a4(V0__A,V1__B,V2__m1,V3__m2),cIntMap_2eFset_2eMapDomRestrBy___24a4(V0__A,V1__B,V2__m1,V4__m_272)) ) ) ) ) ) ) ).

fof('IntMap.Mapaxioms.MapDomRestrBy_m_empty',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__B] :
          ( cType___24t(V1__B)
         => ! [V2__m] :
              ( cIntMap_2eMap_2eMap___24t(V0__A,V2__m)
             => cIntMap_2eMapaxioms_2eeqmap___24a3(V0__A,cIntMap_2eFset_2eMapDomRestrBy___24a4(V0__A,V1__B,V2__m,cIntMap_2eMap_2eM0___24a1(V1__B)),V2__m) ) ) ) ).

fof('IntMap.Mapaxioms.MapDomRestrBy_m_empty_1',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__B] :
          ( cType___24t(V1__B)
         => ! [V2__m] :
              ( cIntMap_2eMap_2eMap___24t(V0__A,V2__m)
             => cIntMap_2eFset_2eMapDomRestrBy___24a4(V0__A,V1__B,V2__m,cIntMap_2eMap_2eM0___24a1(V1__B)) = V2__m ) ) ) ).

fof('IntMap.Mapaxioms.MapDomRestrBy_m_m',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__m] :
          ( cIntMap_2eMap_2eMap___24t(V0__A,V1__m)
         => cIntMap_2eMapaxioms_2eeqmap___24a3(V0__A,cIntMap_2eFset_2eMapDomRestrBy___24a4(V0__A,cCoq_2eInit_2eDatatypes_2eunit,V1__m,cIntMap_2eFset_2eMapDom___24a2(V0__A,V1__m)),cIntMap_2eMap_2eM0___24a1(V0__A)) ) ) ).

fof('IntMap.Mapaxioms.MapDomRestrBy_m_m_1',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__m] :
          ( cIntMap_2eMap_2eMap___24t(V0__A,V1__m)
         => cIntMap_2eMapaxioms_2eeqmap___24a3(V0__A,cIntMap_2eFset_2eMapDomRestrBy___24a4(V0__A,V0__A,V1__m,V1__m),cIntMap_2eMap_2eM0___24a1(V0__A)) ) ) ).

fof('IntMap.Mapaxioms.MapDomRestrTo_By',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__B] :
          ( cType___24t(V1__B)
         => ! [V2__C] :
              ( cType___24t(V2__C)
             => ! [V3__m] :
                  ( cIntMap_2eMap_2eMap___24t(V0__A,V3__m)
                 => ! [V4__m_27] :
                      ( cIntMap_2eMap_2eMap___24t(V1__B,V4__m_27)
                     => ! [V5__m_27_27] :
                          ( cIntMap_2eMap_2eMap___24t(V2__C,V5__m_27_27)
                         => cIntMap_2eMapaxioms_2eeqmap___24a3(V0__A,cIntMap_2eFset_2eMapDomRestrTo___24a4(V0__A,V2__C,cIntMap_2eFset_2eMapDomRestrBy___24a4(V0__A,V1__B,V3__m,V4__m_27),V5__m_27_27),cIntMap_2eFset_2eMapDomRestrTo___24a4(V0__A,V2__C,V3__m,cIntMap_2eFset_2eMapDomRestrBy___24a4(V2__C,V1__B,V5__m_27_27,V4__m_27))) ) ) ) ) ) ) ).

fof('IntMap.Mapaxioms.MapDomRestrTo_By_comm',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__B] :
          ( cType___24t(V1__B)
         => ! [V2__C] :
              ( cType___24t(V2__C)
             => ! [V3__m] :
                  ( cIntMap_2eMap_2eMap___24t(V0__A,V3__m)
                 => ! [V4__m_27] :
                      ( cIntMap_2eMap_2eMap___24t(V1__B,V4__m_27)
                     => ! [V5__m_27_27] :
                          ( cIntMap_2eMap_2eMap___24t(V2__C,V5__m_27_27)
                         => cIntMap_2eMapaxioms_2eeqmap___24a3(V0__A,cIntMap_2eFset_2eMapDomRestrTo___24a4(V0__A,V2__C,cIntMap_2eFset_2eMapDomRestrBy___24a4(V0__A,V1__B,V3__m,V4__m_27),V5__m_27_27),cIntMap_2eFset_2eMapDomRestrBy___24a4(V0__A,V1__B,cIntMap_2eFset_2eMapDomRestrTo___24a4(V0__A,V2__C,V3__m,V5__m_27_27),V4__m_27)) ) ) ) ) ) ) ).

fof('IntMap.Mapaxioms.MapDomRestrTo_Dom',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__B] :
          ( cType___24t(V1__B)
         => ! [V2__m] :
              ( cIntMap_2eMap_2eMap___24t(V0__A,V2__m)
             => ! [V3__m_27] :
                  ( cIntMap_2eMap_2eMap___24t(V1__B,V3__m_27)
                 => cIntMap_2eMapaxioms_2eeqmap___24a3(V0__A,cIntMap_2eFset_2eMapDomRestrTo___24a4(V0__A,V1__B,V2__m,V3__m_27),cIntMap_2eFset_2eMapDomRestrTo___24a4(V0__A,cCoq_2eInit_2eDatatypes_2eunit,V2__m,cIntMap_2eFset_2eMapDom___24a2(V1__B,V3__m_27))) ) ) ) ) ).

fof('IntMap.Mapaxioms.MapDomRestrTo_To_comm',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__B] :
          ( cType___24t(V1__B)
         => ! [V2__C] :
              ( cType___24t(V2__C)
             => ! [V3__m] :
                  ( cIntMap_2eMap_2eMap___24t(V0__A,V3__m)
                 => ! [V4__m_27] :
                      ( cIntMap_2eMap_2eMap___24t(V1__B,V4__m_27)
                     => ! [V5__m_27_27] :
                          ( cIntMap_2eMap_2eMap___24t(V2__C,V5__m_27_27)
                         => cIntMap_2eMapaxioms_2eeqmap___24a3(V0__A,cIntMap_2eFset_2eMapDomRestrTo___24a4(V0__A,V2__C,cIntMap_2eFset_2eMapDomRestrTo___24a4(V0__A,V1__B,V3__m,V4__m_27),V5__m_27_27),cIntMap_2eFset_2eMapDomRestrTo___24a4(V0__A,V1__B,cIntMap_2eFset_2eMapDomRestrTo___24a4(V0__A,V2__C,V3__m,V5__m_27_27),V4__m_27)) ) ) ) ) ) ) ).

fof('IntMap.Mapaxioms.MapDomRestrTo_assoc',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__B] :
          ( cType___24t(V1__B)
         => ! [V2__C] :
              ( cType___24t(V2__C)
             => ! [V3__m] :
                  ( cIntMap_2eMap_2eMap___24t(V0__A,V3__m)
                 => ! [V4__m_27] :
                      ( cIntMap_2eMap_2eMap___24t(V1__B,V4__m_27)
                     => ! [V5__m_27_27] :
                          ( cIntMap_2eMap_2eMap___24t(V2__C,V5__m_27_27)
                         => cIntMap_2eMapaxioms_2eeqmap___24a3(V0__A,cIntMap_2eFset_2eMapDomRestrTo___24a4(V0__A,V2__C,cIntMap_2eFset_2eMapDomRestrTo___24a4(V0__A,V1__B,V3__m,V4__m_27),V5__m_27_27),cIntMap_2eFset_2eMapDomRestrTo___24a4(V0__A,V1__B,V3__m,cIntMap_2eFset_2eMapDomRestrTo___24a4(V1__B,V2__C,V4__m_27,V5__m_27_27))) ) ) ) ) ) ) ).

fof('IntMap.Mapaxioms.MapDomRestrTo_empty_m',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__B] :
          ( cType___24t(V1__B)
         => ! [V2__m] :
              ( cIntMap_2eMap_2eMap___24t(V1__B,V2__m)
             => cIntMap_2eMapaxioms_2eeqmap___24a3(V0__A,cIntMap_2eFset_2eMapDomRestrTo___24a4(V0__A,V1__B,cIntMap_2eMap_2eM0___24a1(V0__A),V2__m),cIntMap_2eMap_2eM0___24a1(V0__A)) ) ) ) ).

fof('IntMap.Mapaxioms.MapDomRestrTo_empty_m_1',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__B] :
          ( cType___24t(V1__B)
         => ! [V2__m] :
              ( cIntMap_2eMap_2eMap___24t(V1__B,V2__m)
             => cIntMap_2eFset_2eMapDomRestrTo___24a4(V0__A,V1__B,cIntMap_2eMap_2eM0___24a1(V0__A),V2__m) = cIntMap_2eMap_2eM0___24a1(V0__A) ) ) ) ).

fof('IntMap.Mapaxioms.MapDomRestrTo_ext',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__B] :
          ( cType___24t(V1__B)
         => ! [V2__m1] :
              ( cIntMap_2eMap_2eMap___24t(V0__A,V2__m1)
             => ! [V3__m2] :
                  ( cIntMap_2eMap_2eMap___24t(V1__B,V3__m2)
                 => ! [V4__m_271] :
                      ( cIntMap_2eMap_2eMap___24t(V0__A,V4__m_271)
                     => ! [V5__m_272] :
                          ( cIntMap_2eMap_2eMap___24t(V1__B,V5__m_272)
                         => ( cIntMap_2eMapaxioms_2eeqmap___24a3(V0__A,V2__m1,V4__m_271)
                           => ( cIntMap_2eMapaxioms_2eeqmap___24a3(V1__B,V3__m2,V5__m_272)
                             => cIntMap_2eMapaxioms_2eeqmap___24a3(V0__A,cIntMap_2eFset_2eMapDomRestrTo___24a4(V0__A,V1__B,V2__m1,V3__m2),cIntMap_2eFset_2eMapDomRestrTo___24a4(V0__A,V1__B,V4__m_271,V5__m_272)) ) ) ) ) ) ) ) ) ).

fof('IntMap.Mapaxioms.MapDomRestrTo_ext_l',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__B] :
          ( cType___24t(V1__B)
         => ! [V2__m1] :
              ( cIntMap_2eMap_2eMap___24t(V0__A,V2__m1)
             => ! [V3__m2] :
                  ( cIntMap_2eMap_2eMap___24t(V1__B,V3__m2)
                 => ! [V4__m_271] :
                      ( cIntMap_2eMap_2eMap___24t(V0__A,V4__m_271)
                     => ( cIntMap_2eMapaxioms_2eeqmap___24a3(V0__A,V2__m1,V4__m_271)
                       => cIntMap_2eMapaxioms_2eeqmap___24a3(V0__A,cIntMap_2eFset_2eMapDomRestrTo___24a4(V0__A,V1__B,V2__m1,V3__m2),cIntMap_2eFset_2eMapDomRestrTo___24a4(V0__A,V1__B,V4__m_271,V3__m2)) ) ) ) ) ) ) ).

fof('IntMap.Mapaxioms.MapDomRestrTo_ext_r',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__B] :
          ( cType___24t(V1__B)
         => ! [V2__m1] :
              ( cIntMap_2eMap_2eMap___24t(V0__A,V2__m1)
             => ! [V3__m2] :
                  ( cIntMap_2eMap_2eMap___24t(V1__B,V3__m2)
                 => ! [V4__m_272] :
                      ( cIntMap_2eMap_2eMap___24t(V1__B,V4__m_272)
                     => ( cIntMap_2eMapaxioms_2eeqmap___24a3(V1__B,V3__m2,V4__m_272)
                       => cIntMap_2eMapaxioms_2eeqmap___24a3(V0__A,cIntMap_2eFset_2eMapDomRestrTo___24a4(V0__A,V1__B,V2__m1,V3__m2),cIntMap_2eFset_2eMapDomRestrTo___24a4(V0__A,V1__B,V2__m1,V4__m_272)) ) ) ) ) ) ) ).

fof('IntMap.Mapaxioms.MapDomRestrTo_idempotent',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__m] :
          ( cIntMap_2eMap_2eMap___24t(V0__A,V1__m)
         => cIntMap_2eMapaxioms_2eeqmap___24a3(V0__A,cIntMap_2eFset_2eMapDomRestrTo___24a4(V0__A,V0__A,V1__m,V1__m),V1__m) ) ) ).

fof('IntMap.Mapaxioms.MapDomRestrTo_m_empty',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__B] :
          ( cType___24t(V1__B)
         => ! [V2__m] :
              ( cIntMap_2eMap_2eMap___24t(V0__A,V2__m)
             => cIntMap_2eMapaxioms_2eeqmap___24a3(V0__A,cIntMap_2eFset_2eMapDomRestrTo___24a4(V0__A,V1__B,V2__m,cIntMap_2eMap_2eM0___24a1(V1__B)),cIntMap_2eMap_2eM0___24a1(V0__A)) ) ) ) ).

fof('IntMap.Mapaxioms.MapDomRestrTo_m_empty_1',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__B] :
          ( cType___24t(V1__B)
         => ! [V2__m] :
              ( cIntMap_2eMap_2eMap___24t(V0__A,V2__m)
             => cIntMap_2eFset_2eMapDomRestrTo___24a4(V0__A,V1__B,V2__m,cIntMap_2eMap_2eM0___24a1(V1__B)) = cIntMap_2eMap_2eM0___24a1(V0__A) ) ) ) ).

fof('IntMap.Mapaxioms.MapDom_Split_1',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__B] :
          ( cType___24t(V1__B)
         => ! [V2__m] :
              ( cIntMap_2eMap_2eMap___24t(V0__A,V2__m)
             => ! [V3__m_27] :
                  ( cIntMap_2eMap_2eMap___24t(V1__B,V3__m_27)
                 => cIntMap_2eMapaxioms_2eeqmap___24a3(V0__A,V2__m,cIntMap_2eMap_2eMapMerge___24a3(V0__A,cIntMap_2eFset_2eMapDomRestrTo___24a4(V0__A,V1__B,V2__m,V3__m_27),cIntMap_2eFset_2eMapDomRestrBy___24a4(V0__A,V1__B,V2__m,V3__m_27))) ) ) ) ) ).

fof('IntMap.Mapaxioms.MapDom_Split_2',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__B] :
          ( cType___24t(V1__B)
         => ! [V2__m] :
              ( cIntMap_2eMap_2eMap___24t(V0__A,V2__m)
             => ! [V3__m_27] :
                  ( cIntMap_2eMap_2eMap___24t(V1__B,V3__m_27)
                 => cIntMap_2eMapaxioms_2eeqmap___24a3(V0__A,V2__m,cIntMap_2eMap_2eMapMerge___24a3(V0__A,cIntMap_2eFset_2eMapDomRestrBy___24a4(V0__A,V1__B,V2__m,V3__m_27),cIntMap_2eFset_2eMapDomRestrTo___24a4(V0__A,V1__B,V2__m,V3__m_27))) ) ) ) ) ).

fof('IntMap.Mapaxioms.MapDom_Split_3',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__B] :
          ( cType___24t(V1__B)
         => ! [V2__m] :
              ( cIntMap_2eMap_2eMap___24t(V0__A,V2__m)
             => ! [V3__m_27] :
                  ( cIntMap_2eMap_2eMap___24t(V1__B,V3__m_27)
                 => cIntMap_2eMapaxioms_2eeqmap___24a3(V0__A,cIntMap_2eFset_2eMapDomRestrTo___24a4(V0__A,V0__A,cIntMap_2eFset_2eMapDomRestrTo___24a4(V0__A,V1__B,V2__m,V3__m_27),cIntMap_2eFset_2eMapDomRestrBy___24a4(V0__A,V1__B,V2__m,V3__m_27)),cIntMap_2eMap_2eM0___24a1(V0__A)) ) ) ) ) ).

fof('IntMap.Mapaxioms.MapMerge_DomRestrBy',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__B] :
          ( cType___24t(V1__B)
         => ! [V2__m] :
              ( cIntMap_2eMap_2eMap___24t(V0__A,V2__m)
             => ! [V3__m_27] :
                  ( cIntMap_2eMap_2eMap___24t(V0__A,V3__m_27)
                 => ! [V4__m_27_27] :
                      ( cIntMap_2eMap_2eMap___24t(V1__B,V4__m_27_27)
                     => cIntMap_2eMapaxioms_2eeqmap___24a3(V0__A,cIntMap_2eFset_2eMapDomRestrBy___24a4(V0__A,V1__B,cIntMap_2eMap_2eMapMerge___24a3(V0__A,V2__m,V3__m_27),V4__m_27_27),cIntMap_2eMap_2eMapMerge___24a3(V0__A,cIntMap_2eFset_2eMapDomRestrBy___24a4(V0__A,V1__B,V2__m,V4__m_27_27),cIntMap_2eFset_2eMapDomRestrBy___24a4(V0__A,V1__B,V3__m_27,V4__m_27_27))) ) ) ) ) ) ).

fof('IntMap.Mapaxioms.MapMerge_DomRestrTo',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__B] :
          ( cType___24t(V1__B)
         => ! [V2__m] :
              ( cIntMap_2eMap_2eMap___24t(V0__A,V2__m)
             => ! [V3__m_27] :
                  ( cIntMap_2eMap_2eMap___24t(V0__A,V3__m_27)
                 => ! [V4__m_27_27] :
                      ( cIntMap_2eMap_2eMap___24t(V1__B,V4__m_27_27)
                     => cIntMap_2eMapaxioms_2eeqmap___24a3(V0__A,cIntMap_2eFset_2eMapDomRestrTo___24a4(V0__A,V1__B,cIntMap_2eMap_2eMapMerge___24a3(V0__A,V2__m,V3__m_27),V4__m_27_27),cIntMap_2eMap_2eMapMerge___24a3(V0__A,cIntMap_2eFset_2eMapDomRestrTo___24a4(V0__A,V1__B,V2__m,V4__m_27_27),cIntMap_2eFset_2eMapDomRestrTo___24a4(V0__A,V1__B,V3__m_27,V4__m_27_27))) ) ) ) ) ) ).

fof('IntMap.Mapaxioms.MapMerge_RestrTo_l',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__m] :
          ( cIntMap_2eMap_2eMap___24t(V0__A,V1__m)
         => ! [V2__m_27] :
              ( cIntMap_2eMap_2eMap___24t(V0__A,V2__m_27)
             => ! [V3__m_27_27] :
                  ( cIntMap_2eMap_2eMap___24t(V0__A,V3__m_27_27)
                 => cIntMap_2eMapaxioms_2eeqmap___24a3(V0__A,cIntMap_2eMap_2eMapMerge___24a3(V0__A,cIntMap_2eFset_2eMapDomRestrTo___24a4(V0__A,V0__A,V1__m,V2__m_27),V3__m_27_27),cIntMap_2eFset_2eMapDomRestrTo___24a4(V0__A,V0__A,cIntMap_2eMap_2eMapMerge___24a3(V0__A,V1__m,V3__m_27_27),cIntMap_2eMap_2eMapMerge___24a3(V0__A,V2__m_27,V3__m_27_27))) ) ) ) ) ).

fof('IntMap.Mapaxioms.MapMerge_assoc',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__m] :
          ( cIntMap_2eMap_2eMap___24t(V0__A,V1__m)
         => ! [V2__m_27] :
              ( cIntMap_2eMap_2eMap___24t(V0__A,V2__m_27)
             => ! [V3__m_27_27] :
                  ( cIntMap_2eMap_2eMap___24t(V0__A,V3__m_27_27)
                 => cIntMap_2eMapaxioms_2eeqmap___24a3(V0__A,cIntMap_2eMap_2eMapMerge___24a3(V0__A,cIntMap_2eMap_2eMapMerge___24a3(V0__A,V1__m,V2__m_27),V3__m_27_27),cIntMap_2eMap_2eMapMerge___24a3(V0__A,V1__m,cIntMap_2eMap_2eMapMerge___24a3(V0__A,V2__m_27,V3__m_27_27))) ) ) ) ) ).

fof('IntMap.Mapaxioms.MapMerge_empty_l',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__m] :
          ( cIntMap_2eMap_2eMap___24t(V0__A,V1__m)
         => ! [V2__m_27] :
              ( cIntMap_2eMap_2eMap___24t(V0__A,V2__m_27)
             => ( cIntMap_2eMapaxioms_2eeqmap___24a3(V0__A,cIntMap_2eMap_2eMapMerge___24a3(V0__A,V1__m,V2__m_27),cIntMap_2eMap_2eM0___24a1(V0__A))
               => cIntMap_2eMapaxioms_2eeqmap___24a3(V0__A,V1__m,cIntMap_2eMap_2eM0___24a1(V0__A)) ) ) ) ) ).

fof('IntMap.Mapaxioms.MapMerge_empty_m',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__m] :
          ( cIntMap_2eMap_2eMap___24t(V0__A,V1__m)
         => cIntMap_2eMapaxioms_2eeqmap___24a3(V0__A,cIntMap_2eMap_2eMapMerge___24a3(V0__A,cIntMap_2eMap_2eM0___24a1(V0__A),V1__m),V1__m) ) ) ).

fof('IntMap.Mapaxioms.MapMerge_empty_m_1',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__m] :
          ( cIntMap_2eMap_2eMap___24t(V0__A,V1__m)
         => cIntMap_2eMap_2eMapMerge___24a3(V0__A,cIntMap_2eMap_2eM0___24a1(V0__A),V1__m) = V1__m ) ) ).

fof('IntMap.Mapaxioms.MapMerge_empty_r',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__m] :
          ( cIntMap_2eMap_2eMap___24t(V0__A,V1__m)
         => ! [V2__m_27] :
              ( cIntMap_2eMap_2eMap___24t(V0__A,V2__m_27)
             => ( cIntMap_2eMapaxioms_2eeqmap___24a3(V0__A,cIntMap_2eMap_2eMapMerge___24a3(V0__A,V1__m,V2__m_27),cIntMap_2eMap_2eM0___24a1(V0__A))
               => cIntMap_2eMapaxioms_2eeqmap___24a3(V0__A,V2__m_27,cIntMap_2eMap_2eM0___24a1(V0__A)) ) ) ) ) ).

fof('IntMap.Mapaxioms.MapMerge_ext',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__m1] :
          ( cIntMap_2eMap_2eMap___24t(V0__A,V1__m1)
         => ! [V2__m2] :
              ( cIntMap_2eMap_2eMap___24t(V0__A,V2__m2)
             => ! [V3__m_271] :
                  ( cIntMap_2eMap_2eMap___24t(V0__A,V3__m_271)
                 => ! [V4__m_272] :
                      ( cIntMap_2eMap_2eMap___24t(V0__A,V4__m_272)
                     => ( cIntMap_2eMapaxioms_2eeqmap___24a3(V0__A,V1__m1,V3__m_271)
                       => ( cIntMap_2eMapaxioms_2eeqmap___24a3(V0__A,V2__m2,V4__m_272)
                         => cIntMap_2eMapaxioms_2eeqmap___24a3(V0__A,cIntMap_2eMap_2eMapMerge___24a3(V0__A,V1__m1,V2__m2),cIntMap_2eMap_2eMapMerge___24a3(V0__A,V3__m_271,V4__m_272)) ) ) ) ) ) ) ) ).

fof('IntMap.Mapaxioms.MapMerge_ext_l',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__m1] :
          ( cIntMap_2eMap_2eMap___24t(V0__A,V1__m1)
         => ! [V2__m_271] :
              ( cIntMap_2eMap_2eMap___24t(V0__A,V2__m_271)
             => ! [V3__m2] :
                  ( cIntMap_2eMap_2eMap___24t(V0__A,V3__m2)
                 => ( cIntMap_2eMapaxioms_2eeqmap___24a3(V0__A,V1__m1,V2__m_271)
                   => cIntMap_2eMapaxioms_2eeqmap___24a3(V0__A,cIntMap_2eMap_2eMapMerge___24a3(V0__A,V1__m1,V3__m2),cIntMap_2eMap_2eMapMerge___24a3(V0__A,V2__m_271,V3__m2)) ) ) ) ) ) ).

fof('IntMap.Mapaxioms.MapMerge_ext_r',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__m1] :
          ( cIntMap_2eMap_2eMap___24t(V0__A,V1__m1)
         => ! [V2__m2] :
              ( cIntMap_2eMap_2eMap___24t(V0__A,V2__m2)
             => ! [V3__m_272] :
                  ( cIntMap_2eMap_2eMap___24t(V0__A,V3__m_272)
                 => ( cIntMap_2eMapaxioms_2eeqmap___24a3(V0__A,V2__m2,V3__m_272)
                   => cIntMap_2eMapaxioms_2eeqmap___24a3(V0__A,cIntMap_2eMap_2eMapMerge___24a3(V0__A,V1__m1,V2__m2),cIntMap_2eMap_2eMapMerge___24a3(V0__A,V1__m1,V3__m_272)) ) ) ) ) ) ).

fof('IntMap.Mapaxioms.MapMerge_idempotent',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__m] :
          ( cIntMap_2eMap_2eMap___24t(V0__A,V1__m)
         => cIntMap_2eMapaxioms_2eeqmap___24a3(V0__A,cIntMap_2eMap_2eMapMerge___24a3(V0__A,V1__m,V1__m),V1__m) ) ) ).

fof('IntMap.Mapaxioms.MapMerge_m_empty',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__m] :
          ( cIntMap_2eMap_2eMap___24t(V0__A,V1__m)
         => cIntMap_2eMapaxioms_2eeqmap___24a3(V0__A,cIntMap_2eMap_2eMapMerge___24a3(V0__A,V1__m,cIntMap_2eMap_2eM0___24a1(V0__A)),V1__m) ) ) ).

fof('IntMap.Mapaxioms.MapMerge_m_empty_1',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__m] :
          ( cIntMap_2eMap_2eMap___24t(V0__A,V1__m)
         => cIntMap_2eMap_2eMapMerge___24a3(V0__A,V1__m,cIntMap_2eMap_2eM0___24a1(V0__A)) = V1__m ) ) ).

fof('IntMap.Mapaxioms.MapPut_as_Merge',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__m] :
          ( cIntMap_2eMap_2eMap___24t(V0__A,V1__m)
         => ! [V2__a] :
              ( cIntMap_2eMap_2ead___24t(V2__a)
             => ! [V3__y] :
                  ( t(V3__y,V0__A)
                 => cIntMap_2eMapaxioms_2eeqmap___24a3(V0__A,cIntMap_2eMap_2eMapPut___24a4(V0__A,V1__m,V2__a,V3__y),cIntMap_2eMap_2eMapMerge___24a3(V0__A,V1__m,cIntMap_2eMap_2eM1___24a3(V0__A,V2__a,V3__y))) ) ) ) ) ).

fof('IntMap.Mapaxioms.MapPut_behind_as_Merge',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__m] :
          ( cIntMap_2eMap_2eMap___24t(V0__A,V1__m)
         => ! [V2__a] :
              ( cIntMap_2eMap_2ead___24t(V2__a)
             => ! [V3__y] :
                  ( t(V3__y,V0__A)
                 => cIntMap_2eMapaxioms_2eeqmap___24a3(V0__A,cIntMap_2eMap_2eMapPut__behind___24a4(V0__A,V1__m,V2__a,V3__y),cIntMap_2eMap_2eMapMerge___24a3(V0__A,cIntMap_2eMap_2eM1___24a3(V0__A,V2__a,V3__y),V1__m)) ) ) ) ) ).

fof('IntMap.Mapaxioms.MapPut_behind_ext',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__m] :
          ( cIntMap_2eMap_2eMap___24t(V0__A,V1__m)
         => ! [V2__m_27] :
              ( cIntMap_2eMap_2eMap___24t(V0__A,V2__m_27)
             => ( cIntMap_2eMapaxioms_2eeqmap___24a3(V0__A,V1__m,V2__m_27)
               => ! [V4__a] :
                    ( cIntMap_2eMap_2ead___24t(V4__a)
                   => ! [V5__y] :
                        ( t(V5__y,V0__A)
                       => cIntMap_2eMapaxioms_2eeqmap___24a3(V0__A,cIntMap_2eMap_2eMapPut__behind___24a4(V0__A,V1__m,V4__a,V5__y),cIntMap_2eMap_2eMapPut__behind___24a4(V0__A,V2__m_27,V4__a,V5__y)) ) ) ) ) ) ) ).

fof('IntMap.Mapaxioms.MapPut_ext',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__m] :
          ( cIntMap_2eMap_2eMap___24t(V0__A,V1__m)
         => ! [V2__m_27] :
              ( cIntMap_2eMap_2eMap___24t(V0__A,V2__m_27)
             => ( cIntMap_2eMapaxioms_2eeqmap___24a3(V0__A,V1__m,V2__m_27)
               => ! [V4__a] :
                    ( cIntMap_2eMap_2ead___24t(V4__a)
                   => ! [V5__y] :
                        ( t(V5__y,V0__A)
                       => cIntMap_2eMapaxioms_2eeqmap___24a3(V0__A,cIntMap_2eMap_2eMapPut___24a4(V0__A,V1__m,V4__a,V5__y),cIntMap_2eMap_2eMapPut___24a4(V0__A,V2__m_27,V4__a,V5__y)) ) ) ) ) ) ) ).

fof('IntMap.Mapaxioms.MapRemove_as_RestrBy',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__B] :
          ( cType___24t(V1__B)
         => ! [V2__m] :
              ( cIntMap_2eMap_2eMap___24t(V0__A,V2__m)
             => ! [V3__a] :
                  ( cIntMap_2eMap_2ead___24t(V3__a)
                 => ! [V4__y] :
                      ( t(V4__y,V1__B)
                     => cIntMap_2eMapaxioms_2eeqmap___24a3(V0__A,cIntMap_2eMap_2eMapRemove___24a3(V0__A,V2__m,V3__a),cIntMap_2eFset_2eMapDomRestrBy___24a4(V0__A,V1__B,V2__m,cIntMap_2eMap_2eM1___24a3(V1__B,V3__a,V4__y))) ) ) ) ) ) ).

fof('IntMap.Mapaxioms.MapRemove_ext',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__m] :
          ( cIntMap_2eMap_2eMap___24t(V0__A,V1__m)
         => ! [V2__m_27] :
              ( cIntMap_2eMap_2eMap___24t(V0__A,V2__m_27)
             => ( cIntMap_2eMapaxioms_2eeqmap___24a3(V0__A,V1__m,V2__m_27)
               => ! [V4__a] :
                    ( cIntMap_2eMap_2ead___24t(V4__a)
                   => cIntMap_2eMapaxioms_2eeqmap___24a3(V0__A,cIntMap_2eMap_2eMapRemove___24a3(V0__A,V1__m,V4__a),cIntMap_2eMap_2eMapRemove___24a3(V0__A,V2__m_27,V4__a)) ) ) ) ) ) ).

fof('IntMap.Mapaxioms.eqm_refl',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__f] :
          ( c_24__type__1987___24t(V0__A,V1__f)
         => cIntMap_2eMap_2eeqm___24a3(V0__A,V1__f,V1__f) ) ) ).

fof('IntMap.Mapaxioms.eqm_sym',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__f] :
          ( c_24__type__1987___24t(V0__A,V1__f)
         => ! [V2__f_27] :
              ( c_24__type__1987___24t(V0__A,V2__f_27)
             => ( cIntMap_2eMap_2eeqm___24a3(V0__A,V1__f,V2__f_27)
               => cIntMap_2eMap_2eeqm___24a3(V0__A,V2__f_27,V1__f) ) ) ) ) ).

fof('IntMap.Mapaxioms.eqm_trans',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__f] :
          ( c_24__type__1987___24t(V0__A,V1__f)
         => ! [V2__f_27] :
              ( c_24__type__1987___24t(V0__A,V2__f_27)
             => ! [V3__f_27_27] :
                  ( c_24__type__1987___24t(V0__A,V3__f_27_27)
                 => ( cIntMap_2eMap_2eeqm___24a3(V0__A,V1__f,V2__f_27)
                   => ( cIntMap_2eMap_2eeqm___24a3(V0__A,V2__f_27,V3__f_27_27)
                     => cIntMap_2eMap_2eeqm___24a3(V0__A,V1__f,V3__f_27_27) ) ) ) ) ) ) ).

fof('IntMap.Mapaxioms.eqmap_refl',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__m] :
          ( cIntMap_2eMap_2eMap___24t(V0__A,V1__m)
         => cIntMap_2eMapaxioms_2eeqmap___24a3(V0__A,V1__m,V1__m) ) ) ).

fof('IntMap.Mapaxioms.eqmap_sym',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__m] :
          ( cIntMap_2eMap_2eMap___24t(V0__A,V1__m)
         => ! [V2__m_27] :
              ( cIntMap_2eMap_2eMap___24t(V0__A,V2__m_27)
             => ( cIntMap_2eMapaxioms_2eeqmap___24a3(V0__A,V1__m,V2__m_27)
               => cIntMap_2eMapaxioms_2eeqmap___24a3(V0__A,V2__m_27,V1__m) ) ) ) ) ).

fof('IntMap.Mapaxioms.eqmap_trans',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__m] :
          ( cIntMap_2eMap_2eMap___24t(V0__A,V1__m)
         => ! [V2__m_27] :
              ( cIntMap_2eMap_2eMap___24t(V0__A,V2__m_27)
             => ! [V3__m_27_27] :
                  ( cIntMap_2eMap_2eMap___24t(V0__A,V3__m_27_27)
                 => ( cIntMap_2eMapaxioms_2eeqmap___24a3(V0__A,V1__m,V2__m_27)
                   => ( cIntMap_2eMapaxioms_2eeqmap___24a3(V0__A,V2__m_27,V3__m_27_27)
                     => cIntMap_2eMapaxioms_2eeqmap___24a3(V0__A,V1__m,V3__m_27_27) ) ) ) ) ) ) ).

fof('IntMap.Mapcanon.M0_canon',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => cIntMap_2eMapcanon_2emapcanon___24a2(V0__A,cIntMap_2eMap_2eM0___24a1(V0__A)) ) ).

fof('IntMap.Mapcanon.M1_canon',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__a] :
          ( cIntMap_2eMap_2ead___24t(V1__a)
         => ! [V2__y] :
              ( t(V2__y,V0__A)
             => cIntMap_2eMapcanon_2emapcanon___24a2(V0__A,cIntMap_2eMap_2eM1___24a3(V0__A,V1__a,V2__y)) ) ) ) ).

fof('IntMap.Mapcanon.M2_canon',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__m1] :
          ( cIntMap_2eMap_2eMap___24t(V0__A,V1__m1)
         => ! [V2__m2] :
              ( cIntMap_2eMap_2eMap___24t(V0__A,V2__m2)
             => ( cIntMap_2eMapcanon_2emapcanon___24a2(V0__A,V1__m1)
               => ( cIntMap_2eMapcanon_2emapcanon___24a2(V0__A,V2__m2)
                 => ( cCoq_2eInit_2ePeano_2ele___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO)),cIntMap_2eMap_2eMapCard___24a2(V0__A,cIntMap_2eMap_2eM2___24a3(V0__A,V1__m1,V2__m2)))
                   => cIntMap_2eMapcanon_2emapcanon___24a2(V0__A,cIntMap_2eMap_2eM2___24a3(V0__A,V1__m1,V2__m2)) ) ) ) ) ) ) ).

fof('IntMap.Mapcanon.M2_eqmap_1',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__m0] :
          ( cIntMap_2eMap_2eMap___24t(V0__A,V1__m0)
         => ! [V2__m1] :
              ( cIntMap_2eMap_2eMap___24t(V0__A,V2__m1)
             => ! [V3__m2] :
                  ( cIntMap_2eMap_2eMap___24t(V0__A,V3__m2)
                 => ! [V4__m3] :
                      ( cIntMap_2eMap_2eMap___24t(V0__A,V4__m3)
                     => ( cIntMap_2eMapaxioms_2eeqmap___24a3(V0__A,cIntMap_2eMap_2eM2___24a3(V0__A,V1__m0,V2__m1),cIntMap_2eMap_2eM2___24a3(V0__A,V3__m2,V4__m3))
                       => cIntMap_2eMapaxioms_2eeqmap___24a3(V0__A,V1__m0,V3__m2) ) ) ) ) ) ) ).

fof('IntMap.Mapcanon.M2_eqmap_2',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__m0] :
          ( cIntMap_2eMap_2eMap___24t(V0__A,V1__m0)
         => ! [V2__m1] :
              ( cIntMap_2eMap_2eMap___24t(V0__A,V2__m1)
             => ! [V3__m2] :
                  ( cIntMap_2eMap_2eMap___24t(V0__A,V3__m2)
                 => ! [V4__m3] :
                      ( cIntMap_2eMap_2eMap___24t(V0__A,V4__m3)
                     => ( cIntMap_2eMapaxioms_2eeqmap___24a3(V0__A,cIntMap_2eMap_2eM2___24a3(V0__A,V1__m0,V2__m1),cIntMap_2eMap_2eM2___24a3(V0__A,V3__m2,V4__m3))
                       => cIntMap_2eMapaxioms_2eeqmap___24a3(V0__A,V2__m1,V4__m3) ) ) ) ) ) ) ).

fof('IntMap.Mapcanon.MapCollect_canon',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__B] :
          ( cType___24t(V1__B)
         => ! [V2__f] :
              ( c_24__type__1574___24t(V0__A,V1__B,V2__f)
             => ( ! [V3__a] :
                    ( cIntMap_2eMap_2ead___24t(V3__a)
                   => ! [V4__y] :
                        ( t(V4__y,V0__A)
                       => cIntMap_2eMapcanon_2emapcanon___24a2(V1__B,happ(happ(V2__f,V3__a),V4__y)) ) )
               => ! [V4__m] :
                    ( cIntMap_2eMap_2eMap___24t(V0__A,V4__m)
                   => cIntMap_2eMapcanon_2emapcanon___24a2(V1__B,cIntMap_2eMapiter_2eMapCollect___24a4(V0__A,V1__B,V2__f,V4__m)) ) ) ) ) ) ).

fof('IntMap.Mapcanon.MapDelta_canon',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__m] :
          ( cIntMap_2eMap_2eMap___24t(V0__A,V1__m)
         => ! [V2__m_27] :
              ( cIntMap_2eMap_2eMap___24t(V0__A,V2__m_27)
             => ( cIntMap_2eMapcanon_2emapcanon___24a2(V0__A,V1__m)
               => ( cIntMap_2eMapcanon_2emapcanon___24a2(V0__A,V2__m_27)
                 => cIntMap_2eMapcanon_2emapcanon___24a2(V0__A,cIntMap_2eMap_2eMapDelta___24a3(V0__A,V1__m,V2__m_27)) ) ) ) ) ) ).

fof('IntMap.Mapcanon.MapDomRestrBy_canon',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__B] :
          ( cType___24t(V1__B)
         => ! [V2__m] :
              ( cIntMap_2eMap_2eMap___24t(V0__A,V2__m)
             => ( cIntMap_2eMapcanon_2emapcanon___24a2(V0__A,V2__m)
               => ! [V4__m_27] :
                    ( cIntMap_2eMap_2eMap___24t(V1__B,V4__m_27)
                   => cIntMap_2eMapcanon_2emapcanon___24a2(V0__A,cIntMap_2eFset_2eMapDomRestrBy___24a4(V0__A,V1__B,V2__m,V4__m_27)) ) ) ) ) ) ).

fof('IntMap.Mapcanon.MapDomRestrTo_canon',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__B] :
          ( cType___24t(V1__B)
         => ! [V2__m] :
              ( cIntMap_2eMap_2eMap___24t(V0__A,V2__m)
             => ( cIntMap_2eMapcanon_2emapcanon___24a2(V0__A,V2__m)
               => ! [V4__m_27] :
                    ( cIntMap_2eMap_2eMap___24t(V1__B,V4__m_27)
                   => cIntMap_2eMapcanon_2emapcanon___24a2(V0__A,cIntMap_2eFset_2eMapDomRestrTo___24a4(V0__A,V1__B,V2__m,V4__m_27)) ) ) ) ) ) ).

fof('IntMap.Mapcanon.MapDom_canon',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__m] :
          ( cIntMap_2eMap_2eMap___24t(V0__A,V1__m)
         => ( cIntMap_2eMapcanon_2emapcanon___24a2(V0__A,V1__m)
           => cIntMap_2eMapcanon_2emapcanon___24a2(cCoq_2eInit_2eDatatypes_2eunit,cIntMap_2eFset_2eMapDom___24a2(V0__A,V1__m)) ) ) ) ).

fof('IntMap.Mapcanon.MapFold_canon',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__B] :
          ( cType___24t(V1__B)
         => ! [V2__m0] :
              ( cIntMap_2eMap_2eMap___24t(V1__B,V2__m0)
             => ( cIntMap_2eMapcanon_2emapcanon___24a2(V1__B,V2__m0)
               => ! [V4__op] :
                    ( c_24__type__1563___24t(V1__B,V4__op)
                   => ( ! [V5__m1] :
                          ( cIntMap_2eMap_2eMap___24t(V1__B,V5__m1)
                         => ( cIntMap_2eMapcanon_2emapcanon___24a2(V1__B,V5__m1)
                           => ! [V7__m2] :
                                ( cIntMap_2eMap_2eMap___24t(V1__B,V7__m2)
                               => ( cIntMap_2eMapcanon_2emapcanon___24a2(V1__B,V7__m2)
                                 => cIntMap_2eMapcanon_2emapcanon___24a2(V1__B,happ(happ(V4__op,V5__m1),V7__m2)) ) ) ) )
                     => ! [V6__f] :
                          ( c_24__type__1574___24t(V0__A,V1__B,V6__f)
                         => ( ! [V7__a] :
                                ( cIntMap_2eMap_2ead___24t(V7__a)
                               => ! [V8__y] :
                                    ( t(V8__y,V0__A)
                                   => cIntMap_2eMapcanon_2emapcanon___24a2(V1__B,happ(happ(V6__f,V7__a),V8__y)) ) )
                           => ! [V8__m] :
                                ( cIntMap_2eMap_2eMap___24t(V0__A,V8__m)
                               => cIntMap_2eMapcanon_2emapcanon___24a2(V1__B,cIntMap_2eMapiter_2eMapFold___24a6(V0__A,cIntMap_2eMap_2eMap___24a1(V1__B),V2__m0,V4__op,V6__f,V8__m)) ) ) ) ) ) ) ) ) ) ).

fof('IntMap.Mapcanon.MapFold_canon_1',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__B] :
          ( cType___24t(V1__B)
         => ! [V2__m0] :
              ( cIntMap_2eMap_2eMap___24t(V1__B,V2__m0)
             => ( cIntMap_2eMapcanon_2emapcanon___24a2(V1__B,V2__m0)
               => ! [V4__op] :
                    ( c_24__type__1563___24t(V1__B,V4__op)
                   => ( ! [V5__m1] :
                          ( cIntMap_2eMap_2eMap___24t(V1__B,V5__m1)
                         => ( cIntMap_2eMapcanon_2emapcanon___24a2(V1__B,V5__m1)
                           => ! [V7__m2] :
                                ( cIntMap_2eMap_2eMap___24t(V1__B,V7__m2)
                               => ( cIntMap_2eMapcanon_2emapcanon___24a2(V1__B,V7__m2)
                                 => cIntMap_2eMapcanon_2emapcanon___24a2(V1__B,happ(happ(V4__op,V5__m1),V7__m2)) ) ) ) )
                     => ! [V6__f] :
                          ( c_24__type__1574___24t(V0__A,V1__B,V6__f)
                         => ( ! [V7__a] :
                                ( cIntMap_2eMap_2ead___24t(V7__a)
                               => ! [V8__y] :
                                    ( t(V8__y,V0__A)
                                   => cIntMap_2eMapcanon_2emapcanon___24a2(V1__B,happ(happ(V6__f,V7__a),V8__y)) ) )
                           => ! [V8__m] :
                                ( cIntMap_2eMap_2eMap___24t(V0__A,V8__m)
                               => ! [V9__pf] :
                                    ( c_24__type__1580___24t(V0__A,V1__B,V9__pf)
                                   => cIntMap_2eMapcanon_2emapcanon___24a2(V1__B,cIntMap_2eMapiter_2eMapFold1___24a7(V0__A,cIntMap_2eMap_2eMap___24a1(V1__B),V2__m0,V4__op,V6__f,V9__pf,V8__m)) ) ) ) ) ) ) ) ) ) ) ).

fof('IntMap.Mapcanon.MapMerge_canon',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__m] :
          ( cIntMap_2eMap_2eMap___24t(V0__A,V1__m)
         => ! [V2__m_27] :
              ( cIntMap_2eMap_2eMap___24t(V0__A,V2__m_27)
             => ( cIntMap_2eMapcanon_2emapcanon___24a2(V0__A,V1__m)
               => ( cIntMap_2eMapcanon_2emapcanon___24a2(V0__A,V2__m_27)
                 => cIntMap_2eMapcanon_2emapcanon___24a2(V0__A,cIntMap_2eMap_2eMapMerge___24a3(V0__A,V1__m,V2__m_27)) ) ) ) ) ) ).

fof('IntMap.Mapcanon.MapPut1_canon',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__p] :
          ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__p)
         => ! [V2__a] :
              ( cIntMap_2eMap_2ead___24t(V2__a)
             => ! [V3__a_27] :
                  ( cIntMap_2eMap_2ead___24t(V3__a_27)
                 => ! [V4__y] :
                      ( t(V4__y,V0__A)
                     => ! [V5__y_27] :
                          ( t(V5__y_27,V0__A)
                         => cIntMap_2eMapcanon_2emapcanon___24a2(V0__A,cIntMap_2eMap_2eMapPut1___24a6(V0__A,V2__a,V4__y,V3__a_27,V5__y_27,V1__p)) ) ) ) ) ) ) ).

fof('IntMap.Mapcanon.MapPut_behind_canon',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__m] :
          ( cIntMap_2eMap_2eMap___24t(V0__A,V1__m)
         => ( cIntMap_2eMapcanon_2emapcanon___24a2(V0__A,V1__m)
           => ! [V3__a] :
                ( cIntMap_2eMap_2ead___24t(V3__a)
               => ! [V4__y] :
                    ( t(V4__y,V0__A)
                   => cIntMap_2eMapcanon_2emapcanon___24a2(V0__A,cIntMap_2eMap_2eMapPut__behind___24a4(V0__A,V1__m,V3__a,V4__y)) ) ) ) ) ) ).

fof('IntMap.Mapcanon.MapPut_canon',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__m] :
          ( cIntMap_2eMap_2eMap___24t(V0__A,V1__m)
         => ( cIntMap_2eMapcanon_2emapcanon___24a2(V0__A,V1__m)
           => ! [V3__a] :
                ( cIntMap_2eMap_2ead___24t(V3__a)
               => ! [V4__y] :
                    ( t(V4__y,V0__A)
                   => cIntMap_2eMapcanon_2emapcanon___24a2(V0__A,cIntMap_2eMap_2eMapPut___24a4(V0__A,V1__m,V3__a,V4__y)) ) ) ) ) ) ).

fof('IntMap.Mapcanon.MapRemove_canon',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__m] :
          ( cIntMap_2eMap_2eMap___24t(V0__A,V1__m)
         => ( cIntMap_2eMapcanon_2emapcanon___24a2(V0__A,V1__m)
           => ! [V3__a] :
                ( cIntMap_2eMap_2ead___24t(V3__a)
               => cIntMap_2eMapcanon_2emapcanon___24a2(V0__A,cIntMap_2eMap_2eMapRemove___24a3(V0__A,V1__m,V3__a)) ) ) ) ) ).

fof('IntMap.Mapcanon.MapSubset_c_1',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__B] :
          ( cType___24t(V1__B)
         => ! [V2__m] :
              ( cIntMap_2eMap_2eMap___24t(V0__A,V2__m)
             => ! [V3__m_27] :
                  ( cIntMap_2eMap_2eMap___24t(V1__B,V3__m_27)
                 => ( cIntMap_2eMapcanon_2emapcanon___24a2(V0__A,V2__m)
                   => ( cIntMap_2eMapsubset_2eMapSubset___24a4(V0__A,V1__B,V2__m,V3__m_27)
                     => cIntMap_2eFset_2eMapDomRestrBy___24a4(V0__A,V1__B,V2__m,V3__m_27) = cIntMap_2eMap_2eM0___24a1(V0__A) ) ) ) ) ) ) ).

fof('IntMap.Mapcanon.MapSubset_c_2',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__B] :
          ( cType___24t(V1__B)
         => ! [V2__m] :
              ( cIntMap_2eMap_2eMap___24t(V0__A,V2__m)
             => ! [V3__m_27] :
                  ( cIntMap_2eMap_2eMap___24t(V1__B,V3__m_27)
                 => ( cIntMap_2eFset_2eMapDomRestrBy___24a4(V0__A,V1__B,V2__m,V3__m_27) = cIntMap_2eMap_2eM0___24a1(V0__A)
                   => cIntMap_2eMapsubset_2eMapSubset___24a4(V0__A,V1__B,V2__m,V3__m_27) ) ) ) ) ) ).

fof('IntMap.Mapcanon.Map_of_alist_canon',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__l] :
          ( cIntMap_2eMapiter_2ealist___24t(V0__A,V1__l)
         => cIntMap_2eMapcanon_2emapcanon___24a2(V0__A,cIntMap_2eMapiter_2eMap__of__alist___24a2(V0__A,V1__l)) ) ) ).

fof('IntMap.Mapcanon.makeM2_canon',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__m] :
          ( cIntMap_2eMap_2eMap___24t(V0__A,V1__m)
         => ! [V2__m_27] :
              ( cIntMap_2eMap_2eMap___24t(V0__A,V2__m_27)
             => ( cIntMap_2eMapcanon_2emapcanon___24a2(V0__A,V1__m)
               => ( cIntMap_2eMapcanon_2emapcanon___24a2(V0__A,V2__m_27)
                 => cIntMap_2eMapcanon_2emapcanon___24a2(V0__A,cIntMap_2eMap_2emakeM2___24a3(V0__A,V1__m,V2__m_27)) ) ) ) ) ) ).

fof('IntMap.Mapcanon.mapcanon_M2',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__m1] :
          ( cIntMap_2eMap_2eMap___24t(V0__A,V1__m1)
         => ! [V2__m2] :
              ( cIntMap_2eMap_2eMap___24t(V0__A,V2__m2)
             => ( cIntMap_2eMapcanon_2emapcanon___24a2(V0__A,cIntMap_2eMap_2eM2___24a3(V0__A,V1__m1,V2__m2))
               => cCoq_2eInit_2ePeano_2ele___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO)),cIntMap_2eMap_2eMapCard___24a2(V0__A,cIntMap_2eMap_2eM2___24a3(V0__A,V1__m1,V2__m2))) ) ) ) ) ).

fof('IntMap.Mapcanon.mapcanon_M2_1',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__m1] :
          ( cIntMap_2eMap_2eMap___24t(V0__A,V1__m1)
         => ! [V2__m2] :
              ( cIntMap_2eMap_2eMap___24t(V0__A,V2__m2)
             => ( cIntMap_2eMapcanon_2emapcanon___24a2(V0__A,cIntMap_2eMap_2eM2___24a3(V0__A,V1__m1,V2__m2))
               => cIntMap_2eMapcanon_2emapcanon___24a2(V0__A,V1__m1) ) ) ) ) ).

fof('IntMap.Mapcanon.mapcanon_M2_2',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__m1] :
          ( cIntMap_2eMap_2eMap___24t(V0__A,V1__m1)
         => ! [V2__m2] :
              ( cIntMap_2eMap_2eMap___24t(V0__A,V2__m2)
             => ( cIntMap_2eMapcanon_2emapcanon___24a2(V0__A,cIntMap_2eMap_2eM2___24a3(V0__A,V1__m1,V2__m2))
               => cIntMap_2eMapcanon_2emapcanon___24a2(V0__A,V2__m2) ) ) ) ) ).

fof('IntMap.Mapcanon.mapcanon_exists_1',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__m] :
          ( cIntMap_2eMap_2eMap___24t(V0__A,V1__m)
         => cIntMap_2eMapaxioms_2eeqmap___24a3(V0__A,V1__m,cIntMap_2eMapcanon_2eMapCanonicalize___24a2(V0__A,V1__m)) ) ) ).

fof('IntMap.Mapcanon.mapcanon_exists_2',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__m] :
          ( cIntMap_2eMap_2eMap___24t(V0__A,V1__m)
         => cIntMap_2eMapcanon_2emapcanon___24a2(V0__A,cIntMap_2eMapcanon_2eMapCanonicalize___24a2(V0__A,V1__m)) ) ) ).

fof('IntMap.Mapcanon.mapcanon_ind',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__P] :
          ( c_24__type__554___24t(V0__A,V1__P)
         => ( p(happ(V1__P,cIntMap_2eMap_2eM0___24a1(V0__A)))
           => ( ! [V3__a] :
                  ( cIntMap_2eMap_2ead___24t(V3__a)
                 => ! [V4__y] :
                      ( t(V4__y,V0__A)
                     => p(happ(V1__P,cIntMap_2eMap_2eM1___24a3(V0__A,V3__a,V4__y))) ) )
             => ( ! [V4__m1] :
                    ( cIntMap_2eMap_2eMap___24t(V0__A,V4__m1)
                   => ! [V5__m2] :
                        ( cIntMap_2eMap_2eMap___24t(V0__A,V5__m2)
                       => ( cIntMap_2eMapcanon_2emapcanon___24a2(V0__A,V4__m1)
                         => ( p(happ(V1__P,V4__m1))
                           => ( cIntMap_2eMapcanon_2emapcanon___24a2(V0__A,V5__m2)
                             => ( p(happ(V1__P,V5__m2))
                               => ( cCoq_2eInit_2ePeano_2ele___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO)),cIntMap_2eMap_2eMapCard___24a2(V0__A,cIntMap_2eMap_2eM2___24a3(V0__A,V4__m1,V5__m2)))
                                 => p(happ(V1__P,cIntMap_2eMap_2eM2___24a3(V0__A,V4__m1,V5__m2))) ) ) ) ) ) ) )
               => ! [V5__m] :
                    ( cIntMap_2eMap_2eMap___24t(V0__A,V5__m)
                   => ( cIntMap_2eMapcanon_2emapcanon___24a2(V0__A,V5__m)
                     => p(happ(V1__P,V5__m)) ) ) ) ) ) ) ) ).

fof('IntMap.Mapcanon.mapcanon_unique',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__m] :
          ( cIntMap_2eMap_2eMap___24t(V0__A,V1__m)
         => ! [V2__m_27] :
              ( cIntMap_2eMap_2eMap___24t(V0__A,V2__m_27)
             => ( cIntMap_2eMapcanon_2emapcanon___24a2(V0__A,V1__m)
               => ( cIntMap_2eMapcanon_2emapcanon___24a2(V0__A,V2__m_27)
                 => ( cIntMap_2eMapaxioms_2eeqmap___24a3(V0__A,V1__m,V2__m_27)
                   => V1__m = V2__m_27 ) ) ) ) ) ) ).

fof('IntMap.Mapcard.MapCard_Dom',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__m] :
          ( cIntMap_2eMap_2eMap___24t(V0__A,V1__m)
         => cIntMap_2eMap_2eMapCard___24a2(V0__A,V1__m) = cIntMap_2eMap_2eMapCard___24a2(cCoq_2eInit_2eDatatypes_2eunit,cIntMap_2eFset_2eMapDom___24a2(V0__A,V1__m)) ) ) ).

fof('IntMap.Mapcard.MapCard_Dom_Put_behind',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__m] :
          ( cIntMap_2eMap_2eMap___24t(V0__A,V1__m)
         => ! [V2__a] :
              ( cIntMap_2eMap_2ead___24t(V2__a)
             => ! [V3__y] :
                  ( t(V3__y,V0__A)
                 => cIntMap_2eFset_2eMapDom___24a2(V0__A,cIntMap_2eMap_2eMapPut__behind___24a4(V0__A,V1__m,V2__a,V3__y)) = cIntMap_2eFset_2eMapDom___24a2(V0__A,cIntMap_2eMap_2eMapPut___24a4(V0__A,V1__m,V2__a,V3__y)) ) ) ) ) ).

fof('IntMap.Mapcard.MapCard_Put1_equals_2',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__p] :
          ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__p)
         => ! [V2__a] :
              ( cIntMap_2eMap_2ead___24t(V2__a)
             => ! [V3__a_27] :
                  ( cIntMap_2eMap_2ead___24t(V3__a_27)
                 => ! [V4__y] :
                      ( t(V4__y,V0__A)
                     => ! [V5__y_27] :
                          ( t(V5__y_27,V0__A)
                         => cIntMap_2eMap_2eMapCard___24a2(V0__A,cIntMap_2eMap_2eMapPut1___24a6(V0__A,V2__a,V4__y,V3__a_27,V5__y_27,V1__p)) = cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO)) ) ) ) ) ) ) ).

fof('IntMap.Mapcard.MapCard_Put_1_conv',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__m] :
          ( cIntMap_2eMap_2eMap___24t(V0__A,V1__m)
         => ! [V2__a] :
              ( cIntMap_2eMap_2ead___24t(V2__a)
             => ! [V3__y] :
                  ( t(V3__y,V0__A)
                 => ! [V4__y_27] :
                      ( t(V4__y_27,V0__A)
                     => ( cIntMap_2eMap_2eMapGet___24a3(V0__A,V1__m,V2__a) = cCoq_2eInit_2eDatatypes_2eSome___24a2(V0__A,V3__y)
                       => cIntMap_2eMap_2eMapCard___24a2(V0__A,cIntMap_2eMap_2eMapPut___24a4(V0__A,V1__m,V2__a,V4__y_27)) = cIntMap_2eMap_2eMapCard___24a2(V0__A,V1__m) ) ) ) ) ) ) ).

fof('IntMap.Mapcard.MapCard_Put_2',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__m] :
          ( cIntMap_2eMap_2eMap___24t(V0__A,V1__m)
         => ! [V2__a] :
              ( cIntMap_2eMap_2ead___24t(V2__a)
             => ! [V3__y] :
                  ( t(V3__y,V0__A)
                 => ( cIntMap_2eMap_2eMapCard___24a2(V0__A,cIntMap_2eMap_2eMapPut___24a4(V0__A,V1__m,V2__a,V3__y)) = cCoq_2eInit_2eDatatypes_2eS___24a1(cIntMap_2eMap_2eMapCard___24a2(V0__A,V1__m))
                   => cIntMap_2eMap_2eMapGet___24a3(V0__A,V1__m,V2__a) = cCoq_2eInit_2eDatatypes_2eNone___24a1(V0__A) ) ) ) ) ) ).

fof('IntMap.Mapcard.MapCard_Put_2_conv',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__m] :
          ( cIntMap_2eMap_2eMap___24t(V0__A,V1__m)
         => ! [V2__a] :
              ( cIntMap_2eMap_2ead___24t(V2__a)
             => ! [V3__y] :
                  ( t(V3__y,V0__A)
                 => ( cIntMap_2eMap_2eMapGet___24a3(V0__A,V1__m,V2__a) = cCoq_2eInit_2eDatatypes_2eNone___24a1(V0__A)
                   => cIntMap_2eMap_2eMapCard___24a2(V0__A,cIntMap_2eMap_2eMapPut___24a4(V0__A,V1__m,V2__a,V3__y)) = cCoq_2eInit_2eDatatypes_2eS___24a1(cIntMap_2eMap_2eMapCard___24a2(V0__A,V1__m)) ) ) ) ) ) ).

fof('IntMap.Mapcard.MapCard_Put_behind_Put',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__m] :
          ( cIntMap_2eMap_2eMap___24t(V0__A,V1__m)
         => ! [V2__a] :
              ( cIntMap_2eMap_2ead___24t(V2__a)
             => ! [V3__y] :
                  ( t(V3__y,V0__A)
                 => cIntMap_2eMap_2eMapCard___24a2(V0__A,cIntMap_2eMap_2eMapPut__behind___24a4(V0__A,V1__m,V2__a,V3__y)) = cIntMap_2eMap_2eMapCard___24a2(V0__A,cIntMap_2eMap_2eMapPut___24a4(V0__A,V1__m,V2__a,V3__y)) ) ) ) ) ).

fof('IntMap.Mapcard.MapCard_Put_lb',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__m] :
          ( cIntMap_2eMap_2eMap___24t(V0__A,V1__m)
         => ! [V2__a] :
              ( cIntMap_2eMap_2ead___24t(V2__a)
             => ! [V3__y] :
                  ( t(V3__y,V0__A)
                 => cCoq_2eInit_2ePeano_2ege___24a2(cIntMap_2eMap_2eMapCard___24a2(V0__A,cIntMap_2eMap_2eMapPut___24a4(V0__A,V1__m,V2__a,V3__y)),cIntMap_2eMap_2eMapCard___24a2(V0__A,V1__m)) ) ) ) ) ).

fof('IntMap.Mapcard.MapCard_Put_ub',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__m] :
          ( cIntMap_2eMap_2eMap___24t(V0__A,V1__m)
         => ! [V2__a] :
              ( cIntMap_2eMap_2ead___24t(V2__a)
             => ! [V3__y] :
                  ( t(V3__y,V0__A)
                 => cCoq_2eInit_2ePeano_2ele___24a2(cIntMap_2eMap_2eMapCard___24a2(V0__A,cIntMap_2eMap_2eMapPut___24a4(V0__A,V1__m,V2__a,V3__y)),cCoq_2eInit_2eDatatypes_2eS___24a1(cIntMap_2eMap_2eMapCard___24a2(V0__A,V1__m))) ) ) ) ) ).

fof('IntMap.Mapcard.MapCard_Remove_1',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__m] :
          ( cIntMap_2eMap_2eMap___24t(V0__A,V1__m)
         => ! [V2__a] :
              ( cIntMap_2eMap_2ead___24t(V2__a)
             => ( cIntMap_2eMap_2eMapCard___24a2(V0__A,cIntMap_2eMap_2eMapRemove___24a3(V0__A,V1__m,V2__a)) = cIntMap_2eMap_2eMapCard___24a2(V0__A,V1__m)
               => cIntMap_2eMap_2eMapGet___24a3(V0__A,V1__m,V2__a) = cCoq_2eInit_2eDatatypes_2eNone___24a1(V0__A) ) ) ) ) ).

fof('IntMap.Mapcard.MapCard_Remove_2_conv',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__m] :
          ( cIntMap_2eMap_2eMap___24t(V0__A,V1__m)
         => ! [V2__a] :
              ( cIntMap_2eMap_2ead___24t(V2__a)
             => ! [V3__y] :
                  ( t(V3__y,V0__A)
                 => ( cIntMap_2eMap_2eMapGet___24a3(V0__A,V1__m,V2__a) = cCoq_2eInit_2eDatatypes_2eSome___24a2(V0__A,V3__y)
                   => cCoq_2eInit_2eDatatypes_2eS___24a1(cIntMap_2eMap_2eMapCard___24a2(V0__A,cIntMap_2eMap_2eMapRemove___24a3(V0__A,V1__m,V2__a))) = cIntMap_2eMap_2eMapCard___24a2(V0__A,V1__m) ) ) ) ) ) ).

fof('IntMap.Mapcard.MapCard_Remove_lb',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__m] :
          ( cIntMap_2eMap_2eMap___24t(V0__A,V1__m)
         => ! [V2__a] :
              ( cIntMap_2eMap_2ead___24t(V2__a)
             => cCoq_2eInit_2ePeano_2ege___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(cIntMap_2eMap_2eMapCard___24a2(V0__A,cIntMap_2eMap_2eMapRemove___24a3(V0__A,V1__m,V2__a))),cIntMap_2eMap_2eMapCard___24a2(V0__A,V1__m)) ) ) ) ).

fof('IntMap.Mapcard.MapCard_Remove_ub',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__m] :
          ( cIntMap_2eMap_2eMap___24t(V0__A,V1__m)
         => ! [V2__a] :
              ( cIntMap_2eMap_2ead___24t(V2__a)
             => cCoq_2eInit_2ePeano_2ele___24a2(cIntMap_2eMap_2eMapCard___24a2(V0__A,cIntMap_2eMap_2eMapRemove___24a3(V0__A,V1__m,V2__a)),cIntMap_2eMap_2eMapCard___24a2(V0__A,V1__m)) ) ) ) ).

fof('IntMap.Mapcard.MapCard_as_Fold',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__m] :
          ( cIntMap_2eMap_2eMap___24t(V0__A,V1__m)
         => cIntMap_2eMap_2eMapCard___24a2(V0__A,V1__m) = cIntMap_2eMapiter_2eMapFold___24a6(V0__A,cCoq_2eInit_2eDatatypes_2enat,cCoq_2eInit_2eDatatypes_2eO,cCoq_2eInit_2eNat_2eadd,c_24__lam__13414___24a1(V0__A),V1__m) ) ) ).

fof('IntMap.Mapcard.MapCard_as_Fold_1',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__m] :
          ( cIntMap_2eMap_2eMap___24t(V0__A,V1__m)
         => ! [V2__pf] :
              ( c_24__type__13176___24t(V0__A,V2__pf)
             => cIntMap_2eMap_2eMapCard___24a2(V0__A,V1__m) = cIntMap_2eMapiter_2eMapFold1___24a7(V0__A,cCoq_2eInit_2eDatatypes_2enat,cCoq_2eInit_2eDatatypes_2eO,cCoq_2eInit_2eNat_2eadd,c_24__lam__13414___24a1(V0__A),V2__pf,V1__m) ) ) ) ).

fof('IntMap.Mapcard.MapCard_as_length',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__m] :
          ( cIntMap_2eMap_2eMap___24t(V0__A,V1__m)
         => cIntMap_2eMap_2eMapCard___24a2(V0__A,V1__m) = cCoq_2eInit_2eDatatypes_2elength___24a2(cCoq_2eInit_2eDatatypes_2eprod___24a2(cIntMap_2eMap_2ead,V0__A),cIntMap_2eMapiter_2ealist__of__Map___24a2(V0__A,V1__m)) ) ) ).

fof('IntMap.Mapcard.MapCard_ext',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__m] :
          ( cIntMap_2eMap_2eMap___24t(V0__A,V1__m)
         => ! [V2__m_27] :
              ( cIntMap_2eMap_2eMap___24t(V0__A,V2__m_27)
             => ( cIntMap_2eMap_2eeqm___24a3(V0__A,cIntMap_2eMap_2eMapGet___24a2(V0__A,V1__m),cIntMap_2eMap_2eMapGet___24a2(V0__A,V2__m_27))
               => cIntMap_2eMap_2eMapCard___24a2(V0__A,V1__m) = cIntMap_2eMap_2eMapCard___24a2(V0__A,V2__m_27) ) ) ) ) ).

fof('IntMap.Mapcard.MapCard_is_O',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__m] :
          ( cIntMap_2eMap_2eMap___24t(V0__A,V1__m)
         => ( cIntMap_2eMap_2eMapCard___24a2(V0__A,V1__m) = cCoq_2eInit_2eDatatypes_2eO
           => ! [V3__a] :
                ( cIntMap_2eMap_2ead___24t(V3__a)
               => cIntMap_2eMap_2eMapGet___24a3(V0__A,V1__m,V3__a) = cCoq_2eInit_2eDatatypes_2eNone___24a1(V0__A) ) ) ) ) ).

fof('IntMap.Mapcard.MapCard_is_one_unique',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__m] :
          ( cIntMap_2eMap_2eMap___24t(V0__A,V1__m)
         => ( cIntMap_2eMap_2eMapCard___24a2(V0__A,V1__m) = cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO)
           => ! [V3__a] :
                ( cIntMap_2eMap_2ead___24t(V3__a)
               => ! [V4__a_27] :
                    ( cIntMap_2eMap_2ead___24t(V4__a_27)
                   => ! [V5__y] :
                        ( t(V5__y,V0__A)
                       => ! [V6__y_27] :
                            ( t(V6__y_27,V0__A)
                           => ( cIntMap_2eMap_2eMapGet___24a3(V0__A,V1__m,V3__a) = cCoq_2eInit_2eDatatypes_2eSome___24a2(V0__A,V5__y)
                             => ( cIntMap_2eMap_2eMapGet___24a3(V0__A,V1__m,V4__a_27) = cCoq_2eInit_2eDatatypes_2eSome___24a2(V0__A,V6__y_27)
                               => ( V3__a = V4__a_27
                                  & V5__y = V6__y_27 ) ) ) ) ) ) ) ) ) ) ).

fof('IntMap.Mapcard.MapCard_makeM2',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__m] :
          ( cIntMap_2eMap_2eMap___24t(V0__A,V1__m)
         => ! [V2__m_27] :
              ( cIntMap_2eMap_2eMap___24t(V0__A,V2__m_27)
             => cIntMap_2eMap_2eMapCard___24a2(V0__A,cIntMap_2eMap_2emakeM2___24a3(V0__A,V1__m,V2__m_27)) = cCoq_2eInit_2eNat_2eadd___24a2(cIntMap_2eMap_2eMapCard___24a2(V0__A,V1__m),cIntMap_2eMap_2eMapCard___24a2(V0__A,V2__m_27)) ) ) ) ).

fof('IntMap.Mapcard.MapDomRestrBy_Card_lb',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__B] :
          ( cType___24t(V1__B)
         => ! [V2__m] :
              ( cIntMap_2eMap_2eMap___24t(V0__A,V2__m)
             => ! [V3__m_27] :
                  ( cIntMap_2eMap_2eMap___24t(V1__B,V3__m_27)
                 => cCoq_2eInit_2ePeano_2ege___24a2(cCoq_2eInit_2eNat_2eadd___24a2(cIntMap_2eMap_2eMapCard___24a2(V1__B,V3__m_27),cIntMap_2eMap_2eMapCard___24a2(V0__A,cIntMap_2eFset_2eMapDomRestrBy___24a4(V0__A,V1__B,V2__m,V3__m_27))),cIntMap_2eMap_2eMapCard___24a2(V0__A,V2__m)) ) ) ) ) ).

fof('IntMap.Mapcard.MapDomRestrBy_Card_ub_l',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__B] :
          ( cType___24t(V1__B)
         => ! [V2__m] :
              ( cIntMap_2eMap_2eMap___24t(V0__A,V2__m)
             => ! [V3__m_27] :
                  ( cIntMap_2eMap_2eMap___24t(V1__B,V3__m_27)
                 => cCoq_2eInit_2ePeano_2ele___24a2(cIntMap_2eMap_2eMapCard___24a2(V0__A,cIntMap_2eFset_2eMapDomRestrBy___24a4(V0__A,V1__B,V2__m,V3__m_27)),cIntMap_2eMap_2eMapCard___24a2(V0__A,V2__m)) ) ) ) ) ).

fof('IntMap.Mapcard.MapDomRestrTo_Card_ub_l',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__B] :
          ( cType___24t(V1__B)
         => ! [V2__m] :
              ( cIntMap_2eMap_2eMap___24t(V0__A,V2__m)
             => ! [V3__m_27] :
                  ( cIntMap_2eMap_2eMap___24t(V1__B,V3__m_27)
                 => cCoq_2eInit_2ePeano_2ele___24a2(cIntMap_2eMap_2eMapCard___24a2(V0__A,cIntMap_2eFset_2eMapDomRestrTo___24a4(V0__A,V1__B,V2__m,V3__m_27)),cIntMap_2eMap_2eMapCard___24a2(V0__A,V2__m)) ) ) ) ) ).

fof('IntMap.Mapcard.MapDomRestrTo_Card_ub_r',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__B] :
          ( cType___24t(V1__B)
         => ! [V2__m] :
              ( cIntMap_2eMap_2eMap___24t(V0__A,V2__m)
             => ! [V3__m_27] :
                  ( cIntMap_2eMap_2eMap___24t(V1__B,V3__m_27)
                 => cCoq_2eInit_2ePeano_2ele___24a2(cIntMap_2eMap_2eMapCard___24a2(V0__A,cIntMap_2eFset_2eMapDomRestrTo___24a4(V0__A,V1__B,V2__m,V3__m_27)),cIntMap_2eMap_2eMapCard___24a2(V1__B,V3__m_27)) ) ) ) ) ).

fof('IntMap.Mapcard.MapMerge_Card_disjoint',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__m] :
          ( cIntMap_2eMap_2eMap___24t(V0__A,V1__m)
         => ! [V2__m_27] :
              ( cIntMap_2eMap_2eMap___24t(V0__A,V2__m_27)
             => ( cIntMap_2eMap_2eMapCard___24a2(V0__A,cIntMap_2eMap_2eMapMerge___24a3(V0__A,V1__m,V2__m_27)) = cCoq_2eInit_2eNat_2eadd___24a2(cIntMap_2eMap_2eMapCard___24a2(V0__A,V1__m),cIntMap_2eMap_2eMapCard___24a2(V0__A,V2__m_27))
               => cIntMap_2eMapsubset_2eMapDisjoint___24a4(V0__A,V0__A,V1__m,V2__m_27) ) ) ) ) ).

fof('IntMap.Mapcard.MapMerge_Card_lb_l',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__m] :
          ( cIntMap_2eMap_2eMap___24t(V0__A,V1__m)
         => ! [V2__m_27] :
              ( cIntMap_2eMap_2eMap___24t(V0__A,V2__m_27)
             => cCoq_2eInit_2ePeano_2ege___24a2(cIntMap_2eMap_2eMapCard___24a2(V0__A,cIntMap_2eMap_2eMapMerge___24a3(V0__A,V1__m,V2__m_27)),cIntMap_2eMap_2eMapCard___24a2(V0__A,V1__m)) ) ) ) ).

fof('IntMap.Mapcard.MapMerge_Card_lb_r',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__m] :
          ( cIntMap_2eMap_2eMap___24t(V0__A,V1__m)
         => ! [V2__m_27] :
              ( cIntMap_2eMap_2eMap___24t(V0__A,V2__m_27)
             => cCoq_2eInit_2ePeano_2ege___24a2(cIntMap_2eMap_2eMapCard___24a2(V0__A,cIntMap_2eMap_2eMapMerge___24a3(V0__A,V1__m,V2__m_27)),cIntMap_2eMap_2eMapCard___24a2(V0__A,V2__m_27)) ) ) ) ).

fof('IntMap.Mapcard.MapMerge_Card_ub',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__m] :
          ( cIntMap_2eMap_2eMap___24t(V0__A,V1__m)
         => ! [V2__m_27] :
              ( cIntMap_2eMap_2eMap___24t(V0__A,V2__m_27)
             => cCoq_2eInit_2ePeano_2ele___24a2(cIntMap_2eMap_2eMapCard___24a2(V0__A,cIntMap_2eMap_2eMapMerge___24a3(V0__A,V1__m,V2__m_27)),cCoq_2eInit_2eNat_2eadd___24a2(cIntMap_2eMap_2eMapCard___24a2(V0__A,V1__m),cIntMap_2eMap_2eMapCard___24a2(V0__A,V2__m_27))) ) ) ) ).

fof('IntMap.Mapcard.MapMerge_Restr_Card',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__m] :
          ( cIntMap_2eMap_2eMap___24t(V0__A,V1__m)
         => ! [V2__m_27] :
              ( cIntMap_2eMap_2eMap___24t(V0__A,V2__m_27)
             => cCoq_2eInit_2eNat_2eadd___24a2(cIntMap_2eMap_2eMapCard___24a2(V0__A,V1__m),cIntMap_2eMap_2eMapCard___24a2(V0__A,V2__m_27)) = cCoq_2eInit_2eNat_2eadd___24a2(cIntMap_2eMap_2eMapCard___24a2(V0__A,cIntMap_2eMap_2eMapMerge___24a3(V0__A,V1__m,V2__m_27)),cIntMap_2eMap_2eMapCard___24a2(V0__A,cIntMap_2eFset_2eMapDomRestrTo___24a4(V0__A,V0__A,V1__m,V2__m_27))) ) ) ) ).

fof('IntMap.Mapcard.MapMerge_disjoint_Card',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__m] :
          ( cIntMap_2eMap_2eMap___24t(V0__A,V1__m)
         => ! [V2__m_27] :
              ( cIntMap_2eMap_2eMap___24t(V0__A,V2__m_27)
             => ( cIntMap_2eMapsubset_2eMapDisjoint___24a4(V0__A,V0__A,V1__m,V2__m_27)
               => cIntMap_2eMap_2eMapCard___24a2(V0__A,cIntMap_2eMap_2eMapMerge___24a3(V0__A,V1__m,V2__m_27)) = cCoq_2eInit_2eNat_2eadd___24a2(cIntMap_2eMap_2eMapCard___24a2(V0__A,V1__m),cIntMap_2eMap_2eMapCard___24a2(V0__A,V2__m_27)) ) ) ) ) ).

fof('IntMap.Mapcard.MapSplit_Card',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__B] :
          ( cType___24t(V1__B)
         => ! [V2__m] :
              ( cIntMap_2eMap_2eMap___24t(V0__A,V2__m)
             => ! [V3__m_27] :
                  ( cIntMap_2eMap_2eMap___24t(V1__B,V3__m_27)
                 => cIntMap_2eMap_2eMapCard___24a2(V0__A,V2__m) = cCoq_2eInit_2eNat_2eadd___24a2(cIntMap_2eMap_2eMapCard___24a2(V0__A,cIntMap_2eFset_2eMapDomRestrTo___24a4(V0__A,V1__B,V2__m,V3__m_27)),cIntMap_2eMap_2eMapCard___24a2(V0__A,cIntMap_2eFset_2eMapDomRestrBy___24a4(V0__A,V1__B,V2__m,V3__m_27))) ) ) ) ) ).

fof('IntMap.Mapcard.MapSubset_Card_le',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__B] :
          ( cType___24t(V1__B)
         => ! [V2__m] :
              ( cIntMap_2eMap_2eMap___24t(V0__A,V2__m)
             => ! [V3__m_27] :
                  ( cIntMap_2eMap_2eMap___24t(V1__B,V3__m_27)
                 => ( cIntMap_2eMapsubset_2eMapSubset___24a4(V0__A,V1__B,V2__m,V3__m_27)
                   => cCoq_2eInit_2ePeano_2ele___24a2(cIntMap_2eMap_2eMapCard___24a2(V0__A,V2__m),cIntMap_2eMap_2eMapCard___24a2(V1__B,V3__m_27)) ) ) ) ) ) ).

fof('IntMap.Mapcard.MapSubset_card_eq',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__B] :
          ( cType___24t(V1__B)
         => ! [V2__m] :
              ( cIntMap_2eMap_2eMap___24t(V0__A,V2__m)
             => ! [V3__m_27] :
                  ( cIntMap_2eMap_2eMap___24t(V1__B,V3__m_27)
                 => ( cIntMap_2eMapsubset_2eMapSubset___24a4(V0__A,V1__B,V2__m,V3__m_27)
                   => ( cCoq_2eInit_2ePeano_2ele___24a2(cIntMap_2eMap_2eMapCard___24a2(V1__B,V3__m_27),cIntMap_2eMap_2eMapCard___24a2(V0__A,V2__m))
                     => cIntMap_2eMapaxioms_2eeqmap___24a3(cCoq_2eInit_2eDatatypes_2eunit,cIntMap_2eFset_2eMapDom___24a2(V0__A,V2__m),cIntMap_2eFset_2eMapDom___24a2(V1__B,V3__m_27)) ) ) ) ) ) ) ).

fof('IntMap.Mapcard.MapSubset_card_eq_1',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__B] :
          ( cType___24t(V1__B)
         => ! [V2__n] :
              ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__n)
             => ! [V3__m] :
                  ( cIntMap_2eMap_2eMap___24t(V0__A,V3__m)
                 => ! [V4__m_27] :
                      ( cIntMap_2eMap_2eMap___24t(V1__B,V4__m_27)
                     => ( cIntMap_2eMapsubset_2eMapSubset___24a4(V0__A,V1__B,V3__m,V4__m_27)
                       => ( cIntMap_2eMap_2eMapCard___24a2(V0__A,V3__m) = V2__n
                         => ( cIntMap_2eMap_2eMapCard___24a2(V1__B,V4__m_27) = V2__n
                           => cIntMap_2eMapsubset_2eMapSubset___24a4(V1__B,V0__A,V4__m_27,V3__m) ) ) ) ) ) ) ) ) ).

fof('IntMap.Mapiter.MapCollect_as_Fold',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__B] :
          ( cType___24t(V1__B)
         => ! [V2__f] :
              ( c_24__type__1574___24t(V0__A,V1__B,V2__f)
             => ! [V3__m] :
                  ( cIntMap_2eMap_2eMap___24t(V0__A,V3__m)
                 => cIntMap_2eMapiter_2eMapCollect___24a4(V0__A,V1__B,V2__f,V3__m) = cIntMap_2eMapiter_2eMapFold___24a6(V0__A,cIntMap_2eMap_2eMap___24a1(V1__B),cIntMap_2eMap_2eM0___24a1(V1__B),cIntMap_2eMap_2eMapMerge___24a1(V1__B),V2__f,V3__m) ) ) ) ) ).

fof('IntMap.Mapiter.MapFold_as_fold',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__M] :
          ( cType___24t(V1__M)
         => ! [V2__neutral] :
              ( t(V2__neutral,V1__M)
             => ! [V3__op] :
                  ( c_24__type__1698___24t(V1__M,V3__op)
                 => ( ! [V4__a] :
                        ( t(V4__a,V1__M)
                       => ! [V5__b] :
                            ( t(V5__b,V1__M)
                           => ! [V6__c] :
                                ( t(V6__c,V1__M)
                               => happ(happ(V3__op,happ(happ(V3__op,V4__a),V5__b)),V6__c) = happ(happ(V3__op,V4__a),happ(happ(V3__op,V5__b),V6__c)) ) ) )
                   => ( ! [V5__a] :
                          ( t(V5__a,V1__M)
                         => happ(happ(V3__op,V2__neutral),V5__a) = V5__a )
                     => ( ! [V6__a] :
                            ( t(V6__a,V1__M)
                           => happ(happ(V3__op,V6__a),V2__neutral) = V6__a )
                       => ! [V7__f] :
                            ( c_24__type__1705___24t(V0__A,V1__M,V7__f)
                           => ! [V8__m] :
                                ( cIntMap_2eMap_2eMap___24t(V0__A,V8__m)
                               => cIntMap_2eMapiter_2eMapFold___24a6(V0__A,V1__M,V2__neutral,V3__op,V7__f,V8__m) = cCoq_2eLists_2eList_2efold__right___24a5(V1__M,cCoq_2eInit_2eDatatypes_2eprod___24a2(cIntMap_2eMap_2ead,V0__A),c_24__lam__14505___24a4(V0__A,V1__M,V3__op,V7__f),V2__neutral,cIntMap_2eMapiter_2ealist__of__Map___24a2(V0__A,V8__m)) ) ) ) ) ) ) ) ) ) ).

fof('IntMap.Mapiter.MapFold_state_stateless',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__M] :
          ( cType___24t(V1__M)
         => ! [V2__neutral] :
              ( t(V2__neutral,V1__M)
             => ! [V3__op] :
                  ( c_24__type__1698___24t(V1__M,V3__op)
                 => ! [V4__State] :
                      ( cType___24t(V4__State)
                     => ! [V5__f] :
                          ( c_24__type__13915___24t(V0__A,V1__M,V4__State,V5__f)
                         => ! [V6__g] :
                              ( c_24__type__14144___24t(V0__A,V1__M,V4__State,V6__g)
                             => ( ! [V7__state] :
                                    ( t(V7__state,V4__State)
                                   => ! [V8__a] :
                                        ( cIntMap_2eMap_2ead___24t(V8__a)
                                       => ! [V9__y] :
                                            ( t(V9__y,V0__A)
                                           => cCoq_2eInit_2eDatatypes_2esnd___24a3(V4__State,V1__M,happ(happ(happ(V5__f,V7__state),V8__a),V9__y)) = happ(happ(V6__g,V8__a),V9__y) ) ) )
                               => ! [V8__state] :
                                    ( t(V8__state,V4__State)
                                   => ! [V9__m] :
                                        ( cIntMap_2eMap_2eMap___24t(V0__A,V9__m)
                                       => cCoq_2eInit_2eDatatypes_2esnd___24a3(V4__State,V1__M,cIntMap_2eMapiter_2eMapFold__state___24a8(V0__A,V1__M,V2__neutral,V3__op,V4__State,V5__f,V8__state,V9__m)) = cIntMap_2eMapiter_2eMapFold___24a6(V0__A,V1__M,V2__neutral,V3__op,V6__g,V9__m) ) ) ) ) ) ) ) ) ) ) ).

fof('IntMap.Mapiter.MapFold_state_stateless_1',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__M] :
          ( cType___24t(V1__M)
         => ! [V2__neutral] :
              ( t(V2__neutral,V1__M)
             => ! [V3__op] :
                  ( c_24__type__1698___24t(V1__M,V3__op)
                 => ! [V4__State] :
                      ( cType___24t(V4__State)
                     => ! [V5__f] :
                          ( c_24__type__13915___24t(V0__A,V1__M,V4__State,V5__f)
                         => ! [V6__m] :
                              ( cIntMap_2eMap_2eMap___24t(V0__A,V6__m)
                             => ! [V7__g] :
                                  ( c_24__type__14144___24t(V0__A,V1__M,V4__State,V7__g)
                                 => ! [V8__pf] :
                                      ( c_24__type__13920___24t(V0__A,V1__M,V4__State,V8__pf)
                                     => ( ! [V9__state] :
                                            ( t(V9__state,V4__State)
                                           => ! [V10__a] :
                                                ( cIntMap_2eMap_2ead___24t(V10__a)
                                               => ! [V11__y] :
                                                    ( t(V11__y,V0__A)
                                                   => cCoq_2eInit_2eDatatypes_2esnd___24a3(V4__State,V1__M,happ(happ(happ(V5__f,V9__state),V10__a),V11__y)) = happ(happ(V7__g,V10__a),V11__y) ) ) )
                                       => ! [V10__state] :
                                            ( t(V10__state,V4__State)
                                           => cCoq_2eInit_2eDatatypes_2esnd___24a3(V4__State,V1__M,cIntMap_2eMapiter_2eMapFold1__state___24a9(V0__A,V1__M,V2__neutral,V3__op,V4__State,V5__f,V10__state,V8__pf,V6__m)) = cIntMap_2eMapiter_2eMapFold1___24a7(V0__A,V1__M,V2__neutral,V3__op,V7__g,V8__pf,V6__m) ) ) ) ) ) ) ) ) ) ) ) ).

fof('IntMap.Mapiter.MapSweep_semantics_1',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__f] :
          ( c_24__type__13540___24t(V0__A,V1__f)
         => ! [V2__m] :
              ( cIntMap_2eMap_2eMap___24t(V0__A,V2__m)
             => ! [V3__a] :
                  ( cIntMap_2eMap_2ead___24t(V3__a)
                 => ! [V4__y] :
                      ( t(V4__y,V0__A)
                     => ( cIntMap_2eMapiter_2eMapSweep___24a3(V0__A,V1__f,V2__m) = cCoq_2eInit_2eDatatypes_2eSome___24a2(cCoq_2eInit_2eDatatypes_2eprod___24a2(cIntMap_2eMap_2ead,V0__A),cCoq_2eInit_2eDatatypes_2epair___24a4(cIntMap_2eMap_2ead,V0__A,V3__a,V4__y))
                       => happ(happ(V1__f,V3__a),V4__y) = cCoq_2eInit_2eDatatypes_2etrue ) ) ) ) ) ) ).

fof('IntMap.Mapiter.MapSweep_semantics_1_1',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__f] :
          ( c_24__type__13540___24t(V0__A,V1__f)
         => ! [V2__m] :
              ( cIntMap_2eMap_2eMap___24t(V0__A,V2__m)
             => ! [V3__pf] :
                  ( c_24__type__13176___24t(V0__A,V3__pf)
                 => ! [V4__a] :
                      ( cIntMap_2eMap_2ead___24t(V4__a)
                     => ! [V5__y] :
                          ( t(V5__y,V0__A)
                         => ( cIntMap_2eMapiter_2eMapSweep1___24a4(V0__A,V1__f,V3__pf,V2__m) = cCoq_2eInit_2eDatatypes_2eSome___24a2(cCoq_2eInit_2eDatatypes_2eprod___24a2(cIntMap_2eMap_2ead,V0__A),cCoq_2eInit_2eDatatypes_2epair___24a4(cIntMap_2eMap_2ead,V0__A,V4__a,V5__y))
                           => happ(happ(V1__f,V4__a),V5__y) = cCoq_2eInit_2eDatatypes_2etrue ) ) ) ) ) ) ) ).

fof('IntMap.Mapiter.MapSweep_semantics_3',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__f] :
          ( c_24__type__13540___24t(V0__A,V1__f)
         => ! [V2__m] :
              ( cIntMap_2eMap_2eMap___24t(V0__A,V2__m)
             => ( cIntMap_2eMapiter_2eMapSweep___24a3(V0__A,V1__f,V2__m) = cCoq_2eInit_2eDatatypes_2eNone___24a1(cCoq_2eInit_2eDatatypes_2eprod___24a2(cIntMap_2eMap_2ead,V0__A))
               => ! [V4__a] :
                    ( cIntMap_2eMap_2ead___24t(V4__a)
                   => ! [V5__y] :
                        ( t(V5__y,V0__A)
                       => ( cIntMap_2eMap_2eMapGet___24a3(V0__A,V2__m,V4__a) = cCoq_2eInit_2eDatatypes_2eSome___24a2(V0__A,V5__y)
                         => happ(happ(V1__f,V4__a),V5__y) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ) ) ) ).

fof('IntMap.Mapiter.Map_of_alist_of_Map',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__m] :
          ( cIntMap_2eMap_2eMap___24t(V0__A,V1__m)
         => cIntMap_2eMapaxioms_2eeqmap___24a3(V0__A,cIntMap_2eMapiter_2eMap__of__alist___24a2(V0__A,cIntMap_2eMapiter_2ealist__of__Map___24a2(V0__A,V1__m)),V1__m) ) ) ).

fof('IntMap.Mapiter.ad_comp_double_inj',axiom,
    ! [V0__pf] :
      ( c_24__type__13191___24t(V0__pf)
     => ( cIntMap_2eMapiter_2ead__inj___24a1(V0__pf)
       => cIntMap_2eMapiter_2ead__inj___24a1(c_24__lam__13198___24a1(V0__pf)) ) ) ).

fof('IntMap.Mapiter.ad_comp_double_plus_un_inj',axiom,
    ! [V0__pf] :
      ( c_24__type__13191___24t(V0__pf)
     => ( cIntMap_2eMapiter_2ead__inj___24a1(V0__pf)
       => cIntMap_2eMapiter_2ead__inj___24a1(c_24__lam__13200___24a1(V0__pf)) ) ) ).

fof('IntMap.Mapiter.alist_MapMerge_semantics',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__m] :
          ( cIntMap_2eMap_2eMap___24t(V0__A,V1__m)
         => ! [V2__m_27] :
              ( cIntMap_2eMap_2eMap___24t(V0__A,V2__m_27)
             => cIntMap_2eMap_2eeqm___24a3(V0__A,cIntMap_2eMapiter_2ealist__semantics___24a2(V0__A,cIntMap_2eMapiter_2eaapp___24a3(V0__A,cIntMap_2eMapiter_2ealist__of__Map___24a2(V0__A,V2__m_27),cIntMap_2eMapiter_2ealist__of__Map___24a2(V0__A,V1__m))),cIntMap_2eMapiter_2ealist__semantics___24a2(V0__A,cIntMap_2eMapiter_2ealist__of__Map___24a2(V0__A,cIntMap_2eMap_2eMapMerge___24a3(V0__A,V1__m,V2__m_27)))) ) ) ) ).

fof('IntMap.Mapiter.alist_MapMerge_semantics_disjoint',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__m] :
          ( cIntMap_2eMap_2eMap___24t(V0__A,V1__m)
         => ! [V2__m_27] :
              ( cIntMap_2eMap_2eMap___24t(V0__A,V2__m_27)
             => ( cIntMap_2eMapaxioms_2eeqmap___24a3(V0__A,cIntMap_2eFset_2eMapDomRestrTo___24a4(V0__A,V0__A,V1__m,V2__m_27),cIntMap_2eMap_2eM0___24a1(V0__A))
               => cIntMap_2eMap_2eeqm___24a3(V0__A,cIntMap_2eMapiter_2ealist__semantics___24a2(V0__A,cIntMap_2eMapiter_2eaapp___24a3(V0__A,cIntMap_2eMapiter_2ealist__of__Map___24a2(V0__A,V1__m),cIntMap_2eMapiter_2ealist__of__Map___24a2(V0__A,V2__m_27))),cIntMap_2eMapiter_2ealist__semantics___24a2(V0__A,cIntMap_2eMapiter_2ealist__of__Map___24a2(V0__A,cIntMap_2eMap_2eMapMerge___24a3(V0__A,V1__m,V2__m_27)))) ) ) ) ) ).

fof('IntMap.Mapiter.alist_of_Map_semantics',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__m] :
          ( cIntMap_2eMap_2eMap___24t(V0__A,V1__m)
         => cIntMap_2eMap_2eeqm___24a3(V0__A,cIntMap_2eMap_2eMapGet___24a2(V0__A,V1__m),cIntMap_2eMapiter_2ealist__semantics___24a2(V0__A,cIntMap_2eMapiter_2ealist__of__Map___24a2(V0__A,V1__m))) ) ) ).

fof('IntMap.Mapiter.alist_semantics_app',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__l] :
          ( cIntMap_2eMapiter_2ealist___24t(V0__A,V1__l)
         => ! [V2__l_27] :
              ( cIntMap_2eMapiter_2ealist___24t(V0__A,V2__l_27)
             => ! [V3__a] :
                  ( cIntMap_2eMap_2ead___24t(V3__a)
                 => cIntMap_2eMapiter_2ealist__semantics___24a3(V0__A,cIntMap_2eMapiter_2eaapp___24a3(V0__A,V1__l,V2__l_27),V3__a) = c_24__case__Coq_2eInit_2eDatatypes_2eoption_242237___24a4(V0__A,V1__l,V2__l_27,V3__a) ) ) ) ) ).

fof('IntMap.Mapiter.fold_right_aapp',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__M] :
          ( cType___24t(V1__M)
         => ! [V2__neutral] :
              ( t(V2__neutral,V1__M)
             => ! [V3__op] :
                  ( c_24__type__1698___24t(V1__M,V3__op)
                 => ( ! [V4__a] :
                        ( t(V4__a,V1__M)
                       => ! [V5__b] :
                            ( t(V5__b,V1__M)
                           => ! [V6__c] :
                                ( t(V6__c,V1__M)
                               => happ(happ(V3__op,happ(happ(V3__op,V4__a),V5__b)),V6__c) = happ(happ(V3__op,V4__a),happ(happ(V3__op,V5__b),V6__c)) ) ) )
                   => ( ! [V5__a] :
                          ( t(V5__a,V1__M)
                         => happ(happ(V3__op,V2__neutral),V5__a) = V5__a )
                     => ! [V6__f] :
                          ( c_24__type__1705___24t(V0__A,V1__M,V6__f)
                         => ! [V7__l] :
                              ( cIntMap_2eMapiter_2ealist___24t(V0__A,V7__l)
                             => ! [V8__l_27] :
                                  ( cIntMap_2eMapiter_2ealist___24t(V0__A,V8__l_27)
                                 => cCoq_2eLists_2eList_2efold__right___24a5(V1__M,cCoq_2eInit_2eDatatypes_2eprod___24a2(cIntMap_2eMap_2ead,V0__A),c_24__lam__14287___24a4(V0__A,V1__M,V3__op,V6__f),V2__neutral,cIntMap_2eMapiter_2eaapp___24a3(V0__A,V7__l,V8__l_27)) = happ(happ(V3__op,cCoq_2eLists_2eList_2efold__right___24a5(V1__M,cCoq_2eInit_2eDatatypes_2eprod___24a2(cIntMap_2eMap_2ead,V0__A),c_24__lam__14333___24a4(V0__A,V1__M,V3__op,V6__f),V2__neutral,V7__l)),cCoq_2eLists_2eList_2efold__right___24a5(V1__M,cCoq_2eInit_2eDatatypes_2eprod___24a2(cIntMap_2eMap_2ead,V0__A),c_24__lam__14379___24a4(V0__A,V1__M,V3__op,V6__f),V2__neutral,V8__l_27)) ) ) ) ) ) ) ) ) ) ).

fof('IntMap.Mapiter.pair_sp',axiom,
    ! [V0__B] :
      ( cType___24t(V0__B)
     => ! [V1__C] :
          ( cType___24t(V1__C)
         => ! [V2__x] :
              ( cCoq_2eInit_2eDatatypes_2eprod___24t(V0__B,V1__C,V2__x)
             => V2__x = cCoq_2eInit_2eDatatypes_2epair___24a4(V0__B,V1__C,cCoq_2eInit_2eDatatypes_2efst___24a3(V0__B,V1__C,V2__x),cCoq_2eInit_2eDatatypes_2esnd___24a3(V0__B,V1__C,V2__x)) ) ) ) ).

fof('IntMap.Mapsubset.MapDelta_RestrTo_disjoint',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__m] :
          ( cIntMap_2eMap_2eMap___24t(V0__A,V1__m)
         => ! [V2__m_27] :
              ( cIntMap_2eMap_2eMap___24t(V0__A,V2__m_27)
             => cIntMap_2eMapsubset_2eMapDisjoint___24a4(V0__A,V0__A,cIntMap_2eMap_2eMapDelta___24a3(V0__A,V1__m,V2__m_27),cIntMap_2eFset_2eMapDomRestrTo___24a4(V0__A,V0__A,V1__m,V2__m_27)) ) ) ) ).

fof('IntMap.Mapsubset.MapDelta_RestrTo_disjoint_2',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__m] :
          ( cIntMap_2eMap_2eMap___24t(V0__A,V1__m)
         => ! [V2__m_27] :
              ( cIntMap_2eMap_2eMap___24t(V0__A,V2__m_27)
             => cIntMap_2eMapsubset_2eMapDisjoint___24a4(V0__A,V0__A,cIntMap_2eMap_2eMapDelta___24a3(V0__A,V1__m,V2__m_27),cIntMap_2eFset_2eMapDomRestrTo___24a4(V0__A,V0__A,V2__m_27,V1__m)) ) ) ) ).

fof('IntMap.Mapsubset.MapDelta_disjoint',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__m] :
          ( cIntMap_2eMap_2eMap___24t(V0__A,V1__m)
         => ! [V2__m_27] :
              ( cIntMap_2eMap_2eMap___24t(V0__A,V2__m_27)
             => ( cIntMap_2eMapsubset_2eMapDisjoint___24a4(V0__A,V0__A,V1__m,V2__m_27)
               => cIntMap_2eMapaxioms_2eeqmap___24a3(V0__A,cIntMap_2eMap_2eMapDelta___24a3(V0__A,V1__m,V2__m_27),cIntMap_2eMap_2eMapMerge___24a3(V0__A,V1__m,V2__m_27)) ) ) ) ) ).

fof('IntMap.Mapsubset.MapDisjoint_1_imp',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__B] :
          ( cType___24t(V1__B)
         => ! [V2__m] :
              ( cIntMap_2eMap_2eMap___24t(V0__A,V2__m)
             => ! [V3__m_27] :
                  ( cIntMap_2eMap_2eMap___24t(V1__B,V3__m_27)
                 => ( cIntMap_2eMapsubset_2eMapDisjoint__1___24a4(V0__A,V1__B,V2__m,V3__m_27) = cCoq_2eInit_2eDatatypes_2etrue
                   => cIntMap_2eMapsubset_2eMapDisjoint___24a4(V0__A,V1__B,V2__m,V3__m_27) ) ) ) ) ) ).

fof('IntMap.Mapsubset.MapDisjoint_2_imp',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__B] :
          ( cType___24t(V1__B)
         => ! [V2__m] :
              ( cIntMap_2eMap_2eMap___24t(V0__A,V2__m)
             => ! [V3__m_27] :
                  ( cIntMap_2eMap_2eMap___24t(V1__B,V3__m_27)
                 => ( cIntMap_2eMapsubset_2eMapDisjoint__2___24a4(V0__A,V1__B,V2__m,V3__m_27)
                   => cIntMap_2eMapsubset_2eMapDisjoint___24a4(V0__A,V1__B,V2__m,V3__m_27) ) ) ) ) ) ).

fof('IntMap.Mapsubset.MapDisjoint_M1_conv_l',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__B] :
          ( cType___24t(V1__B)
         => ! [V2__m] :
              ( cIntMap_2eMap_2eMap___24t(V0__A,V2__m)
             => ! [V3__a] :
                  ( cIntMap_2eMap_2ead___24t(V3__a)
                 => ! [V4__y] :
                      ( t(V4__y,V1__B)
                     => ( cIntMap_2eFset_2ein__dom___24a3(V0__A,V3__a,V2__m) = cCoq_2eInit_2eDatatypes_2efalse
                       => cIntMap_2eMapsubset_2eMapDisjoint___24a4(V1__B,V0__A,cIntMap_2eMap_2eM1___24a3(V1__B,V3__a,V4__y),V2__m) ) ) ) ) ) ) ).

fof('IntMap.Mapsubset.MapDisjoint_M1_conv_r',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__B] :
          ( cType___24t(V1__B)
         => ! [V2__m] :
              ( cIntMap_2eMap_2eMap___24t(V0__A,V2__m)
             => ! [V3__a] :
                  ( cIntMap_2eMap_2ead___24t(V3__a)
                 => ! [V4__y] :
                      ( t(V4__y,V1__B)
                     => ( cIntMap_2eFset_2ein__dom___24a3(V0__A,V3__a,V2__m) = cCoq_2eInit_2eDatatypes_2efalse
                       => cIntMap_2eMapsubset_2eMapDisjoint___24a4(V0__A,V1__B,V2__m,cIntMap_2eMap_2eM1___24a3(V1__B,V3__a,V4__y)) ) ) ) ) ) ) ).

fof('IntMap.Mapsubset.MapDisjoint_M1_l',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__B] :
          ( cType___24t(V1__B)
         => ! [V2__m] :
              ( cIntMap_2eMap_2eMap___24t(V0__A,V2__m)
             => ! [V3__a] :
                  ( cIntMap_2eMap_2ead___24t(V3__a)
                 => ! [V4__y] :
                      ( t(V4__y,V1__B)
                     => ( cIntMap_2eMapsubset_2eMapDisjoint___24a4(V1__B,V0__A,cIntMap_2eMap_2eM1___24a3(V1__B,V3__a,V4__y),V2__m)
                       => cIntMap_2eFset_2ein__dom___24a3(V0__A,V3__a,V2__m) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ) ) ).

fof('IntMap.Mapsubset.MapDisjoint_M1_r',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__B] :
          ( cType___24t(V1__B)
         => ! [V2__m] :
              ( cIntMap_2eMap_2eMap___24t(V0__A,V2__m)
             => ! [V3__a] :
                  ( cIntMap_2eMap_2ead___24t(V3__a)
                 => ! [V4__y] :
                      ( t(V4__y,V1__B)
                     => ( cIntMap_2eMapsubset_2eMapDisjoint___24a4(V0__A,V1__B,V2__m,cIntMap_2eMap_2eM1___24a3(V1__B,V3__a,V4__y))
                       => cIntMap_2eFset_2ein__dom___24a3(V0__A,V3__a,V2__m) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ) ) ).

fof('IntMap.Mapsubset.MapDisjoint_M2',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__B] :
          ( cType___24t(V1__B)
         => ! [V2__m0] :
              ( cIntMap_2eMap_2eMap___24t(V0__A,V2__m0)
             => ! [V3__m1] :
                  ( cIntMap_2eMap_2eMap___24t(V0__A,V3__m1)
                 => ! [V4__m2] :
                      ( cIntMap_2eMap_2eMap___24t(V1__B,V4__m2)
                     => ! [V5__m3] :
                          ( cIntMap_2eMap_2eMap___24t(V1__B,V5__m3)
                         => ( cIntMap_2eMapsubset_2eMapDisjoint___24a4(V0__A,V1__B,V2__m0,V4__m2)
                           => ( cIntMap_2eMapsubset_2eMapDisjoint___24a4(V0__A,V1__B,V3__m1,V5__m3)
                             => cIntMap_2eMapsubset_2eMapDisjoint___24a4(V0__A,V1__B,cIntMap_2eMap_2eM2___24a3(V0__A,V2__m0,V3__m1),cIntMap_2eMap_2eM2___24a3(V1__B,V4__m2,V5__m3)) ) ) ) ) ) ) ) ) ).

fof('IntMap.Mapsubset.MapDisjoint_M2_l',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__B] :
          ( cType___24t(V1__B)
         => ! [V2__m0] :
              ( cIntMap_2eMap_2eMap___24t(V0__A,V2__m0)
             => ! [V3__m1] :
                  ( cIntMap_2eMap_2eMap___24t(V0__A,V3__m1)
                 => ! [V4__m2] :
                      ( cIntMap_2eMap_2eMap___24t(V1__B,V4__m2)
                     => ! [V5__m3] :
                          ( cIntMap_2eMap_2eMap___24t(V1__B,V5__m3)
                         => ( cIntMap_2eMapsubset_2eMapDisjoint___24a4(V0__A,V1__B,cIntMap_2eMap_2eM2___24a3(V0__A,V2__m0,V3__m1),cIntMap_2eMap_2eM2___24a3(V1__B,V4__m2,V5__m3))
                           => cIntMap_2eMapsubset_2eMapDisjoint___24a4(V0__A,V1__B,V2__m0,V4__m2) ) ) ) ) ) ) ) ).

fof('IntMap.Mapsubset.MapDisjoint_M2_r',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__B] :
          ( cType___24t(V1__B)
         => ! [V2__m0] :
              ( cIntMap_2eMap_2eMap___24t(V0__A,V2__m0)
             => ! [V3__m1] :
                  ( cIntMap_2eMap_2eMap___24t(V0__A,V3__m1)
                 => ! [V4__m2] :
                      ( cIntMap_2eMap_2eMap___24t(V1__B,V4__m2)
                     => ! [V5__m3] :
                          ( cIntMap_2eMap_2eMap___24t(V1__B,V5__m3)
                         => ( cIntMap_2eMapsubset_2eMapDisjoint___24a4(V0__A,V1__B,cIntMap_2eMap_2eM2___24a3(V0__A,V2__m0,V3__m1),cIntMap_2eMap_2eM2___24a3(V1__B,V4__m2,V5__m3))
                           => cIntMap_2eMapsubset_2eMapDisjoint___24a4(V0__A,V1__B,V3__m1,V5__m3) ) ) ) ) ) ) ) ).

fof('IntMap.Mapsubset.MapDisjoint_empty',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__m] :
          ( cIntMap_2eMap_2eMap___24t(V0__A,V1__m)
         => ( cIntMap_2eMapsubset_2eMapDisjoint___24a4(V0__A,V0__A,V1__m,V1__m)
           => cIntMap_2eMapaxioms_2eeqmap___24a3(V0__A,V1__m,cIntMap_2eMap_2eM0___24a1(V0__A)) ) ) ) ).

fof('IntMap.Mapsubset.MapDisjoint_ext',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__B] :
          ( cType___24t(V1__B)
         => ! [V2__m0] :
              ( cIntMap_2eMap_2eMap___24t(V0__A,V2__m0)
             => ! [V3__m1] :
                  ( cIntMap_2eMap_2eMap___24t(V0__A,V3__m1)
                 => ! [V4__m2] :
                      ( cIntMap_2eMap_2eMap___24t(V1__B,V4__m2)
                     => ! [V5__m3] :
                          ( cIntMap_2eMap_2eMap___24t(V1__B,V5__m3)
                         => ( cIntMap_2eMapaxioms_2eeqmap___24a3(V0__A,V2__m0,V3__m1)
                           => ( cIntMap_2eMapaxioms_2eeqmap___24a3(V1__B,V4__m2,V5__m3)
                             => ( cIntMap_2eMapsubset_2eMapDisjoint___24a4(V0__A,V1__B,V2__m0,V4__m2)
                               => cIntMap_2eMapsubset_2eMapDisjoint___24a4(V0__A,V1__B,V3__m1,V5__m3) ) ) ) ) ) ) ) ) ) ).

fof('IntMap.Mapsubset.MapDisjoint_imp_1',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__B] :
          ( cType___24t(V1__B)
         => ! [V2__m] :
              ( cIntMap_2eMap_2eMap___24t(V0__A,V2__m)
             => ! [V3__m_27] :
                  ( cIntMap_2eMap_2eMap___24t(V1__B,V3__m_27)
                 => ( cIntMap_2eMapsubset_2eMapDisjoint___24a4(V0__A,V1__B,V2__m,V3__m_27)
                   => cIntMap_2eMapsubset_2eMapDisjoint__1___24a4(V0__A,V1__B,V2__m,V3__m_27) = cCoq_2eInit_2eDatatypes_2etrue ) ) ) ) ) ).

fof('IntMap.Mapsubset.MapDisjoint_imp_2',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__B] :
          ( cType___24t(V1__B)
         => ! [V2__m] :
              ( cIntMap_2eMap_2eMap___24t(V0__A,V2__m)
             => ! [V3__m_27] :
                  ( cIntMap_2eMap_2eMap___24t(V1__B,V3__m_27)
                 => ( cIntMap_2eMapsubset_2eMapDisjoint___24a4(V0__A,V1__B,V2__m,V3__m_27)
                   => cIntMap_2eMapsubset_2eMapDisjoint__2___24a4(V0__A,V1__B,V2__m,V3__m_27) ) ) ) ) ) ).

fof('IntMap.Mapsubset.MapDisjoint_sym',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__B] :
          ( cType___24t(V1__B)
         => ! [V2__m] :
              ( cIntMap_2eMap_2eMap___24t(V0__A,V2__m)
             => ! [V3__m_27] :
                  ( cIntMap_2eMap_2eMap___24t(V1__B,V3__m_27)
                 => ( cIntMap_2eMapsubset_2eMapDisjoint___24a4(V0__A,V1__B,V2__m,V3__m_27)
                   => cIntMap_2eMapsubset_2eMapDisjoint___24a4(V1__B,V0__A,V3__m_27,V2__m) ) ) ) ) ) ).

fof('IntMap.Mapsubset.MapDomRestr_disjoint',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__B] :
          ( cType___24t(V1__B)
         => ! [V2__C] :
              ( cType___24t(V2__C)
             => ! [V3__m] :
                  ( cIntMap_2eMap_2eMap___24t(V0__A,V3__m)
                 => ! [V4__m_27] :
                      ( cIntMap_2eMap_2eMap___24t(V1__B,V4__m_27)
                     => ! [V5__m_27_27] :
                          ( cIntMap_2eMap_2eMap___24t(V2__C,V5__m_27_27)
                         => cIntMap_2eMapsubset_2eMapDisjoint___24a4(V0__A,V1__B,cIntMap_2eFset_2eMapDomRestrTo___24a4(V0__A,V2__C,V3__m,V5__m_27_27),cIntMap_2eFset_2eMapDomRestrBy___24a4(V1__B,V2__C,V4__m_27,V5__m_27_27)) ) ) ) ) ) ) ).

fof('IntMap.Mapsubset.MapMerge_disjoint',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__m] :
          ( cIntMap_2eMap_2eMap___24t(V0__A,V1__m)
         => ! [V2__m_27] :
              ( cIntMap_2eMap_2eMap___24t(V0__A,V2__m_27)
             => ( cIntMap_2eMapsubset_2eMapDisjoint___24a4(V0__A,V0__A,V1__m,V2__m_27)
               => ! [V4__a] :
                    ( cIntMap_2eMap_2ead___24t(V4__a)
                   => cIntMap_2eFset_2ein__dom___24a3(V0__A,V4__a,cIntMap_2eMap_2eMapMerge___24a3(V0__A,V1__m,V2__m_27)) = cCoq_2eInit_2eDatatypes_2eorb___24a2(cCoq_2eInit_2eDatatypes_2eandb___24a2(cIntMap_2eFset_2ein__dom___24a3(V0__A,V4__a,V1__m),cCoq_2eInit_2eDatatypes_2enegb___24a1(cIntMap_2eFset_2ein__dom___24a3(V0__A,V4__a,V2__m_27))),cCoq_2eInit_2eDatatypes_2eandb___24a2(cIntMap_2eFset_2ein__dom___24a3(V0__A,V4__a,V2__m_27),cCoq_2eInit_2eDatatypes_2enegb___24a1(cIntMap_2eFset_2ein__dom___24a3(V0__A,V4__a,V1__m)))) ) ) ) ) ) ).

fof('IntMap.Mapsubset.MapSubset_1_Dom',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__B] :
          ( cType___24t(V1__B)
         => ! [V2__m] :
              ( cIntMap_2eMap_2eMap___24t(V0__A,V2__m)
             => ! [V3__m_27] :
                  ( cIntMap_2eMap_2eMap___24t(V1__B,V3__m_27)
                 => cIntMap_2eMapsubset_2eMapSubset__1___24a4(V0__A,V1__B,V2__m,V3__m_27) = cIntMap_2eMapsubset_2eMapSubset__1___24a4(cCoq_2eInit_2eDatatypes_2eunit,cCoq_2eInit_2eDatatypes_2eunit,cIntMap_2eFset_2eMapDom___24a2(V0__A,V2__m),cIntMap_2eFset_2eMapDom___24a2(V1__B,V3__m_27)) ) ) ) ) ).

fof('IntMap.Mapsubset.MapSubset_1_imp',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__B] :
          ( cType___24t(V1__B)
         => ! [V2__m] :
              ( cIntMap_2eMap_2eMap___24t(V0__A,V2__m)
             => ! [V3__m_27] :
                  ( cIntMap_2eMap_2eMap___24t(V1__B,V3__m_27)
                 => ( cIntMap_2eMapsubset_2eMapSubset__1___24a4(V0__A,V1__B,V2__m,V3__m_27) = cCoq_2eInit_2eDatatypes_2etrue
                   => cIntMap_2eMapsubset_2eMapSubset___24a4(V0__A,V1__B,V2__m,V3__m_27) ) ) ) ) ) ).

fof('IntMap.Mapsubset.MapSubset_2_imp',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__B] :
          ( cType___24t(V1__B)
         => ! [V2__m] :
              ( cIntMap_2eMap_2eMap___24t(V0__A,V2__m)
             => ! [V3__m_27] :
                  ( cIntMap_2eMap_2eMap___24t(V1__B,V3__m_27)
                 => ( cIntMap_2eMapsubset_2eMapSubset__2___24a4(V0__A,V1__B,V2__m,V3__m_27)
                   => cIntMap_2eMapsubset_2eMapSubset___24a4(V0__A,V1__B,V2__m,V3__m_27) ) ) ) ) ) ).

fof('IntMap.Mapsubset.MapSubset_Disjoint',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__B] :
          ( cType___24t(V1__B)
         => ! [V2__C] :
              ( cType___24t(V2__C)
             => ! [V3__D] :
                  ( cType___24t(V3__D)
                 => ! [V4__m] :
                      ( cIntMap_2eMap_2eMap___24t(V0__A,V4__m)
                     => ! [V5__m_27] :
                          ( cIntMap_2eMap_2eMap___24t(V1__B,V5__m_27)
                         => ! [V6__m_27_27] :
                              ( cIntMap_2eMap_2eMap___24t(V2__C,V6__m_27_27)
                             => ! [V7__m_27_27_27] :
                                  ( cIntMap_2eMap_2eMap___24t(V3__D,V7__m_27_27_27)
                                 => ( cIntMap_2eMapsubset_2eMapSubset___24a4(V0__A,V1__B,V4__m,V5__m_27)
                                   => ( cIntMap_2eMapsubset_2eMapSubset___24a4(V2__C,V3__D,V6__m_27_27,V7__m_27_27_27)
                                     => ( cIntMap_2eMapsubset_2eMapDisjoint___24a4(V1__B,V3__D,V5__m_27,V7__m_27_27_27)
                                       => cIntMap_2eMapsubset_2eMapDisjoint___24a4(V0__A,V2__C,V4__m,V6__m_27_27) ) ) ) ) ) ) ) ) ) ) ) ).

fof('IntMap.Mapsubset.MapSubset_Disjoint_l',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__B] :
          ( cType___24t(V1__B)
         => ! [V2__C] :
              ( cType___24t(V2__C)
             => ! [V3__m] :
                  ( cIntMap_2eMap_2eMap___24t(V0__A,V3__m)
                 => ! [V4__m_27] :
                      ( cIntMap_2eMap_2eMap___24t(V1__B,V4__m_27)
                     => ! [V5__m_27_27] :
                          ( cIntMap_2eMap_2eMap___24t(V2__C,V5__m_27_27)
                         => ( cIntMap_2eMapsubset_2eMapSubset___24a4(V0__A,V1__B,V3__m,V4__m_27)
                           => ( cIntMap_2eMapsubset_2eMapDisjoint___24a4(V1__B,V2__C,V4__m_27,V5__m_27_27)
                             => cIntMap_2eMapsubset_2eMapDisjoint___24a4(V0__A,V2__C,V3__m,V5__m_27_27) ) ) ) ) ) ) ) ) ).

fof('IntMap.Mapsubset.MapSubset_Disjoint_r',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__C] :
          ( cType___24t(V1__C)
         => ! [V2__D] :
              ( cType___24t(V2__D)
             => ! [V3__m] :
                  ( cIntMap_2eMap_2eMap___24t(V0__A,V3__m)
                 => ! [V4__m_27_27] :
                      ( cIntMap_2eMap_2eMap___24t(V1__C,V4__m_27_27)
                     => ! [V5__m_27_27_27] :
                          ( cIntMap_2eMap_2eMap___24t(V2__D,V5__m_27_27_27)
                         => ( cIntMap_2eMapsubset_2eMapSubset___24a4(V1__C,V2__D,V4__m_27_27,V5__m_27_27_27)
                           => ( cIntMap_2eMapsubset_2eMapDisjoint___24a4(V0__A,V2__D,V3__m,V5__m_27_27_27)
                             => cIntMap_2eMapsubset_2eMapDisjoint___24a4(V0__A,V1__C,V3__m,V4__m_27_27) ) ) ) ) ) ) ) ) ).

fof('IntMap.Mapsubset.MapSubset_DomRestrBy_l',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__B] :
          ( cType___24t(V1__B)
         => ! [V2__m] :
              ( cIntMap_2eMap_2eMap___24t(V0__A,V2__m)
             => ! [V3__m_27] :
                  ( cIntMap_2eMap_2eMap___24t(V1__B,V3__m_27)
                 => cIntMap_2eMapsubset_2eMapSubset___24a4(V0__A,V0__A,cIntMap_2eFset_2eMapDomRestrBy___24a4(V0__A,V1__B,V2__m,V3__m_27),V2__m) ) ) ) ) ).

fof('IntMap.Mapsubset.MapSubset_DomRestrBy_mono',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__B] :
          ( cType___24t(V1__B)
         => ! [V2__C] :
              ( cType___24t(V2__C)
             => ! [V3__D] :
                  ( cType___24t(V3__D)
                 => ! [V4__m] :
                      ( cIntMap_2eMap_2eMap___24t(V0__A,V4__m)
                     => ! [V5__m_27] :
                          ( cIntMap_2eMap_2eMap___24t(V1__B,V5__m_27)
                         => ! [V6__m_27_27] :
                              ( cIntMap_2eMap_2eMap___24t(V2__C,V6__m_27_27)
                             => ! [V7__m_27_27_27] :
                                  ( cIntMap_2eMap_2eMap___24t(V3__D,V7__m_27_27_27)
                                 => ( cIntMap_2eMapsubset_2eMapSubset___24a4(V0__A,V2__C,V4__m,V6__m_27_27)
                                   => ( cIntMap_2eMapsubset_2eMapSubset___24a4(V3__D,V1__B,V7__m_27_27_27,V5__m_27)
                                     => cIntMap_2eMapsubset_2eMapSubset___24a4(V0__A,V2__C,cIntMap_2eFset_2eMapDomRestrBy___24a4(V0__A,V1__B,V4__m,V5__m_27),cIntMap_2eFset_2eMapDomRestrBy___24a4(V2__C,V3__D,V6__m_27_27,V7__m_27_27_27)) ) ) ) ) ) ) ) ) ) ) ).

fof('IntMap.Mapsubset.MapSubset_DomRestrTo_l',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__B] :
          ( cType___24t(V1__B)
         => ! [V2__m] :
              ( cIntMap_2eMap_2eMap___24t(V0__A,V2__m)
             => ! [V3__m_27] :
                  ( cIntMap_2eMap_2eMap___24t(V1__B,V3__m_27)
                 => cIntMap_2eMapsubset_2eMapSubset___24a4(V0__A,V0__A,cIntMap_2eFset_2eMapDomRestrTo___24a4(V0__A,V1__B,V2__m,V3__m_27),V2__m) ) ) ) ) ).

fof('IntMap.Mapsubset.MapSubset_DomRestrTo_mono',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__B] :
          ( cType___24t(V1__B)
         => ! [V2__C] :
              ( cType___24t(V2__C)
             => ! [V3__D] :
                  ( cType___24t(V3__D)
                 => ! [V4__m] :
                      ( cIntMap_2eMap_2eMap___24t(V0__A,V4__m)
                     => ! [V5__m_27] :
                          ( cIntMap_2eMap_2eMap___24t(V1__B,V5__m_27)
                         => ! [V6__m_27_27] :
                              ( cIntMap_2eMap_2eMap___24t(V2__C,V6__m_27_27)
                             => ! [V7__m_27_27_27] :
                                  ( cIntMap_2eMap_2eMap___24t(V3__D,V7__m_27_27_27)
                                 => ( cIntMap_2eMapsubset_2eMapSubset___24a4(V0__A,V2__C,V4__m,V6__m_27_27)
                                   => ( cIntMap_2eMapsubset_2eMapSubset___24a4(V1__B,V3__D,V5__m_27,V7__m_27_27_27)
                                     => cIntMap_2eMapsubset_2eMapSubset___24a4(V0__A,V2__C,cIntMap_2eFset_2eMapDomRestrTo___24a4(V0__A,V1__B,V4__m,V5__m_27),cIntMap_2eFset_2eMapDomRestrTo___24a4(V2__C,V3__D,V6__m_27_27,V7__m_27_27_27)) ) ) ) ) ) ) ) ) ) ) ).

fof('IntMap.Mapsubset.MapSubset_DomRestrTo_r',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__B] :
          ( cType___24t(V1__B)
         => ! [V2__m] :
              ( cIntMap_2eMap_2eMap___24t(V0__A,V2__m)
             => ! [V3__m_27] :
                  ( cIntMap_2eMap_2eMap___24t(V1__B,V3__m_27)
                 => cIntMap_2eMapsubset_2eMapSubset___24a4(V0__A,V1__B,cIntMap_2eFset_2eMapDomRestrTo___24a4(V0__A,V1__B,V2__m,V3__m_27),V3__m_27) ) ) ) ) ).

fof('IntMap.Mapsubset.MapSubset_Dom_1',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__B] :
          ( cType___24t(V1__B)
         => ! [V2__m] :
              ( cIntMap_2eMap_2eMap___24t(V0__A,V2__m)
             => ! [V3__m_27] :
                  ( cIntMap_2eMap_2eMap___24t(V1__B,V3__m_27)
                 => ( cIntMap_2eMapsubset_2eMapSubset___24a4(V0__A,V1__B,V2__m,V3__m_27)
                   => cIntMap_2eMapsubset_2eMapSubset___24a4(cCoq_2eInit_2eDatatypes_2eunit,cCoq_2eInit_2eDatatypes_2eunit,cIntMap_2eFset_2eMapDom___24a2(V0__A,V2__m),cIntMap_2eFset_2eMapDom___24a2(V1__B,V3__m_27)) ) ) ) ) ) ).

fof('IntMap.Mapsubset.MapSubset_Dom_2',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__B] :
          ( cType___24t(V1__B)
         => ! [V2__m] :
              ( cIntMap_2eMap_2eMap___24t(V0__A,V2__m)
             => ! [V3__m_27] :
                  ( cIntMap_2eMap_2eMap___24t(V1__B,V3__m_27)
                 => ( cIntMap_2eMapsubset_2eMapSubset___24a4(cCoq_2eInit_2eDatatypes_2eunit,cCoq_2eInit_2eDatatypes_2eunit,cIntMap_2eFset_2eMapDom___24a2(V0__A,V2__m),cIntMap_2eFset_2eMapDom___24a2(V1__B,V3__m_27))
                   => cIntMap_2eMapsubset_2eMapSubset___24a4(V0__A,V1__B,V2__m,V3__m_27) ) ) ) ) ) ).

fof('IntMap.Mapsubset.MapSubset_Merge_l',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__m] :
          ( cIntMap_2eMap_2eMap___24t(V0__A,V1__m)
         => ! [V2__m_27] :
              ( cIntMap_2eMap_2eMap___24t(V0__A,V2__m_27)
             => cIntMap_2eMapsubset_2eMapSubset___24a4(V0__A,V0__A,V1__m,cIntMap_2eMap_2eMapMerge___24a3(V0__A,V1__m,V2__m_27)) ) ) ) ).

fof('IntMap.Mapsubset.MapSubset_Merge_mono',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__B] :
          ( cType___24t(V1__B)
         => ! [V2__m] :
              ( cIntMap_2eMap_2eMap___24t(V0__A,V2__m)
             => ! [V3__m_27] :
                  ( cIntMap_2eMap_2eMap___24t(V0__A,V3__m_27)
                 => ! [V4__m_27_27] :
                      ( cIntMap_2eMap_2eMap___24t(V1__B,V4__m_27_27)
                     => ! [V5__m_27_27_27] :
                          ( cIntMap_2eMap_2eMap___24t(V1__B,V5__m_27_27_27)
                         => ( cIntMap_2eMapsubset_2eMapSubset___24a4(V0__A,V1__B,V2__m,V4__m_27_27)
                           => ( cIntMap_2eMapsubset_2eMapSubset___24a4(V0__A,V1__B,V3__m_27,V5__m_27_27_27)
                             => cIntMap_2eMapsubset_2eMapSubset___24a4(V0__A,V1__B,cIntMap_2eMap_2eMapMerge___24a3(V0__A,V2__m,V3__m_27),cIntMap_2eMap_2eMapMerge___24a3(V1__B,V4__m_27_27,V5__m_27_27_27)) ) ) ) ) ) ) ) ) ).

fof('IntMap.Mapsubset.MapSubset_Merge_r',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__m] :
          ( cIntMap_2eMap_2eMap___24t(V0__A,V1__m)
         => ! [V2__m_27] :
              ( cIntMap_2eMap_2eMap___24t(V0__A,V2__m_27)
             => cIntMap_2eMapsubset_2eMapSubset___24a4(V0__A,V0__A,V2__m_27,cIntMap_2eMap_2eMapMerge___24a3(V0__A,V1__m,V2__m_27)) ) ) ) ).

fof('IntMap.Mapsubset.MapSubset_Put',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__m] :
          ( cIntMap_2eMap_2eMap___24t(V0__A,V1__m)
         => ! [V2__a] :
              ( cIntMap_2eMap_2ead___24t(V2__a)
             => ! [V3__y] :
                  ( t(V3__y,V0__A)
                 => cIntMap_2eMapsubset_2eMapSubset___24a4(V0__A,V0__A,V1__m,cIntMap_2eMap_2eMapPut___24a4(V0__A,V1__m,V2__a,V3__y)) ) ) ) ) ).

fof('IntMap.Mapsubset.MapSubset_Put_behind',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__m] :
          ( cIntMap_2eMap_2eMap___24t(V0__A,V1__m)
         => ! [V2__a] :
              ( cIntMap_2eMap_2ead___24t(V2__a)
             => ! [V3__y] :
                  ( t(V3__y,V0__A)
                 => cIntMap_2eMapsubset_2eMapSubset___24a4(V0__A,V0__A,V1__m,cIntMap_2eMap_2eMapPut__behind___24a4(V0__A,V1__m,V2__a,V3__y)) ) ) ) ) ).

fof('IntMap.Mapsubset.MapSubset_Put_behind_mono',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__B] :
          ( cType___24t(V1__B)
         => ! [V2__m] :
              ( cIntMap_2eMap_2eMap___24t(V0__A,V2__m)
             => ! [V3__m_27] :
                  ( cIntMap_2eMap_2eMap___24t(V1__B,V3__m_27)
                 => ! [V4__a] :
                      ( cIntMap_2eMap_2ead___24t(V4__a)
                     => ! [V5__y] :
                          ( t(V5__y,V0__A)
                         => ! [V6__y_27] :
                              ( t(V6__y_27,V1__B)
                             => ( cIntMap_2eMapsubset_2eMapSubset___24a4(V0__A,V1__B,V2__m,V3__m_27)
                               => cIntMap_2eMapsubset_2eMapSubset___24a4(V0__A,V1__B,cIntMap_2eMap_2eMapPut__behind___24a4(V0__A,V2__m,V4__a,V5__y),cIntMap_2eMap_2eMapPut__behind___24a4(V1__B,V3__m_27,V4__a,V6__y_27)) ) ) ) ) ) ) ) ) ).

fof('IntMap.Mapsubset.MapSubset_Put_mono',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__B] :
          ( cType___24t(V1__B)
         => ! [V2__m] :
              ( cIntMap_2eMap_2eMap___24t(V0__A,V2__m)
             => ! [V3__m_27] :
                  ( cIntMap_2eMap_2eMap___24t(V1__B,V3__m_27)
                 => ! [V4__a] :
                      ( cIntMap_2eMap_2ead___24t(V4__a)
                     => ! [V5__y] :
                          ( t(V5__y,V0__A)
                         => ! [V6__y_27] :
                              ( t(V6__y_27,V1__B)
                             => ( cIntMap_2eMapsubset_2eMapSubset___24a4(V0__A,V1__B,V2__m,V3__m_27)
                               => cIntMap_2eMapsubset_2eMapSubset___24a4(V0__A,V1__B,cIntMap_2eMap_2eMapPut___24a4(V0__A,V2__m,V4__a,V5__y),cIntMap_2eMap_2eMapPut___24a4(V1__B,V3__m_27,V4__a,V6__y_27)) ) ) ) ) ) ) ) ) ).

fof('IntMap.Mapsubset.MapSubset_Remove',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__m] :
          ( cIntMap_2eMap_2eMap___24t(V0__A,V1__m)
         => ! [V2__a] :
              ( cIntMap_2eMap_2ead___24t(V2__a)
             => cIntMap_2eMapsubset_2eMapSubset___24a4(V0__A,V0__A,cIntMap_2eMap_2eMapRemove___24a3(V0__A,V1__m,V2__a),V1__m) ) ) ) ).

fof('IntMap.Mapsubset.MapSubset_Remove_mono',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__B] :
          ( cType___24t(V1__B)
         => ! [V2__m] :
              ( cIntMap_2eMap_2eMap___24t(V0__A,V2__m)
             => ! [V3__m_27] :
                  ( cIntMap_2eMap_2eMap___24t(V1__B,V3__m_27)
                 => ! [V4__a] :
                      ( cIntMap_2eMap_2ead___24t(V4__a)
                     => ( cIntMap_2eMapsubset_2eMapSubset___24a4(V0__A,V1__B,V2__m,V3__m_27)
                       => cIntMap_2eMapsubset_2eMapSubset___24a4(V0__A,V1__B,cIntMap_2eMap_2eMapRemove___24a3(V0__A,V2__m,V4__a),cIntMap_2eMap_2eMapRemove___24a3(V1__B,V3__m_27,V4__a)) ) ) ) ) ) ) ).

fof('IntMap.Mapsubset.MapSubset_antisym',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__B] :
          ( cType___24t(V1__B)
         => ! [V2__m] :
              ( cIntMap_2eMap_2eMap___24t(V0__A,V2__m)
             => ! [V3__m_27] :
                  ( cIntMap_2eMap_2eMap___24t(V1__B,V3__m_27)
                 => ( cIntMap_2eMapsubset_2eMapSubset___24a4(V0__A,V1__B,V2__m,V3__m_27)
                   => ( cIntMap_2eMapsubset_2eMapSubset___24a4(V1__B,V0__A,V3__m_27,V2__m)
                     => cIntMap_2eMapaxioms_2eeqmap___24a3(cCoq_2eInit_2eDatatypes_2eunit,cIntMap_2eFset_2eMapDom___24a2(V0__A,V2__m),cIntMap_2eFset_2eMapDom___24a2(V1__B,V3__m_27)) ) ) ) ) ) ) ).

fof('IntMap.Mapsubset.MapSubset_ext',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__B] :
          ( cType___24t(V1__B)
         => ! [V2__m0] :
              ( cIntMap_2eMap_2eMap___24t(V0__A,V2__m0)
             => ! [V3__m1] :
                  ( cIntMap_2eMap_2eMap___24t(V0__A,V3__m1)
                 => ! [V4__m2] :
                      ( cIntMap_2eMap_2eMap___24t(V1__B,V4__m2)
                     => ! [V5__m3] :
                          ( cIntMap_2eMap_2eMap___24t(V1__B,V5__m3)
                         => ( cIntMap_2eMapaxioms_2eeqmap___24a3(V0__A,V2__m0,V3__m1)
                           => ( cIntMap_2eMapaxioms_2eeqmap___24a3(V1__B,V4__m2,V5__m3)
                             => ( cIntMap_2eMapsubset_2eMapSubset___24a4(V0__A,V1__B,V2__m0,V4__m2)
                               => cIntMap_2eMapsubset_2eMapSubset___24a4(V0__A,V1__B,V3__m1,V5__m3) ) ) ) ) ) ) ) ) ) ).

fof('IntMap.Mapsubset.MapSubset_imp_1',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__B] :
          ( cType___24t(V1__B)
         => ! [V2__m] :
              ( cIntMap_2eMap_2eMap___24t(V0__A,V2__m)
             => ! [V3__m_27] :
                  ( cIntMap_2eMap_2eMap___24t(V1__B,V3__m_27)
                 => ( cIntMap_2eMapsubset_2eMapSubset___24a4(V0__A,V1__B,V2__m,V3__m_27)
                   => cIntMap_2eMapsubset_2eMapSubset__1___24a4(V0__A,V1__B,V2__m,V3__m_27) = cCoq_2eInit_2eDatatypes_2etrue ) ) ) ) ) ).

fof('IntMap.Mapsubset.MapSubset_imp_2',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__B] :
          ( cType___24t(V1__B)
         => ! [V2__m] :
              ( cIntMap_2eMap_2eMap___24t(V0__A,V2__m)
             => ! [V3__m_27] :
                  ( cIntMap_2eMap_2eMap___24t(V1__B,V3__m_27)
                 => ( cIntMap_2eMapsubset_2eMapSubset___24a4(V0__A,V1__B,V2__m,V3__m_27)
                   => cIntMap_2eMapsubset_2eMapSubset__2___24a4(V0__A,V1__B,V2__m,V3__m_27) ) ) ) ) ) ).

fof('IntMap.Mapsubset.MapSubset_refl',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__m] :
          ( cIntMap_2eMap_2eMap___24t(V0__A,V1__m)
         => cIntMap_2eMapsubset_2eMapSubset___24a4(V0__A,V0__A,V1__m,V1__m) ) ) ).

fof('IntMap.Mapsubset.MapSubset_trans',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__B] :
          ( cType___24t(V1__B)
         => ! [V2__C] :
              ( cType___24t(V2__C)
             => ! [V3__m] :
                  ( cIntMap_2eMap_2eMap___24t(V0__A,V3__m)
                 => ! [V4__m_27] :
                      ( cIntMap_2eMap_2eMap___24t(V1__B,V4__m_27)
                     => ! [V5__m_27_27] :
                          ( cIntMap_2eMap_2eMap___24t(V2__C,V5__m_27_27)
                         => ( cIntMap_2eMapsubset_2eMapSubset___24a4(V0__A,V1__B,V3__m,V4__m_27)
                           => ( cIntMap_2eMapsubset_2eMapSubset___24a4(V1__B,V2__C,V4__m_27,V5__m_27_27)
                             => cIntMap_2eMapsubset_2eMapSubset___24a4(V0__A,V2__C,V3__m,V5__m_27_27) ) ) ) ) ) ) ) ) ).

fof('IntMap.Mapsubset.Map_M0_disjoint',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__B] :
          ( cType___24t(V1__B)
         => ! [V2__m] :
              ( cIntMap_2eMap_2eMap___24t(V1__B,V2__m)
             => cIntMap_2eMapsubset_2eMapDisjoint___24a4(V0__A,V1__B,cIntMap_2eMap_2eM0___24a1(V0__A),V2__m) ) ) ) ).

fof('IntMap.Mapsubset.Map_disjoint_M0',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__B] :
          ( cType___24t(V1__B)
         => ! [V2__m] :
              ( cIntMap_2eMap_2eMap___24t(V0__A,V2__m)
             => cIntMap_2eMapsubset_2eMapDisjoint___24a4(V0__A,V1__B,V2__m,cIntMap_2eMap_2eM0___24a1(V1__B)) ) ) ) ).

fof('IntMap.Mapsubset.map_dom_empty_1',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__m] :
          ( cIntMap_2eMap_2eMap___24t(V0__A,V1__m)
         => ( cIntMap_2eMapaxioms_2eeqmap___24a3(V0__A,V1__m,cIntMap_2eMap_2eM0___24a1(V0__A))
           => ! [V3__a] :
                ( cIntMap_2eMap_2ead___24t(V3__a)
               => cIntMap_2eFset_2ein__dom___24a3(V0__A,V3__a,V1__m) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ).

fof('IntMap.Mapsubset.map_dom_empty_2',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__m] :
          ( cIntMap_2eMap_2eMap___24t(V0__A,V1__m)
         => ( ! [V2__a] :
                ( cIntMap_2eMap_2ead___24t(V2__a)
               => cIntMap_2eFset_2ein__dom___24a3(V0__A,V2__a,V1__m) = cCoq_2eInit_2eDatatypes_2efalse )
           => cIntMap_2eMapaxioms_2eeqmap___24a3(V0__A,V1__m,cIntMap_2eMap_2eM0___24a1(V0__A)) ) ) ) ).

fof('Mapc.MapC.MapDelta_as_DomRestrBy_2_c',axiom,
    ! [V0__m] :
      ( cIntMap_2eMap_2eMap___24t(cA,V0__m)
     => ! [V1__m_27] :
          ( cIntMap_2eMap_2eMap___24t(cA,V1__m_27)
         => ( cIntMap_2eMapcanon_2emapcanon___24a2(cA,V0__m)
           => ( cIntMap_2eMapcanon_2emapcanon___24a2(cA,V1__m_27)
             => cIntMap_2eMap_2eMapDelta___24a3(cA,V0__m,V1__m_27) = cIntMap_2eFset_2eMapDomRestrBy___24a4(cA,cA,cIntMap_2eMap_2eMapMerge___24a3(cA,V0__m,V1__m_27),cIntMap_2eFset_2eMapDomRestrTo___24a4(cA,cA,V1__m_27,V0__m)) ) ) ) ) ).

fof('Mapc.MapC.MapDelta_as_DomRestrBy_c',axiom,
    ! [V0__m] :
      ( cIntMap_2eMap_2eMap___24t(cA,V0__m)
     => ! [V1__m_27] :
          ( cIntMap_2eMap_2eMap___24t(cA,V1__m_27)
         => ( cIntMap_2eMapcanon_2emapcanon___24a2(cA,V0__m)
           => ( cIntMap_2eMapcanon_2emapcanon___24a2(cA,V1__m_27)
             => cIntMap_2eMap_2eMapDelta___24a3(cA,V0__m,V1__m_27) = cIntMap_2eFset_2eMapDomRestrBy___24a4(cA,cA,cIntMap_2eMap_2eMapMerge___24a3(cA,V0__m,V1__m_27),cIntMap_2eFset_2eMapDomRestrTo___24a4(cA,cA,V0__m,V1__m_27)) ) ) ) ) ).

fof('Mapc.MapC.MapDelta_as_Merge_c',axiom,
    ! [V0__m] :
      ( cIntMap_2eMap_2eMap___24t(cA,V0__m)
     => ! [V1__m_27] :
          ( cIntMap_2eMap_2eMap___24t(cA,V1__m_27)
         => ( cIntMap_2eMapcanon_2emapcanon___24a2(cA,V0__m)
           => ( cIntMap_2eMapcanon_2emapcanon___24a2(cA,V1__m_27)
             => cIntMap_2eMap_2eMapDelta___24a3(cA,V0__m,V1__m_27) = cIntMap_2eMap_2eMapMerge___24a3(cA,cIntMap_2eFset_2eMapDomRestrBy___24a4(cA,cA,V0__m,V1__m_27),cIntMap_2eFset_2eMapDomRestrBy___24a4(cA,cA,V1__m_27,V0__m)) ) ) ) ) ).

fof('Mapc.MapC.MapDelta_nilpotent_c',axiom,
    ! [V0__m] :
      ( cIntMap_2eMap_2eMap___24t(cA,V0__m)
     => ( cIntMap_2eMapcanon_2emapcanon___24a2(cA,V0__m)
       => cIntMap_2eMap_2eMapDelta___24a3(cA,V0__m,V0__m) = cIntMap_2eMap_2eM0___24a1(cA) ) ) ).

fof('Mapc.MapC.MapDelta_sym_c',axiom,
    ! [V0__m] :
      ( cIntMap_2eMap_2eMap___24t(cA,V0__m)
     => ! [V1__m_27] :
          ( cIntMap_2eMap_2eMap___24t(cA,V1__m_27)
         => ( cIntMap_2eMapcanon_2emapcanon___24a2(cA,V0__m)
           => ( cIntMap_2eMapcanon_2emapcanon___24a2(cA,V1__m_27)
             => cIntMap_2eMap_2eMapDelta___24a3(cA,V0__m,V1__m_27) = cIntMap_2eMap_2eMapDelta___24a3(cA,V1__m_27,V0__m) ) ) ) ) ).

fof('Mapc.MapC.MapDomRestrBy_By_c',axiom,
    ! [V0__m] :
      ( cIntMap_2eMap_2eMap___24t(cA,V0__m)
     => ! [V1__m_27] :
          ( cIntMap_2eMap_2eMap___24t(cB,V1__m_27)
         => ! [V2__m_27_27] :
              ( cIntMap_2eMap_2eMap___24t(cB,V2__m_27_27)
             => ( cIntMap_2eMapcanon_2emapcanon___24a2(cA,V0__m)
               => cIntMap_2eFset_2eMapDomRestrBy___24a4(cA,cB,cIntMap_2eFset_2eMapDomRestrBy___24a4(cA,cB,V0__m,V1__m_27),V2__m_27_27) = cIntMap_2eFset_2eMapDomRestrBy___24a4(cA,cB,V0__m,cIntMap_2eMap_2eMapMerge___24a3(cB,V1__m_27,V2__m_27_27)) ) ) ) ) ).

fof('Mapc.MapC.MapDomRestrBy_By_comm_c',axiom,
    ! [V0__m] :
      ( cIntMap_2eMap_2eMap___24t(cA,V0__m)
     => ! [V1__m_27] :
          ( cIntMap_2eMap_2eMap___24t(cB,V1__m_27)
         => ! [V2__m_27_27] :
              ( cIntMap_2eMap_2eMap___24t(cC,V2__m_27_27)
             => ( cIntMap_2eMapcanon_2emapcanon___24a2(cA,V0__m)
               => cIntMap_2eFset_2eMapDomRestrBy___24a4(cA,cC,cIntMap_2eFset_2eMapDomRestrBy___24a4(cA,cB,V0__m,V1__m_27),V2__m_27_27) = cIntMap_2eFset_2eMapDomRestrBy___24a4(cA,cB,cIntMap_2eFset_2eMapDomRestrBy___24a4(cA,cC,V0__m,V2__m_27_27),V1__m_27) ) ) ) ) ).

fof('Mapc.MapC.MapDomRestrBy_Dom_c',axiom,
    ! [V0__m] :
      ( cIntMap_2eMap_2eMap___24t(cA,V0__m)
     => ! [V1__m_27] :
          ( cIntMap_2eMap_2eMap___24t(cB,V1__m_27)
         => ( cIntMap_2eMapcanon_2emapcanon___24a2(cA,V0__m)
           => cIntMap_2eFset_2eMapDomRestrBy___24a4(cA,cB,V0__m,V1__m_27) = cIntMap_2eFset_2eMapDomRestrBy___24a4(cA,cCoq_2eInit_2eDatatypes_2eunit,V0__m,cIntMap_2eFset_2eMapDom___24a2(cB,V1__m_27)) ) ) ) ).

fof('Mapc.MapC.MapDomRestrBy_To_c',axiom,
    ! [V0__m] :
      ( cIntMap_2eMap_2eMap___24t(cA,V0__m)
     => ! [V1__m_27] :
          ( cIntMap_2eMap_2eMap___24t(cB,V1__m_27)
         => ! [V2__m_27_27] :
              ( cIntMap_2eMap_2eMap___24t(cC,V2__m_27_27)
             => ( cIntMap_2eMapcanon_2emapcanon___24a2(cA,V0__m)
               => cIntMap_2eFset_2eMapDomRestrBy___24a4(cA,cC,cIntMap_2eFset_2eMapDomRestrTo___24a4(cA,cB,V0__m,V1__m_27),V2__m_27_27) = cIntMap_2eFset_2eMapDomRestrTo___24a4(cA,cB,V0__m,cIntMap_2eFset_2eMapDomRestrBy___24a4(cB,cC,V1__m_27,V2__m_27_27)) ) ) ) ) ).

fof('Mapc.MapC.MapDomRestrBy_To_comm_c',axiom,
    ! [V0__m] :
      ( cIntMap_2eMap_2eMap___24t(cA,V0__m)
     => ! [V1__m_27] :
          ( cIntMap_2eMap_2eMap___24t(cB,V1__m_27)
         => ! [V2__m_27_27] :
              ( cIntMap_2eMap_2eMap___24t(cC,V2__m_27_27)
             => ( cIntMap_2eMapcanon_2emapcanon___24a2(cA,V0__m)
               => cIntMap_2eFset_2eMapDomRestrBy___24a4(cA,cC,cIntMap_2eFset_2eMapDomRestrTo___24a4(cA,cB,V0__m,V1__m_27),V2__m_27_27) = cIntMap_2eFset_2eMapDomRestrTo___24a4(cA,cB,cIntMap_2eFset_2eMapDomRestrBy___24a4(cA,cC,V0__m,V2__m_27_27),V1__m_27) ) ) ) ) ).

fof('Mapc.MapC.MapDomRestrTo_By_c',axiom,
    ! [V0__m] :
      ( cIntMap_2eMap_2eMap___24t(cA,V0__m)
     => ! [V1__m_27] :
          ( cIntMap_2eMap_2eMap___24t(cB,V1__m_27)
         => ! [V2__m_27_27] :
              ( cIntMap_2eMap_2eMap___24t(cC,V2__m_27_27)
             => ( cIntMap_2eMapcanon_2emapcanon___24a2(cA,V0__m)
               => cIntMap_2eFset_2eMapDomRestrTo___24a4(cA,cC,cIntMap_2eFset_2eMapDomRestrBy___24a4(cA,cB,V0__m,V1__m_27),V2__m_27_27) = cIntMap_2eFset_2eMapDomRestrTo___24a4(cA,cC,V0__m,cIntMap_2eFset_2eMapDomRestrBy___24a4(cC,cB,V2__m_27_27,V1__m_27)) ) ) ) ) ).

fof('Mapc.MapC.MapDomRestrTo_By_comm_c',axiom,
    ! [V0__m] :
      ( cIntMap_2eMap_2eMap___24t(cA,V0__m)
     => ! [V1__m_27] :
          ( cIntMap_2eMap_2eMap___24t(cB,V1__m_27)
         => ! [V2__m_27_27] :
              ( cIntMap_2eMap_2eMap___24t(cC,V2__m_27_27)
             => ( cIntMap_2eMapcanon_2emapcanon___24a2(cA,V0__m)
               => cIntMap_2eFset_2eMapDomRestrTo___24a4(cA,cC,cIntMap_2eFset_2eMapDomRestrBy___24a4(cA,cB,V0__m,V1__m_27),V2__m_27_27) = cIntMap_2eFset_2eMapDomRestrBy___24a4(cA,cB,cIntMap_2eFset_2eMapDomRestrTo___24a4(cA,cC,V0__m,V2__m_27_27),V1__m_27) ) ) ) ) ).

fof('Mapc.MapC.MapDomRestrTo_Dom_c',axiom,
    ! [V0__m] :
      ( cIntMap_2eMap_2eMap___24t(cA,V0__m)
     => ! [V1__m_27] :
          ( cIntMap_2eMap_2eMap___24t(cB,V1__m_27)
         => ( cIntMap_2eMapcanon_2emapcanon___24a2(cA,V0__m)
           => cIntMap_2eFset_2eMapDomRestrTo___24a4(cA,cB,V0__m,V1__m_27) = cIntMap_2eFset_2eMapDomRestrTo___24a4(cA,cCoq_2eInit_2eDatatypes_2eunit,V0__m,cIntMap_2eFset_2eMapDom___24a2(cB,V1__m_27)) ) ) ) ).

fof('Mapc.MapC.MapDomRestrTo_To_comm_c',axiom,
    ! [V0__m] :
      ( cIntMap_2eMap_2eMap___24t(cA,V0__m)
     => ! [V1__m_27] :
          ( cIntMap_2eMap_2eMap___24t(cB,V1__m_27)
         => ! [V2__m_27_27] :
              ( cIntMap_2eMap_2eMap___24t(cC,V2__m_27_27)
             => ( cIntMap_2eMapcanon_2emapcanon___24a2(cA,V0__m)
               => cIntMap_2eFset_2eMapDomRestrTo___24a4(cA,cC,cIntMap_2eFset_2eMapDomRestrTo___24a4(cA,cB,V0__m,V1__m_27),V2__m_27_27) = cIntMap_2eFset_2eMapDomRestrTo___24a4(cA,cB,cIntMap_2eFset_2eMapDomRestrTo___24a4(cA,cC,V0__m,V2__m_27_27),V1__m_27) ) ) ) ) ).

fof('Mapc.MapC.MapDomRestrTo_assoc_c',axiom,
    ! [V0__m] :
      ( cIntMap_2eMap_2eMap___24t(cA,V0__m)
     => ! [V1__m_27] :
          ( cIntMap_2eMap_2eMap___24t(cB,V1__m_27)
         => ! [V2__m_27_27] :
              ( cIntMap_2eMap_2eMap___24t(cC,V2__m_27_27)
             => ( cIntMap_2eMapcanon_2emapcanon___24a2(cA,V0__m)
               => cIntMap_2eFset_2eMapDomRestrTo___24a4(cA,cC,cIntMap_2eFset_2eMapDomRestrTo___24a4(cA,cB,V0__m,V1__m_27),V2__m_27_27) = cIntMap_2eFset_2eMapDomRestrTo___24a4(cA,cB,V0__m,cIntMap_2eFset_2eMapDomRestrTo___24a4(cB,cC,V1__m_27,V2__m_27_27)) ) ) ) ) ).

fof('Mapc.MapC.MapDomRestrTo_idempotent_c',axiom,
    ! [V0__m] :
      ( cIntMap_2eMap_2eMap___24t(cA,V0__m)
     => ( cIntMap_2eMapcanon_2emapcanon___24a2(cA,V0__m)
       => cIntMap_2eFset_2eMapDomRestrTo___24a4(cA,cA,V0__m,V0__m) = V0__m ) ) ).

fof('Mapc.MapC.MapDom_Split_1_c',axiom,
    ! [V0__m] :
      ( cIntMap_2eMap_2eMap___24t(cA,V0__m)
     => ! [V1__m_27] :
          ( cIntMap_2eMap_2eMap___24t(cB,V1__m_27)
         => ( cIntMap_2eMapcanon_2emapcanon___24a2(cA,V0__m)
           => V0__m = cIntMap_2eMap_2eMapMerge___24a3(cA,cIntMap_2eFset_2eMapDomRestrTo___24a4(cA,cB,V0__m,V1__m_27),cIntMap_2eFset_2eMapDomRestrBy___24a4(cA,cB,V0__m,V1__m_27)) ) ) ) ).

fof('Mapc.MapC.MapMerge_DomRestrBy_c',axiom,
    ! [V0__m] :
      ( cIntMap_2eMap_2eMap___24t(cA,V0__m)
     => ! [V1__m_27] :
          ( cIntMap_2eMap_2eMap___24t(cA,V1__m_27)
         => ! [V2__m_27_27] :
              ( cIntMap_2eMap_2eMap___24t(cB,V2__m_27_27)
             => ( cIntMap_2eMapcanon_2emapcanon___24a2(cA,V0__m)
               => ( cIntMap_2eMapcanon_2emapcanon___24a2(cA,V1__m_27)
                 => cIntMap_2eFset_2eMapDomRestrBy___24a4(cA,cB,cIntMap_2eMap_2eMapMerge___24a3(cA,V0__m,V1__m_27),V2__m_27_27) = cIntMap_2eMap_2eMapMerge___24a3(cA,cIntMap_2eFset_2eMapDomRestrBy___24a4(cA,cB,V0__m,V2__m_27_27),cIntMap_2eFset_2eMapDomRestrBy___24a4(cA,cB,V1__m_27,V2__m_27_27)) ) ) ) ) ) ).

fof('Mapc.MapC.MapMerge_DomRestrTo_c',axiom,
    ! [V0__m] :
      ( cIntMap_2eMap_2eMap___24t(cA,V0__m)
     => ! [V1__m_27] :
          ( cIntMap_2eMap_2eMap___24t(cA,V1__m_27)
         => ! [V2__m_27_27] :
              ( cIntMap_2eMap_2eMap___24t(cB,V2__m_27_27)
             => ( cIntMap_2eMapcanon_2emapcanon___24a2(cA,V0__m)
               => ( cIntMap_2eMapcanon_2emapcanon___24a2(cA,V1__m_27)
                 => cIntMap_2eFset_2eMapDomRestrTo___24a4(cA,cB,cIntMap_2eMap_2eMapMerge___24a3(cA,V0__m,V1__m_27),V2__m_27_27) = cIntMap_2eMap_2eMapMerge___24a3(cA,cIntMap_2eFset_2eMapDomRestrTo___24a4(cA,cB,V0__m,V2__m_27_27),cIntMap_2eFset_2eMapDomRestrTo___24a4(cA,cB,V1__m_27,V2__m_27_27)) ) ) ) ) ) ).

fof('Mapc.MapC.MapMerge_RestrTo_l_c',axiom,
    ! [V0__m] :
      ( cIntMap_2eMap_2eMap___24t(cA,V0__m)
     => ! [V1__m_27] :
          ( cIntMap_2eMap_2eMap___24t(cA,V1__m_27)
         => ! [V2__m_27_27] :
              ( cIntMap_2eMap_2eMap___24t(cA,V2__m_27_27)
             => ( cIntMap_2eMapcanon_2emapcanon___24a2(cA,V0__m)
               => ( cIntMap_2eMapcanon_2emapcanon___24a2(cA,V2__m_27_27)
                 => cIntMap_2eMap_2eMapMerge___24a3(cA,cIntMap_2eFset_2eMapDomRestrTo___24a4(cA,cA,V0__m,V1__m_27),V2__m_27_27) = cIntMap_2eFset_2eMapDomRestrTo___24a4(cA,cA,cIntMap_2eMap_2eMapMerge___24a3(cA,V0__m,V2__m_27_27),cIntMap_2eMap_2eMapMerge___24a3(cA,V1__m_27,V2__m_27_27)) ) ) ) ) ) ).

fof('Mapc.MapC.MapMerge_assoc_c',axiom,
    ! [V0__m] :
      ( cIntMap_2eMap_2eMap___24t(cA,V0__m)
     => ! [V1__m_27] :
          ( cIntMap_2eMap_2eMap___24t(cA,V1__m_27)
         => ! [V2__m_27_27] :
              ( cIntMap_2eMap_2eMap___24t(cA,V2__m_27_27)
             => ( cIntMap_2eMapcanon_2emapcanon___24a2(cA,V0__m)
               => ( cIntMap_2eMapcanon_2emapcanon___24a2(cA,V1__m_27)
                 => ( cIntMap_2eMapcanon_2emapcanon___24a2(cA,V2__m_27_27)
                   => cIntMap_2eMap_2eMapMerge___24a3(cA,cIntMap_2eMap_2eMapMerge___24a3(cA,V0__m,V1__m_27),V2__m_27_27) = cIntMap_2eMap_2eMapMerge___24a3(cA,V0__m,cIntMap_2eMap_2eMapMerge___24a3(cA,V1__m_27,V2__m_27_27)) ) ) ) ) ) ) ).

fof('Mapc.MapC.MapMerge_empty_m_c',axiom,
    ! [V0__m] :
      ( cIntMap_2eMap_2eMap___24t(cA,V0__m)
     => cIntMap_2eMap_2eMapMerge___24a3(cA,cIntMap_2eMap_2eM0___24a1(cA),V0__m) = V0__m ) ).

fof('Mapc.MapC.MapMerge_idempotent_c',axiom,
    ! [V0__m] :
      ( cIntMap_2eMap_2eMap___24t(cA,V0__m)
     => ( cIntMap_2eMapcanon_2emapcanon___24a2(cA,V0__m)
       => cIntMap_2eMap_2eMapMerge___24a3(cA,V0__m,V0__m) = V0__m ) ) ).

fof('Mapc.MapC.MapPut_as_Merge_c',axiom,
    ! [V0__m] :
      ( cIntMap_2eMap_2eMap___24t(cA,V0__m)
     => ( cIntMap_2eMapcanon_2emapcanon___24a2(cA,V0__m)
       => ! [V2__a] :
            ( cIntMap_2eMap_2ead___24t(V2__a)
           => ! [V3__y] :
                ( cA___24t(V3__y)
               => cIntMap_2eMap_2eMapPut___24a4(cA,V0__m,V2__a,V3__y) = cIntMap_2eMap_2eMapMerge___24a3(cA,V0__m,cIntMap_2eMap_2eM1___24a3(cA,V2__a,V3__y)) ) ) ) ) ).

fof('Mapc.MapC.MapPut_behind_as_Merge_c',axiom,
    ! [V0__m] :
      ( cIntMap_2eMap_2eMap___24t(cA,V0__m)
     => ( cIntMap_2eMapcanon_2emapcanon___24a2(cA,V0__m)
       => ! [V2__a] :
            ( cIntMap_2eMap_2ead___24t(V2__a)
           => ! [V3__y] :
                ( cA___24t(V3__y)
               => cIntMap_2eMap_2eMapPut__behind___24a4(cA,V0__m,V2__a,V3__y) = cIntMap_2eMap_2eMapMerge___24a3(cA,cIntMap_2eMap_2eM1___24a3(cA,V2__a,V3__y),V0__m) ) ) ) ) ).

fof('Mapc.MapC.MapRemove_as_RestrBy_c',axiom,
    ! [V0__m] :
      ( cIntMap_2eMap_2eMap___24t(cA,V0__m)
     => ( cIntMap_2eMapcanon_2emapcanon___24a2(cA,V0__m)
       => ! [V2__a] :
            ( cIntMap_2eMap_2ead___24t(V2__a)
           => ! [V3__y] :
                ( cB___24t(V3__y)
               => cIntMap_2eMap_2eMapRemove___24a3(cA,V0__m,V2__a) = cIntMap_2eFset_2eMapDomRestrBy___24a4(cA,cB,V0__m,cIntMap_2eMap_2eM1___24a3(cB,V2__a,V3__y)) ) ) ) ) ).

fof('$adef_IntMap.Map.M0_$a1',axiom,
    ! [V_24X1] : happ(cIntMap_2eMap_2eM0,V_24X1) = cIntMap_2eMap_2eM0___24a1(V_24X1) ).

fof('$adef_$_lam_2223_$a5',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(c_24__lam__2223,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = c_24__lam__2223___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).

fof('$adef_$_lam_2135_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__lam__2135,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__lam__2135___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).

fof('$adef_$_lam_2008_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__lam__2008,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__lam__2008___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).

fof('$adef_$_lam_355_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__lam__355,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__lam__355___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).

fof('$adef_Coq.PArith.BinPos.Pos.le_$a2',axiom,
    ! [V_24X1,V_24X2] :
      ( p(happ(happ(cCoq_2ePArith_2eBinPos_2ePos_2ele,V_24X1),V_24X2))
    <=> cCoq_2ePArith_2eBinPos_2ePos_2ele___24a2(V_24X1,V_24X2) ) ).

fof('$adef_Coq.ZArith.BinIntDef.Z.max_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eBinIntDef_2eZ_2emax,V_24X1),V_24X2) = cCoq_2eZArith_2eBinIntDef_2eZ_2emax___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.Arith.PeanoNat.Nat.eqf_$a2',axiom,
    ! [V_24X1,V_24X2] :
      ( p(happ(happ(cCoq_2eArith_2ePeanoNat_2eNat_2eeqf,V_24X1),V_24X2))
    <=> cCoq_2eArith_2ePeanoNat_2eNat_2eeqf___24a2(V_24X1,V_24X2) ) ).

fof('$adef_Coq.Init.Nat.mul_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eNat_2emul,V_24X1),V_24X2) = cCoq_2eInit_2eNat_2emul___24a2(V_24X1,V_24X2) ).

fof('$adef_$_lam_14616_$a2',axiom,
    ! [V_24X1,V_24X2] :
      ( p(happ(happ(c_24__lam__14616,V_24X1),V_24X2))
    <=> c_24__lam__14616___24a2(V_24X1,V_24X2) ) ).

fof('$adef_Coq.FSets.FSetPositive.PositiveSet.Node_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eNode,V_24X1),V_24X2),V_24X3) = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eNode___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_Coq.Init.Peano.le_$a2',axiom,
    ! [V_24X1,V_24X2] :
      ( p(happ(happ(cCoq_2eInit_2ePeano_2ele,V_24X1),V_24X2))
    <=> cCoq_2eInit_2ePeano_2ele___24a2(V_24X1,V_24X2) ) ).

fof('$adef_Coq.Arith.PeanoNat.Nat.divide_$a2',axiom,
    ! [V_24X1,V_24X2] :
      ( p(happ(happ(cCoq_2eArith_2ePeanoNat_2eNat_2edivide,V_24X1),V_24X2))
    <=> cCoq_2eArith_2ePeanoNat_2eNat_2edivide___24a2(V_24X1,V_24X2) ) ).

fof('$adef_Coq.Logic.EqdepFacts.Streicher_K__$a1',axiom,
    ! [V_24X1] :
      ( p(happ(cCoq_2eLogic_2eEqdepFacts_2eStreicher__K__,V_24X1))
    <=> cCoq_2eLogic_2eEqdepFacts_2eStreicher__K_____24a1(V_24X1) ) ).

fof('$adef_Coq.NArith.Ndigits.eqf_$a2',axiom,
    ! [V_24X1,V_24X2] :
      ( p(happ(happ(cCoq_2eNArith_2eNdigits_2eeqf,V_24X1),V_24X2))
    <=> cCoq_2eNArith_2eNdigits_2eeqf___24a2(V_24X1,V_24X2) ) ).

fof('$adef_$_lam_2108_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__2108,V_24X1),V_24X2),V_24X3) = c_24__lam__2108___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_$_lam_1515_$a5',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(c_24__lam__1515,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = c_24__lam__1515___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).

fof('$adef_Coq.Classes.RelationClasses.Equivalence_$a2',axiom,
    ! [V_24X1,V_24X2] :
      ( p(happ(happ(cCoq_2eClasses_2eRelationClasses_2eEquivalence,V_24X1),V_24X2))
    <=> cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(V_24X1,V_24X2) ) ).

fof('$adef_Coq.Arith.Even.even_$a1',axiom,
    ! [V_24X1] :
      ( p(happ(cCoq_2eArith_2eEven_2eeven,V_24X1))
    <=> cCoq_2eArith_2eEven_2eeven___24a1(V_24X1) ) ).

fof('$adef_Coq.micromega.Tauto.TT_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2emicromega_2eTauto_2eTT,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2emicromega_2eTauto_2eTT___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).

fof('$adef_Coq.PArith.BinPos.Pos.PeanoSucc_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2ePArith_2eBinPos_2ePos_2ePeanoSucc,V_24X1),V_24X2) = cCoq_2ePArith_2eBinPos_2ePos_2ePeanoSucc___24a2(V_24X1,V_24X2) ).

fof('$adef_IntMap.Map.MapSingleton_$a1',axiom,
    ! [V_24X1] : happ(cIntMap_2eMap_2eMapSingleton,V_24X1) = cIntMap_2eMap_2eMapSingleton___24a1(V_24X1) ).

fof('$adef_Coq.Logic.Decidable.decidable_$a1',axiom,
    ! [V_24X1] :
      ( p(happ(cCoq_2eLogic_2eDecidable_2edecidable,V_24X1))
    <=> cCoq_2eLogic_2eDecidable_2edecidable___24a1(V_24X1) ) ).

fof('$adef_Coq.Bool.Bool.orb_true_elim_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eBool_2eBool_2eorb__true__elim,V_24X1) = cCoq_2eBool_2eBool_2eorb__true__elim___24a1(V_24X1) ).

fof('$adef_IntMap.Mapaxioms.eqmap_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] :
      ( p(happ(happ(happ(cIntMap_2eMapaxioms_2eeqmap,V_24X1),V_24X2),V_24X3))
    <=> cIntMap_2eMapaxioms_2eeqmap___24a3(V_24X1,V_24X2,V_24X3) ) ).

fof('$adef_Coq.micromega.EnvRing.PEmul_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2emicromega_2eEnvRing_2ePEmul,V_24X1),V_24X2),V_24X3) = cCoq_2emicromega_2eEnvRing_2ePEmul___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_Coq.Reals.Rdefinitions.IZR_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eReals_2eRdefinitions_2eIZR,V_24X1) = cCoq_2eReals_2eRdefinitions_2eIZR___24a1(V_24X1) ).

fof('$adef_Coq.Init.Datatypes.snd_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eInit_2eDatatypes_2esnd,V_24X1),V_24X2),V_24X3) = cCoq_2eInit_2eDatatypes_2esnd___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_$_lam_292_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__lam__292,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__lam__292___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).

fof('$adef_IntMap.Fset.in_dom_$a1',axiom,
    ! [V_24X1] : happ(cIntMap_2eFset_2ein__dom,V_24X1) = cIntMap_2eFset_2ein__dom___24a1(V_24X1) ).

fof('$adef_Coq.ZArith.BinInt.Z.eqf_$a2',axiom,
    ! [V_24X1,V_24X2] :
      ( p(happ(happ(cCoq_2eZArith_2eBinInt_2eZ_2eeqf,V_24X1),V_24X2))
    <=> cCoq_2eZArith_2eBinInt_2eZ_2eeqf___24a2(V_24X1,V_24X2) ) ).

fof('$adef_$_lam_718_$a5',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(c_24__lam__718,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = c_24__lam__718___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).

fof('$adef_$_lam_13951_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__lam__13951,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__lam__13951___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).

fof('$adef_Coq.PArith.BinPos.Pos.lt_$a2',axiom,
    ! [V_24X1,V_24X2] :
      ( p(happ(happ(cCoq_2ePArith_2eBinPos_2ePos_2elt,V_24X1),V_24X2))
    <=> cCoq_2ePArith_2eBinPos_2ePos_2elt___24a2(V_24X1,V_24X2) ) ).

fof('$adef_Coq.Init.Datatypes.None_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eInit_2eDatatypes_2eNone,V_24X1) = cCoq_2eInit_2eDatatypes_2eNone___24a1(V_24X1) ).

fof('$adef_Coq.NArith.BinNat.N.lt_$a2',axiom,
    ! [V_24X1,V_24X2] :
      ( p(happ(happ(cCoq_2eNArith_2eBinNat_2eN_2elt,V_24X1),V_24X2))
    <=> cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V_24X1,V_24X2) ) ).

fof('$adef_IntMap.Map.MapMerge_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cIntMap_2eMap_2eMapMerge,V_24X1),V_24X2),V_24X3) = cIntMap_2eMap_2eMapMerge___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_Coq.NArith.BinNatDef.N.testbit_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2eNArith_2eBinNatDef_2eN_2etestbit,V_24X1),V_24X2) = cCoq_2eNArith_2eBinNatDef_2eN_2etestbit___24a2(V_24X1,V_24X2) ).

fof('$adef_$_prop_36755_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(c_24__prop__36755,V_24X1),V_24X2) = c_24__prop__36755___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.Vectors.VectorDef.cons_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2eVectors_2eVectorDef_2econs,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2eVectors_2eVectorDef_2econs___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).

fof('$adef_Coq.ZArith.BinIntDef.Z.of_N_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eZArith_2eBinIntDef_2eZ_2eof__N,V_24X1) = cCoq_2eZArith_2eBinIntDef_2eZ_2eof__N___24a1(V_24X1) ).

fof('$adef_Coq.PArith.BinPosDef.Pos.to_nat_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2ePArith_2eBinPosDef_2ePos_2eto__nat,V_24X1) = cCoq_2ePArith_2eBinPosDef_2ePos_2eto__nat___24a1(V_24X1) ).

fof('$adef_Coq.Relations.Relation_Definitions.antisymmetric_$a2',axiom,
    ! [V_24X1,V_24X2] :
      ( p(happ(happ(cCoq_2eRelations_2eRelation__Definitions_2eantisymmetric,V_24X1),V_24X2))
    <=> cCoq_2eRelations_2eRelation__Definitions_2eantisymmetric___24a2(V_24X1,V_24X2) ) ).

fof('$adef_$_lam_13367_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(c_24__lam__13367,V_24X1),V_24X2) = c_24__lam__13367___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.ZArith.BinIntDef.Z.modulo_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eBinIntDef_2eZ_2emodulo,V_24X1),V_24X2) = cCoq_2eZArith_2eBinIntDef_2eZ_2emodulo___24a2(V_24X1,V_24X2) ).

fof('$adef_IntMap.Lsort.ad_monotonic_$a1',axiom,
    ! [V_24X1] :
      ( p(happ(cIntMap_2eLsort_2ead__monotonic,V_24X1))
    <=> cIntMap_2eLsort_2ead__monotonic___24a1(V_24X1) ) ).

fof('$adef_$_lam_380_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__380,V_24X1),V_24X2),V_24X3) = c_24__lam__380___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_$_prop_1974_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(c_24__prop__1974,V_24X1),V_24X2) = c_24__prop__1974___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.setoid_ring.Ring_theory.SRopp_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2esetoid__ring_2eRing__theory_2eSRopp,V_24X1),V_24X2) = cCoq_2esetoid__ring_2eRing__theory_2eSRopp___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.Init.Datatypes.CompLtT_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eInit_2eDatatypes_2eCompLtT,V_24X1),V_24X2),V_24X3) = cCoq_2eInit_2eDatatypes_2eCompLtT___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_$_lam_36722_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__36722,V_24X1),V_24X2),V_24X3) = c_24__lam__36722___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_Coq.ZArith.Znumtheory.prime_$a1',axiom,
    ! [V_24X1] :
      ( p(happ(cCoq_2eZArith_2eZnumtheory_2eprime,V_24X1))
    <=> cCoq_2eZArith_2eZnumtheory_2eprime___24a1(V_24X1) ) ).

fof('$adef_$_prop_33478_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__prop__33478,V_24X1),V_24X2),V_24X3) = c_24__prop__33478___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_IntMap.Fset.MapDomRestrBy_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cIntMap_2eFset_2eMapDomRestrBy,V_24X1),V_24X2),V_24X3) = cIntMap_2eFset_2eMapDomRestrBy___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_$_lam_262_$a5',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(c_24__lam__262,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = c_24__lam__262___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).

fof('$adef_$_lam_13414_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__13414,V_24X1),V_24X2),V_24X3) = c_24__lam__13414___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_Coq.Init.Specif.sig_rect_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eInit_2eSpecif_2esig__rect,V_24X1),V_24X2),V_24X3) = cCoq_2eInit_2eSpecif_2esig__rect___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_IntMap.Mapsubset.MapSubset_2_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] :
      ( p(happ(happ(happ(happ(cIntMap_2eMapsubset_2eMapSubset__2,V_24X1),V_24X2),V_24X3),V_24X4))
    <=> cIntMap_2eMapsubset_2eMapSubset__2___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).

fof('$adef_$_lam_13613_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(c_24__lam__13613,V_24X1),V_24X2) = c_24__lam__13613___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.Reals.Rfunctions.ZintPos_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2eReals_2eRfunctions_2eZintPos,V_24X1),V_24X2) = cCoq_2eReals_2eRfunctions_2eZintPos___24a2(V_24X1,V_24X2) ).

fof('$adef_$_fix_33571_v_CANONICAL_0_$a1',axiom,
    ! [V_24X1] : happ(c_24__fix__33571__v__CANONICAL__0,V_24X1) = c_24__fix__33571__v__CANONICAL__0___24a1(V_24X1) ).

fof('$adef_Coq.Init.Datatypes.inr_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eInit_2eDatatypes_2einr,V_24X1),V_24X2),V_24X3) = cCoq_2eInit_2eDatatypes_2einr___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_$_prop_36756_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(c_24__prop__36756,V_24X1),V_24X2) = c_24__prop__36756___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.setoid_ring.Ring_theory.sring_eq_ext_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] :
      ( p(happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__theory_2esring__eq__ext,V_24X1),V_24X2),V_24X3),V_24X4))
    <=> cCoq_2esetoid__ring_2eRing__theory_2esring__eq__ext___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).

fof('$adef_Coq.setoid_ring.Ring_polynom.PEc_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2ePEc,V_24X1),V_24X2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEc___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.Vectors.Fin.F1_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eVectors_2eFin_2eF1,V_24X1) = cCoq_2eVectors_2eFin_2eF1___24a1(V_24X1) ).

fof('$adef_Coq.QArith.QArith_base.Qnum_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eQArith_2eQArith__base_2eQnum,V_24X1) = cCoq_2eQArith_2eQArith__base_2eQnum___24a1(V_24X1) ).

fof('$adef_$_lam_686_$a5',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(c_24__lam__686,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = c_24__lam__686___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).

fof('$adef_$_case_Coq.Init.Datatypes.option$2237_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__case__Coq_2eInit_2eDatatypes_2eoption_242237,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__case__Coq_2eInit_2eDatatypes_2eoption_242237___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).

fof('$adef_Coq.micromega.EnvRing.Pol_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2emicromega_2eEnvRing_2ePol,V_24X1) = cCoq_2emicromega_2eEnvRing_2ePol___24a1(V_24X1) ).

fof('$adef_$_lam_1228_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__lam__1228,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__lam__1228___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).

fof('$adef_$_case_Coq.Init.Datatypes.bool$1994_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__case__Coq_2eInit_2eDatatypes_2ebool_241994,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__case__Coq_2eInit_2eDatatypes_2ebool_241994___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).

fof('$adef_$_lam_1098_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__lam__1098,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__lam__1098___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).

fof('$adef_Coq.Init.Specif.sumor_rect_$a6',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(cCoq_2eInit_2eSpecif_2esumor__rect,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = cCoq_2eInit_2eSpecif_2esumor__rect___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).

fof('$adef_Coq.micromega.Tauto.Cj_$a6',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(cCoq_2emicromega_2eTauto_2eCj,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = cCoq_2emicromega_2eTauto_2eCj___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).

fof('$adef_$_prop_1816_$a1',axiom,
    ! [V_24X1] : happ(c_24__prop__1816,V_24X1) = c_24__prop__1816___24a1(V_24X1) ).

fof('$adef_$_lam_136_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__lam__136,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__lam__136___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).

fof('$adef_Coq.setoid_ring.Ring_polynom.PEmul_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2ePEmul,V_24X1),V_24X2),V_24X3) = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_$_case_Coq.Init.Datatypes.nat$23394_$a1',axiom,
    ! [V_24X1] : happ(c_24__case__Coq_2eInit_2eDatatypes_2enat_2423394,V_24X1) = c_24__case__Coq_2eInit_2eDatatypes_2enat_2423394___24a1(V_24X1) ).

fof('$adef_Coq.NArith.BinNatDef.N.succ_double_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eNArith_2eBinNatDef_2eN_2esucc__double,V_24X1) = cCoq_2eNArith_2eBinNatDef_2eN_2esucc__double___24a1(V_24X1) ).

fof('$adef_$_lam_14614_$a1',axiom,
    ! [V_24X1] : happ(c_24__lam__14614,V_24X1) = c_24__lam__14614___24a1(V_24X1) ).

fof('$adef_Coq.setoid_ring.Ring_polynom.Pc_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2ePc,V_24X1),V_24X2) = cCoq_2esetoid__ring_2eRing__polynom_2ePc___24a2(V_24X1,V_24X2) ).

fof('$adef_$_case_Coq.Init.Datatypes.bool$36649_$a5',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(c_24__case__Coq_2eInit_2eDatatypes_2ebool_2436649,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = c_24__case__Coq_2eInit_2eDatatypes_2ebool_2436649___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).

fof('$adef_IntMap.Fset.in_FSet_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cIntMap_2eFset_2ein__FSet,V_24X1),V_24X2) = cIntMap_2eFset_2ein__FSet___24a2(V_24X1,V_24X2) ).

fof('$adef_IntMap.Mapiter.MapFold1_$a7',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7] : happ(happ(happ(happ(happ(happ(happ(cIntMap_2eMapiter_2eMapFold1,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7) = cIntMap_2eMapiter_2eMapFold1___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7) ).

fof('$adef_Coq.Init.Nat.even_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eInit_2eNat_2eeven,V_24X1) = cCoq_2eInit_2eNat_2eeven___24a1(V_24X1) ).

fof('$adef_Coq.setoid_ring.Ring_polynom.vmon_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2evmon,V_24X1),V_24X2) = cCoq_2esetoid__ring_2eRing__polynom_2evmon___24a2(V_24X1,V_24X2) ).

fof('$adef_$_lam_14524_$a5',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(c_24__lam__14524,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = c_24__lam__14524___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).

fof('$adef_Coq.PArith.BinPosDef.Pos.succ_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2ePArith_2eBinPosDef_2ePos_2esucc,V_24X1) = cCoq_2ePArith_2eBinPosDef_2ePos_2esucc___24a1(V_24X1) ).

fof('$adef_Coq.setoid_ring.Field_theory.FEsub_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2esetoid__ring_2eField__theory_2eFEsub,V_24X1),V_24X2),V_24X3) = cCoq_2esetoid__ring_2eField__theory_2eFEsub___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_$_cast_1814_$a1',axiom,
    ! [V_24X1] : happ(c_24__cast__1814,V_24X1) = c_24__cast__1814___24a1(V_24X1) ).

fof('$adef_Coq.setoid_ring.Ring_polynom.Pol_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2esetoid__ring_2eRing__polynom_2ePol,V_24X1) = cCoq_2esetoid__ring_2eRing__polynom_2ePol___24a1(V_24X1) ).

fof('$adef_$_lam_1605_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(c_24__lam__1605,V_24X1),V_24X2) = c_24__lam__1605___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.FSets.FSetPositive.PositiveSet.mem_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2emem,V_24X1),V_24X2) = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2emem___24a2(V_24X1,V_24X2) ).

fof('$adef_$_prop_36758_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(c_24__prop__36758,V_24X1),V_24X2) = c_24__prop__36758___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.micromega.Tauto.D_$a6',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(cCoq_2emicromega_2eTauto_2eD,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = cCoq_2emicromega_2eTauto_2eD___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).

fof('$adef_IntMap.Mapsubset.MapSubset_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] :
      ( p(happ(happ(happ(happ(cIntMap_2eMapsubset_2eMapSubset,V_24X1),V_24X2),V_24X3),V_24X4))
    <=> cIntMap_2eMapsubset_2eMapSubset___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).

fof('$adef_Coq.Init.Datatypes.prod_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eDatatypes_2eprod,V_24X1),V_24X2) = cCoq_2eInit_2eDatatypes_2eprod___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.Reals.Rdefinitions.IPR_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eReals_2eRdefinitions_2eIPR,V_24X1) = cCoq_2eReals_2eRdefinitions_2eIPR___24a1(V_24X1) ).

fof('$adef_Coq.Arith.PeanoNat.Nat.le_alt_$a2',axiom,
    ! [V_24X1,V_24X2] :
      ( p(happ(happ(cCoq_2eArith_2ePeanoNat_2eNat_2ele__alt,V_24X1),V_24X2))
    <=> cCoq_2eArith_2ePeanoNat_2eNat_2ele__alt___24a2(V_24X1,V_24X2) ) ).

fof('$adef_Coq.micromega.Env.Env_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2emicromega_2eEnv_2eEnv,V_24X1) = cCoq_2emicromega_2eEnv_2eEnv___24a1(V_24X1) ).

fof('$adef_Coq.Init.Datatypes.CompareSpecT_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2eInit_2eDatatypes_2eCompareSpecT,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2eInit_2eDatatypes_2eCompareSpecT___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).

fof('$adef_Coq.micromega.ZMicromega.Vars.Facts.MP.Dec.FSetDecideAuxiliary.FSet_elt_Prop_$a1',axiom,
    ! [V_24X1] :
      ( p(happ(cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__elt__Prop,V_24X1))
    <=> cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__elt__Prop___24a1(V_24X1) ) ).

fof('$adef_$_lam_14287_$a6',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(c_24__lam__14287,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = c_24__lam__14287___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).

fof('$adef_IntMap.Map.MapDelta_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cIntMap_2eMap_2eMapDelta,V_24X1),V_24X2),V_24X3) = cIntMap_2eMap_2eMapDelta___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_Coq.setoid_ring.Field_theory.FEdiv_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2esetoid__ring_2eField__theory_2eFEdiv,V_24X1),V_24X2),V_24X3) = cCoq_2esetoid__ring_2eField__theory_2eFEdiv___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_Coq.ZArith.BinIntDef.Z.compare_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare,V_24X1),V_24X2) = cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.setoid_ring.Ring_theory.ring_theory_$a8',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8] :
      ( p(happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__theory_2ering__theory,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8))
    <=> cCoq_2esetoid__ring_2eRing__theory_2ering__theory___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8) ) ).

fof('$adef_Coq.Init.Specif.sigT_rect_$a5',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2eInit_2eSpecif_2esigT__rect,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2eInit_2eSpecif_2esigT__rect___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).

fof('$adef_Coq.setoid_ring.Ring_theory.almost_ring_theory_$a8',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8] :
      ( p(happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__theory_2ealmost__ring__theory,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8))
    <=> cCoq_2esetoid__ring_2eRing__theory_2ealmost__ring__theory___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8) ) ).

fof('$adef_Coq.QArith.QArith_base.Qden_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eQArith_2eQArith__base_2eQden,V_24X1) = cCoq_2eQArith_2eQArith__base_2eQden___24a1(V_24X1) ).

fof('$adef_$_lam_36722_$a5',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] :
      ( p(happ(happ(happ(happ(happ(c_24__lam__36722,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5))
    <=> c_24__lam__36722___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ) ).

fof('$adef_IntMap.Mapsubset.MapDisjoint_2_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] :
      ( p(happ(happ(happ(happ(cIntMap_2eMapsubset_2eMapDisjoint__2,V_24X1),V_24X2),V_24X3),V_24X4))
    <=> cIntMap_2eMapsubset_2eMapDisjoint__2___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).

fof('$adef_$_lam_649_$a6',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(c_24__lam__649,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = c_24__lam__649___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).

fof('$adef_Coq.setoid_ring.InitialRing.gen_phiPOS_$a5',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).

fof('$adef_Coq.Init.Datatypes.app_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eInit_2eDatatypes_2eapp,V_24X1),V_24X2),V_24X3) = cCoq_2eInit_2eDatatypes_2eapp___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_Coq.NArith.BinNatDef.N.div2_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eNArith_2eBinNatDef_2eN_2ediv2,V_24X1) = cCoq_2eNArith_2eBinNatDef_2eN_2ediv2___24a1(V_24X1) ).

fof('$adef_Coq.Init.Specif.existT_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2eInit_2eSpecif_2eexistT,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2eInit_2eSpecif_2eexistT___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).

fof('$adef_$_lam_1083_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(c_24__lam__1083,V_24X1),V_24X2) = c_24__lam__1083___24a2(V_24X1,V_24X2) ).

fof('$adef_$_lam_14614_$a2',axiom,
    ! [V_24X1,V_24X2] :
      ( p(happ(happ(c_24__lam__14614,V_24X1),V_24X2))
    <=> c_24__lam__14614___24a2(V_24X1,V_24X2) ) ).

fof('$adef_Coq.Init.Specif.sig_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eSpecif_2esig,V_24X1),V_24X2) = cCoq_2eInit_2eSpecif_2esig___24a2(V_24X1,V_24X2) ).

fof('$adef_$_lam_1156_$a6',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(c_24__lam__1156,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = c_24__lam__1156___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).

fof('$adef_$_case_Coq.Init.Datatypes.bool$2000_$a5',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(c_24__case__Coq_2eInit_2eDatatypes_2ebool_242000,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = c_24__case__Coq_2eInit_2eDatatypes_2ebool_242000___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).

fof('$adef_$_lam_13198_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(c_24__lam__13198,V_24X1),V_24X2) = c_24__lam__13198___24a2(V_24X1,V_24X2) ).

fof('$adef_$_lam_14051_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__14051,V_24X1),V_24X2),V_24X3) = c_24__lam__14051___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_IntMap.Lsort.alist_sorted_2_$a2',axiom,
    ! [V_24X1,V_24X2] :
      ( p(happ(happ(cIntMap_2eLsort_2ealist__sorted__2,V_24X1),V_24X2))
    <=> cIntMap_2eLsort_2ealist__sorted__2___24a2(V_24X1,V_24X2) ) ).

fof('$adef_Coq.setoid_ring.Field_theory.FEmul_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2esetoid__ring_2eField__theory_2eFEmul,V_24X1),V_24X2),V_24X3) = cCoq_2esetoid__ring_2eField__theory_2eFEmul___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_Coq.ZArith.BinIntDef.Z.mul_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eBinIntDef_2eZ_2emul,V_24X1),V_24X2) = cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V_24X1,V_24X2) ).

fof('$adef_IntMap.Map.MapPut_behind_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cIntMap_2eMap_2eMapPut__behind,V_24X1),V_24X2) = cIntMap_2eMap_2eMapPut__behind___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.PArith.BinPosDef.Pos.iter_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2ePArith_2eBinPosDef_2ePos_2eiter,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2ePArith_2eBinPosDef_2ePos_2eiter___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).

fof('$adef_Coq.Bool.Bool.eqb_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2eBool_2eBool_2eeqb,V_24X1),V_24X2) = cCoq_2eBool_2eBool_2eeqb___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.PArith.BinPosDef.Pos.divide_$a2',axiom,
    ! [V_24X1,V_24X2] :
      ( p(happ(happ(cCoq_2ePArith_2eBinPosDef_2ePos_2edivide,V_24X1),V_24X2))
    <=> cCoq_2ePArith_2eBinPosDef_2ePos_2edivide___24a2(V_24X1,V_24X2) ) ).

fof('$adef_$_lam_13200_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(c_24__lam__13200,V_24X1),V_24X2) = c_24__lam__13200___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.ZArith.BinInt.Z.lt_$a2',axiom,
    ! [V_24X1,V_24X2] :
      ( p(happ(happ(cCoq_2eZArith_2eBinInt_2eZ_2elt,V_24X1),V_24X2))
    <=> cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V_24X1,V_24X2) ) ).

fof('$adef_$_case_Coq.Init.Datatypes.bool$36665_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__case__Coq_2eInit_2eDatatypes_2ebool_2436665,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__case__Coq_2eInit_2eDatatypes_2ebool_2436665___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).

fof('$adef_Coq.setoid_ring.Field_theory.linear_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2esetoid__ring_2eField__theory_2elinear,V_24X1) = cCoq_2esetoid__ring_2eField__theory_2elinear___24a1(V_24X1) ).

fof('$adef_$_case_Coq.Init.Datatypes.option$13336_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__case__Coq_2eInit_2eDatatypes_2eoption_2413336,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__case__Coq_2eInit_2eDatatypes_2eoption_2413336___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).

fof('$adef_$_lam_1228_$a5',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(c_24__lam__1228,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = c_24__lam__1228___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).

fof('$adef_$_lam_13959_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__lam__13959,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__lam__13959___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).

fof('$adef_Coq.Init.Specif.sumbool_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eSpecif_2esumbool,V_24X1),V_24X2) = cCoq_2eInit_2eSpecif_2esumbool___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.PArith.BinPosDef.Pos.eqb_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2ePArith_2eBinPosDef_2ePos_2eeqb,V_24X1),V_24X2) = cCoq_2ePArith_2eBinPosDef_2ePos_2eeqb___24a2(V_24X1,V_24X2) ).

fof('$adef_$_lam_13594_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(c_24__lam__13594,V_24X1),V_24X2) = c_24__lam__13594___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.ZArith.Zlogarithm.Is_power_$a1',axiom,
    ! [V_24X1] :
      ( p(happ(cCoq_2eZArith_2eZlogarithm_2eIs__power,V_24X1))
    <=> cCoq_2eZArith_2eZlogarithm_2eIs__power___24a1(V_24X1) ) ).

fof('$adef_$_lam_13275_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__13275,V_24X1),V_24X2),V_24X3) = c_24__lam__13275___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_$_prop_33479_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(c_24__prop__33479,V_24X1),V_24X2) = c_24__prop__33479___24a2(V_24X1,V_24X2) ).

fof('$adef_$_prop_19859_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(c_24__prop__19859,V_24X1),V_24X2) = c_24__prop__19859___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.ZArith.BinIntDef.Z.opp_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eZArith_2eBinIntDef_2eZ_2eopp,V_24X1) = cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V_24X1) ).

fof('$adef_IntMap.Map.Map_rec_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cIntMap_2eMap_2eMap__rec,V_24X1),V_24X2) = cIntMap_2eMap_2eMap__rec___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.Init.Specif.sig_rect_$a5',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2eInit_2eSpecif_2esig__rect,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2eInit_2eSpecif_2esig__rect___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).

fof('$adef_$_prop_13465_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__prop__13465,V_24X1),V_24X2),V_24X3) = c_24__prop__13465___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_IntMap.Map.MapPut_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cIntMap_2eMap_2eMapPut,V_24X1),V_24X2) = cIntMap_2eMap_2eMapPut___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.Sets.Relations_1.Relation_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eSets_2eRelations__1_2eRelation,V_24X1) = cCoq_2eSets_2eRelations__1_2eRelation___24a1(V_24X1) ).

fof('$adef_Coq.Init.Specif.sumor_rec_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eInit_2eSpecif_2esumor__rec,V_24X1),V_24X2),V_24X3) = cCoq_2eInit_2eSpecif_2esumor__rec___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_$_lam_128_$a1',axiom,
    ! [V_24X1] : happ(c_24__lam__128,V_24X1) = c_24__lam__128___24a1(V_24X1) ).

fof('$adef_Coq.Numbers.BinNums.Zneg_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eNumbers_2eBinNums_2eZneg,V_24X1) = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(V_24X1) ).

fof('$adef_$_lam_380_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__lam__380,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__lam__380___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).

fof('$adef_$_lam_14558_$a5',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(c_24__lam__14558,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = c_24__lam__14558___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).

fof('$adef_Coq.Reals.Rdefinitions.Rgt_$a2',axiom,
    ! [V_24X1,V_24X2] :
      ( p(happ(happ(cCoq_2eReals_2eRdefinitions_2eRgt,V_24X1),V_24X2))
    <=> cCoq_2eReals_2eRdefinitions_2eRgt___24a2(V_24X1,V_24X2) ) ).

fof('$adef_Coq.setoid_ring.Ring_polynom.PEpow_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2ePEpow,V_24X1),V_24X2),V_24X3) = cCoq_2esetoid__ring_2eRing__polynom_2ePEpow___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_IntMap.Map.MapCard_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cIntMap_2eMap_2eMapCard,V_24X1),V_24X2) = cIntMap_2eMap_2eMapCard___24a2(V_24X1,V_24X2) ).

fof('$adef_$_lam_1156_$a5',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(c_24__lam__1156,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = c_24__lam__1156___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).

fof('$adef_Coq.NArith.BinNatDef.N.to_nat_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eNArith_2eBinNatDef_2eN_2eto__nat,V_24X1) = cCoq_2eNArith_2eBinNatDef_2eN_2eto__nat___24a1(V_24X1) ).

fof('$adef_$_prop_784_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__prop__784,V_24X1),V_24X2),V_24X3) = c_24__prop__784___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_$_prop_433_$a1',axiom,
    ! [V_24X1] : happ(c_24__prop__433,V_24X1) = c_24__prop__433___24a1(V_24X1) ).

fof('$adef_IntMap.Map.MapEmptyp_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cIntMap_2eMap_2eMapEmptyp,V_24X1),V_24X2) = cIntMap_2eMap_2eMapEmptyp___24a2(V_24X1,V_24X2) ).

fof('$adef_IntMap.Mapiter.MapFold_$a5',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cIntMap_2eMapiter_2eMapFold,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cIntMap_2eMapiter_2eMapFold___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).

fof('$adef_IntMap.Map.makeM2_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cIntMap_2eMap_2emakeM2,V_24X1),V_24X2),V_24X3) = cIntMap_2eMap_2emakeM2___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_Coq.ZArith.Zeven.Zeven_$a1',axiom,
    ! [V_24X1] :
      ( p(happ(cCoq_2eZArith_2eZeven_2eZeven,V_24X1))
    <=> cCoq_2eZArith_2eZeven_2eZeven___24a1(V_24X1) ) ).

fof('$adef_$_lam_13256_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__13256,V_24X1),V_24X2),V_24X3) = c_24__lam__13256___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_$_lam_13367_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] :
      ( p(happ(happ(happ(c_24__lam__13367,V_24X1),V_24X2),V_24X3))
    <=> c_24__lam__13367___24a3(V_24X1,V_24X2,V_24X3) ) ).

fof('$adef_IntMap.Mapcanon.MapCanonicalize_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cIntMap_2eMapcanon_2eMapCanonicalize,V_24X1),V_24X2) = cIntMap_2eMapcanon_2eMapCanonicalize___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.setoid_ring.Ring_polynom.PEsub_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2ePEsub,V_24X1),V_24X2),V_24X3) = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_IntMap.Mapiter.MapSweep2_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cIntMap_2eMapiter_2eMapSweep2,V_24X1),V_24X2),V_24X3),V_24X4) = cIntMap_2eMapiter_2eMapSweep2___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).

fof('$adef_Coq.Bool.Bool.reflect_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2eBool_2eBool_2ereflect,V_24X1),V_24X2) = cCoq_2eBool_2eBool_2ereflect___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.NArith.Ndigits.Nless_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2eNArith_2eNdigits_2eNless,V_24X1),V_24X2) = cCoq_2eNArith_2eNdigits_2eNless___24a2(V_24X1,V_24X2) ).

fof('$adef_IntMap.Lsort.alist_sorted_1_$a2',axiom,
    ! [V_24X1,V_24X2] :
      ( p(happ(happ(cIntMap_2eLsort_2ealist__sorted__1,V_24X1),V_24X2))
    <=> cIntMap_2eLsort_2ealist__sorted__1___24a2(V_24X1,V_24X2) ) ).

fof('$adef_Coq.setoid_ring.Ring_polynom.PX_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2ePX,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2esetoid__ring_2eRing__polynom_2ePX___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).

fof('$adef_Coq.Init.Nat.max_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eNat_2emax,V_24X1),V_24X2) = cCoq_2eInit_2eNat_2emax___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.PArith.BinPosDef.Pos.pred_N_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2ePArith_2eBinPosDef_2ePos_2epred__N,V_24X1) = cCoq_2ePArith_2eBinPosDef_2ePos_2epred__N___24a1(V_24X1) ).

fof('$adef_IntMap.Mapsubset.MapDisjoint_1_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cIntMap_2eMapsubset_2eMapDisjoint__1,V_24X1),V_24X2),V_24X3),V_24X4) = cIntMap_2eMapsubset_2eMapDisjoint__1___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).

fof('$adef_Coq.Init.Datatypes.option_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eInit_2eDatatypes_2eoption,V_24X1) = cCoq_2eInit_2eDatatypes_2eoption___24a1(V_24X1) ).

fof('$adef_IntMap.Mapiter.Map_of_alist_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cIntMap_2eMapiter_2eMap__of__alist,V_24X1),V_24X2) = cIntMap_2eMapiter_2eMap__of__alist___24a2(V_24X1,V_24X2) ).

fof('$adef_$_prop_36754_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__prop__36754,V_24X1),V_24X2),V_24X3) = c_24__prop__36754___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_Coq.Relations.Relation_Definitions.relation_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eRelations_2eRelation__Definitions_2erelation,V_24X1) = cCoq_2eRelations_2eRelation__Definitions_2erelation___24a1(V_24X1) ).

fof('$adef_$_lam_1605_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__1605,V_24X1),V_24X2),V_24X3) = c_24__lam__1605___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_$_lam_13275_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__lam__13275,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__lam__13275___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).

fof('$adef_Coq.setoid_ring.Ring_polynom.PEI_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2esetoid__ring_2eRing__polynom_2ePEI,V_24X1) = cCoq_2esetoid__ring_2eRing__polynom_2ePEI___24a1(V_24X1) ).

fof('$adef_IntMap.Map.Map_rect_$a6',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(cIntMap_2eMap_2eMap__rect,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = cIntMap_2eMap_2eMap__rect___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).

fof('$adef_Coq.Init.Specif.inright_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eSpecif_2einright,V_24X1),V_24X2) = cCoq_2eInit_2eSpecif_2einright___24a2(V_24X1,V_24X2) ).

fof('$adef_$_lam_1870_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__lam__1870,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__lam__1870___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).

fof('$adef_Coq.NArith.Ndigits.Neven_$a1',axiom,
    ! [V_24X1] :
      ( p(happ(cCoq_2eNArith_2eNdigits_2eNeven,V_24X1))
    <=> cCoq_2eNArith_2eNdigits_2eNeven___24a1(V_24X1) ) ).

fof('$adef_$_lam_262_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__262,V_24X1),V_24X2),V_24X3) = c_24__lam__262___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_Coq.Structures.OrderedType.LT_$a5',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2eStructures_2eOrderedType_2eLT,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2eStructures_2eOrderedType_2eLT___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).

fof('$adef_Coq.NArith.Ndigits.Nless_aux_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eNArith_2eNdigits_2eNless__aux,V_24X1),V_24X2),V_24X3) = cCoq_2eNArith_2eNdigits_2eNless__aux___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_$_lam_1973_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(c_24__lam__1973,V_24X1),V_24X2) = c_24__lam__1973___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.Vectors.VectorDef.t_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2eVectors_2eVectorDef_2et,V_24X1),V_24X2) = cCoq_2eVectors_2eVectorDef_2et___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.Init.Datatypes.prod_rect_$a5',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2eInit_2eDatatypes_2eprod__rect,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2eInit_2eDatatypes_2eprod__rect___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).

fof('$adef_Coq.setoid_ring.Ring_polynom.PExpr_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr,V_24X1) = cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V_24X1) ).

fof('$adef_Coq.Init.Datatypes.orb_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eDatatypes_2eorb,V_24X1),V_24X2) = cCoq_2eInit_2eDatatypes_2eorb___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.setoid_ring.Ring_polynom.PEadd_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2ePEadd,V_24X1),V_24X2),V_24X3) = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_Coq.setoid_ring.Ring_theory.ring_morph_$a17',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17] :
      ( p(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__theory_2ering__morph,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9),V_24X10),V_24X11),V_24X12),V_24X13),V_24X14),V_24X15),V_24X16),V_24X17))
    <=> cCoq_2esetoid__ring_2eRing__theory_2ering__morph___24a17(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17) ) ).

fof('$adef_$_lam_14051_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__lam__14051,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__lam__14051___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).

fof('$adef_$_prop_33475_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__prop__33475,V_24X1),V_24X2),V_24X3) = c_24__prop__33475___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_Coq.setoid_ring.Field_theory.FEopp_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2esetoid__ring_2eField__theory_2eFEopp,V_24X1),V_24X2) = cCoq_2esetoid__ring_2eField__theory_2eFEopp___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.micromega.EnvRing.PEopp_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2emicromega_2eEnvRing_2ePEopp,V_24X1),V_24X2) = cCoq_2emicromega_2eEnvRing_2ePEopp___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.Init.Specif.exist2_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2eInit_2eSpecif_2eexist2,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2eInit_2eSpecif_2eexist2___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).

fof('$adef_Coq.Init.Datatypes.CompareSpec_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] :
      ( p(happ(happ(happ(happ(cCoq_2eInit_2eDatatypes_2eCompareSpec,V_24X1),V_24X2),V_24X3),V_24X4))
    <=> cCoq_2eInit_2eDatatypes_2eCompareSpec___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).

fof('$adef_Coq.Init.Datatypes.xorb_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eDatatypes_2exorb,V_24X1),V_24X2) = cCoq_2eInit_2eDatatypes_2exorb___24a2(V_24X1,V_24X2) ).

fof('$adef_$_lam_14505_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__lam__14505,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__lam__14505___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).

fof('$adef_$_lam_2108_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] :
      ( p(happ(happ(happ(happ(c_24__lam__2108,V_24X1),V_24X2),V_24X3),V_24X4))
    <=> c_24__lam__2108___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).

fof('$adef_Coq.micromega.RingMicromega.SORaddon_$a22',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22] :
      ( p(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2emicromega_2eRingMicromega_2eSORaddon,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9),V_24X10),V_24X11),V_24X12),V_24X13),V_24X14),V_24X15),V_24X16),V_24X17),V_24X18),V_24X19),V_24X20),V_24X21),V_24X22))
    <=> cCoq_2emicromega_2eRingMicromega_2eSORaddon___24a22(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22) ) ).

fof('$adef_Coq.ZArith.Zpower.two_power_pos_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eZArith_2eZpower_2etwo__power__pos,V_24X1) = cCoq_2eZArith_2eZpower_2etwo__power__pos___24a1(V_24X1) ).

fof('$adef_IntMap.Map.MapGet_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cIntMap_2eMap_2eMapGet,V_24X1),V_24X2) = cIntMap_2eMap_2eMapGet___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.Strings.String.String_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2eStrings_2eString_2eString,V_24X1),V_24X2) = cCoq_2eStrings_2eString_2eString___24a2(V_24X1,V_24X2) ).

fof('$adef_IntMap.Mapiter.MapCollect_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cIntMap_2eMapiter_2eMapCollect,V_24X1),V_24X2),V_24X3),V_24X4) = cIntMap_2eMapiter_2eMapCollect___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).

fof('$adef_$_case_Coq.Init.Datatypes.bool$13303_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__case__Coq_2eInit_2eDatatypes_2ebool_2413303,V_24X1),V_24X2),V_24X3) = c_24__case__Coq_2eInit_2eDatatypes_2ebool_2413303___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_$_lam_1270_$a5',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(c_24__lam__1270,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = c_24__lam__1270___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).

fof('$adef_Coq.Relations.Relation_Definitions.equivalence_$a2',axiom,
    ! [V_24X1,V_24X2] :
      ( p(happ(happ(cCoq_2eRelations_2eRelation__Definitions_2eequivalence,V_24X1),V_24X2))
    <=> cCoq_2eRelations_2eRelation__Definitions_2eequivalence___24a2(V_24X1,V_24X2) ) ).

fof('$adef_Coq.ZArith.Znumtheory.Euclid_intro_$a5',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2eZArith_2eZnumtheory_2eEuclid__intro,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2eZArith_2eZnumtheory_2eEuclid__intro___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).

fof('$adef_Coq.Init.Datatypes.CompEqT_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eInit_2eDatatypes_2eCompEqT,V_24X1),V_24X2),V_24X3) = cCoq_2eInit_2eDatatypes_2eCompEqT___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_Coq.Init.Datatypes.app_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eInit_2eDatatypes_2eapp,V_24X1) = cCoq_2eInit_2eDatatypes_2eapp___24a1(V_24X1) ).

fof('$adef_Coq.setoid_ring.Field_theory.FExpr_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2esetoid__ring_2eField__theory_2eFExpr,V_24X1) = cCoq_2esetoid__ring_2eField__theory_2eFExpr___24a1(V_24X1) ).

fof('$adef_Coq.Classes.Morphisms.respectful_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2eClasses_2eMorphisms_2erespectful,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).

fof('$adef_Coq.micromega.RingMicromega.PolEnv_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2emicromega_2eRingMicromega_2ePolEnv,V_24X1) = cCoq_2emicromega_2eRingMicromega_2ePolEnv___24a1(V_24X1) ).

fof('$adef_Coq.Init.Specif.sumor_rect_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eInit_2eSpecif_2esumor__rect,V_24X1),V_24X2),V_24X3) = cCoq_2eInit_2eSpecif_2esumor__rect___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_$_lam_13959_$a5',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(c_24__lam__13959,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = c_24__lam__13959___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).

fof('$adef_Coq.Init.Specif.sumbool_rec_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eInit_2eSpecif_2esumbool__rec,V_24X1),V_24X2),V_24X3) = cCoq_2eInit_2eSpecif_2esumbool__rec___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_IntMap.Mapiter.MapFold1_state_$a8',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8] : happ(happ(happ(happ(happ(happ(happ(happ(cIntMap_2eMapiter_2eMapFold1__state,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8) = cIntMap_2eMapiter_2eMapFold1__state___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8) ).

fof('$adef_IntMap.Mapiter.acons_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cIntMap_2eMapiter_2eacons,V_24X1),V_24X2),V_24X3) = cIntMap_2eMapiter_2eacons___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_Coq.micromega.Tauto.FF_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2emicromega_2eTauto_2eFF,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2emicromega_2eTauto_2eFF___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).

fof('$adef_Coq.ZArith.BinIntDef.Z.abs_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eZArith_2eBinIntDef_2eZ_2eabs,V_24X1) = cCoq_2eZArith_2eBinIntDef_2eZ_2eabs___24a1(V_24X1) ).

fof('$adef_Coq.PArith.BinPosDef.Pos.min_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2ePArith_2eBinPosDef_2ePos_2emin,V_24X1),V_24X2) = cCoq_2ePArith_2eBinPosDef_2ePos_2emin___24a2(V_24X1,V_24X2) ).

fof('$adef_$_case_Coq.Init.Datatypes.bool$13299_$a5',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(c_24__case__Coq_2eInit_2eDatatypes_2ebool_2413299,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = c_24__case__Coq_2eInit_2eDatatypes_2ebool_2413299___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).

fof('$adef_Coq.FSets.FSetPositive.PositiveSet.In_$a2',axiom,
    ! [V_24X1,V_24X2] :
      ( p(happ(happ(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eIn,V_24X1),V_24X2))
    <=> cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eIn___24a2(V_24X1,V_24X2) ) ).

fof('$adef_Coq.NArith.BinNatDef.N.odd_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eNArith_2eBinNatDef_2eN_2eodd,V_24X1) = cCoq_2eNArith_2eBinNatDef_2eN_2eodd___24a1(V_24X1) ).

fof('$adef_IntMap.Map.MapPut_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cIntMap_2eMap_2eMapPut,V_24X1),V_24X2),V_24X3),V_24X4) = cIntMap_2eMap_2eMapPut___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).

fof('$adef_Coq.NArith.BinNatDef.N.succ_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eNArith_2eBinNatDef_2eN_2esucc,V_24X1) = cCoq_2eNArith_2eBinNatDef_2eN_2esucc___24a1(V_24X1) ).

fof('$adef_Coq.Structures.OrderedType.GT_$a5',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2eStructures_2eOrderedType_2eGT,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2eStructures_2eOrderedType_2eGT___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).

fof('$adef_$_lam_2223_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__lam__2223,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__lam__2223___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).

fof('$adef_Coq.Reals.Rdefinitions.Rle_$a2',axiom,
    ! [V_24X1,V_24X2] :
      ( p(happ(happ(cCoq_2eReals_2eRdefinitions_2eRle,V_24X1),V_24X2))
    <=> cCoq_2eReals_2eRdefinitions_2eRle___24a2(V_24X1,V_24X2) ) ).

fof('$adef_$_case_Coq.Init.Datatypes.bool$282_$a5',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(c_24__case__Coq_2eInit_2eDatatypes_2ebool_24282,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = c_24__case__Coq_2eInit_2eDatatypes_2ebool_24282___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).

fof('$adef_IntMap.Map.Map_rect_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cIntMap_2eMap_2eMap__rect,V_24X1),V_24X2) = cIntMap_2eMap_2eMap__rect___24a2(V_24X1,V_24X2) ).

fof('$adef_$_lam_13198_$a1',axiom,
    ! [V_24X1] : happ(c_24__lam__13198,V_24X1) = c_24__lam__13198___24a1(V_24X1) ).

fof('$adef_$_lam_1083_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__1083,V_24X1),V_24X2),V_24X3) = c_24__lam__1083___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_$_lam_13594_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__13594,V_24X1),V_24X2),V_24X3) = c_24__lam__13594___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_$_lam_13256_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__lam__13256,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__lam__13256___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).

fof('$adef_IntMap.Mapiter.alist_$a1',axiom,
    ! [V_24X1] : happ(cIntMap_2eMapiter_2ealist,V_24X1) = cIntMap_2eMapiter_2ealist___24a1(V_24X1) ).

fof('$adef_$_prop_13466_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__prop__13466,V_24X1),V_24X2),V_24X3) = c_24__prop__13466___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_Coq.micromega.EnvRing.zmon_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2emicromega_2eEnvRing_2ezmon,V_24X1),V_24X2) = cCoq_2emicromega_2eEnvRing_2ezmon___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.Vectors.Fin.FS_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2eVectors_2eFin_2eFS,V_24X1),V_24X2) = cCoq_2eVectors_2eFin_2eFS___24a2(V_24X1,V_24X2) ).

fof('$adef_$_lam_1406_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__1406,V_24X1),V_24X2),V_24X3) = c_24__lam__1406___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_IntMap.Map.MapMerge_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cIntMap_2eMap_2eMapMerge,V_24X1),V_24X2) = cIntMap_2eMap_2eMapMerge___24a2(V_24X1,V_24X2) ).

fof('$adef_$_prop_1823_$a1',axiom,
    ! [V_24X1] : happ(c_24__prop__1823,V_24X1) = c_24__prop__1823___24a1(V_24X1) ).

fof('$adef_$_lam_1889_$a5',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(c_24__lam__1889,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = c_24__lam__1889___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).

fof('$adef_Coq.Logic.EqdepFacts.eq_dep_$a6',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] :
      ( p(happ(happ(happ(happ(happ(happ(cCoq_2eLogic_2eEqdepFacts_2eeq__dep,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6))
    <=> cCoq_2eLogic_2eEqdepFacts_2eeq__dep___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ) ).

fof('$adef_$_lam_1644_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__lam__1644,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__lam__1644___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).

fof('$adef_$_lam_1398_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(c_24__lam__1398,V_24X1),V_24X2) = c_24__lam__1398___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.micromega.EnvRing.PExpr_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2emicromega_2eEnvRing_2ePExpr,V_24X1) = cCoq_2emicromega_2eEnvRing_2ePExpr___24a1(V_24X1) ).

fof('$adef_IntMap.Map.M1_$a1',axiom,
    ! [V_24X1] : happ(cIntMap_2eMap_2eM1,V_24X1) = cIntMap_2eMap_2eM1___24a1(V_24X1) ).

fof('$adef_Coq.Init.Nat.eqb_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eNat_2eeqb,V_24X1),V_24X2) = cCoq_2eInit_2eNat_2eeqb___24a2(V_24X1,V_24X2) ).

fof('$adef_$_lam_14333_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__lam__14333,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__lam__14333___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).

fof('$adef_Coq.Init.Peano.ge_$a2',axiom,
    ! [V_24X1,V_24X2] :
      ( p(happ(happ(cCoq_2eInit_2ePeano_2ege,V_24X1),V_24X2))
    <=> cCoq_2eInit_2ePeano_2ege___24a2(V_24X1,V_24X2) ) ).

fof('$adef_$_lam_2129_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__2129,V_24X1),V_24X2),V_24X3) = c_24__lam__2129___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_Coq.Reals.Rfunctions.Z_spec_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2eReals_2eRfunctions_2eZ__spec,V_24X1),V_24X2) = cCoq_2eReals_2eRfunctions_2eZ__spec___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.Init.Datatypes.inl_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eInit_2eDatatypes_2einl,V_24X1),V_24X2),V_24X3) = cCoq_2eInit_2eDatatypes_2einl___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_IntMap.Lsort.alist_sorted_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cIntMap_2eLsort_2ealist__sorted,V_24X1),V_24X2) = cIntMap_2eLsort_2ealist__sorted___24a2(V_24X1,V_24X2) ).

fof('$adef_$_lam_355_$a5',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(c_24__lam__355,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = c_24__lam__355___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).

fof('$adef_Coq.NArith.BinNat.N.divide_$a2',axiom,
    ! [V_24X1,V_24X2] :
      ( p(happ(happ(cCoq_2eNArith_2eBinNat_2eN_2edivide,V_24X1),V_24X2))
    <=> cCoq_2eNArith_2eBinNat_2eN_2edivide___24a2(V_24X1,V_24X2) ) ).

fof('$adef_Coq.Lists.SetoidList.NoDupA_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] :
      ( p(happ(happ(happ(cCoq_2eLists_2eSetoidList_2eNoDupA,V_24X1),V_24X2),V_24X3))
    <=> cCoq_2eLists_2eSetoidList_2eNoDupA___24a3(V_24X1,V_24X2,V_24X3) ) ).

fof('$adef_Coq.setoid_ring.Ring_theory.ring_eq_ext_$a5',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] :
      ( p(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__theory_2ering__eq__ext,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5))
    <=> cCoq_2esetoid__ring_2eRing__theory_2ering__eq__ext___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ) ).

fof('$adef_Coq.Logic.EqdepFacts.Streicher_K_on__$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] :
      ( p(happ(happ(happ(cCoq_2eLogic_2eEqdepFacts_2eStreicher__K__on__,V_24X1),V_24X2),V_24X3))
    <=> cCoq_2eLogic_2eEqdepFacts_2eStreicher__K__on_____24a3(V_24X1,V_24X2,V_24X3) ) ).

fof('$adef_$_lam_292_$a5',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(c_24__lam__292,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = c_24__lam__292___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).

fof('$adef_Coq.Logic.EqdepFacts.Eq_dep_eq_on_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] :
      ( p(happ(happ(happ(happ(cCoq_2eLogic_2eEqdepFacts_2eEq__dep__eq__on,V_24X1),V_24X2),V_24X3),V_24X4))
    <=> cCoq_2eLogic_2eEqdepFacts_2eEq__dep__eq__on___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).

fof('$adef_IntMap.Map.MapRemove_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cIntMap_2eMap_2eMapRemove,V_24X1),V_24X2),V_24X3) = cIntMap_2eMap_2eMapRemove___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_$_lam_13613_$a1',axiom,
    ! [V_24X1] : happ(c_24__lam__13613,V_24X1) = c_24__lam__13613___24a1(V_24X1) ).

fof('$adef_$_lam_14616_$a1',axiom,
    ! [V_24X1] : happ(c_24__lam__14616,V_24X1) = c_24__lam__14616___24a1(V_24X1) ).

fof('$adef_Coq.Logic.EqdepFacts.UIP_on__$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] :
      ( p(happ(happ(happ(cCoq_2eLogic_2eEqdepFacts_2eUIP__on__,V_24X1),V_24X2),V_24X3))
    <=> cCoq_2eLogic_2eEqdepFacts_2eUIP__on_____24a3(V_24X1,V_24X2,V_24X3) ) ).

fof('$adef_$_lam_13536_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] :
      ( p(happ(happ(happ(c_24__lam__13536,V_24X1),V_24X2),V_24X3))
    <=> c_24__lam__13536___24a3(V_24X1,V_24X2,V_24X3) ) ).

fof('$adef_IntMap.Mapiter.aapp_$a1',axiom,
    ! [V_24X1] : happ(cIntMap_2eMapiter_2eaapp,V_24X1) = cIntMap_2eMapiter_2eaapp___24a1(V_24X1) ).

fof('$adef_$_prop_785_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__prop__785,V_24X1),V_24X2),V_24X3) = c_24__prop__785___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_$_lam_686_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__686,V_24X1),V_24X2),V_24X3) = c_24__lam__686___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_Coq.Arith.EqNat.eq_nat_$a2',axiom,
    ! [V_24X1,V_24X2] :
      ( p(happ(happ(cCoq_2eArith_2eEqNat_2eeq__nat,V_24X1),V_24X2))
    <=> cCoq_2eArith_2eEqNat_2eeq__nat___24a2(V_24X1,V_24X2) ) ).

fof('$adef_IntMap.Fset.FSetUnion_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cIntMap_2eFset_2eFSetUnion,V_24X1),V_24X2) = cIntMap_2eFset_2eFSetUnion___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.micromega.Tauto.A_$a6',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(cCoq_2emicromega_2eTauto_2eA,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = cCoq_2emicromega_2eTauto_2eA___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).

fof('$adef_$_let_var_6_p_28908_28910_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__let__var__6__p__28908__28910,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__let__var__6__p__28908__28910___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).

fof('$adef_IntMap.Mapiter.alist_of_Map_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cIntMap_2eMapiter_2ealist__of__Map,V_24X1),V_24X2) = cIntMap_2eMapiter_2ealist__of__Map___24a2(V_24X1,V_24X2) ).

fof('$adef_$_lam_2087_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(c_24__lam__2087,V_24X1),V_24X2) = c_24__lam__2087___24a2(V_24X1,V_24X2) ).

fof('$adef_IntMap.Map.M1_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cIntMap_2eMap_2eM1,V_24X1),V_24X2),V_24X3) = cIntMap_2eMap_2eM1___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_$_prop_13505_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__prop__13505,V_24X1),V_24X2),V_24X3) = c_24__prop__13505___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_Coq.micromega.EnvRing.vmon_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2emicromega_2eEnvRing_2evmon,V_24X1),V_24X2) = cCoq_2emicromega_2eEnvRing_2evmon___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.Init.Datatypes.is_true_$a1',axiom,
    ! [V_24X1] :
      ( p(happ(cCoq_2eInit_2eDatatypes_2eis__true,V_24X1))
    <=> cCoq_2eInit_2eDatatypes_2eis__true___24a1(V_24X1) ) ).

fof('$adef_Coq.Init.Datatypes.nil_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eInit_2eDatatypes_2enil,V_24X1) = cCoq_2eInit_2eDatatypes_2enil___24a1(V_24X1) ).

fof('$adef_$_lam_13414_$a1',axiom,
    ! [V_24X1] : happ(c_24__lam__13414,V_24X1) = c_24__lam__13414___24a1(V_24X1) ).

fof('$adef_Coq.micromega.Tauto.X_$a5',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2emicromega_2eTauto_2eX,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2emicromega_2eTauto_2eX___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).

fof('$adef_$_lam_128_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(c_24__lam__128,V_24X1),V_24X2) = c_24__lam__128___24a2(V_24X1,V_24X2) ).

fof('$adef_$_prop_33473_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__prop__33473,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__prop__33473___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).

fof('$adef_Coq.Logic.EqdepFacts.eq_dep1_$a6',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] :
      ( p(happ(happ(happ(happ(happ(happ(cCoq_2eLogic_2eEqdepFacts_2eeq__dep1,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6))
    <=> cCoq_2eLogic_2eEqdepFacts_2eeq__dep1___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ) ).

fof('$adef_Coq.setoid_ring.Field_theory.almost_field_theory_$a10',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10] :
      ( p(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eField__theory_2ealmost__field__theory,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9),V_24X10))
    <=> cCoq_2esetoid__ring_2eField__theory_2ealmost__field__theory___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10) ) ).

fof('$adef_Coq.Init.Datatypes.cons_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eInit_2eDatatypes_2econs,V_24X1) = cCoq_2eInit_2eDatatypes_2econs___24a1(V_24X1) ).

fof('$adef_$_lam_13586_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(c_24__lam__13586,V_24X1),V_24X2) = c_24__lam__13586___24a2(V_24X1,V_24X2) ).

fof('$adef_$_case_Coq.Init.Datatypes.nat$23372_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__case__Coq_2eInit_2eDatatypes_2enat_2423372,V_24X1),V_24X2),V_24X3) = c_24__case__Coq_2eInit_2eDatatypes_2enat_2423372___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_Coq.NArith.BinNatDef.N.max_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2eNArith_2eBinNatDef_2eN_2emax,V_24X1),V_24X2) = cCoq_2eNArith_2eBinNatDef_2eN_2emax___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.Init.Specif.sumor_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eSpecif_2esumor,V_24X1),V_24X2) = cCoq_2eInit_2eSpecif_2esumor___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.Reals.Rdefinitions.Rge_$a2',axiom,
    ! [V_24X1,V_24X2] :
      ( p(happ(happ(cCoq_2eReals_2eRdefinitions_2eRge,V_24X1),V_24X2))
    <=> cCoq_2eReals_2eRdefinitions_2eRge___24a2(V_24X1,V_24X2) ) ).

fof('$adef_Coq.PArith.BinPosDef.Pos.mul_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2ePArith_2eBinPosDef_2ePos_2emul,V_24X1),V_24X2) = cCoq_2ePArith_2eBinPosDef_2ePos_2emul___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.Init.Datatypes.CompGtT_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eInit_2eDatatypes_2eCompGtT,V_24X1),V_24X2),V_24X3) = cCoq_2eInit_2eDatatypes_2eCompGtT___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_Coq.PArith.BinPosDef.Pos.testbit_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2ePArith_2eBinPosDef_2ePos_2etestbit,V_24X1),V_24X2) = cCoq_2ePArith_2eBinPosDef_2ePos_2etestbit___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.Reals.Rfunctions.ZintNeg_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2eReals_2eRfunctions_2eZintNeg,V_24X1),V_24X2) = cCoq_2eReals_2eRfunctions_2eZintNeg___24a2(V_24X1,V_24X2) ).

fof('$adef_IntMap.Map.newMap_$a1',axiom,
    ! [V_24X1] : happ(cIntMap_2eMap_2enewMap,V_24X1) = cIntMap_2eMap_2enewMap___24a1(V_24X1) ).

fof('$adef_Coq.ZArith.Znumtheory.rel_prime_$a2',axiom,
    ! [V_24X1,V_24X2] :
      ( p(happ(happ(cCoq_2eZArith_2eZnumtheory_2erel__prime,V_24X1),V_24X2))
    <=> cCoq_2eZArith_2eZnumtheory_2erel__prime___24a2(V_24X1,V_24X2) ) ).

fof('$adef_Coq.NArith.BinNatDef.N.mul_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2eNArith_2eBinNatDef_2eN_2emul,V_24X1),V_24X2) = cCoq_2eNArith_2eBinNatDef_2eN_2emul___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.Init.Nat.pred_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eInit_2eNat_2epred,V_24X1) = cCoq_2eInit_2eNat_2epred___24a1(V_24X1) ).

fof('$adef_IntMap.Mapiter.MapFold_state_$a7',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7] : happ(happ(happ(happ(happ(happ(happ(cIntMap_2eMapiter_2eMapFold__state,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7) = cIntMap_2eMapiter_2eMapFold__state___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7) ).

fof('$adef_IntMap.Mapiter.MapFold1_state_$a9',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9] : happ(happ(happ(happ(happ(happ(happ(happ(happ(cIntMap_2eMapiter_2eMapFold1__state,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9) = cIntMap_2eMapiter_2eMapFold1__state___24a9(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9) ).

fof('$adef_$_case_Coq.Init.Datatypes.bool$13267_$a5',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(c_24__case__Coq_2eInit_2eDatatypes_2ebool_2413267,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = c_24__case__Coq_2eInit_2eDatatypes_2ebool_2413267___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).

fof('$adef_$_prop_1815_$a1',axiom,
    ! [V_24X1] : happ(c_24__prop__1815,V_24X1) = c_24__prop__1815___24a1(V_24X1) ).

fof('$adef_Coq.micromega.Tauto.GFormula_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2emicromega_2eTauto_2eGFormula,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2emicromega_2eTauto_2eGFormula___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).

fof('$adef_Coq.ZArith.Znumtheory.Bezout_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] :
      ( p(happ(happ(happ(cCoq_2eZArith_2eZnumtheory_2eBezout,V_24X1),V_24X2),V_24X3))
    <=> cCoq_2eZArith_2eZnumtheory_2eBezout___24a3(V_24X1,V_24X2,V_24X3) ) ).

fof('$adef_Coq.Numbers.BinNums.Npos_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eNumbers_2eBinNums_2eNpos,V_24X1) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(V_24X1) ).

fof('$adef_$_lam_14505_$a6',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(c_24__lam__14505,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = c_24__lam__14505___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).

fof('$adef_Coq.setoid_ring.Ring_theory.Morphism_$a17',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17] : happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__theory_2eMorphism,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9),V_24X10),V_24X11),V_24X12),V_24X13),V_24X14),V_24X15),V_24X16),V_24X17) = cCoq_2esetoid__ring_2eRing__theory_2eMorphism___24a17(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17) ).

fof('$adef_$_lam_323_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__323,V_24X1),V_24X2),V_24X3) = c_24__lam__323___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_Coq.setoid_ring.Ring_theory.IDphi_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2esetoid__ring_2eRing__theory_2eIDphi,V_24X1),V_24X2) = cCoq_2esetoid__ring_2eRing__theory_2eIDphi___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.Init.Specif.exist_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eInit_2eSpecif_2eexist,V_24X1),V_24X2),V_24X3) = cCoq_2eInit_2eSpecif_2eexist___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_$_lam_1889_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__lam__1889,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__lam__1889___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).

fof('$adef_IntMap.Map.MapPut1_$a6',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(cIntMap_2eMap_2eMapPut1,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = cIntMap_2eMap_2eMapPut1___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).

fof('$adef_$_prop_33476_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__prop__33476,V_24X1),V_24X2),V_24X3) = c_24__prop__33476___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_Coq.ZArith.BinInt.Z.le_$a2',axiom,
    ! [V_24X1,V_24X2] :
      ( p(happ(happ(cCoq_2eZArith_2eBinInt_2eZ_2ele,V_24X1),V_24X2))
    <=> cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V_24X1,V_24X2) ) ).

fof('$adef_IntMap.Mapiter.alist_of_Map_$a1',axiom,
    ! [V_24X1] : happ(cIntMap_2eMapiter_2ealist__of__Map,V_24X1) = cIntMap_2eMapiter_2ealist__of__Map___24a1(V_24X1) ).

fof('$adef_$_lam_1098_$a5',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(c_24__lam__1098,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = c_24__lam__1098___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).

fof('$adef_IntMap.Mapiter.MapSweep1_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cIntMap_2eMapiter_2eMapSweep1,V_24X1),V_24X2),V_24X3),V_24X4) = cIntMap_2eMapiter_2eMapSweep1___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).

fof('$adef_$_lam_14558_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__14558,V_24X1),V_24X2),V_24X3) = c_24__lam__14558___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_Coq.Numbers.BinNums.xI_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eNumbers_2eBinNums_2exI,V_24X1) = cCoq_2eNumbers_2eBinNums_2exI___24a1(V_24X1) ).

fof('$adef_$_prop_1813_$a1',axiom,
    ! [V_24X1] : happ(c_24__prop__1813,V_24X1) = c_24__prop__1813___24a1(V_24X1) ).

fof('$adef_IntMap.Map.MapRemove_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cIntMap_2eMap_2eMapRemove,V_24X1),V_24X2) = cIntMap_2eMap_2eMapRemove___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.PArith.BinPosDef.Pos.compare_cont_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare__cont,V_24X1) = cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare__cont___24a1(V_24X1) ).

fof('$adef_Coq.ZArith.Zeven.Zodd_$a1',axiom,
    ! [V_24X1] :
      ( p(happ(cCoq_2eZArith_2eZeven_2eZodd,V_24X1))
    <=> cCoq_2eZArith_2eZeven_2eZodd___24a1(V_24X1) ) ).

fof('$adef_$_lam_2087_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] :
      ( p(happ(happ(happ(c_24__lam__2087,V_24X1),V_24X2),V_24X3))
    <=> c_24__lam__2087___24a3(V_24X1,V_24X2,V_24X3) ) ).

fof('$adef_Coq.Init.Specif.inleft_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eInit_2eSpecif_2einleft,V_24X1),V_24X2),V_24X3) = cCoq_2eInit_2eSpecif_2einleft___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_Coq.micromega.EnvRing.Pinj_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2emicromega_2eEnvRing_2ePinj,V_24X1),V_24X2),V_24X3) = cCoq_2emicromega_2eEnvRing_2ePinj___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_$_cast_1811_$a1',axiom,
    ! [V_24X1] : happ(c_24__cast__1811,V_24X1) = c_24__cast__1811___24a1(V_24X1) ).

fof('$adef_$_let_var_8_m_567_570_$a6',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(c_24__let__var__8__m__567__570,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = c_24__let__var__8__m__567__570___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).

fof('$adef_$_lam_1650_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__lam__1650,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__lam__1650___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).

fof('$adef_Coq.Init.Datatypes.cons_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eInit_2eDatatypes_2econs,V_24X1),V_24X2),V_24X3) = cCoq_2eInit_2eDatatypes_2econs___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_IntMap.Map.MapMerge_$a1',axiom,
    ! [V_24X1] : happ(cIntMap_2eMap_2eMapMerge,V_24X1) = cIntMap_2eMap_2eMapMerge___24a1(V_24X1) ).

fof('$adef_Coq.NArith.Ndigits.Nodd_$a1',axiom,
    ! [V_24X1] :
      ( p(happ(cCoq_2eNArith_2eNdigits_2eNodd,V_24X1))
    <=> cCoq_2eNArith_2eNdigits_2eNodd___24a1(V_24X1) ) ).

fof('$adef_Coq.setoid_ring.Field_theory.field_theory_$a10',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10] :
      ( p(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eField__theory_2efield__theory,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9),V_24X10))
    <=> cCoq_2esetoid__ring_2eField__theory_2efield__theory___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10) ) ).

fof('$adef_Coq.setoid_ring.Ring_theory.Computational_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2esetoid__ring_2eRing__theory_2eComputational,V_24X1),V_24X2),V_24X3) = cCoq_2esetoid__ring_2eRing__theory_2eComputational___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_Coq.ZArith.BinIntDef.Z.to_pos_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eZArith_2eBinIntDef_2eZ_2eto__pos,V_24X1) = cCoq_2eZArith_2eBinIntDef_2eZ_2eto__pos___24a1(V_24X1) ).

fof('$adef_Coq.ZArith.BinIntDef.Z.of_nat_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat,V_24X1) = cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat___24a1(V_24X1) ).

fof('$adef_Coq.Init.Nat.div2_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eInit_2eNat_2ediv2,V_24X1) = cCoq_2eInit_2eNat_2ediv2___24a1(V_24X1) ).

fof('$adef_Coq.Init.Datatypes.pair_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2eInit_2eDatatypes_2epair,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2eInit_2eDatatypes_2epair___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).

fof('$adef_Coq.Init.Datatypes.negb_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eInit_2eDatatypes_2enegb,V_24X1) = cCoq_2eInit_2eDatatypes_2enegb___24a1(V_24X1) ).

fof('$adef_IntMap.Mapiter.MapSweep_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cIntMap_2eMapiter_2eMapSweep,V_24X1),V_24X2),V_24X3) = cIntMap_2eMapiter_2eMapSweep___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_$_lam_36687_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(c_24__lam__36687,V_24X1),V_24X2) = c_24__lam__36687___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.Init.Nat.testbit_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eNat_2etestbit,V_24X1),V_24X2) = cCoq_2eInit_2eNat_2etestbit___24a2(V_24X1,V_24X2) ).

fof('$adef_$_case_Coq.Init.Datatypes.bool$577_$a6',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(c_24__case__Coq_2eInit_2eDatatypes_2ebool_24577,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = c_24__case__Coq_2eInit_2eDatatypes_2ebool_24577___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).

fof('$adef_Coq.PArith.BinPosDef.Pos.IsPos_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2ePArith_2eBinPosDef_2ePos_2eIsPos,V_24X1) = cCoq_2ePArith_2eBinPosDef_2ePos_2eIsPos___24a1(V_24X1) ).

fof('$adef_$_lam_13590_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__13590,V_24X1),V_24X2),V_24X3) = c_24__lam__13590___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_Coq.Reals.Rdefinitions.Ropp_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eReals_2eRdefinitions_2eRopp,V_24X1) = cCoq_2eReals_2eRdefinitions_2eRopp___24a1(V_24X1) ).

fof('$adef_Coq.PArith.BinPosDef.Pos.max_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2ePArith_2eBinPosDef_2ePos_2emax,V_24X1),V_24X2) = cCoq_2ePArith_2eBinPosDef_2ePos_2emax___24a2(V_24X1,V_24X2) ).

fof('$adef_$_prop_33474_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__prop__33474,V_24X1),V_24X2),V_24X3) = c_24__prop__33474___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_Coq.ZArith.BinIntDef.Z.pow_pos_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eBinIntDef_2eZ_2epow__pos,V_24X1),V_24X2) = cCoq_2eZArith_2eBinIntDef_2eZ_2epow__pos___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.Init.Datatypes.Some_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eDatatypes_2eSome,V_24X1),V_24X2) = cCoq_2eInit_2eDatatypes_2eSome___24a2(V_24X1,V_24X2) ).

fof('$adef_$_lam_13200_$a1',axiom,
    ! [V_24X1] : happ(c_24__lam__13200,V_24X1) = c_24__lam__13200___24a1(V_24X1) ).

fof('$adef_IntMap.Mapcanon.mapcanon_$a2',axiom,
    ! [V_24X1,V_24X2] :
      ( p(happ(happ(cIntMap_2eMapcanon_2emapcanon,V_24X1),V_24X2))
    <=> cIntMap_2eMapcanon_2emapcanon___24a2(V_24X1,V_24X2) ) ).

fof('$adef_Coq.micromega.EnvRing.Pc_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2emicromega_2eEnvRing_2ePc,V_24X1),V_24X2) = cCoq_2emicromega_2eEnvRing_2ePc___24a2(V_24X1,V_24X2) ).

fof('$adef_$_lam_14379_$a6',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(c_24__lam__14379,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = c_24__lam__14379___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).

fof('$adef_Coq.Structures.OrderedType.EQ_$a5',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2eStructures_2eOrderedType_2eEQ,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2eStructures_2eOrderedType_2eEQ___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).

fof('$adef_$_lam_1270_$a6',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(c_24__lam__1270,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = c_24__lam__1270___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).

fof('$adef_Coq.Numbers.BinNums.Zpos_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eNumbers_2eBinNums_2eZpos,V_24X1) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(V_24X1) ).

fof('$adef_Coq.Arith.Even.odd_$a1',axiom,
    ! [V_24X1] :
      ( p(happ(cCoq_2eArith_2eEven_2eodd,V_24X1))
    <=> cCoq_2eArith_2eEven_2eodd___24a1(V_24X1) ) ).

fof('$adef_$_case_Coq.Init.Datatypes.bool$36670_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__case__Coq_2eInit_2eDatatypes_2ebool_2436670,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__case__Coq_2eInit_2eDatatypes_2ebool_2436670___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).

fof('$adef_IntMap.Mapiter.aapp_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cIntMap_2eMapiter_2eaapp,V_24X1),V_24X2),V_24X3) = cIntMap_2eMapiter_2eaapp___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_$_lam_1465_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__lam__1465,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__lam__1465___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).

fof('$adef_$_prop_33477_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__prop__33477,V_24X1),V_24X2),V_24X3) = c_24__prop__33477___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_Coq.ZArith.BinIntDef.Z.succ_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eZArith_2eBinIntDef_2eZ_2esucc,V_24X1) = cCoq_2eZArith_2eBinIntDef_2eZ_2esucc___24a1(V_24X1) ).

fof('$adef_$_lam_2129_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__lam__2129,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__lam__2129___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).

fof('$adef_Coq.NArith.BinNatDef.N.double_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eNArith_2eBinNatDef_2eN_2edouble,V_24X1) = cCoq_2eNArith_2eBinNatDef_2eN_2edouble___24a1(V_24X1) ).

fof('$adef_Coq.Init.Datatypes.list_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eInit_2eDatatypes_2elist,V_24X1) = cCoq_2eInit_2eDatatypes_2elist___24a1(V_24X1) ).

fof('$adef_IntMap.Fset.MapDomRestrBy_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cIntMap_2eFset_2eMapDomRestrBy,V_24X1),V_24X2),V_24X3),V_24X4) = cIntMap_2eFset_2eMapDomRestrBy___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).

fof('$adef_$_lam_649_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__lam__649,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__lam__649___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).

fof('$adef_$_lam_319_$a1',axiom,
    ! [V_24X1] : happ(c_24__lam__319,V_24X1) = c_24__lam__319___24a1(V_24X1) ).

fof('$adef_Coq.Init.Nat.add_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eNat_2eadd,V_24X1),V_24X2) = cCoq_2eInit_2eNat_2eadd___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.Init.Specif.sigT2_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eInit_2eSpecif_2esigT2,V_24X1),V_24X2),V_24X3) = cCoq_2eInit_2eSpecif_2esigT2___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_Coq.Init.Nat.sub_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eNat_2esub,V_24X1),V_24X2) = cCoq_2eInit_2eNat_2esub___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.Structures.OrderedType.Compare_$a5',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2eStructures_2eOrderedType_2eCompare,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2eStructures_2eOrderedType_2eCompare___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).

fof('$adef_Coq.PArith.BinPos.Pos.SubMaskSpec_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] :
      ( p(happ(happ(happ(cCoq_2ePArith_2eBinPos_2ePos_2eSubMaskSpec,V_24X1),V_24X2),V_24X3))
    <=> cCoq_2ePArith_2eBinPos_2ePos_2eSubMaskSpec___24a3(V_24X1,V_24X2,V_24X3) ) ).

fof('$adef_Coq.NArith.BinNatDef.N.add_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2eNArith_2eBinNatDef_2eN_2eadd,V_24X1),V_24X2) = cCoq_2eNArith_2eBinNatDef_2eN_2eadd___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.ZArith.BinInt.Z.divide_$a2',axiom,
    ! [V_24X1,V_24X2] :
      ( p(happ(happ(cCoq_2eZArith_2eBinInt_2eZ_2edivide,V_24X1),V_24X2))
    <=> cCoq_2eZArith_2eBinInt_2eZ_2edivide___24a2(V_24X1,V_24X2) ) ).

fof('$adef_Coq.setoid_ring.Field_theory.FEc_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2esetoid__ring_2eField__theory_2eFEc,V_24X1),V_24X2) = cCoq_2esetoid__ring_2eField__theory_2eFEc___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.Classes.Morphisms.Proper_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] :
      ( p(happ(happ(happ(cCoq_2eClasses_2eMorphisms_2eProper,V_24X1),V_24X2),V_24X3))
    <=> cCoq_2eClasses_2eMorphisms_2eProper___24a3(V_24X1,V_24X2,V_24X3) ) ).

fof('$adef_Coq.Bool.Bool.ReflectF_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eBool_2eBool_2eReflectF,V_24X1) = cCoq_2eBool_2eBool_2eReflectF___24a1(V_24X1) ).

fof('$adef_Coq.Reals.Rfunctions.ZintNull_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eReals_2eRfunctions_2eZintNull,V_24X1) = cCoq_2eReals_2eRfunctions_2eZintNull___24a1(V_24X1) ).

fof('$adef_Coq.setoid_ring.Field_theory.FEI_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2esetoid__ring_2eField__theory_2eFEI,V_24X1) = cCoq_2esetoid__ring_2eField__theory_2eFEI___24a1(V_24X1) ).

fof('$adef_Coq.micromega.EnvRing.PEX_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2emicromega_2eEnvRing_2ePEX,V_24X1),V_24X2) = cCoq_2emicromega_2eEnvRing_2ePEX___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.ZArith.BinIntDef.Z.pos_sub_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eBinIntDef_2eZ_2epos__sub,V_24X1),V_24X2) = cCoq_2eZArith_2eBinIntDef_2eZ_2epos__sub___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.Bool.Bool.ReflectT_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eBool_2eBool_2eReflectT,V_24X1) = cCoq_2eBool_2eBool_2eReflectT___24a1(V_24X1) ).

fof('$adef_Coq.ZArith.Znumtheory.Euclid_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eZnumtheory_2eEuclid,V_24X1),V_24X2) = cCoq_2eZArith_2eZnumtheory_2eEuclid___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.Init.Specif.right_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eSpecif_2eright,V_24X1),V_24X2) = cCoq_2eInit_2eSpecif_2eright___24a2(V_24X1,V_24X2) ).

fof('$adef_$_lam_14333_$a6',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(c_24__lam__14333,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = c_24__lam__14333___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).

fof('$adef_Coq.setoid_ring.Ring_theory.power_theory_$a7',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7] :
      ( p(happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__theory_2epower__theory,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7))
    <=> cCoq_2esetoid__ring_2eRing__theory_2epower__theory___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7) ) ).

fof('$adef_$_case_Coq.Init.Datatypes.bool$13293_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__case__Coq_2eInit_2eDatatypes_2ebool_2413293,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__case__Coq_2eInit_2eDatatypes_2ebool_2413293___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).

fof('$adef_Coq.Lists.List.fold_left_$a5',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2eLists_2eList_2efold__left,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2eLists_2eList_2efold__left___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).

fof('$adef_Coq.Init.Logic.eq_refl_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eLogic_2eeq__refl,V_24X1),V_24X2) = cCoq_2eInit_2eLogic_2eeq__refl___24a2(V_24X1,V_24X2) ).

fof('$adef_$_lam_13590_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(c_24__lam__13590,V_24X1),V_24X2) = c_24__lam__13590___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.setoid_ring.Ring_polynom.Pinj_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2ePinj,V_24X1),V_24X2),V_24X3) = cCoq_2esetoid__ring_2eRing__polynom_2ePinj___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_$_lam_1414_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__1414,V_24X1),V_24X2),V_24X3) = c_24__lam__1414___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_$_lam_2135_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__2135,V_24X1),V_24X2),V_24X3) = c_24__lam__2135___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_Coq.NArith.BinNatDef.N.lxor_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2eNArith_2eBinNatDef_2eN_2elxor,V_24X1),V_24X2) = cCoq_2eNArith_2eBinNatDef_2eN_2elxor___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.ZArith.BinIntDef.Z.div_eucl_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eBinIntDef_2eZ_2ediv__eucl,V_24X1),V_24X2) = cCoq_2eZArith_2eBinIntDef_2eZ_2ediv__eucl___24a2(V_24X1,V_24X2) ).

fof('$adef_$_lam_163_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__163,V_24X1),V_24X2),V_24X3) = c_24__lam__163___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_IntMap.Lsort.alist_nth_ad_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cIntMap_2eLsort_2ealist__nth__ad,V_24X1),V_24X2),V_24X3) = cIntMap_2eLsort_2ealist__nth__ad___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_Coq.NArith.BinNatDef.N.compare_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2eNArith_2eBinNatDef_2eN_2ecompare,V_24X1),V_24X2) = cCoq_2eNArith_2eBinNatDef_2eN_2ecompare___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.Init.Specif.sig_rec_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eInit_2eSpecif_2esig__rec,V_24X1),V_24X2),V_24X3) = cCoq_2eInit_2eSpecif_2esig__rec___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_Coq.setoid_ring.Field_theory.FEadd_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2esetoid__ring_2eField__theory_2eFEadd,V_24X1),V_24X2),V_24X3) = cCoq_2esetoid__ring_2eField__theory_2eFEadd___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_$_lam_1398_$a1',axiom,
    ! [V_24X1] : happ(c_24__lam__1398,V_24X1) = c_24__lam__1398___24a1(V_24X1) ).

fof('$adef_Coq.ZArith.BinIntDef.Z.odd_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eZArith_2eBinIntDef_2eZ_2eodd,V_24X1) = cCoq_2eZArith_2eBinIntDef_2eZ_2eodd___24a1(V_24X1) ).

fof('$adef_Coq.PArith.BinPosDef.Pos.lxor_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2ePArith_2eBinPosDef_2ePos_2elxor,V_24X1),V_24X2) = cCoq_2ePArith_2eBinPosDef_2ePos_2elxor___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.Init.Datatypes.fst_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eInit_2eDatatypes_2efst,V_24X1),V_24X2),V_24X3) = cCoq_2eInit_2eDatatypes_2efst___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_$_lam_225_$a5',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(c_24__lam__225,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = c_24__lam__225___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).

fof('$adef_$_lam_14524_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__14524,V_24X1),V_24X2),V_24X3) = c_24__lam__14524___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_Coq.Init.Datatypes.S_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eInit_2eDatatypes_2eS,V_24X1) = cCoq_2eInit_2eDatatypes_2eS___24a1(V_24X1) ).

fof('$adef_$_lam_1414_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__lam__1414,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__lam__1414___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).

fof('$adef_$_lam_13247_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__lam__13247,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__lam__13247___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).

fof('$adef_Coq.Strings.Ascii.Ascii_$a8',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8] : happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2eStrings_2eAscii_2eAscii,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8) = cCoq_2eStrings_2eAscii_2eAscii___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8) ).

fof('$adef_$_lam_13951_$a5',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(c_24__lam__13951,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = c_24__lam__13951___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).

fof('$adef_Coq.micromega.EnvRing.PEpow_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2emicromega_2eEnvRing_2ePEpow,V_24X1),V_24X2),V_24X3) = cCoq_2emicromega_2eEnvRing_2ePEpow___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_Coq.setoid_ring.Ring_polynom.zmon_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2ezmon,V_24X1),V_24X2) = cCoq_2esetoid__ring_2eRing__polynom_2ezmon___24a2(V_24X1,V_24X2) ).

fof('$adef_$_lam_2179_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__2179,V_24X1),V_24X2),V_24X3) = c_24__lam__2179___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_Coq.setoid_ring.Ring_theory.semi_morph_$a13',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13] :
      ( p(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__theory_2esemi__morph,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9),V_24X10),V_24X11),V_24X12),V_24X13))
    <=> cCoq_2esetoid__ring_2eRing__theory_2esemi__morph___24a13(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13) ) ).

fof('$adef_IntMap.Map.MapDelta_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cIntMap_2eMap_2eMapDelta,V_24X1),V_24X2) = cIntMap_2eMap_2eMapDelta___24a2(V_24X1,V_24X2) ).

fof('$adef_$_case_Coq.Numbers.BinNums.Z$23389_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__case__Coq_2eNumbers_2eBinNums_2eZ_2423389,V_24X1),V_24X2),V_24X3) = c_24__case__Coq_2eNumbers_2eBinNums_2eZ_2423389___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_$_lam_1973_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] :
      ( p(happ(happ(happ(c_24__lam__1973,V_24X1),V_24X2),V_24X3))
    <=> c_24__lam__1973___24a3(V_24X1,V_24X2,V_24X3) ) ).

fof('$adef_$_lam_1650_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__1650,V_24X1),V_24X2),V_24X3) = c_24__lam__1650___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_$_lam_14287_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__lam__14287,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__lam__14287___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).

fof('$adef_Coq.PArith.BinPos.Pos.PeanoView_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2ePArith_2eBinPos_2ePos_2ePeanoView,V_24X1) = cCoq_2ePArith_2eBinPos_2ePos_2ePeanoView___24a1(V_24X1) ).

fof('$adef_Coq.ZArith.BinIntDef.Z.add_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eBinIntDef_2eZ_2eadd,V_24X1),V_24X2) = cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.ZArith.BinIntDef.Z.min_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eBinIntDef_2eZ_2emin,V_24X1),V_24X2) = cCoq_2eZArith_2eBinIntDef_2eZ_2emin___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.micromega.Tauto.N_$a5',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2emicromega_2eTauto_2eN,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2emicromega_2eTauto_2eN___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).

fof('$adef_IntMap.Fset.FSetInter_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cIntMap_2eFset_2eFSetInter,V_24X1),V_24X2) = cIntMap_2eFset_2eFSetInter___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.ZArith.Znat.neq_$a2',axiom,
    ! [V_24X1,V_24X2] :
      ( p(happ(happ(cCoq_2eZArith_2eZnat_2eneq,V_24X1),V_24X2))
    <=> cCoq_2eZArith_2eZnat_2eneq___24a2(V_24X1,V_24X2) ) ).

fof('$adef_IntMap.Fset.FSetDiff_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cIntMap_2eFset_2eFSetDiff,V_24X1),V_24X2) = cIntMap_2eFset_2eFSetDiff___24a2(V_24X1,V_24X2) ).

fof('$adef_$_lam_13247_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__13247,V_24X1),V_24X2),V_24X3) = c_24__lam__13247___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_Coq.setoid_ring.InitialRing.gen_phiPOS1_$a5',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS1,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS1___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).

fof('$adef_IntMap.Mapiter.MapCollect1_$a5',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cIntMap_2eMapiter_2eMapCollect1,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cIntMap_2eMapiter_2eMapCollect1___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).

fof('$adef_IntMap.Mapiter.MapFold_$a6',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(cIntMap_2eMapiter_2eMapFold,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = cIntMap_2eMapiter_2eMapFold___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).

fof('$adef_Coq.Init.Nat.min_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eNat_2emin,V_24X1),V_24X2) = cCoq_2eInit_2eNat_2emin___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.Init.Specif.existT2_$a6',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(cCoq_2eInit_2eSpecif_2eexistT2,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = cCoq_2eInit_2eSpecif_2eexistT2___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).

fof('$adef_$_lam_225_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__225,V_24X1),V_24X2),V_24X3) = c_24__lam__225___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_Coq.ZArith.BinInt.Zne_$a2',axiom,
    ! [V_24X1,V_24X2] :
      ( p(happ(happ(cCoq_2eZArith_2eBinInt_2eZne,V_24X1),V_24X2))
    <=> cCoq_2eZArith_2eBinInt_2eZne___24a2(V_24X1,V_24X2) ) ).

fof('$adef_Coq.PArith.BinPosDef.Pos.compare_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare,V_24X1),V_24X2) = cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare___24a2(V_24X1,V_24X2) ).

fof('$adef_IntMap.Map.M2_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cIntMap_2eMap_2eM2,V_24X1),V_24X2),V_24X3) = cIntMap_2eMap_2eM2___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_Coq.Lists.SetoidList.InA_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] :
      ( p(happ(happ(happ(happ(cCoq_2eLists_2eSetoidList_2eInA,V_24X1),V_24X2),V_24X3),V_24X4))
    <=> cCoq_2eLists_2eSetoidList_2eInA___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).

fof('$adef_$_prop_1822_$a1',axiom,
    ! [V_24X1] : happ(c_24__prop__1822,V_24X1) = c_24__prop__1822___24a1(V_24X1) ).

fof('$adef_Coq.Reals.Rdefinitions.Rlt_$a2',axiom,
    ! [V_24X1,V_24X2] :
      ( p(happ(happ(cCoq_2eReals_2eRdefinitions_2eRlt,V_24X1),V_24X2))
    <=> cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V_24X1,V_24X2) ) ).

fof('$adef_Coq.Reals.RIneq.mknonzeroreal_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eReals_2eRIneq_2emknonzeroreal,V_24X1) = cCoq_2eReals_2eRIneq_2emknonzeroreal___24a1(V_24X1) ).

fof('$adef_Coq.ZArith.BinIntDef.Z.sub_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eBinIntDef_2eZ_2esub,V_24X1),V_24X2) = cCoq_2eZArith_2eBinIntDef_2eZ_2esub___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.ZArith.BinIntDef.Z.div_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eBinIntDef_2eZ_2ediv,V_24X1),V_24X2) = cCoq_2eZArith_2eBinIntDef_2eZ_2ediv___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.setoid_ring.Ring_polynom.PEopp_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2ePEopp,V_24X1),V_24X2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEopp___24a2(V_24X1,V_24X2) ).

fof('$adef_$_lam_1515_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__lam__1515,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__lam__1515___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).

fof('$adef_IntMap.Mapiter.acons_$a1',axiom,
    ! [V_24X1] : happ(cIntMap_2eMapiter_2eacons,V_24X1) = cIntMap_2eMapiter_2eacons___24a1(V_24X1) ).

fof('$adef_$_lam_2008_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__2008,V_24X1),V_24X2),V_24X3) = c_24__lam__2008___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_$_lam_718_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__lam__718,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__lam__718___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).

fof('$adef_Coq.Init.Specif.left_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eInit_2eSpecif_2eleft,V_24X1),V_24X2),V_24X3) = cCoq_2eInit_2eSpecif_2eleft___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_Coq.Bool.Bool.Is_true_$a1',axiom,
    ! [V_24X1] :
      ( p(happ(cCoq_2eBool_2eBool_2eIs__true,V_24X1))
    <=> cCoq_2eBool_2eBool_2eIs__true___24a1(V_24X1) ) ).

fof('$adef_IntMap.Map.MapGet_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cIntMap_2eMap_2eMapGet,V_24X1),V_24X2),V_24X3) = cIntMap_2eMap_2eMapGet___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_$_lam_163_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__lam__163,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__lam__163___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).

fof('$adef_$_lam_319_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(c_24__lam__319,V_24X1),V_24X2) = c_24__lam__319___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.setoid_ring.Field_theory.mk_linear_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2esetoid__ring_2eField__theory_2emk__linear,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2esetoid__ring_2eField__theory_2emk__linear___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).

fof('$adef_Coq.Lists.List.fold_right_$a5',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2eLists_2eList_2efold__right,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2eLists_2eList_2efold__right___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).

fof('$adef_Coq.setoid_ring.Ring_theory.pow_pos_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__theory_2epow__pos,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2esetoid__ring_2eRing__theory_2epow__pos___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).

fof('$adef_IntMap.Fset.MapDomRestrTo_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cIntMap_2eFset_2eMapDomRestrTo,V_24X1),V_24X2),V_24X3),V_24X4) = cIntMap_2eFset_2eMapDomRestrTo___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).

fof('$adef_Coq.Init.Nat.pow_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eNat_2epow,V_24X1),V_24X2) = cCoq_2eInit_2eNat_2epow___24a2(V_24X1,V_24X2) ).

fof('$adef_$_case_Coq.Init.Datatypes.bool$2675_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__case__Coq_2eInit_2eDatatypes_2ebool_242675,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__case__Coq_2eInit_2eDatatypes_2ebool_242675___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).

fof('$adef_$_lam_2038_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__lam__2038,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__lam__2038___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).

fof('$adef_Coq.micromega.Tauto.I_$a7',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7] : happ(happ(happ(happ(happ(happ(happ(cCoq_2emicromega_2eTauto_2eI,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7) = cCoq_2emicromega_2eTauto_2eI___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7) ).

fof('$adef_Coq.micromega.Refl.make_conj_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] :
      ( p(happ(happ(happ(cCoq_2emicromega_2eRefl_2emake__conj,V_24X1),V_24X2),V_24X3))
    <=> cCoq_2emicromega_2eRefl_2emake__conj___24a3(V_24X1,V_24X2,V_24X3) ) ).

fof('$adef_Coq.Init.Nat.odd_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eInit_2eNat_2eodd,V_24X1) = cCoq_2eInit_2eNat_2eodd___24a1(V_24X1) ).

fof('$adef_Coq.ZArith.BinInt.Z.gt_$a2',axiom,
    ! [V_24X1,V_24X2] :
      ( p(happ(happ(cCoq_2eZArith_2eBinInt_2eZ_2egt,V_24X1),V_24X2))
    <=> cCoq_2eZArith_2eBinInt_2eZ_2egt___24a2(V_24X1,V_24X2) ) ).

fof('$adef_Coq.setoid_ring.Ring_polynom.PEO_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2esetoid__ring_2eRing__polynom_2ePEO,V_24X1) = cCoq_2esetoid__ring_2eRing__polynom_2ePEO___24a1(V_24X1) ).

fof('$adef_Coq.Init.Logic.eq_rect_$a5',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2eInit_2eLogic_2eeq__rect,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2eInit_2eLogic_2eeq__rect___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).

fof('$adef_Coq.Bool.Sumbool.sumbool_of_bool_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eBool_2eSumbool_2esumbool__of__bool,V_24X1) = cCoq_2eBool_2eSumbool_2esumbool__of__bool___24a1(V_24X1) ).

fof('$adef_$_let_var_6_p_28906_28909_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__let__var__6__p__28906__28909,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__let__var__6__p__28906__28909___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).

fof('$adef_IntMap.Mapiter.alist_semantics_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cIntMap_2eMapiter_2ealist__semantics,V_24X1),V_24X2) = cIntMap_2eMapiter_2ealist__semantics___24a2(V_24X1,V_24X2) ).

fof('$adef_$_lam_1644_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__1644,V_24X1),V_24X2),V_24X3) = c_24__lam__1644___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_Coq.Numbers.BinNums.xO_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eNumbers_2eBinNums_2exO,V_24X1) = cCoq_2eNumbers_2eBinNums_2exO___24a1(V_24X1) ).

fof('$adef_$_lam_14379_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__lam__14379,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__lam__14379___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).

fof('$adef_$_prop_13506_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__prop__13506,V_24X1),V_24X2),V_24X3) = c_24__prop__13506___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_Coq.NArith.BinNatDef.N.even_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eNArith_2eBinNatDef_2eN_2eeven,V_24X1) = cCoq_2eNArith_2eBinNatDef_2eN_2eeven___24a1(V_24X1) ).

fof('$adef_IntMap.Mapsubset.MapDisjoint_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] :
      ( p(happ(happ(happ(happ(cIntMap_2eMapsubset_2eMapDisjoint,V_24X1),V_24X2),V_24X3),V_24X4))
    <=> cIntMap_2eMapsubset_2eMapDisjoint___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).

fof('$adef_Coq.setoid_ring.Field_theory.FEX_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2esetoid__ring_2eField__theory_2eFEX,V_24X1),V_24X2) = cCoq_2esetoid__ring_2eField__theory_2eFEX___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.Bool.Bool.leb_$a2',axiom,
    ! [V_24X1,V_24X2] :
      ( p(happ(happ(cCoq_2eBool_2eBool_2eleb,V_24X1),V_24X2))
    <=> cCoq_2eBool_2eBool_2eleb___24a2(V_24X1,V_24X2) ) ).

fof('$adef_IntMap.Mapsubset.MapSubset_1_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cIntMap_2eMapsubset_2eMapSubset__1,V_24X1),V_24X2),V_24X3),V_24X4) = cIntMap_2eMapsubset_2eMapSubset__1___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).

fof('$adef_Coq.Lists.List.NoDup_$a2',axiom,
    ! [V_24X1,V_24X2] :
      ( p(happ(happ(cCoq_2eLists_2eList_2eNoDup,V_24X1),V_24X2))
    <=> cCoq_2eLists_2eList_2eNoDup___24a2(V_24X1,V_24X2) ) ).

fof('$adef_$_lam_323_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__lam__323,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__lam__323___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).

fof('$adef_Coq.Vectors.VectorDef.nil_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eVectors_2eVectorDef_2enil,V_24X1) = cCoq_2eVectors_2eVectorDef_2enil___24a1(V_24X1) ).

fof('$adef_$_lam_1870_$a5',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(c_24__lam__1870,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = c_24__lam__1870___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).

fof('$adef_Coq.Logic.EqdepFacts.Eq_rect_eq_on_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] :
      ( p(happ(happ(happ(happ(cCoq_2eLogic_2eEqdepFacts_2eEq__rect__eq__on,V_24X1),V_24X2),V_24X3),V_24X4))
    <=> cCoq_2eLogic_2eEqdepFacts_2eEq__rect__eq__on___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).

fof('$adef_Coq.Init.Specif.left_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eSpecif_2eleft,V_24X1),V_24X2) = cCoq_2eInit_2eSpecif_2eleft___24a2(V_24X1,V_24X2) ).

fof('$adef_IntMap.Fset.MapDomRestrTo_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cIntMap_2eFset_2eMapDomRestrTo,V_24X1),V_24X2),V_24X3) = cIntMap_2eFset_2eMapDomRestrTo___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_Coq.setoid_ring.Field_theory.FEinv_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2esetoid__ring_2eField__theory_2eFEinv,V_24X1),V_24X2) = cCoq_2esetoid__ring_2eField__theory_2eFEinv___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.ZArith.Zpower.Zdiv_rest_proof_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2eZArith_2eZpower_2eZdiv__rest__proof,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2eZArith_2eZpower_2eZdiv__rest__proof___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).

fof('$adef_Coq.Init.Wf.Acc_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] :
      ( p(happ(happ(happ(cCoq_2eInit_2eWf_2eAcc,V_24X1),V_24X2),V_24X3))
    <=> cCoq_2eInit_2eWf_2eAcc___24a3(V_24X1,V_24X2,V_24X3) ) ).

fof('$adef_Coq.setoid_ring.Ring_theory.pow_N_$a5',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__theory_2epow__N,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2esetoid__ring_2eRing__theory_2epow__N___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).

fof('$adef_Coq.Init.Specif.sigT_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eSpecif_2esigT,V_24X1),V_24X2) = cCoq_2eInit_2eSpecif_2esigT___24a2(V_24X1,V_24X2) ).

fof('$adef_$_prop_432_$a1',axiom,
    ! [V_24X1] : happ(c_24__prop__432,V_24X1) = c_24__prop__432___24a1(V_24X1) ).

fof('$adef_IntMap.Mapiter.anil_$a1',axiom,
    ! [V_24X1] : happ(cIntMap_2eMapiter_2eanil,V_24X1) = cIntMap_2eMapiter_2eanil___24a1(V_24X1) ).

fof('$adef_IntMap.Map.eqm_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] :
      ( p(happ(happ(happ(cIntMap_2eMap_2eeqm,V_24X1),V_24X2),V_24X3))
    <=> cIntMap_2eMap_2eeqm___24a3(V_24X1,V_24X2,V_24X3) ) ).

fof('$adef_$_lam_2179_$a1',axiom,
    ! [V_24X1] : happ(c_24__lam__2179,V_24X1) = c_24__lam__2179___24a1(V_24X1) ).

fof('$adef_Coq.ZArith.BinInt.Z.ge_$a2',axiom,
    ! [V_24X1,V_24X2] :
      ( p(happ(happ(cCoq_2eZArith_2eBinInt_2eZ_2ege,V_24X1),V_24X2))
    <=> cCoq_2eZArith_2eBinInt_2eZ_2ege___24a2(V_24X1,V_24X2) ) ).

fof('$adef_Coq.ZArith.Zbool.Zeq_bool_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eZbool_2eZeq__bool,V_24X1),V_24X2) = cCoq_2eZArith_2eZbool_2eZeq__bool___24a2(V_24X1,V_24X2) ).

fof('$adef_$_lam_2038_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__2038,V_24X1),V_24X2),V_24X3) = c_24__lam__2038___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_Coq.ZArith.BinIntDef.Z.pow_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eBinIntDef_2eZ_2epow,V_24X1),V_24X2) = cCoq_2eZArith_2eBinIntDef_2eZ_2epow___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.QArith.QArith_base.Qmake_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2eQArith_2eQArith__base_2eQmake,V_24X1),V_24X2) = cCoq_2eQArith_2eQArith__base_2eQmake___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.Init.Specif.sumbool_rect_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eInit_2eSpecif_2esumbool__rect,V_24X1),V_24X2),V_24X3) = cCoq_2eInit_2eSpecif_2esumbool__rect___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_$_lam_1465_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__1465,V_24X1),V_24X2),V_24X3) = c_24__lam__1465___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_IntMap.Map.Map_$a1',axiom,
    ! [V_24X1] : happ(cIntMap_2eMap_2eMap,V_24X1) = cIntMap_2eMap_2eMap___24a1(V_24X1) ).

fof('$adef_Coq.setoid_ring.Ring_polynom.PEX_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2ePEX,V_24X1),V_24X2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEX___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.micromega.EnvRing.PEc_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2emicromega_2eEnvRing_2ePEc,V_24X1),V_24X2) = cCoq_2emicromega_2eEnvRing_2ePEc___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.NArith.BinNatDef.N.pred_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eNArith_2eBinNatDef_2eN_2epred,V_24X1) = cCoq_2eNArith_2eBinNatDef_2eN_2epred___24a1(V_24X1) ).

fof('$adef_Coq.micromega.EnvRing.PX_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2emicromega_2eEnvRing_2ePX,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2emicromega_2eEnvRing_2ePX___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).

fof('$adef_Coq.Init.Datatypes.sum_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eDatatypes_2esum,V_24X1),V_24X2) = cCoq_2eInit_2eDatatypes_2esum___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.micromega.EnvRing.PEadd_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2emicromega_2eEnvRing_2ePEadd,V_24X1),V_24X2),V_24X3) = cCoq_2emicromega_2eEnvRing_2ePEadd___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_Coq.NArith.BinNatDef.N.min_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2eNArith_2eBinNatDef_2eN_2emin,V_24X1),V_24X2) = cCoq_2eNArith_2eBinNatDef_2eN_2emin___24a2(V_24X1,V_24X2) ).

fof('$adef_IntMap.Mapiter.MapFold_state_$a8',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8] : happ(happ(happ(happ(happ(happ(happ(happ(cIntMap_2eMapiter_2eMapFold__state,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8) = cIntMap_2eMapiter_2eMapFold__state___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8) ).

fof('$adef_Coq.ZArith.Znumtheory.Zis_gcd_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] :
      ( p(happ(happ(happ(cCoq_2eZArith_2eZnumtheory_2eZis__gcd,V_24X1),V_24X2),V_24X3))
    <=> cCoq_2eZArith_2eZnumtheory_2eZis__gcd___24a3(V_24X1,V_24X2,V_24X3) ) ).

fof('$adef_Coq.PArith.BinPosDef.Pos.iter_op_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2ePArith_2eBinPosDef_2ePos_2eiter__op,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2ePArith_2eBinPosDef_2ePos_2eiter__op___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).

fof('$adef_$_case_Coq.Init.Datatypes.bool$13309_$a5',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(c_24__case__Coq_2eInit_2eDatatypes_2ebool_2413309,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = c_24__case__Coq_2eInit_2eDatatypes_2ebool_2413309___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).

fof('$adef_$_lam_13536_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(c_24__lam__13536,V_24X1),V_24X2) = c_24__lam__13536___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.Init.Specif.sig2_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eInit_2eSpecif_2esig2,V_24X1),V_24X2),V_24X3) = cCoq_2eInit_2eSpecif_2esig2___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_Coq.Init.Specif.sumbool_rect_$a6',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(cCoq_2eInit_2eSpecif_2esumbool__rect,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = cCoq_2eInit_2eSpecif_2esumbool__rect___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).

fof('$adef_Coq.setoid_ring.Field_theory.FEpow_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2esetoid__ring_2eField__theory_2eFEpow,V_24X1),V_24X2),V_24X3) = cCoq_2esetoid__ring_2eField__theory_2eFEpow___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_Coq.Init.Datatypes.length_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eDatatypes_2elength,V_24X1),V_24X2) = cCoq_2eInit_2eDatatypes_2elength___24a2(V_24X1,V_24X2) ).

fof('$adef_$_lam_1406_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__lam__1406,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__lam__1406___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).

fof('$adef_$_case_Coq.Numbers.BinNums.positive$33555_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(c_24__case__Coq_2eNumbers_2eBinNums_2epositive_2433555,V_24X1),V_24X2) = c_24__case__Coq_2eNumbers_2eBinNums_2epositive_2433555___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.NArith.BinNatDef.N.eqb_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2eNArith_2eBinNatDef_2eN_2eeqb,V_24X1),V_24X2) = cCoq_2eNArith_2eBinNatDef_2eN_2eeqb___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.NArith.BinNat.N.eqf_$a2',axiom,
    ! [V_24X1,V_24X2] :
      ( p(happ(happ(cCoq_2eNArith_2eBinNat_2eN_2eeqf,V_24X1),V_24X2))
    <=> cCoq_2eNArith_2eBinNat_2eN_2eeqf___24a2(V_24X1,V_24X2) ) ).

fof('$adef_Coq.Init.Specif.right_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eInit_2eSpecif_2eright,V_24X1),V_24X2),V_24X3) = cCoq_2eInit_2eSpecif_2eright___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_$_case_Coq.Init.Datatypes.bool$2680_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__case__Coq_2eInit_2eDatatypes_2ebool_242680,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__case__Coq_2eInit_2eDatatypes_2ebool_242680___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).

fof('$adef_Coq.micromega.ZMicromega.is_diff_env_elt_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] :
      ( p(happ(happ(happ(happ(cCoq_2emicromega_2eZMicromega_2eis__diff__env__elt,V_24X1),V_24X2),V_24X3),V_24X4))
    <=> cCoq_2emicromega_2eZMicromega_2eis__diff__env__elt___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).

fof('$adef_Coq.Vectors.Fin.t_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eVectors_2eFin_2et,V_24X1) = cCoq_2eVectors_2eFin_2et___24a1(V_24X1) ).

fof('$adef_Coq.NArith.BinNat.N.le_$a2',axiom,
    ! [V_24X1,V_24X2] :
      ( p(happ(happ(cCoq_2eNArith_2eBinNat_2eN_2ele,V_24X1),V_24X2))
    <=> cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(V_24X1,V_24X2) ) ).

fof('$adef_$_case_Coq.Init.Datatypes.bool$36660_$a5',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(c_24__case__Coq_2eInit_2eDatatypes_2ebool_2436660,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = c_24__case__Coq_2eInit_2eDatatypes_2ebool_2436660___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).

fof('$adef_$_lam_36687_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__36687,V_24X1),V_24X2),V_24X3) = c_24__lam__36687___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_Coq.setoid_ring.Field_theory.FEO_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2esetoid__ring_2eField__theory_2eFEO,V_24X1) = cCoq_2esetoid__ring_2eField__theory_2eFEO___24a1(V_24X1) ).

fof('$adef_IntMap.Mapiter.alist_semantics_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cIntMap_2eMapiter_2ealist__semantics,V_24X1),V_24X2),V_24X3) = cIntMap_2eMapiter_2ealist__semantics___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_IntMap.Fset.MapDom_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cIntMap_2eFset_2eMapDom,V_24X1),V_24X2) = cIntMap_2eFset_2eMapDom___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.Lists.List.In_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] :
      ( p(happ(happ(happ(cCoq_2eLists_2eList_2eIn,V_24X1),V_24X2),V_24X3))
    <=> cCoq_2eLists_2eList_2eIn___24a3(V_24X1,V_24X2,V_24X3) ) ).

fof('$adef_$_lam_136_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__136,V_24X1),V_24X2),V_24X3) = c_24__lam__136___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_IntMap.Map.MapPut_behind_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cIntMap_2eMap_2eMapPut__behind,V_24X1),V_24X2),V_24X3),V_24X4) = cIntMap_2eMap_2eMapPut__behind___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).

fof('$adef_Coq.ZArith.Zpower.Zdiv_rest_proofs_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eZpower_2eZdiv__rest__proofs,V_24X1),V_24X2) = cCoq_2eZArith_2eZpower_2eZdiv__rest__proofs___24a2(V_24X1,V_24X2) ).

fof('$adef_$_lam_13586_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__13586,V_24X1),V_24X2),V_24X3) = c_24__lam__13586___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_Coq.PArith.BinPosDef.Pos.of_succ_nat_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2ePArith_2eBinPosDef_2ePos_2eof__succ__nat,V_24X1) = cCoq_2ePArith_2eBinPosDef_2ePos_2eof__succ__nat___24a1(V_24X1) ).

fof('$adef_Coq.micromega.EnvRing.PEsub_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2emicromega_2eEnvRing_2ePEsub,V_24X1),V_24X2),V_24X3) = cCoq_2emicromega_2eEnvRing_2ePEsub___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_IntMap.Mapiter.ad_inj_$a1',axiom,
    ! [V_24X1] :
      ( p(happ(cIntMap_2eMapiter_2ead__inj,V_24X1))
    <=> cIntMap_2eMapiter_2ead__inj___24a1(V_24X1) ) ).

fof('$adef_Coq.PArith.BinPosDef.Pos.add_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2ePArith_2eBinPosDef_2ePos_2eadd,V_24X1),V_24X2) = cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.Init.Nat.double_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eInit_2eNat_2edouble,V_24X1) = cCoq_2eInit_2eNat_2edouble___24a1(V_24X1) ).

fof('$adef_Coq.Init.Datatypes.andb_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eDatatypes_2eandb,V_24X1),V_24X2) = cCoq_2eInit_2eDatatypes_2eandb___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.Init.Peano.lt_$a2',axiom,
    ! [V_24X1,V_24X2] :
      ( p(happ(happ(cCoq_2eInit_2ePeano_2elt,V_24X1),V_24X2))
    <=> cCoq_2eInit_2ePeano_2elt___24a2(V_24X1,V_24X2) ) ).

fof('$adef_Coq.Init.Peano.gt_$a2',axiom,
    ! [V_24X1,V_24X2] :
      ( p(happ(happ(cCoq_2eInit_2ePeano_2egt,V_24X1),V_24X2))
    <=> cCoq_2eInit_2ePeano_2egt___24a2(V_24X1,V_24X2) ) ).

fof('$adef_IntMap.Fset.in_dom_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cIntMap_2eFset_2ein__dom,V_24X1),V_24X2),V_24X3) = cIntMap_2eFset_2ein__dom___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$tdef_$_type_11426',axiom,
    ! [V_24Y] :
      ( c_24__type__11426___24t(V_24Y)
    <=> t(V_24Y,c_24__type__11426) ) ).

fof('$tdef_$_type_32350',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y] :
      ( c_24__type__32350___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y)
    <=> t(V_24Y,c_24__type__32350___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7)) ) ).

fof('$tdef_Coq.ZArith.Znumtheory.Euclid',axiom,
    ! [V_24X1,V_24X2,V_24Y] :
      ( cCoq_2eZArith_2eZnumtheory_2eEuclid___24t(V_24X1,V_24X2,V_24Y)
    <=> t(V_24Y,cCoq_2eZArith_2eZnumtheory_2eEuclid___24a2(V_24X1,V_24X2)) ) ).

fof('$tdef_Coq.Structures.OrderedTypeEx.Nat_as_OT.t',axiom,
    ! [V_24Y] :
      ( cCoq_2eStructures_2eOrderedTypeEx_2eNat__as__OT_2et___24t(V_24Y)
    <=> t(V_24Y,cCoq_2eStructures_2eOrderedTypeEx_2eNat__as__OT_2et) ) ).

fof('$tdef_$_type_30704',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
      ( c_24__type__30704___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
    <=> t(V_24Y,c_24__type__30704___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).

fof('$tdef_$_type_15511',axiom,
    ! [V_24Y] :
      ( c_24__type__15511___24t(V_24Y)
    <=> t(V_24Y,c_24__type__15511) ) ).

fof('$tdef_$_type_33345',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
      ( c_24__type__33345___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
    <=> t(V_24Y,c_24__type__33345___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).

fof('$tdef_$_type_21699',axiom,
    ! [V_24Y] :
      ( c_24__type__21699___24t(V_24Y)
    <=> t(V_24Y,c_24__type__21699) ) ).

fof('$tdef_$_type_1742',axiom,
    ! [V_24Y] :
      ( c_24__type__1742___24t(V_24Y)
    <=> t(V_24Y,c_24__type__1742) ) ).

fof('$tdef_$_type_14722',axiom,
    ! [V_24Y] :
      ( c_24__type__14722___24t(V_24Y)
    <=> t(V_24Y,c_24__type__14722) ) ).

fof('$tdef_$_type_16522',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y] :
      ( c_24__type__16522___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y)
    <=> t(V_24Y,c_24__type__16522___24a17(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17)) ) ).

fof('$tdef_$_type_11367',axiom,
    ! [V_24X1,V_24X2,V_24Y] :
      ( c_24__type__11367___24t(V_24X1,V_24X2,V_24Y)
    <=> t(V_24Y,c_24__type__11367___24a2(V_24X1,V_24X2)) ) ).

fof('$tdef_Coq.micromega.EnvRing.Mon',axiom,
    ! [V_24Y] :
      ( cCoq_2emicromega_2eEnvRing_2eMon___24t(V_24Y)
    <=> t(V_24Y,cCoq_2emicromega_2eEnvRing_2eMon) ) ).

fof('$tdef_$_type_18808',axiom,
    ! [V_24Y] :
      ( c_24__type__18808___24t(V_24Y)
    <=> t(V_24Y,c_24__type__18808) ) ).

fof('$tdef_$_type_458',axiom,
    ! [V_24Y] :
      ( c_24__type__458___24t(V_24Y)
    <=> t(V_24Y,c_24__type__458) ) ).

fof('$tdef_$_type_12',axiom,
    ! [V_24Y] :
      ( c_24__type__12___24t(V_24Y)
    <=> t(V_24Y,c_24__type__12) ) ).

fof('$tdef_$_type_422',axiom,
    ! [V_24X1,V_24X2,V_24Y] :
      ( c_24__type__422___24t(V_24X1,V_24X2,V_24Y)
    <=> t(V_24Y,c_24__type__422___24a2(V_24X1,V_24X2)) ) ).

fof('$tdef_$_type_33209',axiom,
    ! [V_24Y] :
      ( c_24__type__33209___24t(V_24Y)
    <=> t(V_24Y,c_24__type__33209) ) ).

fof('$tdef_$_type_10885',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24Y] :
      ( c_24__type__10885___24t(V_24X1,V_24X2,V_24X3,V_24Y)
    <=> t(V_24Y,c_24__type__10885___24a3(V_24X1,V_24X2,V_24X3)) ) ).

fof('$tdef_Coq.Init.Specif.sigT2',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24Y] :
      ( cCoq_2eInit_2eSpecif_2esigT2___24t(V_24X1,V_24X2,V_24X3,V_24Y)
    <=> t(V_24Y,cCoq_2eInit_2eSpecif_2esigT2___24a3(V_24X1,V_24X2,V_24X3)) ) ).

fof('$tdef_$_type_460',axiom,
    ! [V_24Y] :
      ( c_24__type__460___24t(V_24Y)
    <=> t(V_24Y,c_24__type__460) ) ).

fof('$tdef_$_type_400',axiom,
    ! [V_24Y] :
      ( c_24__type__400___24t(V_24Y)
    <=> t(V_24Y,c_24__type__400) ) ).

fof('$tdef_$_type_21497',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y] :
      ( c_24__type__21497___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y)
    <=> t(V_24Y,c_24__type__21497___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).

fof('$tdef_$_type_27',axiom,
    ! [V_24Y] :
      ( c_24__type__27___24t(V_24Y)
    <=> t(V_24Y,c_24__type__27) ) ).

fof('$tdef_$_type_10800',axiom,
    ! [V_24Y] :
      ( c_24__type__10800___24t(V_24Y)
    <=> t(V_24Y,c_24__type__10800) ) ).

fof('$tdef_$_type_17143',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y] :
      ( c_24__type__17143___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y)
    <=> t(V_24Y,c_24__type__17143___24a17(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17)) ) ).

fof('$tdef_$_type_21147',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y] :
      ( c_24__type__21147___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y)
    <=> t(V_24Y,c_24__type__21147___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).

fof('$tdef_$_type_23309',axiom,
    ! [V_24Y] :
      ( c_24__type__23309___24t(V_24Y)
    <=> t(V_24Y,c_24__type__23309) ) ).

fof('$tdef_$_type_30394',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
      ( c_24__type__30394___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
    <=> t(V_24Y,c_24__type__30394___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).

fof('$tdef_$_type_1778',axiom,
    ! [V_24Y] :
      ( c_24__type__1778___24t(V_24Y)
    <=> t(V_24Y,c_24__type__1778) ) ).

fof('$tdef_IntMap.Map.Map',axiom,
    ! [V_24X1,V_24Y] :
      ( cIntMap_2eMap_2eMap___24t(V_24X1,V_24Y)
    <=> t(V_24Y,cIntMap_2eMap_2eMap___24a1(V_24X1)) ) ).

fof('$tdef_Coq.Init.Datatypes.bool',axiom,
    ! [V_24Y] :
      ( cCoq_2eInit_2eDatatypes_2ebool___24t(V_24Y)
    <=> t(V_24Y,cCoq_2eInit_2eDatatypes_2ebool) ) ).

fof('$tdef_$_type_36708',axiom,
    ! [V_24X1,V_24Y] :
      ( c_24__type__36708___24t(V_24X1,V_24Y)
    <=> t(V_24Y,c_24__type__36708___24a1(V_24X1)) ) ).

fof('$tdef_$_type_14144',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24Y] :
      ( c_24__type__14144___24t(V_24X1,V_24X2,V_24X3,V_24Y)
    <=> t(V_24Y,c_24__type__14144___24a3(V_24X1,V_24X2,V_24X3)) ) ).

fof('$tdef_Coq.Init.Datatypes.list',axiom,
    ! [V_24X1,V_24Y] :
      ( cCoq_2eInit_2eDatatypes_2elist___24t(V_24X1,V_24Y)
    <=> t(V_24Y,cCoq_2eInit_2eDatatypes_2elist___24a1(V_24X1)) ) ).

fof('$tdef_$_type_974',axiom,
    ! [V_24X1,V_24X2,V_24Y] :
      ( c_24__type__974___24t(V_24X1,V_24X2,V_24Y)
    <=> t(V_24Y,c_24__type__974___24a2(V_24X1,V_24X2)) ) ).

fof('$tdef_$_type_28902',axiom,
    ! [V_24Y] :
      ( c_24__type__28902___24t(V_24Y)
    <=> t(V_24Y,c_24__type__28902) ) ).

fof('$tdef_Coq.Structures.OrderedTypeEx.Positive_as_OT.t',axiom,
    ! [V_24Y] :
      ( cCoq_2eStructures_2eOrderedTypeEx_2ePositive__as__OT_2et___24t(V_24Y)
    <=> t(V_24Y,cCoq_2eStructures_2eOrderedTypeEx_2ePositive__as__OT_2et) ) ).

fof('$tdef_$_type_36',axiom,
    ! [V_24Y] :
      ( c_24__type__36___24t(V_24Y)
    <=> t(V_24Y,c_24__type__36) ) ).

fof('$tdef_$_type_11405',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y] :
      ( c_24__type__11405___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y)
    <=> t(V_24Y,c_24__type__11405___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6)) ) ).

fof('$tdef_$_type_900',axiom,
    ! [V_24X1,V_24X2,V_24Y] :
      ( c_24__type__900___24t(V_24X1,V_24X2,V_24Y)
    <=> t(V_24Y,c_24__type__900___24a2(V_24X1,V_24X2)) ) ).

fof('$tdef_Coq.Structures.OrdersTac.ord',axiom,
    ! [V_24Y] :
      ( cCoq_2eStructures_2eOrdersTac_2eord___24t(V_24Y)
    <=> t(V_24Y,cCoq_2eStructures_2eOrdersTac_2eord) ) ).

fof('$tdef_$_type_23152',axiom,
    ! [V_24Y] :
      ( c_24__type__23152___24t(V_24Y)
    <=> t(V_24Y,c_24__type__23152) ) ).

fof('$tdef_Coq.micromega.EnvRing.PExpr',axiom,
    ! [V_24X1,V_24Y] :
      ( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(V_24X1,V_24Y)
    <=> t(V_24Y,cCoq_2emicromega_2eEnvRing_2ePExpr___24a1(V_24X1)) ) ).

fof('$tdef_Coq.Init.Datatypes.option',axiom,
    ! [V_24X1,V_24Y] :
      ( cCoq_2eInit_2eDatatypes_2eoption___24t(V_24X1,V_24Y)
    <=> t(V_24Y,cCoq_2eInit_2eDatatypes_2eoption___24a1(V_24X1)) ) ).

fof('$tdef_$_type_30456',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
      ( c_24__type__30456___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
    <=> t(V_24Y,c_24__type__30456___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).

fof('$tdef_$_type_31169',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24Y] :
      ( c_24__type__31169___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24Y)
    <=> t(V_24Y,c_24__type__31169___24a13(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13)) ) ).

fof('$tdef_$_type_28893',axiom,
    ! [V_24Y] :
      ( c_24__type__28893___24t(V_24Y)
    <=> t(V_24Y,c_24__type__28893) ) ).

fof('$tdef_$_type_18759',axiom,
    ! [V_24Y] :
      ( c_24__type__18759___24t(V_24Y)
    <=> t(V_24Y,c_24__type__18759) ) ).

fof('$tdef_$_type_12973',axiom,
    ! [V_24X1,V_24X2,V_24Y] :
      ( c_24__type__12973___24t(V_24X1,V_24X2,V_24Y)
    <=> t(V_24Y,c_24__type__12973___24a2(V_24X1,V_24X2)) ) ).

fof('$tdef_$_type_23013',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
      ( c_24__type__23013___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
    <=> t(V_24Y,c_24__type__23013___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).

fof('$tdef_Coq.Structures.OrderedTypeEx.PositiveOrderedTypeBits.t',axiom,
    ! [V_24Y] :
      ( cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2et___24t(V_24Y)
    <=> t(V_24Y,cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2et) ) ).

fof('$tdef_$_type_36683',axiom,
    ! [V_24Y] :
      ( c_24__type__36683___24t(V_24Y)
    <=> t(V_24Y,c_24__type__36683) ) ).

fof('$tdef_$_type_33602',axiom,
    ! [V_24Y] :
      ( c_24__type__33602___24t(V_24Y)
    <=> t(V_24Y,c_24__type__33602) ) ).

fof('$tdef_$_type_23337',axiom,
    ! [V_24Y] :
      ( c_24__type__23337___24t(V_24Y)
    <=> t(V_24Y,c_24__type__23337) ) ).

fof('$tdef_$_type_18451',axiom,
    ! [V_24Y] :
      ( c_24__type__18451___24t(V_24Y)
    <=> t(V_24Y,c_24__type__18451) ) ).

fof('$tdef_$_type_20665',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y] :
      ( c_24__type__20665___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y)
    <=> t(V_24Y,c_24__type__20665___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).

fof('$tdef_$_type_809',axiom,
    ! [V_24Y] :
      ( c_24__type__809___24t(V_24Y)
    <=> t(V_24Y,c_24__type__809) ) ).

fof('$tdef_$_type_25329',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y] :
      ( c_24__type__25329___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y)
    <=> t(V_24Y,c_24__type__25329___24a22(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22)) ) ).

fof('$tdef_Coq.Structures.OrderedTypeEx.N_as_OT.t',axiom,
    ! [V_24Y] :
      ( cCoq_2eStructures_2eOrderedTypeEx_2eN__as__OT_2et___24t(V_24Y)
    <=> t(V_24Y,cCoq_2eStructures_2eOrderedTypeEx_2eN__as__OT_2et) ) ).

fof('$tdef_$_type_1698',axiom,
    ! [V_24X1,V_24Y] :
      ( c_24__type__1698___24t(V_24X1,V_24Y)
    <=> t(V_24Y,c_24__type__1698___24a1(V_24X1)) ) ).

fof('$tdef_Coq.FSets.FSetPositive.PositiveSet.elt',axiom,
    ! [V_24Y] :
      ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(V_24Y)
    <=> t(V_24Y,cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt) ) ).

fof('$tdef_$_type_2258',axiom,
    ! [V_24Y] :
      ( c_24__type__2258___24t(V_24Y)
    <=> t(V_24Y,c_24__type__2258) ) ).

fof('$tdef_$_type_23968',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y] :
      ( c_24__type__23968___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y)
    <=> t(V_24Y,c_24__type__23968___24a22(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22)) ) ).

fof('$tdef_$_type_18826',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24Y] :
      ( c_24__type__18826___24t(V_24X1,V_24X2,V_24X3,V_24Y)
    <=> t(V_24Y,c_24__type__18826___24a3(V_24X1,V_24X2,V_24X3)) ) ).

fof('$tdef_$_type_1837',axiom,
    ! [V_24Y] :
      ( c_24__type__1837___24t(V_24Y)
    <=> t(V_24Y,c_24__type__1837) ) ).

fof('$tdef_$_type_32306',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y] :
      ( c_24__type__32306___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y)
    <=> t(V_24Y,c_24__type__32306___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7)) ) ).

fof('$tdef_$_type_896',axiom,
    ! [V_24Y] :
      ( c_24__type__896___24t(V_24Y)
    <=> t(V_24Y,c_24__type__896) ) ).

fof('$tdef_$_type_2181',axiom,
    ! [V_24Y] :
      ( c_24__type__2181___24t(V_24Y)
    <=> t(V_24Y,c_24__type__2181) ) ).

fof('$tdef_$_type_14716',axiom,
    ! [V_24Y] :
      ( c_24__type__14716___24t(V_24Y)
    <=> t(V_24Y,c_24__type__14716) ) ).

fof('$tdef_$_type_13503',axiom,
    ! [V_24Y] :
      ( c_24__type__13503___24t(V_24Y)
    <=> t(V_24Y,c_24__type__13503) ) ).

fof('$tdef_$_type_30039',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
      ( c_24__type__30039___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y)
    <=> t(V_24Y,c_24__type__30039___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).

fof('$tdef_$_type_805',axiom,
    ! [V_24X1,V_24X2,V_24Y] :
      ( c_24__type__805___24t(V_24X1,V_24X2,V_24Y)
    <=> t(V_24Y,c_24__type__805___24a2(V_24X1,V_24X2)) ) ).

fof('$tdef_$_type_10772',axiom,
    ! [V_24Y] :
      ( c_24__type__10772___24t(V_24Y)
    <=> t(V_24Y,c_24__type__10772) ) ).

fof('$tdef_$_type_30620',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
      ( c_24__type__30620___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
    <=> t(V_24Y,c_24__type__30620___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).

fof('$tdef_$_type_14182',axiom,
    ! [V_24Y] :
      ( c_24__type__14182___24t(V_24Y)
    <=> t(V_24Y,c_24__type__14182) ) ).

fof('$tdef_$_type_10770',axiom,
    ! [V_24Y] :
      ( c_24__type__10770___24t(V_24Y)
    <=> t(V_24Y,c_24__type__10770) ) ).

fof('$tdef_Coq.setoid_ring.Ring_polynom.Mon',axiom,
    ! [V_24Y] :
      ( cCoq_2esetoid__ring_2eRing__polynom_2eMon___24t(V_24Y)
    <=> t(V_24Y,cCoq_2esetoid__ring_2eRing__polynom_2eMon) ) ).

fof('$tdef_Coq.Init.Datatypes.comparison',axiom,
    ! [V_24Y] :
      ( cCoq_2eInit_2eDatatypes_2ecomparison___24t(V_24Y)
    <=> t(V_24Y,cCoq_2eInit_2eDatatypes_2ecomparison) ) ).

fof('$tdef_$_type_20490',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y] :
      ( c_24__type__20490___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y)
    <=> t(V_24Y,c_24__type__20490___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).

fof('$tdef_$_type_1820',axiom,
    ! [V_24Y] :
      ( c_24__type__1820___24t(V_24Y)
    <=> t(V_24Y,c_24__type__1820) ) ).

fof('$tdef_$_type_31419',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24Y] :
      ( c_24__type__31419___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24Y)
    <=> t(V_24Y,c_24__type__31419___24a13(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13)) ) ).

fof('$tdef_$_type_13189',axiom,
    ! [V_24Y] :
      ( c_24__type__13189___24t(V_24Y)
    <=> t(V_24Y,c_24__type__13189) ) ).

fof('$tdef_$_type_551',axiom,
    ! [V_24X1,V_24X2,V_24Y] :
      ( c_24__type__551___24t(V_24X1,V_24X2,V_24Y)
    <=> t(V_24Y,c_24__type__551___24a2(V_24X1,V_24X2)) ) ).

fof('$tdef_$_type_29639',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
      ( c_24__type__29639___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y)
    <=> t(V_24Y,c_24__type__29639___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).

fof('$tdef_$_type_534',axiom,
    ! [V_24X1,V_24X2,V_24Y] :
      ( c_24__type__534___24t(V_24X1,V_24X2,V_24Y)
    <=> t(V_24Y,c_24__type__534___24a2(V_24X1,V_24X2)) ) ).

fof('$tdef_$_type_32436',axiom,
    ! [V_24Y] :
      ( c_24__type__32436___24t(V_24Y)
    <=> t(V_24Y,c_24__type__32436) ) ).

fof('$tdef_$_type_1984',axiom,
    ! [V_24Y] :
      ( c_24__type__1984___24t(V_24Y)
    <=> t(V_24Y,c_24__type__1984) ) ).

fof('$tdef_$_type_18852',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24Y] :
      ( c_24__type__18852___24t(V_24X1,V_24X2,V_24X3,V_24Y)
    <=> t(V_24Y,c_24__type__18852___24a3(V_24X1,V_24X2,V_24X3)) ) ).

fof('$tdef_Coq.micromega.Tauto.GFormula',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
      ( cCoq_2emicromega_2eTauto_2eGFormula___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
    <=> t(V_24Y,cCoq_2emicromega_2eTauto_2eGFormula___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).

fof('$tdef_$_type_28374',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y] :
      ( c_24__type__28374___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y)
    <=> t(V_24Y,c_24__type__28374___24a22(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22)) ) ).

fof('$tdef_Coq.Numbers.BinNums.N',axiom,
    ! [V_24Y] :
      ( cCoq_2eNumbers_2eBinNums_2eN___24t(V_24Y)
    <=> t(V_24Y,cCoq_2eNumbers_2eBinNums_2eN) ) ).

fof('$tdef_$_type_32732',axiom,
    ! [V_24Y] :
      ( c_24__type__32732___24t(V_24Y)
    <=> t(V_24Y,c_24__type__32732) ) ).

fof('$tdef_Coq.Init.Specif.sig2',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24Y] :
      ( cCoq_2eInit_2eSpecif_2esig2___24t(V_24X1,V_24X2,V_24X3,V_24Y)
    <=> t(V_24Y,cCoq_2eInit_2eSpecif_2esig2___24a3(V_24X1,V_24X2,V_24X3)) ) ).

fof('$tdef_$_type_18778',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24Y] :
      ( c_24__type__18778___24t(V_24X1,V_24X2,V_24X3,V_24Y)
    <=> t(V_24Y,c_24__type__18778___24a3(V_24X1,V_24X2,V_24X3)) ) ).

fof('$tdef_$_type_30438',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
      ( c_24__type__30438___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
    <=> t(V_24Y,c_24__type__30438___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).

fof('$tdef_$_type_11408',axiom,
    ! [V_24X1,V_24Y] :
      ( c_24__type__11408___24t(V_24X1,V_24Y)
    <=> t(V_24Y,c_24__type__11408___24a1(V_24X1)) ) ).

fof('$tdef_Coq.Init.Specif.sumbool',axiom,
    ! [V_24X1,V_24X2,V_24Y] :
      ( cCoq_2eInit_2eSpecif_2esumbool___24t(V_24X1,V_24X2,V_24Y)
    <=> t(V_24Y,cCoq_2eInit_2eSpecif_2esumbool___24a2(V_24X1,V_24X2)) ) ).

fof('$tdef_$_type_18868',axiom,
    ! [V_24Y] :
      ( c_24__type__18868___24t(V_24Y)
    <=> t(V_24Y,c_24__type__18868) ) ).

fof('$tdef_$_type_10985',axiom,
    ! [V_24Y] :
      ( c_24__type__10985___24t(V_24Y)
    <=> t(V_24Y,c_24__type__10985) ) ).

fof('$tdef_$_type_17356',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y] :
      ( c_24__type__17356___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y)
    <=> t(V_24Y,c_24__type__17356___24a17(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17)) ) ).

fof('$tdef_$_type_31294',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24Y] :
      ( c_24__type__31294___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24Y)
    <=> t(V_24Y,c_24__type__31294___24a13(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13)) ) ).

fof('$tdef_Coq.Reals.Rdefinitions.R',axiom,
    ! [V_24Y] :
      ( cCoq_2eReals_2eRdefinitions_2eR___24t(V_24Y)
    <=> t(V_24Y,cCoq_2eReals_2eRdefinitions_2eR) ) ).

fof('$tdef_$_type_18429',axiom,
    ! [V_24X1,V_24X2,V_24Y] :
      ( c_24__type__18429___24t(V_24X1,V_24X2,V_24Y)
    <=> t(V_24Y,c_24__type__18429___24a2(V_24X1,V_24X2)) ) ).

fof('$tdef_$_type_21054',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y] :
      ( c_24__type__21054___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y)
    <=> t(V_24Y,c_24__type__21054___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).

fof('$tdef_$_type_14',axiom,
    ! [V_24Y] :
      ( c_24__type__14___24t(V_24Y)
    <=> t(V_24Y,c_24__type__14) ) ).

fof('$tdef_$_type_14177',axiom,
    ! [V_24Y] :
      ( c_24__type__14177___24t(V_24Y)
    <=> t(V_24Y,c_24__type__14177) ) ).

fof('$tdef_$_type_14607',axiom,
    ! [V_24Y] :
      ( c_24__type__14607___24t(V_24Y)
    <=> t(V_24Y,c_24__type__14607) ) ).

fof('$tdef_$_type_2227',axiom,
    ! [V_24Y] :
      ( c_24__type__2227___24t(V_24Y)
    <=> t(V_24Y,c_24__type__2227) ) ).

fof('$tdef_$_type_13092',axiom,
    ! [V_24Y] :
      ( c_24__type__13092___24t(V_24Y)
    <=> t(V_24Y,c_24__type__13092) ) ).

fof('$tdef_$_type_1841',axiom,
    ! [V_24X1,V_24X2,V_24Y] :
      ( c_24__type__1841___24t(V_24X1,V_24X2,V_24Y)
    <=> t(V_24Y,c_24__type__1841___24a2(V_24X1,V_24X2)) ) ).

fof('$tdef_$_type_19983',axiom,
    ! [V_24Y] :
      ( c_24__type__19983___24t(V_24Y)
    <=> t(V_24Y,c_24__type__19983) ) ).

fof('$tdef_$_type_13540',axiom,
    ! [V_24X1,V_24Y] :
      ( c_24__type__13540___24t(V_24X1,V_24Y)
    <=> t(V_24Y,c_24__type__13540___24a1(V_24X1)) ) ).

fof('$tdef_$_type_19719',axiom,
    ! [V_24Y] :
      ( c_24__type__19719___24t(V_24Y)
    <=> t(V_24Y,c_24__type__19719) ) ).

fof('$tdef_Coq.setoid_ring.Field_theory.FExpr',axiom,
    ! [V_24X1,V_24Y] :
      ( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(V_24X1,V_24Y)
    <=> t(V_24Y,cCoq_2esetoid__ring_2eField__theory_2eFExpr___24a1(V_24X1)) ) ).

fof('$tdef_Coq.FSets.FSetPositive.PositiveSet.t',axiom,
    ! [V_24Y] :
      ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(V_24Y)
    <=> t(V_24Y,cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et) ) ).

fof('$tdef_$_type_29522',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
      ( c_24__type__29522___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y)
    <=> t(V_24Y,c_24__type__29522___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).

fof('$tdef_$_type_388',axiom,
    ! [V_24Y] :
      ( c_24__type__388___24t(V_24Y)
    <=> t(V_24Y,c_24__type__388) ) ).

fof('$tdef_$_type_19869',axiom,
    ! [V_24Y] :
      ( c_24__type__19869___24t(V_24Y)
    <=> t(V_24Y,c_24__type__19869) ) ).

fof('$tdef_$_type_12419',axiom,
    ! [V_24X1,V_24Y] :
      ( c_24__type__12419___24t(V_24X1,V_24Y)
    <=> t(V_24Y,c_24__type__12419___24a1(V_24X1)) ) ).

fof('$tdef_Coq.Init.Datatypes.unit',axiom,
    ! [V_24Y] :
      ( cCoq_2eInit_2eDatatypes_2eunit___24t(V_24Y)
    <=> t(V_24Y,cCoq_2eInit_2eDatatypes_2eunit) ) ).

fof('$tdef_$_type_30650',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
      ( c_24__type__30650___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
    <=> t(V_24Y,c_24__type__30650___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).

fof('$tdef_$_type_32386',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y] :
      ( c_24__type__32386___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y)
    <=> t(V_24Y,c_24__type__32386___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7)) ) ).

fof('$tdef_$_type_20092',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y] :
      ( c_24__type__20092___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y)
    <=> t(V_24Y,c_24__type__20092___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6)) ) ).

fof('$tdef_$_type_1580',axiom,
    ! [V_24X1,V_24X2,V_24Y] :
      ( c_24__type__1580___24t(V_24X1,V_24X2,V_24Y)
    <=> t(V_24Y,c_24__type__1580___24a2(V_24X1,V_24X2)) ) ).

fof('$tdef_$_type_13363',axiom,
    ! [V_24Y] :
      ( c_24__type__13363___24t(V_24Y)
    <=> t(V_24Y,c_24__type__13363) ) ).

fof('$tdef_$_type_2359',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24Y] :
      ( c_24__type__2359___24t(V_24X1,V_24X2,V_24X3,V_24Y)
    <=> t(V_24Y,c_24__type__2359___24a3(V_24X1,V_24X2,V_24X3)) ) ).

fof('$tdef_$_type_14538',axiom,
    ! [V_24Y] :
      ( c_24__type__14538___24t(V_24Y)
    <=> t(V_24Y,c_24__type__14538) ) ).

fof('$tdef_$_type_30325',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
      ( c_24__type__30325___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
    <=> t(V_24Y,c_24__type__30325___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).

fof('$tdef_$_type_27036',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y] :
      ( c_24__type__27036___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y)
    <=> t(V_24Y,c_24__type__27036___24a22(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22)) ) ).

fof('$tdef_$_type_26021',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y] :
      ( c_24__type__26021___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y)
    <=> t(V_24Y,c_24__type__26021___24a22(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22)) ) ).

fof('$tdef_$_type_11363',axiom,
    ! [V_24X1,V_24Y] :
      ( c_24__type__11363___24t(V_24X1,V_24Y)
    <=> t(V_24Y,c_24__type__11363___24a1(V_24X1)) ) ).

fof('$tdef_$_type_20397',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y] :
      ( c_24__type__20397___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y)
    <=> t(V_24Y,c_24__type__20397___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).

fof('$tdef_Coq.Init.Specif.sig',axiom,
    ! [V_24X1,V_24X2,V_24Y] :
      ( cCoq_2eInit_2eSpecif_2esig___24t(V_24X1,V_24X2,V_24Y)
    <=> t(V_24Y,cCoq_2eInit_2eSpecif_2esig___24a2(V_24X1,V_24X2)) ) ).

fof('$tdef_$_type_18860',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24Y] :
      ( c_24__type__18860___24t(V_24X1,V_24X2,V_24X3,V_24Y)
    <=> t(V_24Y,c_24__type__18860___24a3(V_24X1,V_24X2,V_24X3)) ) ).

fof('$tdef_IntMap.Fset.FSet',axiom,
    ! [V_24Y] :
      ( cIntMap_2eFset_2eFSet___24t(V_24Y)
    <=> t(V_24Y,cIntMap_2eFset_2eFSet) ) ).

fof('$tdef_$_type_19184',axiom,
    ! [V_24Y] :
      ( c_24__type__19184___24t(V_24Y)
    <=> t(V_24Y,c_24__type__19184) ) ).

fof('$tdef_$_type_26367',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y] :
      ( c_24__type__26367___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y)
    <=> t(V_24Y,c_24__type__26367___24a22(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22)) ) ).

fof('$tdef_Coq.Init.Datatypes.sum',axiom,
    ! [V_24X1,V_24X2,V_24Y] :
      ( cCoq_2eInit_2eDatatypes_2esum___24t(V_24X1,V_24X2,V_24Y)
    <=> t(V_24Y,cCoq_2eInit_2eDatatypes_2esum___24a2(V_24X1,V_24X2)) ) ).

fof('$tdef_$_type_12935',axiom,
    ! [V_24Y] :
      ( c_24__type__12935___24t(V_24Y)
    <=> t(V_24Y,c_24__type__12935) ) ).

fof('$tdef_$_type_29976',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
      ( c_24__type__29976___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y)
    <=> t(V_24Y,c_24__type__29976___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).

fof('$tdef_$_type_10897',axiom,
    ! [V_24Y] :
      ( c_24__type__10897___24t(V_24Y)
    <=> t(V_24Y,c_24__type__10897) ) ).

fof('$tdef_$_type_28051',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y] :
      ( c_24__type__28051___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y)
    <=> t(V_24Y,c_24__type__28051___24a22(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22)) ) ).

fof('$tdef_Coq.Strings.Ascii.ascii',axiom,
    ! [V_24Y] :
      ( cCoq_2eStrings_2eAscii_2eascii___24t(V_24Y)
    <=> t(V_24Y,cCoq_2eStrings_2eAscii_2eascii) ) ).

fof('$tdef_$_type_50',axiom,
    ! [V_24Y] :
      ( c_24__type__50___24t(V_24Y)
    <=> t(V_24Y,c_24__type__50) ) ).

fof('$tdef_$_type_1617',axiom,
    ! [V_24Y] :
      ( c_24__type__1617___24t(V_24Y)
    <=> t(V_24Y,c_24__type__1617) ) ).

fof('$tdef_$_type_33637',axiom,
    ! [V_24Y] :
      ( c_24__type__33637___24t(V_24Y)
    <=> t(V_24Y,c_24__type__33637) ) ).

fof('$tdef_$_type_2320',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24Y] :
      ( c_24__type__2320___24t(V_24X1,V_24X2,V_24X3,V_24Y)
    <=> t(V_24Y,c_24__type__2320___24a3(V_24X1,V_24X2,V_24X3)) ) ).

fof('$tdef_Coq.FSets.FSetPositive.PositiveSet.tree',axiom,
    ! [V_24Y] :
      ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree___24t(V_24Y)
    <=> t(V_24Y,cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree) ) ).

fof('$tdef_$_type_33487',axiom,
    ! [V_24Y] :
      ( c_24__type__33487___24t(V_24Y)
    <=> t(V_24Y,c_24__type__33487) ) ).

fof('$tdef_$_type_12942',axiom,
    ! [V_24X1,V_24X2,V_24Y] :
      ( c_24__type__12942___24t(V_24X1,V_24X2,V_24Y)
    <=> t(V_24Y,c_24__type__12942___24a2(V_24X1,V_24X2)) ) ).

fof('$tdef_Coq.Relations.Relation_Definitions.relation',axiom,
    ! [V_24X1,V_24Y] :
      ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V_24X1,V_24Y)
    <=> t(V_24Y,cCoq_2eRelations_2eRelation__Definitions_2erelation___24a1(V_24X1)) ) ).

fof('$tdef_$_type_24314',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y] :
      ( c_24__type__24314___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y)
    <=> t(V_24Y,c_24__type__24314___24a22(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22)) ) ).

fof('$tdef_$_type_476',axiom,
    ! [V_24X1,V_24X2,V_24Y] :
      ( c_24__type__476___24t(V_24X1,V_24X2,V_24Y)
    <=> t(V_24Y,c_24__type__476___24a2(V_24X1,V_24X2)) ) ).

fof('$tdef_$_type_33606',axiom,
    ! [V_24Y] :
      ( c_24__type__33606___24t(V_24Y)
    <=> t(V_24Y,c_24__type__33606) ) ).

fof('$tdef_$_type_173',axiom,
    ! [V_24Y] :
      ( c_24__type__173___24t(V_24Y)
    <=> t(V_24Y,c_24__type__173) ) ).

fof('$tdef_$_type_17569',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y] :
      ( c_24__type__17569___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y)
    <=> t(V_24Y,c_24__type__17569___24a17(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17)) ) ).

fof('$tdef_$_type_29459',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
      ( c_24__type__29459___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y)
    <=> t(V_24Y,c_24__type__29459___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).

fof('$tdef_$_type_18190',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y] :
      ( c_24__type__18190___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y)
    <=> t(V_24Y,c_24__type__18190___24a17(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17)) ) ).

fof('$tdef_$_type_13176',axiom,
    ! [V_24X1,V_24Y] :
      ( c_24__type__13176___24t(V_24X1,V_24Y)
    <=> t(V_24Y,c_24__type__13176___24a1(V_24X1)) ) ).

fof('$tdef_$_type_2078',axiom,
    ! [V_24Y] :
      ( c_24__type__2078___24t(V_24Y)
    <=> t(V_24Y,c_24__type__2078) ) ).

fof('$tdef_$_type_18934',axiom,
    ! [V_24Y] :
      ( c_24__type__18934___24t(V_24Y)
    <=> t(V_24Y,c_24__type__18934) ) ).

fof('$tdef_Coq.setoid_ring.Field_theory.linear',axiom,
    ! [V_24X1,V_24Y] :
      ( cCoq_2esetoid__ring_2eField__theory_2elinear___24t(V_24X1,V_24Y)
    <=> t(V_24Y,cCoq_2esetoid__ring_2eField__theory_2elinear___24a1(V_24X1)) ) ).

fof('$tdef_$_type_24983',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y] :
      ( c_24__type__24983___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y)
    <=> t(V_24Y,c_24__type__24983___24a22(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22)) ) ).

fof('$tdef_Prop',axiom,
    ! [V_24Y] :
      ( cProp___24t(V_24Y)
    <=> t(V_24Y,cProp) ) ).

fof('$tdef_$_type_842',axiom,
    ! [V_24Y] :
      ( c_24__type__842___24t(V_24Y)
    <=> t(V_24Y,c_24__type__842) ) ).

fof('$tdef_$_type_449',axiom,
    ! [V_24Y] :
      ( c_24__type__449___24t(V_24Y)
    <=> t(V_24Y,c_24__type__449) ) ).

fof('$tdef_$_type_526',axiom,
    ! [V_24X1,V_24Y] :
      ( c_24__type__526___24t(V_24X1,V_24Y)
    <=> t(V_24Y,c_24__type__526___24a1(V_24X1)) ) ).

fof('$tdef_$_type_23052',axiom,
    ! [V_24Y] :
      ( c_24__type__23052___24t(V_24Y)
    <=> t(V_24Y,c_24__type__23052) ) ).

fof('$tdef_$_type_12824',axiom,
    ! [V_24Y] :
      ( c_24__type__12824___24t(V_24Y)
    <=> t(V_24Y,c_24__type__12824) ) ).

fof('$tdef_$_type_1574',axiom,
    ! [V_24X1,V_24X2,V_24Y] :
      ( c_24__type__1574___24t(V_24X1,V_24X2,V_24Y)
    <=> t(V_24Y,c_24__type__1574___24a2(V_24X1,V_24X2)) ) ).

fof('$tdef_$_type_11418',axiom,
    ! [V_24Y] :
      ( c_24__type__11418___24t(V_24Y)
    <=> t(V_24Y,c_24__type__11418) ) ).

fof('$tdef_$_type_29585',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
      ( c_24__type__29585___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y)
    <=> t(V_24Y,c_24__type__29585___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).

fof('$tdef_$_type_24660',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y] :
      ( c_24__type__24660___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y)
    <=> t(V_24Y,c_24__type__24660___24a22(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22)) ) ).

fof('$tdef_$_type_970',axiom,
    ! [V_24Y] :
      ( c_24__type__970___24t(V_24Y)
    <=> t(V_24Y,c_24__type__970) ) ).

fof('$tdef_$_type_18436',axiom,
    ! [V_24X1,V_24X2,V_24Y] :
      ( c_24__type__18436___24t(V_24X1,V_24X2,V_24Y)
    <=> t(V_24Y,c_24__type__18436___24a2(V_24X1,V_24X2)) ) ).

fof('$tdef_$_type_30566',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
      ( c_24__type__30566___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
    <=> t(V_24Y,c_24__type__30566___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).

fof('$tdef_Coq.micromega.RingMicromega.Op2',axiom,
    ! [V_24Y] :
      ( cCoq_2emicromega_2eRingMicromega_2eOp2___24t(V_24Y)
    <=> t(V_24Y,cCoq_2emicromega_2eRingMicromega_2eOp2) ) ).

fof('$tdef_$_type_21860',axiom,
    ! [V_24Y] :
      ( c_24__type__21860___24t(V_24Y)
    <=> t(V_24Y,c_24__type__21860) ) ).

fof('$tdef_$_type_14619',axiom,
    ! [V_24Y] :
      ( c_24__type__14619___24t(V_24Y)
    <=> t(V_24Y,c_24__type__14619) ) ).

fof('$tdef_$_type_16735',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y] :
      ( c_24__type__16735___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y)
    <=> t(V_24Y,c_24__type__16735___24a17(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17)) ) ).

fof('$tdef_$_type_10911',axiom,
    ! [V_24Y] :
      ( c_24__type__10911___24t(V_24Y)
    <=> t(V_24Y,c_24__type__10911) ) ).

fof('$tdef_B',axiom,
    ! [V_24Y] :
      ( cB___24t(V_24Y)
    <=> t(V_24Y,cB) ) ).

fof('$tdef_$_type_30761',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
      ( c_24__type__30761___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
    <=> t(V_24Y,c_24__type__30761___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).

fof('$tdef_$_type_2669',axiom,
    ! [V_24Y] :
      ( c_24__type__2669___24t(V_24Y)
    <=> t(V_24Y,c_24__type__2669) ) ).

fof('$tdef_$_type_1916',axiom,
    ! [V_24Y] :
      ( c_24__type__1916___24t(V_24Y)
    <=> t(V_24Y,c_24__type__1916) ) ).

fof('$tdef_$_type_13620',axiom,
    ! [V_24Y] :
      ( c_24__type__13620___24t(V_24Y)
    <=> t(V_24Y,c_24__type__13620) ) ).

fof('$tdef_$_type_26713',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y] :
      ( c_24__type__26713___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y)
    <=> t(V_24Y,c_24__type__26713___24a22(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22)) ) ).

fof('$tdef_Coq.Init.Byte.byte',axiom,
    ! [V_24Y] :
      ( cCoq_2eInit_2eByte_2ebyte___24t(V_24Y)
    <=> t(V_24Y,cCoq_2eInit_2eByte_2ebyte) ) ).

fof('$tdef_$_type_23401',axiom,
    ! [V_24Y] :
      ( c_24__type__23401___24t(V_24Y)
    <=> t(V_24Y,c_24__type__23401) ) ).

fof('$tdef_$_type_21322',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y] :
      ( c_24__type__21322___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y)
    <=> t(V_24Y,c_24__type__21322___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).

fof('$tdef_Coq.Reals.Rfunctions.Z_spec',axiom,
    ! [V_24X1,V_24X2,V_24Y] :
      ( cCoq_2eReals_2eRfunctions_2eZ__spec___24t(V_24X1,V_24X2,V_24Y)
    <=> t(V_24Y,cCoq_2eReals_2eRfunctions_2eZ__spec___24a2(V_24X1,V_24X2)) ) ).

fof('$tdef_$_type_21635',axiom,
    ! [V_24Y] :
      ( c_24__type__21635___24t(V_24Y)
    <=> t(V_24Y,c_24__type__21635) ) ).

fof('$tdef_$_type_12842',axiom,
    ! [V_24Y] :
      ( c_24__type__12842___24t(V_24Y)
    <=> t(V_24Y,c_24__type__12842) ) ).

fof('$tdef_$_type_98',axiom,
    ! [V_24Y] :
      ( c_24__type__98___24t(V_24Y)
    <=> t(V_24Y,c_24__type__98) ) ).

fof('$tdef_$_type_19933',axiom,
    ! [V_24Y] :
      ( c_24__type__19933___24t(V_24Y)
    <=> t(V_24Y,c_24__type__19933) ) ).

fof('$tdef_$_type_1851',axiom,
    ! [V_24X1,V_24Y] :
      ( c_24__type__1851___24t(V_24X1,V_24Y)
    <=> t(V_24Y,c_24__type__1851___24a1(V_24X1)) ) ).

fof('$tdef_Coq.ZArith.Zpower.Zdiv_rest_proofs',axiom,
    ! [V_24X1,V_24X2,V_24Y] :
      ( cCoq_2eZArith_2eZpower_2eZdiv__rest__proofs___24t(V_24X1,V_24X2,V_24Y)
    <=> t(V_24Y,cCoq_2eZArith_2eZpower_2eZdiv__rest__proofs___24a2(V_24X1,V_24X2)) ) ).

fof('$tdef_Coq.Strings.String.string',axiom,
    ! [V_24Y] :
      ( cCoq_2eStrings_2eString_2estring___24t(V_24Y)
    <=> t(V_24Y,cCoq_2eStrings_2eString_2estring) ) ).

fof('$tdef_$_type_1563',axiom,
    ! [V_24X1,V_24Y] :
      ( c_24__type__1563___24t(V_24X1,V_24Y)
    <=> t(V_24Y,c_24__type__1563___24a1(V_24X1)) ) ).

fof('$tdef_$_type_12649',axiom,
    ! [V_24X1,V_24Y] :
      ( c_24__type__12649___24t(V_24X1,V_24Y)
    <=> t(V_24Y,c_24__type__12649___24a1(V_24X1)) ) ).

fof('$tdef_$_type_20747',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y] :
      ( c_24__type__20747___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y)
    <=> t(V_24Y,c_24__type__20747___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).

fof('$tdef_$_type_30219',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
      ( c_24__type__30219___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y)
    <=> t(V_24Y,c_24__type__30219___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).

fof('$tdef_$_type_32513',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24Y] :
      ( c_24__type__32513___24t(V_24X1,V_24X2,V_24X3,V_24Y)
    <=> t(V_24Y,c_24__type__32513___24a3(V_24X1,V_24X2,V_24X3)) ) ).

fof('$tdef_$_type_451',axiom,
    ! [V_24Y] :
      ( c_24__type__451___24t(V_24Y)
    <=> t(V_24Y,c_24__type__451) ) ).

fof('$tdef_$_type_1693',axiom,
    ! [V_24Y] :
      ( c_24__type__1693___24t(V_24Y)
    <=> t(V_24Y,c_24__type__1693) ) ).

fof('$tdef_IntMap.Map.ad',axiom,
    ! [V_24Y] :
      ( cIntMap_2eMap_2ead___24t(V_24Y)
    <=> t(V_24Y,cIntMap_2eMap_2ead) ) ).

fof('$tdef_$_type_1987',axiom,
    ! [V_24X1,V_24Y] :
      ( c_24__type__1987___24t(V_24X1,V_24Y)
    <=> t(V_24Y,c_24__type__1987___24a1(V_24X1)) ) ).

fof('$tdef_$_type_13915',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24Y] :
      ( c_24__type__13915___24t(V_24X1,V_24X2,V_24X3,V_24Y)
    <=> t(V_24Y,c_24__type__13915___24a3(V_24X1,V_24X2,V_24X3)) ) ).

fof('$tdef_$_type_11430',axiom,
    ! [V_24X1,V_24X2,V_24Y] :
      ( c_24__type__11430___24t(V_24X1,V_24X2,V_24Y)
    <=> t(V_24Y,c_24__type__11430___24a2(V_24X1,V_24X2)) ) ).

fof('$tdef_$_type_848',axiom,
    ! [V_24X1,V_24X2,V_24Y] :
      ( c_24__type__848___24t(V_24X1,V_24X2,V_24Y)
    <=> t(V_24Y,c_24__type__848___24a2(V_24X1,V_24X2)) ) ).

fof('$tdef_$_type_2154',axiom,
    ! [V_24Y] :
      ( c_24__type__2154___24t(V_24Y)
    <=> t(V_24Y,c_24__type__2154) ) ).

fof('$tdef_$_type_19236',axiom,
    ! [V_24Y] :
      ( c_24__type__19236___24t(V_24Y)
    <=> t(V_24Y,c_24__type__19236) ) ).

fof('$tdef_$_type_36678',axiom,
    ! [V_24Y] :
      ( c_24__type__36678___24t(V_24Y)
    <=> t(V_24Y,c_24__type__36678) ) ).

fof('$tdef_$_type_32724',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24Y] :
      ( c_24__type__32724___24t(V_24X1,V_24X2,V_24X3,V_24Y)
    <=> t(V_24Y,c_24__type__32724___24a3(V_24X1,V_24X2,V_24X3)) ) ).

fof('$tdef_Coq.micromega.RingMicromega.Op1',axiom,
    ! [V_24Y] :
      ( cCoq_2emicromega_2eRingMicromega_2eOp1___24t(V_24Y)
    <=> t(V_24Y,cCoq_2emicromega_2eRingMicromega_2eOp1) ) ).

fof('$tdef_Coq.Init.Datatypes.CompareSpecT',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
      ( cCoq_2eInit_2eDatatypes_2eCompareSpecT___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
    <=> t(V_24Y,cCoq_2eInit_2eDatatypes_2eCompareSpecT___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).

fof('$tdef_$_type_93',axiom,
    ! [V_24Y] :
      ( c_24__type__93___24t(V_24Y)
    <=> t(V_24Y,c_24__type__93) ) ).

fof('$tdef_$_type_23147',axiom,
    ! [V_24Y] :
      ( c_24__type__23147___24t(V_24Y)
    <=> t(V_24Y,c_24__type__23147) ) ).

fof('$tdef_$_type_19006',axiom,
    ! [V_24Y] :
      ( c_24__type__19006___24t(V_24Y)
    <=> t(V_24Y,c_24__type__19006) ) ).

fof('$tdef_Coq.Init.Specif.sigT',axiom,
    ! [V_24X1,V_24X2,V_24Y] :
      ( cCoq_2eInit_2eSpecif_2esigT___24t(V_24X1,V_24X2,V_24Y)
    <=> t(V_24Y,cCoq_2eInit_2eSpecif_2esigT___24a2(V_24X1,V_24X2)) ) ).

fof('$tdef_$_type_19055',axiom,
    ! [V_24Y] :
      ( c_24__type__19055___24t(V_24Y)
    <=> t(V_24Y,c_24__type__19055) ) ).

fof('$tdef_$_type_19141',axiom,
    ! [V_24Y] :
      ( c_24__type__19141___24t(V_24Y)
    <=> t(V_24Y,c_24__type__19141) ) ).

fof('$tdef_A',axiom,
    ! [V_24Y] :
      ( cA___24t(V_24Y)
    <=> t(V_24Y,cA) ) ).

fof('$tdef_$_type_1799',axiom,
    ! [V_24X1,V_24X2,V_24Y] :
      ( c_24__type__1799___24t(V_24X1,V_24X2,V_24Y)
    <=> t(V_24Y,c_24__type__1799___24a2(V_24X1,V_24X2)) ) ).

fof('$tdef_$_type_19009',axiom,
    ! [V_24Y] :
      ( c_24__type__19009___24t(V_24Y)
    <=> t(V_24Y,c_24__type__19009) ) ).

fof('$tdef_$_type_19189',axiom,
    ! [V_24X1,V_24X2,V_24Y] :
      ( c_24__type__19189___24t(V_24X1,V_24X2,V_24Y)
    <=> t(V_24Y,c_24__type__19189___24a2(V_24X1,V_24X2)) ) ).

fof('$tdef_$_type_2174',axiom,
    ! [V_24Y] :
      ( c_24__type__2174___24t(V_24Y)
    <=> t(V_24Y,c_24__type__2174) ) ).

fof('$tdef_$_type_18786',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24Y] :
      ( c_24__type__18786___24t(V_24X1,V_24X2,V_24X3,V_24Y)
    <=> t(V_24Y,c_24__type__18786___24a3(V_24X1,V_24X2,V_24X3)) ) ).

fof('$tdef_Coq.micromega.EnvRing.Pol',axiom,
    ! [V_24X1,V_24Y] :
      ( cCoq_2emicromega_2eEnvRing_2ePol___24t(V_24X1,V_24Y)
    <=> t(V_24Y,cCoq_2emicromega_2eEnvRing_2ePol___24a1(V_24X1)) ) ).

fof('$tdef_$_type_23307',axiom,
    ! [V_24Y] :
      ( c_24__type__23307___24t(V_24Y)
    <=> t(V_24Y,c_24__type__23307) ) ).

fof('$tdef_$_type_18385',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y] :
      ( c_24__type__18385___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y)
    <=> t(V_24Y,c_24__type__18385___24a17(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17)) ) ).

fof('$tdef_$_type_1418',axiom,
    ! [V_24Y] :
      ( c_24__type__1418___24t(V_24Y)
    <=> t(V_24Y,c_24__type__1418) ) ).

fof('$tdef_$_type_907',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24Y] :
      ( c_24__type__907___24t(V_24X1,V_24X2,V_24X3,V_24Y)
    <=> t(V_24Y,c_24__type__907___24a3(V_24X1,V_24X2,V_24X3)) ) ).

fof('$tdef_$_type_30156',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
      ( c_24__type__30156___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y)
    <=> t(V_24Y,c_24__type__30156___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).

fof('$tdef_$_type_735',axiom,
    ! [V_24Y] :
      ( c_24__type__735___24t(V_24Y)
    <=> t(V_24Y,c_24__type__735) ) ).

fof('$tdef_IntMap.Mapiter.alist',axiom,
    ! [V_24X1,V_24Y] :
      ( cIntMap_2eMapiter_2ealist___24t(V_24X1,V_24Y)
    <=> t(V_24Y,cIntMap_2eMapiter_2ealist___24a1(V_24X1)) ) ).

fof('$tdef_$_type_13191',axiom,
    ! [V_24Y] :
      ( c_24__type__13191___24t(V_24Y)
    <=> t(V_24Y,c_24__type__13191) ) ).

fof('$tdef_$_type_33336',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
      ( c_24__type__33336___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
    <=> t(V_24Y,c_24__type__33336___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).

fof('$tdef_$_type_13920',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24Y] :
      ( c_24__type__13920___24t(V_24X1,V_24X2,V_24X3,V_24Y)
    <=> t(V_24Y,c_24__type__13920___24a3(V_24X1,V_24X2,V_24X3)) ) ).

fof('$tdef_$_type_865',axiom,
    ! [V_24Y] :
      ( c_24__type__865___24t(V_24Y)
    <=> t(V_24Y,c_24__type__865) ) ).

fof('$tdef_$_type_789',axiom,
    ! [V_24Y] :
      ( c_24__type__789___24t(V_24Y)
    <=> t(V_24Y,c_24__type__789) ) ).

fof('$tdef_$_type_33431',axiom,
    ! [V_24Y] :
      ( c_24__type__33431___24t(V_24Y)
    <=> t(V_24Y,c_24__type__33431) ) ).

fof('$tdef_$_type_782',axiom,
    ! [V_24Y] :
      ( c_24__type__782___24t(V_24Y)
    <=> t(V_24Y,c_24__type__782) ) ).

fof('$tdef_Coq.Structures.OrderedType.Compare',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
      ( cCoq_2eStructures_2eOrderedType_2eCompare___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
    <=> t(V_24Y,cCoq_2eStructures_2eOrderedType_2eCompare___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).

fof('$tdef_Coq.Init.Specif.sumor',axiom,
    ! [V_24X1,V_24X2,V_24Y] :
      ( cCoq_2eInit_2eSpecif_2esumor___24t(V_24X1,V_24X2,V_24Y)
    <=> t(V_24Y,cCoq_2eInit_2eSpecif_2esumor___24a2(V_24X1,V_24X2)) ) ).

fof('$tdef_$_type_30596',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
      ( c_24__type__30596___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
    <=> t(V_24Y,c_24__type__30596___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).

fof('$tdef_$_type_10973',axiom,
    ! [V_24Y] :
      ( c_24__type__10973___24t(V_24Y)
    <=> t(V_24Y,c_24__type__10973) ) ).

fof('$tdef_$_type_13901',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24Y] :
      ( c_24__type__13901___24t(V_24X1,V_24X2,V_24X3,V_24Y)
    <=> t(V_24Y,c_24__type__13901___24a3(V_24X1,V_24X2,V_24X3)) ) ).

fof('$tdef_$_type_21415',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y] :
      ( c_24__type__21415___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y)
    <=> t(V_24Y,c_24__type__21415___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).

fof('$tdef_Coq.Structures.OrderedTypeEx.String_as_OT.t',axiom,
    ! [V_24Y] :
      ( cCoq_2eStructures_2eOrderedTypeEx_2eString__as__OT_2et___24t(V_24Y)
    <=> t(V_24Y,cCoq_2eStructures_2eOrderedTypeEx_2eString__as__OT_2et) ) ).

fof('$tdef_$_type_10849',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24Y] :
      ( c_24__type__10849___24t(V_24X1,V_24X2,V_24X3,V_24Y)
    <=> t(V_24Y,c_24__type__10849___24a3(V_24X1,V_24X2,V_24X3)) ) ).

fof('$tdef_$_type_33511',axiom,
    ! [V_24Y] :
      ( c_24__type__33511___24t(V_24Y)
    <=> t(V_24Y,c_24__type__33511) ) ).

fof('$tdef_$_type_12830',axiom,
    ! [V_24Y] :
      ( c_24__type__12830___24t(V_24Y)
    <=> t(V_24Y,c_24__type__12830) ) ).

fof('$tdef_$_type_28720',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y] :
      ( c_24__type__28720___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y)
    <=> t(V_24Y,c_24__type__28720___24a22(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22)) ) ).

fof('$tdef_Coq.Bool.Bool.reflect',axiom,
    ! [V_24X1,V_24X2,V_24Y] :
      ( cCoq_2eBool_2eBool_2ereflect___24t(V_24X1,V_24X2,V_24Y)
    <=> t(V_24Y,cCoq_2eBool_2eBool_2ereflect___24a2(V_24X1,V_24X2)) ) ).

fof('$tdef_$_type_860',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24Y] :
      ( c_24__type__860___24t(V_24X1,V_24X2,V_24X3,V_24Y)
    <=> t(V_24Y,c_24__type__860___24a3(V_24X1,V_24X2,V_24X3)) ) ).

fof('$tdef_$_type_18737',axiom,
    ! [V_24X1,V_24X2,V_24Y] :
      ( c_24__type__18737___24t(V_24X1,V_24X2,V_24Y)
    <=> t(V_24Y,c_24__type__18737___24a2(V_24X1,V_24X2)) ) ).

fof('$tdef_Coq.setoid_ring.Ring_polynom.Pol',axiom,
    ! [V_24X1,V_24Y] :
      ( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V_24X1,V_24Y)
    <=> t(V_24Y,cCoq_2esetoid__ring_2eRing__polynom_2ePol___24a1(V_24X1)) ) ).

fof('$tdef_$_type_36642',axiom,
    ! [V_24Y] :
      ( c_24__type__36642___24t(V_24Y)
    <=> t(V_24Y,c_24__type__36642) ) ).

fof('$tdef_$_type_18814',axiom,
    ! [V_24X1,V_24X2,V_24Y] :
      ( c_24__type__18814___24t(V_24X1,V_24X2,V_24Y)
    <=> t(V_24Y,c_24__type__18814___24a2(V_24X1,V_24X2)) ) ).

fof('$tdef_$_type_10870',axiom,
    ! [V_24Y] :
      ( c_24__type__10870___24t(V_24Y)
    <=> t(V_24Y,c_24__type__10870) ) ).

fof('$tdef_$_type_32811',axiom,
    ! [V_24Y] :
      ( c_24__type__32811___24t(V_24Y)
    <=> t(V_24Y,c_24__type__32811) ) ).

fof('$tdef_$_type_30788',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
      ( c_24__type__30788___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
    <=> t(V_24Y,c_24__type__30788___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).

fof('$tdef_$_type_1919',axiom,
    ! [V_24Y] :
      ( c_24__type__1919___24t(V_24Y)
    <=> t(V_24Y,c_24__type__1919) ) ).

fof('$tdef_$_type_13606',axiom,
    ! [V_24Y] :
      ( c_24__type__13606___24t(V_24Y)
    <=> t(V_24Y,c_24__type__13606) ) ).

fof('$tdef_$_type_36702',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
      ( c_24__type__36702___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
    <=> t(V_24Y,c_24__type__36702___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).

fof('$tdef_$_type_2083',axiom,
    ! [V_24Y] :
      ( c_24__type__2083___24t(V_24Y)
    <=> t(V_24Y,c_24__type__2083) ) ).

fof('$tdef_$_type_30348',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
      ( c_24__type__30348___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
    <=> t(V_24Y,c_24__type__30348___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).

fof('$tdef_$_type_30737',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
      ( c_24__type__30737___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
    <=> t(V_24Y,c_24__type__30737___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).

fof('$tdef_Coq.Numbers.BinNums.Z',axiom,
    ! [V_24Y] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V_24Y)
    <=> t(V_24Y,cCoq_2eNumbers_2eBinNums_2eZ) ) ).

fof('$tdef_$_type_20840',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y] :
      ( c_24__type__20840___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y)
    <=> t(V_24Y,c_24__type__20840___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).

fof('$tdef_$_type_27382',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y] :
      ( c_24__type__27382___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y)
    <=> t(V_24Y,c_24__type__27382___24a22(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22)) ) ).

fof('$tdef_$_type_30102',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
      ( c_24__type__30102___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y)
    <=> t(V_24Y,c_24__type__30102___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).

fof('$tdef_Coq.QArith.QArith_base.Q',axiom,
    ! [V_24Y] :
      ( cCoq_2eQArith_2eQArith__base_2eQ___24t(V_24Y)
    <=> t(V_24Y,cCoq_2eQArith_2eQArith__base_2eQ) ) ).

fof('$tdef_$_type_812',axiom,
    ! [V_24X1,V_24Y] :
      ( c_24__type__812___24t(V_24X1,V_24Y)
    <=> t(V_24Y,c_24__type__812___24a1(V_24X1)) ) ).

fof('$tdef_$_type_2249',axiom,
    ! [V_24Y] :
      ( c_24__type__2249___24t(V_24Y)
    <=> t(V_24Y,c_24__type__2249) ) ).

fof('$tdef_$_type_1826',axiom,
    ! [V_24Y] :
      ( c_24__type__1826___24t(V_24Y)
    <=> t(V_24Y,c_24__type__1826) ) ).

fof('$tdef_Coq.PArith.BinPos.Pos.PeanoView',axiom,
    ! [V_24X1,V_24Y] :
      ( cCoq_2ePArith_2eBinPos_2ePos_2ePeanoView___24t(V_24X1,V_24Y)
    <=> t(V_24Y,cCoq_2ePArith_2eBinPos_2ePos_2ePeanoView___24a1(V_24X1)) ) ).

fof('$tdef_Coq.Numbers.BinNums.positive',axiom,
    ! [V_24Y] :
      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V_24Y)
    <=> t(V_24Y,cCoq_2eNumbers_2eBinNums_2epositive) ) ).

fof('$tdef_$_type_29702',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
      ( c_24__type__29702___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y)
    <=> t(V_24Y,c_24__type__29702___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).

fof('$tdef_Coq.Init.Datatypes.nat',axiom,
    ! [V_24Y] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(V_24Y)
    <=> t(V_24Y,cCoq_2eInit_2eDatatypes_2enat) ) ).

fof('$tdef_$_type_1020',axiom,
    ! [V_24Y] :
      ( c_24__type__1020___24t(V_24Y)
    <=> t(V_24Y,c_24__type__1020) ) ).

fof('$tdef_$_type_914',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24Y] :
      ( c_24__type__914___24t(V_24X1,V_24X2,V_24X3,V_24Y)
    <=> t(V_24Y,c_24__type__914___24a3(V_24X1,V_24X2,V_24X3)) ) ).

fof('$tdef_$_type_19168',axiom,
    ! [V_24Y] :
      ( c_24__type__19168___24t(V_24Y)
    <=> t(V_24Y,c_24__type__19168) ) ).

fof('$tdef_$_type_988',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24Y] :
      ( c_24__type__988___24t(V_24X1,V_24X2,V_24X3,V_24Y)
    <=> t(V_24Y,c_24__type__988___24a3(V_24X1,V_24X2,V_24X3)) ) ).

fof('$tdef_$_type_2064',axiom,
    ! [V_24Y] :
      ( c_24__type__2064___24t(V_24Y)
    <=> t(V_24Y,c_24__type__2064) ) ).

fof('$tdef_Coq.Structures.OrderedTypeEx.Z_as_OT.t',axiom,
    ! [V_24Y] :
      ( cCoq_2eStructures_2eOrderedTypeEx_2eZ__as__OT_2et___24t(V_24Y)
    <=> t(V_24Y,cCoq_2eStructures_2eOrderedTypeEx_2eZ__as__OT_2et) ) ).

fof('$tdef_$_type_33574',axiom,
    ! [V_24Y] :
      ( c_24__type__33574___24t(V_24Y)
    <=> t(V_24Y,c_24__type__33574) ) ).

fof('$tdef_$_type_17977',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y] :
      ( c_24__type__17977___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y)
    <=> t(V_24Y,c_24__type__17977___24a17(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17)) ) ).

fof('$tdef_$_type_14028',axiom,
    ! [V_24Y] :
      ( c_24__type__14028___24t(V_24Y)
    <=> t(V_24Y,c_24__type__14028) ) ).

fof('$tdef_$_type_20572',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y] :
      ( c_24__type__20572___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y)
    <=> t(V_24Y,c_24__type__20572___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).

fof('$tdef_Coq.Init.Datatypes.prod',axiom,
    ! [V_24X1,V_24X2,V_24Y] :
      ( cCoq_2eInit_2eDatatypes_2eprod___24t(V_24X1,V_24X2,V_24Y)
    <=> t(V_24Y,cCoq_2eInit_2eDatatypes_2eprod___24a2(V_24X1,V_24X2)) ) ).

fof('$tdef_$_type_20100',axiom,
    ! [V_24Y] :
      ( c_24__type__20100___24t(V_24Y)
    <=> t(V_24Y,c_24__type__20100) ) ).

fof('$tdef_$_type_18741',axiom,
    ! [V_24Y] :
      ( c_24__type__18741___24t(V_24Y)
    <=> t(V_24Y,c_24__type__18741) ) ).

fof('$tdef_$_type_31669',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24Y] :
      ( c_24__type__31669___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24Y)
    <=> t(V_24Y,c_24__type__31669___24a13(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13)) ) ).

fof('$tdef_$_type_19986',axiom,
    ! [V_24X1,V_24Y] :
      ( c_24__type__19986___24t(V_24X1,V_24Y)
    <=> t(V_24Y,c_24__type__19986___24a1(V_24X1)) ) ).

fof('$tdef_Coq.setoid_ring.Ring_polynom.PExpr',axiom,
    ! [V_24X1,V_24Y] :
      ( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V_24X1,V_24Y)
    <=> t(V_24Y,cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V_24X1)) ) ).

fof('$tdef_$_type_554',axiom,
    ! [V_24X1,V_24Y] :
      ( c_24__type__554___24t(V_24X1,V_24Y)
    <=> t(V_24Y,c_24__type__554___24a1(V_24X1)) ) ).

fof('$tdef_$_type_10793',axiom,
    ! [V_24Y] :
      ( c_24__type__10793___24t(V_24Y)
    <=> t(V_24Y,c_24__type__10793) ) ).

fof('$tdef_$_type_32430',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y] :
      ( c_24__type__32430___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y)
    <=> t(V_24Y,c_24__type__32430___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7)) ) ).

fof('$tdef_$_type_21240',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y] :
      ( c_24__type__21240___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y)
    <=> t(V_24Y,c_24__type__21240___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).

fof('$tdef_$_type_19715',axiom,
    ! [V_24Y] :
      ( c_24__type__19715___24t(V_24Y)
    <=> t(V_24Y,c_24__type__19715) ) ).

fof('$tdef_$_type_16309',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y] :
      ( c_24__type__16309___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y)
    <=> t(V_24Y,c_24__type__16309___24a17(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17)) ) ).

fof('$tdef_$_type_870',axiom,
    ! [V_24Y] :
      ( c_24__type__870___24t(V_24Y)
    <=> t(V_24Y,c_24__type__870) ) ).

fof('$tdef_Coq.setoid_ring.Ring_theory.ring_kind',axiom,
    ! [V_24Y] :
      ( cCoq_2esetoid__ring_2eRing__theory_2ering__kind___24t(V_24Y)
    <=> t(V_24Y,cCoq_2esetoid__ring_2eRing__theory_2ering__kind) ) ).

fof('$tdef_$_type_23032',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
      ( c_24__type__23032___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
    <=> t(V_24Y,c_24__type__23032___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).

fof('$tdef_$_type_48',axiom,
    ! [V_24Y] :
      ( c_24__type__48___24t(V_24Y)
    <=> t(V_24Y,c_24__type__48) ) ).

fof('$tdef_$_type_23142',axiom,
    ! [V_24Y] :
      ( c_24__type__23142___24t(V_24Y)
    <=> t(V_24Y,c_24__type__23142) ) ).

fof('$tdef_$_type_981',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24Y] :
      ( c_24__type__981___24t(V_24X1,V_24X2,V_24X3,V_24Y)
    <=> t(V_24Y,c_24__type__981___24a3(V_24X1,V_24X2,V_24X3)) ) ).

fof('$tdef_$_type_275',axiom,
    ! [V_24Y] :
      ( c_24__type__275___24t(V_24Y)
    <=> t(V_24Y,c_24__type__275) ) ).

fof('$tdef_$_type_13532',axiom,
    ! [V_24Y] :
      ( c_24__type__13532___24t(V_24Y)
    <=> t(V_24Y,c_24__type__13532) ) ).

fof('$tdef_$_type_1829',axiom,
    ! [V_24Y] :
      ( c_24__type__1829___24t(V_24Y)
    <=> t(V_24Y,c_24__type__1829) ) ).

fof('$tdef_$_type_31044',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24Y] :
      ( c_24__type__31044___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24Y)
    <=> t(V_24Y,c_24__type__31044___24a13(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13)) ) ).

fof('$tdef_Coq.Vectors.VectorDef.t',axiom,
    ! [V_24X1,V_24X2,V_24Y] :
      ( cCoq_2eVectors_2eVectorDef_2et___24t(V_24X1,V_24X2,V_24Y)
    <=> t(V_24Y,cCoq_2eVectors_2eVectorDef_2et___24a2(V_24X1,V_24X2)) ) ).

fof('$tdef_$_type_1181',axiom,
    ! [V_24Y] :
      ( c_24__type__1181___24t(V_24Y)
    <=> t(V_24Y,c_24__type__1181) ) ).

fof('$tdef_$_type_523',axiom,
    ! [V_24Y] :
      ( c_24__type__523___24t(V_24Y)
    <=> t(V_24Y,c_24__type__523) ) ).

fof('$tdef_$_type_14713',axiom,
    ! [V_24Y] :
      ( c_24__type__14713___24t(V_24Y)
    <=> t(V_24Y,c_24__type__14713) ) ).

fof('$tdef_$_type_14593',axiom,
    ! [V_24Y] :
      ( c_24__type__14593___24t(V_24Y)
    <=> t(V_24Y,c_24__type__14593) ) ).

fof('$tdef_$_type_30412',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
      ( c_24__type__30412___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
    <=> t(V_24Y,c_24__type__30412___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).

fof('$tdef_$_type_1848',axiom,
    ! [V_24Y] :
      ( c_24__type__1848___24t(V_24Y)
    <=> t(V_24Y,c_24__type__1848) ) ).

fof('$tdef_$_type_1786',axiom,
    ! [V_24Y] :
      ( c_24__type__1786___24t(V_24Y)
    <=> t(V_24Y,c_24__type__1786) ) ).

fof('$tdef_$_type_12966',axiom,
    ! [V_24Y] :
      ( c_24__type__12966___24t(V_24Y)
    <=> t(V_24Y,c_24__type__12966) ) ).

fof('$tdef_$_type_2277',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24Y] :
      ( c_24__type__2277___24t(V_24X1,V_24X2,V_24X3,V_24Y)
    <=> t(V_24Y,c_24__type__2277___24a3(V_24X1,V_24X2,V_24X3)) ) ).

fof('$tdef_Type',axiom,
    ! [V_24Y] :
      ( cType___24t(V_24Y)
    <=> t(V_24Y,cType) ) ).

fof('$tdef_$_type_20304',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y] :
      ( c_24__type__20304___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y)
    <=> t(V_24Y,c_24__type__20304___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).

fof('$tdef_Coq.PArith.BinPosDef.Pos.mask',axiom,
    ! [V_24Y] :
      ( cCoq_2ePArith_2eBinPosDef_2ePos_2emask___24t(V_24Y)
    <=> t(V_24Y,cCoq_2ePArith_2eBinPosDef_2ePos_2emask) ) ).

fof('$tdef_$_type_14611',axiom,
    ! [V_24Y] :
      ( c_24__type__14611___24t(V_24Y)
    <=> t(V_24Y,c_24__type__14611) ) ).

fof('$tdef_$_type_16930',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y] :
      ( c_24__type__16930___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y)
    <=> t(V_24Y,c_24__type__16930___24a17(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17)) ) ).

fof('$tdef_$_type_32478',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
      ( c_24__type__32478___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
    <=> t(V_24Y,c_24__type__32478___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).

fof('$tdef_$_type_25675',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y] :
      ( c_24__type__25675___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y)
    <=> t(V_24Y,c_24__type__25675___24a22(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22)) ) ).

fof('$tdef_$_type_33620',axiom,
    ! [V_24Y] :
      ( c_24__type__33620___24t(V_24Y)
    <=> t(V_24Y,c_24__type__33620) ) ).

fof('$tdef_$_type_1969',axiom,
    ! [V_24Y] :
      ( c_24__type__1969___24t(V_24Y)
    <=> t(V_24Y,c_24__type__1969) ) ).

fof('$tdef_$_type_32716',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24Y] :
      ( c_24__type__32716___24t(V_24X1,V_24X2,V_24X3,V_24Y)
    <=> t(V_24Y,c_24__type__32716___24a3(V_24X1,V_24X2,V_24X3)) ) ).

fof('$tdef_Coq.Vectors.Fin.t',axiom,
    ! [V_24X1,V_24Y] :
      ( cCoq_2eVectors_2eFin_2et___24t(V_24X1,V_24Y)
    <=> t(V_24Y,cCoq_2eVectors_2eFin_2et___24a1(V_24X1)) ) ).

fof('$tdef_Coq.Reals.RIneq.nonzeroreal',axiom,
    ! [V_24Y] :
      ( cCoq_2eReals_2eRIneq_2enonzeroreal___24t(V_24Y)
    <=> t(V_24Y,cCoq_2eReals_2eRIneq_2enonzeroreal) ) ).

fof('$tdef_$_type_995',axiom,
    ! [V_24Y] :
      ( c_24__type__995___24t(V_24Y)
    <=> t(V_24Y,c_24__type__995) ) ).

fof('$tdef_$_type_430',axiom,
    ! [V_24Y] :
      ( c_24__type__430___24t(V_24Y)
    <=> t(V_24Y,c_24__type__430) ) ).

fof('$tdef_$_type_1901',axiom,
    ! [V_24Y] :
      ( c_24__type__1901___24t(V_24Y)
    <=> t(V_24Y,c_24__type__1901) ) ).

fof('$tdef_$_type_13463',axiom,
    ! [V_24Y] :
      ( c_24__type__13463___24t(V_24Y)
    <=> t(V_24Y,c_24__type__13463) ) ).

fof('$tdef_$_type_31780',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24Y] :
      ( c_24__type__31780___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24Y)
    <=> t(V_24Y,c_24__type__31780___24a13(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13)) ) ).

fof('$tdef_$_type_33261',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24Y] :
      ( c_24__type__33261___24t(V_24X1,V_24X2,V_24X3,V_24Y)
    <=> t(V_24Y,c_24__type__33261___24a3(V_24X1,V_24X2,V_24X3)) ) ).

fof('$tdef_$_type_2285',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24Y] :
      ( c_24__type__2285___24t(V_24X1,V_24X2,V_24X3,V_24Y)
    <=> t(V_24Y,c_24__type__2285___24a3(V_24X1,V_24X2,V_24X3)) ) ).

fof('$tdef_$_type_25',axiom,
    ! [V_24Y] :
      ( c_24__type__25___24t(V_24Y)
    <=> t(V_24Y,c_24__type__25) ) ).

fof('$tdef_$_type_15506',axiom,
    ! [V_24Y] :
      ( c_24__type__15506___24t(V_24Y)
    <=> t(V_24Y,c_24__type__15506) ) ).

fof('$tdef_$_type_10909',axiom,
    ! [V_24Y] :
      ( c_24__type__10909___24t(V_24Y)
    <=> t(V_24Y,c_24__type__10909) ) ).

fof('$tdef_$_type_1805',axiom,
    ! [V_24X1,V_24X2,V_24Y] :
      ( c_24__type__1805___24t(V_24X1,V_24X2,V_24Y)
    <=> t(V_24Y,c_24__type__1805___24a2(V_24X1,V_24X2)) ) ).

fof('$tdef_$_type_18415',axiom,
    ! [V_24X1,V_24X2,V_24Y] :
      ( c_24__type__18415___24t(V_24X1,V_24X2,V_24Y)
    <=> t(V_24Y,c_24__type__18415___24a2(V_24X1,V_24X2)) ) ).

fof('$tdef_$_type_27728',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y] :
      ( c_24__type__27728___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y)
    <=> t(V_24Y,c_24__type__27728___24a22(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22)) ) ).

fof('$tdef_$_type_14105',axiom,
    ! [V_24Y] :
      ( c_24__type__14105___24t(V_24Y)
    <=> t(V_24Y,c_24__type__14105) ) ).

fof('$tdef_$_type_593',axiom,
    ! [V_24Y] :
      ( c_24__type__593___24t(V_24Y)
    <=> t(V_24Y,c_24__type__593) ) ).

fof('$tdef_$_type_10874',axiom,
    ! [V_24X1,V_24X2,V_24Y] :
      ( c_24__type__10874___24t(V_24X1,V_24X2,V_24Y)
    <=> t(V_24Y,c_24__type__10874___24a2(V_24X1,V_24X2)) ) ).

fof('$tdef_$_type_31544',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24Y] :
      ( c_24__type__31544___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24Y)
    <=> t(V_24Y,c_24__type__31544___24a13(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13)) ) ).

fof('$tdef_$_type_441',axiom,
    ! [V_24Y] :
      ( c_24__type__441___24t(V_24Y)
    <=> t(V_24Y,c_24__type__441) ) ).

fof('$tdef_$_type_19382',axiom,
    ! [V_24Y] :
      ( c_24__type__19382___24t(V_24Y)
    <=> t(V_24Y,c_24__type__19382) ) ).

fof('$tdef_$_type_19093',axiom,
    ! [V_24Y] :
      ( c_24__type__19093___24t(V_24Y)
    <=> t(V_24Y,c_24__type__19093) ) ).

fof('$tdef_$_type_28920',axiom,
    ! [V_24Y] :
      ( c_24__type__28920___24t(V_24Y)
    <=> t(V_24Y,c_24__type__28920) ) ).

fof('$tdef_$_type_13551',axiom,
    ! [V_24Y] :
      ( c_24__type__13551___24t(V_24Y)
    <=> t(V_24Y,c_24__type__13551) ) ).

fof('$tdef_$_type_30680',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
      ( c_24__type__30680___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
    <=> t(V_24Y,c_24__type__30680___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).

fof('$tdef_$_type_21590',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y] :
      ( c_24__type__21590___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y)
    <=> t(V_24Y,c_24__type__21590___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).

fof('$tdef_$_type_926',axiom,
    ! [V_24Y] :
      ( c_24__type__926___24t(V_24Y)
    <=> t(V_24Y,c_24__type__926) ) ).

fof('$tdef_$_type_2656',axiom,
    ! [V_24Y] :
      ( c_24__type__2656___24t(V_24Y)
    <=> t(V_24Y,c_24__type__2656) ) ).

fof('$tdef_$_type_2438',axiom,
    ! [V_24Y] :
      ( c_24__type__2438___24t(V_24Y)
    <=> t(V_24Y,c_24__type__2438) ) ).

fof('$tdef_$_type_1705',axiom,
    ! [V_24X1,V_24X2,V_24Y] :
      ( c_24__type__1705___24t(V_24X1,V_24X2,V_24Y)
    <=> t(V_24Y,c_24__type__1705___24a2(V_24X1,V_24X2)) ) ).

fof('$tdef_$_type_30371',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
      ( c_24__type__30371___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
    <=> t(V_24Y,c_24__type__30371___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).

fof('$tdef_$_type_17782',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y] :
      ( c_24__type__17782___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y)
    <=> t(V_24Y,c_24__type__17782___24a17(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17)) ) ).

fof('_HAMMER_GOAL',conjecture,
    ! [V0__m] :
      ( cIntMap_2eMap_2eMap___24t(cA,V0__m)
     => ! [V1__m_27] :
          ( cIntMap_2eMap_2eMap___24t(cB,V1__m_27)
         => ( cIntMap_2eMapcanon_2emapcanon___24a2(cA,V0__m)
           => V0__m = cIntMap_2eMap_2eMapMerge___24a3(cA,cIntMap_2eFset_2eMapDomRestrBy___24a4(cA,cB,V0__m,V1__m_27),cIntMap_2eFset_2eMapDomRestrTo___24a4(cA,cB,V0__m,V1__m_27)) ) ) ) ).

%------------------------------------------------------------------------------