TPTP Problem File: SEV647+1.p

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%------------------------------------------------------------------------------
% File     : SEV647+1 : TPTP v9.3.1. Released v9.3.0.
% Domain   : Set theory
% Problem  : CoqHammer - Mapcanon MapDomRestrTo canon
% 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    : Mapcanon.MapDomRestrTo.canon.p [Kal26]

% Status   : Unknown
% Rating   : 1.00 v9.3.0
% Syntax   : Number of formulae    : 3001 (1263 unt;   0 def)
%            Number of atoms       : 9669 (2820 equ)
%            Maximal formula atoms :  257 (   3 avg)
%            Number of connectives : 6738 (  70   ~; 698   |;1593   &)
%                                         (1034 <=>;3343  =>;   0  <=;   0 <~>)
%            Maximal formula depth :  258 (   6 avg)
%            Maximal term depth    :   23 (   1 avg)
%            Number of predicates  :  558 ( 557 usr;   0 prp; 1-23 aty)
%            Number of functors    : 1792 (1792 usr;1102 con; 0-22 aty)
%            Number of variables   : 10068 (9431   !; 637   ?)
% SPC      : FOF_UNK_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$1167',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_241167___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_241167___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$1173',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_241173___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_241173___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$1210',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_241210___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__1200__1203___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_241210___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__1200__1203___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.bool$1232',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_241232___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_241232___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = Vv__CANONICAL__3 ) ) ) ) ).

fof('$_case_Coq.Init.Datatypes.bool$1238',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_241238___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_241238___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$1244',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_241244___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_241244___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$1250',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_241250___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_241250___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$1360',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_241360___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_241360___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$76528',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_2476528___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_2476528___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = Vv__CANONICAL__1 ) ) ) ) ).

fof('$_case_Coq.Init.Datatypes.list$97885',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5] :
      ( cType___24t(Vv__CANONICAL__0)
     => ( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
       => ( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__5)
         => ( ( c_24__case__Coq_2eInit_2eDatatypes_2elist_2497972___24a3(Vv__CANONICAL__0,Vv__CANONICAL__4,Vv__CANONICAL__5) = cCoq_2eInit_2eDatatypes_2enil___24a1(Vv__CANONICAL__0)
              & c_24__case__Coq_2eInit_2eDatatypes_2elist_2497885___24a6(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5) = cCoq_2eInit_2eDatatypes_2econs___24a3(Vv__CANONICAL__0,Vv__CANONICAL__3,cCoq_2eInit_2eDatatypes_2enil___24a1(Vv__CANONICAL__0)) )
            | ? [Vvar__1___24Anonymous__97889] :
                ( t(Vvar__1___24Anonymous__97889,Vv__CANONICAL__0)
                & ? [Vvar__2___24Anonymous__97890] :
                    ( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vvar__2___24Anonymous__97890)
                    & c_24__case__Coq_2eInit_2eDatatypes_2elist_2497972___24a3(Vv__CANONICAL__0,Vv__CANONICAL__4,Vv__CANONICAL__5) = cCoq_2eInit_2eDatatypes_2econs___24a3(Vv__CANONICAL__0,Vvar__1___24Anonymous__97889,Vvar__2___24Anonymous__97890)
                    & c_24__case__Coq_2eInit_2eDatatypes_2elist_2497885___24a6(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5) = cCoq_2eInit_2eDatatypes_2econs___24a3(Vv__CANONICAL__0,Vvar__1___24Anonymous__97889,c_24__fix__98017__v__CANONICAL__1___24a3(Vv__CANONICAL__0,Vvar__2___24Anonymous__97890,cCoq_2eInit_2eDatatypes_2econs___24a3(Vv__CANONICAL__0,Vv__CANONICAL__3,cCoq_2eInit_2eDatatypes_2enil___24a1(Vv__CANONICAL__0)))) ) ) ) ) ) ) ).

fof('$_case_Coq.Init.Datatypes.list$97972',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] :
      ( cType___24t(Vv__CANONICAL__0)
     => ( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
       => ( ( Vv__CANONICAL__2 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vv__CANONICAL__0)
            & c_24__case__Coq_2eInit_2eDatatypes_2elist_2497972___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = cCoq_2eInit_2eDatatypes_2econs___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,cCoq_2eInit_2eDatatypes_2enil___24a1(Vv__CANONICAL__0)) )
          | ? [Vvar__1___24Anonymous__97976] :
              ( t(Vvar__1___24Anonymous__97976,Vv__CANONICAL__0)
              & ? [Vvar__2___24Anonymous__97977] :
                  ( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vvar__2___24Anonymous__97977)
                  & Vv__CANONICAL__2 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vv__CANONICAL__0,Vvar__1___24Anonymous__97976,Vvar__2___24Anonymous__97977)
                  & c_24__case__Coq_2eInit_2eDatatypes_2elist_2497972___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = cCoq_2eInit_2eDatatypes_2econs___24a3(Vv__CANONICAL__0,Vvar__1___24Anonymous__97976,c_24__fix__98017__v__CANONICAL__1___24a3(Vv__CANONICAL__0,Vvar__2___24Anonymous__97977,cCoq_2eInit_2eDatatypes_2econs___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,cCoq_2eInit_2eDatatypes_2enil___24a1(Vv__CANONICAL__0)))) ) ) ) ) ) ).

fof('$_case_Coq.Init.Datatypes.nat$98139',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_2498139___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = cCoq_2eNumbers_2eBinNums_2eZ0 )
        | ? [Vvar__0___24Anonymous__98140] :
            ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__98140)
            & Vv__CANONICAL__2 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__98140)
            & c_24__case__Coq_2eInit_2eDatatypes_2enat_2498139___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__98140)) ) ) ) ).

fof('$_case_Coq.Init.Datatypes.nat$98161',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_2498161___24a1(Vv__CANONICAL__0) = cCoq_2eNumbers_2eBinNums_2eZ0 )
        | ? [Vvar__0___24Anonymous__98162] :
            ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__98162)
            & Vv__CANONICAL__0 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__98162)
            & c_24__case__Coq_2eInit_2eDatatypes_2enat_2498161___24a1(Vv__CANONICAL__0) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eof__succ__nat___24a1(Vvar__0___24Anonymous__98162)) ) ) ) ).

fof('$_case_Coq.Init.Datatypes.option$76560',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__76563] :
                ( t(Vvar__1___24Anonymous__76563,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__76563)
                & c_24__case__Coq_2eInit_2eDatatypes_2eoption_2476560___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = cCoq_2eInit_2eDatatypes_2eSome___24a2(Vv__CANONICAL__0,Vvar__1___24Anonymous__76563) )
            | ( 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_2476560___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$77526',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__77529] :
                ( t(Vvar__1___24Anonymous__77529,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__77529)
                & c_24__case__Coq_2eInit_2eDatatypes_2eoption_2477526___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = cCoq_2eInit_2eDatatypes_2eSome___24a2(Vv__CANONICAL__0,Vvar__1___24Anonymous__77529) )
            | ( 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_2477526___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.Init.Datatypes.prod$104828',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] :
      ( cType___24t(Vv__CANONICAL__0)
     => ( cType___24t(Vv__CANONICAL__2)
       => ( c_24__type__104841___24t(Vv__CANONICAL__0,Vv__CANONICAL__2,Vv__CANONICAL__6)
         => ( t(Vv__CANONICAL__7,Vv__CANONICAL__2)
           => ( t(Vv__CANONICAL__8,Vv__CANONICAL__2)
             => ? [Vvar__2___24Anonymous__104833] :
                  ( t(Vvar__2___24Anonymous__104833,Vv__CANONICAL__2)
                  & ? [Vvar__3___24Anonymous__104834] :
                      ( t(Vvar__3___24Anonymous__104834,Vv__CANONICAL__2)
                      & happ(happ(Vv__CANONICAL__6,Vv__CANONICAL__7),Vv__CANONICAL__8) = cCoq_2eInit_2eDatatypes_2epair___24a4(Vv__CANONICAL__2,Vv__CANONICAL__2,Vvar__2___24Anonymous__104833,Vvar__3___24Anonymous__104834)
                      & ( c_24__case__Coq_2eInit_2eDatatypes_2eprod_24104828___24a9(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)
                      <=> p(happ(happ(Vv__CANONICAL__1,happ(Vv__CANONICAL__5,Vv__CANONICAL__7)),happ(Vv__CANONICAL__5,happ(happ(Vv__CANONICAL__3,happ(happ(Vv__CANONICAL__4,Vv__CANONICAL__8),Vvar__2___24Anonymous__104833)),Vvar__3___24Anonymous__104834)))) ) ) ) ) ) ) ) ) ).

fof('$_case_Coq.Numbers.BinNums.Z$98156',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_2498161___24a1(Vv__CANONICAL__2) = cCoq_2eNumbers_2eBinNums_2eZ0
          & c_24__case__Coq_2eNumbers_2eBinNums_2eZ_2498156___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = cCoq_2eNumbers_2eBinNums_2eZ0 )
        | ? [Vvar__0___24Anonymous__98157] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__98157)
            & c_24__case__Coq_2eInit_2eDatatypes_2enat_2498161___24a1(Vv__CANONICAL__2) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__98157)
            & c_24__case__Coq_2eNumbers_2eBinNums_2eZ_2498156___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__98157) )
        | ? [Vvar__0___24Anonymous__98158] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__98158)
            & c_24__case__Coq_2eInit_2eDatatypes_2enat_2498161___24a1(Vv__CANONICAL__2) = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__98158)
            & c_24__case__Coq_2eNumbers_2eBinNums_2eZ_2498156___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__98158) ) ) ) ).

fof('$_case_Coq.Numbers.BinNums.positive$105648',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1] :
      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__1)
     => ( ? [Vvar__0___24Anonymous__105649] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__105649)
            & Vv__CANONICAL__1 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__105649)
            & c_24__case__Coq_2eNumbers_2eBinNums_2epositive_24105648___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = cCoq_2eNumbers_2eBinNums_2exO___24a1(c_24__fix__105664__v__CANONICAL__0___24a1(Vvar__0___24Anonymous__105649)) )
        | ? [Vvar__0___24Anonymous__105656] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__105656)
            & Vv__CANONICAL__1 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__105656)
            & c_24__case__Coq_2eNumbers_2eBinNums_2epositive_24105648___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__105656) )
        | ( Vv__CANONICAL__1 = cCoq_2eNumbers_2eBinNums_2exH
          & c_24__case__Coq_2eNumbers_2eBinNums_2epositive_24105648___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2eNumbers_2eBinNums_2exH) ) ) ) ).

fof('$_def_$_let_var_6_p_86189_86192',axiom,
    ! [V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__86188] : c_24__let__var__6__p__86189__86192___24a4(V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__86188) = cCoq_2esetoid__ring_2eRing__theory_2epow__pos___24a4(V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__86188) ).

fof('$_def_$_let_var_6_p_86191_86193',axiom,
    ! [V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__86190] : c_24__let__var__6__p__86191__86193___24a4(V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__86190) = cCoq_2esetoid__ring_2eRing__theory_2epow__pos___24a4(V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__86190) ).

fof('$_def_$_let_var_8_m_1200_1203',axiom,
    ! [V0__A,V2__a,V3__y,V4__a_27,V5__y_27,Vvar__0___24Anonymous__1198] : c_24__let__var__8__m__1200__1203___24a6(V0__A,V2__a,V3__y,V4__a_27,V5__y_27,Vvar__0___24Anonymous__1198) = 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__1198) ).

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__80499] :
                  ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__80499)
                  & V2__m = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__80499)
                  & ( cCoq_2eArith_2eEqNat_2eeq__nat___24a2(V1__n,V2__m)
                  <=> p(c_24False) ) ) ) ) )
        | ? [Vvar__0___24Anonymous__80500] :
            ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__80500)
            & ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__m)
             => ( V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__80500)
                & ( ( V2__m = cCoq_2eInit_2eDatatypes_2eO
                    & ( cCoq_2eArith_2eEqNat_2eeq__nat___24a2(V1__n,V2__m)
                    <=> p(c_24False) ) )
                  | ? [Vvar__0___24Anonymous__80503] :
                      ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__80503)
                      & V2__m = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__80503)
                      & ( cCoq_2eArith_2eEqNat_2eeq__nat___24a2(V1__n,V2__m)
                      <=> cCoq_2eArith_2eEqNat_2eeq__nat___24a2(Vvar__0___24Anonymous__80500,Vvar__0___24Anonymous__80503) ) ) ) ) ) ) ) ) ).

fof('$_def_Coq.Arith.PeanoNat.Nat.eq',axiom,
    cCoq_2eArith_2ePeanoNat_2eNat_2eeq = c_3d___24a1(cCoq_2eInit_2eDatatypes_2enat) ).

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',axiom,
    cCoq_2eArith_2ePeanoNat_2eNat_2ele = cCoq_2eInit_2ePeano_2ele ).

fof('$_def_Coq.Arith.PeanoNat.Nat.lt',axiom,
    cCoq_2eArith_2ePeanoNat_2eNat_2elt = cCoq_2eInit_2ePeano_2elt ).

fof('$_def_Coq.Arith.PeanoNat.Nat.recursion',axiom,
    ! [V0__A] : cCoq_2eArith_2ePeanoNat_2eNat_2erecursion___24a1(V0__A) = cCoq_2eInit_2eDatatypes_2enat__rect___24a1(c_24__lam__105565___24a1(V0__A)) ).

fof('$_def_Coq.Arith.Plus.tail_plus',axiom,
    ! [V1__n,V2__m] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
     => ( ( V1__n = cCoq_2eInit_2eDatatypes_2eO
          & cCoq_2eArith_2ePlus_2etail__plus___24a2(V1__n,V2__m) = V2__m )
        | ? [Vvar__0___24Anonymous__97174] :
            ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__97174)
            & V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__97174)
            & cCoq_2eArith_2ePlus_2etail__plus___24a2(V1__n,V2__m) = cCoq_2eArith_2ePlus_2etail__plus___24a2(Vvar__0___24Anonymous__97174,cCoq_2eInit_2eDatatypes_2eS___24a1(V2__m)) ) ) ) ).

fof('$_def_Coq.Arith.Wf_nat.ltof',axiom,
    ! [V0__A,V1__f,V2__a,V3__b] :
      ( cCoq_2eArith_2eWf__nat_2eltof___24a4(V0__A,V1__f,V2__a,V3__b)
    <=> cCoq_2eInit_2ePeano_2elt___24a2(happ(V1__f,V2__a),happ(V1__f,V3__b)) ) ).

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.ifb',axiom,
    ! [V0__b1,V1__b2,V2__b3] :
      ( cCoq_2eInit_2eDatatypes_2ebool___24t(V0__b1)
     => ( ( V0__b1 = cCoq_2eInit_2eDatatypes_2etrue
          & cCoq_2eBool_2eBool_2eifb___24a3(V0__b1,V1__b2,V2__b3) = V1__b2 )
        | ( V0__b1 = cCoq_2eInit_2eDatatypes_2efalse
          & cCoq_2eBool_2eBool_2eifb___24a3(V0__b1,V1__b2,V2__b3) = V2__b3 ) ) ) ).

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__1430,c_24__prop__1431,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__1432,c_24__prop__1433,cCoq_2eInit_2eLogic_2eeq__refl___24a2(cCoq_2eInit_2eDatatypes_2ebool,cCoq_2eInit_2eDatatypes_2efalse)) ) ) ) ).

fof('$_def_Coq.FSets.FSetPositive.PositiveSet.elt',axiom,
    ! [Vvar__82488] :
      ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(Vvar__82488)
    <=> cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__82488) ) ).

fof('$_def_Coq.FSets.FSetPositive.PositiveSet.eq',axiom,
    cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eeq = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eEqual ).

fof('$_def_Coq.FSets.FSetPositive.PositiveSet.t',axiom,
    ! [Vvar__82489] :
      ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(Vvar__82489)
    <=> cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree___24t(Vvar__82489) ) ).

fof('$_def_Coq.Init.Byte.byte_of_byte',axiom,
    ! [V0__b] : cCoq_2eInit_2eByte_2ebyte__of__byte___24a1(V0__b) = V0__b ).

fof('$_def_Coq.Init.Datatypes.ID',axiom,
    ! [Vvar__94200] :
      ( cCoq_2eInit_2eDatatypes_2eID___24t(Vvar__94200)
    <=> ! [V0__A] :
          ( cType___24t(V0__A)
         => ! [V1___24Anonymous] :
              ( t(V1___24Anonymous,V0__A)
             => t(happ(happ(Vvar__94200,V0__A),V1___24Anonymous),V0__A) ) ) ) ).

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__94186] :
              ( t(Vvar__1___24Anonymous__94186,V0__A)
              & ? [Vvar__2___24Anonymous__94187] :
                  ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__94187)
                  & V2__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__94186,Vvar__2___24Anonymous__94187)
                  & cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V2__l,V3__m) = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__94186,cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,Vvar__2___24Anonymous__94187,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__75622] :
              ( t(Vvar__2___24Anonymous__75622,V0__A)
              & ? [Vvar__3___24Anonymous__75623] :
                  ( t(Vvar__3___24Anonymous__75623,V1__B)
                  & V2__p = cCoq_2eInit_2eDatatypes_2epair___24a4(V0__A,V1__B,Vvar__2___24Anonymous__75622,Vvar__3___24Anonymous__75623)
                  & cCoq_2eInit_2eDatatypes_2efst___24a3(V0__A,V1__B,V2__p) = Vvar__2___24Anonymous__75622 ) ) ) ) ) ).

fof('$_def_Coq.Init.Datatypes.implb',axiom,
    ! [V0__b1,V1__b2] :
      ( cCoq_2eInit_2eDatatypes_2ebool___24t(V0__b1)
     => ( ( V0__b1 = cCoq_2eInit_2eDatatypes_2etrue
          & cCoq_2eInit_2eDatatypes_2eimplb___24a2(V0__b1,V1__b2) = V1__b2 )
        | ( V0__b1 = cCoq_2eInit_2eDatatypes_2efalse
          & cCoq_2eInit_2eDatatypes_2eimplb___24a2(V0__b1,V1__b2) = 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__67046] :
              ( t(Vvar__1___24Anonymous__67046,V0__A)
              & ? [Vvar__2___24Anonymous__67047] :
                  ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__67047)
                  & V2__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__67046,Vvar__2___24Anonymous__67047)
                  & cCoq_2eInit_2eDatatypes_2elength___24a2(V0__A,V2__l) = cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2elength___24a2(V0__A,Vvar__2___24Anonymous__67047)) ) ) ) ) ) ).

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__75574___24t(V0__A,V1__B,V2__P,V2__P)
         => ( cCoq_2eInit_2eDatatypes_2eprod___24t(V0__A,V1__B,V4__p)
           => ? [Vvar__2___24Anonymous__75567] :
                ( t(Vvar__2___24Anonymous__75567,V0__A)
                & ? [Vvar__3___24Anonymous__75568] :
                    ( t(Vvar__3___24Anonymous__75568,V1__B)
                    & V4__p = cCoq_2eInit_2eDatatypes_2epair___24a4(V0__A,V1__B,Vvar__2___24Anonymous__75567,Vvar__3___24Anonymous__75568)
                    & cCoq_2eInit_2eDatatypes_2eprod__rect___24a5(V0__A,V1__B,V2__P,V3__f,V4__p) = happ(happ(V3__f,Vvar__2___24Anonymous__75567),Vvar__3___24Anonymous__75568) ) ) ) ) ) ) ).

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__75634] :
              ( t(Vvar__2___24Anonymous__75634,V0__A)
              & ? [Vvar__3___24Anonymous__75635] :
                  ( t(Vvar__3___24Anonymous__75635,V1__B)
                  & V2__p = cCoq_2eInit_2eDatatypes_2epair___24a4(V0__A,V1__B,Vvar__2___24Anonymous__75634,Vvar__3___24Anonymous__75635)
                  & cCoq_2eInit_2eDatatypes_2esnd___24a3(V0__A,V1__B,V2__p) = Vvar__3___24Anonymous__75635 ) ) ) ) ) ).

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.Logic_Type.notT',axiom,
    ! [V0__A] :
      ( cCoq_2eInit_2eLogic__Type_2enotT___24a1(V0__A)
    <=> ! [V1___24Anonymous] :
          ( t(V1___24Anonymous,V0__A)
         => p(c_24False) ) ) ).

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__565] :
            ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__565)
            & V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__565)
            & cCoq_2eInit_2eNat_2eadd___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eNat_2eadd___24a2(Vvar__0___24Anonymous__565,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__77942] :
            ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__77942)
            & ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__77942)
             => ( V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__77942)
                & ( ( Vvar__0___24Anonymous__77942 = cCoq_2eInit_2eDatatypes_2eO
                    & cCoq_2eInit_2eNat_2ediv2___24a1(V1__n) = cCoq_2eInit_2eDatatypes_2eO )
                  | ? [Vvar__0___24Anonymous__77945] :
                      ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__77945)
                      & Vvar__0___24Anonymous__77942 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__77945)
                      & cCoq_2eInit_2eNat_2ediv2___24a1(V1__n) = cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eNat_2ediv2___24a1(Vvar__0___24Anonymous__77945)) ) ) ) ) ) ) ) ).

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.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__77889] :
            ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__77889)
            & ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__77889)
             => ( V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__77889)
                & ( ( Vvar__0___24Anonymous__77889 = cCoq_2eInit_2eDatatypes_2eO
                    & cCoq_2eInit_2eNat_2eeven___24a1(V1__n) = cCoq_2eInit_2eDatatypes_2efalse )
                  | ? [Vvar__0___24Anonymous__77892] :
                      ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__77892)
                      & Vvar__0___24Anonymous__77889 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__77892)
                      & cCoq_2eInit_2eNat_2eeven___24a1(V1__n) = cCoq_2eInit_2eNat_2eeven___24a1(Vvar__0___24Anonymous__77892) ) ) ) ) ) ) ) ).

fof('$_def_Coq.Init.Nat.leb',axiom,
    ! [V1__n,V2__m] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
     => ( ( V1__n = cCoq_2eInit_2eDatatypes_2eO
          & cCoq_2eInit_2eNat_2eleb___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2etrue )
        | ? [Vvar__0___24Anonymous__67478] :
            ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__67478)
            & ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__m)
             => ( V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__67478)
                & ( ( V2__m = cCoq_2eInit_2eDatatypes_2eO
                    & cCoq_2eInit_2eNat_2eleb___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2efalse )
                  | ? [Vvar__0___24Anonymous__67481] :
                      ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__67481)
                      & V2__m = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__67481)
                      & cCoq_2eInit_2eNat_2eleb___24a2(V1__n,V2__m) = cCoq_2eInit_2eNat_2eleb___24a2(Vvar__0___24Anonymous__67478,Vvar__0___24Anonymous__67481) ) ) ) ) ) ) ) ).

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__77883] :
            ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__77883)
            & ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__m)
             => ( V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__77883)
                & ( ( V2__m = cCoq_2eInit_2eDatatypes_2eO
                    & cCoq_2eInit_2eNat_2emax___24a2(V1__n,V2__m) = V1__n )
                  | ? [Vvar__0___24Anonymous__77886] :
                      ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__77886)
                      & V2__m = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__77886)
                      & cCoq_2eInit_2eNat_2emax___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eNat_2emax___24a2(Vvar__0___24Anonymous__77883,Vvar__0___24Anonymous__77886)) ) ) ) ) ) ) ) ).

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__80545] :
            ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__80545)
            & ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__m)
             => ( V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__80545)
                & ( ( V2__m = cCoq_2eInit_2eDatatypes_2eO
                    & cCoq_2eInit_2eNat_2emin___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2eO )
                  | ? [Vvar__0___24Anonymous__80548] :
                      ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__80548)
                      & V2__m = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__80548)
                      & cCoq_2eInit_2eNat_2emin___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eNat_2emin___24a2(Vvar__0___24Anonymous__80545,Vvar__0___24Anonymous__80548)) ) ) ) ) ) ) ) ).

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__67475] :
            ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__67475)
            & V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__67475)
            & cCoq_2eInit_2eNat_2emul___24a2(V1__n,V2__m) = cCoq_2eInit_2eNat_2eadd___24a2(V2__m,cCoq_2eInit_2eNat_2emul___24a2(Vvar__0___24Anonymous__67475,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__77896] :
            ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__77896)
            & V2__m = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__77896)
            & 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__77896)) ) ) ) ).

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__67473] :
            ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__67473)
            & V0__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__67473)
            & cCoq_2eInit_2eNat_2epred___24a1(V0__n) = Vvar__0___24Anonymous__67473 ) ) ) ).

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__77861] :
            ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__77861)
            & ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__m)
             => ( V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__77861)
                & ( ( V2__m = cCoq_2eInit_2eDatatypes_2eO
                    & cCoq_2eInit_2eNat_2esub___24a2(V1__n,V2__m) = V1__n )
                  | ? [Vvar__0___24Anonymous__77864] :
                      ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__77864)
                      & V2__m = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__77864)
                      & cCoq_2eInit_2eNat_2esub___24a2(V1__n,V2__m) = cCoq_2eInit_2eNat_2esub___24a2(Vvar__0___24Anonymous__77861,Vvar__0___24Anonymous__77864) ) ) ) ) ) ) ) ).

fof('$_def_Coq.Init.Nat.succ',axiom,
    cCoq_2eInit_2eNat_2esucc = cCoq_2eInit_2eDatatypes_2eS ).

fof('$_def_Coq.Init.Nat.t',axiom,
    ! [Vvar__96976] :
      ( cCoq_2eInit_2eNat_2et___24t(Vvar__96976)
    <=> cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__96976) ) ).

fof('$_def_Coq.Init.Nat.tail_add',axiom,
    ! [V1__n,V2__m] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
     => ( ( V1__n = cCoq_2eInit_2eDatatypes_2eO
          & cCoq_2eInit_2eNat_2etail__add___24a2(V1__n,V2__m) = V2__m )
        | ? [Vvar__0___24Anonymous__96978] :
            ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__96978)
            & V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__96978)
            & cCoq_2eInit_2eNat_2etail__add___24a2(V1__n,V2__m) = cCoq_2eInit_2eNat_2etail__add___24a2(Vvar__0___24Anonymous__96978,cCoq_2eInit_2eDatatypes_2eS___24a1(V2__m)) ) ) ) ).

fof('$_def_Coq.Init.Nat.zero',axiom,
    cCoq_2eInit_2eNat_2ezero = cCoq_2eInit_2eDatatypes_2eO ).

fof('$_def_Coq.Init.Peano.IsSucc',axiom,
    ! [V0__n] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
     => ( ( V0__n = cCoq_2eInit_2eDatatypes_2eO
          & ( cCoq_2eInit_2ePeano_2eIsSucc___24a1(V0__n)
          <=> p(c_24False) ) )
        | ? [Vvar__0___24Anonymous__97172] :
            ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__97172)
            & V0__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__97172)
            & ( cCoq_2eInit_2ePeano_2eIsSucc___24a1(V0__n)
            <=> p(c_24True) ) ) ) ) ).

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.except',axiom,
    cCoq_2eInit_2eSpecif_2eexcept = cCoq_2eInit_2eLogic_2eFalse__rec ).

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__67686___24t(V0__A,V1__P,V2__P,V1__P)
       => ( c_24__type__67694___24t(V0__A,V1__P,V2__P,V2__P)
         => ( cCoq_2eInit_2eSpecif_2esigT___24t(V0__A,V1__P,V4__s)
           => ? [Vvar__2__x__67678] :
                ( t(Vvar__2__x__67678,V0__A)
                & ? [Vvar__3___24Anonymous__67679] :
                    ( t(Vvar__3___24Anonymous__67679,happ(V1__P,Vvar__2__x__67678))
                    & V4__s = cCoq_2eInit_2eSpecif_2eexistT___24a4(V0__A,V1__P,Vvar__2__x__67678,Vvar__3___24Anonymous__67679)
                    & cCoq_2eInit_2eSpecif_2esigT__rect___24a5(V0__A,V1__P,V2__P,V3__f,V4__s) = happ(happ(V3__f,Vvar__2__x__67678),Vvar__3___24Anonymous__67679) ) ) ) ) ) ) ).

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__78909___24t(V0__A,V1__P,V2__P,V1__P)
       => ( c_24__type__78917___24t(V0__A,V1__P,V2__P,V2__P)
         => ( cCoq_2eInit_2eSpecif_2esig___24t(V0__A,V1__P,V4__s)
           => ? [Vvar__2__x__78901] :
                ( t(Vvar__2__x__78901,V0__A)
                & p(happ(V1__P,Vvar__2__x__78901))
                & V4__s = cCoq_2eInit_2eSpecif_2eexist___24a3(V0__A,V1__P,Vvar__2__x__78901)
                & cCoq_2eInit_2eSpecif_2esig__rect___24a5(V0__A,V1__P,V2__P,V3__f,V4__s) = happ(V3__f,Vvar__2__x__78901) ) ) ) ) ) ).

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__67759___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__78986___24t(V0__A,V1__B,V2__P,V2__P)
         => ( cCoq_2eInit_2eSpecif_2esumor___24t(V0__A,V1__B,V5__s)
           => ( ? [Vvar__2___24Anonymous__78977] :
                  ( t(Vvar__2___24Anonymous__78977,V0__A)
                  & V5__s = cCoq_2eInit_2eSpecif_2einleft___24a3(V0__A,V1__B,Vvar__2___24Anonymous__78977)
                  & cCoq_2eInit_2eSpecif_2esumor__rect___24a6(V0__A,V1__B,V2__P,V3__f,V4__f,V5__s) = happ(V3__f,Vvar__2___24Anonymous__78977) )
              | ( 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.Init.Wf.well_founded',axiom,
    ! [V0__A,V1__R] :
      ( cCoq_2eInit_2eWf_2ewell__founded___24a2(V0__A,V1__R)
    <=> ! [V2__a] :
          ( t(V2__a,V0__A)
         => cCoq_2eInit_2eWf_2eAcc___24a3(V0__A,V1__R,V2__a) ) ) ).

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__76200] :
              ( t(Vvar__1___24Anonymous__76200,V0__A)
              & ? [Vvar__2___24Anonymous__76201] :
                  ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__76201)
                  & V3__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__76200,Vvar__2___24Anonymous__76201)
                  & ( cCoq_2eLists_2eList_2eIn___24a3(V0__A,V2__a,V3__l)
                  <=> ( Vvar__1___24Anonymous__76200 = V2__a
                      | cCoq_2eLists_2eList_2eIn___24a3(V0__A,V2__a,Vvar__2___24Anonymous__76201) ) ) ) ) ) ) ) ).

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__84665] :
                ( t(Vvar__1___24Anonymous__84665,V1__B)
                & ? [Vvar__2___24Anonymous__84666] :
                    ( cCoq_2eInit_2eDatatypes_2elist___24t(V1__B,Vvar__2___24Anonymous__84666)
                    & V4__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V1__B,Vvar__1___24Anonymous__84665,Vvar__2___24Anonymous__84666)
                    & 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__84666,happ(happ(V2__f,V5__a0),Vvar__1___24Anonymous__84665)) ) ) ) ) ) ) ).

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__67081] :
                ( t(Vvar__1___24Anonymous__67081,V1__B)
                & ? [Vvar__2___24Anonymous__67082] :
                    ( cCoq_2eInit_2eDatatypes_2elist___24t(V1__B,Vvar__2___24Anonymous__67082)
                    & V5__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V1__B,Vvar__1___24Anonymous__67081,Vvar__2___24Anonymous__67082)
                    & cCoq_2eLists_2eList_2efold__right___24a5(V0__A,V1__B,V2__f,V3__a0,V5__l) = happ(happ(V2__f,Vvar__1___24Anonymous__67081),cCoq_2eLists_2eList_2efold__right___24a5(V0__A,V1__B,V2__f,V3__a0,Vvar__2___24Anonymous__67082)) ) ) ) ) ) ) ).

fof('$_def_Coq.Lists.List.hd',axiom,
    ! [V0__A,V1__default,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_2eLists_2eList_2ehd___24a3(V0__A,V1__default,V2__l) = V1__default )
          | ? [Vvar__1___24Anonymous__96820] :
              ( t(Vvar__1___24Anonymous__96820,V0__A)
              & ? [Vvar__2___24Anonymous__96821] :
                  ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__96821)
                  & V2__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__96820,Vvar__2___24Anonymous__96821)
                  & cCoq_2eLists_2eList_2ehd___24a3(V0__A,V1__default,V2__l) = Vvar__1___24Anonymous__96820 ) ) ) ) ) ).

fof('$_def_Coq.Lists.SetoidList.transpose',axiom,
    ! [V0__A,V1__B,V2__eqB,V3__f] :
      ( cCoq_2eLists_2eSetoidList_2etranspose___24a4(V0__A,V1__B,V2__eqB,V3__f)
    <=> ! [V4__x] :
          ( t(V4__x,V0__A)
         => ! [V5__y] :
              ( t(V5__y,V0__A)
             => ! [V6__z] :
                  ( t(V6__z,V1__B)
                 => p(happ(happ(V2__eqB,happ(happ(V3__f,V4__x),happ(happ(V3__f,V5__y),V6__z))),happ(happ(V3__f,V5__y),happ(happ(V3__f,V4__x),V6__z)))) ) ) ) ) ).

fof('$_def_Coq.Lists.SetoidList.transpose2',axiom,
    ! [V0__A,V1__B,V2__eqB,V3__f] :
      ( cCoq_2eLists_2eSetoidList_2etranspose2___24a4(V0__A,V1__B,V2__eqB,V3__f)
    <=> ! [V4__x] :
          ( t(V4__x,V0__A)
         => ! [V5__y] :
              ( t(V5__y,V0__A)
             => ! [V6__z] :
                  ( t(V6__z,V1__B)
                 => ! [V7__z_27] :
                      ( t(V7__z_27,V1__B)
                     => ( p(happ(happ(V2__eqB,V6__z),V7__z_27))
                       => p(happ(happ(V2__eqB,happ(happ(V3__f,V4__x),happ(happ(V3__f,V5__y),V6__z))),happ(happ(V3__f,V5__y),happ(happ(V3__f,V4__x),V7__z_27)))) ) ) ) ) ) ) ).

fof('$_def_Coq.Lists.SetoidList.transpose_restr',axiom,
    ! [V0__A,V1__B,V2__eqB,V3__R,V4__f] :
      ( cCoq_2eLists_2eSetoidList_2etranspose__restr___24a5(V0__A,V1__B,V2__eqB,V3__R,V4__f)
    <=> ! [V5__x] :
          ( t(V5__x,V0__A)
         => ! [V6__y] :
              ( t(V6__y,V0__A)
             => ! [V7__z] :
                  ( t(V7__z,V1__B)
                 => ( p(happ(happ(V3__R,V5__x),V6__y))
                   => p(happ(happ(V2__eqB,happ(happ(V4__f,V5__x),happ(happ(V4__f,V6__y),V7__z))),happ(happ(V4__f,V6__y),happ(happ(V4__f,V5__x),V7__z)))) ) ) ) ) ) ).

fof('$_def_Coq.Lists.SetoidList.transpose_restr2',axiom,
    ! [V0__A,V1__B,V2__eqB,V3__R,V4__f] :
      ( cCoq_2eLists_2eSetoidList_2etranspose__restr2___24a5(V0__A,V1__B,V2__eqB,V3__R,V4__f)
    <=> ! [V5__x] :
          ( t(V5__x,V0__A)
         => ! [V6__y] :
              ( t(V6__y,V0__A)
             => ! [V7__z] :
                  ( t(V7__z,V1__B)
                 => ! [V8__z_27] :
                      ( t(V8__z_27,V1__B)
                     => ( p(happ(happ(V3__R,V5__x),V6__y))
                       => ( p(happ(happ(V2__eqB,V7__z),V8__z_27))
                         => p(happ(happ(V2__eqB,happ(happ(V4__f,V5__x),happ(happ(V4__f,V6__y),V7__z))),happ(happ(V4__f,V6__y),happ(happ(V4__f,V5__x),V8__z_27)))) ) ) ) ) ) ) ) ).

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.NArith.BinNat.N.eq',axiom,
    cCoq_2eNArith_2eBinNat_2eN_2eeq = c_3d___24a1(cCoq_2eNumbers_2eBinNums_2eN) ).

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__80214] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__80214)
            & ( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
             => ( V0__n = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__80214)
                & ( ( V1__m = cCoq_2eNumbers_2eBinNums_2eN0
                    & cCoq_2eNArith_2eBinNatDef_2eN_2eadd___24a2(V0__n,V1__m) = V0__n )
                  | ? [Vvar__0___24Anonymous__80217] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__80217)
                      & V1__m = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__80217)
                      & cCoq_2eNArith_2eBinNatDef_2eN_2eadd___24a2(V0__n,V1__m) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(Vvar__0___24Anonymous__80214,Vvar__0___24Anonymous__80217)) ) ) ) ) ) ) ) ).

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__1448] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__1448)
            & ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__1448)
             => ( V0__n = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__1448)
                & ( ? [Vvar__0___24Anonymous__1452] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__1452)
                      & Vvar__0___24Anonymous__1448 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__1452)
                      & cCoq_2eNArith_2eBinNatDef_2eN_2ediv2___24a1(V0__n) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__1452) )
                  | ? [Vvar__0___24Anonymous__1453] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__1453)
                      & Vvar__0___24Anonymous__1448 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__1453)
                      & cCoq_2eNArith_2eBinNatDef_2eN_2ediv2___24a1(V0__n) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__1453) )
                  | ( Vvar__0___24Anonymous__1448 = 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__1438] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__1438)
            & V0__n = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__1438)
            & cCoq_2eNArith_2eBinNatDef_2eN_2edouble___24a1(V0__n) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__1438)) ) ) ) ).

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__1440] :
                  ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__1440)
                  & V2__m = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__1440)
                  & cCoq_2eNArith_2eBinNatDef_2eN_2eeqb___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) )
        | ? [Vvar__0___24Anonymous__1441] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__1441)
            & ( cCoq_2eNumbers_2eBinNums_2eN___24t(V2__m)
             => ( V1__n = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__1441)
                & ( ( V2__m = cCoq_2eNumbers_2eBinNums_2eN0
                    & cCoq_2eNArith_2eBinNatDef_2eN_2eeqb___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2efalse )
                  | ? [Vvar__0___24Anonymous__1444] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__1444)
                      & V2__m = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__1444)
                      & cCoq_2eNArith_2eBinNatDef_2eN_2eeqb___24a2(V1__n,V2__m) = cCoq_2ePArith_2eBinPosDef_2ePos_2eeqb___24a2(Vvar__0___24Anonymous__1441,Vvar__0___24Anonymous__1444) ) ) ) ) ) ) ) ).

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__1456] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__1456)
            & ( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
             => ( V0__n = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__1456)
                & ( ( V1__m = cCoq_2eNumbers_2eBinNums_2eN0
                    & cCoq_2eNArith_2eBinNatDef_2eN_2elxor___24a2(V0__n,V1__m) = V0__n )
                  | ? [Vvar__0___24Anonymous__1459] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__1459)
                      & V1__m = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__1459)
                      & cCoq_2eNArith_2eBinNatDef_2eN_2elxor___24a2(V0__n,V1__m) = cCoq_2ePArith_2eBinPosDef_2ePos_2elxor___24a2(Vvar__0___24Anonymous__1456,Vvar__0___24Anonymous__1459) ) ) ) ) ) ) ) ).

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__80219] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__80219)
            & ( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
             => ( V0__n = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__80219)
                & ( ( V1__m = cCoq_2eNumbers_2eBinNums_2eN0
                    & cCoq_2eNArith_2eBinNatDef_2eN_2emul___24a2(V0__n,V1__m) = cCoq_2eNumbers_2eBinNums_2eN0 )
                  | ? [Vvar__0___24Anonymous__80222] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__80222)
                      & V1__m = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__80222)
                      & cCoq_2eNArith_2eBinNatDef_2eN_2emul___24a2(V0__n,V1__m) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2emul___24a2(Vvar__0___24Anonymous__80219,Vvar__0___24Anonymous__80222)) ) ) ) ) ) ) ) ).

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.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__93033] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__93033)
            & V0__n = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__93033)
            & cCoq_2eNArith_2eBinNatDef_2eN_2esucc___24a1(V0__n) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2esucc___24a1(Vvar__0___24Anonymous__93033)) ) ) ) ).

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__1105] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__1105)
            & V0__x = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__1105)
            & cCoq_2eNArith_2eBinNatDef_2eN_2esucc__double___24a1(V0__x) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__1105)) ) ) ) ).

fof('$_def_Coq.NArith.BinNatDef.N.t',axiom,
    ! [Vvar__105550] :
      ( cCoq_2eNArith_2eBinNatDef_2eN_2et___24t(Vvar__105550)
    <=> cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__105550) ) ).

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__105554] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__105554)
            & V0__a = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__105554)
            & cCoq_2eNArith_2eBinNatDef_2eN_2etestbit___24a2(V0__a,V1__n) = cCoq_2ePArith_2eBinPosDef_2ePos_2etestbit___24a2(Vvar__0___24Anonymous__105554,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__80244] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__80244)
            & V0__a = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__80244)
            & cCoq_2eNArith_2eBinNatDef_2eN_2eto__nat___24a1(V0__a) = cCoq_2ePArith_2eBinPosDef_2ePos_2eto__nat___24a1(Vvar__0___24Anonymous__80244) ) ) ) ).

fof('$_def_Coq.NArith.BinNatDef.N.zero',axiom,
    cCoq_2eNArith_2eBinNatDef_2eN_2ezero = cCoq_2eNumbers_2eBinNums_2eN0 ).

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__77986] :
              ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__77986)
              & cCoq_2eNArith_2eBinNatDef_2eN_2elxor___24a2(V0__a,V1__a_27) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__77986)
              & cCoq_2eNArith_2eNdigits_2eNless___24a2(V0__a,V1__a_27) = cCoq_2eNArith_2eNdigits_2eNless__aux___24a3(V0__a,V1__a_27,Vvar__0___24Anonymous__77986) ) ) ) ) ).

fof('$_def_Coq.PArith.BinPos.Pos.eq',axiom,
    cCoq_2ePArith_2eBinPos_2ePos_2eeq = c_3d___24a1(cCoq_2eNumbers_2eBinNums_2epositive) ).

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.div2',axiom,
    ! [V0__p] :
      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V0__p)
     => ( ? [Vvar__0___24Anonymous__105591] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__105591)
            & V0__p = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__105591)
            & cCoq_2ePArith_2eBinPosDef_2ePos_2ediv2___24a1(V0__p) = Vvar__0___24Anonymous__105591 )
        | ? [Vvar__0___24Anonymous__105592] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__105592)
            & V0__p = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__105592)
            & cCoq_2ePArith_2eBinPosDef_2ePos_2ediv2___24a1(V0__p) = Vvar__0___24Anonymous__105592 )
        | ( V0__p = cCoq_2eNumbers_2eBinNums_2exH
          & cCoq_2ePArith_2eBinPosDef_2ePos_2ediv2___24a1(V0__p) = cCoq_2eNumbers_2eBinNums_2exH ) ) ) ).

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__93124] :
              ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__93124)
              & V4__n = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__93124)
              & 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__93124),Vvar__0___24Anonymous__93124)) )
          | ? [Vvar__0___24Anonymous__93125] :
              ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__93125)
              & V4__n = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__93125)
              & 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__93125),Vvar__0___24Anonymous__93125) )
          | ( 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__80289] :
              ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__80289)
              & V3__p = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__80289)
              & 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__80289,happ(happ(V1__op,V4__a),V4__a))) )
          | ? [Vvar__0___24Anonymous__80290] :
              ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__80290)
              & V3__p = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__80290)
              & 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__80290,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.t',axiom,
    ! [Vvar__105590] :
      ( cCoq_2ePArith_2eBinPosDef_2ePos_2et___24t(Vvar__105590)
    <=> cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__105590) ) ).

fof('$_def_Coq.QArith.QArith_base.Qden',axiom,
    ! [V0__q] :
      ( cCoq_2eQArith_2eQArith__base_2eQ___24t(V0__q)
     => ? [Vvar__0__Qnum__97191] :
          ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__0__Qnum__97191)
          & ? [Vvar__1__Qden__97192] :
              ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1__Qden__97192)
              & V0__q = cCoq_2eQArith_2eQArith__base_2eQmake___24a2(Vvar__0__Qnum__97191,Vvar__1__Qden__97192)
              & cCoq_2eQArith_2eQArith__base_2eQden___24a1(V0__q) = Vvar__1__Qden__97192 ) ) ) ).

fof('$_def_Coq.QArith.QArith_base.Qnum',axiom,
    ! [V0__q] :
      ( cCoq_2eQArith_2eQArith__base_2eQ___24t(V0__q)
     => ? [Vvar__0__Qnum__97186] :
          ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__0__Qnum__97186)
          & ? [Vvar__1__Qden__97187] :
              ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1__Qden__97187)
              & V0__q = cCoq_2eQArith_2eQArith__base_2eQmake___24a2(Vvar__0__Qnum__97186,Vvar__1__Qden__97187)
              & cCoq_2eQArith_2eQArith__base_2eQnum___24a1(V0__q) = Vvar__0__Qnum__97186 ) ) ) ).

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.relation',axiom,
    ! [V0__A] : cCoq_2eRelations_2eRelation__Definitions_2erelation___24a1(V0__A) = c_24__type__78044___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__78044___24a1(V0__U) ).

fof('$_def_Coq.Structures.GenericMinMax.gmax',axiom,
    ! [V0__A,V1__cmp,V2__x,V3__y] :
      ( cType___24t(V0__A)
     => ( c_24__type__96713___24t(V0__A,V1__cmp)
       => ( t(V2__x,V0__A)
         => ( t(V3__y,V0__A)
           => ( ( happ(happ(V1__cmp,V2__x),V3__y) = cCoq_2eInit_2eDatatypes_2eEq
                & cCoq_2eStructures_2eGenericMinMax_2egmax___24a4(V0__A,V1__cmp,V2__x,V3__y) = V2__x )
              | ( happ(happ(V1__cmp,V2__x),V3__y) = cCoq_2eInit_2eDatatypes_2eLt
                & cCoq_2eStructures_2eGenericMinMax_2egmax___24a4(V0__A,V1__cmp,V2__x,V3__y) = V3__y )
              | ( happ(happ(V1__cmp,V2__x),V3__y) = cCoq_2eInit_2eDatatypes_2eGt
                & cCoq_2eStructures_2eGenericMinMax_2egmax___24a4(V0__A,V1__cmp,V2__x,V3__y) = V2__x ) ) ) ) ) ) ).

fof('$_def_Coq.Structures.GenericMinMax.gmin',axiom,
    ! [V0__A,V1__cmp,V2__x,V3__y] :
      ( cType___24t(V0__A)
     => ( c_24__type__96713___24t(V0__A,V1__cmp)
       => ( t(V2__x,V0__A)
         => ( t(V3__y,V0__A)
           => ( ( happ(happ(V1__cmp,V2__x),V3__y) = cCoq_2eInit_2eDatatypes_2eEq
                & cCoq_2eStructures_2eGenericMinMax_2egmin___24a4(V0__A,V1__cmp,V2__x,V3__y) = V2__x )
              | ( happ(happ(V1__cmp,V2__x),V3__y) = cCoq_2eInit_2eDatatypes_2eLt
                & cCoq_2eStructures_2eGenericMinMax_2egmin___24a4(V0__A,V1__cmp,V2__x,V3__y) = V2__x )
              | ( happ(happ(V1__cmp,V2__x),V3__y) = cCoq_2eInit_2eDatatypes_2eGt
                & cCoq_2eStructures_2eGenericMinMax_2egmin___24a4(V0__A,V1__cmp,V2__x,V3__y) = V3__y ) ) ) ) ) ) ).

fof('$_def_Coq.Structures.OrderedTypeEx.N_as_OT.eq',axiom,
    cCoq_2eStructures_2eOrderedTypeEx_2eN__as__OT_2eeq = c_3d___24a1(cCoq_2eNumbers_2eBinNums_2eN) ).

fof('$_def_Coq.Structures.OrderedTypeEx.N_as_OT.lt',axiom,
    cCoq_2eStructures_2eOrderedTypeEx_2eN__as__OT_2elt = cCoq_2eNArith_2eBinNat_2eN_2elt ).

fof('$_def_Coq.Structures.OrderedTypeEx.N_as_OT.t',axiom,
    ! [Vvar__105561] :
      ( cCoq_2eStructures_2eOrderedTypeEx_2eN__as__OT_2et___24t(Vvar__105561)
    <=> cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__105561) ) ).

fof('$_def_Coq.Structures.OrderedTypeEx.Nat_as_OT.eq',axiom,
    cCoq_2eStructures_2eOrderedTypeEx_2eNat__as__OT_2eeq = c_3d___24a1(cCoq_2eInit_2eDatatypes_2enat) ).

fof('$_def_Coq.Structures.OrderedTypeEx.Nat_as_OT.lt',axiom,
    cCoq_2eStructures_2eOrderedTypeEx_2eNat__as__OT_2elt = cCoq_2eInit_2ePeano_2elt ).

fof('$_def_Coq.Structures.OrderedTypeEx.Nat_as_OT.t',axiom,
    ! [Vvar__105587] :
      ( cCoq_2eStructures_2eOrderedTypeEx_2eNat__as__OT_2et___24t(Vvar__105587)
    <=> cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__105587) ) ).

fof('$_def_Coq.Structures.OrderedTypeEx.PositiveOrderedTypeBits.bits_lt',axiom,
    ! [V1__p,V2__q] :
      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__p)
     => ( ? [Vvar__0___24Anonymous__105487] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__105487)
            & ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V2__q)
             => ( V1__p = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__105487)
                & ( ? [Vvar__0___24Anonymous__105491] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__105491)
                      & V2__q = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__105491)
                      & ( cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2ebits__lt___24a2(V1__p,V2__q)
                      <=> cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2ebits__lt___24a2(Vvar__0___24Anonymous__105487,Vvar__0___24Anonymous__105491) ) )
                  | ? [Vvar__0___24Anonymous__105492] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__105492)
                      & V2__q = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__105492)
                      & ( cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2ebits__lt___24a2(V1__p,V2__q)
                      <=> p(c_24False) ) )
                  | ( V2__q = cCoq_2eNumbers_2eBinNums_2exH
                    & ( cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2ebits__lt___24a2(V1__p,V2__q)
                    <=> p(c_24False) ) ) ) ) ) )
        | ? [Vvar__0___24Anonymous__105493] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__105493)
            & ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V2__q)
             => ( V1__p = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__105493)
                & ( ? [Vvar__0___24Anonymous__105497] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__105497)
                      & V2__q = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__105497)
                      & ( cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2ebits__lt___24a2(V1__p,V2__q)
                      <=> p(c_24True) ) )
                  | ? [Vvar__0___24Anonymous__105498] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__105498)
                      & V2__q = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__105498)
                      & ( cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2ebits__lt___24a2(V1__p,V2__q)
                      <=> cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2ebits__lt___24a2(Vvar__0___24Anonymous__105493,Vvar__0___24Anonymous__105498) ) )
                  | ( V2__q = cCoq_2eNumbers_2eBinNums_2exH
                    & ( cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2ebits__lt___24a2(V1__p,V2__q)
                    <=> p(c_24True) ) ) ) ) ) )
        | ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V2__q)
         => ( V1__p = cCoq_2eNumbers_2eBinNums_2exH
            & ( ? [Vvar__0___24Anonymous__105499] :
                  ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__105499)
                  & V2__q = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__105499)
                  & ( cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2ebits__lt___24a2(V1__p,V2__q)
                  <=> p(c_24True) ) )
              | ? [Vvar__0___24Anonymous__105500] :
                  ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__105500)
                  & V2__q = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__105500)
                  & ( cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2ebits__lt___24a2(V1__p,V2__q)
                  <=> p(c_24False) ) )
              | ( V2__q = cCoq_2eNumbers_2eBinNums_2exH
                & ( cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2ebits__lt___24a2(V1__p,V2__q)
                <=> p(c_24False) ) ) ) ) ) ) ) ).

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.lt',axiom,
    cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2elt = cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2ebits__lt ).

fof('$_def_Coq.Structures.OrderedTypeEx.PositiveOrderedTypeBits.t',axiom,
    ! [Vvar__105484] :
      ( cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2et___24t(Vvar__105484)
    <=> cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__105484) ) ).

fof('$_def_Coq.Structures.OrderedTypeEx.Positive_as_OT.eq',axiom,
    cCoq_2eStructures_2eOrderedTypeEx_2ePositive__as__OT_2eeq = c_3d___24a1(cCoq_2eNumbers_2eBinNums_2epositive) ).

fof('$_def_Coq.Structures.OrderedTypeEx.Positive_as_OT.lt',axiom,
    cCoq_2eStructures_2eOrderedTypeEx_2ePositive__as__OT_2elt = cCoq_2ePArith_2eBinPos_2ePos_2elt ).

fof('$_def_Coq.Structures.OrderedTypeEx.Positive_as_OT.t',axiom,
    ! [Vvar__93380] :
      ( cCoq_2eStructures_2eOrderedTypeEx_2ePositive__as__OT_2et___24t(Vvar__93380)
    <=> cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__93380) ) ).

fof('$_def_Coq.Structures.OrderedTypeEx.String_as_OT.t',axiom,
    ! [Vvar__105695] :
      ( cCoq_2eStructures_2eOrderedTypeEx_2eString__as__OT_2et___24t(Vvar__105695)
    <=> cCoq_2eStrings_2eString_2estring___24t(Vvar__105695) ) ).

fof('$_def_Coq.Structures.OrderedTypeEx.Z_as_OT.eq',axiom,
    cCoq_2eStructures_2eOrderedTypeEx_2eZ__as__OT_2eeq = c_3d___24a1(cCoq_2eNumbers_2eBinNums_2eZ) ).

fof('$_def_Coq.Structures.OrderedTypeEx.Z_as_OT.t',axiom,
    ! [Vvar__105720] :
      ( cCoq_2eStructures_2eOrderedTypeEx_2eZ__as__OT_2et___24t(Vvar__105720)
    <=> cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__105720) ) ).

fof('$_def_Coq.ZArith.BinInt.Z.Private_Div.Quot2Div.div',axiom,
    cCoq_2eZArith_2eBinInt_2eZ_2ePrivate__Div_2eQuot2Div_2ediv = cCoq_2eZArith_2eBinIntDef_2eZ_2equot ).

fof('$_def_Coq.ZArith.BinInt.Z.Private_Div.Quot2Div.modulo',axiom,
    cCoq_2eZArith_2eBinInt_2eZ_2ePrivate__Div_2eQuot2Div_2emodulo = cCoq_2eZArith_2eBinIntDef_2eZ_2erem ).

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.eq',axiom,
    cCoq_2eZArith_2eBinInt_2eZ_2eeq = c_3d___24a1(cCoq_2eNumbers_2eBinNums_2eZ) ).

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__93642] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__93642)
            & V0__z = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__93642)
            & cCoq_2eZArith_2eBinIntDef_2eZ_2eabs___24a1(V0__z) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__93642) )
        | ? [Vvar__0___24Anonymous__93643] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__93643)
            & V0__z = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__93643)
            & cCoq_2eZArith_2eBinIntDef_2eZ_2eabs___24a1(V0__z) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__93643) ) ) ) ).

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__80307] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__80307)
            & ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
             => ( V0__x = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__80307)
                & ( ( V1__y = cCoq_2eNumbers_2eBinNums_2eZ0
                    & cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__x,V1__y) = V0__x )
                  | ? [Vvar__0___24Anonymous__80311] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__80311)
                      & V1__y = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__80311)
                      & cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(Vvar__0___24Anonymous__80307,Vvar__0___24Anonymous__80311)) )
                  | ? [Vvar__0___24Anonymous__80312] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__80312)
                      & V1__y = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__80312)
                      & cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__x,V1__y) = cCoq_2eZArith_2eBinIntDef_2eZ_2epos__sub___24a2(Vvar__0___24Anonymous__80307,Vvar__0___24Anonymous__80312) ) ) ) ) )
        | ? [Vvar__0___24Anonymous__80313] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__80313)
            & ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
             => ( V0__x = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__80313)
                & ( ( V1__y = cCoq_2eNumbers_2eBinNums_2eZ0
                    & cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__x,V1__y) = V0__x )
                  | ? [Vvar__0___24Anonymous__80317] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__80317)
                      & V1__y = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__80317)
                      & cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__x,V1__y) = cCoq_2eZArith_2eBinIntDef_2eZ_2epos__sub___24a2(Vvar__0___24Anonymous__80317,Vvar__0___24Anonymous__80313) )
                  | ? [Vvar__0___24Anonymous__80318] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__80318)
                      & V1__y = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__80318)
                      & cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(Vvar__0___24Anonymous__80313,Vvar__0___24Anonymous__80318)) ) ) ) ) ) ) ) ).

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__93661] :
            ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__2___24Anonymous__93661)
            & ? [Vvar__3___24Anonymous__93662] :
                ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__3___24Anonymous__93662)
                & 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__93661,Vvar__3___24Anonymous__93662)
                & cCoq_2eZArith_2eBinIntDef_2eZ_2ediv___24a2(V0__a,V1__b) = Vvar__2___24Anonymous__93661 ) ) ) ) ).

fof('$_def_Coq.ZArith.BinIntDef.Z.even',axiom,
    ! [V0__z] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__z)
     => ( ( V0__z = cCoq_2eNumbers_2eBinNums_2eZ0
          & cCoq_2eZArith_2eBinIntDef_2eZ_2eeven___24a1(V0__z) = cCoq_2eInit_2eDatatypes_2etrue )
        | ? [Vvar__0___24Anonymous__93674] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__93674)
            & ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__93674)
             => ( V0__z = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__93674)
                & ( ? [Vvar__0___24Anonymous__93678] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__93678)
                      & Vvar__0___24Anonymous__93674 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__93678)
                      & cCoq_2eZArith_2eBinIntDef_2eZ_2eeven___24a1(V0__z) = cCoq_2eInit_2eDatatypes_2efalse )
                  | ? [Vvar__0___24Anonymous__93679] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__93679)
                      & Vvar__0___24Anonymous__93674 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__93679)
                      & cCoq_2eZArith_2eBinIntDef_2eZ_2eeven___24a1(V0__z) = cCoq_2eInit_2eDatatypes_2etrue )
                  | ( Vvar__0___24Anonymous__93674 = cCoq_2eNumbers_2eBinNums_2exH
                    & cCoq_2eZArith_2eBinIntDef_2eZ_2eeven___24a1(V0__z) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) )
        | ? [Vvar__0___24Anonymous__93680] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__93680)
            & ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__93680)
             => ( V0__z = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__93680)
                & ( ? [Vvar__0___24Anonymous__93684] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__93684)
                      & Vvar__0___24Anonymous__93680 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__93684)
                      & cCoq_2eZArith_2eBinIntDef_2eZ_2eeven___24a1(V0__z) = cCoq_2eInit_2eDatatypes_2efalse )
                  | ? [Vvar__0___24Anonymous__93685] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__93685)
                      & Vvar__0___24Anonymous__93680 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__93685)
                      & cCoq_2eZArith_2eBinIntDef_2eZ_2eeven___24a1(V0__z) = cCoq_2eInit_2eDatatypes_2etrue )
                  | ( Vvar__0___24Anonymous__93680 = cCoq_2eNumbers_2eBinNums_2exH
                    & cCoq_2eZArith_2eBinIntDef_2eZ_2eeven___24a1(V0__z) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ) ) ) ).

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__93669] :
            ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__2___24Anonymous__93669)
            & ? [Vvar__3___24Anonymous__93670] :
                ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__3___24Anonymous__93670)
                & 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__93669,Vvar__3___24Anonymous__93670)
                & cCoq_2eZArith_2eBinIntDef_2eZ_2emodulo___24a2(V0__a,V1__b) = Vvar__3___24Anonymous__93670 ) ) ) ) ).

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__80327] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__80327)
            & ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
             => ( V0__x = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__80327)
                & ( ( V1__y = cCoq_2eNumbers_2eBinNums_2eZ0
                    & cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZ0 )
                  | ? [Vvar__0___24Anonymous__80331] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__80331)
                      & V1__y = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__80331)
                      & cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2emul___24a2(Vvar__0___24Anonymous__80327,Vvar__0___24Anonymous__80331)) )
                  | ? [Vvar__0___24Anonymous__80332] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__80332)
                      & V1__y = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__80332)
                      & cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2emul___24a2(Vvar__0___24Anonymous__80327,Vvar__0___24Anonymous__80332)) ) ) ) ) )
        | ? [Vvar__0___24Anonymous__80333] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__80333)
            & ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
             => ( V0__x = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__80333)
                & ( ( V1__y = cCoq_2eNumbers_2eBinNums_2eZ0
                    & cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZ0 )
                  | ? [Vvar__0___24Anonymous__80337] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__80337)
                      & V1__y = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__80337)
                      & cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2emul___24a2(Vvar__0___24Anonymous__80333,Vvar__0___24Anonymous__80337)) )
                  | ? [Vvar__0___24Anonymous__80338] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__80338)
                      & V1__y = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__80338)
                      & cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2emul___24a2(Vvar__0___24Anonymous__80333,Vvar__0___24Anonymous__80338)) ) ) ) ) ) ) ) ).

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__93688] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__93688)
            & ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__93688)
             => ( V0__z = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__93688)
                & ( ? [Vvar__0___24Anonymous__93692] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__93692)
                      & Vvar__0___24Anonymous__93688 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__93692)
                      & cCoq_2eZArith_2eBinIntDef_2eZ_2eodd___24a1(V0__z) = cCoq_2eInit_2eDatatypes_2etrue )
                  | ? [Vvar__0___24Anonymous__93693] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__93693)
                      & Vvar__0___24Anonymous__93688 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__93693)
                      & cCoq_2eZArith_2eBinIntDef_2eZ_2eodd___24a1(V0__z) = cCoq_2eInit_2eDatatypes_2efalse )
                  | ( Vvar__0___24Anonymous__93688 = cCoq_2eNumbers_2eBinNums_2exH
                    & cCoq_2eZArith_2eBinIntDef_2eZ_2eodd___24a1(V0__z) = cCoq_2eInit_2eDatatypes_2etrue ) ) ) ) )
        | ? [Vvar__0___24Anonymous__93694] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__93694)
            & ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__93694)
             => ( V0__z = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__93694)
                & ( ? [Vvar__0___24Anonymous__93698] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__93698)
                      & Vvar__0___24Anonymous__93694 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__93698)
                      & cCoq_2eZArith_2eBinIntDef_2eZ_2eodd___24a1(V0__z) = cCoq_2eInit_2eDatatypes_2etrue )
                  | ? [Vvar__0___24Anonymous__93699] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__93699)
                      & Vvar__0___24Anonymous__93694 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__93699)
                      & cCoq_2eZArith_2eBinIntDef_2eZ_2eodd___24a1(V0__z) = cCoq_2eInit_2eDatatypes_2efalse )
                  | ( Vvar__0___24Anonymous__93694 = 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__105711] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__105711)
            & V0__n = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__105711)
            & cCoq_2eZArith_2eBinIntDef_2eZ_2eof__N___24a1(V0__n) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__105711) ) ) ) ).

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__80322] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__80322)
            & V0__x = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__80322)
            & cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V0__x) = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__80322) )
        | ? [Vvar__0___24Anonymous__80323] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__80323)
            & V0__x = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__80323)
            & cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V0__x) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__80323) ) ) ) ).

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.t',axiom,
    ! [Vvar__105710] :
      ( cCoq_2eZArith_2eBinIntDef_2eZ_2et___24t(Vvar__105710)
    <=> cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__105710) ) ).

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__105714] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__105714)
            & V0__z = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__105714)
            & cCoq_2eZArith_2eBinIntDef_2eZ_2eto__pos___24a1(V0__z) = Vvar__0___24Anonymous__105714 )
        | ? [Vvar__0___24Anonymous__105715] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__105715)
            & V0__z = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__105715)
            & cCoq_2eZArith_2eBinIntDef_2eZ_2eto__pos___24a1(V0__z) = cCoq_2eNumbers_2eBinNums_2exH ) ) ) ).

fof('$_def_Coq.ZArith.BinIntDef.Z.zero',axiom,
    cCoq_2eZArith_2eBinIntDef_2eZ_2ezero = cCoq_2eNumbers_2eBinNums_2eZ0 ).

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__105343] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__105343)
            & ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__105343)
             => ( V0__z = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__105343)
                & ( ? [Vvar__0___24Anonymous__105347] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__105347)
                      & Vvar__0___24Anonymous__105343 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__105347)
                      & ( cCoq_2eZArith_2eZeven_2eZeven___24a1(V0__z)
                      <=> p(c_24False) ) )
                  | ? [Vvar__0___24Anonymous__105348] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__105348)
                      & Vvar__0___24Anonymous__105343 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__105348)
                      & ( cCoq_2eZArith_2eZeven_2eZeven___24a1(V0__z)
                      <=> p(c_24True) ) )
                  | ( Vvar__0___24Anonymous__105343 = cCoq_2eNumbers_2eBinNums_2exH
                    & ( cCoq_2eZArith_2eZeven_2eZeven___24a1(V0__z)
                    <=> p(c_24False) ) ) ) ) ) )
        | ? [Vvar__0___24Anonymous__105349] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__105349)
            & ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__105349)
             => ( V0__z = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__105349)
                & ( ? [Vvar__0___24Anonymous__105353] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__105353)
                      & Vvar__0___24Anonymous__105349 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__105353)
                      & ( cCoq_2eZArith_2eZeven_2eZeven___24a1(V0__z)
                      <=> p(c_24False) ) )
                  | ? [Vvar__0___24Anonymous__105354] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__105354)
                      & Vvar__0___24Anonymous__105349 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__105354)
                      & ( cCoq_2eZArith_2eZeven_2eZeven___24a1(V0__z)
                      <=> p(c_24True) ) )
                  | ( Vvar__0___24Anonymous__105349 = 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__105355] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__105355)
            & ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__105355)
             => ( V0__z = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__105355)
                & ( ? [Vvar__0___24Anonymous__105359] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__105359)
                      & Vvar__0___24Anonymous__105355 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__105359)
                      & ( cCoq_2eZArith_2eZeven_2eZodd___24a1(V0__z)
                      <=> p(c_24True) ) )
                  | ? [Vvar__0___24Anonymous__105360] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__105360)
                      & Vvar__0___24Anonymous__105355 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__105360)
                      & ( cCoq_2eZArith_2eZeven_2eZodd___24a1(V0__z)
                      <=> p(c_24False) ) )
                  | ( Vvar__0___24Anonymous__105355 = cCoq_2eNumbers_2eBinNums_2exH
                    & ( cCoq_2eZArith_2eZeven_2eZodd___24a1(V0__z)
                    <=> p(c_24True) ) ) ) ) ) )
        | ? [Vvar__0___24Anonymous__105361] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__105361)
            & ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__105361)
             => ( V0__z = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__105361)
                & ( ? [Vvar__0___24Anonymous__105365] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__105365)
                      & Vvar__0___24Anonymous__105361 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__105365)
                      & ( cCoq_2eZArith_2eZeven_2eZodd___24a1(V0__z)
                      <=> p(c_24True) ) )
                  | ? [Vvar__0___24Anonymous__105366] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__105366)
                      & Vvar__0___24Anonymous__105361 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__105366)
                      & ( cCoq_2eZArith_2eZeven_2eZodd___24a1(V0__z)
                      <=> p(c_24False) ) )
                  | ( Vvar__0___24Anonymous__105361 = 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__105368] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__105368)
            & V1__p = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__105368)
            & ( cCoq_2eZArith_2eZlogarithm_2eIs__power___24a1(V1__p)
            <=> p(c_24False) ) )
        | ? [Vvar__0___24Anonymous__105369] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__105369)
            & V1__p = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__105369)
            & ( cCoq_2eZArith_2eZlogarithm_2eIs__power___24a1(V1__p)
            <=> cCoq_2eZArith_2eZlogarithm_2eIs__power___24a1(Vvar__0___24Anonymous__105369) ) )
        | ( V1__p = cCoq_2eNumbers_2eBinNums_2exH
          & ( cCoq_2eZArith_2eZlogarithm_2eIs__power___24a1(V1__p)
          <=> p(c_24True) ) ) ) ) ).

fof('$_def_Coq.micromega.Env.Env',axiom,
    ! [V0__D] : cCoq_2emicromega_2eEnv_2eEnv___24a1(V0__D) = c_24__type__94244___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__97408] :
              ( t(Vvar__1___24Anonymous__97408,V1__A)
              & ? [Vvar__2___24Anonymous__97409] :
                  ( cCoq_2eInit_2eDatatypes_2elist___24t(V1__A,Vvar__2___24Anonymous__97409)
                  & ( cType___24t(V1__A)
                   => ( cCoq_2eInit_2eDatatypes_2elist___24t(V1__A,Vvar__2___24Anonymous__97409)
                     => ( V3__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V1__A,Vvar__1___24Anonymous__97408,Vvar__2___24Anonymous__97409)
                        & ( ( Vvar__2___24Anonymous__97409 = 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__97408)) ) )
                          | ? [Vvar__1___24Anonymous__97420] :
                              ( t(Vvar__1___24Anonymous__97420,V1__A)
                              & ? [Vvar__2___24Anonymous__97421] :
                                  ( cCoq_2eInit_2eDatatypes_2elist___24t(V1__A,Vvar__2___24Anonymous__97421)
                                  & Vvar__2___24Anonymous__97409 = cCoq_2eInit_2eDatatypes_2econs___24a3(V1__A,Vvar__1___24Anonymous__97420,Vvar__2___24Anonymous__97421)
                                  & ( cCoq_2emicromega_2eRefl_2emake__conj___24a3(V1__A,V2__eval,V3__l)
                                  <=> ( p(happ(V2__eval,Vvar__1___24Anonymous__97408))
                                      & cCoq_2emicromega_2eRefl_2emake__conj___24a3(V1__A,V2__eval,Vvar__2___24Anonymous__97409) ) ) ) ) ) ) ) ) ) ) ) ) ) ).

fof('$_def_Coq.micromega.Refl.make_impl',axiom,
    ! [V1__A,V2__eval,V3__l,V4__goal] :
      ( 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__impl___24a4(V1__A,V2__eval,V3__l,V4__goal)
            <=> p(V4__goal) ) )
          | ? [Vvar__1___24Anonymous__97389] :
              ( t(Vvar__1___24Anonymous__97389,V1__A)
              & ? [Vvar__2___24Anonymous__97390] :
                  ( cCoq_2eInit_2eDatatypes_2elist___24t(V1__A,Vvar__2___24Anonymous__97390)
                  & V3__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V1__A,Vvar__1___24Anonymous__97389,Vvar__2___24Anonymous__97390)
                  & ( cCoq_2emicromega_2eRefl_2emake__impl___24a4(V1__A,V2__eval,V3__l,V4__goal)
                  <=> ( p(happ(V2__eval,Vvar__1___24Anonymous__97389))
                     => cCoq_2emicromega_2eRefl_2emake__impl___24a4(V1__A,V2__eval,Vvar__2___24Anonymous__97390,V4__goal) ) ) ) ) ) ) ) ).

fof('$_def_Coq.micromega.RingMicromega.PolC',axiom,
    ! [V0__C] : cCoq_2emicromega_2eRingMicromega_2ePolC___24a1(V0__C) = cCoq_2emicromega_2eEnvRing_2ePol___24a1(V0__C) ).

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.micromega.ZMicromega.coneMember',axiom,
    ! [Vvar__105342] :
      ( cCoq_2emicromega_2eZMicromega_2econeMember___24t(Vvar__105342)
    <=> cCoq_2emicromega_2eZMicromega_2eZWitness___24t(Vvar__105342) ) ).

fof('$_def_Coq.omega.PreOmega.Z_of_nat\'',axiom,
    cCoq_2eomega_2ePreOmega_2eZ__of__nat_27 = cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat ).

fof('$_def_Coq.omega.PreOmega.Zpos\'',axiom,
    cCoq_2eomega_2ePreOmega_2eZpos_27 = cCoq_2eNumbers_2eBinNums_2eZpos ).

fof('$_def_Coq.setoid_ring.InitialRing.NotConstant',axiom,
    cCoq_2esetoid__ring_2eInitialRing_2eNotConstant = cCoq_2eInit_2eDatatypes_2efalse ).

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__96775] :
              ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__96775)
              & ( cType___24t(V0__R)
               => ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__96775)
                 => ( V5__p = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__96775)
                    & ( ? [Vvar__0___24Anonymous__96779] :
                          ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__96779)
                          & Vvar__0___24Anonymous__96775 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__96779)
                          & 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__96775))) )
                      | ? [Vvar__0___24Anonymous__96780] :
                          ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__96780)
                          & Vvar__0___24Anonymous__96775 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__96780)
                          & 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__96775))) )
                      | ( Vvar__0___24Anonymous__96775 = 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__96781] :
              ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__96781)
              & ( cType___24t(V0__R)
               => ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__96781)
                 => ( V5__p = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__96781)
                    & ( ? [Vvar__0___24Anonymous__96785] :
                          ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__96785)
                          & Vvar__0___24Anonymous__96781 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__96785)
                          & 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__96781)) )
                      | ? [Vvar__0___24Anonymous__96786] :
                          ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__96786)
                          & Vvar__0___24Anonymous__96781 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__96786)
                          & 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__96781)) )
                      | ( Vvar__0___24Anonymous__96781 = 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__96742] :
              ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__96742)
              & V5__p = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__96742)
              & 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__96742))) )
          | ? [Vvar__0___24Anonymous__96743] :
              ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__96743)
              & V5__p = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__96743)
              & 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__96743)) )
          | ( 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_polynom.mkmult_pow',axiom,
    ! [V0__R,V1__rmul,V3__r,V4__x,V5__p] :
      ( cType___24t(V0__R)
     => ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V5__p)
       => ( ? [Vvar__0___24Anonymous__103649] :
              ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__103649)
              & V5__p = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__103649)
              & cCoq_2esetoid__ring_2eRing__polynom_2emkmult__pow___24a5(V0__R,V1__rmul,V3__r,V4__x,V5__p) = cCoq_2esetoid__ring_2eRing__polynom_2emkmult__pow___24a5(V0__R,V1__rmul,cCoq_2esetoid__ring_2eRing__polynom_2emkmult__pow___24a5(V0__R,V1__rmul,happ(happ(V1__rmul,V3__r),V4__x),V4__x,Vvar__0___24Anonymous__103649),V4__x,Vvar__0___24Anonymous__103649) )
          | ? [Vvar__0___24Anonymous__103650] :
              ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__103650)
              & V5__p = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__103650)
              & cCoq_2esetoid__ring_2eRing__polynom_2emkmult__pow___24a5(V0__R,V1__rmul,V3__r,V4__x,V5__p) = cCoq_2esetoid__ring_2eRing__polynom_2emkmult__pow___24a5(V0__R,V1__rmul,cCoq_2esetoid__ring_2eRing__polynom_2emkmult__pow___24a5(V0__R,V1__rmul,V3__r,V4__x,Vvar__0___24Anonymous__103650),V4__x,Vvar__0___24Anonymous__103650) )
          | ( V5__p = cCoq_2eNumbers_2eBinNums_2exH
            & cCoq_2esetoid__ring_2eRing__polynom_2emkmult__pow___24a5(V0__R,V1__rmul,V3__r,V4__x,V5__p) = happ(happ(V1__rmul,V3__r),V4__x) ) ) ) ) ).

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.id_phi_N',axiom,
    ! [V0__x] : cCoq_2esetoid__ring_2eRing__theory_2eid__phi__N___24a1(V0__x) = V0__x ).

fof('$_def_Coq.setoid_ring.Ring_theory.pow_N',axiom,
    ! [V0__R,V1__rI,V2__rmul,V3__x,V4__p] :
      ( cType___24t(V0__R)
     => ( cCoq_2eNumbers_2eBinNums_2eN___24t(V4__p)
       => ( ( V4__p = cCoq_2eNumbers_2eBinNums_2eN0
            & cCoq_2esetoid__ring_2eRing__theory_2epow__N___24a5(V0__R,V1__rI,V2__rmul,V3__x,V4__p) = V1__rI )
          | ? [Vvar__0___24Anonymous__80821] :
              ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__80821)
              & V4__p = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__80821)
              & cCoq_2esetoid__ring_2eRing__theory_2epow__N___24a5(V0__R,V1__rI,V2__rmul,V3__x,V4__p) = cCoq_2esetoid__ring_2eRing__theory_2epow__pos___24a4(V0__R,V2__rmul,V3__x,Vvar__0___24Anonymous__80821) ) ) ) ) ).

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__86188] :
              ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__86188)
              & V4__i = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__86188)
              & 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__86189__86192___24a4(V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__86188)),c_24__let__var__6__p__86189__86192___24a4(V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__86188))) )
          | ? [Vvar__0___24Anonymous__86190] :
              ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__86190)
              & V4__i = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__86190)
              & 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__86191__86193___24a4(V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__86190)),c_24__let__var__6__p__86191__86193___24a4(V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__86190)) )
          | ( 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_Hammer.Tactics.Reconstr.rdone',axiom,
    ! [V0__T,V1__x] :
      ( cHammer_2eTactics_2eReconstr_2erdone___24a2(V0__T,V1__x)
    <=> p(c_24True) ) ).

fof('$_def_Hammer.Tactics.Tactics.rdone',axiom,
    ! [V0__T,V1__x] :
      ( cHammer_2eTactics_2eTactics_2erdone___24a2(V0__T,V1__x)
    <=> p(c_24True) ) ).

fof('$_def_IntMap.Fset.FSet',axiom,
    ! [Vvar__1139] :
      ( cIntMap_2eFset_2eFSet___24t(Vvar__1139)
    <=> cIntMap_2eMap_2eMap___24t(cCoq_2eInit_2eDatatypes_2eunit,Vvar__1139) ) ).

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.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__1144] :
              ( cIntMap_2eMap_2ead___24t(Vvar__1___24Anonymous__1144)
              & ? [Vvar__2___24Anonymous__1145] :
                  ( t(Vvar__2___24Anonymous__1145,V0__A)
                  & V2__m = cIntMap_2eMap_2eM1___24a3(V0__A,Vvar__1___24Anonymous__1144,Vvar__2___24Anonymous__1145)
                  & cIntMap_2eFset_2eMapDom___24a2(V0__A,V2__m) = cIntMap_2eMap_2eM1___24a3(cCoq_2eInit_2eDatatypes_2eunit,Vvar__1___24Anonymous__1144,cCoq_2eInit_2eDatatypes_2ett) ) )
          | ? [Vvar__1___24Anonymous__1148] :
              ( cIntMap_2eMap_2eMap___24t(V0__A,Vvar__1___24Anonymous__1148)
              & ? [Vvar__2___24Anonymous__1149] :
                  ( cIntMap_2eMap_2eMap___24t(V0__A,Vvar__2___24Anonymous__1149)
                  & V2__m = cIntMap_2eMap_2eM2___24a3(V0__A,Vvar__1___24Anonymous__1148,Vvar__2___24Anonymous__1149)
                  & 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__1148),cIntMap_2eFset_2eMapDom___24a2(V0__A,Vvar__2___24Anonymous__1149)) ) ) ) ) ) ).

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__43___24a2(V0__A,V1__B) )
          | ? [Vvar__1___24Anonymous__147] :
              ( cIntMap_2eMap_2ead___24t(Vvar__1___24Anonymous__147)
              & ? [Vvar__2___24Anonymous__148] :
                  ( t(Vvar__2___24Anonymous__148,V0__A)
                  & V3__m = cIntMap_2eMap_2eM1___24a3(V0__A,Vvar__1___24Anonymous__147,Vvar__2___24Anonymous__148)
                  & cIntMap_2eFset_2eMapDomRestrBy___24a3(V0__A,V1__B,V3__m) = c_24__lam__188___24a4(V0__A,V1__B,V3__m,Vvar__1___24Anonymous__147) ) )
          | ? [Vvar__1___24Anonymous__157] :
              ( cIntMap_2eMap_2eMap___24t(V0__A,Vvar__1___24Anonymous__157)
              & ? [Vvar__2___24Anonymous__158] :
                  ( cIntMap_2eMap_2eMap___24t(V0__A,Vvar__2___24Anonymous__158)
                  & V3__m = cIntMap_2eMap_2eM2___24a3(V0__A,Vvar__1___24Anonymous__157,Vvar__2___24Anonymous__158)
                  & cIntMap_2eFset_2eMapDomRestrBy___24a3(V0__A,V1__B,V3__m) = c_24__lam__230___24a5(V0__A,V1__B,V3__m,Vvar__1___24Anonymous__157,Vvar__2___24Anonymous__158) ) ) ) ) ) ).

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__43___24a2(V0__A,V1__B) )
          | ? [Vvar__1___24Anonymous__12] :
              ( cIntMap_2eMap_2ead___24t(Vvar__1___24Anonymous__12)
              & ? [Vvar__2___24Anonymous__13] :
                  ( t(Vvar__2___24Anonymous__13,V0__A)
                  & V3__m = cIntMap_2eMap_2eM1___24a3(V0__A,Vvar__1___24Anonymous__12,Vvar__2___24Anonymous__13)
                  & cIntMap_2eFset_2eMapDomRestrTo___24a3(V0__A,V1__B,V3__m) = c_24__lam__58___24a4(V0__A,V1__B,V3__m,Vvar__1___24Anonymous__12) ) )
          | ? [Vvar__1___24Anonymous__22] :
              ( cIntMap_2eMap_2eMap___24t(V0__A,Vvar__1___24Anonymous__22)
              & ? [Vvar__2___24Anonymous__23] :
                  ( cIntMap_2eMap_2eMap___24t(V0__A,Vvar__2___24Anonymous__23)
                  & V3__m = cIntMap_2eMap_2eM2___24a3(V0__A,Vvar__1___24Anonymous__22,Vvar__2___24Anonymous__23)
                  & cIntMap_2eFset_2eMapDomRestrTo___24a3(V0__A,V1__B,V3__m) = c_24__lam__116___24a5(V0__A,V1__B,V3__m,Vvar__1___24Anonymous__22,Vvar__2___24Anonymous__23) ) ) ) ) ) ).

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__67054] :
                ( t(Vvar__1___24Anonymous__67054,V0__A)
                & cIntMap_2eMap_2eMapGet___24a3(V0__A,V2__m,V1__a) = cCoq_2eInit_2eDatatypes_2eSome___24a2(V0__A,Vvar__1___24Anonymous__67054)
                & 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__76369] :
              ( cCoq_2eInit_2eDatatypes_2eprod___24t(cIntMap_2eMap_2ead,V0__A,Vvar__1___24Anonymous__76369)
              & ? [Vvar__2___24Anonymous__76370] :
                  ( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eInit_2eDatatypes_2eprod___24a2(cIntMap_2eMap_2ead,V0__A),Vvar__2___24Anonymous__76370)
                  & ( cType___24t(V0__A)
                   => ( cCoq_2eInit_2eDatatypes_2eprod___24t(cIntMap_2eMap_2ead,V0__A,Vvar__1___24Anonymous__76369)
                     => ( V3__l = cCoq_2eInit_2eDatatypes_2econs___24a3(cCoq_2eInit_2eDatatypes_2eprod___24a2(cIntMap_2eMap_2ead,V0__A),Vvar__1___24Anonymous__76369,Vvar__2___24Anonymous__76370)
                        & ? [Vvar__2___24Anonymous__76386] :
                            ( cIntMap_2eMap_2ead___24t(Vvar__2___24Anonymous__76386)
                            & ? [Vvar__3___24Anonymous__76387] :
                                ( t(Vvar__3___24Anonymous__76387,V0__A)
                                & ( cType___24t(V0__A)
                                 => ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__n)
                                   => ( Vvar__1___24Anonymous__76369 = cCoq_2eInit_2eDatatypes_2epair___24a4(cIntMap_2eMap_2ead,V0__A,Vvar__2___24Anonymous__76386,Vvar__3___24Anonymous__76387)
                                      & ( ( V2__n = cCoq_2eInit_2eDatatypes_2eO
                                          & cIntMap_2eLsort_2ealist__nth__ad___24a3(V0__A,V2__n,V3__l) = Vvar__2___24Anonymous__76386 )
                                        | ? [Vvar__0___24Anonymous__76393] :
                                            ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__76393)
                                            & V2__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__76393)
                                            & cIntMap_2eLsort_2ealist__nth__ad___24a3(V0__A,V2__n,V3__l) = cIntMap_2eLsort_2ealist__nth__ad___24a3(V0__A,Vvar__0___24Anonymous__76393,Vvar__2___24Anonymous__76370) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).

fof('$_def_IntMap.Lsort.alist_sorted',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_2eLsort_2ealist__sorted___24a2(V0__A,V2__l) = cCoq_2eInit_2eDatatypes_2etrue )
          | ? [Vvar__1___24Anonymous__76303] :
              ( cCoq_2eInit_2eDatatypes_2eprod___24t(cIntMap_2eMap_2ead,V0__A,Vvar__1___24Anonymous__76303)
              & ? [Vvar__2___24Anonymous__76304] :
                  ( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eInit_2eDatatypes_2eprod___24a2(cIntMap_2eMap_2ead,V0__A),Vvar__2___24Anonymous__76304)
                  & ( cType___24t(V0__A)
                   => ( cCoq_2eInit_2eDatatypes_2eprod___24t(cIntMap_2eMap_2ead,V0__A,Vvar__1___24Anonymous__76303)
                     => ( V2__l = cCoq_2eInit_2eDatatypes_2econs___24a3(cCoq_2eInit_2eDatatypes_2eprod___24a2(cIntMap_2eMap_2ead,V0__A),Vvar__1___24Anonymous__76303,Vvar__2___24Anonymous__76304)
                        & ? [Vvar__2___24Anonymous__76328] :
                            ( cIntMap_2eMap_2ead___24t(Vvar__2___24Anonymous__76328)
                            & ? [Vvar__3___24Anonymous__76329] :
                                ( t(Vvar__3___24Anonymous__76329,V0__A)
                                & ( cType___24t(V0__A)
                                 => ( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eInit_2eDatatypes_2eprod___24a2(cIntMap_2eMap_2ead,V0__A),Vvar__2___24Anonymous__76304)
                                   => ( Vvar__1___24Anonymous__76303 = cCoq_2eInit_2eDatatypes_2epair___24a4(cIntMap_2eMap_2ead,V0__A,Vvar__2___24Anonymous__76328,Vvar__3___24Anonymous__76329)
                                      & ( ( Vvar__2___24Anonymous__76304 = cCoq_2eInit_2eDatatypes_2enil___24a1(cCoq_2eInit_2eDatatypes_2eprod___24a2(cIntMap_2eMap_2ead,V0__A))
                                          & cIntMap_2eLsort_2ealist__sorted___24a2(V0__A,V2__l) = cCoq_2eInit_2eDatatypes_2etrue )
                                        | ? [Vvar__1___24Anonymous__76346] :
                                            ( cCoq_2eInit_2eDatatypes_2eprod___24t(cIntMap_2eMap_2ead,V0__A,Vvar__1___24Anonymous__76346)
                                            & ? [Vvar__2___24Anonymous__76347] :
                                                ( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eInit_2eDatatypes_2eprod___24a2(cIntMap_2eMap_2ead,V0__A),Vvar__2___24Anonymous__76347)
                                                & ( cType___24t(V0__A)
                                                 => ( cCoq_2eInit_2eDatatypes_2eprod___24t(cIntMap_2eMap_2ead,V0__A,Vvar__1___24Anonymous__76346)
                                                   => ( Vvar__2___24Anonymous__76304 = cCoq_2eInit_2eDatatypes_2econs___24a3(cCoq_2eInit_2eDatatypes_2eprod___24a2(cIntMap_2eMap_2ead,V0__A),Vvar__1___24Anonymous__76346,Vvar__2___24Anonymous__76347)
                                                      & ? [Vvar__2___24Anonymous__76359] :
                                                          ( cIntMap_2eMap_2ead___24t(Vvar__2___24Anonymous__76359)
                                                          & ? [Vvar__3___24Anonymous__76360] :
                                                              ( t(Vvar__3___24Anonymous__76360,V0__A)
                                                              & Vvar__1___24Anonymous__76346 = cCoq_2eInit_2eDatatypes_2epair___24a4(cIntMap_2eMap_2ead,V0__A,Vvar__2___24Anonymous__76359,Vvar__3___24Anonymous__76360)
                                                              & cIntMap_2eLsort_2ealist__sorted___24a2(V0__A,V2__l) = cCoq_2eInit_2eDatatypes_2eandb___24a2(cCoq_2eNArith_2eNdigits_2eNless___24a2(Vvar__2___24Anonymous__76328,Vvar__2___24Anonymous__76359),cIntMap_2eLsort_2ealist__sorted___24a2(V0__A,Vvar__2___24Anonymous__76304)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).

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__505] :
              ( cIntMap_2eMap_2ead___24t(Vvar__1___24Anonymous__505)
              & ? [Vvar__2___24Anonymous__506] :
                  ( t(Vvar__2___24Anonymous__506,V0__A)
                  & V2__m = cIntMap_2eMap_2eM1___24a3(V0__A,Vvar__1___24Anonymous__505,Vvar__2___24Anonymous__506)
                  & cIntMap_2eMap_2eMapCard___24a2(V0__A,V2__m) = cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO) ) )
          | ? [Vvar__1___24Anonymous__509] :
              ( cIntMap_2eMap_2eMap___24t(V0__A,Vvar__1___24Anonymous__509)
              & ? [Vvar__2___24Anonymous__510] :
                  ( cIntMap_2eMap_2eMap___24t(V0__A,Vvar__2___24Anonymous__510)
                  & V2__m = cIntMap_2eMap_2eM2___24a3(V0__A,Vvar__1___24Anonymous__509,Vvar__2___24Anonymous__510)
                  & cIntMap_2eMap_2eMapCard___24a2(V0__A,V2__m) = cCoq_2eInit_2eNat_2eadd___24a2(cIntMap_2eMap_2eMapCard___24a2(V0__A,Vvar__1___24Anonymous__509),cIntMap_2eMap_2eMapCard___24a2(V0__A,Vvar__2___24Anonymous__510)) ) ) ) ) ) ).

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__912___24a1(V0__A) )
          | ? [Vvar__1___24Anonymous__76617] :
              ( cIntMap_2eMap_2ead___24t(Vvar__1___24Anonymous__76617)
              & ? [Vvar__2___24Anonymous__76618] :
                  ( t(Vvar__2___24Anonymous__76618,V0__A)
                  & V2__m = cIntMap_2eMap_2eM1___24a3(V0__A,Vvar__1___24Anonymous__76617,Vvar__2___24Anonymous__76618)
                  & cIntMap_2eMap_2eMapDelta___24a2(V0__A,V2__m) = c_24__lam__76658___24a3(V0__A,Vvar__1___24Anonymous__76617,Vvar__2___24Anonymous__76618) ) )
          | ? [Vvar__1___24Anonymous__76627] :
              ( cIntMap_2eMap_2eMap___24t(V0__A,Vvar__1___24Anonymous__76627)
              & ? [Vvar__2___24Anonymous__76628] :
                  ( cIntMap_2eMap_2eMap___24t(V0__A,Vvar__2___24Anonymous__76628)
                  & V2__m = cIntMap_2eMap_2eM2___24a3(V0__A,Vvar__1___24Anonymous__76627,Vvar__2___24Anonymous__76628)
                  & cIntMap_2eMap_2eMapDelta___24a2(V0__A,V2__m) = c_24__lam__76708___24a4(V0__A,V2__m,Vvar__1___24Anonymous__76627,Vvar__2___24Anonymous__76628) ) ) ) ) ) ).

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__76777] :
              ( cIntMap_2eMap_2ead___24t(Vvar__1___24Anonymous__76777)
              & ? [Vvar__2___24Anonymous__76778] :
                  ( t(Vvar__2___24Anonymous__76778,V0__A)
                  & V1__m = cIntMap_2eMap_2eM1___24a3(V0__A,Vvar__1___24Anonymous__76777,Vvar__2___24Anonymous__76778)
                  & cIntMap_2eMap_2eMapEmptyp___24a2(V0__A,V1__m) = cCoq_2eInit_2eDatatypes_2efalse ) )
          | ? [Vvar__1___24Anonymous__76781] :
              ( cIntMap_2eMap_2eMap___24t(V0__A,Vvar__1___24Anonymous__76781)
              & ? [Vvar__2___24Anonymous__76782] :
                  ( cIntMap_2eMap_2eMap___24t(V0__A,Vvar__2___24Anonymous__76782)
                  & V1__m = cIntMap_2eMap_2eM2___24a3(V0__A,Vvar__1___24Anonymous__76781,Vvar__2___24Anonymous__76782)
                  & 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__733___24a1(V0__A) )
          | ? [Vvar__1___24Anonymous__709] :
              ( cIntMap_2eMap_2ead___24t(Vvar__1___24Anonymous__709)
              & ? [Vvar__2___24Anonymous__710] :
                  ( t(Vvar__2___24Anonymous__710,V0__A)
                  & V2__m = cIntMap_2eMap_2eM1___24a3(V0__A,Vvar__1___24Anonymous__709,Vvar__2___24Anonymous__710)
                  & cIntMap_2eMap_2eMapGet___24a2(V0__A,V2__m) = c_24__lam__741___24a3(V0__A,Vvar__1___24Anonymous__709,Vvar__2___24Anonymous__710) ) )
          | ? [Vvar__1___24Anonymous__717] :
              ( cIntMap_2eMap_2eMap___24t(V0__A,Vvar__1___24Anonymous__717)
              & ? [Vvar__2___24Anonymous__718] :
                  ( cIntMap_2eMap_2eMap___24t(V0__A,Vvar__2___24Anonymous__718)
                  & V2__m = cIntMap_2eMap_2eM2___24a3(V0__A,Vvar__1___24Anonymous__717,Vvar__2___24Anonymous__718)
                  & cIntMap_2eMap_2eMapGet___24a2(V0__A,V2__m) = c_24__lam__768___24a3(V0__A,Vvar__1___24Anonymous__717,Vvar__2___24Anonymous__718) ) ) ) ) ) ).

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__912___24a1(V0__A) )
          | ? [Vvar__1___24Anonymous__890] :
              ( cIntMap_2eMap_2ead___24t(Vvar__1___24Anonymous__890)
              & ? [Vvar__2___24Anonymous__891] :
                  ( t(Vvar__2___24Anonymous__891,V0__A)
                  & V2__m = cIntMap_2eMap_2eM1___24a3(V0__A,Vvar__1___24Anonymous__890,Vvar__2___24Anonymous__891)
                  & cIntMap_2eMap_2eMapMerge___24a2(V0__A,V2__m) = c_24__lam__916___24a3(V0__A,Vvar__1___24Anonymous__890,Vvar__2___24Anonymous__891) ) )
          | ? [Vvar__1___24Anonymous__896] :
              ( cIntMap_2eMap_2eMap___24t(V0__A,Vvar__1___24Anonymous__896)
              & ? [Vvar__2___24Anonymous__897] :
                  ( cIntMap_2eMap_2eMap___24t(V0__A,Vvar__2___24Anonymous__897)
                  & V2__m = cIntMap_2eMap_2eM2___24a3(V0__A,Vvar__1___24Anonymous__896,Vvar__2___24Anonymous__897)
                  & cIntMap_2eMap_2eMapMerge___24a2(V0__A,V2__m) = c_24__lam__948___24a4(V0__A,V2__m,Vvar__1___24Anonymous__896,Vvar__2___24Anonymous__897) ) ) ) ) ) ).

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__403] :
              ( cIntMap_2eMap_2ead___24t(Vvar__1___24Anonymous__403)
              & ? [Vvar__2___24Anonymous__404] :
                  ( t(Vvar__2___24Anonymous__404,V0__A)
                  & V2__m = cIntMap_2eMap_2eM1___24a3(V0__A,Vvar__1___24Anonymous__403,Vvar__2___24Anonymous__404)
                  & cIntMap_2eMap_2eMapPut___24a2(V0__A,V2__m) = c_24__lam__449___24a3(V0__A,Vvar__1___24Anonymous__403,Vvar__2___24Anonymous__404) ) )
          | ? [Vvar__1___24Anonymous__415] :
              ( cIntMap_2eMap_2eMap___24t(V0__A,Vvar__1___24Anonymous__415)
              & ? [Vvar__2___24Anonymous__416] :
                  ( cIntMap_2eMap_2eMap___24t(V0__A,Vvar__2___24Anonymous__416)
                  & V2__m = cIntMap_2eMap_2eM2___24a3(V0__A,Vvar__1___24Anonymous__415,Vvar__2___24Anonymous__416)
                  & cIntMap_2eMap_2eMapPut___24a2(V0__A,V2__m) = c_24__lam__486___24a3(V0__A,Vvar__1___24Anonymous__415,Vvar__2___24Anonymous__416) ) ) ) ) ) ).

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__1196] :
              ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__1196)
              & ( cType___24t(V0__A)
               => ( cIntMap_2eMap_2ead___24t(V2__a)
                 => ( V6__p = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__1196)
                    & ( ( 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__1198] :
              ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__1198)
              & V6__p = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__1198)
              & 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_241210___24a6(V0__A,V2__a,V3__y,V4__a_27,V5__y_27,Vvar__0___24Anonymous__1198) )
          | ( 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__1255] :
              ( cIntMap_2eMap_2ead___24t(Vvar__1___24Anonymous__1255)
              & ? [Vvar__2___24Anonymous__1256] :
                  ( t(Vvar__2___24Anonymous__1256,V0__A)
                  & V2__m = cIntMap_2eMap_2eM1___24a3(V0__A,Vvar__1___24Anonymous__1255,Vvar__2___24Anonymous__1256)
                  & cIntMap_2eMap_2eMapPut__behind___24a2(V0__A,V2__m) = c_24__lam__1305___24a4(V0__A,V2__m,Vvar__1___24Anonymous__1255,Vvar__2___24Anonymous__1256) ) )
          | ? [Vvar__1___24Anonymous__1267] :
              ( cIntMap_2eMap_2eMap___24t(V0__A,Vvar__1___24Anonymous__1267)
              & ? [Vvar__2___24Anonymous__1268] :
                  ( cIntMap_2eMap_2eMap___24t(V0__A,Vvar__2___24Anonymous__1268)
                  & V2__m = cIntMap_2eMap_2eM2___24a3(V0__A,Vvar__1___24Anonymous__1267,Vvar__2___24Anonymous__1268)
                  & cIntMap_2eMap_2eMapPut__behind___24a2(V0__A,V2__m) = c_24__lam__1342___24a3(V0__A,Vvar__1___24Anonymous__1267,Vvar__2___24Anonymous__1268) ) ) ) ) ) ).

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__864___24a1(V0__A) )
          | ? [Vvar__1___24Anonymous__848] :
              ( cIntMap_2eMap_2ead___24t(Vvar__1___24Anonymous__848)
              & ? [Vvar__2___24Anonymous__849] :
                  ( t(Vvar__2___24Anonymous__849,V0__A)
                  & V2__m = cIntMap_2eMap_2eM1___24a3(V0__A,Vvar__1___24Anonymous__848,Vvar__2___24Anonymous__849)
                  & cIntMap_2eMap_2eMapRemove___24a2(V0__A,V2__m) = c_24__lam__872___24a3(V0__A,V2__m,Vvar__1___24Anonymous__848) ) )
          | ? [Vvar__1___24Anonymous__856] :
              ( cIntMap_2eMap_2eMap___24t(V0__A,Vvar__1___24Anonymous__856)
              & ? [Vvar__2___24Anonymous__857] :
                  ( cIntMap_2eMap_2eMap___24t(V0__A,Vvar__2___24Anonymous__857)
                  & V2__m = cIntMap_2eMap_2eM2___24a3(V0__A,Vvar__1___24Anonymous__856,Vvar__2___24Anonymous__857)
                  & cIntMap_2eMap_2eMapRemove___24a2(V0__A,V2__m) = c_24__lam__880___24a3(V0__A,Vvar__1___24Anonymous__856,Vvar__2___24Anonymous__857) ) ) ) ) ) ).

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__313___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__303] :
                ( cIntMap_2eMap_2ead___24t(Vvar__1___24Anonymous__303)
                & ? [Vvar__2___24Anonymous__304] :
                    ( t(Vvar__2___24Anonymous__304,V0__A)
                    & V6__m = cIntMap_2eMap_2eM1___24a3(V0__A,Vvar__1___24Anonymous__303,Vvar__2___24Anonymous__304)
                    & cIntMap_2eMap_2eMap__rect___24a6(V0__A,V1__P,V2__f,V3__f,V4__f,V6__m) = happ(happ(V3__f,Vvar__1___24Anonymous__303),Vvar__2___24Anonymous__304) ) )
            | ? [Vvar__1___24Anonymous__307] :
                ( cIntMap_2eMap_2eMap___24t(V0__A,Vvar__1___24Anonymous__307)
                & ? [Vvar__2___24Anonymous__308] :
                    ( cIntMap_2eMap_2eMap___24t(V0__A,Vvar__2___24Anonymous__308)
                    & V6__m = cIntMap_2eMap_2eM2___24a3(V0__A,Vvar__1___24Anonymous__307,Vvar__2___24Anonymous__308)
                    & 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__307),cIntMap_2eMap_2eMap__rect___24a6(V0__A,V1__P,V2__f,V3__f,V4__f,Vvar__1___24Anonymous__307)),Vvar__2___24Anonymous__308),cIntMap_2eMap_2eMap__rect___24a6(V0__A,V1__P,V2__f,V3__f,V4__f,Vvar__2___24Anonymous__308)) ) ) ) ) ) ) ).

fof('$_def_IntMap.Map.ad',axiom,
    ! [Vvar__247] :
      ( cIntMap_2eMap_2ead___24t(Vvar__247)
    <=> cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__247) ) ).

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__806] :
                      ( cIntMap_2eMap_2ead___24t(Vvar__1___24Anonymous__806)
                      & ? [Vvar__2___24Anonymous__807] :
                          ( t(Vvar__2___24Anonymous__807,V0__A)
                          & V2__m_27 = cIntMap_2eMap_2eM1___24a3(V0__A,Vvar__1___24Anonymous__806,Vvar__2___24Anonymous__807)
                          & 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__806),Vvar__2___24Anonymous__807) ) )
                  | ? [Vvar__1___24Anonymous__810] :
                      ( cIntMap_2eMap_2eMap___24t(V0__A,Vvar__1___24Anonymous__810)
                      & ? [Vvar__2___24Anonymous__811] :
                          ( cIntMap_2eMap_2eMap___24t(V0__A,Vvar__2___24Anonymous__811)
                          & V2__m_27 = cIntMap_2eMap_2eM2___24a3(V0__A,Vvar__1___24Anonymous__810,Vvar__2___24Anonymous__811)
                          & 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__814] :
              ( cIntMap_2eMap_2ead___24t(Vvar__1___24Anonymous__814)
              & ? [Vvar__2___24Anonymous__815] :
                  ( t(Vvar__2___24Anonymous__815,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__814,Vvar__2___24Anonymous__815)
                        & ( ( 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__814),Vvar__2___24Anonymous__815) )
                          | ? [Vvar__1___24Anonymous__830] :
                              ( cIntMap_2eMap_2ead___24t(Vvar__1___24Anonymous__830)
                              & ? [Vvar__2___24Anonymous__831] :
                                  ( t(Vvar__2___24Anonymous__831,V0__A)
                                  & V2__m_27 = cIntMap_2eMap_2eM1___24a3(V0__A,Vvar__1___24Anonymous__830,Vvar__2___24Anonymous__831)
                                  & 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__834] :
                              ( cIntMap_2eMap_2eMap___24t(V0__A,Vvar__1___24Anonymous__834)
                              & ? [Vvar__2___24Anonymous__835] :
                                  ( cIntMap_2eMap_2eMap___24t(V0__A,Vvar__2___24Anonymous__835)
                                  & V2__m_27 = cIntMap_2eMap_2eM2___24a3(V0__A,Vvar__1___24Anonymous__834,Vvar__2___24Anonymous__835)
                                  & 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__838] :
              ( cIntMap_2eMap_2eMap___24t(V0__A,Vvar__1___24Anonymous__838)
              & ? [Vvar__2___24Anonymous__839] :
                  ( cIntMap_2eMap_2eMap___24t(V0__A,Vvar__2___24Anonymous__839)
                  & V1__m = cIntMap_2eMap_2eM2___24a3(V0__A,Vvar__1___24Anonymous__838,Vvar__2___24Anonymous__839)
                  & 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.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__1378___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__77097] :
                ( cIntMap_2eMap_2ead___24t(Vvar__1___24Anonymous__77097)
                & ? [Vvar__2___24Anonymous__77098] :
                    ( t(Vvar__2___24Anonymous__77098,V0__A)
                    & V5__m = cIntMap_2eMap_2eM1___24a3(V0__A,Vvar__1___24Anonymous__77097,Vvar__2___24Anonymous__77098)
                    & cIntMap_2eMapiter_2eMapCollect1___24a5(V0__A,V1__B,V3__f,V4__pf,V5__m) = happ(happ(V3__f,happ(V4__pf,Vvar__1___24Anonymous__77097)),Vvar__2___24Anonymous__77098) ) )
            | ? [Vvar__1___24Anonymous__77101] :
                ( cIntMap_2eMap_2eMap___24t(V0__A,Vvar__1___24Anonymous__77101)
                & ? [Vvar__2___24Anonymous__77102] :
                    ( cIntMap_2eMap_2eMap___24t(V0__A,Vvar__2___24Anonymous__77102)
                    & V5__m = cIntMap_2eMap_2eM2___24a3(V0__A,Vvar__1___24Anonymous__77101,Vvar__2___24Anonymous__77102)
                    & 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__77113___24a3(V0__A,V1__B,V4__pf),Vvar__1___24Anonymous__77101),cIntMap_2eMapiter_2eMapCollect1___24a5(V0__A,V1__B,V3__f,c_24__lam__77119___24a3(V0__A,V1__B,V4__pf),Vvar__2___24Anonymous__77102)) ) ) ) ) ) ) ).

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__1378___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__67253] :
                ( cIntMap_2eMap_2ead___24t(Vvar__1___24Anonymous__67253)
                & ? [Vvar__2___24Anonymous__67254] :
                    ( t(Vvar__2___24Anonymous__67254,V0__A)
                    & V7__m = cIntMap_2eMap_2eM1___24a3(V0__A,Vvar__1___24Anonymous__67253,Vvar__2___24Anonymous__67254)
                    & 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__67253)),Vvar__2___24Anonymous__67254) ) )
            | ? [Vvar__1___24Anonymous__67257] :
                ( cIntMap_2eMap_2eMap___24t(V0__A,Vvar__1___24Anonymous__67257)
                & ? [Vvar__2___24Anonymous__67258] :
                    ( cIntMap_2eMap_2eMap___24t(V0__A,Vvar__2___24Anonymous__67258)
                    & V7__m = cIntMap_2eMap_2eM2___24a3(V0__A,Vvar__1___24Anonymous__67257,Vvar__2___24Anonymous__67258)
                    & 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__67269___24a3(V0__A,V1__M,V6__pf),Vvar__1___24Anonymous__67257)),cIntMap_2eMapiter_2eMapFold1___24a7(V0__A,V1__M,V2__neutral,V3__op,V5__f,c_24__lam__67275___24a3(V0__A,V1__M,V6__pf),Vvar__2___24Anonymous__67258)) ) ) ) ) ) ) ).

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__77173] :
                  ( cIntMap_2eMap_2ead___24t(Vvar__1___24Anonymous__77173)
                  & ? [Vvar__2___24Anonymous__77174] :
                      ( t(Vvar__2___24Anonymous__77174,V0__A)
                      & V9__m = cIntMap_2eMap_2eM1___24a3(V0__A,Vvar__1___24Anonymous__77173,Vvar__2___24Anonymous__77174)
                      & 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__77173)),Vvar__2___24Anonymous__77174) ) )
              | ? [Vvar__1___24Anonymous__77177] :
                  ( cIntMap_2eMap_2eMap___24t(V0__A,Vvar__1___24Anonymous__77177)
                  & ? [Vvar__2___24Anonymous__77178] :
                      ( cIntMap_2eMap_2eMap___24t(V0__A,Vvar__2___24Anonymous__77178)
                      & ( cType___24t(V0__A)
                       => ( cType___24t(V1__M)
                         => ( t(V2__neutral,V1__M)
                           => ( c_24__type__77225___24t(V0__A,V1__M,V4__State,V3__op)
                             => ( cType___24t(V4__State)
                               => ( c_24__type__77239___24t(V0__A,V1__M,V4__State,V5__f)
                                 => ( t(V7__state,V4__State)
                                   => ( c_24__type__77244___24t(V0__A,V1__M,V4__State,V8__pf)
                                     => ( cIntMap_2eMap_2eMap___24t(V0__A,Vvar__1___24Anonymous__77177)
                                       => ( V9__m = cIntMap_2eMap_2eM2___24a3(V0__A,Vvar__1___24Anonymous__77177,Vvar__2___24Anonymous__77178)
                                          & ? [Vvar__2___24Anonymous__77200] :
                                              ( t(Vvar__2___24Anonymous__77200,V4__State)
                                              & ? [Vvar__3___24Anonymous__77201] :
                                                  ( t(Vvar__3___24Anonymous__77201,V1__M)
                                                  & ( cType___24t(V0__A)
                                                   => ( cType___24t(V1__M)
                                                     => ( t(V2__neutral,V1__M)
                                                       => ( c_24__type__77225___24t(V0__A,V1__M,V4__State,V3__op)
                                                         => ( cType___24t(V4__State)
                                                           => ( c_24__type__77239___24t(V0__A,V1__M,V4__State,V5__f)
                                                             => ( c_24__type__77244___24t(V0__A,V1__M,V4__State,V8__pf)
                                                               => ( cIntMap_2eMap_2eMap___24t(V0__A,Vvar__2___24Anonymous__77178)
                                                                 => ( t(Vvar__2___24Anonymous__77200,V4__State)
                                                                   => ( cIntMap_2eMapiter_2eMapFold1__state___24a9(V0__A,V1__M,V2__neutral,V3__op,V4__State,V5__f,V7__state,c_24__lam__77275___24a4(V0__A,V1__M,V4__State,V8__pf),Vvar__1___24Anonymous__77177) = cCoq_2eInit_2eDatatypes_2epair___24a4(V4__State,V1__M,Vvar__2___24Anonymous__77200,Vvar__3___24Anonymous__77201)
                                                                      & ? [Vvar__2___24Anonymous__77215] :
                                                                          ( t(Vvar__2___24Anonymous__77215,V4__State)
                                                                          & ? [Vvar__3___24Anonymous__77216] :
                                                                              ( t(Vvar__3___24Anonymous__77216,V1__M)
                                                                              & cIntMap_2eMapiter_2eMapFold1__state___24a9(V0__A,V1__M,V2__neutral,V3__op,V4__State,V5__f,Vvar__2___24Anonymous__77200,c_24__lam__77283___24a4(V0__A,V1__M,V4__State,V8__pf),Vvar__2___24Anonymous__77178) = cCoq_2eInit_2eDatatypes_2epair___24a4(V4__State,V1__M,Vvar__2___24Anonymous__77215,Vvar__3___24Anonymous__77216)
                                                                              & 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__77215,happ(happ(V3__op,Vvar__3___24Anonymous__77201),Vvar__3___24Anonymous__77216)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).

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__77375___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__76869___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__76816] :
              ( cIntMap_2eMap_2ead___24t(Vvar__1___24Anonymous__76816)
              & ? [Vvar__2___24Anonymous__76817] :
                  ( t(Vvar__2___24Anonymous__76817,V0__A)
                  & V4__m = cIntMap_2eMap_2eM1___24a3(V0__A,Vvar__1___24Anonymous__76816,Vvar__2___24Anonymous__76817)
                  & 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__76816),Vvar__2___24Anonymous__76817) ) )
          | ? [Vvar__1___24Anonymous__76820] :
              ( cIntMap_2eMap_2eMap___24t(V0__A,Vvar__1___24Anonymous__76820)
              & ? [Vvar__2___24Anonymous__76821] :
                  ( cIntMap_2eMap_2eMap___24t(V0__A,Vvar__2___24Anonymous__76821)
                  & ( cType___24t(V0__A)
                   => ( c_24__type__76796___24t(V0__A,V1__f)
                     => ( c_24__type__1367___24t(V0__A,V3__pf)
                       => ( cIntMap_2eMap_2eMap___24t(V0__A,Vvar__1___24Anonymous__76820)
                         => ( V4__m = cIntMap_2eMap_2eM2___24a3(V0__A,Vvar__1___24Anonymous__76820,Vvar__2___24Anonymous__76821)
                            & ( ? [Vvar__1___24Anonymous__76833] :
                                  ( cCoq_2eInit_2eDatatypes_2eprod___24t(cIntMap_2eMap_2ead,V0__A,Vvar__1___24Anonymous__76833)
                                  & cIntMap_2eMapiter_2eMapSweep1___24a4(V0__A,V1__f,c_24__lam__76842___24a2(V0__A,V3__pf),Vvar__1___24Anonymous__76820) = cCoq_2eInit_2eDatatypes_2eSome___24a2(cCoq_2eInit_2eDatatypes_2eprod___24a2(cIntMap_2eMap_2ead,V0__A),Vvar__1___24Anonymous__76833)
                                  & 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__76833) )
                              | ( cIntMap_2eMapiter_2eMapSweep1___24a4(V0__A,V1__f,c_24__lam__76846___24a2(V0__A,V3__pf),Vvar__1___24Anonymous__76820) = 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__76850___24a2(V0__A,V3__pf),Vvar__2___24Anonymous__76821) ) ) ) ) ) ) ) ) ) ) ) ) ).

fof('$_def_IntMap.Mapiter.MapSweep2',axiom,
    ! [V0__A,V1__f,V2__a0,V3__y] :
      ( cType___24t(V0__A)
     => ( c_24__type__76796___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__67389] :
              ( cCoq_2eInit_2eDatatypes_2eprod___24t(cIntMap_2eMap_2ead,V0__A,Vvar__1___24Anonymous__67389)
              & ? [Vvar__2___24Anonymous__67390] :
                  ( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eInit_2eDatatypes_2eprod___24a2(cIntMap_2eMap_2ead,V0__A),Vvar__2___24Anonymous__67390)
                  & ( cType___24t(V0__A)
                   => ( cCoq_2eInit_2eDatatypes_2eprod___24t(cIntMap_2eMap_2ead,V0__A,Vvar__1___24Anonymous__67389)
                     => ( V2__l = cCoq_2eInit_2eDatatypes_2econs___24a3(cCoq_2eInit_2eDatatypes_2eprod___24a2(cIntMap_2eMap_2ead,V0__A),Vvar__1___24Anonymous__67389,Vvar__2___24Anonymous__67390)
                        & ? [Vvar__2___24Anonymous__67402] :
                            ( cIntMap_2eMap_2ead___24t(Vvar__2___24Anonymous__67402)
                            & ? [Vvar__3___24Anonymous__67403] :
                                ( t(Vvar__3___24Anonymous__67403,V0__A)
                                & Vvar__1___24Anonymous__67389 = cCoq_2eInit_2eDatatypes_2epair___24a4(cIntMap_2eMap_2ead,V0__A,Vvar__2___24Anonymous__67402,Vvar__3___24Anonymous__67403)
                                & 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__67390),Vvar__2___24Anonymous__67402,Vvar__3___24Anonymous__67403) ) ) ) ) ) ) ) ) ) ) ).

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__67335___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__733___24a1(V0__A) )
          | ? [Vvar__1___24Anonymous__67343] :
              ( cCoq_2eInit_2eDatatypes_2eprod___24t(cIntMap_2eMap_2ead,V0__A,Vvar__1___24Anonymous__67343)
              & ? [Vvar__2___24Anonymous__67344] :
                  ( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eInit_2eDatatypes_2eprod___24a2(cIntMap_2eMap_2ead,V0__A),Vvar__2___24Anonymous__67344)
                  & ( cType___24t(V0__A)
                   => ( cCoq_2eInit_2eDatatypes_2eprod___24t(cIntMap_2eMap_2ead,V0__A,Vvar__1___24Anonymous__67343)
                     => ( V2__l = cCoq_2eInit_2eDatatypes_2econs___24a3(cCoq_2eInit_2eDatatypes_2eprod___24a2(cIntMap_2eMap_2ead,V0__A),Vvar__1___24Anonymous__67343,Vvar__2___24Anonymous__67344)
                        & ? [Vvar__2___24Anonymous__67362] :
                            ( cIntMap_2eMap_2ead___24t(Vvar__2___24Anonymous__67362)
                            & ? [Vvar__3___24Anonymous__67363] :
                                ( t(Vvar__3___24Anonymous__67363,V0__A)
                                & Vvar__1___24Anonymous__67343 = cCoq_2eInit_2eDatatypes_2epair___24a4(cIntMap_2eMap_2ead,V0__A,Vvar__2___24Anonymous__67362,Vvar__3___24Anonymous__67363)
                                & cIntMap_2eMapiter_2ealist__semantics___24a2(V0__A,V2__l) = c_24__lam__67379___24a4(V0__A,Vvar__2___24Anonymous__67344,Vvar__2___24Anonymous__67362,Vvar__3___24Anonymous__67363) ) ) ) ) ) ) ) ) ) ) ).

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__77837] :
                  ( cCoq_2eInit_2eDatatypes_2eprod___24t(cIntMap_2eMap_2ead,V0__A,Vvar__1___24Anonymous__77837)
                  & cIntMap_2eMapiter_2eMapSweep___24a3(V0__A,c_24__lam__77846___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__77837)
                  & 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__77846___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__77803] :
                  ( cCoq_2eInit_2eDatatypes_2eprod___24t(cIntMap_2eMap_2ead,V0__A,Vvar__1___24Anonymous__77803)
                  & cIntMap_2eMapiter_2eMapSweep___24a3(V0__A,c_24__lam__77812___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__77803)
                  & 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__77812___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('$_def_Mapcanon.MapCanon.MapCanonicalize',axiom,
    ! [V1__m] :
      ( cIntMap_2eMap_2eMap___24t(cA,V1__m)
     => ( ( V1__m = cIntMap_2eMap_2eM0___24a1(cA)
          & cMapcanon_2eMapCanon_2eMapCanonicalize___24a1(V1__m) = V1__m )
        | ? [Vvar__1___24Anonymous__122076] :
            ( cIntMap_2eMap_2ead___24t(Vvar__1___24Anonymous__122076)
            & ? [Vvar__2___24Anonymous__122077] :
                ( cA___24t(Vvar__2___24Anonymous__122077)
                & V1__m = cIntMap_2eMap_2eM1___24a3(cA,Vvar__1___24Anonymous__122076,Vvar__2___24Anonymous__122077)
                & cMapcanon_2eMapCanon_2eMapCanonicalize___24a1(V1__m) = V1__m ) )
        | ? [Vvar__1___24Anonymous__122080] :
            ( cIntMap_2eMap_2eMap___24t(cA,Vvar__1___24Anonymous__122080)
            & ? [Vvar__2___24Anonymous__122081] :
                ( cIntMap_2eMap_2eMap___24t(cA,Vvar__2___24Anonymous__122081)
                & V1__m = cIntMap_2eMap_2eM2___24a3(cA,Vvar__1___24Anonymous__122080,Vvar__2___24Anonymous__122081)
                & cMapcanon_2eMapCanon_2eMapCanonicalize___24a1(V1__m) = cIntMap_2eMap_2emakeM2___24a3(cA,cMapcanon_2eMapCanon_2eMapCanonicalize___24a1(Vvar__1___24Anonymous__122080),cMapcanon_2eMapCanon_2eMapCanonicalize___24a1(Vvar__2___24Anonymous__122081)) ) ) ) ) ).

fof('$_discrim_Coq.Bool.Bool.ReflectT$Coq.Bool.Bool.ReflectF',axiom,
    ! [Vvar__0__P__94164,Vvar__1___24Anonymous__94165,Vvar__0__P__94166,Vvar__1___24Anonymous__94167] : cCoq_2eBool_2eBool_2eReflectT___24a1(Vvar__0__P__94164) != cCoq_2eBool_2eBool_2eReflectF___24a1(Vvar__0__P__94166) ).

fof('$_discrim_Coq.FSets.FSetPositive.PositiveSet.Leaf$Coq.FSets.FSetPositive.PositiveSet.Node',axiom,
    ! [Vvar__0___24Anonymous__93197,Vvar__1___24Anonymous__93198,Vvar__2___24Anonymous__93199] : cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eLeaf != cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eNode___24a3(Vvar__0___24Anonymous__93197,Vvar__1___24Anonymous__93198,Vvar__2___24Anonymous__93199) ).

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__83396,Vvar__1__Plt__83397,Vvar__2__Pgt__83398,Vvar__3___24Anonymous__83399,Vvar__0__Peq__83400,Vvar__1__Plt__83401,Vvar__2__Pgt__83402,Vvar__3___24Anonymous__83403] : cCoq_2eInit_2eDatatypes_2eCompEqT___24a3(Vvar__0__Peq__83396,Vvar__1__Plt__83397,Vvar__2__Pgt__83398) != cCoq_2eInit_2eDatatypes_2eCompLtT___24a3(Vvar__0__Peq__83400,Vvar__1__Plt__83401,Vvar__2__Pgt__83402) ).

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__3] : cCoq_2eInit_2eDatatypes_2eO != cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__3) ).

fof('$_discrim_Coq.Init.Datatypes.Some$Coq.Init.Datatypes.None',axiom,
    ! [Vvar__0__A__637,Vvar__1___24Anonymous__638,Vvar__0__A__639] : cCoq_2eInit_2eDatatypes_2eSome___24a2(Vvar__0__A__637,Vvar__1___24Anonymous__638) != cCoq_2eInit_2eDatatypes_2eNone___24a1(Vvar__0__A__639) ).

fof('$_discrim_Coq.Init.Datatypes.inl$Coq.Init.Datatypes.inr',axiom,
    ! [Vvar__0__A__75531,Vvar__1__B__75532,Vvar__2___24Anonymous__75533,Vvar__0__A__75534,Vvar__1__B__75535,Vvar__2___24Anonymous__75536] : cCoq_2eInit_2eDatatypes_2einl___24a3(Vvar__0__A__75531,Vvar__1__B__75532,Vvar__2___24Anonymous__75533) != cCoq_2eInit_2eDatatypes_2einr___24a3(Vvar__0__A__75534,Vvar__1__B__75535,Vvar__2___24Anonymous__75536) ).

fof('$_discrim_Coq.Init.Datatypes.nil$Coq.Init.Datatypes.cons',axiom,
    ! [Vvar__0__A__75648,Vvar__0__A__75649,Vvar__1___24Anonymous__75650,Vvar__2___24Anonymous__75651] : cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__75648) != cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__75649,Vvar__1___24Anonymous__75650,Vvar__2___24Anonymous__75651) ).

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

fof('$_discrim_Coq.Init.Decimal.Decimal$Coq.Init.Decimal.DecimalExp',axiom,
    ! [Vvar__0__i__94218,Vvar__1__f__94219,Vvar__0__i__94220,Vvar__1__f__94221,Vvar__2__e__94222] : cCoq_2eInit_2eDecimal_2eDecimal___24a2(Vvar__0__i__94218,Vvar__1__f__94219) != cCoq_2eInit_2eDecimal_2eDecimalExp___24a3(Vvar__0__i__94220,Vvar__1__f__94221,Vvar__2__e__94222) ).

fof('$_discrim_Coq.Init.Decimal.Nil$Coq.Init.Decimal.D0',axiom,
    ! [Vvar__0___24Anonymous__75855] : cCoq_2eInit_2eDecimal_2eNil != cCoq_2eInit_2eDecimal_2eD0___24a1(Vvar__0___24Anonymous__75855) ).

fof('$_discrim_Coq.Init.Decimal.Pos$Coq.Init.Decimal.Neg',axiom,
    ! [Vvar__0__d__94206,Vvar__0__d__94207] : cCoq_2eInit_2eDecimal_2ePos___24a1(Vvar__0__d__94206) != cCoq_2eInit_2eDecimal_2eNeg___24a1(Vvar__0__d__94207) ).

fof('$_discrim_Coq.Init.Specif.inleft$Coq.Init.Specif.inright',axiom,
    ! [Vvar__0__A__1081,Vvar__1__B__1082,Vvar__2___24Anonymous__1083,Vvar__0__A__1084,Vvar__1__B__1085,Vvar__2___24Anonymous__1086] : cCoq_2eInit_2eSpecif_2einleft___24a3(Vvar__0__A__1081,Vvar__1__B__1082,Vvar__2___24Anonymous__1083) != cCoq_2eInit_2eSpecif_2einright___24a2(Vvar__0__A__1084,Vvar__1__B__1085) ).

fof('$_discrim_Coq.Init.Specif.left$Coq.Init.Specif.right',axiom,
    ! [Vvar__0__A__588,Vvar__1__B__589,Vvar__2___24Anonymous__590,Vvar__0__A__591,Vvar__1__B__592,Vvar__2___24Anonymous__593] : cCoq_2eInit_2eSpecif_2eleft___24a2(Vvar__0__A__588,Vvar__1__B__589) != cCoq_2eInit_2eSpecif_2eright___24a2(Vvar__0__A__591,Vvar__1__B__592) ).

fof('$_discrim_Coq.Numbers.BinNums.N0$Coq.Numbers.BinNums.Npos',axiom,
    ! [Vvar__0___24Anonymous__1129] : cCoq_2eNumbers_2eBinNums_2eN0 != cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__1129) ).

fof('$_discrim_Coq.Numbers.BinNums.Z0$Coq.Numbers.BinNums.Zpos',axiom,
    ! [Vvar__0___24Anonymous__68102] : cCoq_2eNumbers_2eBinNums_2eZ0 != cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__68102) ).

fof('$_discrim_Coq.Numbers.BinNums.xI$Coq.Numbers.BinNums.xO',axiom,
    ! [Vvar__0___24Anonymous__1113,Vvar__0___24Anonymous__1114] : cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__1113) != cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__1114) ).

fof('$_discrim_Coq.PArith.BinPos.Pos.PeanoOne$Coq.PArith.BinPos.Pos.PeanoSucc',axiom,
    ! [Vvar__0__p__105669,Vvar__1___24Anonymous__105670] : cCoq_2ePArith_2eBinPos_2ePos_2ePeanoOne != cCoq_2ePArith_2eBinPos_2ePos_2ePeanoSucc___24a2(Vvar__0__p__105669,Vvar__1___24Anonymous__105670) ).

fof('$_discrim_Coq.PArith.BinPosDef.Pos.IsNul$Coq.PArith.BinPosDef.Pos.IsPos',axiom,
    ! [Vvar__0___24Anonymous__93084] : cCoq_2ePArith_2eBinPosDef_2ePos_2eIsNul != cCoq_2ePArith_2eBinPosDef_2ePos_2eIsPos___24a1(Vvar__0___24Anonymous__93084) ).

fof('$_discrim_Coq.Reals.Rfunctions.ZintNull$Coq.Reals.Rfunctions.ZintPos',axiom,
    ! [Vvar__0__x__98181,Vvar__1___24Anonymous__98182,Vvar__0__x__98183,Vvar__1__n__98184,Vvar__2___24Anonymous__98185] : cCoq_2eReals_2eRfunctions_2eZintNull___24a1(Vvar__0__x__98181) != cCoq_2eReals_2eRfunctions_2eZintPos___24a2(Vvar__0__x__98183,Vvar__1__n__98184) ).

fof('$_discrim_Coq.Strings.String.EmptyString$Coq.Strings.String.String',axiom,
    ! [Vvar__0___24Anonymous__82306,Vvar__1___24Anonymous__82307] : cCoq_2eStrings_2eString_2eEmptyString != cCoq_2eStrings_2eString_2eString___24a2(Vvar__0___24Anonymous__82306,Vvar__1___24Anonymous__82307) ).

fof('$_discrim_Coq.Structures.OrderedType.LT$Coq.Structures.OrderedType.EQ',axiom,
    ! [Vvar__0__X__97124,Vvar__1__lt__97125,Vvar__2__eq__97126,Vvar__3__x__97127,Vvar__4__y__97128,Vvar__5___24Anonymous__97129,Vvar__0__X__97130,Vvar__1__lt__97131,Vvar__2__eq__97132,Vvar__3__x__97133,Vvar__4__y__97134,Vvar__5___24Anonymous__97135] : cCoq_2eStructures_2eOrderedType_2eLT___24a5(Vvar__0__X__97124,Vvar__1__lt__97125,Vvar__2__eq__97126,Vvar__3__x__97127,Vvar__4__y__97128) != cCoq_2eStructures_2eOrderedType_2eEQ___24a5(Vvar__0__X__97130,Vvar__1__lt__97131,Vvar__2__eq__97132,Vvar__3__x__97133,Vvar__4__y__97134) ).

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__75889,Vvar__0__n__75890,Vvar__1___24Anonymous__75891] : cCoq_2eVectors_2eFin_2eF1___24a1(Vvar__0__n__75889) != cCoq_2eVectors_2eFin_2eFS___24a2(Vvar__0__n__75890,Vvar__1___24Anonymous__75891) ).

fof('$_discrim_Coq.Vectors.VectorDef.nil$Coq.Vectors.VectorDef.cons',axiom,
    ! [Vvar__0__A__79267,Vvar__0__A__79268,Vvar__1__h__79269,Vvar__2__n__79270,Vvar__3___24Anonymous__79271] : cCoq_2eVectors_2eVectorDef_2enil___24a1(Vvar__0__A__79267) != cCoq_2eVectors_2eVectorDef_2econs___24a4(Vvar__0__A__79268,Vvar__1__h__79269,Vvar__2__n__79270,Vvar__3___24Anonymous__79271) ).

fof('$_discrim_Coq.micromega.EnvRing.PEc$Coq.micromega.EnvRing.PEX',axiom,
    ! [Vvar__0__C__94370,Vvar__1___24Anonymous__94371,Vvar__0__C__94372,Vvar__1___24Anonymous__94373] : cCoq_2emicromega_2eEnvRing_2ePEc___24a2(Vvar__0__C__94370,Vvar__1___24Anonymous__94371) != cCoq_2emicromega_2eEnvRing_2ePEX___24a2(Vvar__0__C__94372,Vvar__1___24Anonymous__94373) ).

fof('$_discrim_Coq.micromega.EnvRing.Pc$Coq.micromega.EnvRing.Pinj',axiom,
    ! [Vvar__0__C__83547,Vvar__1___24Anonymous__83548,Vvar__0__C__83549,Vvar__1___24Anonymous__83550,Vvar__2___24Anonymous__83551] : cCoq_2emicromega_2eEnvRing_2ePc___24a2(Vvar__0__C__83547,Vvar__1___24Anonymous__83548) != cCoq_2emicromega_2eEnvRing_2ePinj___24a3(Vvar__0__C__83549,Vvar__1___24Anonymous__83550,Vvar__2___24Anonymous__83551) ).

fof('$_discrim_Coq.micromega.EnvRing.mon0$Coq.micromega.EnvRing.zmon',axiom,
    ! [Vvar__0___24Anonymous__94421,Vvar__1___24Anonymous__94422] : cCoq_2emicromega_2eEnvRing_2emon0 != cCoq_2emicromega_2eEnvRing_2ezmon___24a2(Vvar__0___24Anonymous__94421,Vvar__1___24Anonymous__94422) ).

fof('$_discrim_Coq.micromega.RMicromega.C0$Coq.micromega.RMicromega.C1',axiom,
    cCoq_2emicromega_2eRMicromega_2eC0 != cCoq_2emicromega_2eRMicromega_2eC1 ).

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('$_discrim_Coq.micromega.RingMicromega.PsatzIn$Coq.micromega.RingMicromega.PsatzSquare',axiom,
    ! [Vvar__0__C__103606,Vvar__1___24Anonymous__103607,Vvar__0__C__103608,Vvar__1___24Anonymous__103609] : cCoq_2emicromega_2eRingMicromega_2ePsatzIn___24a2(Vvar__0__C__103606,Vvar__1___24Anonymous__103607) != cCoq_2emicromega_2eRingMicromega_2ePsatzSquare___24a2(Vvar__0__C__103608,Vvar__1___24Anonymous__103609) ).

fof('$_discrim_Coq.micromega.Tauto.TT$Coq.micromega.Tauto.FF',axiom,
    ! [Vvar__0__TA__91355,Vvar__1__TX__91356,Vvar__2__AA__91357,Vvar__3__AF__91358,Vvar__0__TA__91359,Vvar__1__TX__91360,Vvar__2__AA__91361,Vvar__3__AF__91362] : cCoq_2emicromega_2eTauto_2eTT___24a4(Vvar__0__TA__91355,Vvar__1__TX__91356,Vvar__2__AA__91357,Vvar__3__AF__91358) != cCoq_2emicromega_2eTauto_2eFF___24a4(Vvar__0__TA__91359,Vvar__1__TX__91360,Vvar__2__AA__91361,Vvar__3__AF__91362) ).

fof('$_discrim_Coq.micromega.VarMap.Empty$Coq.micromega.VarMap.Elt',axiom,
    ! [Vvar__0__A__105313,Vvar__0__A__105314,Vvar__1___24Anonymous__105315] : cCoq_2emicromega_2eVarMap_2eEmpty___24a1(Vvar__0__A__105313) != cCoq_2emicromega_2eVarMap_2eElt___24a2(Vvar__0__A__105314,Vvar__1___24Anonymous__105315) ).

fof('$_discrim_Coq.micromega.ZMicromega.DoneProof$Coq.micromega.ZMicromega.RatProof',axiom,
    ! [Vvar__0___24Anonymous__92876,Vvar__1___24Anonymous__92877] : cCoq_2emicromega_2eZMicromega_2eDoneProof != cCoq_2emicromega_2eZMicromega_2eRatProof___24a2(Vvar__0___24Anonymous__92876,Vvar__1___24Anonymous__92877) ).

fof('$_discrim_Coq.setoid_ring.Field_theory.FEO$Coq.setoid_ring.Field_theory.FEI',axiom,
    ! [Vvar__0__C__95494,Vvar__0__C__95495] : cCoq_2esetoid__ring_2eField__theory_2eFEO___24a1(Vvar__0__C__95494) != cCoq_2esetoid__ring_2eField__theory_2eFEI___24a1(Vvar__0__C__95495) ).

fof('$_discrim_Coq.setoid_ring.Ring_polynom.PEO$Coq.setoid_ring.Ring_polynom.PEI',axiom,
    ! [Vvar__0__C__78428,Vvar__0__C__78429] : cCoq_2esetoid__ring_2eRing__polynom_2ePEO___24a1(Vvar__0__C__78428) != cCoq_2esetoid__ring_2eRing__polynom_2ePEI___24a1(Vvar__0__C__78429) ).

fof('$_discrim_Coq.setoid_ring.Ring_polynom.Pc$Coq.setoid_ring.Ring_polynom.Pinj',axiom,
    ! [Vvar__0__C__78070,Vvar__1___24Anonymous__78071,Vvar__0__C__78072,Vvar__1___24Anonymous__78073,Vvar__2___24Anonymous__78074] : cCoq_2esetoid__ring_2eRing__polynom_2ePc___24a2(Vvar__0__C__78070,Vvar__1___24Anonymous__78071) != cCoq_2esetoid__ring_2eRing__polynom_2ePinj___24a3(Vvar__0__C__78072,Vvar__1___24Anonymous__78073,Vvar__2___24Anonymous__78074) ).

fof('$_discrim_Coq.setoid_ring.Ring_polynom.mon0$Coq.setoid_ring.Ring_polynom.zmon',axiom,
    ! [Vvar__0___24Anonymous__78238,Vvar__1___24Anonymous__78239] : cCoq_2esetoid__ring_2eRing__polynom_2emon0 != cCoq_2esetoid__ring_2eRing__polynom_2ezmon___24a2(Vvar__0___24Anonymous__78238,Vvar__1___24Anonymous__78239) ).

fof('$_discrim_Coq.setoid_ring.Ring_theory.Abstract$Coq.setoid_ring.Ring_theory.Computational',axiom,
    ! [Vvar__0__R__89823,Vvar__1__req__89824,Vvar__2__reqb__89825,Vvar__3___24Anonymous__89826] : cCoq_2esetoid__ring_2eRing__theory_2eAbstract != cCoq_2esetoid__ring_2eRing__theory_2eComputational___24a3(Vvar__0__R__89823,Vvar__1__req__89824,Vvar__2__reqb__89825) ).

fof('$_discrim_Hammer.Tactics.Reconstr.Empty$Hammer.Tactics.Reconstr.AllHyps',axiom,
    cHammer_2eTactics_2eReconstr_2eEmpty != cHammer_2eTactics_2eReconstr_2eAllHyps ).

fof('$_discrim_IntMap.Map.M0$IntMap.Map.M1',axiom,
    ! [Vvar__0__A__269,Vvar__0__A__270,Vvar__1___24Anonymous__271,Vvar__2___24Anonymous__272] : cIntMap_2eMap_2eM0___24a1(Vvar__0__A__269) != cIntMap_2eMap_2eM1___24a3(Vvar__0__A__270,Vvar__1___24Anonymous__271,Vvar__2___24Anonymous__272) ).

fof('$_fix_105664_v_CANONICAL_0',axiom,
    ! [Vv__CANONICAL__1] :
      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__1)
     => ( ? [Vvar__0___24Anonymous__105665] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__105665)
            & Vv__CANONICAL__1 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__105665)
            & c_24__fix__105664__v__CANONICAL__0___24a1(Vv__CANONICAL__1) = cCoq_2eNumbers_2eBinNums_2exO___24a1(c_24__fix__105664__v__CANONICAL__0___24a1(Vvar__0___24Anonymous__105665)) )
        | ? [Vvar__0___24Anonymous__105666] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__105666)
            & Vv__CANONICAL__1 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__105666)
            & c_24__fix__105664__v__CANONICAL__0___24a1(Vv__CANONICAL__1) = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__105666) )
        | ( Vv__CANONICAL__1 = cCoq_2eNumbers_2eBinNums_2exH
          & c_24__fix__105664__v__CANONICAL__0___24a1(Vv__CANONICAL__1) = cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2eNumbers_2eBinNums_2exH) ) ) ) ).

fof('$_fix_98017_v_CANONICAL_1',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__2,Vv__CANONICAL__3] :
      ( cType___24t(Vv__CANONICAL__0)
     => ( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
       => ( ( Vv__CANONICAL__2 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vv__CANONICAL__0)
            & c_24__fix__98017__v__CANONICAL__1___24a3(Vv__CANONICAL__0,Vv__CANONICAL__2,Vv__CANONICAL__3) = Vv__CANONICAL__3 )
          | ? [Vvar__1___24Anonymous__98021] :
              ( t(Vvar__1___24Anonymous__98021,Vv__CANONICAL__0)
              & ? [Vvar__2___24Anonymous__98022] :
                  ( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vvar__2___24Anonymous__98022)
                  & Vv__CANONICAL__2 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vv__CANONICAL__0,Vvar__1___24Anonymous__98021,Vvar__2___24Anonymous__98022)
                  & c_24__fix__98017__v__CANONICAL__1___24a3(Vv__CANONICAL__0,Vv__CANONICAL__2,Vv__CANONICAL__3) = cCoq_2eInit_2eDatatypes_2econs___24a3(Vv__CANONICAL__0,Vvar__1___24Anonymous__98021,c_24__fix__98017__v__CANONICAL__1___24a3(Vv__CANONICAL__0,Vvar__2___24Anonymous__98022,Vv__CANONICAL__3)) ) ) ) ) ) ).

fof('$_inj_Coq.Bool.Bool.ReflectF',axiom,
    ! [Vvar__0__P__94172,Vvar__0__P__94173,Vvar__1___24Anonymous__94174,Vvar__1___24Anonymous__94175] :
      ( cCoq_2eBool_2eBool_2eReflectF___24a1(Vvar__0__P__94172) = cCoq_2eBool_2eBool_2eReflectF___24a1(Vvar__0__P__94173)
     => ( c_24Proof = c_24Proof
        & Vvar__0__P__94172 = Vvar__0__P__94173 ) ) ).

fof('$_inj_Coq.Bool.Bool.ReflectT',axiom,
    ! [Vvar__0__P__94168,Vvar__0__P__94169,Vvar__1___24Anonymous__94170,Vvar__1___24Anonymous__94171] :
      ( cCoq_2eBool_2eBool_2eReflectT___24a1(Vvar__0__P__94168) = cCoq_2eBool_2eBool_2eReflectT___24a1(Vvar__0__P__94169)
     => ( c_24Proof = c_24Proof
        & Vvar__0__P__94168 = Vvar__0__P__94169 ) ) ).

fof('$_inj_Coq.FSets.FSetPositive.PositiveSet.Node',axiom,
    ! [Vvar__0___24Anonymous__93200,Vvar__0___24Anonymous__93201,Vvar__1___24Anonymous__93202,Vvar__1___24Anonymous__93203,Vvar__2___24Anonymous__93204,Vvar__2___24Anonymous__93205] :
      ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eNode___24a3(Vvar__0___24Anonymous__93200,Vvar__1___24Anonymous__93202,Vvar__2___24Anonymous__93204) = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eNode___24a3(Vvar__0___24Anonymous__93201,Vvar__1___24Anonymous__93203,Vvar__2___24Anonymous__93205)
     => ( Vvar__2___24Anonymous__93204 = Vvar__2___24Anonymous__93205
        & Vvar__1___24Anonymous__93202 = Vvar__1___24Anonymous__93203
        & Vvar__0___24Anonymous__93200 = Vvar__0___24Anonymous__93201 ) ) ).

fof('$_inj_Coq.Init.Datatypes.CompEqT',axiom,
    ! [Vvar__0__Peq__83404,Vvar__0__Peq__83405,Vvar__1__Plt__83406,Vvar__1__Plt__83407,Vvar__2__Pgt__83408,Vvar__2__Pgt__83409,Vvar__3___24Anonymous__83410,Vvar__3___24Anonymous__83411] :
      ( cCoq_2eInit_2eDatatypes_2eCompEqT___24a3(Vvar__0__Peq__83404,Vvar__1__Plt__83406,Vvar__2__Pgt__83408) = cCoq_2eInit_2eDatatypes_2eCompEqT___24a3(Vvar__0__Peq__83405,Vvar__1__Plt__83407,Vvar__2__Pgt__83409)
     => ( c_24Proof = c_24Proof
        & Vvar__2__Pgt__83408 = Vvar__2__Pgt__83409
        & Vvar__1__Plt__83406 = Vvar__1__Plt__83407
        & Vvar__0__Peq__83404 = Vvar__0__Peq__83405 ) ) ).

fof('$_inj_Coq.Init.Datatypes.CompGtT',axiom,
    ! [Vvar__0__Peq__83420,Vvar__0__Peq__83421,Vvar__1__Plt__83422,Vvar__1__Plt__83423,Vvar__2__Pgt__83424,Vvar__2__Pgt__83425,Vvar__3___24Anonymous__83426,Vvar__3___24Anonymous__83427] :
      ( cCoq_2eInit_2eDatatypes_2eCompGtT___24a3(Vvar__0__Peq__83420,Vvar__1__Plt__83422,Vvar__2__Pgt__83424) = cCoq_2eInit_2eDatatypes_2eCompGtT___24a3(Vvar__0__Peq__83421,Vvar__1__Plt__83423,Vvar__2__Pgt__83425)
     => ( c_24Proof = c_24Proof
        & Vvar__2__Pgt__83424 = Vvar__2__Pgt__83425
        & Vvar__1__Plt__83422 = Vvar__1__Plt__83423
        & Vvar__0__Peq__83420 = Vvar__0__Peq__83421 ) ) ).

fof('$_inj_Coq.Init.Datatypes.CompLtT',axiom,
    ! [Vvar__0__Peq__83412,Vvar__0__Peq__83413,Vvar__1__Plt__83414,Vvar__1__Plt__83415,Vvar__2__Pgt__83416,Vvar__2__Pgt__83417,Vvar__3___24Anonymous__83418,Vvar__3___24Anonymous__83419] :
      ( cCoq_2eInit_2eDatatypes_2eCompLtT___24a3(Vvar__0__Peq__83412,Vvar__1__Plt__83414,Vvar__2__Pgt__83416) = cCoq_2eInit_2eDatatypes_2eCompLtT___24a3(Vvar__0__Peq__83413,Vvar__1__Plt__83415,Vvar__2__Pgt__83417)
     => ( c_24Proof = c_24Proof
        & Vvar__2__Pgt__83416 = Vvar__2__Pgt__83417
        & Vvar__1__Plt__83414 = Vvar__1__Plt__83415
        & Vvar__0__Peq__83412 = Vvar__0__Peq__83413 ) ) ).

fof('$_inj_Coq.Init.Datatypes.None',axiom,
    ! [Vvar__0__A__644,Vvar__0__A__645] :
      ( cCoq_2eInit_2eDatatypes_2eNone___24a1(Vvar__0__A__644) = cCoq_2eInit_2eDatatypes_2eNone___24a1(Vvar__0__A__645)
     => Vvar__0__A__644 = Vvar__0__A__645 ) ).

fof('$_inj_Coq.Init.Datatypes.S',axiom,
    ! [Vvar__0___24Anonymous__4,Vvar__0___24Anonymous__5] :
      ( cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__4) = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__5)
     => Vvar__0___24Anonymous__4 = Vvar__0___24Anonymous__5 ) ).

fof('$_inj_Coq.Init.Datatypes.Some',axiom,
    ! [Vvar__0__A__640,Vvar__0__A__641,Vvar__1___24Anonymous__642,Vvar__1___24Anonymous__643] :
      ( cCoq_2eInit_2eDatatypes_2eSome___24a2(Vvar__0__A__640,Vvar__1___24Anonymous__642) = cCoq_2eInit_2eDatatypes_2eSome___24a2(Vvar__0__A__641,Vvar__1___24Anonymous__643)
     => ( Vvar__1___24Anonymous__642 = Vvar__1___24Anonymous__643
        & Vvar__0__A__640 = Vvar__0__A__641 ) ) ).

fof('$_inj_Coq.Init.Datatypes.cons',axiom,
    ! [Vvar__0__A__75654,Vvar__0__A__75655,Vvar__1___24Anonymous__75656,Vvar__1___24Anonymous__75657,Vvar__2___24Anonymous__75658,Vvar__2___24Anonymous__75659] :
      ( cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__75654,Vvar__1___24Anonymous__75656,Vvar__2___24Anonymous__75658) = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__75655,Vvar__1___24Anonymous__75657,Vvar__2___24Anonymous__75659)
     => ( Vvar__2___24Anonymous__75658 = Vvar__2___24Anonymous__75659
        & Vvar__1___24Anonymous__75656 = Vvar__1___24Anonymous__75657
        & Vvar__0__A__75654 = Vvar__0__A__75655 ) ) ).

fof('$_inj_Coq.Init.Datatypes.inl',axiom,
    ! [Vvar__0__A__75537,Vvar__0__A__75538,Vvar__1__B__75539,Vvar__1__B__75540,Vvar__2___24Anonymous__75541,Vvar__2___24Anonymous__75542] :
      ( cCoq_2eInit_2eDatatypes_2einl___24a3(Vvar__0__A__75537,Vvar__1__B__75539,Vvar__2___24Anonymous__75541) = cCoq_2eInit_2eDatatypes_2einl___24a3(Vvar__0__A__75538,Vvar__1__B__75540,Vvar__2___24Anonymous__75542)
     => ( Vvar__2___24Anonymous__75541 = Vvar__2___24Anonymous__75542
        & Vvar__1__B__75539 = Vvar__1__B__75540
        & Vvar__0__A__75537 = Vvar__0__A__75538 ) ) ).

fof('$_inj_Coq.Init.Datatypes.inr',axiom,
    ! [Vvar__0__A__75543,Vvar__0__A__75544,Vvar__1__B__75545,Vvar__1__B__75546,Vvar__2___24Anonymous__75547,Vvar__2___24Anonymous__75548] :
      ( cCoq_2eInit_2eDatatypes_2einr___24a3(Vvar__0__A__75543,Vvar__1__B__75545,Vvar__2___24Anonymous__75547) = cCoq_2eInit_2eDatatypes_2einr___24a3(Vvar__0__A__75544,Vvar__1__B__75546,Vvar__2___24Anonymous__75548)
     => ( Vvar__2___24Anonymous__75547 = Vvar__2___24Anonymous__75548
        & Vvar__1__B__75545 = Vvar__1__B__75546
        & Vvar__0__A__75543 = Vvar__0__A__75544 ) ) ).

fof('$_inj_Coq.Init.Datatypes.nil',axiom,
    ! [Vvar__0__A__75652,Vvar__0__A__75653] :
      ( cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__75652) = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__75653)
     => Vvar__0__A__75652 = Vvar__0__A__75653 ) ).

fof('$_inj_Coq.Init.Datatypes.pair',axiom,
    ! [Vvar__0__A__67034,Vvar__0__A__67035,Vvar__1__B__67036,Vvar__1__B__67037,Vvar__2___24Anonymous__67038,Vvar__2___24Anonymous__67039,Vvar__3___24Anonymous__67040,Vvar__3___24Anonymous__67041] :
      ( cCoq_2eInit_2eDatatypes_2epair___24a4(Vvar__0__A__67034,Vvar__1__B__67036,Vvar__2___24Anonymous__67038,Vvar__3___24Anonymous__67040) = cCoq_2eInit_2eDatatypes_2epair___24a4(Vvar__0__A__67035,Vvar__1__B__67037,Vvar__2___24Anonymous__67039,Vvar__3___24Anonymous__67041)
     => ( Vvar__3___24Anonymous__67040 = Vvar__3___24Anonymous__67041
        & Vvar__2___24Anonymous__67038 = Vvar__2___24Anonymous__67039
        & Vvar__1__B__67036 = Vvar__1__B__67037
        & Vvar__0__A__67034 = Vvar__0__A__67035 ) ) ).

fof('$_inj_Coq.Init.Decimal.D0',axiom,
    ! [Vvar__0___24Anonymous__75856,Vvar__0___24Anonymous__75857] :
      ( cCoq_2eInit_2eDecimal_2eD0___24a1(Vvar__0___24Anonymous__75856) = cCoq_2eInit_2eDecimal_2eD0___24a1(Vvar__0___24Anonymous__75857)
     => Vvar__0___24Anonymous__75856 = Vvar__0___24Anonymous__75857 ) ).

fof('$_inj_Coq.Init.Decimal.D1',axiom,
    ! [Vvar__0___24Anonymous__75858,Vvar__0___24Anonymous__75859] :
      ( cCoq_2eInit_2eDecimal_2eD1___24a1(Vvar__0___24Anonymous__75858) = cCoq_2eInit_2eDecimal_2eD1___24a1(Vvar__0___24Anonymous__75859)
     => Vvar__0___24Anonymous__75858 = Vvar__0___24Anonymous__75859 ) ).

fof('$_inj_Coq.Init.Decimal.D2',axiom,
    ! [Vvar__0___24Anonymous__75860,Vvar__0___24Anonymous__75861] :
      ( cCoq_2eInit_2eDecimal_2eD2___24a1(Vvar__0___24Anonymous__75860) = cCoq_2eInit_2eDecimal_2eD2___24a1(Vvar__0___24Anonymous__75861)
     => Vvar__0___24Anonymous__75860 = Vvar__0___24Anonymous__75861 ) ).

fof('$_inj_Coq.Init.Decimal.D3',axiom,
    ! [Vvar__0___24Anonymous__75862,Vvar__0___24Anonymous__75863] :
      ( cCoq_2eInit_2eDecimal_2eD3___24a1(Vvar__0___24Anonymous__75862) = cCoq_2eInit_2eDecimal_2eD3___24a1(Vvar__0___24Anonymous__75863)
     => Vvar__0___24Anonymous__75862 = Vvar__0___24Anonymous__75863 ) ).

fof('$_inj_Coq.Init.Decimal.D4',axiom,
    ! [Vvar__0___24Anonymous__75864,Vvar__0___24Anonymous__75865] :
      ( cCoq_2eInit_2eDecimal_2eD4___24a1(Vvar__0___24Anonymous__75864) = cCoq_2eInit_2eDecimal_2eD4___24a1(Vvar__0___24Anonymous__75865)
     => Vvar__0___24Anonymous__75864 = Vvar__0___24Anonymous__75865 ) ).

fof('$_inj_Coq.Init.Decimal.D5',axiom,
    ! [Vvar__0___24Anonymous__75866,Vvar__0___24Anonymous__75867] :
      ( cCoq_2eInit_2eDecimal_2eD5___24a1(Vvar__0___24Anonymous__75866) = cCoq_2eInit_2eDecimal_2eD5___24a1(Vvar__0___24Anonymous__75867)
     => Vvar__0___24Anonymous__75866 = Vvar__0___24Anonymous__75867 ) ).

fof('$_inj_Coq.Init.Decimal.D6',axiom,
    ! [Vvar__0___24Anonymous__75868,Vvar__0___24Anonymous__75869] :
      ( cCoq_2eInit_2eDecimal_2eD6___24a1(Vvar__0___24Anonymous__75868) = cCoq_2eInit_2eDecimal_2eD6___24a1(Vvar__0___24Anonymous__75869)
     => Vvar__0___24Anonymous__75868 = Vvar__0___24Anonymous__75869 ) ).

fof('$_inj_Coq.Init.Decimal.D7',axiom,
    ! [Vvar__0___24Anonymous__75870,Vvar__0___24Anonymous__75871] :
      ( cCoq_2eInit_2eDecimal_2eD7___24a1(Vvar__0___24Anonymous__75870) = cCoq_2eInit_2eDecimal_2eD7___24a1(Vvar__0___24Anonymous__75871)
     => Vvar__0___24Anonymous__75870 = Vvar__0___24Anonymous__75871 ) ).

fof('$_inj_Coq.Init.Decimal.D8',axiom,
    ! [Vvar__0___24Anonymous__75872,Vvar__0___24Anonymous__75873] :
      ( cCoq_2eInit_2eDecimal_2eD8___24a1(Vvar__0___24Anonymous__75872) = cCoq_2eInit_2eDecimal_2eD8___24a1(Vvar__0___24Anonymous__75873)
     => Vvar__0___24Anonymous__75872 = Vvar__0___24Anonymous__75873 ) ).

fof('$_inj_Coq.Init.Decimal.D9',axiom,
    ! [Vvar__0___24Anonymous__75874,Vvar__0___24Anonymous__75875] :
      ( cCoq_2eInit_2eDecimal_2eD9___24a1(Vvar__0___24Anonymous__75874) = cCoq_2eInit_2eDecimal_2eD9___24a1(Vvar__0___24Anonymous__75875)
     => Vvar__0___24Anonymous__75874 = Vvar__0___24Anonymous__75875 ) ).

fof('$_inj_Coq.Init.Decimal.Decimal',axiom,
    ! [Vvar__0__i__94223,Vvar__0__i__94224,Vvar__1__f__94225,Vvar__1__f__94226] :
      ( cCoq_2eInit_2eDecimal_2eDecimal___24a2(Vvar__0__i__94223,Vvar__1__f__94225) = cCoq_2eInit_2eDecimal_2eDecimal___24a2(Vvar__0__i__94224,Vvar__1__f__94226)
     => ( Vvar__1__f__94225 = Vvar__1__f__94226
        & Vvar__0__i__94223 = Vvar__0__i__94224 ) ) ).

fof('$_inj_Coq.Init.Decimal.DecimalExp',axiom,
    ! [Vvar__0__i__94227,Vvar__0__i__94228,Vvar__1__f__94229,Vvar__1__f__94230,Vvar__2__e__94231,Vvar__2__e__94232] :
      ( cCoq_2eInit_2eDecimal_2eDecimalExp___24a3(Vvar__0__i__94227,Vvar__1__f__94229,Vvar__2__e__94231) = cCoq_2eInit_2eDecimal_2eDecimalExp___24a3(Vvar__0__i__94228,Vvar__1__f__94230,Vvar__2__e__94232)
     => ( Vvar__2__e__94231 = Vvar__2__e__94232
        & Vvar__1__f__94229 = Vvar__1__f__94230
        & Vvar__0__i__94227 = Vvar__0__i__94228 ) ) ).

fof('$_inj_Coq.Init.Decimal.Neg',axiom,
    ! [Vvar__0__d__94210,Vvar__0__d__94211] :
      ( cCoq_2eInit_2eDecimal_2eNeg___24a1(Vvar__0__d__94210) = cCoq_2eInit_2eDecimal_2eNeg___24a1(Vvar__0__d__94211)
     => Vvar__0__d__94210 = Vvar__0__d__94211 ) ).

fof('$_inj_Coq.Init.Decimal.Pos',axiom,
    ! [Vvar__0__d__94208,Vvar__0__d__94209] :
      ( cCoq_2eInit_2eDecimal_2ePos___24a1(Vvar__0__d__94208) = cCoq_2eInit_2eDecimal_2ePos___24a1(Vvar__0__d__94209)
     => Vvar__0__d__94208 = Vvar__0__d__94209 ) ).

fof('$_inj_Coq.Init.Specif.exist',axiom,
    ! [Vvar__0__A__1053,Vvar__0__A__1054,Vvar__1__P__1055,Vvar__1__P__1056,Vvar__2__x__1057,Vvar__2__x__1058,Vvar__3___24Anonymous__1059,Vvar__3___24Anonymous__1060] :
      ( cCoq_2eInit_2eSpecif_2eexist___24a3(Vvar__0__A__1053,Vvar__1__P__1055,Vvar__2__x__1057) = cCoq_2eInit_2eSpecif_2eexist___24a3(Vvar__0__A__1054,Vvar__1__P__1056,Vvar__2__x__1058)
     => ( c_24Proof = c_24Proof
        & Vvar__2__x__1057 = Vvar__2__x__1058
        & Vvar__1__P__1055 = Vvar__1__P__1056
        & Vvar__0__A__1053 = Vvar__0__A__1054 ) ) ).

fof('$_inj_Coq.Init.Specif.exist2',axiom,
    ! [Vvar__0__A__90114,Vvar__0__A__90115,Vvar__1__P__90116,Vvar__1__P__90117,Vvar__2__Q__90118,Vvar__2__Q__90119,Vvar__3__x__90120,Vvar__3__x__90121,Vvar__4___24Anonymous__90122,Vvar__4___24Anonymous__90123,Vvar__5___24Anonymous__90124,Vvar__5___24Anonymous__90125] :
      ( cCoq_2eInit_2eSpecif_2eexist2___24a4(Vvar__0__A__90114,Vvar__1__P__90116,Vvar__2__Q__90118,Vvar__3__x__90120) = cCoq_2eInit_2eSpecif_2eexist2___24a4(Vvar__0__A__90115,Vvar__1__P__90117,Vvar__2__Q__90119,Vvar__3__x__90121)
     => ( c_24Proof = c_24Proof
        & c_24Proof = c_24Proof
        & Vvar__3__x__90120 = Vvar__3__x__90121
        & Vvar__2__Q__90118 = Vvar__2__Q__90119
        & Vvar__1__P__90116 = Vvar__1__P__90117
        & Vvar__0__A__90114 = Vvar__0__A__90115 ) ) ).

fof('$_inj_Coq.Init.Specif.existT',axiom,
    ! [Vvar__0__A__67652,Vvar__0__A__67653,Vvar__1__P__67654,Vvar__1__P__67655,Vvar__2__x__67656,Vvar__2__x__67657,Vvar__3___24Anonymous__67658,Vvar__3___24Anonymous__67659] :
      ( cCoq_2eInit_2eSpecif_2eexistT___24a4(Vvar__0__A__67652,Vvar__1__P__67654,Vvar__2__x__67656,Vvar__3___24Anonymous__67658) = cCoq_2eInit_2eSpecif_2eexistT___24a4(Vvar__0__A__67653,Vvar__1__P__67655,Vvar__2__x__67657,Vvar__3___24Anonymous__67659)
     => ( Vvar__3___24Anonymous__67658 = Vvar__3___24Anonymous__67659
        & Vvar__2__x__67656 = Vvar__2__x__67657
        & Vvar__1__P__67654 = Vvar__1__P__67655
        & Vvar__0__A__67652 = Vvar__0__A__67653 ) ) ).

fof('$_inj_Coq.Init.Specif.existT2',axiom,
    ! [Vvar__0__A__90352,Vvar__0__A__90353,Vvar__1__P__90354,Vvar__1__P__90355,Vvar__2__Q__90356,Vvar__2__Q__90357,Vvar__3__x__90358,Vvar__3__x__90359,Vvar__4___24Anonymous__90360,Vvar__4___24Anonymous__90361,Vvar__5___24Anonymous__90362,Vvar__5___24Anonymous__90363] :
      ( cCoq_2eInit_2eSpecif_2eexistT2___24a6(Vvar__0__A__90352,Vvar__1__P__90354,Vvar__2__Q__90356,Vvar__3__x__90358,Vvar__4___24Anonymous__90360,Vvar__5___24Anonymous__90362) = cCoq_2eInit_2eSpecif_2eexistT2___24a6(Vvar__0__A__90353,Vvar__1__P__90355,Vvar__2__Q__90357,Vvar__3__x__90359,Vvar__4___24Anonymous__90361,Vvar__5___24Anonymous__90363)
     => ( Vvar__5___24Anonymous__90362 = Vvar__5___24Anonymous__90363
        & Vvar__4___24Anonymous__90360 = Vvar__4___24Anonymous__90361
        & Vvar__3__x__90358 = Vvar__3__x__90359
        & Vvar__2__Q__90356 = Vvar__2__Q__90357
        & Vvar__1__P__90354 = Vvar__1__P__90355
        & Vvar__0__A__90352 = Vvar__0__A__90353 ) ) ).

fof('$_inj_Coq.Init.Specif.inleft',axiom,
    ! [Vvar__0__A__1087,Vvar__0__A__1088,Vvar__1__B__1089,Vvar__1__B__1090,Vvar__2___24Anonymous__1091,Vvar__2___24Anonymous__1092] :
      ( cCoq_2eInit_2eSpecif_2einleft___24a3(Vvar__0__A__1087,Vvar__1__B__1089,Vvar__2___24Anonymous__1091) = cCoq_2eInit_2eSpecif_2einleft___24a3(Vvar__0__A__1088,Vvar__1__B__1090,Vvar__2___24Anonymous__1092)
     => ( Vvar__2___24Anonymous__1091 = Vvar__2___24Anonymous__1092
        & Vvar__1__B__1089 = Vvar__1__B__1090
        & Vvar__0__A__1087 = Vvar__0__A__1088 ) ) ).

fof('$_inj_Coq.Init.Specif.inright',axiom,
    ! [Vvar__0__A__1093,Vvar__0__A__1094,Vvar__1__B__1095,Vvar__1__B__1096,Vvar__2___24Anonymous__1097,Vvar__2___24Anonymous__1098] :
      ( cCoq_2eInit_2eSpecif_2einright___24a2(Vvar__0__A__1093,Vvar__1__B__1095) = cCoq_2eInit_2eSpecif_2einright___24a2(Vvar__0__A__1094,Vvar__1__B__1096)
     => ( c_24Proof = c_24Proof
        & Vvar__1__B__1095 = Vvar__1__B__1096
        & Vvar__0__A__1093 = Vvar__0__A__1094 ) ) ).

fof('$_inj_Coq.Init.Specif.left',axiom,
    ! [Vvar__0__A__594,Vvar__0__A__595,Vvar__1__B__596,Vvar__1__B__597,Vvar__2___24Anonymous__598,Vvar__2___24Anonymous__599] :
      ( cCoq_2eInit_2eSpecif_2eleft___24a2(Vvar__0__A__594,Vvar__1__B__596) = cCoq_2eInit_2eSpecif_2eleft___24a2(Vvar__0__A__595,Vvar__1__B__597)
     => ( c_24Proof = c_24Proof
        & Vvar__1__B__596 = Vvar__1__B__597
        & Vvar__0__A__594 = Vvar__0__A__595 ) ) ).

fof('$_inj_Coq.Init.Specif.right',axiom,
    ! [Vvar__0__A__600,Vvar__0__A__601,Vvar__1__B__602,Vvar__1__B__603,Vvar__2___24Anonymous__604,Vvar__2___24Anonymous__605] :
      ( cCoq_2eInit_2eSpecif_2eright___24a2(Vvar__0__A__600,Vvar__1__B__602) = cCoq_2eInit_2eSpecif_2eright___24a2(Vvar__0__A__601,Vvar__1__B__603)
     => ( c_24Proof = c_24Proof
        & Vvar__1__B__602 = Vvar__1__B__603
        & Vvar__0__A__600 = Vvar__0__A__601 ) ) ).

fof('$_inj_Coq.Numbers.BinNums.Npos',axiom,
    ! [Vvar__0___24Anonymous__1130,Vvar__0___24Anonymous__1131] :
      ( cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__1130) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__1131)
     => Vvar__0___24Anonymous__1130 = Vvar__0___24Anonymous__1131 ) ).

fof('$_inj_Coq.Numbers.BinNums.Zneg',axiom,
    ! [Vvar__0___24Anonymous__68105,Vvar__0___24Anonymous__68106] :
      ( cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__68105) = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__68106)
     => Vvar__0___24Anonymous__68105 = Vvar__0___24Anonymous__68106 ) ).

fof('$_inj_Coq.Numbers.BinNums.Zpos',axiom,
    ! [Vvar__0___24Anonymous__68103,Vvar__0___24Anonymous__68104] :
      ( cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__68103) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__68104)
     => Vvar__0___24Anonymous__68103 = Vvar__0___24Anonymous__68104 ) ).

fof('$_inj_Coq.Numbers.BinNums.xI',axiom,
    ! [Vvar__0___24Anonymous__1115,Vvar__0___24Anonymous__1116] :
      ( cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__1115) = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__1116)
     => Vvar__0___24Anonymous__1115 = Vvar__0___24Anonymous__1116 ) ).

fof('$_inj_Coq.Numbers.BinNums.xO',axiom,
    ! [Vvar__0___24Anonymous__1117,Vvar__0___24Anonymous__1118] :
      ( cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__1117) = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__1118)
     => Vvar__0___24Anonymous__1117 = Vvar__0___24Anonymous__1118 ) ).

fof('$_inj_Coq.PArith.BinPos.Pos.PeanoSucc',axiom,
    ! [Vvar__0__p__105671,Vvar__0__p__105672,Vvar__1___24Anonymous__105673,Vvar__1___24Anonymous__105674] :
      ( cCoq_2ePArith_2eBinPos_2ePos_2ePeanoSucc___24a2(Vvar__0__p__105671,Vvar__1___24Anonymous__105673) = cCoq_2ePArith_2eBinPos_2ePos_2ePeanoSucc___24a2(Vvar__0__p__105672,Vvar__1___24Anonymous__105674)
     => ( Vvar__1___24Anonymous__105673 = Vvar__1___24Anonymous__105674
        & Vvar__0__p__105671 = Vvar__0__p__105672 ) ) ).

fof('$_inj_Coq.PArith.BinPosDef.Pos.IsPos',axiom,
    ! [Vvar__0___24Anonymous__93085,Vvar__0___24Anonymous__93086] :
      ( cCoq_2ePArith_2eBinPosDef_2ePos_2eIsPos___24a1(Vvar__0___24Anonymous__93085) = cCoq_2ePArith_2eBinPosDef_2ePos_2eIsPos___24a1(Vvar__0___24Anonymous__93086)
     => Vvar__0___24Anonymous__93085 = Vvar__0___24Anonymous__93086 ) ).

fof('$_inj_Coq.QArith.QArith_base.Qmake',axiom,
    ! [Vvar__0__Qnum__97179,Vvar__0__Qnum__97180,Vvar__1__Qden__97181,Vvar__1__Qden__97182] :
      ( cCoq_2eQArith_2eQArith__base_2eQmake___24a2(Vvar__0__Qnum__97179,Vvar__1__Qden__97181) = cCoq_2eQArith_2eQArith__base_2eQmake___24a2(Vvar__0__Qnum__97180,Vvar__1__Qden__97182)
     => ( Vvar__1__Qden__97181 = Vvar__1__Qden__97182
        & Vvar__0__Qnum__97179 = Vvar__0__Qnum__97180 ) ) ).

fof('$_inj_Coq.Reals.RIneq.mknegreal',axiom,
    ! [Vvar__0__neg__97220,Vvar__0__neg__97221,Vvar__1__cond__neg__97222,Vvar__1__cond__neg__97223] :
      ( cCoq_2eReals_2eRIneq_2emknegreal___24a1(Vvar__0__neg__97220) = cCoq_2eReals_2eRIneq_2emknegreal___24a1(Vvar__0__neg__97221)
     => ( c_24Proof = c_24Proof
        & Vvar__0__neg__97220 = Vvar__0__neg__97221 ) ) ).

fof('$_inj_Coq.Reals.RIneq.mknonnegreal',axiom,
    ! [Vvar__0__nonneg__97199,Vvar__0__nonneg__97200,Vvar__1__cond__nonneg__97201,Vvar__1__cond__nonneg__97202] :
      ( cCoq_2eReals_2eRIneq_2emknonnegreal___24a1(Vvar__0__nonneg__97199) = cCoq_2eReals_2eRIneq_2emknonnegreal___24a1(Vvar__0__nonneg__97200)
     => ( c_24Proof = c_24Proof
        & Vvar__0__nonneg__97199 = Vvar__0__nonneg__97200 ) ) ).

fof('$_inj_Coq.Reals.RIneq.mknonposreal',axiom,
    ! [Vvar__0__nonpos__97213,Vvar__0__nonpos__97214,Vvar__1__cond__nonpos__97215,Vvar__1__cond__nonpos__97216] :
      ( cCoq_2eReals_2eRIneq_2emknonposreal___24a1(Vvar__0__nonpos__97213) = cCoq_2eReals_2eRIneq_2emknonposreal___24a1(Vvar__0__nonpos__97214)
     => ( c_24Proof = c_24Proof
        & Vvar__0__nonpos__97213 = Vvar__0__nonpos__97214 ) ) ).

fof('$_inj_Coq.Reals.RIneq.mknonzeroreal',axiom,
    ! [Vvar__0__nonzero__97227,Vvar__0__nonzero__97228,Vvar__1__cond__nonzero__97229,Vvar__1__cond__nonzero__97230] :
      ( cCoq_2eReals_2eRIneq_2emknonzeroreal___24a1(Vvar__0__nonzero__97227) = cCoq_2eReals_2eRIneq_2emknonzeroreal___24a1(Vvar__0__nonzero__97228)
     => ( c_24Proof = c_24Proof
        & Vvar__0__nonzero__97227 = Vvar__0__nonzero__97228 ) ) ).

fof('$_inj_Coq.Reals.RIneq.mkposreal',axiom,
    ! [Vvar__0__pos__97206,Vvar__0__pos__97207,Vvar__1__cond__pos__97208,Vvar__1__cond__pos__97209] :
      ( cCoq_2eReals_2eRIneq_2emkposreal___24a1(Vvar__0__pos__97206) = cCoq_2eReals_2eRIneq_2emkposreal___24a1(Vvar__0__pos__97207)
     => ( c_24Proof = c_24Proof
        & Vvar__0__pos__97206 = Vvar__0__pos__97207 ) ) ).

fof('$_inj_Coq.Reals.Rfunctions.ZintNeg',axiom,
    ! [Vvar__0__x__98196,Vvar__0__x__98197,Vvar__1__n__98198,Vvar__1__n__98199,Vvar__2___24Anonymous__98200,Vvar__2___24Anonymous__98201] :
      ( cCoq_2eReals_2eRfunctions_2eZintNeg___24a2(Vvar__0__x__98196,Vvar__1__n__98198) = cCoq_2eReals_2eRfunctions_2eZintNeg___24a2(Vvar__0__x__98197,Vvar__1__n__98199)
     => ( c_24Proof = c_24Proof
        & Vvar__1__n__98198 = Vvar__1__n__98199
        & Vvar__0__x__98196 = Vvar__0__x__98197 ) ) ).

fof('$_inj_Coq.Reals.Rfunctions.ZintNull',axiom,
    ! [Vvar__0__x__98186,Vvar__0__x__98187,Vvar__1___24Anonymous__98188,Vvar__1___24Anonymous__98189] :
      ( cCoq_2eReals_2eRfunctions_2eZintNull___24a1(Vvar__0__x__98186) = cCoq_2eReals_2eRfunctions_2eZintNull___24a1(Vvar__0__x__98187)
     => ( c_24Proof = c_24Proof
        & Vvar__0__x__98186 = Vvar__0__x__98187 ) ) ).

fof('$_inj_Coq.Reals.Rfunctions.ZintPos',axiom,
    ! [Vvar__0__x__98190,Vvar__0__x__98191,Vvar__1__n__98192,Vvar__1__n__98193,Vvar__2___24Anonymous__98194,Vvar__2___24Anonymous__98195] :
      ( cCoq_2eReals_2eRfunctions_2eZintPos___24a2(Vvar__0__x__98190,Vvar__1__n__98192) = cCoq_2eReals_2eRfunctions_2eZintPos___24a2(Vvar__0__x__98191,Vvar__1__n__98193)
     => ( c_24Proof = c_24Proof
        & Vvar__1__n__98192 = Vvar__1__n__98193
        & Vvar__0__x__98190 = Vvar__0__x__98191 ) ) ).

fof('$_inj_Coq.Strings.Ascii.Ascii',axiom,
    ! [Vvar__0___24Anonymous__67911,Vvar__0___24Anonymous__67912,Vvar__1___24Anonymous__67913,Vvar__1___24Anonymous__67914,Vvar__2___24Anonymous__67915,Vvar__2___24Anonymous__67916,Vvar__3___24Anonymous__67917,Vvar__3___24Anonymous__67918,Vvar__4___24Anonymous__67919,Vvar__4___24Anonymous__67920,Vvar__5___24Anonymous__67921,Vvar__5___24Anonymous__67922,Vvar__6___24Anonymous__67923,Vvar__6___24Anonymous__67924,Vvar__7___24Anonymous__67925,Vvar__7___24Anonymous__67926] :
      ( cCoq_2eStrings_2eAscii_2eAscii___24a8(Vvar__0___24Anonymous__67911,Vvar__1___24Anonymous__67913,Vvar__2___24Anonymous__67915,Vvar__3___24Anonymous__67917,Vvar__4___24Anonymous__67919,Vvar__5___24Anonymous__67921,Vvar__6___24Anonymous__67923,Vvar__7___24Anonymous__67925) = cCoq_2eStrings_2eAscii_2eAscii___24a8(Vvar__0___24Anonymous__67912,Vvar__1___24Anonymous__67914,Vvar__2___24Anonymous__67916,Vvar__3___24Anonymous__67918,Vvar__4___24Anonymous__67920,Vvar__5___24Anonymous__67922,Vvar__6___24Anonymous__67924,Vvar__7___24Anonymous__67926)
     => ( Vvar__7___24Anonymous__67925 = Vvar__7___24Anonymous__67926
        & Vvar__6___24Anonymous__67923 = Vvar__6___24Anonymous__67924
        & Vvar__5___24Anonymous__67921 = Vvar__5___24Anonymous__67922
        & Vvar__4___24Anonymous__67919 = Vvar__4___24Anonymous__67920
        & Vvar__3___24Anonymous__67917 = Vvar__3___24Anonymous__67918
        & Vvar__2___24Anonymous__67915 = Vvar__2___24Anonymous__67916
        & Vvar__1___24Anonymous__67913 = Vvar__1___24Anonymous__67914
        & Vvar__0___24Anonymous__67911 = Vvar__0___24Anonymous__67912 ) ) ).

fof('$_inj_Coq.Strings.String.String',axiom,
    ! [Vvar__0___24Anonymous__82308,Vvar__0___24Anonymous__82309,Vvar__1___24Anonymous__82310,Vvar__1___24Anonymous__82311] :
      ( cCoq_2eStrings_2eString_2eString___24a2(Vvar__0___24Anonymous__82308,Vvar__1___24Anonymous__82310) = cCoq_2eStrings_2eString_2eString___24a2(Vvar__0___24Anonymous__82309,Vvar__1___24Anonymous__82311)
     => ( Vvar__1___24Anonymous__82310 = Vvar__1___24Anonymous__82311
        & Vvar__0___24Anonymous__82308 = Vvar__0___24Anonymous__82309 ) ) ).

fof('$_inj_Coq.Structures.OrderedType.EQ',axiom,
    ! [Vvar__0__X__97148,Vvar__0__X__97149,Vvar__1__lt__97150,Vvar__1__lt__97151,Vvar__2__eq__97152,Vvar__2__eq__97153,Vvar__3__x__97154,Vvar__3__x__97155,Vvar__4__y__97156,Vvar__4__y__97157,Vvar__5___24Anonymous__97158,Vvar__5___24Anonymous__97159] :
      ( cCoq_2eStructures_2eOrderedType_2eEQ___24a5(Vvar__0__X__97148,Vvar__1__lt__97150,Vvar__2__eq__97152,Vvar__3__x__97154,Vvar__4__y__97156) = cCoq_2eStructures_2eOrderedType_2eEQ___24a5(Vvar__0__X__97149,Vvar__1__lt__97151,Vvar__2__eq__97153,Vvar__3__x__97155,Vvar__4__y__97157)
     => ( c_24Proof = c_24Proof
        & Vvar__4__y__97156 = Vvar__4__y__97157
        & Vvar__3__x__97154 = Vvar__3__x__97155
        & Vvar__2__eq__97152 = Vvar__2__eq__97153
        & Vvar__1__lt__97150 = Vvar__1__lt__97151
        & Vvar__0__X__97148 = Vvar__0__X__97149 ) ) ).

fof('$_inj_Coq.Structures.OrderedType.GT',axiom,
    ! [Vvar__0__X__97160,Vvar__0__X__97161,Vvar__1__lt__97162,Vvar__1__lt__97163,Vvar__2__eq__97164,Vvar__2__eq__97165,Vvar__3__x__97166,Vvar__3__x__97167,Vvar__4__y__97168,Vvar__4__y__97169,Vvar__5___24Anonymous__97170,Vvar__5___24Anonymous__97171] :
      ( cCoq_2eStructures_2eOrderedType_2eGT___24a5(Vvar__0__X__97160,Vvar__1__lt__97162,Vvar__2__eq__97164,Vvar__3__x__97166,Vvar__4__y__97168) = cCoq_2eStructures_2eOrderedType_2eGT___24a5(Vvar__0__X__97161,Vvar__1__lt__97163,Vvar__2__eq__97165,Vvar__3__x__97167,Vvar__4__y__97169)
     => ( c_24Proof = c_24Proof
        & Vvar__4__y__97168 = Vvar__4__y__97169
        & Vvar__3__x__97166 = Vvar__3__x__97167
        & Vvar__2__eq__97164 = Vvar__2__eq__97165
        & Vvar__1__lt__97162 = Vvar__1__lt__97163
        & Vvar__0__X__97160 = Vvar__0__X__97161 ) ) ).

fof('$_inj_Coq.Structures.OrderedType.LT',axiom,
    ! [Vvar__0__X__97136,Vvar__0__X__97137,Vvar__1__lt__97138,Vvar__1__lt__97139,Vvar__2__eq__97140,Vvar__2__eq__97141,Vvar__3__x__97142,Vvar__3__x__97143,Vvar__4__y__97144,Vvar__4__y__97145,Vvar__5___24Anonymous__97146,Vvar__5___24Anonymous__97147] :
      ( cCoq_2eStructures_2eOrderedType_2eLT___24a5(Vvar__0__X__97136,Vvar__1__lt__97138,Vvar__2__eq__97140,Vvar__3__x__97142,Vvar__4__y__97144) = cCoq_2eStructures_2eOrderedType_2eLT___24a5(Vvar__0__X__97137,Vvar__1__lt__97139,Vvar__2__eq__97141,Vvar__3__x__97143,Vvar__4__y__97145)
     => ( c_24Proof = c_24Proof
        & Vvar__4__y__97144 = Vvar__4__y__97145
        & Vvar__3__x__97142 = Vvar__3__x__97143
        & Vvar__2__eq__97140 = Vvar__2__eq__97141
        & Vvar__1__lt__97138 = Vvar__1__lt__97139
        & Vvar__0__X__97136 = Vvar__0__X__97137 ) ) ).

fof('$_inj_Coq.Vectors.Fin.F1',axiom,
    ! [Vvar__0__n__75892,Vvar__0__n__75893] :
      ( cCoq_2eVectors_2eFin_2eF1___24a1(Vvar__0__n__75892) = cCoq_2eVectors_2eFin_2eF1___24a1(Vvar__0__n__75893)
     => Vvar__0__n__75892 = Vvar__0__n__75893 ) ).

fof('$_inj_Coq.Vectors.Fin.FS',axiom,
    ! [Vvar__0__n__75894,Vvar__0__n__75895,Vvar__1___24Anonymous__75896,Vvar__1___24Anonymous__75897] :
      ( cCoq_2eVectors_2eFin_2eFS___24a2(Vvar__0__n__75894,Vvar__1___24Anonymous__75896) = cCoq_2eVectors_2eFin_2eFS___24a2(Vvar__0__n__75895,Vvar__1___24Anonymous__75897)
     => ( Vvar__1___24Anonymous__75896 = Vvar__1___24Anonymous__75897
        & Vvar__0__n__75894 = Vvar__0__n__75895 ) ) ).

fof('$_inj_Coq.Vectors.VectorDef.cons',axiom,
    ! [Vvar__0__A__79274,Vvar__0__A__79275,Vvar__1__h__79276,Vvar__1__h__79277,Vvar__2__n__79278,Vvar__2__n__79279,Vvar__3___24Anonymous__79280,Vvar__3___24Anonymous__79281] :
      ( cCoq_2eVectors_2eVectorDef_2econs___24a4(Vvar__0__A__79274,Vvar__1__h__79276,Vvar__2__n__79278,Vvar__3___24Anonymous__79280) = cCoq_2eVectors_2eVectorDef_2econs___24a4(Vvar__0__A__79275,Vvar__1__h__79277,Vvar__2__n__79279,Vvar__3___24Anonymous__79281)
     => ( Vvar__3___24Anonymous__79280 = Vvar__3___24Anonymous__79281
        & Vvar__2__n__79278 = Vvar__2__n__79279
        & Vvar__1__h__79276 = Vvar__1__h__79277
        & Vvar__0__A__79274 = Vvar__0__A__79275 ) ) ).

fof('$_inj_Coq.Vectors.VectorDef.nil',axiom,
    ! [Vvar__0__A__79272,Vvar__0__A__79273] :
      ( cCoq_2eVectors_2eVectorDef_2enil___24a1(Vvar__0__A__79272) = cCoq_2eVectors_2eVectorDef_2enil___24a1(Vvar__0__A__79273)
     => Vvar__0__A__79272 = Vvar__0__A__79273 ) ).

fof('$_inj_Coq.ZArith.Znumtheory.Euclid_intro',axiom,
    ! [Vvar__0__a__105409,Vvar__0__a__105410,Vvar__1__b__105411,Vvar__1__b__105412,Vvar__2__u__105413,Vvar__2__u__105414,Vvar__3__v__105415,Vvar__3__v__105416,Vvar__4__d__105417,Vvar__4__d__105418,Vvar__5___24Anonymous__105419,Vvar__5___24Anonymous__105420,Vvar__6___24Anonymous__105421,Vvar__6___24Anonymous__105422] :
      ( cCoq_2eZArith_2eZnumtheory_2eEuclid__intro___24a5(Vvar__0__a__105409,Vvar__1__b__105411,Vvar__2__u__105413,Vvar__3__v__105415,Vvar__4__d__105417) = cCoq_2eZArith_2eZnumtheory_2eEuclid__intro___24a5(Vvar__0__a__105410,Vvar__1__b__105412,Vvar__2__u__105414,Vvar__3__v__105416,Vvar__4__d__105418)
     => ( c_24Proof = c_24Proof
        & c_24Proof = c_24Proof
        & Vvar__4__d__105417 = Vvar__4__d__105418
        & Vvar__3__v__105415 = Vvar__3__v__105416
        & Vvar__2__u__105413 = Vvar__2__u__105414
        & Vvar__1__b__105411 = Vvar__1__b__105412
        & Vvar__0__a__105409 = Vvar__0__a__105410 ) ) ).

fof('$_inj_Coq.ZArith.Zpower.Zdiv_rest_proof',axiom,
    ! [Vvar__0__x__105470,Vvar__0__x__105471,Vvar__1__p__105472,Vvar__1__p__105473,Vvar__2__q__105474,Vvar__2__q__105475,Vvar__3__r__105476,Vvar__3__r__105477,Vvar__4___24Anonymous__105478,Vvar__4___24Anonymous__105479,Vvar__5___24Anonymous__105480,Vvar__5___24Anonymous__105481,Vvar__6___24Anonymous__105482,Vvar__6___24Anonymous__105483] :
      ( cCoq_2eZArith_2eZpower_2eZdiv__rest__proof___24a4(Vvar__0__x__105470,Vvar__1__p__105472,Vvar__2__q__105474,Vvar__3__r__105476) = cCoq_2eZArith_2eZpower_2eZdiv__rest__proof___24a4(Vvar__0__x__105471,Vvar__1__p__105473,Vvar__2__q__105475,Vvar__3__r__105477)
     => ( c_24Proof = c_24Proof
        & c_24Proof = c_24Proof
        & c_24Proof = c_24Proof
        & Vvar__3__r__105476 = Vvar__3__r__105477
        & Vvar__2__q__105474 = Vvar__2__q__105475
        & Vvar__1__p__105472 = Vvar__1__p__105473
        & Vvar__0__x__105470 = Vvar__0__x__105471 ) ) ).

fof('$_inj_Coq.micromega.EnvRing.PEX',axiom,
    ! [Vvar__0__C__94378,Vvar__0__C__94379,Vvar__1___24Anonymous__94380,Vvar__1___24Anonymous__94381] :
      ( cCoq_2emicromega_2eEnvRing_2ePEX___24a2(Vvar__0__C__94378,Vvar__1___24Anonymous__94380) = cCoq_2emicromega_2eEnvRing_2ePEX___24a2(Vvar__0__C__94379,Vvar__1___24Anonymous__94381)
     => ( Vvar__1___24Anonymous__94380 = Vvar__1___24Anonymous__94381
        & Vvar__0__C__94378 = Vvar__0__C__94379 ) ) ).

fof('$_inj_Coq.micromega.EnvRing.PEadd',axiom,
    ! [Vvar__0__C__94382,Vvar__0__C__94383,Vvar__1___24Anonymous__94384,Vvar__1___24Anonymous__94385,Vvar__2___24Anonymous__94386,Vvar__2___24Anonymous__94387] :
      ( cCoq_2emicromega_2eEnvRing_2ePEadd___24a3(Vvar__0__C__94382,Vvar__1___24Anonymous__94384,Vvar__2___24Anonymous__94386) = cCoq_2emicromega_2eEnvRing_2ePEadd___24a3(Vvar__0__C__94383,Vvar__1___24Anonymous__94385,Vvar__2___24Anonymous__94387)
     => ( Vvar__2___24Anonymous__94386 = Vvar__2___24Anonymous__94387
        & Vvar__1___24Anonymous__94384 = Vvar__1___24Anonymous__94385
        & Vvar__0__C__94382 = Vvar__0__C__94383 ) ) ).

fof('$_inj_Coq.micromega.EnvRing.PEc',axiom,
    ! [Vvar__0__C__94374,Vvar__0__C__94375,Vvar__1___24Anonymous__94376,Vvar__1___24Anonymous__94377] :
      ( cCoq_2emicromega_2eEnvRing_2ePEc___24a2(Vvar__0__C__94374,Vvar__1___24Anonymous__94376) = cCoq_2emicromega_2eEnvRing_2ePEc___24a2(Vvar__0__C__94375,Vvar__1___24Anonymous__94377)
     => ( Vvar__1___24Anonymous__94376 = Vvar__1___24Anonymous__94377
        & Vvar__0__C__94374 = Vvar__0__C__94375 ) ) ).

fof('$_inj_Coq.micromega.EnvRing.PEmul',axiom,
    ! [Vvar__0__C__94394,Vvar__0__C__94395,Vvar__1___24Anonymous__94396,Vvar__1___24Anonymous__94397,Vvar__2___24Anonymous__94398,Vvar__2___24Anonymous__94399] :
      ( cCoq_2emicromega_2eEnvRing_2ePEmul___24a3(Vvar__0__C__94394,Vvar__1___24Anonymous__94396,Vvar__2___24Anonymous__94398) = cCoq_2emicromega_2eEnvRing_2ePEmul___24a3(Vvar__0__C__94395,Vvar__1___24Anonymous__94397,Vvar__2___24Anonymous__94399)
     => ( Vvar__2___24Anonymous__94398 = Vvar__2___24Anonymous__94399
        & Vvar__1___24Anonymous__94396 = Vvar__1___24Anonymous__94397
        & Vvar__0__C__94394 = Vvar__0__C__94395 ) ) ).

fof('$_inj_Coq.micromega.EnvRing.PEopp',axiom,
    ! [Vvar__0__C__94400,Vvar__0__C__94401,Vvar__1___24Anonymous__94402,Vvar__1___24Anonymous__94403] :
      ( cCoq_2emicromega_2eEnvRing_2ePEopp___24a2(Vvar__0__C__94400,Vvar__1___24Anonymous__94402) = cCoq_2emicromega_2eEnvRing_2ePEopp___24a2(Vvar__0__C__94401,Vvar__1___24Anonymous__94403)
     => ( Vvar__1___24Anonymous__94402 = Vvar__1___24Anonymous__94403
        & Vvar__0__C__94400 = Vvar__0__C__94401 ) ) ).

fof('$_inj_Coq.micromega.EnvRing.PEpow',axiom,
    ! [Vvar__0__C__94404,Vvar__0__C__94405,Vvar__1___24Anonymous__94406,Vvar__1___24Anonymous__94407,Vvar__2___24Anonymous__94408,Vvar__2___24Anonymous__94409] :
      ( cCoq_2emicromega_2eEnvRing_2ePEpow___24a3(Vvar__0__C__94404,Vvar__1___24Anonymous__94406,Vvar__2___24Anonymous__94408) = cCoq_2emicromega_2eEnvRing_2ePEpow___24a3(Vvar__0__C__94405,Vvar__1___24Anonymous__94407,Vvar__2___24Anonymous__94409)
     => ( Vvar__2___24Anonymous__94408 = Vvar__2___24Anonymous__94409
        & Vvar__1___24Anonymous__94406 = Vvar__1___24Anonymous__94407
        & Vvar__0__C__94404 = Vvar__0__C__94405 ) ) ).

fof('$_inj_Coq.micromega.EnvRing.PEsub',axiom,
    ! [Vvar__0__C__94388,Vvar__0__C__94389,Vvar__1___24Anonymous__94390,Vvar__1___24Anonymous__94391,Vvar__2___24Anonymous__94392,Vvar__2___24Anonymous__94393] :
      ( cCoq_2emicromega_2eEnvRing_2ePEsub___24a3(Vvar__0__C__94388,Vvar__1___24Anonymous__94390,Vvar__2___24Anonymous__94392) = cCoq_2emicromega_2eEnvRing_2ePEsub___24a3(Vvar__0__C__94389,Vvar__1___24Anonymous__94391,Vvar__2___24Anonymous__94393)
     => ( Vvar__2___24Anonymous__94392 = Vvar__2___24Anonymous__94393
        & Vvar__1___24Anonymous__94390 = Vvar__1___24Anonymous__94391
        & Vvar__0__C__94388 = Vvar__0__C__94389 ) ) ).

fof('$_inj_Coq.micromega.EnvRing.PX',axiom,
    ! [Vvar__0__C__83562,Vvar__0__C__83563,Vvar__1___24Anonymous__83564,Vvar__1___24Anonymous__83565,Vvar__2___24Anonymous__83566,Vvar__2___24Anonymous__83567,Vvar__3___24Anonymous__83568,Vvar__3___24Anonymous__83569] :
      ( cCoq_2emicromega_2eEnvRing_2ePX___24a4(Vvar__0__C__83562,Vvar__1___24Anonymous__83564,Vvar__2___24Anonymous__83566,Vvar__3___24Anonymous__83568) = cCoq_2emicromega_2eEnvRing_2ePX___24a4(Vvar__0__C__83563,Vvar__1___24Anonymous__83565,Vvar__2___24Anonymous__83567,Vvar__3___24Anonymous__83569)
     => ( Vvar__3___24Anonymous__83568 = Vvar__3___24Anonymous__83569
        & Vvar__2___24Anonymous__83566 = Vvar__2___24Anonymous__83567
        & Vvar__1___24Anonymous__83564 = Vvar__1___24Anonymous__83565
        & Vvar__0__C__83562 = Vvar__0__C__83563 ) ) ).

fof('$_inj_Coq.micromega.EnvRing.Pc',axiom,
    ! [Vvar__0__C__83552,Vvar__0__C__83553,Vvar__1___24Anonymous__83554,Vvar__1___24Anonymous__83555] :
      ( cCoq_2emicromega_2eEnvRing_2ePc___24a2(Vvar__0__C__83552,Vvar__1___24Anonymous__83554) = cCoq_2emicromega_2eEnvRing_2ePc___24a2(Vvar__0__C__83553,Vvar__1___24Anonymous__83555)
     => ( Vvar__1___24Anonymous__83554 = Vvar__1___24Anonymous__83555
        & Vvar__0__C__83552 = Vvar__0__C__83553 ) ) ).

fof('$_inj_Coq.micromega.EnvRing.Pinj',axiom,
    ! [Vvar__0__C__83556,Vvar__0__C__83557,Vvar__1___24Anonymous__83558,Vvar__1___24Anonymous__83559,Vvar__2___24Anonymous__83560,Vvar__2___24Anonymous__83561] :
      ( cCoq_2emicromega_2eEnvRing_2ePinj___24a3(Vvar__0__C__83556,Vvar__1___24Anonymous__83558,Vvar__2___24Anonymous__83560) = cCoq_2emicromega_2eEnvRing_2ePinj___24a3(Vvar__0__C__83557,Vvar__1___24Anonymous__83559,Vvar__2___24Anonymous__83561)
     => ( Vvar__2___24Anonymous__83560 = Vvar__2___24Anonymous__83561
        & Vvar__1___24Anonymous__83558 = Vvar__1___24Anonymous__83559
        & Vvar__0__C__83556 = Vvar__0__C__83557 ) ) ).

fof('$_inj_Coq.micromega.EnvRing.vmon',axiom,
    ! [Vvar__0___24Anonymous__94427,Vvar__0___24Anonymous__94428,Vvar__1___24Anonymous__94429,Vvar__1___24Anonymous__94430] :
      ( cCoq_2emicromega_2eEnvRing_2evmon___24a2(Vvar__0___24Anonymous__94427,Vvar__1___24Anonymous__94429) = cCoq_2emicromega_2eEnvRing_2evmon___24a2(Vvar__0___24Anonymous__94428,Vvar__1___24Anonymous__94430)
     => ( Vvar__1___24Anonymous__94429 = Vvar__1___24Anonymous__94430
        & Vvar__0___24Anonymous__94427 = Vvar__0___24Anonymous__94428 ) ) ).

fof('$_inj_Coq.micromega.EnvRing.zmon',axiom,
    ! [Vvar__0___24Anonymous__94423,Vvar__0___24Anonymous__94424,Vvar__1___24Anonymous__94425,Vvar__1___24Anonymous__94426] :
      ( cCoq_2emicromega_2eEnvRing_2ezmon___24a2(Vvar__0___24Anonymous__94423,Vvar__1___24Anonymous__94425) = cCoq_2emicromega_2eEnvRing_2ezmon___24a2(Vvar__0___24Anonymous__94424,Vvar__1___24Anonymous__94426)
     => ( Vvar__1___24Anonymous__94425 = Vvar__1___24Anonymous__94426
        & Vvar__0___24Anonymous__94423 = Vvar__0___24Anonymous__94424 ) ) ).

fof('$_inj_Coq.micromega.RMicromega.CInv',axiom,
    ! [Vvar__0__r__97372,Vvar__0__r__97373] :
      ( cCoq_2emicromega_2eRMicromega_2eCInv___24a1(Vvar__0__r__97372) = cCoq_2emicromega_2eRMicromega_2eCInv___24a1(Vvar__0__r__97373)
     => Vvar__0__r__97372 = Vvar__0__r__97373 ) ).

fof('$_inj_Coq.micromega.RMicromega.CMinus',axiom,
    ! [Vvar__0__r1__97360,Vvar__0__r1__97361,Vvar__1__r2__97362,Vvar__1__r2__97363] :
      ( cCoq_2emicromega_2eRMicromega_2eCMinus___24a2(Vvar__0__r1__97360,Vvar__1__r2__97362) = cCoq_2emicromega_2eRMicromega_2eCMinus___24a2(Vvar__0__r1__97361,Vvar__1__r2__97363)
     => ( Vvar__1__r2__97362 = Vvar__1__r2__97363
        & Vvar__0__r1__97360 = Vvar__0__r1__97361 ) ) ).

fof('$_inj_Coq.micromega.RMicromega.CMult',axiom,
    ! [Vvar__0__r1__97364,Vvar__0__r1__97365,Vvar__1__r2__97366,Vvar__1__r2__97367] :
      ( cCoq_2emicromega_2eRMicromega_2eCMult___24a2(Vvar__0__r1__97364,Vvar__1__r2__97366) = cCoq_2emicromega_2eRMicromega_2eCMult___24a2(Vvar__0__r1__97365,Vvar__1__r2__97367)
     => ( Vvar__1__r2__97366 = Vvar__1__r2__97367
        & Vvar__0__r1__97364 = Vvar__0__r1__97365 ) ) ).

fof('$_inj_Coq.micromega.RMicromega.COpp',axiom,
    ! [Vvar__0__r__97374,Vvar__0__r__97375] :
      ( cCoq_2emicromega_2eRMicromega_2eCOpp___24a1(Vvar__0__r__97374) = cCoq_2emicromega_2eRMicromega_2eCOpp___24a1(Vvar__0__r__97375)
     => Vvar__0__r__97374 = Vvar__0__r__97375 ) ).

fof('$_inj_Coq.micromega.RMicromega.CPlus',axiom,
    ! [Vvar__0__r1__97356,Vvar__0__r1__97357,Vvar__1__r2__97358,Vvar__1__r2__97359] :
      ( cCoq_2emicromega_2eRMicromega_2eCPlus___24a2(Vvar__0__r1__97356,Vvar__1__r2__97358) = cCoq_2emicromega_2eRMicromega_2eCPlus___24a2(Vvar__0__r1__97357,Vvar__1__r2__97359)
     => ( Vvar__1__r2__97358 = Vvar__1__r2__97359
        & Vvar__0__r1__97356 = Vvar__0__r1__97357 ) ) ).

fof('$_inj_Coq.micromega.RMicromega.CPow',axiom,
    ! [Vvar__0__r1__97368,Vvar__0__r1__97369,Vvar__1__z__97370,Vvar__1__z__97371] :
      ( cCoq_2emicromega_2eRMicromega_2eCPow___24a2(Vvar__0__r1__97368,Vvar__1__z__97370) = cCoq_2emicromega_2eRMicromega_2eCPow___24a2(Vvar__0__r1__97369,Vvar__1__z__97371)
     => ( Vvar__1__z__97370 = Vvar__1__z__97371
        & Vvar__0__r1__97368 = Vvar__0__r1__97369 ) ) ).

fof('$_inj_Coq.micromega.RMicromega.CQ',axiom,
    ! [Vvar__0__r__97352,Vvar__0__r__97353] :
      ( cCoq_2emicromega_2eRMicromega_2eCQ___24a1(Vvar__0__r__97352) = cCoq_2emicromega_2eRMicromega_2eCQ___24a1(Vvar__0__r__97353)
     => Vvar__0__r__97352 = Vvar__0__r__97353 ) ).

fof('$_inj_Coq.micromega.RMicromega.CZ',axiom,
    ! [Vvar__0__r__97354,Vvar__0__r__97355] :
      ( cCoq_2emicromega_2eRMicromega_2eCZ___24a1(Vvar__0__r__97354) = cCoq_2emicromega_2eRMicromega_2eCZ___24a1(Vvar__0__r__97355)
     => Vvar__0__r__97354 = Vvar__0__r__97355 ) ).

fof('$_inj_Coq.micromega.RingMicromega.Build_Formula',axiom,
    ! [Vvar__0__T__85927,Vvar__0__T__85928,Vvar__1__Flhs__85929,Vvar__1__Flhs__85930,Vvar__2__Fop__85931,Vvar__2__Fop__85932,Vvar__3__Frhs__85933,Vvar__3__Frhs__85934] :
      ( cCoq_2emicromega_2eRingMicromega_2eBuild__Formula___24a4(Vvar__0__T__85927,Vvar__1__Flhs__85929,Vvar__2__Fop__85931,Vvar__3__Frhs__85933) = cCoq_2emicromega_2eRingMicromega_2eBuild__Formula___24a4(Vvar__0__T__85928,Vvar__1__Flhs__85930,Vvar__2__Fop__85932,Vvar__3__Frhs__85934)
     => ( Vvar__3__Frhs__85933 = Vvar__3__Frhs__85934
        & Vvar__2__Fop__85931 = Vvar__2__Fop__85932
        & Vvar__1__Flhs__85929 = Vvar__1__Flhs__85930
        & Vvar__0__T__85927 = Vvar__0__T__85928 ) ) ).

fof('$_inj_Coq.micromega.RingMicromega.PsatzAdd',axiom,
    ! [Vvar__0__C__103630,Vvar__0__C__103631,Vvar__1___24Anonymous__103632,Vvar__1___24Anonymous__103633,Vvar__2___24Anonymous__103634,Vvar__2___24Anonymous__103635] :
      ( cCoq_2emicromega_2eRingMicromega_2ePsatzAdd___24a3(Vvar__0__C__103630,Vvar__1___24Anonymous__103632,Vvar__2___24Anonymous__103634) = cCoq_2emicromega_2eRingMicromega_2ePsatzAdd___24a3(Vvar__0__C__103631,Vvar__1___24Anonymous__103633,Vvar__2___24Anonymous__103635)
     => ( Vvar__2___24Anonymous__103634 = Vvar__2___24Anonymous__103635
        & Vvar__1___24Anonymous__103632 = Vvar__1___24Anonymous__103633
        & Vvar__0__C__103630 = Vvar__0__C__103631 ) ) ).

fof('$_inj_Coq.micromega.RingMicromega.PsatzC',axiom,
    ! [Vvar__0__C__103636,Vvar__0__C__103637,Vvar__1___24Anonymous__103638,Vvar__1___24Anonymous__103639] :
      ( cCoq_2emicromega_2eRingMicromega_2ePsatzC___24a2(Vvar__0__C__103636,Vvar__1___24Anonymous__103638) = cCoq_2emicromega_2eRingMicromega_2ePsatzC___24a2(Vvar__0__C__103637,Vvar__1___24Anonymous__103639)
     => ( Vvar__1___24Anonymous__103638 = Vvar__1___24Anonymous__103639
        & Vvar__0__C__103636 = Vvar__0__C__103637 ) ) ).

fof('$_inj_Coq.micromega.RingMicromega.PsatzIn',axiom,
    ! [Vvar__0__C__103610,Vvar__0__C__103611,Vvar__1___24Anonymous__103612,Vvar__1___24Anonymous__103613] :
      ( cCoq_2emicromega_2eRingMicromega_2ePsatzIn___24a2(Vvar__0__C__103610,Vvar__1___24Anonymous__103612) = cCoq_2emicromega_2eRingMicromega_2ePsatzIn___24a2(Vvar__0__C__103611,Vvar__1___24Anonymous__103613)
     => ( Vvar__1___24Anonymous__103612 = Vvar__1___24Anonymous__103613
        & Vvar__0__C__103610 = Vvar__0__C__103611 ) ) ).

fof('$_inj_Coq.micromega.RingMicromega.PsatzMulC',axiom,
    ! [Vvar__0__C__103618,Vvar__0__C__103619,Vvar__1___24Anonymous__103620,Vvar__1___24Anonymous__103621,Vvar__2___24Anonymous__103622,Vvar__2___24Anonymous__103623] :
      ( cCoq_2emicromega_2eRingMicromega_2ePsatzMulC___24a3(Vvar__0__C__103618,Vvar__1___24Anonymous__103620,Vvar__2___24Anonymous__103622) = cCoq_2emicromega_2eRingMicromega_2ePsatzMulC___24a3(Vvar__0__C__103619,Vvar__1___24Anonymous__103621,Vvar__2___24Anonymous__103623)
     => ( Vvar__2___24Anonymous__103622 = Vvar__2___24Anonymous__103623
        & Vvar__1___24Anonymous__103620 = Vvar__1___24Anonymous__103621
        & Vvar__0__C__103618 = Vvar__0__C__103619 ) ) ).

fof('$_inj_Coq.micromega.RingMicromega.PsatzMulE',axiom,
    ! [Vvar__0__C__103624,Vvar__0__C__103625,Vvar__1___24Anonymous__103626,Vvar__1___24Anonymous__103627,Vvar__2___24Anonymous__103628,Vvar__2___24Anonymous__103629] :
      ( cCoq_2emicromega_2eRingMicromega_2ePsatzMulE___24a3(Vvar__0__C__103624,Vvar__1___24Anonymous__103626,Vvar__2___24Anonymous__103628) = cCoq_2emicromega_2eRingMicromega_2ePsatzMulE___24a3(Vvar__0__C__103625,Vvar__1___24Anonymous__103627,Vvar__2___24Anonymous__103629)
     => ( Vvar__2___24Anonymous__103628 = Vvar__2___24Anonymous__103629
        & Vvar__1___24Anonymous__103626 = Vvar__1___24Anonymous__103627
        & Vvar__0__C__103624 = Vvar__0__C__103625 ) ) ).

fof('$_inj_Coq.micromega.RingMicromega.PsatzSquare',axiom,
    ! [Vvar__0__C__103614,Vvar__0__C__103615,Vvar__1___24Anonymous__103616,Vvar__1___24Anonymous__103617] :
      ( cCoq_2emicromega_2eRingMicromega_2ePsatzSquare___24a2(Vvar__0__C__103614,Vvar__1___24Anonymous__103616) = cCoq_2emicromega_2eRingMicromega_2ePsatzSquare___24a2(Vvar__0__C__103615,Vvar__1___24Anonymous__103617)
     => ( Vvar__1___24Anonymous__103616 = Vvar__1___24Anonymous__103617
        & Vvar__0__C__103614 = Vvar__0__C__103615 ) ) ).

fof('$_inj_Coq.micromega.RingMicromega.PsatzZ',axiom,
    ! [Vvar__0__C__103640,Vvar__0__C__103641] :
      ( cCoq_2emicromega_2eRingMicromega_2ePsatzZ___24a1(Vvar__0__C__103640) = cCoq_2emicromega_2eRingMicromega_2ePsatzZ___24a1(Vvar__0__C__103641)
     => Vvar__0__C__103640 = Vvar__0__C__103641 ) ).

fof('$_inj_Coq.micromega.Tauto.A',axiom,
    ! [Vvar__0__TA__91389,Vvar__0__TA__91390,Vvar__1__TX__91391,Vvar__1__TX__91392,Vvar__2__AA__91393,Vvar__2__AA__91394,Vvar__3__AF__91395,Vvar__3__AF__91396,Vvar__4___24Anonymous__91397,Vvar__4___24Anonymous__91398,Vvar__5___24Anonymous__91399,Vvar__5___24Anonymous__91400] :
      ( cCoq_2emicromega_2eTauto_2eA___24a6(Vvar__0__TA__91389,Vvar__1__TX__91391,Vvar__2__AA__91393,Vvar__3__AF__91395,Vvar__4___24Anonymous__91397,Vvar__5___24Anonymous__91399) = cCoq_2emicromega_2eTauto_2eA___24a6(Vvar__0__TA__91390,Vvar__1__TX__91392,Vvar__2__AA__91394,Vvar__3__AF__91396,Vvar__4___24Anonymous__91398,Vvar__5___24Anonymous__91400)
     => ( Vvar__5___24Anonymous__91399 = Vvar__5___24Anonymous__91400
        & Vvar__4___24Anonymous__91397 = Vvar__4___24Anonymous__91398
        & Vvar__3__AF__91395 = Vvar__3__AF__91396
        & Vvar__2__AA__91393 = Vvar__2__AA__91394
        & Vvar__1__TX__91391 = Vvar__1__TX__91392
        & Vvar__0__TA__91389 = Vvar__0__TA__91390 ) ) ).

fof('$_inj_Coq.micromega.Tauto.Cj',axiom,
    ! [Vvar__0__TA__91401,Vvar__0__TA__91402,Vvar__1__TX__91403,Vvar__1__TX__91404,Vvar__2__AA__91405,Vvar__2__AA__91406,Vvar__3__AF__91407,Vvar__3__AF__91408,Vvar__4___24Anonymous__91409,Vvar__4___24Anonymous__91410,Vvar__5___24Anonymous__91411,Vvar__5___24Anonymous__91412] :
      ( cCoq_2emicromega_2eTauto_2eCj___24a6(Vvar__0__TA__91401,Vvar__1__TX__91403,Vvar__2__AA__91405,Vvar__3__AF__91407,Vvar__4___24Anonymous__91409,Vvar__5___24Anonymous__91411) = cCoq_2emicromega_2eTauto_2eCj___24a6(Vvar__0__TA__91402,Vvar__1__TX__91404,Vvar__2__AA__91406,Vvar__3__AF__91408,Vvar__4___24Anonymous__91410,Vvar__5___24Anonymous__91412)
     => ( Vvar__5___24Anonymous__91411 = Vvar__5___24Anonymous__91412
        & Vvar__4___24Anonymous__91409 = Vvar__4___24Anonymous__91410
        & Vvar__3__AF__91407 = Vvar__3__AF__91408
        & Vvar__2__AA__91405 = Vvar__2__AA__91406
        & Vvar__1__TX__91403 = Vvar__1__TX__91404
        & Vvar__0__TA__91401 = Vvar__0__TA__91402 ) ) ).

fof('$_inj_Coq.micromega.Tauto.D',axiom,
    ! [Vvar__0__TA__91413,Vvar__0__TA__91414,Vvar__1__TX__91415,Vvar__1__TX__91416,Vvar__2__AA__91417,Vvar__2__AA__91418,Vvar__3__AF__91419,Vvar__3__AF__91420,Vvar__4___24Anonymous__91421,Vvar__4___24Anonymous__91422,Vvar__5___24Anonymous__91423,Vvar__5___24Anonymous__91424] :
      ( cCoq_2emicromega_2eTauto_2eD___24a6(Vvar__0__TA__91413,Vvar__1__TX__91415,Vvar__2__AA__91417,Vvar__3__AF__91419,Vvar__4___24Anonymous__91421,Vvar__5___24Anonymous__91423) = cCoq_2emicromega_2eTauto_2eD___24a6(Vvar__0__TA__91414,Vvar__1__TX__91416,Vvar__2__AA__91418,Vvar__3__AF__91420,Vvar__4___24Anonymous__91422,Vvar__5___24Anonymous__91424)
     => ( Vvar__5___24Anonymous__91423 = Vvar__5___24Anonymous__91424
        & Vvar__4___24Anonymous__91421 = Vvar__4___24Anonymous__91422
        & Vvar__3__AF__91419 = Vvar__3__AF__91420
        & Vvar__2__AA__91417 = Vvar__2__AA__91418
        & Vvar__1__TX__91415 = Vvar__1__TX__91416
        & Vvar__0__TA__91413 = Vvar__0__TA__91414 ) ) ).

fof('$_inj_Coq.micromega.Tauto.FF',axiom,
    ! [Vvar__0__TA__91371,Vvar__0__TA__91372,Vvar__1__TX__91373,Vvar__1__TX__91374,Vvar__2__AA__91375,Vvar__2__AA__91376,Vvar__3__AF__91377,Vvar__3__AF__91378] :
      ( cCoq_2emicromega_2eTauto_2eFF___24a4(Vvar__0__TA__91371,Vvar__1__TX__91373,Vvar__2__AA__91375,Vvar__3__AF__91377) = cCoq_2emicromega_2eTauto_2eFF___24a4(Vvar__0__TA__91372,Vvar__1__TX__91374,Vvar__2__AA__91376,Vvar__3__AF__91378)
     => ( Vvar__3__AF__91377 = Vvar__3__AF__91378
        & Vvar__2__AA__91375 = Vvar__2__AA__91376
        & Vvar__1__TX__91373 = Vvar__1__TX__91374
        & Vvar__0__TA__91371 = Vvar__0__TA__91372 ) ) ).

fof('$_inj_Coq.micromega.Tauto.I',axiom,
    ! [Vvar__0__TA__91435,Vvar__0__TA__91436,Vvar__1__TX__91437,Vvar__1__TX__91438,Vvar__2__AA__91439,Vvar__2__AA__91440,Vvar__3__AF__91441,Vvar__3__AF__91442,Vvar__4___24Anonymous__91443,Vvar__4___24Anonymous__91444,Vvar__5___24Anonymous__91445,Vvar__5___24Anonymous__91446,Vvar__6___24Anonymous__91447,Vvar__6___24Anonymous__91448] :
      ( cCoq_2emicromega_2eTauto_2eI___24a7(Vvar__0__TA__91435,Vvar__1__TX__91437,Vvar__2__AA__91439,Vvar__3__AF__91441,Vvar__4___24Anonymous__91443,Vvar__5___24Anonymous__91445,Vvar__6___24Anonymous__91447) = cCoq_2emicromega_2eTauto_2eI___24a7(Vvar__0__TA__91436,Vvar__1__TX__91438,Vvar__2__AA__91440,Vvar__3__AF__91442,Vvar__4___24Anonymous__91444,Vvar__5___24Anonymous__91446,Vvar__6___24Anonymous__91448)
     => ( Vvar__6___24Anonymous__91447 = Vvar__6___24Anonymous__91448
        & Vvar__5___24Anonymous__91445 = Vvar__5___24Anonymous__91446
        & Vvar__4___24Anonymous__91443 = Vvar__4___24Anonymous__91444
        & Vvar__3__AF__91441 = Vvar__3__AF__91442
        & Vvar__2__AA__91439 = Vvar__2__AA__91440
        & Vvar__1__TX__91437 = Vvar__1__TX__91438
        & Vvar__0__TA__91435 = Vvar__0__TA__91436 ) ) ).

fof('$_inj_Coq.micromega.Tauto.N',axiom,
    ! [Vvar__0__TA__91425,Vvar__0__TA__91426,Vvar__1__TX__91427,Vvar__1__TX__91428,Vvar__2__AA__91429,Vvar__2__AA__91430,Vvar__3__AF__91431,Vvar__3__AF__91432,Vvar__4___24Anonymous__91433,Vvar__4___24Anonymous__91434] :
      ( cCoq_2emicromega_2eTauto_2eN___24a5(Vvar__0__TA__91425,Vvar__1__TX__91427,Vvar__2__AA__91429,Vvar__3__AF__91431,Vvar__4___24Anonymous__91433) = cCoq_2emicromega_2eTauto_2eN___24a5(Vvar__0__TA__91426,Vvar__1__TX__91428,Vvar__2__AA__91430,Vvar__3__AF__91432,Vvar__4___24Anonymous__91434)
     => ( Vvar__4___24Anonymous__91433 = Vvar__4___24Anonymous__91434
        & Vvar__3__AF__91431 = Vvar__3__AF__91432
        & Vvar__2__AA__91429 = Vvar__2__AA__91430
        & Vvar__1__TX__91427 = Vvar__1__TX__91428
        & Vvar__0__TA__91425 = Vvar__0__TA__91426 ) ) ).

fof('$_inj_Coq.micromega.Tauto.TT',axiom,
    ! [Vvar__0__TA__91363,Vvar__0__TA__91364,Vvar__1__TX__91365,Vvar__1__TX__91366,Vvar__2__AA__91367,Vvar__2__AA__91368,Vvar__3__AF__91369,Vvar__3__AF__91370] :
      ( cCoq_2emicromega_2eTauto_2eTT___24a4(Vvar__0__TA__91363,Vvar__1__TX__91365,Vvar__2__AA__91367,Vvar__3__AF__91369) = cCoq_2emicromega_2eTauto_2eTT___24a4(Vvar__0__TA__91364,Vvar__1__TX__91366,Vvar__2__AA__91368,Vvar__3__AF__91370)
     => ( Vvar__3__AF__91369 = Vvar__3__AF__91370
        & Vvar__2__AA__91367 = Vvar__2__AA__91368
        & Vvar__1__TX__91365 = Vvar__1__TX__91366
        & Vvar__0__TA__91363 = Vvar__0__TA__91364 ) ) ).

fof('$_inj_Coq.micromega.Tauto.X',axiom,
    ! [Vvar__0__TA__91379,Vvar__0__TA__91380,Vvar__1__TX__91381,Vvar__1__TX__91382,Vvar__2__AA__91383,Vvar__2__AA__91384,Vvar__3__AF__91385,Vvar__3__AF__91386,Vvar__4___24Anonymous__91387,Vvar__4___24Anonymous__91388] :
      ( cCoq_2emicromega_2eTauto_2eX___24a5(Vvar__0__TA__91379,Vvar__1__TX__91381,Vvar__2__AA__91383,Vvar__3__AF__91385,Vvar__4___24Anonymous__91387) = cCoq_2emicromega_2eTauto_2eX___24a5(Vvar__0__TA__91380,Vvar__1__TX__91382,Vvar__2__AA__91384,Vvar__3__AF__91386,Vvar__4___24Anonymous__91388)
     => ( Vvar__4___24Anonymous__91387 = Vvar__4___24Anonymous__91388
        & Vvar__3__AF__91385 = Vvar__3__AF__91386
        & Vvar__2__AA__91383 = Vvar__2__AA__91384
        & Vvar__1__TX__91381 = Vvar__1__TX__91382
        & Vvar__0__TA__91379 = Vvar__0__TA__91380 ) ) ).

fof('$_inj_Coq.micromega.VarMap.Branch',axiom,
    ! [Vvar__0__A__105322,Vvar__0__A__105323,Vvar__1___24Anonymous__105324,Vvar__1___24Anonymous__105325,Vvar__2___24Anonymous__105326,Vvar__2___24Anonymous__105327,Vvar__3___24Anonymous__105328,Vvar__3___24Anonymous__105329] :
      ( cCoq_2emicromega_2eVarMap_2eBranch___24a4(Vvar__0__A__105322,Vvar__1___24Anonymous__105324,Vvar__2___24Anonymous__105326,Vvar__3___24Anonymous__105328) = cCoq_2emicromega_2eVarMap_2eBranch___24a4(Vvar__0__A__105323,Vvar__1___24Anonymous__105325,Vvar__2___24Anonymous__105327,Vvar__3___24Anonymous__105329)
     => ( Vvar__3___24Anonymous__105328 = Vvar__3___24Anonymous__105329
        & Vvar__2___24Anonymous__105326 = Vvar__2___24Anonymous__105327
        & Vvar__1___24Anonymous__105324 = Vvar__1___24Anonymous__105325
        & Vvar__0__A__105322 = Vvar__0__A__105323 ) ) ).

fof('$_inj_Coq.micromega.VarMap.Elt',axiom,
    ! [Vvar__0__A__105318,Vvar__0__A__105319,Vvar__1___24Anonymous__105320,Vvar__1___24Anonymous__105321] :
      ( cCoq_2emicromega_2eVarMap_2eElt___24a2(Vvar__0__A__105318,Vvar__1___24Anonymous__105320) = cCoq_2emicromega_2eVarMap_2eElt___24a2(Vvar__0__A__105319,Vvar__1___24Anonymous__105321)
     => ( Vvar__1___24Anonymous__105320 = Vvar__1___24Anonymous__105321
        & Vvar__0__A__105318 = Vvar__0__A__105319 ) ) ).

fof('$_inj_Coq.micromega.VarMap.Empty',axiom,
    ! [Vvar__0__A__105316,Vvar__0__A__105317] :
      ( cCoq_2emicromega_2eVarMap_2eEmpty___24a1(Vvar__0__A__105316) = cCoq_2emicromega_2eVarMap_2eEmpty___24a1(Vvar__0__A__105317)
     => Vvar__0__A__105316 = Vvar__0__A__105317 ) ).

fof('$_inj_Coq.micromega.ZMicromega.CutProof',axiom,
    ! [Vvar__0___24Anonymous__92882,Vvar__0___24Anonymous__92883,Vvar__1___24Anonymous__92884,Vvar__1___24Anonymous__92885] :
      ( cCoq_2emicromega_2eZMicromega_2eCutProof___24a2(Vvar__0___24Anonymous__92882,Vvar__1___24Anonymous__92884) = cCoq_2emicromega_2eZMicromega_2eCutProof___24a2(Vvar__0___24Anonymous__92883,Vvar__1___24Anonymous__92885)
     => ( Vvar__1___24Anonymous__92884 = Vvar__1___24Anonymous__92885
        & Vvar__0___24Anonymous__92882 = Vvar__0___24Anonymous__92883 ) ) ).

fof('$_inj_Coq.micromega.ZMicromega.EnumProof',axiom,
    ! [Vvar__0___24Anonymous__92886,Vvar__0___24Anonymous__92887,Vvar__1___24Anonymous__92888,Vvar__1___24Anonymous__92889,Vvar__2___24Anonymous__92890,Vvar__2___24Anonymous__92891] :
      ( cCoq_2emicromega_2eZMicromega_2eEnumProof___24a3(Vvar__0___24Anonymous__92886,Vvar__1___24Anonymous__92888,Vvar__2___24Anonymous__92890) = cCoq_2emicromega_2eZMicromega_2eEnumProof___24a3(Vvar__0___24Anonymous__92887,Vvar__1___24Anonymous__92889,Vvar__2___24Anonymous__92891)
     => ( Vvar__2___24Anonymous__92890 = Vvar__2___24Anonymous__92891
        & Vvar__1___24Anonymous__92888 = Vvar__1___24Anonymous__92889
        & Vvar__0___24Anonymous__92886 = Vvar__0___24Anonymous__92887 ) ) ).

fof('$_inj_Coq.micromega.ZMicromega.RatProof',axiom,
    ! [Vvar__0___24Anonymous__92878,Vvar__0___24Anonymous__92879,Vvar__1___24Anonymous__92880,Vvar__1___24Anonymous__92881] :
      ( cCoq_2emicromega_2eZMicromega_2eRatProof___24a2(Vvar__0___24Anonymous__92878,Vvar__1___24Anonymous__92880) = cCoq_2emicromega_2eZMicromega_2eRatProof___24a2(Vvar__0___24Anonymous__92879,Vvar__1___24Anonymous__92881)
     => ( Vvar__1___24Anonymous__92880 = Vvar__1___24Anonymous__92881
        & Vvar__0___24Anonymous__92878 = Vvar__0___24Anonymous__92879 ) ) ).

fof('$_inj_Coq.setoid_ring.Field_theory.FEI',axiom,
    ! [Vvar__0__C__95498,Vvar__0__C__95499] :
      ( cCoq_2esetoid__ring_2eField__theory_2eFEI___24a1(Vvar__0__C__95498) = cCoq_2esetoid__ring_2eField__theory_2eFEI___24a1(Vvar__0__C__95499)
     => Vvar__0__C__95498 = Vvar__0__C__95499 ) ).

fof('$_inj_Coq.setoid_ring.Field_theory.FEO',axiom,
    ! [Vvar__0__C__95496,Vvar__0__C__95497] :
      ( cCoq_2esetoid__ring_2eField__theory_2eFEO___24a1(Vvar__0__C__95496) = cCoq_2esetoid__ring_2eField__theory_2eFEO___24a1(Vvar__0__C__95497)
     => Vvar__0__C__95496 = Vvar__0__C__95497 ) ).

fof('$_inj_Coq.setoid_ring.Field_theory.FEX',axiom,
    ! [Vvar__0__C__95504,Vvar__0__C__95505,Vvar__1___24Anonymous__95506,Vvar__1___24Anonymous__95507] :
      ( cCoq_2esetoid__ring_2eField__theory_2eFEX___24a2(Vvar__0__C__95504,Vvar__1___24Anonymous__95506) = cCoq_2esetoid__ring_2eField__theory_2eFEX___24a2(Vvar__0__C__95505,Vvar__1___24Anonymous__95507)
     => ( Vvar__1___24Anonymous__95506 = Vvar__1___24Anonymous__95507
        & Vvar__0__C__95504 = Vvar__0__C__95505 ) ) ).

fof('$_inj_Coq.setoid_ring.Field_theory.FEadd',axiom,
    ! [Vvar__0__C__95508,Vvar__0__C__95509,Vvar__1___24Anonymous__95510,Vvar__1___24Anonymous__95511,Vvar__2___24Anonymous__95512,Vvar__2___24Anonymous__95513] :
      ( cCoq_2esetoid__ring_2eField__theory_2eFEadd___24a3(Vvar__0__C__95508,Vvar__1___24Anonymous__95510,Vvar__2___24Anonymous__95512) = cCoq_2esetoid__ring_2eField__theory_2eFEadd___24a3(Vvar__0__C__95509,Vvar__1___24Anonymous__95511,Vvar__2___24Anonymous__95513)
     => ( Vvar__2___24Anonymous__95512 = Vvar__2___24Anonymous__95513
        & Vvar__1___24Anonymous__95510 = Vvar__1___24Anonymous__95511
        & Vvar__0__C__95508 = Vvar__0__C__95509 ) ) ).

fof('$_inj_Coq.setoid_ring.Field_theory.FEc',axiom,
    ! [Vvar__0__C__95500,Vvar__0__C__95501,Vvar__1___24Anonymous__95502,Vvar__1___24Anonymous__95503] :
      ( cCoq_2esetoid__ring_2eField__theory_2eFEc___24a2(Vvar__0__C__95500,Vvar__1___24Anonymous__95502) = cCoq_2esetoid__ring_2eField__theory_2eFEc___24a2(Vvar__0__C__95501,Vvar__1___24Anonymous__95503)
     => ( Vvar__1___24Anonymous__95502 = Vvar__1___24Anonymous__95503
        & Vvar__0__C__95500 = Vvar__0__C__95501 ) ) ).

fof('$_inj_Coq.setoid_ring.Field_theory.FEdiv',axiom,
    ! [Vvar__0__C__95534,Vvar__0__C__95535,Vvar__1___24Anonymous__95536,Vvar__1___24Anonymous__95537,Vvar__2___24Anonymous__95538,Vvar__2___24Anonymous__95539] :
      ( cCoq_2esetoid__ring_2eField__theory_2eFEdiv___24a3(Vvar__0__C__95534,Vvar__1___24Anonymous__95536,Vvar__2___24Anonymous__95538) = cCoq_2esetoid__ring_2eField__theory_2eFEdiv___24a3(Vvar__0__C__95535,Vvar__1___24Anonymous__95537,Vvar__2___24Anonymous__95539)
     => ( Vvar__2___24Anonymous__95538 = Vvar__2___24Anonymous__95539
        & Vvar__1___24Anonymous__95536 = Vvar__1___24Anonymous__95537
        & Vvar__0__C__95534 = Vvar__0__C__95535 ) ) ).

fof('$_inj_Coq.setoid_ring.Field_theory.FEinv',axiom,
    ! [Vvar__0__C__95530,Vvar__0__C__95531,Vvar__1___24Anonymous__95532,Vvar__1___24Anonymous__95533] :
      ( cCoq_2esetoid__ring_2eField__theory_2eFEinv___24a2(Vvar__0__C__95530,Vvar__1___24Anonymous__95532) = cCoq_2esetoid__ring_2eField__theory_2eFEinv___24a2(Vvar__0__C__95531,Vvar__1___24Anonymous__95533)
     => ( Vvar__1___24Anonymous__95532 = Vvar__1___24Anonymous__95533
        & Vvar__0__C__95530 = Vvar__0__C__95531 ) ) ).

fof('$_inj_Coq.setoid_ring.Field_theory.FEmul',axiom,
    ! [Vvar__0__C__95520,Vvar__0__C__95521,Vvar__1___24Anonymous__95522,Vvar__1___24Anonymous__95523,Vvar__2___24Anonymous__95524,Vvar__2___24Anonymous__95525] :
      ( cCoq_2esetoid__ring_2eField__theory_2eFEmul___24a3(Vvar__0__C__95520,Vvar__1___24Anonymous__95522,Vvar__2___24Anonymous__95524) = cCoq_2esetoid__ring_2eField__theory_2eFEmul___24a3(Vvar__0__C__95521,Vvar__1___24Anonymous__95523,Vvar__2___24Anonymous__95525)
     => ( Vvar__2___24Anonymous__95524 = Vvar__2___24Anonymous__95525
        & Vvar__1___24Anonymous__95522 = Vvar__1___24Anonymous__95523
        & Vvar__0__C__95520 = Vvar__0__C__95521 ) ) ).

fof('$_inj_Coq.setoid_ring.Field_theory.FEopp',axiom,
    ! [Vvar__0__C__95526,Vvar__0__C__95527,Vvar__1___24Anonymous__95528,Vvar__1___24Anonymous__95529] :
      ( cCoq_2esetoid__ring_2eField__theory_2eFEopp___24a2(Vvar__0__C__95526,Vvar__1___24Anonymous__95528) = cCoq_2esetoid__ring_2eField__theory_2eFEopp___24a2(Vvar__0__C__95527,Vvar__1___24Anonymous__95529)
     => ( Vvar__1___24Anonymous__95528 = Vvar__1___24Anonymous__95529
        & Vvar__0__C__95526 = Vvar__0__C__95527 ) ) ).

fof('$_inj_Coq.setoid_ring.Field_theory.FEpow',axiom,
    ! [Vvar__0__C__95540,Vvar__0__C__95541,Vvar__1___24Anonymous__95542,Vvar__1___24Anonymous__95543,Vvar__2___24Anonymous__95544,Vvar__2___24Anonymous__95545] :
      ( cCoq_2esetoid__ring_2eField__theory_2eFEpow___24a3(Vvar__0__C__95540,Vvar__1___24Anonymous__95542,Vvar__2___24Anonymous__95544) = cCoq_2esetoid__ring_2eField__theory_2eFEpow___24a3(Vvar__0__C__95541,Vvar__1___24Anonymous__95543,Vvar__2___24Anonymous__95545)
     => ( Vvar__2___24Anonymous__95544 = Vvar__2___24Anonymous__95545
        & Vvar__1___24Anonymous__95542 = Vvar__1___24Anonymous__95543
        & Vvar__0__C__95540 = Vvar__0__C__95541 ) ) ).

fof('$_inj_Coq.setoid_ring.Field_theory.FEsub',axiom,
    ! [Vvar__0__C__95514,Vvar__0__C__95515,Vvar__1___24Anonymous__95516,Vvar__1___24Anonymous__95517,Vvar__2___24Anonymous__95518,Vvar__2___24Anonymous__95519] :
      ( cCoq_2esetoid__ring_2eField__theory_2eFEsub___24a3(Vvar__0__C__95514,Vvar__1___24Anonymous__95516,Vvar__2___24Anonymous__95518) = cCoq_2esetoid__ring_2eField__theory_2eFEsub___24a3(Vvar__0__C__95515,Vvar__1___24Anonymous__95517,Vvar__2___24Anonymous__95519)
     => ( Vvar__2___24Anonymous__95518 = Vvar__2___24Anonymous__95519
        & Vvar__1___24Anonymous__95516 = Vvar__1___24Anonymous__95517
        & Vvar__0__C__95514 = Vvar__0__C__95515 ) ) ).

fof('$_inj_Coq.setoid_ring.Field_theory.mk_linear',axiom,
    ! [Vvar__0__C__95555,Vvar__0__C__95556,Vvar__1__num__95557,Vvar__1__num__95558,Vvar__2__denum__95559,Vvar__2__denum__95560,Vvar__3__condition__95561,Vvar__3__condition__95562] :
      ( cCoq_2esetoid__ring_2eField__theory_2emk__linear___24a4(Vvar__0__C__95555,Vvar__1__num__95557,Vvar__2__denum__95559,Vvar__3__condition__95561) = cCoq_2esetoid__ring_2eField__theory_2emk__linear___24a4(Vvar__0__C__95556,Vvar__1__num__95558,Vvar__2__denum__95560,Vvar__3__condition__95562)
     => ( Vvar__3__condition__95561 = Vvar__3__condition__95562
        & Vvar__2__denum__95559 = Vvar__2__denum__95560
        & Vvar__1__num__95557 = Vvar__1__num__95558
        & Vvar__0__C__95555 = Vvar__0__C__95556 ) ) ).

fof('$_inj_Coq.setoid_ring.Field_theory.mk_rsplit',axiom,
    ! [Vvar__0__C__95569,Vvar__0__C__95570,Vvar__1__rsplit__left__95571,Vvar__1__rsplit__left__95572,Vvar__2__rsplit__common__95573,Vvar__2__rsplit__common__95574,Vvar__3__rsplit__right__95575,Vvar__3__rsplit__right__95576] :
      ( cCoq_2esetoid__ring_2eField__theory_2emk__rsplit___24a4(Vvar__0__C__95569,Vvar__1__rsplit__left__95571,Vvar__2__rsplit__common__95573,Vvar__3__rsplit__right__95575) = cCoq_2esetoid__ring_2eField__theory_2emk__rsplit___24a4(Vvar__0__C__95570,Vvar__1__rsplit__left__95572,Vvar__2__rsplit__common__95574,Vvar__3__rsplit__right__95576)
     => ( Vvar__3__rsplit__right__95575 = Vvar__3__rsplit__right__95576
        & Vvar__2__rsplit__common__95573 = Vvar__2__rsplit__common__95574
        & Vvar__1__rsplit__left__95571 = Vvar__1__rsplit__left__95572
        & Vvar__0__C__95569 = Vvar__0__C__95570 ) ) ).

fof('$_inj_Coq.setoid_ring.InitialRing.mkhypo',axiom,
    ! [Vvar__0__hypo__type__96813,Vvar__0__hypo__type__96814,Vvar__1__hypo__proof__96815,Vvar__1__hypo__proof__96816] :
      ( cCoq_2esetoid__ring_2eInitialRing_2emkhypo___24a2(Vvar__0__hypo__type__96813,Vvar__1__hypo__proof__96815) = cCoq_2esetoid__ring_2eInitialRing_2emkhypo___24a2(Vvar__0__hypo__type__96814,Vvar__1__hypo__proof__96816)
     => ( Vvar__1__hypo__proof__96815 = Vvar__1__hypo__proof__96816
        & Vvar__0__hypo__type__96813 = Vvar__0__hypo__type__96814 ) ) ).

fof('$_inj_Coq.setoid_ring.Ring_polynom.PEI',axiom,
    ! [Vvar__0__C__78432,Vvar__0__C__78433] :
      ( cCoq_2esetoid__ring_2eRing__polynom_2ePEI___24a1(Vvar__0__C__78432) = cCoq_2esetoid__ring_2eRing__polynom_2ePEI___24a1(Vvar__0__C__78433)
     => Vvar__0__C__78432 = Vvar__0__C__78433 ) ).

fof('$_inj_Coq.setoid_ring.Ring_polynom.PEO',axiom,
    ! [Vvar__0__C__78430,Vvar__0__C__78431] :
      ( cCoq_2esetoid__ring_2eRing__polynom_2ePEO___24a1(Vvar__0__C__78430) = cCoq_2esetoid__ring_2eRing__polynom_2ePEO___24a1(Vvar__0__C__78431)
     => Vvar__0__C__78430 = Vvar__0__C__78431 ) ).

fof('$_inj_Coq.setoid_ring.Ring_polynom.PEX',axiom,
    ! [Vvar__0__C__78438,Vvar__0__C__78439,Vvar__1___24Anonymous__78440,Vvar__1___24Anonymous__78441] :
      ( cCoq_2esetoid__ring_2eRing__polynom_2ePEX___24a2(Vvar__0__C__78438,Vvar__1___24Anonymous__78440) = cCoq_2esetoid__ring_2eRing__polynom_2ePEX___24a2(Vvar__0__C__78439,Vvar__1___24Anonymous__78441)
     => ( Vvar__1___24Anonymous__78440 = Vvar__1___24Anonymous__78441
        & Vvar__0__C__78438 = Vvar__0__C__78439 ) ) ).

fof('$_inj_Coq.setoid_ring.Ring_polynom.PEadd',axiom,
    ! [Vvar__0__C__78442,Vvar__0__C__78443,Vvar__1___24Anonymous__78444,Vvar__1___24Anonymous__78445,Vvar__2___24Anonymous__78446,Vvar__2___24Anonymous__78447] :
      ( cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(Vvar__0__C__78442,Vvar__1___24Anonymous__78444,Vvar__2___24Anonymous__78446) = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(Vvar__0__C__78443,Vvar__1___24Anonymous__78445,Vvar__2___24Anonymous__78447)
     => ( Vvar__2___24Anonymous__78446 = Vvar__2___24Anonymous__78447
        & Vvar__1___24Anonymous__78444 = Vvar__1___24Anonymous__78445
        & Vvar__0__C__78442 = Vvar__0__C__78443 ) ) ).

fof('$_inj_Coq.setoid_ring.Ring_polynom.PEc',axiom,
    ! [Vvar__0__C__78434,Vvar__0__C__78435,Vvar__1___24Anonymous__78436,Vvar__1___24Anonymous__78437] :
      ( cCoq_2esetoid__ring_2eRing__polynom_2ePEc___24a2(Vvar__0__C__78434,Vvar__1___24Anonymous__78436) = cCoq_2esetoid__ring_2eRing__polynom_2ePEc___24a2(Vvar__0__C__78435,Vvar__1___24Anonymous__78437)
     => ( Vvar__1___24Anonymous__78436 = Vvar__1___24Anonymous__78437
        & Vvar__0__C__78434 = Vvar__0__C__78435 ) ) ).

fof('$_inj_Coq.setoid_ring.Ring_polynom.PEmul',axiom,
    ! [Vvar__0__C__78454,Vvar__0__C__78455,Vvar__1___24Anonymous__78456,Vvar__1___24Anonymous__78457,Vvar__2___24Anonymous__78458,Vvar__2___24Anonymous__78459] :
      ( cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(Vvar__0__C__78454,Vvar__1___24Anonymous__78456,Vvar__2___24Anonymous__78458) = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(Vvar__0__C__78455,Vvar__1___24Anonymous__78457,Vvar__2___24Anonymous__78459)
     => ( Vvar__2___24Anonymous__78458 = Vvar__2___24Anonymous__78459
        & Vvar__1___24Anonymous__78456 = Vvar__1___24Anonymous__78457
        & Vvar__0__C__78454 = Vvar__0__C__78455 ) ) ).

fof('$_inj_Coq.setoid_ring.Ring_polynom.PEopp',axiom,
    ! [Vvar__0__C__78460,Vvar__0__C__78461,Vvar__1___24Anonymous__78462,Vvar__1___24Anonymous__78463] :
      ( cCoq_2esetoid__ring_2eRing__polynom_2ePEopp___24a2(Vvar__0__C__78460,Vvar__1___24Anonymous__78462) = cCoq_2esetoid__ring_2eRing__polynom_2ePEopp___24a2(Vvar__0__C__78461,Vvar__1___24Anonymous__78463)
     => ( Vvar__1___24Anonymous__78462 = Vvar__1___24Anonymous__78463
        & Vvar__0__C__78460 = Vvar__0__C__78461 ) ) ).

fof('$_inj_Coq.setoid_ring.Ring_polynom.PEpow',axiom,
    ! [Vvar__0__C__78464,Vvar__0__C__78465,Vvar__1___24Anonymous__78466,Vvar__1___24Anonymous__78467,Vvar__2___24Anonymous__78468,Vvar__2___24Anonymous__78469] :
      ( cCoq_2esetoid__ring_2eRing__polynom_2ePEpow___24a3(Vvar__0__C__78464,Vvar__1___24Anonymous__78466,Vvar__2___24Anonymous__78468) = cCoq_2esetoid__ring_2eRing__polynom_2ePEpow___24a3(Vvar__0__C__78465,Vvar__1___24Anonymous__78467,Vvar__2___24Anonymous__78469)
     => ( Vvar__2___24Anonymous__78468 = Vvar__2___24Anonymous__78469
        & Vvar__1___24Anonymous__78466 = Vvar__1___24Anonymous__78467
        & Vvar__0__C__78464 = Vvar__0__C__78465 ) ) ).

fof('$_inj_Coq.setoid_ring.Ring_polynom.PEsub',axiom,
    ! [Vvar__0__C__78448,Vvar__0__C__78449,Vvar__1___24Anonymous__78450,Vvar__1___24Anonymous__78451,Vvar__2___24Anonymous__78452,Vvar__2___24Anonymous__78453] :
      ( cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(Vvar__0__C__78448,Vvar__1___24Anonymous__78450,Vvar__2___24Anonymous__78452) = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(Vvar__0__C__78449,Vvar__1___24Anonymous__78451,Vvar__2___24Anonymous__78453)
     => ( Vvar__2___24Anonymous__78452 = Vvar__2___24Anonymous__78453
        & Vvar__1___24Anonymous__78450 = Vvar__1___24Anonymous__78451
        & Vvar__0__C__78448 = Vvar__0__C__78449 ) ) ).

fof('$_inj_Coq.setoid_ring.Ring_polynom.PX',axiom,
    ! [Vvar__0__C__78085,Vvar__0__C__78086,Vvar__1___24Anonymous__78087,Vvar__1___24Anonymous__78088,Vvar__2___24Anonymous__78089,Vvar__2___24Anonymous__78090,Vvar__3___24Anonymous__78091,Vvar__3___24Anonymous__78092] :
      ( cCoq_2esetoid__ring_2eRing__polynom_2ePX___24a4(Vvar__0__C__78085,Vvar__1___24Anonymous__78087,Vvar__2___24Anonymous__78089,Vvar__3___24Anonymous__78091) = cCoq_2esetoid__ring_2eRing__polynom_2ePX___24a4(Vvar__0__C__78086,Vvar__1___24Anonymous__78088,Vvar__2___24Anonymous__78090,Vvar__3___24Anonymous__78092)
     => ( Vvar__3___24Anonymous__78091 = Vvar__3___24Anonymous__78092
        & Vvar__2___24Anonymous__78089 = Vvar__2___24Anonymous__78090
        & Vvar__1___24Anonymous__78087 = Vvar__1___24Anonymous__78088
        & Vvar__0__C__78085 = Vvar__0__C__78086 ) ) ).

fof('$_inj_Coq.setoid_ring.Ring_polynom.Pc',axiom,
    ! [Vvar__0__C__78075,Vvar__0__C__78076,Vvar__1___24Anonymous__78077,Vvar__1___24Anonymous__78078] :
      ( cCoq_2esetoid__ring_2eRing__polynom_2ePc___24a2(Vvar__0__C__78075,Vvar__1___24Anonymous__78077) = cCoq_2esetoid__ring_2eRing__polynom_2ePc___24a2(Vvar__0__C__78076,Vvar__1___24Anonymous__78078)
     => ( Vvar__1___24Anonymous__78077 = Vvar__1___24Anonymous__78078
        & Vvar__0__C__78075 = Vvar__0__C__78076 ) ) ).

fof('$_inj_Coq.setoid_ring.Ring_polynom.Pinj',axiom,
    ! [Vvar__0__C__78079,Vvar__0__C__78080,Vvar__1___24Anonymous__78081,Vvar__1___24Anonymous__78082,Vvar__2___24Anonymous__78083,Vvar__2___24Anonymous__78084] :
      ( cCoq_2esetoid__ring_2eRing__polynom_2ePinj___24a3(Vvar__0__C__78079,Vvar__1___24Anonymous__78081,Vvar__2___24Anonymous__78083) = cCoq_2esetoid__ring_2eRing__polynom_2ePinj___24a3(Vvar__0__C__78080,Vvar__1___24Anonymous__78082,Vvar__2___24Anonymous__78084)
     => ( Vvar__2___24Anonymous__78083 = Vvar__2___24Anonymous__78084
        & Vvar__1___24Anonymous__78081 = Vvar__1___24Anonymous__78082
        & Vvar__0__C__78079 = Vvar__0__C__78080 ) ) ).

fof('$_inj_Coq.setoid_ring.Ring_polynom.vmon',axiom,
    ! [Vvar__0___24Anonymous__78244,Vvar__0___24Anonymous__78245,Vvar__1___24Anonymous__78246,Vvar__1___24Anonymous__78247] :
      ( cCoq_2esetoid__ring_2eRing__polynom_2evmon___24a2(Vvar__0___24Anonymous__78244,Vvar__1___24Anonymous__78246) = cCoq_2esetoid__ring_2eRing__polynom_2evmon___24a2(Vvar__0___24Anonymous__78245,Vvar__1___24Anonymous__78247)
     => ( Vvar__1___24Anonymous__78246 = Vvar__1___24Anonymous__78247
        & Vvar__0___24Anonymous__78244 = Vvar__0___24Anonymous__78245 ) ) ).

fof('$_inj_Coq.setoid_ring.Ring_polynom.zmon',axiom,
    ! [Vvar__0___24Anonymous__78240,Vvar__0___24Anonymous__78241,Vvar__1___24Anonymous__78242,Vvar__1___24Anonymous__78243] :
      ( cCoq_2esetoid__ring_2eRing__polynom_2ezmon___24a2(Vvar__0___24Anonymous__78240,Vvar__1___24Anonymous__78242) = cCoq_2esetoid__ring_2eRing__polynom_2ezmon___24a2(Vvar__0___24Anonymous__78241,Vvar__1___24Anonymous__78243)
     => ( Vvar__1___24Anonymous__78242 = Vvar__1___24Anonymous__78243
        & Vvar__0___24Anonymous__78240 = Vvar__0___24Anonymous__78241 ) ) ).

fof('$_inj_Coq.setoid_ring.Ring_theory.Computational',axiom,
    ! [Vvar__0__R__89827,Vvar__0__R__89828,Vvar__1__req__89829,Vvar__1__req__89830,Vvar__2__reqb__89831,Vvar__2__reqb__89832,Vvar__3___24Anonymous__89833,Vvar__3___24Anonymous__89834] :
      ( cCoq_2esetoid__ring_2eRing__theory_2eComputational___24a3(Vvar__0__R__89827,Vvar__1__req__89829,Vvar__2__reqb__89831) = cCoq_2esetoid__ring_2eRing__theory_2eComputational___24a3(Vvar__0__R__89828,Vvar__1__req__89830,Vvar__2__reqb__89832)
     => ( c_24Proof = c_24Proof
        & Vvar__2__reqb__89831 = Vvar__2__reqb__89832
        & Vvar__1__req__89829 = Vvar__1__req__89830
        & Vvar__0__R__89827 = Vvar__0__R__89828 ) ) ).

fof('$_inj_Coq.setoid_ring.Ring_theory.Morphism',axiom,
    ! [Vvar__0__R__89835,Vvar__0__R__89836,Vvar__1__rO__89837,Vvar__1__rO__89838,Vvar__2__rI__89839,Vvar__2__rI__89840,Vvar__3__radd__89841,Vvar__3__radd__89842,Vvar__4__rmul__89843,Vvar__4__rmul__89844,Vvar__5__rsub__89845,Vvar__5__rsub__89846,Vvar__6__ropp__89847,Vvar__6__ropp__89848,Vvar__7__req__89849,Vvar__7__req__89850,Vvar__8__C__89851,Vvar__8__C__89852,Vvar__9__cO__89853,Vvar__9__cO__89854,Vvar__10__cI__89855,Vvar__10__cI__89856,Vvar__11__cadd__89857,Vvar__11__cadd__89858,Vvar__12__cmul__89859,Vvar__12__cmul__89860,Vvar__13__csub__89861,Vvar__13__csub__89862,Vvar__14__copp__89863,Vvar__14__copp__89864,Vvar__15__ceqb__89865,Vvar__15__ceqb__89866,Vvar__16__phi__89867,Vvar__16__phi__89868,Vvar__17___24Anonymous__89869,Vvar__17___24Anonymous__89870] :
      ( cCoq_2esetoid__ring_2eRing__theory_2eMorphism___24a17(Vvar__0__R__89835,Vvar__1__rO__89837,Vvar__2__rI__89839,Vvar__3__radd__89841,Vvar__4__rmul__89843,Vvar__5__rsub__89845,Vvar__6__ropp__89847,Vvar__7__req__89849,Vvar__8__C__89851,Vvar__9__cO__89853,Vvar__10__cI__89855,Vvar__11__cadd__89857,Vvar__12__cmul__89859,Vvar__13__csub__89861,Vvar__14__copp__89863,Vvar__15__ceqb__89865,Vvar__16__phi__89867) = cCoq_2esetoid__ring_2eRing__theory_2eMorphism___24a17(Vvar__0__R__89836,Vvar__1__rO__89838,Vvar__2__rI__89840,Vvar__3__radd__89842,Vvar__4__rmul__89844,Vvar__5__rsub__89846,Vvar__6__ropp__89848,Vvar__7__req__89850,Vvar__8__C__89852,Vvar__9__cO__89854,Vvar__10__cI__89856,Vvar__11__cadd__89858,Vvar__12__cmul__89860,Vvar__13__csub__89862,Vvar__14__copp__89864,Vvar__15__ceqb__89866,Vvar__16__phi__89868)
     => ( c_24Proof = c_24Proof
        & Vvar__16__phi__89867 = Vvar__16__phi__89868
        & Vvar__15__ceqb__89865 = Vvar__15__ceqb__89866
        & Vvar__14__copp__89863 = Vvar__14__copp__89864
        & Vvar__13__csub__89861 = Vvar__13__csub__89862
        & Vvar__12__cmul__89859 = Vvar__12__cmul__89860
        & Vvar__11__cadd__89857 = Vvar__11__cadd__89858
        & Vvar__10__cI__89855 = Vvar__10__cI__89856
        & Vvar__9__cO__89853 = Vvar__9__cO__89854
        & Vvar__8__C__89851 = Vvar__8__C__89852
        & Vvar__7__req__89849 = Vvar__7__req__89850
        & Vvar__6__ropp__89847 = Vvar__6__ropp__89848
        & Vvar__5__rsub__89845 = Vvar__5__rsub__89846
        & Vvar__4__rmul__89843 = Vvar__4__rmul__89844
        & Vvar__3__radd__89841 = Vvar__3__radd__89842
        & Vvar__2__rI__89839 = Vvar__2__rI__89840
        & Vvar__1__rO__89837 = Vvar__1__rO__89838
        & Vvar__0__R__89835 = Vvar__0__R__89836 ) ) ).

fof('$_inj_IntMap.Map.M0',axiom,
    ! [Vvar__0__A__273,Vvar__0__A__274] :
      ( cIntMap_2eMap_2eM0___24a1(Vvar__0__A__273) = cIntMap_2eMap_2eM0___24a1(Vvar__0__A__274)
     => Vvar__0__A__273 = Vvar__0__A__274 ) ).

fof('$_inj_IntMap.Map.M1',axiom,
    ! [Vvar__0__A__275,Vvar__0__A__276,Vvar__1___24Anonymous__277,Vvar__1___24Anonymous__278,Vvar__2___24Anonymous__279,Vvar__2___24Anonymous__280] :
      ( cIntMap_2eMap_2eM1___24a3(Vvar__0__A__275,Vvar__1___24Anonymous__277,Vvar__2___24Anonymous__279) = cIntMap_2eMap_2eM1___24a3(Vvar__0__A__276,Vvar__1___24Anonymous__278,Vvar__2___24Anonymous__280)
     => ( Vvar__2___24Anonymous__279 = Vvar__2___24Anonymous__280
        & Vvar__1___24Anonymous__277 = Vvar__1___24Anonymous__278
        & Vvar__0__A__275 = Vvar__0__A__276 ) ) ).

fof('$_inj_IntMap.Map.M2',axiom,
    ! [Vvar__0__A__281,Vvar__0__A__282,Vvar__1___24Anonymous__283,Vvar__1___24Anonymous__284,Vvar__2___24Anonymous__285,Vvar__2___24Anonymous__286] :
      ( cIntMap_2eMap_2eM2___24a3(Vvar__0__A__281,Vvar__1___24Anonymous__283,Vvar__2___24Anonymous__285) = cIntMap_2eMap_2eM2___24a3(Vvar__0__A__282,Vvar__1___24Anonymous__284,Vvar__2___24Anonymous__286)
     => ( Vvar__2___24Anonymous__285 = Vvar__2___24Anonymous__286
        & Vvar__1___24Anonymous__283 = Vvar__1___24Anonymous__284
        & Vvar__0__A__281 = Vvar__0__A__282 ) ) ).

fof('$_inversion_Coq.Arith.Between.P_nth',axiom,
    ! [Vvar__0__P__80412,Vvar__1__Q__80414,Vvar__2__init__80417,Vvar__3___24Anonymous__80418,Vvar__4___24Anonymous__80419] :
      ( c_24__type__80445___24t(Vvar__0__P__80412,Vvar__1__Q__80414,Vvar__2__init__80417,Vvar__3___24Anonymous__80418,Vvar__4___24Anonymous__80419,Vvar__0__P__80412)
     => ( c_24__type__80453___24t(Vvar__0__P__80412,Vvar__1__Q__80414,Vvar__2__init__80417,Vvar__3___24Anonymous__80418,Vvar__4___24Anonymous__80419,Vvar__1__Q__80414)
       => ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__2__init__80417)
         => ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__3___24Anonymous__80418)
           => ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__4___24Anonymous__80419)
             => ( cCoq_2eArith_2eBetween_2eP__nth___24a5(Vvar__0__P__80412,Vvar__1__Q__80414,Vvar__2__init__80417,Vvar__3___24Anonymous__80418,Vvar__4___24Anonymous__80419)
               => ( ( Vvar__4___24Anonymous__80419 = cCoq_2eInit_2eDatatypes_2eO
                    & Vvar__3___24Anonymous__80418 = Vvar__2__init__80417 )
                  | ? [Vvar__3__k__80433] :
                      ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__3__k__80433)
                      & ? [Vvar__4__l__80434] :
                          ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__4__l__80434)
                          & ? [Vvar__5__n__80435] :
                              ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__5__n__80435)
                              & cCoq_2eArith_2eBetween_2eP__nth___24a5(Vvar__0__P__80412,Vvar__1__Q__80414,Vvar__2__init__80417,Vvar__3__k__80433,Vvar__5__n__80435)
                              & cCoq_2eArith_2eBetween_2ebetween___24a3(Vvar__0__P__80412,cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__3__k__80433),Vvar__4__l__80434)
                              & p(happ(Vvar__1__Q__80414,Vvar__4__l__80434))
                              & Vvar__4___24Anonymous__80419 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__5__n__80435)
                              & Vvar__3___24Anonymous__80418 = Vvar__4__l__80434 ) ) ) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.Arith.Between.between',axiom,
    ! [Vvar__0__P__68046,Vvar__1__k__68048,Vvar__2___24Anonymous__68049] :
      ( c_24__type__68063___24t(Vvar__0__P__68046,Vvar__1__k__68048,Vvar__2___24Anonymous__68049,Vvar__0__P__68046)
     => ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__1__k__68048)
       => ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__2___24Anonymous__68049)
         => ( cCoq_2eArith_2eBetween_2ebetween___24a3(Vvar__0__P__68046,Vvar__1__k__68048,Vvar__2___24Anonymous__68049)
           => ( Vvar__2___24Anonymous__68049 = Vvar__1__k__68048
              | ? [Vvar__2__l__68057] :
                  ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__2__l__68057)
                  & cCoq_2eArith_2eBetween_2ebetween___24a3(Vvar__0__P__68046,Vvar__1__k__68048,Vvar__2__l__68057)
                  & p(happ(Vvar__0__P__68046,Vvar__2__l__68057))
                  & Vvar__2___24Anonymous__68049 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__2__l__68057) ) ) ) ) ) ) ).

fof('$_inversion_Coq.Arith.Between.exists_between',axiom,
    ! [Vvar__0__Q__68069,Vvar__1__k__68071,Vvar__2___24Anonymous__68072] :
      ( c_24__type__68088___24t(Vvar__0__Q__68069,Vvar__1__k__68071,Vvar__2___24Anonymous__68072,Vvar__0__Q__68069)
     => ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__1__k__68071)
       => ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__2___24Anonymous__68072)
         => ( cCoq_2eArith_2eBetween_2eexists__between___24a3(Vvar__0__Q__68069,Vvar__1__k__68071,Vvar__2___24Anonymous__68072)
           => ( ? [Vvar__2__l__68077] :
                  ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__2__l__68077)
                  & cCoq_2eArith_2eBetween_2eexists__between___24a3(Vvar__0__Q__68069,Vvar__1__k__68071,Vvar__2__l__68077)
                  & Vvar__2___24Anonymous__68072 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__2__l__68077) )
              | ? [Vvar__2__l__68082] :
                  ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__2__l__68082)
                  & cCoq_2eInit_2ePeano_2ele___24a2(Vvar__1__k__68071,Vvar__2__l__68082)
                  & p(happ(Vvar__0__Q__68069,Vvar__2__l__68082))
                  & Vvar__2___24Anonymous__68072 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__2__l__68082) ) ) ) ) ) ) ).

fof('$_inversion_Coq.Arith.Even.even',axiom,
    ! [Vvar__0___24Anonymous__75876] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__75876)
     => ( cCoq_2eArith_2eEven_2eeven___24a1(Vvar__0___24Anonymous__75876)
       => ( Vvar__0___24Anonymous__75876 = cCoq_2eInit_2eDatatypes_2eO
          | ? [Vvar__0__n__75878] :
              ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0__n__75878)
              & cCoq_2eArith_2eEven_2eodd___24a1(Vvar__0__n__75878)
              & Vvar__0___24Anonymous__75876 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0__n__75878) ) ) ) ) ).

fof('$_inversion_Coq.Arith.Even.odd',axiom,
    ! [Vvar__0___24Anonymous__75880] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__75880)
     => ( cCoq_2eArith_2eEven_2eodd___24a1(Vvar__0___24Anonymous__75880)
       => ? [Vvar__0__n__75882] :
            ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0__n__75882)
            & cCoq_2eArith_2eEven_2eeven___24a1(Vvar__0__n__75882)
            & Vvar__0___24Anonymous__75880 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0__n__75882) ) ) ) ).

fof('$_inversion_Coq.Bool.Bool.reflect',axiom,
    ! [Vvar__0__P__94154,Vvar__1___24Anonymous__94155,VX94156] :
      ( cProp___24t(Vvar__0__P__94154)
     => ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__1___24Anonymous__94155)
       => ( cCoq_2eBool_2eBool_2ereflect___24t(Vvar__0__P__94154,Vvar__1___24Anonymous__94155,VX94156)
         => ( ( p(Vvar__0__P__94154)
              & Vvar__1___24Anonymous__94155 = cCoq_2eInit_2eDatatypes_2etrue
              & VX94156 = cCoq_2eBool_2eBool_2eReflectT___24a1(Vvar__0__P__94154) )
            | ( ~ p(Vvar__0__P__94154)
              & Vvar__1___24Anonymous__94155 = cCoq_2eInit_2eDatatypes_2efalse
              & VX94156 = cCoq_2eBool_2eBool_2eReflectF___24a1(Vvar__0__P__94154) ) ) ) ) ) ).

fof('$_inversion_Coq.FSets.FSetPositive.PositiveSet.ct',axiom,
    ! [Vvar__0___24Anonymous__93360,Vvar__1___24Anonymous__93361,Vvar__2___24Anonymous__93362] :
      ( cCoq_2eInit_2eDatatypes_2ecomparison___24t(Vvar__0___24Anonymous__93360)
     => ( cCoq_2eInit_2eDatatypes_2ecomparison___24t(Vvar__1___24Anonymous__93361)
       => ( cCoq_2eInit_2eDatatypes_2ecomparison___24t(Vvar__2___24Anonymous__93362)
         => ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2ect___24a3(Vvar__0___24Anonymous__93360,Vvar__1___24Anonymous__93361,Vvar__2___24Anonymous__93362)
           => ( ? [Vvar__0__x__93364] :
                  ( cCoq_2eInit_2eDatatypes_2ecomparison___24t(Vvar__0__x__93364)
                  & Vvar__2___24Anonymous__93362 = Vvar__0__x__93364
                  & Vvar__1___24Anonymous__93361 = Vvar__0__x__93364
                  & Vvar__0___24Anonymous__93360 = Vvar__0__x__93364 )
              | ? [Vvar__0__x__93365] :
                  ( cCoq_2eInit_2eDatatypes_2ecomparison___24t(Vvar__0__x__93365)
                  & Vvar__2___24Anonymous__93362 = Vvar__0__x__93365
                  & Vvar__1___24Anonymous__93361 = cCoq_2eInit_2eDatatypes_2eEq
                  & Vvar__0___24Anonymous__93360 = Vvar__0__x__93365 )
              | ? [Vvar__0__x__93366] :
                  ( cCoq_2eInit_2eDatatypes_2ecomparison___24t(Vvar__0__x__93366)
                  & Vvar__2___24Anonymous__93362 = Vvar__0__x__93366
                  & Vvar__1___24Anonymous__93361 = Vvar__0__x__93366
                  & Vvar__0___24Anonymous__93360 = cCoq_2eInit_2eDatatypes_2eEq )
              | ? [Vvar__0__x__93367] :
                  ( cCoq_2eInit_2eDatatypes_2ecomparison___24t(Vvar__0__x__93367)
                  & Vvar__2___24Anonymous__93362 = Vvar__0__x__93367
                  & Vvar__1___24Anonymous__93361 = cCoq_2eInit_2eDatatypes_2eLt
                  & Vvar__0___24Anonymous__93360 = cCoq_2eInit_2eDatatypes_2eGt )
              | ? [Vvar__0__x__93368] :
                  ( cCoq_2eInit_2eDatatypes_2ecomparison___24t(Vvar__0__x__93368)
                  & Vvar__2___24Anonymous__93362 = Vvar__0__x__93368
                  & Vvar__1___24Anonymous__93361 = cCoq_2eInit_2eDatatypes_2eGt
                  & Vvar__0___24Anonymous__93360 = cCoq_2eInit_2eDatatypes_2eLt ) ) ) ) ) ) ).

fof('$_inversion_Coq.FSets.FSetPositive.PositiveSet.tree',axiom,
    ! [VX93193] :
      ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree___24t(VX93193)
     => ( VX93193 = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eLeaf
        | ? [Vvar__0___24Anonymous__93194] :
            ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree___24t(Vvar__0___24Anonymous__93194)
            & ? [Vvar__1___24Anonymous__93195] :
                ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__1___24Anonymous__93195)
                & ? [Vvar__2___24Anonymous__93196] :
                    ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree___24t(Vvar__2___24Anonymous__93196)
                    & VX93193 = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eNode___24a3(Vvar__0___24Anonymous__93194,Vvar__1___24Anonymous__93195,Vvar__2___24Anonymous__93196) ) ) ) ) ) ).

fof('$_inversion_Coq.Init.Byte.byte',axiom,
    ! [VX1463] :
      ( cCoq_2eInit_2eByte_2ebyte___24t(VX1463)
     => ( VX1463 = cCoq_2eInit_2eByte_2ex00
        | VX1463 = cCoq_2eInit_2eByte_2ex01
        | VX1463 = cCoq_2eInit_2eByte_2ex02
        | VX1463 = cCoq_2eInit_2eByte_2ex03
        | VX1463 = cCoq_2eInit_2eByte_2ex04
        | VX1463 = cCoq_2eInit_2eByte_2ex05
        | VX1463 = cCoq_2eInit_2eByte_2ex06
        | VX1463 = cCoq_2eInit_2eByte_2ex07
        | VX1463 = cCoq_2eInit_2eByte_2ex08
        | VX1463 = cCoq_2eInit_2eByte_2ex09
        | VX1463 = cCoq_2eInit_2eByte_2ex0a
        | VX1463 = cCoq_2eInit_2eByte_2ex0b
        | VX1463 = cCoq_2eInit_2eByte_2ex0c
        | VX1463 = cCoq_2eInit_2eByte_2ex0d
        | VX1463 = cCoq_2eInit_2eByte_2ex0e
        | VX1463 = cCoq_2eInit_2eByte_2ex0f
        | VX1463 = cCoq_2eInit_2eByte_2ex10
        | VX1463 = cCoq_2eInit_2eByte_2ex11
        | VX1463 = cCoq_2eInit_2eByte_2ex12
        | VX1463 = cCoq_2eInit_2eByte_2ex13
        | VX1463 = cCoq_2eInit_2eByte_2ex14
        | VX1463 = cCoq_2eInit_2eByte_2ex15
        | VX1463 = cCoq_2eInit_2eByte_2ex16
        | VX1463 = cCoq_2eInit_2eByte_2ex17
        | VX1463 = cCoq_2eInit_2eByte_2ex18
        | VX1463 = cCoq_2eInit_2eByte_2ex19
        | VX1463 = cCoq_2eInit_2eByte_2ex1a
        | VX1463 = cCoq_2eInit_2eByte_2ex1b
        | VX1463 = cCoq_2eInit_2eByte_2ex1c
        | VX1463 = cCoq_2eInit_2eByte_2ex1d
        | VX1463 = cCoq_2eInit_2eByte_2ex1e
        | VX1463 = cCoq_2eInit_2eByte_2ex1f
        | VX1463 = cCoq_2eInit_2eByte_2ex20
        | VX1463 = cCoq_2eInit_2eByte_2ex21
        | VX1463 = cCoq_2eInit_2eByte_2ex22
        | VX1463 = cCoq_2eInit_2eByte_2ex23
        | VX1463 = cCoq_2eInit_2eByte_2ex24
        | VX1463 = cCoq_2eInit_2eByte_2ex25
        | VX1463 = cCoq_2eInit_2eByte_2ex26
        | VX1463 = cCoq_2eInit_2eByte_2ex27
        | VX1463 = cCoq_2eInit_2eByte_2ex28
        | VX1463 = cCoq_2eInit_2eByte_2ex29
        | VX1463 = cCoq_2eInit_2eByte_2ex2a
        | VX1463 = cCoq_2eInit_2eByte_2ex2b
        | VX1463 = cCoq_2eInit_2eByte_2ex2c
        | VX1463 = cCoq_2eInit_2eByte_2ex2d
        | VX1463 = cCoq_2eInit_2eByte_2ex2e
        | VX1463 = cCoq_2eInit_2eByte_2ex2f
        | VX1463 = cCoq_2eInit_2eByte_2ex30
        | VX1463 = cCoq_2eInit_2eByte_2ex31
        | VX1463 = cCoq_2eInit_2eByte_2ex32
        | VX1463 = cCoq_2eInit_2eByte_2ex33
        | VX1463 = cCoq_2eInit_2eByte_2ex34
        | VX1463 = cCoq_2eInit_2eByte_2ex35
        | VX1463 = cCoq_2eInit_2eByte_2ex36
        | VX1463 = cCoq_2eInit_2eByte_2ex37
        | VX1463 = cCoq_2eInit_2eByte_2ex38
        | VX1463 = cCoq_2eInit_2eByte_2ex39
        | VX1463 = cCoq_2eInit_2eByte_2ex3a
        | VX1463 = cCoq_2eInit_2eByte_2ex3b
        | VX1463 = cCoq_2eInit_2eByte_2ex3c
        | VX1463 = cCoq_2eInit_2eByte_2ex3d
        | VX1463 = cCoq_2eInit_2eByte_2ex3e
        | VX1463 = cCoq_2eInit_2eByte_2ex3f
        | VX1463 = cCoq_2eInit_2eByte_2ex40
        | VX1463 = cCoq_2eInit_2eByte_2ex41
        | VX1463 = cCoq_2eInit_2eByte_2ex42
        | VX1463 = cCoq_2eInit_2eByte_2ex43
        | VX1463 = cCoq_2eInit_2eByte_2ex44
        | VX1463 = cCoq_2eInit_2eByte_2ex45
        | VX1463 = cCoq_2eInit_2eByte_2ex46
        | VX1463 = cCoq_2eInit_2eByte_2ex47
        | VX1463 = cCoq_2eInit_2eByte_2ex48
        | VX1463 = cCoq_2eInit_2eByte_2ex49
        | VX1463 = cCoq_2eInit_2eByte_2ex4a
        | VX1463 = cCoq_2eInit_2eByte_2ex4b
        | VX1463 = cCoq_2eInit_2eByte_2ex4c
        | VX1463 = cCoq_2eInit_2eByte_2ex4d
        | VX1463 = cCoq_2eInit_2eByte_2ex4e
        | VX1463 = cCoq_2eInit_2eByte_2ex4f
        | VX1463 = cCoq_2eInit_2eByte_2ex50
        | VX1463 = cCoq_2eInit_2eByte_2ex51
        | VX1463 = cCoq_2eInit_2eByte_2ex52
        | VX1463 = cCoq_2eInit_2eByte_2ex53
        | VX1463 = cCoq_2eInit_2eByte_2ex54
        | VX1463 = cCoq_2eInit_2eByte_2ex55
        | VX1463 = cCoq_2eInit_2eByte_2ex56
        | VX1463 = cCoq_2eInit_2eByte_2ex57
        | VX1463 = cCoq_2eInit_2eByte_2ex58
        | VX1463 = cCoq_2eInit_2eByte_2ex59
        | VX1463 = cCoq_2eInit_2eByte_2ex5a
        | VX1463 = cCoq_2eInit_2eByte_2ex5b
        | VX1463 = cCoq_2eInit_2eByte_2ex5c
        | VX1463 = cCoq_2eInit_2eByte_2ex5d
        | VX1463 = cCoq_2eInit_2eByte_2ex5e
        | VX1463 = cCoq_2eInit_2eByte_2ex5f
        | VX1463 = cCoq_2eInit_2eByte_2ex60
        | VX1463 = cCoq_2eInit_2eByte_2ex61
        | VX1463 = cCoq_2eInit_2eByte_2ex62
        | VX1463 = cCoq_2eInit_2eByte_2ex63
        | VX1463 = cCoq_2eInit_2eByte_2ex64
        | VX1463 = cCoq_2eInit_2eByte_2ex65
        | VX1463 = cCoq_2eInit_2eByte_2ex66
        | VX1463 = cCoq_2eInit_2eByte_2ex67
        | VX1463 = cCoq_2eInit_2eByte_2ex68
        | VX1463 = cCoq_2eInit_2eByte_2ex69
        | VX1463 = cCoq_2eInit_2eByte_2ex6a
        | VX1463 = cCoq_2eInit_2eByte_2ex6b
        | VX1463 = cCoq_2eInit_2eByte_2ex6c
        | VX1463 = cCoq_2eInit_2eByte_2ex6d
        | VX1463 = cCoq_2eInit_2eByte_2ex6e
        | VX1463 = cCoq_2eInit_2eByte_2ex6f
        | VX1463 = cCoq_2eInit_2eByte_2ex70
        | VX1463 = cCoq_2eInit_2eByte_2ex71
        | VX1463 = cCoq_2eInit_2eByte_2ex72
        | VX1463 = cCoq_2eInit_2eByte_2ex73
        | VX1463 = cCoq_2eInit_2eByte_2ex74
        | VX1463 = cCoq_2eInit_2eByte_2ex75
        | VX1463 = cCoq_2eInit_2eByte_2ex76
        | VX1463 = cCoq_2eInit_2eByte_2ex77
        | VX1463 = cCoq_2eInit_2eByte_2ex78
        | VX1463 = cCoq_2eInit_2eByte_2ex79
        | VX1463 = cCoq_2eInit_2eByte_2ex7a
        | VX1463 = cCoq_2eInit_2eByte_2ex7b
        | VX1463 = cCoq_2eInit_2eByte_2ex7c
        | VX1463 = cCoq_2eInit_2eByte_2ex7d
        | VX1463 = cCoq_2eInit_2eByte_2ex7e
        | VX1463 = cCoq_2eInit_2eByte_2ex7f
        | VX1463 = cCoq_2eInit_2eByte_2ex80
        | VX1463 = cCoq_2eInit_2eByte_2ex81
        | VX1463 = cCoq_2eInit_2eByte_2ex82
        | VX1463 = cCoq_2eInit_2eByte_2ex83
        | VX1463 = cCoq_2eInit_2eByte_2ex84
        | VX1463 = cCoq_2eInit_2eByte_2ex85
        | VX1463 = cCoq_2eInit_2eByte_2ex86
        | VX1463 = cCoq_2eInit_2eByte_2ex87
        | VX1463 = cCoq_2eInit_2eByte_2ex88
        | VX1463 = cCoq_2eInit_2eByte_2ex89
        | VX1463 = cCoq_2eInit_2eByte_2ex8a
        | VX1463 = cCoq_2eInit_2eByte_2ex8b
        | VX1463 = cCoq_2eInit_2eByte_2ex8c
        | VX1463 = cCoq_2eInit_2eByte_2ex8d
        | VX1463 = cCoq_2eInit_2eByte_2ex8e
        | VX1463 = cCoq_2eInit_2eByte_2ex8f
        | VX1463 = cCoq_2eInit_2eByte_2ex90
        | VX1463 = cCoq_2eInit_2eByte_2ex91
        | VX1463 = cCoq_2eInit_2eByte_2ex92
        | VX1463 = cCoq_2eInit_2eByte_2ex93
        | VX1463 = cCoq_2eInit_2eByte_2ex94
        | VX1463 = cCoq_2eInit_2eByte_2ex95
        | VX1463 = cCoq_2eInit_2eByte_2ex96
        | VX1463 = cCoq_2eInit_2eByte_2ex97
        | VX1463 = cCoq_2eInit_2eByte_2ex98
        | VX1463 = cCoq_2eInit_2eByte_2ex99
        | VX1463 = cCoq_2eInit_2eByte_2ex9a
        | VX1463 = cCoq_2eInit_2eByte_2ex9b
        | VX1463 = cCoq_2eInit_2eByte_2ex9c
        | VX1463 = cCoq_2eInit_2eByte_2ex9d
        | VX1463 = cCoq_2eInit_2eByte_2ex9e
        | VX1463 = cCoq_2eInit_2eByte_2ex9f
        | VX1463 = cCoq_2eInit_2eByte_2exa0
        | VX1463 = cCoq_2eInit_2eByte_2exa1
        | VX1463 = cCoq_2eInit_2eByte_2exa2
        | VX1463 = cCoq_2eInit_2eByte_2exa3
        | VX1463 = cCoq_2eInit_2eByte_2exa4
        | VX1463 = cCoq_2eInit_2eByte_2exa5
        | VX1463 = cCoq_2eInit_2eByte_2exa6
        | VX1463 = cCoq_2eInit_2eByte_2exa7
        | VX1463 = cCoq_2eInit_2eByte_2exa8
        | VX1463 = cCoq_2eInit_2eByte_2exa9
        | VX1463 = cCoq_2eInit_2eByte_2exaa
        | VX1463 = cCoq_2eInit_2eByte_2exab
        | VX1463 = cCoq_2eInit_2eByte_2exac
        | VX1463 = cCoq_2eInit_2eByte_2exad
        | VX1463 = cCoq_2eInit_2eByte_2exae
        | VX1463 = cCoq_2eInit_2eByte_2exaf
        | VX1463 = cCoq_2eInit_2eByte_2exb0
        | VX1463 = cCoq_2eInit_2eByte_2exb1
        | VX1463 = cCoq_2eInit_2eByte_2exb2
        | VX1463 = cCoq_2eInit_2eByte_2exb3
        | VX1463 = cCoq_2eInit_2eByte_2exb4
        | VX1463 = cCoq_2eInit_2eByte_2exb5
        | VX1463 = cCoq_2eInit_2eByte_2exb6
        | VX1463 = cCoq_2eInit_2eByte_2exb7
        | VX1463 = cCoq_2eInit_2eByte_2exb8
        | VX1463 = cCoq_2eInit_2eByte_2exb9
        | VX1463 = cCoq_2eInit_2eByte_2exba
        | VX1463 = cCoq_2eInit_2eByte_2exbb
        | VX1463 = cCoq_2eInit_2eByte_2exbc
        | VX1463 = cCoq_2eInit_2eByte_2exbd
        | VX1463 = cCoq_2eInit_2eByte_2exbe
        | VX1463 = cCoq_2eInit_2eByte_2exbf
        | VX1463 = cCoq_2eInit_2eByte_2exc0
        | VX1463 = cCoq_2eInit_2eByte_2exc1
        | VX1463 = cCoq_2eInit_2eByte_2exc2
        | VX1463 = cCoq_2eInit_2eByte_2exc3
        | VX1463 = cCoq_2eInit_2eByte_2exc4
        | VX1463 = cCoq_2eInit_2eByte_2exc5
        | VX1463 = cCoq_2eInit_2eByte_2exc6
        | VX1463 = cCoq_2eInit_2eByte_2exc7
        | VX1463 = cCoq_2eInit_2eByte_2exc8
        | VX1463 = cCoq_2eInit_2eByte_2exc9
        | VX1463 = cCoq_2eInit_2eByte_2exca
        | VX1463 = cCoq_2eInit_2eByte_2excb
        | VX1463 = cCoq_2eInit_2eByte_2excc
        | VX1463 = cCoq_2eInit_2eByte_2excd
        | VX1463 = cCoq_2eInit_2eByte_2exce
        | VX1463 = cCoq_2eInit_2eByte_2excf
        | VX1463 = cCoq_2eInit_2eByte_2exd0
        | VX1463 = cCoq_2eInit_2eByte_2exd1
        | VX1463 = cCoq_2eInit_2eByte_2exd2
        | VX1463 = cCoq_2eInit_2eByte_2exd3
        | VX1463 = cCoq_2eInit_2eByte_2exd4
        | VX1463 = cCoq_2eInit_2eByte_2exd5
        | VX1463 = cCoq_2eInit_2eByte_2exd6
        | VX1463 = cCoq_2eInit_2eByte_2exd7
        | VX1463 = cCoq_2eInit_2eByte_2exd8
        | VX1463 = cCoq_2eInit_2eByte_2exd9
        | VX1463 = cCoq_2eInit_2eByte_2exda
        | VX1463 = cCoq_2eInit_2eByte_2exdb
        | VX1463 = cCoq_2eInit_2eByte_2exdc
        | VX1463 = cCoq_2eInit_2eByte_2exdd
        | VX1463 = cCoq_2eInit_2eByte_2exde
        | VX1463 = cCoq_2eInit_2eByte_2exdf
        | VX1463 = cCoq_2eInit_2eByte_2exe0
        | VX1463 = cCoq_2eInit_2eByte_2exe1
        | VX1463 = cCoq_2eInit_2eByte_2exe2
        | VX1463 = cCoq_2eInit_2eByte_2exe3
        | VX1463 = cCoq_2eInit_2eByte_2exe4
        | VX1463 = cCoq_2eInit_2eByte_2exe5
        | VX1463 = cCoq_2eInit_2eByte_2exe6
        | VX1463 = cCoq_2eInit_2eByte_2exe7
        | VX1463 = cCoq_2eInit_2eByte_2exe8
        | VX1463 = cCoq_2eInit_2eByte_2exe9
        | VX1463 = cCoq_2eInit_2eByte_2exea
        | VX1463 = cCoq_2eInit_2eByte_2exeb
        | VX1463 = cCoq_2eInit_2eByte_2exec
        | VX1463 = cCoq_2eInit_2eByte_2exed
        | VX1463 = cCoq_2eInit_2eByte_2exee
        | VX1463 = cCoq_2eInit_2eByte_2exef
        | VX1463 = cCoq_2eInit_2eByte_2exf0
        | VX1463 = cCoq_2eInit_2eByte_2exf1
        | VX1463 = cCoq_2eInit_2eByte_2exf2
        | VX1463 = cCoq_2eInit_2eByte_2exf3
        | VX1463 = cCoq_2eInit_2eByte_2exf4
        | VX1463 = cCoq_2eInit_2eByte_2exf5
        | VX1463 = cCoq_2eInit_2eByte_2exf6
        | VX1463 = cCoq_2eInit_2eByte_2exf7
        | VX1463 = cCoq_2eInit_2eByte_2exf8
        | VX1463 = cCoq_2eInit_2eByte_2exf9
        | VX1463 = cCoq_2eInit_2eByte_2exfa
        | VX1463 = cCoq_2eInit_2eByte_2exfb
        | VX1463 = cCoq_2eInit_2eByte_2exfc
        | VX1463 = cCoq_2eInit_2eByte_2exfd
        | VX1463 = cCoq_2eInit_2eByte_2exfe
        | VX1463 = cCoq_2eInit_2eByte_2exff ) ) ).

fof('$_inversion_Coq.Init.Datatypes.BoolSpec',axiom,
    ! [Vvar__0__P__80470,Vvar__1__Q__80471,Vvar__2___24Anonymous__80472] :
      ( cProp___24t(Vvar__0__P__80470)
     => ( cProp___24t(Vvar__1__Q__80471)
       => ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__2___24Anonymous__80472)
         => ( cCoq_2eInit_2eDatatypes_2eBoolSpec___24a3(Vvar__0__P__80470,Vvar__1__Q__80471,Vvar__2___24Anonymous__80472)
           => ( ( p(Vvar__0__P__80470)
                & Vvar__2___24Anonymous__80472 = cCoq_2eInit_2eDatatypes_2etrue )
              | ( p(Vvar__1__Q__80471)
                & Vvar__2___24Anonymous__80472 = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ) ) ).

fof('$_inversion_Coq.Init.Datatypes.CompareSpec',axiom,
    ! [Vvar__0__Peq__75726,Vvar__1__Plt__75727,Vvar__2__Pgt__75728,Vvar__3___24Anonymous__75729] :
      ( cProp___24t(Vvar__0__Peq__75726)
     => ( cProp___24t(Vvar__1__Plt__75727)
       => ( cProp___24t(Vvar__2__Pgt__75728)
         => ( cCoq_2eInit_2eDatatypes_2ecomparison___24t(Vvar__3___24Anonymous__75729)
           => ( cCoq_2eInit_2eDatatypes_2eCompareSpec___24a4(Vvar__0__Peq__75726,Vvar__1__Plt__75727,Vvar__2__Pgt__75728,Vvar__3___24Anonymous__75729)
             => ( ( p(Vvar__0__Peq__75726)
                  & Vvar__3___24Anonymous__75729 = cCoq_2eInit_2eDatatypes_2eEq )
                | ( p(Vvar__1__Plt__75727)
                  & Vvar__3___24Anonymous__75729 = cCoq_2eInit_2eDatatypes_2eLt )
                | ( p(Vvar__2__Pgt__75728)
                  & Vvar__3___24Anonymous__75729 = cCoq_2eInit_2eDatatypes_2eGt ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.Init.Datatypes.CompareSpecT',axiom,
    ! [Vvar__0__Peq__83355,Vvar__1__Plt__83356,Vvar__2__Pgt__83357,Vvar__3___24Anonymous__83358,VX83359] :
      ( cProp___24t(Vvar__0__Peq__83355)
     => ( cProp___24t(Vvar__1__Plt__83356)
       => ( cProp___24t(Vvar__2__Pgt__83357)
         => ( cCoq_2eInit_2eDatatypes_2ecomparison___24t(Vvar__3___24Anonymous__83358)
           => ( cCoq_2eInit_2eDatatypes_2eCompareSpecT___24t(Vvar__0__Peq__83355,Vvar__1__Plt__83356,Vvar__2__Pgt__83357,Vvar__3___24Anonymous__83358,VX83359)
             => ( ( p(Vvar__0__Peq__83355)
                  & Vvar__3___24Anonymous__83358 = cCoq_2eInit_2eDatatypes_2eEq
                  & VX83359 = cCoq_2eInit_2eDatatypes_2eCompEqT___24a3(Vvar__0__Peq__83355,Vvar__1__Plt__83356,Vvar__2__Pgt__83357) )
                | ( p(Vvar__1__Plt__83356)
                  & Vvar__3___24Anonymous__83358 = cCoq_2eInit_2eDatatypes_2eLt
                  & VX83359 = cCoq_2eInit_2eDatatypes_2eCompLtT___24a3(Vvar__0__Peq__83355,Vvar__1__Plt__83356,Vvar__2__Pgt__83357) )
                | ( p(Vvar__2__Pgt__83357)
                  & Vvar__3___24Anonymous__83358 = cCoq_2eInit_2eDatatypes_2eGt
                  & VX83359 = cCoq_2eInit_2eDatatypes_2eCompGtT___24a3(Vvar__0__Peq__83355,Vvar__1__Plt__83356,Vvar__2__Pgt__83357) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.Init.Datatypes.bool',axiom,
    ! [VX1138] :
      ( cCoq_2eInit_2eDatatypes_2ebool___24t(VX1138)
     => ( VX1138 = cCoq_2eInit_2eDatatypes_2etrue
        | VX1138 = cCoq_2eInit_2eDatatypes_2efalse ) ) ).

fof('$_inversion_Coq.Init.Datatypes.comparison',axiom,
    ! [VX75725] :
      ( cCoq_2eInit_2eDatatypes_2ecomparison___24t(VX75725)
     => ( VX75725 = cCoq_2eInit_2eDatatypes_2eEq
        | VX75725 = cCoq_2eInit_2eDatatypes_2eLt
        | VX75725 = cCoq_2eInit_2eDatatypes_2eGt ) ) ).

fof('$_inversion_Coq.Init.Datatypes.eq_true',axiom,
    ! [Vvar__0___24Anonymous__94180] :
      ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__0___24Anonymous__94180)
     => ( cCoq_2eInit_2eDatatypes_2eeq__true___24a1(Vvar__0___24Anonymous__94180)
       => Vvar__0___24Anonymous__94180 = cCoq_2eInit_2eDatatypes_2etrue ) ) ).

fof('$_inversion_Coq.Init.Datatypes.identity',axiom,
    ! [Vvar__0__A__94194,Vvar__1__a__94195,Vvar__2___24Anonymous__94196] :
      ( cType___24t(Vvar__0__A__94194)
     => ( t(Vvar__1__a__94195,Vvar__0__A__94194)
       => ( t(Vvar__2___24Anonymous__94196,Vvar__0__A__94194)
         => ( cCoq_2eInit_2eDatatypes_2eidentity___24a3(Vvar__0__A__94194,Vvar__1__a__94195,Vvar__2___24Anonymous__94196)
           => Vvar__2___24Anonymous__94196 = Vvar__1__a__94195 ) ) ) ) ).

fof('$_inversion_Coq.Init.Datatypes.list',axiom,
    ! [Vvar__0__A__75642,VX75643] :
      ( cType___24t(Vvar__0__A__75642)
     => ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__75642,VX75643)
       => ( VX75643 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__75642)
          | ? [Vvar__1___24Anonymous__75646] :
              ( t(Vvar__1___24Anonymous__75646,Vvar__0__A__75642)
              & ? [Vvar__2___24Anonymous__75647] :
                  ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__75642,Vvar__2___24Anonymous__75647)
                  & VX75643 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__75642,Vvar__1___24Anonymous__75646,Vvar__2___24Anonymous__75647) ) ) ) ) ) ).

fof('$_inversion_Coq.Init.Datatypes.nat',axiom,
    ! [VX1] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(VX1)
     => ( VX1 = cCoq_2eInit_2eDatatypes_2eO
        | ? [Vvar__0___24Anonymous__2] :
            ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__2)
            & VX1 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__2) ) ) ) ).

fof('$_inversion_Coq.Init.Datatypes.option',axiom,
    ! [Vvar__0__A__632,VX633] :
      ( cType___24t(Vvar__0__A__632)
     => ( cCoq_2eInit_2eDatatypes_2eoption___24t(Vvar__0__A__632,VX633)
       => ( ? [Vvar__1___24Anonymous__635] :
              ( t(Vvar__1___24Anonymous__635,Vvar__0__A__632)
              & VX633 = cCoq_2eInit_2eDatatypes_2eSome___24a2(Vvar__0__A__632,Vvar__1___24Anonymous__635) )
          | VX633 = cCoq_2eInit_2eDatatypes_2eNone___24a1(Vvar__0__A__632) ) ) ) ).

fof('$_inversion_Coq.Init.Datatypes.prod',axiom,
    ! [Vvar__0__A__67024,Vvar__1__B__67025,VX67026] :
      ( cType___24t(Vvar__0__A__67024)
     => ( cType___24t(Vvar__1__B__67025)
       => ( cCoq_2eInit_2eDatatypes_2eprod___24t(Vvar__0__A__67024,Vvar__1__B__67025,VX67026)
         => ? [Vvar__2___24Anonymous__67029] :
              ( t(Vvar__2___24Anonymous__67029,Vvar__0__A__67024)
              & ? [Vvar__3___24Anonymous__67030] :
                  ( t(Vvar__3___24Anonymous__67030,Vvar__1__B__67025)
                  & VX67026 = cCoq_2eInit_2eDatatypes_2epair___24a4(Vvar__0__A__67024,Vvar__1__B__67025,Vvar__2___24Anonymous__67029,Vvar__3___24Anonymous__67030) ) ) ) ) ) ).

fof('$_inversion_Coq.Init.Datatypes.sum',axiom,
    ! [Vvar__0__A__75521,Vvar__1__B__75522,VX75523] :
      ( cType___24t(Vvar__0__A__75521)
     => ( cType___24t(Vvar__1__B__75522)
       => ( cCoq_2eInit_2eDatatypes_2esum___24t(Vvar__0__A__75521,Vvar__1__B__75522,VX75523)
         => ( ? [Vvar__2___24Anonymous__75526] :
                ( t(Vvar__2___24Anonymous__75526,Vvar__0__A__75521)
                & VX75523 = cCoq_2eInit_2eDatatypes_2einl___24a3(Vvar__0__A__75521,Vvar__1__B__75522,Vvar__2___24Anonymous__75526) )
            | ? [Vvar__2___24Anonymous__75529] :
                ( t(Vvar__2___24Anonymous__75529,Vvar__1__B__75522)
                & VX75523 = cCoq_2eInit_2eDatatypes_2einr___24a3(Vvar__0__A__75521,Vvar__1__B__75522,Vvar__2___24Anonymous__75529) ) ) ) ) ) ).

fof('$_inversion_Coq.Init.Datatypes.unit',axiom,
    ! [VX1137] :
      ( cCoq_2eInit_2eDatatypes_2eunit___24t(VX1137)
     => VX1137 = cCoq_2eInit_2eDatatypes_2ett ) ).

fof('$_inversion_Coq.Init.Decimal.decimal',axiom,
    ! [VX94212] :
      ( cCoq_2eInit_2eDecimal_2edecimal___24t(VX94212)
     => ( ? [Vvar__0__i__94213] :
            ( cCoq_2eInit_2eDecimal_2eint___24t(Vvar__0__i__94213)
            & ? [Vvar__1__f__94214] :
                ( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__1__f__94214)
                & VX94212 = cCoq_2eInit_2eDecimal_2eDecimal___24a2(Vvar__0__i__94213,Vvar__1__f__94214) ) )
        | ? [Vvar__0__i__94215] :
            ( cCoq_2eInit_2eDecimal_2eint___24t(Vvar__0__i__94215)
            & ? [Vvar__1__f__94216] :
                ( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__1__f__94216)
                & ? [Vvar__2__e__94217] :
                    ( cCoq_2eInit_2eDecimal_2eint___24t(Vvar__2__e__94217)
                    & VX94212 = cCoq_2eInit_2eDecimal_2eDecimalExp___24a3(Vvar__0__i__94215,Vvar__1__f__94216,Vvar__2__e__94217) ) ) ) ) ) ).

fof('$_inversion_Coq.Init.Decimal.int',axiom,
    ! [VX94203] :
      ( cCoq_2eInit_2eDecimal_2eint___24t(VX94203)
     => ( ? [Vvar__0__d__94204] :
            ( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0__d__94204)
            & VX94203 = cCoq_2eInit_2eDecimal_2ePos___24a1(Vvar__0__d__94204) )
        | ? [Vvar__0__d__94205] :
            ( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0__d__94205)
            & VX94203 = cCoq_2eInit_2eDecimal_2eNeg___24a1(Vvar__0__d__94205) ) ) ) ).

fof('$_inversion_Coq.Init.Decimal.uint',axiom,
    ! [VX75745] :
      ( cCoq_2eInit_2eDecimal_2euint___24t(VX75745)
     => ( VX75745 = cCoq_2eInit_2eDecimal_2eNil
        | ? [Vvar__0___24Anonymous__75746] :
            ( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0___24Anonymous__75746)
            & VX75745 = cCoq_2eInit_2eDecimal_2eD0___24a1(Vvar__0___24Anonymous__75746) )
        | ? [Vvar__0___24Anonymous__75747] :
            ( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0___24Anonymous__75747)
            & VX75745 = cCoq_2eInit_2eDecimal_2eD1___24a1(Vvar__0___24Anonymous__75747) )
        | ? [Vvar__0___24Anonymous__75748] :
            ( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0___24Anonymous__75748)
            & VX75745 = cCoq_2eInit_2eDecimal_2eD2___24a1(Vvar__0___24Anonymous__75748) )
        | ? [Vvar__0___24Anonymous__75749] :
            ( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0___24Anonymous__75749)
            & VX75745 = cCoq_2eInit_2eDecimal_2eD3___24a1(Vvar__0___24Anonymous__75749) )
        | ? [Vvar__0___24Anonymous__75750] :
            ( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0___24Anonymous__75750)
            & VX75745 = cCoq_2eInit_2eDecimal_2eD4___24a1(Vvar__0___24Anonymous__75750) )
        | ? [Vvar__0___24Anonymous__75751] :
            ( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0___24Anonymous__75751)
            & VX75745 = cCoq_2eInit_2eDecimal_2eD5___24a1(Vvar__0___24Anonymous__75751) )
        | ? [Vvar__0___24Anonymous__75752] :
            ( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0___24Anonymous__75752)
            & VX75745 = cCoq_2eInit_2eDecimal_2eD6___24a1(Vvar__0___24Anonymous__75752) )
        | ? [Vvar__0___24Anonymous__75753] :
            ( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0___24Anonymous__75753)
            & VX75745 = cCoq_2eInit_2eDecimal_2eD7___24a1(Vvar__0___24Anonymous__75753) )
        | ? [Vvar__0___24Anonymous__75754] :
            ( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0___24Anonymous__75754)
            & VX75745 = cCoq_2eInit_2eDecimal_2eD8___24a1(Vvar__0___24Anonymous__75754) )
        | ? [Vvar__0___24Anonymous__75755] :
            ( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0___24Anonymous__75755)
            & VX75745 = cCoq_2eInit_2eDecimal_2eD9___24a1(Vvar__0___24Anonymous__75755) ) ) ) ).

fof('$_inversion_Coq.Init.Peano.le',axiom,
    ! [Vvar__0__n__569,Vvar__1___24Anonymous__570] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0__n__569)
     => ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__1___24Anonymous__570)
       => ( cCoq_2eInit_2ePeano_2ele___24a2(Vvar__0__n__569,Vvar__1___24Anonymous__570)
         => ( Vvar__1___24Anonymous__570 = Vvar__0__n__569
            | ? [Vvar__1__m__574] :
                ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__1__m__574)
                & cCoq_2eInit_2ePeano_2ele___24a2(Vvar__0__n__569,Vvar__1__m__574)
                & Vvar__1___24Anonymous__570 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__1__m__574) ) ) ) ) ) ).

fof('$_inversion_Coq.Init.Specif.sig',axiom,
    ! [Vvar__0__A__1030,Vvar__1__P__1031,VX1034] :
      ( cType___24t(Vvar__0__A__1030)
     => ( c_24__type__1044___24t(Vvar__0__A__1030,Vvar__1__P__1031,Vvar__1__P__1031)
       => ( cCoq_2eInit_2eSpecif_2esig___24t(Vvar__0__A__1030,Vvar__1__P__1031,VX1034)
         => ? [Vvar__2__x__1039] :
              ( t(Vvar__2__x__1039,Vvar__0__A__1030)
              & p(happ(Vvar__1__P__1031,Vvar__2__x__1039))
              & VX1034 = cCoq_2eInit_2eSpecif_2eexist___24a3(Vvar__0__A__1030,Vvar__1__P__1031,Vvar__2__x__1039) ) ) ) ) ).

fof('$_inversion_Coq.Init.Specif.sig2',axiom,
    ! [Vvar__0__A__90070,Vvar__1__P__90071,Vvar__2__Q__90074,VX90077] :
      ( cType___24t(Vvar__0__A__90070)
     => ( c_24__type__90094___24t(Vvar__0__A__90070,Vvar__1__P__90071,Vvar__2__Q__90074,Vvar__1__P__90071)
       => ( c_24__type__90102___24t(Vvar__0__A__90070,Vvar__1__P__90071,Vvar__2__Q__90074,Vvar__2__Q__90074)
         => ( cCoq_2eInit_2eSpecif_2esig2___24t(Vvar__0__A__90070,Vvar__1__P__90071,Vvar__2__Q__90074,VX90077)
           => ? [Vvar__3__x__90085] :
                ( t(Vvar__3__x__90085,Vvar__0__A__90070)
                & p(happ(Vvar__1__P__90071,Vvar__3__x__90085))
                & p(happ(Vvar__2__Q__90074,Vvar__3__x__90085))
                & VX90077 = cCoq_2eInit_2eSpecif_2eexist2___24a4(Vvar__0__A__90070,Vvar__1__P__90071,Vvar__2__Q__90074,Vvar__3__x__90085) ) ) ) ) ) ).

fof('$_inversion_Coq.Init.Specif.sigT',axiom,
    ! [Vvar__0__A__67629,Vvar__1__P__67630,VX67633] :
      ( cType___24t(Vvar__0__A__67629)
     => ( c_24__type__67643___24t(Vvar__0__A__67629,Vvar__1__P__67630,Vvar__1__P__67630)
       => ( cCoq_2eInit_2eSpecif_2esigT___24t(Vvar__0__A__67629,Vvar__1__P__67630,VX67633)
         => ? [Vvar__2__x__67638] :
              ( t(Vvar__2__x__67638,Vvar__0__A__67629)
              & ? [Vvar__3___24Anonymous__67639] :
                  ( t(Vvar__3___24Anonymous__67639,happ(Vvar__1__P__67630,Vvar__2__x__67638))
                  & VX67633 = cCoq_2eInit_2eSpecif_2eexistT___24a4(Vvar__0__A__67629,Vvar__1__P__67630,Vvar__2__x__67638,Vvar__3___24Anonymous__67639) ) ) ) ) ) ).

fof('$_inversion_Coq.Init.Specif.sigT2',axiom,
    ! [Vvar__0__A__90308,Vvar__1__P__90309,Vvar__2__Q__90312,VX90315] :
      ( cType___24t(Vvar__0__A__90308)
     => ( c_24__type__90332___24t(Vvar__0__A__90308,Vvar__1__P__90309,Vvar__2__Q__90312,Vvar__1__P__90309)
       => ( c_24__type__90340___24t(Vvar__0__A__90308,Vvar__1__P__90309,Vvar__2__Q__90312,Vvar__2__Q__90312)
         => ( cCoq_2eInit_2eSpecif_2esigT2___24t(Vvar__0__A__90308,Vvar__1__P__90309,Vvar__2__Q__90312,VX90315)
           => ? [Vvar__3__x__90323] :
                ( t(Vvar__3__x__90323,Vvar__0__A__90308)
                & ? [Vvar__4___24Anonymous__90324] :
                    ( t(Vvar__4___24Anonymous__90324,happ(Vvar__1__P__90309,Vvar__3__x__90323))
                    & ? [Vvar__5___24Anonymous__90325] :
                        ( t(Vvar__5___24Anonymous__90325,happ(Vvar__2__Q__90312,Vvar__3__x__90323))
                        & VX90315 = cCoq_2eInit_2eSpecif_2eexistT2___24a6(Vvar__0__A__90308,Vvar__1__P__90309,Vvar__2__Q__90312,Vvar__3__x__90323,Vvar__4___24Anonymous__90324,Vvar__5___24Anonymous__90325) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.Init.Specif.sumbool',axiom,
    ! [Vvar__0__A__576,Vvar__1__B__577,VX578] :
      ( cProp___24t(Vvar__0__A__576)
     => ( cProp___24t(Vvar__1__B__577)
       => ( cCoq_2eInit_2eSpecif_2esumbool___24t(Vvar__0__A__576,Vvar__1__B__577,VX578)
         => ( ( p(Vvar__0__A__576)
              & VX578 = cCoq_2eInit_2eSpecif_2eleft___24a2(Vvar__0__A__576,Vvar__1__B__577) )
            | ( p(Vvar__1__B__577)
              & VX578 = cCoq_2eInit_2eSpecif_2eright___24a2(Vvar__0__A__576,Vvar__1__B__577) ) ) ) ) ) ).

fof('$_inversion_Coq.Init.Specif.sumor',axiom,
    ! [Vvar__0__A__1069,Vvar__1__B__1070,VX1071] :
      ( cType___24t(Vvar__0__A__1069)
     => ( cProp___24t(Vvar__1__B__1070)
       => ( cCoq_2eInit_2eSpecif_2esumor___24t(Vvar__0__A__1069,Vvar__1__B__1070,VX1071)
         => ( ? [Vvar__2___24Anonymous__1074] :
                ( t(Vvar__2___24Anonymous__1074,Vvar__0__A__1069)
                & VX1071 = cCoq_2eInit_2eSpecif_2einleft___24a3(Vvar__0__A__1069,Vvar__1__B__1070,Vvar__2___24Anonymous__1074) )
            | ( p(Vvar__1__B__1070)
              & VX1071 = cCoq_2eInit_2eSpecif_2einright___24a2(Vvar__0__A__1069,Vvar__1__B__1070) ) ) ) ) ) ).

fof('$_inversion_Coq.Init.Wf.Acc',axiom,
    ! [Vvar__0__A__82346,Vvar__1__R__82347,Vvar__2__x__82352] :
      ( cType___24t(Vvar__0__A__82346)
     => ( c_24__type__82381___24t(Vvar__0__A__82346,Vvar__1__R__82347,Vvar__2__x__82352,Vvar__1__R__82347)
       => ( t(Vvar__2__x__82352,Vvar__0__A__82346)
         => ( cCoq_2eInit_2eWf_2eAcc___24a3(Vvar__0__A__82346,Vvar__1__R__82347,Vvar__2__x__82352)
           => ( ! [Vvar__var__var__var__var__3__y__82362__82364__82366__82368__82370] :
                  ( t(Vvar__var__var__var__var__3__y__82362__82364__82366__82368__82370,Vvar__0__A__82346)
                 => ( p(happ(happ(Vvar__1__R__82347,Vvar__var__var__var__var__3__y__82362__82364__82366__82368__82370),Vvar__2__x__82352))
                   => cCoq_2eInit_2eWf_2eAcc___24a3(Vvar__0__A__82346,Vvar__1__R__82347,Vvar__var__var__var__var__3__y__82362__82364__82366__82368__82370) ) )
              & p(c_24True) ) ) ) ) ) ).

fof('$_inversion_Coq.Lists.List.Add',axiom,
    ! [Vvar__0__A__96828,Vvar__1__a__96829,Vvar__2___24Anonymous__96830,Vvar__3___24Anonymous__96831] :
      ( cType___24t(Vvar__0__A__96828)
     => ( t(Vvar__1__a__96829,Vvar__0__A__96828)
       => ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__96828,Vvar__2___24Anonymous__96830)
         => ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__96828,Vvar__3___24Anonymous__96831)
           => ( cCoq_2eLists_2eList_2eAdd___24a4(Vvar__0__A__96828,Vvar__1__a__96829,Vvar__2___24Anonymous__96830,Vvar__3___24Anonymous__96831)
             => ( ? [Vvar__2__l__96835] :
                    ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__96828,Vvar__2__l__96835)
                    & Vvar__3___24Anonymous__96831 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__96828,Vvar__1__a__96829,Vvar__2__l__96835)
                    & Vvar__2___24Anonymous__96830 = Vvar__2__l__96835 )
                | ? [Vvar__2__x__96838] :
                    ( t(Vvar__2__x__96838,Vvar__0__A__96828)
                    & ? [Vvar__3__l__96839] :
                        ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__96828,Vvar__3__l__96839)
                        & ? [Vvar__4__l_27__96840] :
                            ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__96828,Vvar__4__l_27__96840)
                            & cCoq_2eLists_2eList_2eAdd___24a4(Vvar__0__A__96828,Vvar__1__a__96829,Vvar__3__l__96839,Vvar__4__l_27__96840)
                            & Vvar__3___24Anonymous__96831 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__96828,Vvar__2__x__96838,Vvar__4__l_27__96840)
                            & Vvar__2___24Anonymous__96830 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__96828,Vvar__2__x__96838,Vvar__3__l__96839) ) ) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.Lists.List.Exists',axiom,
    ! [Vvar__0__A__96842,Vvar__1__P__96843,Vvar__2___24Anonymous__96846] :
      ( cType___24t(Vvar__0__A__96842)
     => ( c_24__type__96866___24t(Vvar__0__A__96842,Vvar__1__P__96843,Vvar__2___24Anonymous__96846,Vvar__1__P__96843)
       => ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__96842,Vvar__2___24Anonymous__96846)
         => ( cCoq_2eLists_2eList_2eExists___24a3(Vvar__0__A__96842,Vvar__1__P__96843,Vvar__2___24Anonymous__96846)
           => ( ? [Vvar__2__x__96852] :
                  ( t(Vvar__2__x__96852,Vvar__0__A__96842)
                  & ? [Vvar__3__l__96853] :
                      ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__96842,Vvar__3__l__96853)
                      & p(happ(Vvar__1__P__96843,Vvar__2__x__96852))
                      & Vvar__2___24Anonymous__96846 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__96842,Vvar__2__x__96852,Vvar__3__l__96853) ) )
              | ? [Vvar__2__x__96859] :
                  ( t(Vvar__2__x__96859,Vvar__0__A__96842)
                  & ? [Vvar__3__l__96860] :
                      ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__96842,Vvar__3__l__96860)
                      & cCoq_2eLists_2eList_2eExists___24a3(Vvar__0__A__96842,Vvar__1__P__96843,Vvar__3__l__96860)
                      & Vvar__2___24Anonymous__96846 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__96842,Vvar__2__x__96859,Vvar__3__l__96860) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.Lists.List.Forall',axiom,
    ! [Vvar__0__A__96868,Vvar__1__P__96869,Vvar__2___24Anonymous__96872] :
      ( cType___24t(Vvar__0__A__96868)
     => ( c_24__type__96890___24t(Vvar__0__A__96868,Vvar__1__P__96869,Vvar__2___24Anonymous__96872,Vvar__1__P__96869)
       => ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__96868,Vvar__2___24Anonymous__96872)
         => ( cCoq_2eLists_2eList_2eForall___24a3(Vvar__0__A__96868,Vvar__1__P__96869,Vvar__2___24Anonymous__96872)
           => ( Vvar__2___24Anonymous__96872 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__96868)
              | ? [Vvar__2__x__96882] :
                  ( t(Vvar__2__x__96882,Vvar__0__A__96868)
                  & ? [Vvar__3__l__96883] :
                      ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__96868,Vvar__3__l__96883)
                      & p(happ(Vvar__1__P__96869,Vvar__2__x__96882))
                      & cCoq_2eLists_2eList_2eForall___24a3(Vvar__0__A__96868,Vvar__1__P__96869,Vvar__3__l__96883)
                      & Vvar__2___24Anonymous__96872 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__96868,Vvar__2__x__96882,Vvar__3__l__96883) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.Lists.List.Forall2',axiom,
    ! [Vvar__0__A__96892,Vvar__1__B__96893,Vvar__2__R__96894,Vvar__3___24Anonymous__96899,Vvar__4___24Anonymous__96900] :
      ( cType___24t(Vvar__0__A__96892)
     => ( cType___24t(Vvar__1__B__96893)
       => ( c_24__type__96937___24t(Vvar__0__A__96892,Vvar__1__B__96893,Vvar__2__R__96894,Vvar__3___24Anonymous__96899,Vvar__4___24Anonymous__96900,Vvar__2__R__96894)
         => ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__96892,Vvar__3___24Anonymous__96899)
           => ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__1__B__96893,Vvar__4___24Anonymous__96900)
             => ( cCoq_2eLists_2eList_2eForall2___24a5(Vvar__0__A__96892,Vvar__1__B__96893,Vvar__2__R__96894,Vvar__3___24Anonymous__96899,Vvar__4___24Anonymous__96900)
               => ( ( Vvar__4___24Anonymous__96900 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__1__B__96893)
                    & Vvar__3___24Anonymous__96899 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__96892) )
                  | ? [Vvar__3__x__96916] :
                      ( t(Vvar__3__x__96916,Vvar__0__A__96892)
                      & ? [Vvar__4__y__96917] :
                          ( t(Vvar__4__y__96917,Vvar__1__B__96893)
                          & ? [Vvar__5__l__96918] :
                              ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__96892,Vvar__5__l__96918)
                              & ? [Vvar__6__l_27__96919] :
                                  ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__1__B__96893,Vvar__6__l_27__96919)
                                  & p(happ(happ(Vvar__2__R__96894,Vvar__3__x__96916),Vvar__4__y__96917))
                                  & cCoq_2eLists_2eList_2eForall2___24a5(Vvar__0__A__96892,Vvar__1__B__96893,Vvar__2__R__96894,Vvar__5__l__96918,Vvar__6__l_27__96919)
                                  & Vvar__4___24Anonymous__96900 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__1__B__96893,Vvar__4__y__96917,Vvar__6__l_27__96919)
                                  & Vvar__3___24Anonymous__96899 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__96892,Vvar__3__x__96916,Vvar__5__l__96918) ) ) ) ) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.Lists.List.ForallOrdPairs',axiom,
    ! [Vvar__0__A__96939,Vvar__1__R__96940,Vvar__2___24Anonymous__96945] :
      ( cType___24t(Vvar__0__A__96939)
     => ( c_24__type__96972___24t(Vvar__0__A__96939,Vvar__1__R__96940,Vvar__2___24Anonymous__96945,Vvar__1__R__96940)
       => ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__96939,Vvar__2___24Anonymous__96945)
         => ( cCoq_2eLists_2eList_2eForallOrdPairs___24a3(Vvar__0__A__96939,Vvar__1__R__96940,Vvar__2___24Anonymous__96945)
           => ( Vvar__2___24Anonymous__96945 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__96939)
              | ? [Vvar__2__a__96959] :
                  ( t(Vvar__2__a__96959,Vvar__0__A__96939)
                  & ? [Vvar__3__l__96960] :
                      ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__96939,Vvar__3__l__96960)
                      & cCoq_2eLists_2eList_2eForall___24a3(Vvar__0__A__96939,happ(Vvar__1__R__96940,Vvar__2__a__96959),Vvar__3__l__96960)
                      & cCoq_2eLists_2eList_2eForallOrdPairs___24a3(Vvar__0__A__96939,Vvar__1__R__96940,Vvar__3__l__96960)
                      & Vvar__2___24Anonymous__96945 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__96939,Vvar__2__a__96959,Vvar__3__l__96960) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.Lists.List.NoDup',axiom,
    ! [Vvar__0__A__76287,Vvar__1___24Anonymous__76288] :
      ( cType___24t(Vvar__0__A__76287)
     => ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__76287,Vvar__1___24Anonymous__76288)
       => ( cCoq_2eLists_2eList_2eNoDup___24a2(Vvar__0__A__76287,Vvar__1___24Anonymous__76288)
         => ( Vvar__1___24Anonymous__76288 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__76287)
            | ? [Vvar__1__x__76292] :
                ( t(Vvar__1__x__76292,Vvar__0__A__76287)
                & ? [Vvar__2__l__76293] :
                    ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__76287,Vvar__2__l__76293)
                    & ~ cCoq_2eLists_2eList_2eIn___24a3(Vvar__0__A__76287,Vvar__1__x__76292,Vvar__2__l__76293)
                    & cCoq_2eLists_2eList_2eNoDup___24a2(Vvar__0__A__76287,Vvar__2__l__76293)
                    & Vvar__1___24Anonymous__76288 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__76287,Vvar__1__x__76292,Vvar__2__l__76293) ) ) ) ) ) ) ).

fof('$_inversion_Coq.Lists.SetoidList.InA',axiom,
    ! [Vvar__0__A__89874,Vvar__1__eqA__89875,Vvar__2__x__89880,Vvar__3___24Anonymous__89881] :
      ( cType___24t(Vvar__0__A__89874)
     => ( c_24__type__89914___24t(Vvar__0__A__89874,Vvar__1__eqA__89875,Vvar__2__x__89880,Vvar__3___24Anonymous__89881,Vvar__1__eqA__89875)
       => ( t(Vvar__2__x__89880,Vvar__0__A__89874)
         => ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__89874,Vvar__3___24Anonymous__89881)
           => ( cCoq_2eLists_2eSetoidList_2eInA___24a4(Vvar__0__A__89874,Vvar__1__eqA__89875,Vvar__2__x__89880,Vvar__3___24Anonymous__89881)
             => ( ? [Vvar__3__y__89890] :
                    ( t(Vvar__3__y__89890,Vvar__0__A__89874)
                    & ? [Vvar__4__l__89891] :
                        ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__89874,Vvar__4__l__89891)
                        & p(happ(happ(Vvar__1__eqA__89875,Vvar__2__x__89880),Vvar__3__y__89890))
                        & Vvar__3___24Anonymous__89881 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__89874,Vvar__3__y__89890,Vvar__4__l__89891) ) )
                | ? [Vvar__3__y__89900] :
                    ( t(Vvar__3__y__89900,Vvar__0__A__89874)
                    & ? [Vvar__4__l__89901] :
                        ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__89874,Vvar__4__l__89901)
                        & cCoq_2eLists_2eSetoidList_2eInA___24a4(Vvar__0__A__89874,Vvar__1__eqA__89875,Vvar__2__x__89880,Vvar__4__l__89901)
                        & Vvar__3___24Anonymous__89881 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__89874,Vvar__3__y__89900,Vvar__4__l__89901) ) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.Lists.SetoidList.NoDupA',axiom,
    ! [Vvar__0__A__105079,Vvar__1__eqA__105080,Vvar__2___24Anonymous__105085] :
      ( cType___24t(Vvar__0__A__105079)
     => ( c_24__type__105112___24t(Vvar__0__A__105079,Vvar__1__eqA__105080,Vvar__2___24Anonymous__105085,Vvar__1__eqA__105080)
       => ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__105079,Vvar__2___24Anonymous__105085)
         => ( cCoq_2eLists_2eSetoidList_2eNoDupA___24a3(Vvar__0__A__105079,Vvar__1__eqA__105080,Vvar__2___24Anonymous__105085)
           => ( Vvar__2___24Anonymous__105085 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__105079)
              | ? [Vvar__2__x__105099] :
                  ( t(Vvar__2__x__105099,Vvar__0__A__105079)
                  & ? [Vvar__3__l__105100] :
                      ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__105079,Vvar__3__l__105100)
                      & ~ cCoq_2eLists_2eSetoidList_2eInA___24a4(Vvar__0__A__105079,Vvar__1__eqA__105080,Vvar__2__x__105099,Vvar__3__l__105100)
                      & cCoq_2eLists_2eSetoidList_2eNoDupA___24a3(Vvar__0__A__105079,Vvar__1__eqA__105080,Vvar__3__l__105100)
                      & Vvar__2___24Anonymous__105085 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__105079,Vvar__2__x__105099,Vvar__3__l__105100) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.Lists.SetoidList.eqlistA',axiom,
    ! [Vvar__0__A__89930,Vvar__1__eqA__89931,Vvar__2___24Anonymous__89936,Vvar__3___24Anonymous__89937] :
      ( cType___24t(Vvar__0__A__89930)
     => ( c_24__type__89968___24t(Vvar__0__A__89930,Vvar__1__eqA__89931,Vvar__2___24Anonymous__89936,Vvar__3___24Anonymous__89937,Vvar__1__eqA__89931)
       => ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__89930,Vvar__2___24Anonymous__89936)
         => ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__89930,Vvar__3___24Anonymous__89937)
           => ( cCoq_2eLists_2eSetoidList_2eeqlistA___24a4(Vvar__0__A__89930,Vvar__1__eqA__89931,Vvar__2___24Anonymous__89936,Vvar__3___24Anonymous__89937)
             => ( ( Vvar__3___24Anonymous__89937 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__89930)
                  & Vvar__2___24Anonymous__89936 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__89930) )
                | ? [Vvar__2__x__89951] :
                    ( t(Vvar__2__x__89951,Vvar__0__A__89930)
                    & ? [Vvar__3__x_27__89952] :
                        ( t(Vvar__3__x_27__89952,Vvar__0__A__89930)
                        & ? [Vvar__4__l__89953] :
                            ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__89930,Vvar__4__l__89953)
                            & ? [Vvar__5__l_27__89954] :
                                ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__89930,Vvar__5__l_27__89954)
                                & p(happ(happ(Vvar__1__eqA__89931,Vvar__2__x__89951),Vvar__3__x_27__89952))
                                & cCoq_2eLists_2eSetoidList_2eeqlistA___24a4(Vvar__0__A__89930,Vvar__1__eqA__89931,Vvar__4__l__89953,Vvar__5__l_27__89954)
                                & Vvar__3___24Anonymous__89937 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__89930,Vvar__3__x_27__89952,Vvar__5__l_27__89954)
                                & Vvar__2___24Anonymous__89936 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__89930,Vvar__2__x__89951,Vvar__4__l__89953) ) ) ) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.Logic.EqdepFacts.eq_dep',axiom,
    ! [Vvar__0__U__94431,Vvar__1__P__94432,Vvar__2__p__94435,Vvar__3__x__94436,Vvar__4__q__94437,Vvar__5___24Anonymous__94438] :
      ( cType___24t(Vvar__0__U__94431)
     => ( c_24__type__94453___24t(Vvar__0__U__94431,Vvar__1__P__94432,Vvar__2__p__94435,Vvar__3__x__94436,Vvar__4__q__94437,Vvar__5___24Anonymous__94438,Vvar__1__P__94432)
       => ( t(Vvar__2__p__94435,Vvar__0__U__94431)
         => ( t(Vvar__3__x__94436,happ(Vvar__1__P__94432,Vvar__2__p__94435))
           => ( t(Vvar__4__q__94437,Vvar__0__U__94431)
             => ( t(Vvar__5___24Anonymous__94438,happ(Vvar__1__P__94432,Vvar__4__q__94437))
               => ( cCoq_2eLogic_2eEqdepFacts_2eeq__dep___24a6(Vvar__0__U__94431,Vvar__1__P__94432,Vvar__2__p__94435,Vvar__3__x__94436,Vvar__4__q__94437,Vvar__5___24Anonymous__94438)
                 => ( Vvar__5___24Anonymous__94438 = Vvar__3__x__94436
                    & Vvar__4__q__94437 = Vvar__2__p__94435 ) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.Logic.EqdepFacts.eq_dep1',axiom,
    ! [Vvar__0__U__94455,Vvar__1__P__94456,Vvar__2__p__94459,Vvar__3__x__94460,Vvar__4__q__94461,Vvar__5__y__94462] :
      ( cType___24t(Vvar__0__U__94455)
     => ( c_24__type__94481___24t(Vvar__0__U__94455,Vvar__1__P__94456,Vvar__2__p__94459,Vvar__3__x__94460,Vvar__4__q__94461,Vvar__5__y__94462,Vvar__1__P__94456)
       => ( t(Vvar__2__p__94459,Vvar__0__U__94455)
         => ( t(Vvar__3__x__94460,happ(Vvar__1__P__94456,Vvar__2__p__94459))
           => ( t(Vvar__4__q__94461,Vvar__0__U__94455)
             => ( t(Vvar__5__y__94462,happ(Vvar__1__P__94456,Vvar__4__q__94461))
               => ( cCoq_2eLogic_2eEqdepFacts_2eeq__dep1___24a6(Vvar__0__U__94455,Vvar__1__P__94456,Vvar__2__p__94459,Vvar__3__x__94460,Vvar__4__q__94461,Vvar__5__y__94462)
                 => ( Vvar__4__q__94461 = Vvar__2__p__94459
                    & Vvar__3__x__94460 = cCoq_2eInit_2eLogic_2eeq__rect___24a5(Vvar__0__U__94455,Vvar__4__q__94461,Vvar__1__P__94456,Vvar__5__y__94462,Vvar__2__p__94459)
                    & p(c_24True) ) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.Numbers.BinNums.N',axiom,
    ! [VX1127] :
      ( cCoq_2eNumbers_2eBinNums_2eN___24t(VX1127)
     => ( VX1127 = cCoq_2eNumbers_2eBinNums_2eN0
        | ? [Vvar__0___24Anonymous__1128] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__1128)
            & VX1127 = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__1128) ) ) ) ).

fof('$_inversion_Coq.Numbers.BinNums.Z',axiom,
    ! [VX68096] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(VX68096)
     => ( VX68096 = cCoq_2eNumbers_2eBinNums_2eZ0
        | ? [Vvar__0___24Anonymous__68097] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__68097)
            & VX68096 = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__68097) )
        | ? [Vvar__0___24Anonymous__68098] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__68098)
            & VX68096 = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__68098) ) ) ) ).

fof('$_inversion_Coq.Numbers.BinNums.positive',axiom,
    ! [VX1108] :
      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(VX1108)
     => ( ? [Vvar__0___24Anonymous__1109] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__1109)
            & VX1108 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__1109) )
        | ? [Vvar__0___24Anonymous__1110] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__1110)
            & VX1108 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__1110) )
        | VX1108 = cCoq_2eNumbers_2eBinNums_2exH ) ) ).

fof('$_inversion_Coq.PArith.BinPos.Pos.PeanoView',axiom,
    ! [Vvar__0___24Anonymous__105610,VX105611] :
      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__105610)
     => ( cCoq_2ePArith_2eBinPos_2ePos_2ePeanoView___24t(Vvar__0___24Anonymous__105610,VX105611)
       => ( ( Vvar__0___24Anonymous__105610 = cCoq_2eNumbers_2eBinNums_2exH
            & VX105611 = cCoq_2ePArith_2eBinPos_2ePos_2ePeanoOne )
          | ? [Vvar__0__p__105612] :
              ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0__p__105612)
              & ? [Vvar__1___24Anonymous__105613] :
                  ( cCoq_2ePArith_2eBinPos_2ePos_2ePeanoView___24t(Vvar__0__p__105612,Vvar__1___24Anonymous__105613)
                  & Vvar__0___24Anonymous__105610 = c_24__case__Coq_2eNumbers_2eBinNums_2epositive_24105648___24a2(Vvar__0___24Anonymous__105610,Vvar__0__p__105612)
                  & VX105611 = cCoq_2ePArith_2eBinPos_2ePos_2ePeanoSucc___24a2(Vvar__0__p__105612,Vvar__1___24Anonymous__105613) ) ) ) ) ) ).

fof('$_inversion_Coq.PArith.BinPos.Pos.SubMaskSpec',axiom,
    ! [Vvar__0__p__105675,Vvar__1__q__105676,Vvar__2___24Anonymous__105677] :
      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0__p__105675)
     => ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1__q__105676)
       => ( cCoq_2ePArith_2eBinPosDef_2ePos_2emask___24t(Vvar__2___24Anonymous__105677)
         => ( cCoq_2ePArith_2eBinPos_2ePos_2eSubMaskSpec___24a3(Vvar__0__p__105675,Vvar__1__q__105676,Vvar__2___24Anonymous__105677)
           => ( ( Vvar__0__p__105675 = Vvar__1__q__105676
                & Vvar__2___24Anonymous__105677 = cCoq_2ePArith_2eBinPosDef_2ePos_2eIsNul )
              | ? [Vvar__2__r__105684] :
                  ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2__r__105684)
                  & cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(Vvar__1__q__105676,Vvar__2__r__105684) = Vvar__0__p__105675
                  & Vvar__2___24Anonymous__105677 = cCoq_2ePArith_2eBinPosDef_2ePos_2eIsPos___24a1(Vvar__2__r__105684) )
              | ? [Vvar__2__r__105688] :
                  ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2__r__105688)
                  & cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(Vvar__0__p__105675,Vvar__2__r__105688) = Vvar__1__q__105676
                  & Vvar__2___24Anonymous__105677 = cCoq_2ePArith_2eBinPosDef_2ePos_2eIsNeg ) ) ) ) ) ) ).

fof('$_inversion_Coq.PArith.BinPosDef.Pos.mask',axiom,
    ! [VX93081] :
      ( cCoq_2ePArith_2eBinPosDef_2ePos_2emask___24t(VX93081)
     => ( VX93081 = cCoq_2ePArith_2eBinPosDef_2ePos_2eIsNul
        | ? [Vvar__0___24Anonymous__93082] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__93082)
            & VX93081 = cCoq_2ePArith_2eBinPosDef_2ePos_2eIsPos___24a1(Vvar__0___24Anonymous__93082) )
        | VX93081 = cCoq_2ePArith_2eBinPosDef_2ePos_2eIsNeg ) ) ).

fof('$_inversion_Coq.QArith.QArith_base.Q',axiom,
    ! [VX97176] :
      ( cCoq_2eQArith_2eQArith__base_2eQ___24t(VX97176)
     => ? [Vvar__0__Qnum__97177] :
          ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__0__Qnum__97177)
          & ? [Vvar__1__Qden__97178] :
              ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1__Qden__97178)
              & VX97176 = cCoq_2eQArith_2eQArith__base_2eQmake___24a2(Vvar__0__Qnum__97177,Vvar__1__Qden__97178) ) ) ) ).

fof('$_inversion_Coq.Reals.RIneq.negreal',axiom,
    ! [VX97217] :
      ( cCoq_2eReals_2eRIneq_2enegreal___24t(VX97217)
     => ? [Vvar__0__neg__97218] :
          ( cCoq_2eReals_2eRdefinitions_2eR___24t(Vvar__0__neg__97218)
          & cCoq_2eReals_2eRdefinitions_2eRlt___24a2(Vvar__0__neg__97218,cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0))
          & VX97217 = cCoq_2eReals_2eRIneq_2emknegreal___24a1(Vvar__0__neg__97218) ) ) ).

fof('$_inversion_Coq.Reals.RIneq.nonnegreal',axiom,
    ! [VX97196] :
      ( cCoq_2eReals_2eRIneq_2enonnegreal___24t(VX97196)
     => ? [Vvar__0__nonneg__97197] :
          ( cCoq_2eReals_2eRdefinitions_2eR___24t(Vvar__0__nonneg__97197)
          & cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),Vvar__0__nonneg__97197)
          & VX97196 = cCoq_2eReals_2eRIneq_2emknonnegreal___24a1(Vvar__0__nonneg__97197) ) ) ).

fof('$_inversion_Coq.Reals.RIneq.nonposreal',axiom,
    ! [VX97210] :
      ( cCoq_2eReals_2eRIneq_2enonposreal___24t(VX97210)
     => ? [Vvar__0__nonpos__97211] :
          ( cCoq_2eReals_2eRdefinitions_2eR___24t(Vvar__0__nonpos__97211)
          & cCoq_2eReals_2eRdefinitions_2eRle___24a2(Vvar__0__nonpos__97211,cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0))
          & VX97210 = cCoq_2eReals_2eRIneq_2emknonposreal___24a1(Vvar__0__nonpos__97211) ) ) ).

fof('$_inversion_Coq.Reals.RIneq.nonzeroreal',axiom,
    ! [VX97224] :
      ( cCoq_2eReals_2eRIneq_2enonzeroreal___24t(VX97224)
     => ? [Vvar__0__nonzero__97225] :
          ( cCoq_2eReals_2eRdefinitions_2eR___24t(Vvar__0__nonzero__97225)
          & Vvar__0__nonzero__97225 != cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)
          & VX97224 = cCoq_2eReals_2eRIneq_2emknonzeroreal___24a1(Vvar__0__nonzero__97225) ) ) ).

fof('$_inversion_Coq.Reals.RIneq.posreal',axiom,
    ! [VX97203] :
      ( cCoq_2eReals_2eRIneq_2eposreal___24t(VX97203)
     => ? [Vvar__0__pos__97204] :
          ( cCoq_2eReals_2eRdefinitions_2eR___24t(Vvar__0__pos__97204)
          & cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),Vvar__0__pos__97204)
          & VX97203 = cCoq_2eReals_2eRIneq_2emkposreal___24a1(Vvar__0__pos__97204) ) ) ).

fof('$_inversion_Coq.Reals.Rfunctions.Z_spec',axiom,
    ! [Vvar__0__x__98113,Vvar__1___24Anonymous__98114,VX98115] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__0__x__98113)
     => ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__1___24Anonymous__98114)
       => ( cCoq_2eReals_2eRfunctions_2eZ__spec___24t(Vvar__0__x__98113,Vvar__1___24Anonymous__98114,VX98115)
         => ( ( Vvar__0__x__98113 = cCoq_2eNumbers_2eBinNums_2eZ0
              & Vvar__1___24Anonymous__98114 = cCoq_2eNumbers_2eBinNums_2eZ0
              & VX98115 = cCoq_2eReals_2eRfunctions_2eZintNull___24a1(Vvar__0__x__98113) )
            | ? [Vvar__1__n__98119] :
                ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__1__n__98119)
                & Vvar__0__x__98113 = cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat___24a1(Vvar__1__n__98119)
                & Vvar__1___24Anonymous__98114 = c_24__case__Coq_2eInit_2eDatatypes_2enat_2498139___24a3(Vvar__0__x__98113,Vvar__1___24Anonymous__98114,Vvar__1__n__98119)
                & VX98115 = cCoq_2eReals_2eRfunctions_2eZintPos___24a2(Vvar__0__x__98113,Vvar__1__n__98119) )
            | ? [Vvar__1__n__98124] :
                ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__1__n__98124)
                & Vvar__0__x__98113 = cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat___24a1(Vvar__1__n__98124))
                & Vvar__1___24Anonymous__98114 = c_24__case__Coq_2eNumbers_2eBinNums_2eZ_2498156___24a3(Vvar__0__x__98113,Vvar__1___24Anonymous__98114,Vvar__1__n__98124)
                & VX98115 = cCoq_2eReals_2eRfunctions_2eZintNeg___24a2(Vvar__0__x__98113,Vvar__1__n__98124) ) ) ) ) ) ).

fof('$_inversion_Coq.Relations.Relation_Operators.Desc',axiom,
    ! [Vvar__0__A__97591,Vvar__1__leA__97592,Vvar__2___24Anonymous__97597] :
      ( cType___24t(Vvar__0__A__97591)
     => ( c_24__type__97687___24t(Vvar__0__A__97591,Vvar__1__leA__97592,Vvar__2___24Anonymous__97597,Vvar__1__leA__97592)
       => ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__97591,Vvar__2___24Anonymous__97597)
         => ( cCoq_2eRelations_2eRelation__Operators_2eDesc___24a3(Vvar__0__A__97591,Vvar__1__leA__97592,Vvar__2___24Anonymous__97597)
           => ( Vvar__2___24Anonymous__97597 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__97591)
              | ? [Vvar__2__x__97611] :
                  ( t(Vvar__2__x__97611,Vvar__0__A__97591)
                  & Vvar__2___24Anonymous__97597 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__97591,Vvar__2__x__97611,cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__97591)) )
              | ? [Vvar__2__x__97618] :
                  ( t(Vvar__2__x__97618,Vvar__0__A__97591)
                  & ? [Vvar__3__y__97619] :
                      ( t(Vvar__3__y__97619,Vvar__0__A__97591)
                      & ? [Vvar__4__l__97620] :
                          ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__97591,Vvar__4__l__97620)
                          & cCoq_2eRelations_2eRelation__Operators_2eclos__refl___24a4(Vvar__0__A__97591,Vvar__1__leA__97592,Vvar__2__x__97618,Vvar__3__y__97619)
                          & cCoq_2eRelations_2eRelation__Operators_2eDesc___24a3(Vvar__0__A__97591,Vvar__1__leA__97592,cCoq_2eInit_2eDatatypes_2eapp___24a3(Vvar__0__A__97591,Vvar__4__l__97620,cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__97591,Vvar__3__y__97619,cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__97591))))
                          & Vvar__2___24Anonymous__97597 = c_24__case__Coq_2eInit_2eDatatypes_2elist_2497885___24a6(Vvar__0__A__97591,Vvar__1__leA__97592,Vvar__2___24Anonymous__97597,Vvar__2__x__97618,Vvar__3__y__97619,Vvar__4__l__97620) ) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.Relations.Relation_Operators.Ltl',axiom,
    ! [Vvar__0__A__97540,Vvar__1__leA__97541,Vvar__2___24Anonymous__97546,Vvar__3___24Anonymous__97547] :
      ( cType___24t(Vvar__0__A__97540)
     => ( c_24__type__97589___24t(Vvar__0__A__97540,Vvar__1__leA__97541,Vvar__2___24Anonymous__97546,Vvar__3___24Anonymous__97547,Vvar__1__leA__97541)
       => ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__97540,Vvar__2___24Anonymous__97546)
         => ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__97540,Vvar__3___24Anonymous__97547)
           => ( cCoq_2eRelations_2eRelation__Operators_2eLtl___24a4(Vvar__0__A__97540,Vvar__1__leA__97541,Vvar__2___24Anonymous__97546,Vvar__3___24Anonymous__97547)
             => ( ? [Vvar__2__a__97555] :
                    ( t(Vvar__2__a__97555,Vvar__0__A__97540)
                    & ? [Vvar__3__x__97556] :
                        ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__97540,Vvar__3__x__97556)
                        & Vvar__3___24Anonymous__97547 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__97540,Vvar__2__a__97555,Vvar__3__x__97556)
                        & Vvar__2___24Anonymous__97546 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__97540) ) )
                | ? [Vvar__2__a__97563] :
                    ( t(Vvar__2__a__97563,Vvar__0__A__97540)
                    & ? [Vvar__3__b__97564] :
                        ( t(Vvar__3__b__97564,Vvar__0__A__97540)
                        & p(happ(happ(Vvar__1__leA__97541,Vvar__2__a__97563),Vvar__3__b__97564))
                        & ? [Vvar__5__x__97566] :
                            ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__97540,Vvar__5__x__97566)
                            & ? [Vvar__6__y__97567] :
                                ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__97540,Vvar__6__y__97567)
                                & Vvar__3___24Anonymous__97547 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__97540,Vvar__3__b__97564,Vvar__6__y__97567)
                                & Vvar__2___24Anonymous__97546 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__97540,Vvar__2__a__97563,Vvar__5__x__97566) ) ) ) )
                | ? [Vvar__2__a__97574] :
                    ( t(Vvar__2__a__97574,Vvar__0__A__97540)
                    & ? [Vvar__3__x__97575] :
                        ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__97540,Vvar__3__x__97575)
                        & ? [Vvar__4__y__97576] :
                            ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__97540,Vvar__4__y__97576)
                            & cCoq_2eRelations_2eRelation__Operators_2eLtl___24a4(Vvar__0__A__97540,Vvar__1__leA__97541,Vvar__3__x__97575,Vvar__4__y__97576)
                            & Vvar__3___24Anonymous__97547 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__97540,Vvar__2__a__97574,Vvar__4__y__97576)
                            & Vvar__2___24Anonymous__97546 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__97540,Vvar__2__a__97574,Vvar__3__x__97575) ) ) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.Relations.Relation_Operators.clos_refl',axiom,
    ! [Vvar__0__A__97430,Vvar__1__R__97431,Vvar__2__x__97432,Vvar__3___24Anonymous__97433] :
      ( cType___24t(Vvar__0__A__97430)
     => ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vvar__0__A__97430,Vvar__1__R__97431)
       => ( t(Vvar__2__x__97432,Vvar__0__A__97430)
         => ( t(Vvar__3___24Anonymous__97433,Vvar__0__A__97430)
           => ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl___24a4(Vvar__0__A__97430,Vvar__1__R__97431,Vvar__2__x__97432,Vvar__3___24Anonymous__97433)
             => ( ? [Vvar__3__y__97438] :
                    ( t(Vvar__3__y__97438,Vvar__0__A__97430)
                    & p(happ(happ(Vvar__1__R__97431,Vvar__2__x__97432),Vvar__3__y__97438))
                    & Vvar__3___24Anonymous__97433 = Vvar__3__y__97438 )
                | Vvar__3___24Anonymous__97433 = Vvar__2__x__97432 ) ) ) ) ) ) ).

fof('$_inversion_Coq.Relations.Relation_Operators.symprod',axiom,
    ! [Vvar__0__A__97443,Vvar__1__B__97444,Vvar__2__leA__97445,Vvar__3__leB__97450,Vvar__4___24Anonymous__97455,Vvar__5___24Anonymous__97456] :
      ( cType___24t(Vvar__0__A__97443)
     => ( cType___24t(Vvar__1__B__97444)
       => ( c_24__type__97513___24t(Vvar__0__A__97443,Vvar__1__B__97444,Vvar__2__leA__97445,Vvar__3__leB__97450,Vvar__4___24Anonymous__97455,Vvar__5___24Anonymous__97456,Vvar__2__leA__97445)
         => ( c_24__type__97538___24t(Vvar__0__A__97443,Vvar__1__B__97444,Vvar__2__leA__97445,Vvar__3__leB__97450,Vvar__4___24Anonymous__97455,Vvar__5___24Anonymous__97456,Vvar__3__leB__97450)
           => ( cCoq_2eInit_2eDatatypes_2eprod___24t(Vvar__0__A__97443,Vvar__1__B__97444,Vvar__4___24Anonymous__97455)
             => ( cCoq_2eInit_2eDatatypes_2eprod___24t(Vvar__0__A__97443,Vvar__1__B__97444,Vvar__5___24Anonymous__97456)
               => ( cCoq_2eRelations_2eRelation__Operators_2esymprod___24a6(Vvar__0__A__97443,Vvar__1__B__97444,Vvar__2__leA__97445,Vvar__3__leB__97450,Vvar__4___24Anonymous__97455,Vvar__5___24Anonymous__97456)
                 => ( ? [Vvar__4__x__97470] :
                        ( t(Vvar__4__x__97470,Vvar__0__A__97443)
                        & ? [Vvar__5__x_27__97471] :
                            ( t(Vvar__5__x_27__97471,Vvar__0__A__97443)
                            & p(happ(happ(Vvar__2__leA__97445,Vvar__4__x__97470),Vvar__5__x_27__97471))
                            & ? [Vvar__7__y__97473] :
                                ( t(Vvar__7__y__97473,Vvar__1__B__97444)
                                & Vvar__5___24Anonymous__97456 = cCoq_2eInit_2eDatatypes_2epair___24a4(Vvar__0__A__97443,Vvar__1__B__97444,Vvar__5__x_27__97471,Vvar__7__y__97473)
                                & Vvar__4___24Anonymous__97455 = cCoq_2eInit_2eDatatypes_2epair___24a4(Vvar__0__A__97443,Vvar__1__B__97444,Vvar__4__x__97470,Vvar__7__y__97473) ) ) )
                    | ? [Vvar__4__y__97486] :
                        ( t(Vvar__4__y__97486,Vvar__1__B__97444)
                        & ? [Vvar__5__y_27__97487] :
                            ( t(Vvar__5__y_27__97487,Vvar__1__B__97444)
                            & p(happ(happ(Vvar__3__leB__97450,Vvar__4__y__97486),Vvar__5__y_27__97487))
                            & ? [Vvar__7__x__97489] :
                                ( t(Vvar__7__x__97489,Vvar__0__A__97443)
                                & Vvar__5___24Anonymous__97456 = cCoq_2eInit_2eDatatypes_2epair___24a4(Vvar__0__A__97443,Vvar__1__B__97444,Vvar__7__x__97489,Vvar__5__y_27__97487)
                                & Vvar__4___24Anonymous__97455 = cCoq_2eInit_2eDatatypes_2epair___24a4(Vvar__0__A__97443,Vvar__1__B__97444,Vvar__7__x__97489,Vvar__4__y__97486) ) ) ) ) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.Sorting.Sorted.HdRel',axiom,
    ! [Vvar__0__A__89989,Vvar__1__R__89990,Vvar__2__a__89995,Vvar__3___24Anonymous__89996] :
      ( cType___24t(Vvar__0__A__89989)
     => ( c_24__type__90026___24t(Vvar__0__A__89989,Vvar__1__R__89990,Vvar__2__a__89995,Vvar__3___24Anonymous__89996,Vvar__1__R__89990)
       => ( t(Vvar__2__a__89995,Vvar__0__A__89989)
         => ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__89989,Vvar__3___24Anonymous__89996)
           => ( cCoq_2eSorting_2eSorted_2eHdRel___24a4(Vvar__0__A__89989,Vvar__1__R__89990,Vvar__2__a__89995,Vvar__3___24Anonymous__89996)
             => ( Vvar__3___24Anonymous__89996 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__89989)
                | ? [Vvar__3__b__90012] :
                    ( t(Vvar__3__b__90012,Vvar__0__A__89989)
                    & ? [Vvar__4__l__90013] :
                        ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__89989,Vvar__4__l__90013)
                        & p(happ(happ(Vvar__1__R__89990,Vvar__2__a__89995),Vvar__3__b__90012))
                        & Vvar__3___24Anonymous__89996 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__89989,Vvar__3__b__90012,Vvar__4__l__90013) ) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.Sorting.Sorted.LocallySorted',axiom,
    ! [Vvar__0__A__105211,Vvar__1__R__105212,Vvar__2___24Anonymous__105217] :
      ( cType___24t(Vvar__0__A__105211)
     => ( c_24__type__105252___24t(Vvar__0__A__105211,Vvar__1__R__105212,Vvar__2___24Anonymous__105217,Vvar__1__R__105212)
       => ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__105211,Vvar__2___24Anonymous__105217)
         => ( cCoq_2eSorting_2eSorted_2eLocallySorted___24a3(Vvar__0__A__105211,Vvar__1__R__105212,Vvar__2___24Anonymous__105217)
           => ( Vvar__2___24Anonymous__105217 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__105211)
              | ? [Vvar__2__a__105231] :
                  ( t(Vvar__2__a__105231,Vvar__0__A__105211)
                  & Vvar__2___24Anonymous__105217 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__105211,Vvar__2__a__105231,cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__105211)) )
              | ? [Vvar__2__a__105238] :
                  ( t(Vvar__2__a__105238,Vvar__0__A__105211)
                  & ? [Vvar__3__b__105239] :
                      ( t(Vvar__3__b__105239,Vvar__0__A__105211)
                      & ? [Vvar__4__l__105240] :
                          ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__105211,Vvar__4__l__105240)
                          & cCoq_2eSorting_2eSorted_2eLocallySorted___24a3(Vvar__0__A__105211,Vvar__1__R__105212,cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__105211,Vvar__3__b__105239,Vvar__4__l__105240))
                          & p(happ(happ(Vvar__1__R__105212,Vvar__2__a__105238),Vvar__3__b__105239))
                          & Vvar__2___24Anonymous__105217 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__105211,Vvar__2__a__105238,cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__105211,Vvar__3__b__105239,Vvar__4__l__105240)) ) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.Sorting.Sorted.Sorted',axiom,
    ! [Vvar__0__A__90035,Vvar__1__R__90036,Vvar__2___24Anonymous__90041] :
      ( cType___24t(Vvar__0__A__90035)
     => ( c_24__type__90068___24t(Vvar__0__A__90035,Vvar__1__R__90036,Vvar__2___24Anonymous__90041,Vvar__1__R__90036)
       => ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__90035,Vvar__2___24Anonymous__90041)
         => ( cCoq_2eSorting_2eSorted_2eSorted___24a3(Vvar__0__A__90035,Vvar__1__R__90036,Vvar__2___24Anonymous__90041)
           => ( Vvar__2___24Anonymous__90041 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__90035)
              | ? [Vvar__2__a__90055] :
                  ( t(Vvar__2__a__90055,Vvar__0__A__90035)
                  & ? [Vvar__3__l__90056] :
                      ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__90035,Vvar__3__l__90056)
                      & cCoq_2eSorting_2eSorted_2eSorted___24a3(Vvar__0__A__90035,Vvar__1__R__90036,Vvar__3__l__90056)
                      & cCoq_2eSorting_2eSorted_2eHdRel___24a4(Vvar__0__A__90035,Vvar__1__R__90036,Vvar__2__a__90055,Vvar__3__l__90056)
                      & Vvar__2___24Anonymous__90041 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__90035,Vvar__2__a__90055,Vvar__3__l__90056) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.Sorting.Sorted.StronglySorted',axiom,
    ! [Vvar__0__A__105254,Vvar__1__R__105255,Vvar__2___24Anonymous__105260] :
      ( cType___24t(Vvar__0__A__105254)
     => ( c_24__type__105287___24t(Vvar__0__A__105254,Vvar__1__R__105255,Vvar__2___24Anonymous__105260,Vvar__1__R__105255)
       => ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__105254,Vvar__2___24Anonymous__105260)
         => ( cCoq_2eSorting_2eSorted_2eStronglySorted___24a3(Vvar__0__A__105254,Vvar__1__R__105255,Vvar__2___24Anonymous__105260)
           => ( Vvar__2___24Anonymous__105260 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__105254)
              | ? [Vvar__2__a__105274] :
                  ( t(Vvar__2__a__105274,Vvar__0__A__105254)
                  & ? [Vvar__3__l__105275] :
                      ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__105254,Vvar__3__l__105275)
                      & cCoq_2eSorting_2eSorted_2eStronglySorted___24a3(Vvar__0__A__105254,Vvar__1__R__105255,Vvar__3__l__105275)
                      & cCoq_2eLists_2eList_2eForall___24a3(Vvar__0__A__105254,happ(Vvar__1__R__105255,Vvar__2__a__105274),Vvar__3__l__105275)
                      & Vvar__2___24Anonymous__105260 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__105254,Vvar__2__a__105274,Vvar__3__l__105275) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.Strings.Ascii.ascii',axiom,
    ! [VX67902] :
      ( cCoq_2eStrings_2eAscii_2eascii___24t(VX67902)
     => ? [Vvar__0___24Anonymous__67903] :
          ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__0___24Anonymous__67903)
          & ? [Vvar__1___24Anonymous__67904] :
              ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__1___24Anonymous__67904)
              & ? [Vvar__2___24Anonymous__67905] :
                  ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__2___24Anonymous__67905)
                  & ? [Vvar__3___24Anonymous__67906] :
                      ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__3___24Anonymous__67906)
                      & ? [Vvar__4___24Anonymous__67907] :
                          ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__4___24Anonymous__67907)
                          & ? [Vvar__5___24Anonymous__67908] :
                              ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__5___24Anonymous__67908)
                              & ? [Vvar__6___24Anonymous__67909] :
                                  ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__6___24Anonymous__67909)
                                  & ? [Vvar__7___24Anonymous__67910] :
                                      ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__7___24Anonymous__67910)
                                      & VX67902 = cCoq_2eStrings_2eAscii_2eAscii___24a8(Vvar__0___24Anonymous__67903,Vvar__1___24Anonymous__67904,Vvar__2___24Anonymous__67905,Vvar__3___24Anonymous__67906,Vvar__4___24Anonymous__67907,Vvar__5___24Anonymous__67908,Vvar__6___24Anonymous__67909,Vvar__7___24Anonymous__67910) ) ) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.Strings.String.string',axiom,
    ! [VX82303] :
      ( cCoq_2eStrings_2eString_2estring___24t(VX82303)
     => ( VX82303 = cCoq_2eStrings_2eString_2eEmptyString
        | ? [Vvar__0___24Anonymous__82304] :
            ( cCoq_2eStrings_2eAscii_2eascii___24t(Vvar__0___24Anonymous__82304)
            & ? [Vvar__1___24Anonymous__82305] :
                ( cCoq_2eStrings_2eString_2estring___24t(Vvar__1___24Anonymous__82305)
                & VX82303 = cCoq_2eStrings_2eString_2eString___24a2(Vvar__0___24Anonymous__82304,Vvar__1___24Anonymous__82305) ) ) ) ) ).

fof('$_inversion_Coq.Structures.OrderedType.Compare',axiom,
    ! [Vvar__0__X__96980,Vvar__1__lt__96981,Vvar__2__eq__96986,Vvar__3__x__96991,Vvar__4__y__96992,VX96993] :
      ( cType___24t(Vvar__0__X__96980)
     => ( c_24__type__97053___24t(Vvar__0__X__96980,Vvar__1__lt__96981,Vvar__2__eq__96986,Vvar__3__x__96991,Vvar__4__y__96992,Vvar__1__lt__96981)
       => ( c_24__type__97072___24t(Vvar__0__X__96980,Vvar__1__lt__96981,Vvar__2__eq__96986,Vvar__3__x__96991,Vvar__4__y__96992,Vvar__2__eq__96986)
         => ( t(Vvar__3__x__96991,Vvar__0__X__96980)
           => ( t(Vvar__4__y__96992,Vvar__0__X__96980)
             => ( cCoq_2eStructures_2eOrderedType_2eCompare___24t(Vvar__0__X__96980,Vvar__1__lt__96981,Vvar__2__eq__96986,Vvar__3__x__96991,Vvar__4__y__96992,VX96993)
               => ( ( p(happ(happ(Vvar__1__lt__96981,Vvar__3__x__96991),Vvar__4__y__96992))
                    & VX96993 = cCoq_2eStructures_2eOrderedType_2eLT___24a5(Vvar__0__X__96980,Vvar__1__lt__96981,Vvar__2__eq__96986,Vvar__3__x__96991,Vvar__4__y__96992) )
                  | ( p(happ(happ(Vvar__2__eq__96986,Vvar__3__x__96991),Vvar__4__y__96992))
                    & VX96993 = cCoq_2eStructures_2eOrderedType_2eEQ___24a5(Vvar__0__X__96980,Vvar__1__lt__96981,Vvar__2__eq__96986,Vvar__3__x__96991,Vvar__4__y__96992) )
                  | ( p(happ(happ(Vvar__1__lt__96981,Vvar__4__y__96992),Vvar__3__x__96991))
                    & VX96993 = cCoq_2eStructures_2eOrderedType_2eGT___24a5(Vvar__0__X__96980,Vvar__1__lt__96981,Vvar__2__eq__96986,Vvar__3__x__96991,Vvar__4__y__96992) ) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.Structures.OrderedTypeEx.String_as_OT.lts',axiom,
    ! [Vvar__0___24Anonymous__105696,Vvar__1___24Anonymous__105697] :
      ( cCoq_2eStrings_2eString_2estring___24t(Vvar__0___24Anonymous__105696)
     => ( cCoq_2eStrings_2eString_2estring___24t(Vvar__1___24Anonymous__105697)
       => ( cCoq_2eStructures_2eOrderedTypeEx_2eString__as__OT_2elts___24a2(Vvar__0___24Anonymous__105696,Vvar__1___24Anonymous__105697)
         => ( ? [Vvar__0__a__105699] :
                ( cCoq_2eStrings_2eAscii_2eascii___24t(Vvar__0__a__105699)
                & ? [Vvar__1__s__105700] :
                    ( cCoq_2eStrings_2eString_2estring___24t(Vvar__1__s__105700)
                    & Vvar__1___24Anonymous__105697 = cCoq_2eStrings_2eString_2eString___24a2(Vvar__0__a__105699,Vvar__1__s__105700)
                    & Vvar__0___24Anonymous__105696 = cCoq_2eStrings_2eString_2eEmptyString ) )
            | ? [Vvar__0__a__105701] :
                ( cCoq_2eStrings_2eAscii_2eascii___24t(Vvar__0__a__105701)
                & ? [Vvar__1__s1__105702] :
                    ( cCoq_2eStrings_2eString_2estring___24t(Vvar__1__s1__105702)
                    & ? [Vvar__2__s2__105703] :
                        ( cCoq_2eStrings_2eString_2estring___24t(Vvar__2__s2__105703)
                        & cCoq_2eStructures_2eOrderedTypeEx_2eString__as__OT_2elts___24a2(Vvar__1__s1__105702,Vvar__2__s2__105703)
                        & Vvar__1___24Anonymous__105697 = cCoq_2eStrings_2eString_2eString___24a2(Vvar__0__a__105701,Vvar__2__s2__105703)
                        & Vvar__0___24Anonymous__105696 = cCoq_2eStrings_2eString_2eString___24a2(Vvar__0__a__105701,Vvar__1__s1__105702) ) ) )
            | ? [Vvar__0__a__105705] :
                ( cCoq_2eStrings_2eAscii_2eascii___24t(Vvar__0__a__105705)
                & ? [Vvar__1__b__105706] :
                    ( cCoq_2eStrings_2eAscii_2eascii___24t(Vvar__1__b__105706)
                    & ? [Vvar__2__s1__105707] :
                        ( cCoq_2eStrings_2eString_2estring___24t(Vvar__2__s1__105707)
                        & ? [Vvar__3__s2__105708] :
                            ( cCoq_2eStrings_2eString_2estring___24t(Vvar__3__s2__105708)
                            & cCoq_2eInit_2ePeano_2elt___24a2(cCoq_2eStrings_2eAscii_2enat__of__ascii___24a1(Vvar__0__a__105705),cCoq_2eStrings_2eAscii_2enat__of__ascii___24a1(Vvar__1__b__105706))
                            & Vvar__1___24Anonymous__105697 = cCoq_2eStrings_2eString_2eString___24a2(Vvar__1__b__105706,Vvar__3__s2__105708)
                            & Vvar__0___24Anonymous__105696 = cCoq_2eStrings_2eString_2eString___24a2(Vvar__0__a__105705,Vvar__2__s1__105707) ) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.Structures.OrdersTac.ord',axiom,
    ! [VX85869] :
      ( cCoq_2eStructures_2eOrdersTac_2eord___24t(VX85869)
     => ( VX85869 = cCoq_2eStructures_2eOrdersTac_2eOEQ
        | VX85869 = cCoq_2eStructures_2eOrdersTac_2eOLT
        | VX85869 = cCoq_2eStructures_2eOrdersTac_2eOLE ) ) ).

fof('$_inversion_Coq.Vectors.Fin.t',axiom,
    ! [Vvar__0___24Anonymous__75884,VX75885] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__75884)
     => ( cCoq_2eVectors_2eFin_2et___24t(Vvar__0___24Anonymous__75884,VX75885)
       => ( ? [Vvar__0__n__75886] :
              ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0__n__75886)
              & Vvar__0___24Anonymous__75884 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0__n__75886)
              & VX75885 = cCoq_2eVectors_2eFin_2eF1___24a1(Vvar__0__n__75886) )
          | ? [Vvar__0__n__75887] :
              ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0__n__75887)
              & ? [Vvar__1___24Anonymous__75888] :
                  ( cCoq_2eVectors_2eFin_2et___24t(Vvar__0__n__75887,Vvar__1___24Anonymous__75888)
                  & Vvar__0___24Anonymous__75884 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0__n__75887)
                  & VX75885 = cCoq_2eVectors_2eFin_2eFS___24a2(Vvar__0__n__75887,Vvar__1___24Anonymous__75888) ) ) ) ) ) ).

fof('$_inversion_Coq.Vectors.VectorDef.t',axiom,
    ! [Vvar__0__A__79256,Vvar__1___24Anonymous__79257,VX79258] :
      ( cType___24t(Vvar__0__A__79256)
     => ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__1___24Anonymous__79257)
       => ( cCoq_2eVectors_2eVectorDef_2et___24t(Vvar__0__A__79256,Vvar__1___24Anonymous__79257,VX79258)
         => ( ( Vvar__1___24Anonymous__79257 = cCoq_2eInit_2eDatatypes_2eO
              & VX79258 = cCoq_2eVectors_2eVectorDef_2enil___24a1(Vvar__0__A__79256) )
            | ? [Vvar__1__h__79261] :
                ( t(Vvar__1__h__79261,Vvar__0__A__79256)
                & ? [Vvar__2__n__79262] :
                    ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__2__n__79262)
                    & ? [Vvar__3___24Anonymous__79263] :
                        ( cCoq_2eVectors_2eVectorDef_2et___24t(Vvar__0__A__79256,Vvar__2__n__79262,Vvar__3___24Anonymous__79263)
                        & Vvar__1___24Anonymous__79257 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__2__n__79262)
                        & VX79258 = cCoq_2eVectors_2eVectorDef_2econs___24a4(Vvar__0__A__79256,Vvar__1__h__79261,Vvar__2__n__79262,Vvar__3___24Anonymous__79263) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.ZArith.Znumtheory.Bezout',axiom,
    ! [Vvar__0__a__105423,Vvar__1__b__105424,Vvar__2__d__105425] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__0__a__105423)
     => ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__1__b__105424)
       => ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__2__d__105425)
         => ( cCoq_2eZArith_2eZnumtheory_2eBezout___24a3(Vvar__0__a__105423,Vvar__1__b__105424,Vvar__2__d__105425)
           => ? [Vvar__3__u__105430] :
                ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__3__u__105430)
                & ? [Vvar__4__v__105431] :
                    ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__4__v__105431)
                    & cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(Vvar__3__u__105430,Vvar__0__a__105423),cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(Vvar__4__v__105431,Vvar__1__b__105424)) = Vvar__2__d__105425
                    & p(c_24True) ) ) ) ) ) ) ).

fof('$_inversion_Coq.ZArith.Znumtheory.Euclid',axiom,
    ! [Vvar__0__a__105398,Vvar__1__b__105399,VX105400] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__0__a__105398)
     => ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__1__b__105399)
       => ( cCoq_2eZArith_2eZnumtheory_2eEuclid___24t(Vvar__0__a__105398,Vvar__1__b__105399,VX105400)
         => ? [Vvar__2__u__105403] :
              ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__2__u__105403)
              & ? [Vvar__3__v__105404] :
                  ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__3__v__105404)
                  & ? [Vvar__4__d__105405] :
                      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__4__d__105405)
                      & cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(Vvar__2__u__105403,Vvar__0__a__105398),cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(Vvar__3__v__105404,Vvar__1__b__105399)) = Vvar__4__d__105405
                      & cCoq_2eZArith_2eZnumtheory_2eZis__gcd___24a3(Vvar__0__a__105398,Vvar__1__b__105399,Vvar__4__d__105405)
                      & VX105400 = cCoq_2eZArith_2eZnumtheory_2eEuclid__intro___24a5(Vvar__0__a__105398,Vvar__1__b__105399,Vvar__2__u__105403,Vvar__3__v__105404,Vvar__4__d__105405) ) ) ) ) ) ) ).

fof('$_inversion_Coq.ZArith.Znumtheory.Zis_gcd',axiom,
    ! [Vvar__0__a__105370,Vvar__1__b__105371,Vvar__2__g__105372] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__0__a__105370)
     => ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__1__b__105371)
       => ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__2__g__105372)
         => ( cCoq_2eZArith_2eZnumtheory_2eZis__gcd___24a3(Vvar__0__a__105370,Vvar__1__b__105371,Vvar__2__g__105372)
           => ( cCoq_2eZArith_2eBinInt_2eZ_2edivide___24a2(Vvar__2__g__105372,Vvar__0__a__105370)
              & cCoq_2eZArith_2eBinInt_2eZ_2edivide___24a2(Vvar__2__g__105372,Vvar__1__b__105371)
              & ! [Vvar__var__var__var__var__5__x__105380__105383__105386__105389__105392] :
                  ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__var__var__var__var__5__x__105380__105383__105386__105389__105392)
                 => ( cCoq_2eZArith_2eBinInt_2eZ_2edivide___24a2(Vvar__var__var__var__var__5__x__105380__105383__105386__105389__105392,Vvar__0__a__105370)
                   => ( cCoq_2eZArith_2eBinInt_2eZ_2edivide___24a2(Vvar__var__var__var__var__5__x__105380__105383__105386__105389__105392,Vvar__1__b__105371)
                     => cCoq_2eZArith_2eBinInt_2eZ_2edivide___24a2(Vvar__var__var__var__var__5__x__105380__105383__105386__105389__105392,Vvar__2__g__105372) ) ) )
              & p(c_24True) ) ) ) ) ) ).

fof('$_inversion_Coq.ZArith.Znumtheory.prime',axiom,
    ! [Vvar__0__p__105433] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__0__p__105433)
     => ( cCoq_2eZArith_2eZnumtheory_2eprime___24a1(Vvar__0__p__105433)
       => ( cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH),Vvar__0__p__105433)
          & ! [Vvar__var__var__2__n__105438__105440__105442] :
              ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__var__var__2__n__105438__105440__105442)
             => ( ( cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH),Vvar__var__var__2__n__105438__105440__105442)
                  & cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(Vvar__var__var__2__n__105438__105440__105442,Vvar__0__p__105433) )
               => cCoq_2eZArith_2eZnumtheory_2erel__prime___24a2(Vvar__var__var__2__n__105438__105440__105442,Vvar__0__p__105433) ) )
          & p(c_24True) ) ) ) ).

fof('$_inversion_Coq.ZArith.Zpower.Zdiv_rest_proofs',axiom,
    ! [Vvar__0__x__105446,Vvar__1__p__105447,VX105448] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__0__x__105446)
     => ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1__p__105447)
       => ( cCoq_2eZArith_2eZpower_2eZdiv__rest__proofs___24t(Vvar__0__x__105446,Vvar__1__p__105447,VX105448)
         => ? [Vvar__2__q__105451] :
              ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__2__q__105451)
              & ? [Vvar__3__r__105452] :
                  ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__3__r__105452)
                  & Vvar__0__x__105446 = cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(Vvar__2__q__105451,cCoq_2eZArith_2eZpower_2etwo__power__pos___24a1(Vvar__1__p__105447)),Vvar__3__r__105452)
                  & cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,Vvar__3__r__105452)
                  & cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(Vvar__3__r__105452,cCoq_2eZArith_2eZpower_2etwo__power__pos___24a1(Vvar__1__p__105447))
                  & VX105448 = cCoq_2eZArith_2eZpower_2eZdiv__rest__proof___24a4(Vvar__0__x__105446,Vvar__1__p__105447,Vvar__2__q__105451,Vvar__3__r__105452) ) ) ) ) ) ).

fof('$_inversion_Coq.micromega.DeclConstant.DeclaredConstant',axiom,
    ! [Vvar__0__T__94233,Vvar__1__F__94234] :
      ( cType___24t(Vvar__0__T__94233)
     => ( t(Vvar__1__F__94234,Vvar__0__T__94233)
       => ( cCoq_2emicromega_2eDeclConstant_2eDeclaredConstant___24a2(Vvar__0__T__94233,Vvar__1__F__94234)
         => p(c_24True) ) ) ) ).

fof('$_inversion_Coq.micromega.DeclConstant.GT',axiom,
    ! [Vvar__0__T__94238,Vvar__1__F__94239] :
      ( cType___24t(Vvar__0__T__94238)
     => ( t(Vvar__1__F__94239,Vvar__0__T__94238)
       => ( cCoq_2emicromega_2eDeclConstant_2eGT___24a2(Vvar__0__T__94238,Vvar__1__F__94239)
         => p(c_24True) ) ) ) ).

fof('$_inversion_Coq.micromega.EnvRing.Mon',axiom,
    ! [VX94410] :
      ( cCoq_2emicromega_2eEnvRing_2eMon___24t(VX94410)
     => ( VX94410 = cCoq_2emicromega_2eEnvRing_2emon0
        | ? [Vvar__0___24Anonymous__94411] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__94411)
            & ? [Vvar__1___24Anonymous__94412] :
                ( cCoq_2emicromega_2eEnvRing_2eMon___24t(Vvar__1___24Anonymous__94412)
                & VX94410 = cCoq_2emicromega_2eEnvRing_2ezmon___24a2(Vvar__0___24Anonymous__94411,Vvar__1___24Anonymous__94412) ) )
        | ? [Vvar__0___24Anonymous__94413] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__94413)
            & ? [Vvar__1___24Anonymous__94414] :
                ( cCoq_2emicromega_2eEnvRing_2eMon___24t(Vvar__1___24Anonymous__94414)
                & VX94410 = cCoq_2emicromega_2eEnvRing_2evmon___24a2(Vvar__0___24Anonymous__94413,Vvar__1___24Anonymous__94414) ) ) ) ) ).

fof('$_inversion_Coq.micromega.EnvRing.PExpr',axiom,
    ! [Vvar__0__C__94246,VX94247] :
      ( cType___24t(Vvar__0__C__94246)
     => ( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__C__94246,VX94247)
       => ( ? [Vvar__1___24Anonymous__94249] :
              ( t(Vvar__1___24Anonymous__94249,Vvar__0__C__94246)
              & VX94247 = cCoq_2emicromega_2eEnvRing_2ePEc___24a2(Vvar__0__C__94246,Vvar__1___24Anonymous__94249) )
          | ? [Vvar__1___24Anonymous__94251] :
              ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__94251)
              & VX94247 = cCoq_2emicromega_2eEnvRing_2ePEX___24a2(Vvar__0__C__94246,Vvar__1___24Anonymous__94251) )
          | ? [Vvar__1___24Anonymous__94253] :
              ( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__C__94246,Vvar__1___24Anonymous__94253)
              & ? [Vvar__2___24Anonymous__94254] :
                  ( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__C__94246,Vvar__2___24Anonymous__94254)
                  & VX94247 = cCoq_2emicromega_2eEnvRing_2ePEadd___24a3(Vvar__0__C__94246,Vvar__1___24Anonymous__94253,Vvar__2___24Anonymous__94254) ) )
          | ? [Vvar__1___24Anonymous__94256] :
              ( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__C__94246,Vvar__1___24Anonymous__94256)
              & ? [Vvar__2___24Anonymous__94257] :
                  ( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__C__94246,Vvar__2___24Anonymous__94257)
                  & VX94247 = cCoq_2emicromega_2eEnvRing_2ePEsub___24a3(Vvar__0__C__94246,Vvar__1___24Anonymous__94256,Vvar__2___24Anonymous__94257) ) )
          | ? [Vvar__1___24Anonymous__94259] :
              ( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__C__94246,Vvar__1___24Anonymous__94259)
              & ? [Vvar__2___24Anonymous__94260] :
                  ( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__C__94246,Vvar__2___24Anonymous__94260)
                  & VX94247 = cCoq_2emicromega_2eEnvRing_2ePEmul___24a3(Vvar__0__C__94246,Vvar__1___24Anonymous__94259,Vvar__2___24Anonymous__94260) ) )
          | ? [Vvar__1___24Anonymous__94262] :
              ( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__C__94246,Vvar__1___24Anonymous__94262)
              & VX94247 = cCoq_2emicromega_2eEnvRing_2ePEopp___24a2(Vvar__0__C__94246,Vvar__1___24Anonymous__94262) )
          | ? [Vvar__1___24Anonymous__94264] :
              ( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__C__94246,Vvar__1___24Anonymous__94264)
              & ? [Vvar__2___24Anonymous__94265] :
                  ( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__2___24Anonymous__94265)
                  & VX94247 = cCoq_2emicromega_2eEnvRing_2ePEpow___24a3(Vvar__0__C__94246,Vvar__1___24Anonymous__94264,Vvar__2___24Anonymous__94265) ) ) ) ) ) ).

fof('$_inversion_Coq.micromega.EnvRing.Pol',axiom,
    ! [Vvar__0__C__83523,VX83524] :
      ( cType___24t(Vvar__0__C__83523)
     => ( cCoq_2emicromega_2eEnvRing_2ePol___24t(Vvar__0__C__83523,VX83524)
       => ( ? [Vvar__1___24Anonymous__83526] :
              ( t(Vvar__1___24Anonymous__83526,Vvar__0__C__83523)
              & VX83524 = cCoq_2emicromega_2eEnvRing_2ePc___24a2(Vvar__0__C__83523,Vvar__1___24Anonymous__83526) )
          | ? [Vvar__1___24Anonymous__83528] :
              ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__83528)
              & ? [Vvar__2___24Anonymous__83529] :
                  ( cCoq_2emicromega_2eEnvRing_2ePol___24t(Vvar__0__C__83523,Vvar__2___24Anonymous__83529)
                  & VX83524 = cCoq_2emicromega_2eEnvRing_2ePinj___24a3(Vvar__0__C__83523,Vvar__1___24Anonymous__83528,Vvar__2___24Anonymous__83529) ) )
          | ? [Vvar__1___24Anonymous__83531] :
              ( cCoq_2emicromega_2eEnvRing_2ePol___24t(Vvar__0__C__83523,Vvar__1___24Anonymous__83531)
              & ? [Vvar__2___24Anonymous__83532] :
                  ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2___24Anonymous__83532)
                  & ? [Vvar__3___24Anonymous__83533] :
                      ( cCoq_2emicromega_2eEnvRing_2ePol___24t(Vvar__0__C__83523,Vvar__3___24Anonymous__83533)
                      & VX83524 = cCoq_2emicromega_2eEnvRing_2ePX___24a4(Vvar__0__C__83523,Vvar__1___24Anonymous__83531,Vvar__2___24Anonymous__83532,Vvar__3___24Anonymous__83533) ) ) ) ) ) ) ).

fof('$_inversion_Coq.micromega.OrderedRing.SOR',axiom,
    ! [Vvar__0__R__84704,Vvar__1__rO__84705,Vvar__2__rI__84706,Vvar__3__rplus__84707,Vvar__4__rtimes__84712,Vvar__5__rminus__84717,Vvar__6__ropp__84722,Vvar__7__req__84725,Vvar__8__rle__84730,Vvar__9__rlt__84735] :
      ( cType___24t(Vvar__0__R__84704)
     => ( t(Vvar__1__rO__84705,Vvar__0__R__84704)
       => ( t(Vvar__2__rI__84706,Vvar__0__R__84704)
         => ( c_24__type__85136___24t(Vvar__0__R__84704,Vvar__1__rO__84705,Vvar__2__rI__84706,Vvar__3__rplus__84707,Vvar__4__rtimes__84712,Vvar__5__rminus__84717,Vvar__6__ropp__84722,Vvar__7__req__84725,Vvar__8__rle__84730,Vvar__9__rlt__84735,Vvar__3__rplus__84707)
           => ( c_24__type__85237___24t(Vvar__0__R__84704,Vvar__1__rO__84705,Vvar__2__rI__84706,Vvar__3__rplus__84707,Vvar__4__rtimes__84712,Vvar__5__rminus__84717,Vvar__6__ropp__84722,Vvar__7__req__84725,Vvar__8__rle__84730,Vvar__9__rlt__84735,Vvar__4__rtimes__84712)
             => ( c_24__type__85338___24t(Vvar__0__R__84704,Vvar__1__rO__84705,Vvar__2__rI__84706,Vvar__3__rplus__84707,Vvar__4__rtimes__84712,Vvar__5__rminus__84717,Vvar__6__ropp__84722,Vvar__7__req__84725,Vvar__8__rle__84730,Vvar__9__rlt__84735,Vvar__5__rminus__84717)
               => ( c_24__type__85428___24t(Vvar__0__R__84704,Vvar__1__rO__84705,Vvar__2__rI__84706,Vvar__3__rplus__84707,Vvar__4__rtimes__84712,Vvar__5__rminus__84717,Vvar__6__ropp__84722,Vvar__7__req__84725,Vvar__8__rle__84730,Vvar__9__rlt__84735,Vvar__6__ropp__84722)
                 => ( c_24__type__85529___24t(Vvar__0__R__84704,Vvar__1__rO__84705,Vvar__2__rI__84706,Vvar__3__rplus__84707,Vvar__4__rtimes__84712,Vvar__5__rminus__84717,Vvar__6__ropp__84722,Vvar__7__req__84725,Vvar__8__rle__84730,Vvar__9__rlt__84735,Vvar__7__req__84725)
                   => ( c_24__type__85630___24t(Vvar__0__R__84704,Vvar__1__rO__84705,Vvar__2__rI__84706,Vvar__3__rplus__84707,Vvar__4__rtimes__84712,Vvar__5__rminus__84717,Vvar__6__ropp__84722,Vvar__7__req__84725,Vvar__8__rle__84730,Vvar__9__rlt__84735,Vvar__8__rle__84730)
                     => ( c_24__type__85731___24t(Vvar__0__R__84704,Vvar__1__rO__84705,Vvar__2__rI__84706,Vvar__3__rplus__84707,Vvar__4__rtimes__84712,Vvar__5__rminus__84717,Vvar__6__ropp__84722,Vvar__7__req__84725,Vvar__8__rle__84730,Vvar__9__rlt__84735,Vvar__9__rlt__84735)
                       => ( cCoq_2emicromega_2eOrderedRing_2eSOR___24a10(Vvar__0__R__84704,Vvar__1__rO__84705,Vvar__2__rI__84706,Vvar__3__rplus__84707,Vvar__4__rtimes__84712,Vvar__5__rminus__84717,Vvar__6__ropp__84722,Vvar__7__req__84725,Vvar__8__rle__84730,Vvar__9__rlt__84735)
                         => ( cCoq_2eSetoids_2eSetoid_2eSetoid__Theory___24a2(Vvar__0__R__84704,Vvar__7__req__84725)
                            & ! [Vvar__var__var__var__var__11__x1__84779__84785__84890__84896__84902] :
                                ( t(Vvar__var__var__var__var__11__x1__84779__84785__84890__84896__84902,Vvar__0__R__84704)
                               => ! [Vvar__var__var__var__var__12__x2__84780__84786__84891__84897__84903] :
                                    ( t(Vvar__var__var__var__var__12__x2__84780__84786__84891__84897__84903,Vvar__0__R__84704)
                                   => ( p(happ(happ(Vvar__7__req__84725,Vvar__var__var__var__var__11__x1__84779__84785__84890__84896__84902),Vvar__var__var__var__var__12__x2__84780__84786__84891__84897__84903))
                                     => ! [Vvar__var__var__var__var__14__y1__84781__84787__84892__84898__84904] :
                                          ( t(Vvar__var__var__var__var__14__y1__84781__84787__84892__84898__84904,Vvar__0__R__84704)
                                         => ! [Vvar__var__var__var__var__15__y2__84782__84788__84893__84899__84905] :
                                              ( t(Vvar__var__var__var__var__15__y2__84782__84788__84893__84899__84905,Vvar__0__R__84704)
                                             => ( p(happ(happ(Vvar__7__req__84725,Vvar__var__var__var__var__14__y1__84781__84787__84892__84898__84904),Vvar__var__var__var__var__15__y2__84782__84788__84893__84899__84905))
                                               => p(happ(happ(Vvar__7__req__84725,happ(happ(Vvar__3__rplus__84707,Vvar__var__var__var__var__11__x1__84779__84785__84890__84896__84902),Vvar__var__var__var__var__14__y1__84781__84787__84892__84898__84904)),happ(happ(Vvar__3__rplus__84707,Vvar__var__var__var__var__12__x2__84780__84786__84891__84897__84903),Vvar__var__var__var__var__15__y2__84782__84788__84893__84899__84905))) ) ) ) ) ) )
                            & ! [Vvar__var__var__var__var__12__x1__84792__84798__84908__84914__84920] :
                                ( t(Vvar__var__var__var__var__12__x1__84792__84798__84908__84914__84920,Vvar__0__R__84704)
                               => ! [Vvar__var__var__var__var__13__x2__84793__84799__84909__84915__84921] :
                                    ( t(Vvar__var__var__var__var__13__x2__84793__84799__84909__84915__84921,Vvar__0__R__84704)
                                   => ( p(happ(happ(Vvar__7__req__84725,Vvar__var__var__var__var__12__x1__84792__84798__84908__84914__84920),Vvar__var__var__var__var__13__x2__84793__84799__84909__84915__84921))
                                     => ! [Vvar__var__var__var__var__15__y1__84794__84800__84910__84916__84922] :
                                          ( t(Vvar__var__var__var__var__15__y1__84794__84800__84910__84916__84922,Vvar__0__R__84704)
                                         => ! [Vvar__var__var__var__var__16__y2__84795__84801__84911__84917__84923] :
                                              ( t(Vvar__var__var__var__var__16__y2__84795__84801__84911__84917__84923,Vvar__0__R__84704)
                                             => ( p(happ(happ(Vvar__7__req__84725,Vvar__var__var__var__var__15__y1__84794__84800__84910__84916__84922),Vvar__var__var__var__var__16__y2__84795__84801__84911__84917__84923))
                                               => p(happ(happ(Vvar__7__req__84725,happ(happ(Vvar__4__rtimes__84712,Vvar__var__var__var__var__12__x1__84792__84798__84908__84914__84920),Vvar__var__var__var__var__15__y1__84794__84800__84910__84916__84922)),happ(happ(Vvar__4__rtimes__84712,Vvar__var__var__var__var__13__x2__84793__84799__84909__84915__84921),Vvar__var__var__var__var__16__y2__84795__84801__84911__84917__84923))) ) ) ) ) ) )
                            & ! [Vvar__var__var__var__var__13__x1__84805__84808__84926__84929__84932] :
                                ( t(Vvar__var__var__var__var__13__x1__84805__84808__84926__84929__84932,Vvar__0__R__84704)
                               => ! [Vvar__var__var__var__var__14__x2__84806__84809__84927__84930__84933] :
                                    ( t(Vvar__var__var__var__var__14__x2__84806__84809__84927__84930__84933,Vvar__0__R__84704)
                                   => ( p(happ(happ(Vvar__7__req__84725,Vvar__var__var__var__var__13__x1__84805__84808__84926__84929__84932),Vvar__var__var__var__var__14__x2__84806__84809__84927__84930__84933))
                                     => p(happ(happ(Vvar__7__req__84725,happ(Vvar__6__ropp__84722,Vvar__var__var__var__var__13__x1__84805__84808__84926__84929__84932)),happ(Vvar__6__ropp__84722,Vvar__var__var__var__var__14__x2__84806__84809__84927__84930__84933))) ) ) )
                            & ! [Vvar__var__var__var__var__14__x1__84812__84818__84935__84941__84947] :
                                ( t(Vvar__var__var__var__var__14__x1__84812__84818__84935__84941__84947,Vvar__0__R__84704)
                               => ! [Vvar__var__var__var__var__15__x2__84813__84819__84936__84942__84948] :
                                    ( t(Vvar__var__var__var__var__15__x2__84813__84819__84936__84942__84948,Vvar__0__R__84704)
                                   => ( p(happ(happ(Vvar__7__req__84725,Vvar__var__var__var__var__14__x1__84812__84818__84935__84941__84947),Vvar__var__var__var__var__15__x2__84813__84819__84936__84942__84948))
                                     => ! [Vvar__var__var__var__var__17__y1__84814__84820__84937__84943__84949] :
                                          ( t(Vvar__var__var__var__var__17__y1__84814__84820__84937__84943__84949,Vvar__0__R__84704)
                                         => ! [Vvar__var__var__var__var__18__y2__84815__84821__84938__84944__84950] :
                                              ( t(Vvar__var__var__var__var__18__y2__84815__84821__84938__84944__84950,Vvar__0__R__84704)
                                             => ( p(happ(happ(Vvar__7__req__84725,Vvar__var__var__var__var__17__y1__84814__84820__84937__84943__84949),Vvar__var__var__var__var__18__y2__84815__84821__84938__84944__84950))
                                               => ( p(happ(happ(Vvar__8__rle__84730,Vvar__var__var__var__var__14__x1__84812__84818__84935__84941__84947),Vvar__var__var__var__var__17__y1__84814__84820__84937__84943__84949))
                                                <=> p(happ(happ(Vvar__8__rle__84730,Vvar__var__var__var__var__15__x2__84813__84819__84936__84942__84948),Vvar__var__var__var__var__18__y2__84815__84821__84938__84944__84950)) ) ) ) ) ) ) )
                            & ! [Vvar__var__var__var__var__15__x1__84825__84831__84953__84959__84965] :
                                ( t(Vvar__var__var__var__var__15__x1__84825__84831__84953__84959__84965,Vvar__0__R__84704)
                               => ! [Vvar__var__var__var__var__16__x2__84826__84832__84954__84960__84966] :
                                    ( t(Vvar__var__var__var__var__16__x2__84826__84832__84954__84960__84966,Vvar__0__R__84704)
                                   => ( p(happ(happ(Vvar__7__req__84725,Vvar__var__var__var__var__15__x1__84825__84831__84953__84959__84965),Vvar__var__var__var__var__16__x2__84826__84832__84954__84960__84966))
                                     => ! [Vvar__var__var__var__var__18__y1__84827__84833__84955__84961__84967] :
                                          ( t(Vvar__var__var__var__var__18__y1__84827__84833__84955__84961__84967,Vvar__0__R__84704)
                                         => ! [Vvar__var__var__var__var__19__y2__84828__84834__84956__84962__84968] :
                                              ( t(Vvar__var__var__var__var__19__y2__84828__84834__84956__84962__84968,Vvar__0__R__84704)
                                             => ( p(happ(happ(Vvar__7__req__84725,Vvar__var__var__var__var__18__y1__84827__84833__84955__84961__84967),Vvar__var__var__var__var__19__y2__84828__84834__84956__84962__84968))
                                               => ( p(happ(happ(Vvar__9__rlt__84735,Vvar__var__var__var__var__15__x1__84825__84831__84953__84959__84965),Vvar__var__var__var__var__18__y1__84827__84833__84955__84961__84967))
                                                <=> p(happ(happ(Vvar__9__rlt__84735,Vvar__var__var__var__var__16__x2__84826__84832__84954__84960__84966),Vvar__var__var__var__var__19__y2__84828__84834__84956__84962__84968)) ) ) ) ) ) ) )
                            & cCoq_2esetoid__ring_2eRing__theory_2ering__theory___24a8(Vvar__0__R__84704,Vvar__1__rO__84705,Vvar__2__rI__84706,Vvar__3__rplus__84707,Vvar__4__rtimes__84712,Vvar__5__rminus__84717,Vvar__6__ropp__84722,Vvar__7__req__84725)
                            & ! [Vvar__var__var__var__17__n__84839__84840__84971__84972] :
                                ( t(Vvar__var__var__var__17__n__84839__84840__84971__84972,Vvar__0__R__84704)
                               => p(happ(happ(Vvar__8__rle__84730,Vvar__var__var__var__17__n__84839__84840__84971__84972),Vvar__var__var__var__17__n__84839__84840__84971__84972)) )
                            & ! [Vvar__var__var__var__var__18__n__84842__84846__84973__84977__84981] :
                                ( t(Vvar__var__var__var__var__18__n__84842__84846__84973__84977__84981,Vvar__0__R__84704)
                               => ! [Vvar__var__var__var__var__19__m__84843__84847__84974__84978__84982] :
                                    ( t(Vvar__var__var__var__var__19__m__84843__84847__84974__84978__84982,Vvar__0__R__84704)
                                   => ( p(happ(happ(Vvar__8__rle__84730,Vvar__var__var__var__var__18__n__84842__84846__84973__84977__84981),Vvar__var__var__var__var__19__m__84843__84847__84974__84978__84982))
                                     => ( p(happ(happ(Vvar__8__rle__84730,Vvar__var__var__var__var__19__m__84843__84847__84974__84978__84982),Vvar__var__var__var__var__18__n__84842__84846__84973__84977__84981))
                                       => p(happ(happ(Vvar__7__req__84725,Vvar__var__var__var__var__18__n__84842__84846__84973__84977__84981),Vvar__var__var__var__var__19__m__84843__84847__84974__84978__84982)) ) ) ) )
                            & ! [Vvar__var__var__var__19__n__84851__84856__84985__84990] :
                                ( t(Vvar__var__var__var__19__n__84851__84856__84985__84990,Vvar__0__R__84704)
                               => ! [Vvar__var__var__var__20__m__84852__84857__84986__84991] :
                                    ( t(Vvar__var__var__var__20__m__84852__84857__84986__84991,Vvar__0__R__84704)
                                   => ! [Vvar__var__var__var__21__p__84853__84858__84987__84992] :
                                        ( t(Vvar__var__var__var__21__p__84853__84858__84987__84992,Vvar__0__R__84704)
                                       => ( p(happ(happ(Vvar__8__rle__84730,Vvar__var__var__var__19__n__84851__84856__84985__84990),Vvar__var__var__var__20__m__84852__84857__84986__84991))
                                         => ( p(happ(happ(Vvar__8__rle__84730,Vvar__var__var__var__20__m__84852__84857__84986__84991),Vvar__var__var__var__21__p__84853__84858__84987__84992))
                                           => p(happ(happ(Vvar__8__rle__84730,Vvar__var__var__var__19__n__84851__84856__84985__84990),Vvar__var__var__var__21__p__84853__84858__84987__84992)) ) ) ) ) )
                            & ! [Vvar__var__var__var__var__var__20__n__84862__84864__84995__84997__84999__85001] :
                                ( t(Vvar__var__var__var__var__var__20__n__84862__84864__84995__84997__84999__85001,Vvar__0__R__84704)
                               => ! [Vvar__var__var__var__var__var__21__m__84863__84865__84996__84998__85000__85002] :
                                    ( t(Vvar__var__var__var__var__var__21__m__84863__84865__84996__84998__85000__85002,Vvar__0__R__84704)
                                   => ( p(happ(happ(Vvar__9__rlt__84735,Vvar__var__var__var__var__var__20__n__84862__84864__84995__84997__84999__85001),Vvar__var__var__var__var__var__21__m__84863__84865__84996__84998__85000__85002))
                                    <=> ( p(happ(happ(Vvar__8__rle__84730,Vvar__var__var__var__var__var__20__n__84862__84864__84995__84997__84999__85001),Vvar__var__var__var__var__var__21__m__84863__84865__84996__84998__85000__85002))
                                        & ~ p(happ(happ(Vvar__7__req__84725,Vvar__var__var__var__var__var__20__n__84862__84864__84995__84997__84999__85001),Vvar__var__var__var__var__var__21__m__84863__84865__84996__84998__85000__85002)) ) ) ) )
                            & ! [Vvar__var__var__var__var__21__n__84867__84869__85003__85005__85007] :
                                ( t(Vvar__var__var__var__var__21__n__84867__84869__85003__85005__85007,Vvar__0__R__84704)
                               => ! [Vvar__var__var__var__var__22__m__84868__84870__85004__85006__85008] :
                                    ( t(Vvar__var__var__var__var__22__m__84868__84870__85004__85006__85008,Vvar__0__R__84704)
                                   => ( p(happ(happ(Vvar__9__rlt__84735,Vvar__var__var__var__var__21__n__84867__84869__85003__85005__85007),Vvar__var__var__var__var__22__m__84868__84870__85004__85006__85008))
                                      | p(happ(happ(Vvar__7__req__84725,Vvar__var__var__var__var__21__n__84867__84869__85003__85005__85007),Vvar__var__var__var__var__22__m__84868__84870__85004__85006__85008))
                                      | p(happ(happ(Vvar__9__rlt__84735,Vvar__var__var__var__var__22__m__84868__84870__85004__85006__85008),Vvar__var__var__var__var__21__n__84867__84869__85003__85005__85007)) ) ) )
                            & ! [Vvar__var__var__var__var__22__n__84872__84876__85009__85013__85017] :
                                ( t(Vvar__var__var__var__var__22__n__84872__84876__85009__85013__85017,Vvar__0__R__84704)
                               => ! [Vvar__var__var__var__var__23__m__84873__84877__85010__85014__85018] :
                                    ( t(Vvar__var__var__var__var__23__m__84873__84877__85010__85014__85018,Vvar__0__R__84704)
                                   => ! [Vvar__var__var__var__var__24__p__84874__84878__85011__85015__85019] :
                                        ( t(Vvar__var__var__var__var__24__p__84874__84878__85011__85015__85019,Vvar__0__R__84704)
                                       => ( p(happ(happ(Vvar__8__rle__84730,Vvar__var__var__var__var__22__n__84872__84876__85009__85013__85017),Vvar__var__var__var__var__23__m__84873__84877__85010__85014__85018))
                                         => p(happ(happ(Vvar__8__rle__84730,happ(happ(Vvar__3__rplus__84707,Vvar__var__var__var__var__24__p__84874__84878__85011__85015__85019),Vvar__var__var__var__var__22__n__84872__84876__85009__85013__85017)),happ(happ(Vvar__3__rplus__84707,Vvar__var__var__var__var__24__p__84874__84878__85011__85015__85019),Vvar__var__var__var__var__23__m__84873__84877__85010__85014__85018))) ) ) ) )
                            & ! [Vvar__var__var__var__var__var__23__n__84881__84885__85021__85025__85029__85033] :
                                ( t(Vvar__var__var__var__var__var__23__n__84881__84885__85021__85025__85029__85033,Vvar__0__R__84704)
                               => ! [Vvar__var__var__var__var__var__24__m__84882__84886__85022__85026__85030__85034] :
                                    ( t(Vvar__var__var__var__var__var__24__m__84882__84886__85022__85026__85030__85034,Vvar__0__R__84704)
                                   => ( p(happ(happ(Vvar__9__rlt__84735,Vvar__1__rO__84705),Vvar__var__var__var__var__var__23__n__84881__84885__85021__85025__85029__85033))
                                     => ( p(happ(happ(Vvar__9__rlt__84735,Vvar__1__rO__84705),Vvar__var__var__var__var__var__24__m__84882__84886__85022__85026__85030__85034))
                                       => p(happ(happ(Vvar__9__rlt__84735,Vvar__1__rO__84705),happ(happ(Vvar__4__rtimes__84712,Vvar__var__var__var__var__var__23__n__84881__84885__85021__85025__85029__85033),Vvar__var__var__var__var__var__24__m__84882__84886__85022__85026__85030__85034))) ) ) ) )
                            & ~ p(happ(happ(Vvar__7__req__84725,Vvar__1__rO__84705),Vvar__2__rI__84706))
                            & p(c_24True) ) ) ) ) ) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.micromega.RMicromega.Rcst',axiom,
    ! [VX97231] :
      ( cCoq_2emicromega_2eRMicromega_2eRcst___24t(VX97231)
     => ( VX97231 = cCoq_2emicromega_2eRMicromega_2eC0
        | VX97231 = cCoq_2emicromega_2eRMicromega_2eC1
        | ? [Vvar__0__r__97232] :
            ( cCoq_2eQArith_2eQArith__base_2eQ___24t(Vvar__0__r__97232)
            & VX97231 = cCoq_2emicromega_2eRMicromega_2eCQ___24a1(Vvar__0__r__97232) )
        | ? [Vvar__0__r__97233] :
            ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__0__r__97233)
            & VX97231 = cCoq_2emicromega_2eRMicromega_2eCZ___24a1(Vvar__0__r__97233) )
        | ? [Vvar__0__r1__97234] :
            ( cCoq_2emicromega_2eRMicromega_2eRcst___24t(Vvar__0__r1__97234)
            & ? [Vvar__1__r2__97235] :
                ( cCoq_2emicromega_2eRMicromega_2eRcst___24t(Vvar__1__r2__97235)
                & VX97231 = cCoq_2emicromega_2eRMicromega_2eCPlus___24a2(Vvar__0__r1__97234,Vvar__1__r2__97235) ) )
        | ? [Vvar__0__r1__97236] :
            ( cCoq_2emicromega_2eRMicromega_2eRcst___24t(Vvar__0__r1__97236)
            & ? [Vvar__1__r2__97237] :
                ( cCoq_2emicromega_2eRMicromega_2eRcst___24t(Vvar__1__r2__97237)
                & VX97231 = cCoq_2emicromega_2eRMicromega_2eCMinus___24a2(Vvar__0__r1__97236,Vvar__1__r2__97237) ) )
        | ? [Vvar__0__r1__97238] :
            ( cCoq_2emicromega_2eRMicromega_2eRcst___24t(Vvar__0__r1__97238)
            & ? [Vvar__1__r2__97239] :
                ( cCoq_2emicromega_2eRMicromega_2eRcst___24t(Vvar__1__r2__97239)
                & VX97231 = cCoq_2emicromega_2eRMicromega_2eCMult___24a2(Vvar__0__r1__97238,Vvar__1__r2__97239) ) )
        | ? [Vvar__0__r1__97240] :
            ( cCoq_2emicromega_2eRMicromega_2eRcst___24t(Vvar__0__r1__97240)
            & ? [Vvar__1__z__97241] :
                ( cCoq_2eInit_2eDatatypes_2esum___24t(cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eInit_2eDatatypes_2enat,Vvar__1__z__97241)
                & VX97231 = cCoq_2emicromega_2eRMicromega_2eCPow___24a2(Vvar__0__r1__97240,Vvar__1__z__97241) ) )
        | ? [Vvar__0__r__97242] :
            ( cCoq_2emicromega_2eRMicromega_2eRcst___24t(Vvar__0__r__97242)
            & VX97231 = cCoq_2emicromega_2eRMicromega_2eCInv___24a1(Vvar__0__r__97242) )
        | ? [Vvar__0__r__97243] :
            ( cCoq_2emicromega_2eRMicromega_2eRcst___24t(Vvar__0__r__97243)
            & VX97231 = cCoq_2emicromega_2eRMicromega_2eCOpp___24a1(Vvar__0__r__97243) ) ) ) ).

fof('$_inversion_Coq.micromega.RingMicromega.Formula',axiom,
    ! [Vvar__0__T__85921,VX85922] :
      ( cType___24t(Vvar__0__T__85921)
     => ( cCoq_2emicromega_2eRingMicromega_2eFormula___24t(Vvar__0__T__85921,VX85922)
       => ? [Vvar__1__Flhs__85924] :
            ( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__T__85921,Vvar__1__Flhs__85924)
            & ? [Vvar__2__Fop__85925] :
                ( cCoq_2emicromega_2eRingMicromega_2eOp2___24t(Vvar__2__Fop__85925)
                & ? [Vvar__3__Frhs__85926] :
                    ( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__T__85921,Vvar__3__Frhs__85926)
                    & VX85922 = cCoq_2emicromega_2eRingMicromega_2eBuild__Formula___24a4(Vvar__0__T__85921,Vvar__1__Flhs__85924,Vvar__2__Fop__85925,Vvar__3__Frhs__85926) ) ) ) ) ) ).

fof('$_inversion_Coq.micromega.RingMicromega.Op1',axiom,
    ! [VX103495] :
      ( cCoq_2emicromega_2eRingMicromega_2eOp1___24t(VX103495)
     => ( VX103495 = cCoq_2emicromega_2eRingMicromega_2eEqual
        | VX103495 = cCoq_2emicromega_2eRingMicromega_2eNonEqual
        | VX103495 = cCoq_2emicromega_2eRingMicromega_2eStrict
        | VX103495 = cCoq_2emicromega_2eRingMicromega_2eNonStrict ) ) ).

fof('$_inversion_Coq.micromega.RingMicromega.Op2',axiom,
    ! [VX103642] :
      ( cCoq_2emicromega_2eRingMicromega_2eOp2___24t(VX103642)
     => ( VX103642 = cCoq_2emicromega_2eRingMicromega_2eOpEq
        | VX103642 = cCoq_2emicromega_2eRingMicromega_2eOpNEq
        | VX103642 = cCoq_2emicromega_2eRingMicromega_2eOpLe
        | VX103642 = cCoq_2emicromega_2eRingMicromega_2eOpGe
        | VX103642 = cCoq_2emicromega_2eRingMicromega_2eOpLt
        | VX103642 = cCoq_2emicromega_2eRingMicromega_2eOpGt ) ) ).

fof('$_inversion_Coq.micromega.RingMicromega.Psatz',axiom,
    ! [Vvar__0__C__103496,VX103497] :
      ( cType___24t(Vvar__0__C__103496)
     => ( cCoq_2emicromega_2eRingMicromega_2ePsatz___24t(Vvar__0__C__103496,VX103497)
       => ( ? [Vvar__1___24Anonymous__103499] :
              ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__1___24Anonymous__103499)
              & VX103497 = cCoq_2emicromega_2eRingMicromega_2ePsatzIn___24a2(Vvar__0__C__103496,Vvar__1___24Anonymous__103499) )
          | ? [Vvar__1___24Anonymous__103501] :
              ( cCoq_2emicromega_2eRingMicromega_2ePolC___24t(Vvar__0__C__103496,Vvar__1___24Anonymous__103501)
              & VX103497 = cCoq_2emicromega_2eRingMicromega_2ePsatzSquare___24a2(Vvar__0__C__103496,Vvar__1___24Anonymous__103501) )
          | ? [Vvar__1___24Anonymous__103503] :
              ( cCoq_2emicromega_2eRingMicromega_2ePolC___24t(Vvar__0__C__103496,Vvar__1___24Anonymous__103503)
              & ? [Vvar__2___24Anonymous__103504] :
                  ( cCoq_2emicromega_2eRingMicromega_2ePsatz___24t(Vvar__0__C__103496,Vvar__2___24Anonymous__103504)
                  & VX103497 = cCoq_2emicromega_2eRingMicromega_2ePsatzMulC___24a3(Vvar__0__C__103496,Vvar__1___24Anonymous__103503,Vvar__2___24Anonymous__103504) ) )
          | ? [Vvar__1___24Anonymous__103506] :
              ( cCoq_2emicromega_2eRingMicromega_2ePsatz___24t(Vvar__0__C__103496,Vvar__1___24Anonymous__103506)
              & ? [Vvar__2___24Anonymous__103507] :
                  ( cCoq_2emicromega_2eRingMicromega_2ePsatz___24t(Vvar__0__C__103496,Vvar__2___24Anonymous__103507)
                  & VX103497 = cCoq_2emicromega_2eRingMicromega_2ePsatzMulE___24a3(Vvar__0__C__103496,Vvar__1___24Anonymous__103506,Vvar__2___24Anonymous__103507) ) )
          | ? [Vvar__1___24Anonymous__103509] :
              ( cCoq_2emicromega_2eRingMicromega_2ePsatz___24t(Vvar__0__C__103496,Vvar__1___24Anonymous__103509)
              & ? [Vvar__2___24Anonymous__103510] :
                  ( cCoq_2emicromega_2eRingMicromega_2ePsatz___24t(Vvar__0__C__103496,Vvar__2___24Anonymous__103510)
                  & VX103497 = cCoq_2emicromega_2eRingMicromega_2ePsatzAdd___24a3(Vvar__0__C__103496,Vvar__1___24Anonymous__103509,Vvar__2___24Anonymous__103510) ) )
          | ? [Vvar__1___24Anonymous__103512] :
              ( t(Vvar__1___24Anonymous__103512,Vvar__0__C__103496)
              & VX103497 = cCoq_2emicromega_2eRingMicromega_2ePsatzC___24a2(Vvar__0__C__103496,Vvar__1___24Anonymous__103512) )
          | VX103497 = cCoq_2emicromega_2eRingMicromega_2ePsatzZ___24a1(Vvar__0__C__103496) ) ) ) ).

fof('$_inversion_Coq.micromega.RingMicromega.SORaddon',axiom,
    ! [Vvar__0__R__98202,Vvar__1__rO__98203,Vvar__2__rI__98204,Vvar__3__rplus__98205,Vvar__4__rtimes__98210,Vvar__5__rminus__98215,Vvar__6__ropp__98220,Vvar__7__req__98223,Vvar__8__rle__98228,Vvar__9__C__98233,Vvar__10__cO__98234,Vvar__11__cI__98235,Vvar__12__cplus__98236,Vvar__13__ctimes__98241,Vvar__14__cminus__98246,Vvar__15__copp__98251,Vvar__16__ceqb__98254,Vvar__17__cleb__98259,Vvar__18__phi__98264,Vvar__19__E__98267,Vvar__20__pow__phi__98268,Vvar__21__rpow__98271] :
      ( cType___24t(Vvar__0__R__98202)
     => ( t(Vvar__1__rO__98203,Vvar__0__R__98202)
       => ( t(Vvar__2__rI__98204,Vvar__0__R__98202)
         => ( c_24__type__98735___24t(Vvar__0__R__98202,Vvar__1__rO__98203,Vvar__2__rI__98204,Vvar__3__rplus__98205,Vvar__4__rtimes__98210,Vvar__5__rminus__98215,Vvar__6__ropp__98220,Vvar__7__req__98223,Vvar__8__rle__98228,Vvar__9__C__98233,Vvar__10__cO__98234,Vvar__11__cI__98235,Vvar__12__cplus__98236,Vvar__13__ctimes__98241,Vvar__14__cminus__98246,Vvar__15__copp__98251,Vvar__16__ceqb__98254,Vvar__17__cleb__98259,Vvar__18__phi__98264,Vvar__19__E__98267,Vvar__20__pow__phi__98268,Vvar__21__rpow__98271,Vvar__3__rplus__98205)
           => ( c_24__type__99081___24t(Vvar__0__R__98202,Vvar__1__rO__98203,Vvar__2__rI__98204,Vvar__3__rplus__98205,Vvar__4__rtimes__98210,Vvar__5__rminus__98215,Vvar__6__ropp__98220,Vvar__7__req__98223,Vvar__8__rle__98228,Vvar__9__C__98233,Vvar__10__cO__98234,Vvar__11__cI__98235,Vvar__12__cplus__98236,Vvar__13__ctimes__98241,Vvar__14__cminus__98246,Vvar__15__copp__98251,Vvar__16__ceqb__98254,Vvar__17__cleb__98259,Vvar__18__phi__98264,Vvar__19__E__98267,Vvar__20__pow__phi__98268,Vvar__21__rpow__98271,Vvar__4__rtimes__98210)
             => ( c_24__type__99427___24t(Vvar__0__R__98202,Vvar__1__rO__98203,Vvar__2__rI__98204,Vvar__3__rplus__98205,Vvar__4__rtimes__98210,Vvar__5__rminus__98215,Vvar__6__ropp__98220,Vvar__7__req__98223,Vvar__8__rle__98228,Vvar__9__C__98233,Vvar__10__cO__98234,Vvar__11__cI__98235,Vvar__12__cplus__98236,Vvar__13__ctimes__98241,Vvar__14__cminus__98246,Vvar__15__copp__98251,Vvar__16__ceqb__98254,Vvar__17__cleb__98259,Vvar__18__phi__98264,Vvar__19__E__98267,Vvar__20__pow__phi__98268,Vvar__21__rpow__98271,Vvar__5__rminus__98215)
               => ( c_24__type__99750___24t(Vvar__0__R__98202,Vvar__1__rO__98203,Vvar__2__rI__98204,Vvar__3__rplus__98205,Vvar__4__rtimes__98210,Vvar__5__rminus__98215,Vvar__6__ropp__98220,Vvar__7__req__98223,Vvar__8__rle__98228,Vvar__9__C__98233,Vvar__10__cO__98234,Vvar__11__cI__98235,Vvar__12__cplus__98236,Vvar__13__ctimes__98241,Vvar__14__cminus__98246,Vvar__15__copp__98251,Vvar__16__ceqb__98254,Vvar__17__cleb__98259,Vvar__18__phi__98264,Vvar__19__E__98267,Vvar__20__pow__phi__98268,Vvar__21__rpow__98271,Vvar__6__ropp__98220)
                 => ( c_24__type__100096___24t(Vvar__0__R__98202,Vvar__1__rO__98203,Vvar__2__rI__98204,Vvar__3__rplus__98205,Vvar__4__rtimes__98210,Vvar__5__rminus__98215,Vvar__6__ropp__98220,Vvar__7__req__98223,Vvar__8__rle__98228,Vvar__9__C__98233,Vvar__10__cO__98234,Vvar__11__cI__98235,Vvar__12__cplus__98236,Vvar__13__ctimes__98241,Vvar__14__cminus__98246,Vvar__15__copp__98251,Vvar__16__ceqb__98254,Vvar__17__cleb__98259,Vvar__18__phi__98264,Vvar__19__E__98267,Vvar__20__pow__phi__98268,Vvar__21__rpow__98271,Vvar__7__req__98223)
                   => ( c_24__type__100442___24t(Vvar__0__R__98202,Vvar__1__rO__98203,Vvar__2__rI__98204,Vvar__3__rplus__98205,Vvar__4__rtimes__98210,Vvar__5__rminus__98215,Vvar__6__ropp__98220,Vvar__7__req__98223,Vvar__8__rle__98228,Vvar__9__C__98233,Vvar__10__cO__98234,Vvar__11__cI__98235,Vvar__12__cplus__98236,Vvar__13__ctimes__98241,Vvar__14__cminus__98246,Vvar__15__copp__98251,Vvar__16__ceqb__98254,Vvar__17__cleb__98259,Vvar__18__phi__98264,Vvar__19__E__98267,Vvar__20__pow__phi__98268,Vvar__21__rpow__98271,Vvar__8__rle__98228)
                     => ( cType___24t(Vvar__9__C__98233)
                       => ( t(Vvar__10__cO__98234,Vvar__9__C__98233)
                         => ( t(Vvar__11__cI__98235,Vvar__9__C__98233)
                           => ( c_24__type__100788___24t(Vvar__0__R__98202,Vvar__1__rO__98203,Vvar__2__rI__98204,Vvar__3__rplus__98205,Vvar__4__rtimes__98210,Vvar__5__rminus__98215,Vvar__6__ropp__98220,Vvar__7__req__98223,Vvar__8__rle__98228,Vvar__9__C__98233,Vvar__10__cO__98234,Vvar__11__cI__98235,Vvar__12__cplus__98236,Vvar__13__ctimes__98241,Vvar__14__cminus__98246,Vvar__15__copp__98251,Vvar__16__ceqb__98254,Vvar__17__cleb__98259,Vvar__18__phi__98264,Vvar__19__E__98267,Vvar__20__pow__phi__98268,Vvar__21__rpow__98271,Vvar__12__cplus__98236)
                             => ( c_24__type__101134___24t(Vvar__0__R__98202,Vvar__1__rO__98203,Vvar__2__rI__98204,Vvar__3__rplus__98205,Vvar__4__rtimes__98210,Vvar__5__rminus__98215,Vvar__6__ropp__98220,Vvar__7__req__98223,Vvar__8__rle__98228,Vvar__9__C__98233,Vvar__10__cO__98234,Vvar__11__cI__98235,Vvar__12__cplus__98236,Vvar__13__ctimes__98241,Vvar__14__cminus__98246,Vvar__15__copp__98251,Vvar__16__ceqb__98254,Vvar__17__cleb__98259,Vvar__18__phi__98264,Vvar__19__E__98267,Vvar__20__pow__phi__98268,Vvar__21__rpow__98271,Vvar__13__ctimes__98241)
                               => ( c_24__type__101480___24t(Vvar__0__R__98202,Vvar__1__rO__98203,Vvar__2__rI__98204,Vvar__3__rplus__98205,Vvar__4__rtimes__98210,Vvar__5__rminus__98215,Vvar__6__ropp__98220,Vvar__7__req__98223,Vvar__8__rle__98228,Vvar__9__C__98233,Vvar__10__cO__98234,Vvar__11__cI__98235,Vvar__12__cplus__98236,Vvar__13__ctimes__98241,Vvar__14__cminus__98246,Vvar__15__copp__98251,Vvar__16__ceqb__98254,Vvar__17__cleb__98259,Vvar__18__phi__98264,Vvar__19__E__98267,Vvar__20__pow__phi__98268,Vvar__21__rpow__98271,Vvar__14__cminus__98246)
                                 => ( c_24__type__101803___24t(Vvar__0__R__98202,Vvar__1__rO__98203,Vvar__2__rI__98204,Vvar__3__rplus__98205,Vvar__4__rtimes__98210,Vvar__5__rminus__98215,Vvar__6__ropp__98220,Vvar__7__req__98223,Vvar__8__rle__98228,Vvar__9__C__98233,Vvar__10__cO__98234,Vvar__11__cI__98235,Vvar__12__cplus__98236,Vvar__13__ctimes__98241,Vvar__14__cminus__98246,Vvar__15__copp__98251,Vvar__16__ceqb__98254,Vvar__17__cleb__98259,Vvar__18__phi__98264,Vvar__19__E__98267,Vvar__20__pow__phi__98268,Vvar__21__rpow__98271,Vvar__15__copp__98251)
                                   => ( c_24__type__102149___24t(Vvar__0__R__98202,Vvar__1__rO__98203,Vvar__2__rI__98204,Vvar__3__rplus__98205,Vvar__4__rtimes__98210,Vvar__5__rminus__98215,Vvar__6__ropp__98220,Vvar__7__req__98223,Vvar__8__rle__98228,Vvar__9__C__98233,Vvar__10__cO__98234,Vvar__11__cI__98235,Vvar__12__cplus__98236,Vvar__13__ctimes__98241,Vvar__14__cminus__98246,Vvar__15__copp__98251,Vvar__16__ceqb__98254,Vvar__17__cleb__98259,Vvar__18__phi__98264,Vvar__19__E__98267,Vvar__20__pow__phi__98268,Vvar__21__rpow__98271,Vvar__16__ceqb__98254)
                                     => ( c_24__type__102495___24t(Vvar__0__R__98202,Vvar__1__rO__98203,Vvar__2__rI__98204,Vvar__3__rplus__98205,Vvar__4__rtimes__98210,Vvar__5__rminus__98215,Vvar__6__ropp__98220,Vvar__7__req__98223,Vvar__8__rle__98228,Vvar__9__C__98233,Vvar__10__cO__98234,Vvar__11__cI__98235,Vvar__12__cplus__98236,Vvar__13__ctimes__98241,Vvar__14__cminus__98246,Vvar__15__copp__98251,Vvar__16__ceqb__98254,Vvar__17__cleb__98259,Vvar__18__phi__98264,Vvar__19__E__98267,Vvar__20__pow__phi__98268,Vvar__21__rpow__98271,Vvar__17__cleb__98259)
                                       => ( c_24__type__102818___24t(Vvar__0__R__98202,Vvar__1__rO__98203,Vvar__2__rI__98204,Vvar__3__rplus__98205,Vvar__4__rtimes__98210,Vvar__5__rminus__98215,Vvar__6__ropp__98220,Vvar__7__req__98223,Vvar__8__rle__98228,Vvar__9__C__98233,Vvar__10__cO__98234,Vvar__11__cI__98235,Vvar__12__cplus__98236,Vvar__13__ctimes__98241,Vvar__14__cminus__98246,Vvar__15__copp__98251,Vvar__16__ceqb__98254,Vvar__17__cleb__98259,Vvar__18__phi__98264,Vvar__19__E__98267,Vvar__20__pow__phi__98268,Vvar__21__rpow__98271,Vvar__18__phi__98264)
                                         => ( cType___24t(Vvar__19__E__98267)
                                           => ( c_24__type__103141___24t(Vvar__0__R__98202,Vvar__1__rO__98203,Vvar__2__rI__98204,Vvar__3__rplus__98205,Vvar__4__rtimes__98210,Vvar__5__rminus__98215,Vvar__6__ropp__98220,Vvar__7__req__98223,Vvar__8__rle__98228,Vvar__9__C__98233,Vvar__10__cO__98234,Vvar__11__cI__98235,Vvar__12__cplus__98236,Vvar__13__ctimes__98241,Vvar__14__cminus__98246,Vvar__15__copp__98251,Vvar__16__ceqb__98254,Vvar__17__cleb__98259,Vvar__18__phi__98264,Vvar__19__E__98267,Vvar__20__pow__phi__98268,Vvar__21__rpow__98271,Vvar__20__pow__phi__98268)
                                             => ( c_24__type__103487___24t(Vvar__0__R__98202,Vvar__1__rO__98203,Vvar__2__rI__98204,Vvar__3__rplus__98205,Vvar__4__rtimes__98210,Vvar__5__rminus__98215,Vvar__6__ropp__98220,Vvar__7__req__98223,Vvar__8__rle__98228,Vvar__9__C__98233,Vvar__10__cO__98234,Vvar__11__cI__98235,Vvar__12__cplus__98236,Vvar__13__ctimes__98241,Vvar__14__cminus__98246,Vvar__15__copp__98251,Vvar__16__ceqb__98254,Vvar__17__cleb__98259,Vvar__18__phi__98264,Vvar__19__E__98267,Vvar__20__pow__phi__98268,Vvar__21__rpow__98271,Vvar__21__rpow__98271)
                                               => ( cCoq_2emicromega_2eRingMicromega_2eSORaddon___24a22(Vvar__0__R__98202,Vvar__1__rO__98203,Vvar__2__rI__98204,Vvar__3__rplus__98205,Vvar__4__rtimes__98210,Vvar__5__rminus__98215,Vvar__6__ropp__98220,Vvar__7__req__98223,Vvar__8__rle__98228,Vvar__9__C__98233,Vvar__10__cO__98234,Vvar__11__cI__98235,Vvar__12__cplus__98236,Vvar__13__ctimes__98241,Vvar__14__cminus__98246,Vvar__15__copp__98251,Vvar__16__ceqb__98254,Vvar__17__cleb__98259,Vvar__18__phi__98264,Vvar__19__E__98267,Vvar__20__pow__phi__98268,Vvar__21__rpow__98271)
                                                 => ( cCoq_2esetoid__ring_2eRing__theory_2ering__morph___24a17(Vvar__0__R__98202,Vvar__1__rO__98203,Vvar__2__rI__98204,Vvar__3__rplus__98205,Vvar__4__rtimes__98210,Vvar__5__rminus__98215,Vvar__6__ropp__98220,Vvar__7__req__98223,Vvar__9__C__98233,Vvar__10__cO__98234,Vvar__11__cI__98235,Vvar__12__cplus__98236,Vvar__13__ctimes__98241,Vvar__14__cminus__98246,Vvar__15__copp__98251,Vvar__16__ceqb__98254,Vvar__18__phi__98264)
                                                    & cCoq_2esetoid__ring_2eRing__theory_2epower__theory___24a7(Vvar__0__R__98202,Vvar__2__rI__98204,Vvar__4__rtimes__98210,Vvar__7__req__98223,Vvar__19__E__98267,Vvar__20__pow__phi__98268,Vvar__21__rpow__98271)
                                                    & ! [Vvar__var__var__var__var__var__24__x__98354__98357__98367__98370__98373__98376] :
                                                        ( t(Vvar__var__var__var__var__var__24__x__98354__98357__98367__98370__98373__98376,Vvar__9__C__98233)
                                                       => ! [Vvar__var__var__var__var__var__25__y__98355__98358__98368__98371__98374__98377] :
                                                            ( t(Vvar__var__var__var__var__var__25__y__98355__98358__98368__98371__98374__98377,Vvar__9__C__98233)
                                                           => ( happ(happ(Vvar__16__ceqb__98254,Vvar__var__var__var__var__var__24__x__98354__98357__98367__98370__98373__98376),Vvar__var__var__var__var__var__25__y__98355__98358__98368__98371__98374__98377) = cCoq_2eInit_2eDatatypes_2efalse
                                                             => ~ p(happ(happ(Vvar__7__req__98223,happ(Vvar__18__phi__98264,Vvar__var__var__var__var__var__24__x__98354__98357__98367__98370__98373__98376)),happ(Vvar__18__phi__98264,Vvar__var__var__var__var__var__25__y__98355__98358__98368__98371__98374__98377))) ) ) )
                                                    & ! [Vvar__var__var__var__var__var__25__x__98361__98364__98379__98382__98385__98388] :
                                                        ( t(Vvar__var__var__var__var__var__25__x__98361__98364__98379__98382__98385__98388,Vvar__9__C__98233)
                                                       => ! [Vvar__var__var__var__var__var__26__y__98362__98365__98380__98383__98386__98389] :
                                                            ( t(Vvar__var__var__var__var__var__26__y__98362__98365__98380__98383__98386__98389,Vvar__9__C__98233)
                                                           => ( happ(happ(Vvar__17__cleb__98259,Vvar__var__var__var__var__var__25__x__98361__98364__98379__98382__98385__98388),Vvar__var__var__var__var__var__26__y__98362__98365__98380__98383__98386__98389) = cCoq_2eInit_2eDatatypes_2etrue
                                                             => p(happ(happ(Vvar__8__rle__98228,happ(Vvar__18__phi__98264,Vvar__var__var__var__var__var__25__x__98361__98364__98379__98382__98385__98388)),happ(Vvar__18__phi__98264,Vvar__var__var__var__var__var__26__y__98362__98365__98380__98383__98386__98389))) ) ) )
                                                    & p(c_24True) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.micromega.Tauto.GFormula',axiom,
    ! [Vvar__0__TA__91006,Vvar__1__TX__91007,Vvar__2__AA__91008,Vvar__3__AF__91009,VX91010] :
      ( cType___24t(Vvar__0__TA__91006)
     => ( cType___24t(Vvar__1__TX__91007)
       => ( cType___24t(Vvar__2__AA__91008)
         => ( cType___24t(Vvar__3__AF__91009)
           => ( cCoq_2emicromega_2eTauto_2eGFormula___24t(Vvar__0__TA__91006,Vvar__1__TX__91007,Vvar__2__AA__91008,Vvar__3__AF__91009,VX91010)
             => ( VX91010 = cCoq_2emicromega_2eTauto_2eTT___24a4(Vvar__0__TA__91006,Vvar__1__TX__91007,Vvar__2__AA__91008,Vvar__3__AF__91009)
                | VX91010 = cCoq_2emicromega_2eTauto_2eFF___24a4(Vvar__0__TA__91006,Vvar__1__TX__91007,Vvar__2__AA__91008,Vvar__3__AF__91009)
                | ? [Vvar__4___24Anonymous__91023] :
                    ( t(Vvar__4___24Anonymous__91023,Vvar__1__TX__91007)
                    & VX91010 = cCoq_2emicromega_2eTauto_2eX___24a5(Vvar__0__TA__91006,Vvar__1__TX__91007,Vvar__2__AA__91008,Vvar__3__AF__91009,Vvar__4___24Anonymous__91023) )
                | ? [Vvar__4___24Anonymous__91028] :
                    ( t(Vvar__4___24Anonymous__91028,Vvar__0__TA__91006)
                    & ? [Vvar__5___24Anonymous__91029] :
                        ( t(Vvar__5___24Anonymous__91029,Vvar__2__AA__91008)
                        & VX91010 = cCoq_2emicromega_2eTauto_2eA___24a6(Vvar__0__TA__91006,Vvar__1__TX__91007,Vvar__2__AA__91008,Vvar__3__AF__91009,Vvar__4___24Anonymous__91028,Vvar__5___24Anonymous__91029) ) )
                | ? [Vvar__4___24Anonymous__91034] :
                    ( cCoq_2emicromega_2eTauto_2eGFormula___24t(Vvar__0__TA__91006,Vvar__1__TX__91007,Vvar__2__AA__91008,Vvar__3__AF__91009,Vvar__4___24Anonymous__91034)
                    & ? [Vvar__5___24Anonymous__91035] :
                        ( cCoq_2emicromega_2eTauto_2eGFormula___24t(Vvar__0__TA__91006,Vvar__1__TX__91007,Vvar__2__AA__91008,Vvar__3__AF__91009,Vvar__5___24Anonymous__91035)
                        & VX91010 = cCoq_2emicromega_2eTauto_2eCj___24a6(Vvar__0__TA__91006,Vvar__1__TX__91007,Vvar__2__AA__91008,Vvar__3__AF__91009,Vvar__4___24Anonymous__91034,Vvar__5___24Anonymous__91035) ) )
                | ? [Vvar__4___24Anonymous__91040] :
                    ( cCoq_2emicromega_2eTauto_2eGFormula___24t(Vvar__0__TA__91006,Vvar__1__TX__91007,Vvar__2__AA__91008,Vvar__3__AF__91009,Vvar__4___24Anonymous__91040)
                    & ? [Vvar__5___24Anonymous__91041] :
                        ( cCoq_2emicromega_2eTauto_2eGFormula___24t(Vvar__0__TA__91006,Vvar__1__TX__91007,Vvar__2__AA__91008,Vvar__3__AF__91009,Vvar__5___24Anonymous__91041)
                        & VX91010 = cCoq_2emicromega_2eTauto_2eD___24a6(Vvar__0__TA__91006,Vvar__1__TX__91007,Vvar__2__AA__91008,Vvar__3__AF__91009,Vvar__4___24Anonymous__91040,Vvar__5___24Anonymous__91041) ) )
                | ? [Vvar__4___24Anonymous__91046] :
                    ( cCoq_2emicromega_2eTauto_2eGFormula___24t(Vvar__0__TA__91006,Vvar__1__TX__91007,Vvar__2__AA__91008,Vvar__3__AF__91009,Vvar__4___24Anonymous__91046)
                    & VX91010 = cCoq_2emicromega_2eTauto_2eN___24a5(Vvar__0__TA__91006,Vvar__1__TX__91007,Vvar__2__AA__91008,Vvar__3__AF__91009,Vvar__4___24Anonymous__91046) )
                | ? [Vvar__4___24Anonymous__91051] :
                    ( cCoq_2emicromega_2eTauto_2eGFormula___24t(Vvar__0__TA__91006,Vvar__1__TX__91007,Vvar__2__AA__91008,Vvar__3__AF__91009,Vvar__4___24Anonymous__91051)
                    & ? [Vvar__5___24Anonymous__91052] :
                        ( cCoq_2eInit_2eDatatypes_2eoption___24t(Vvar__3__AF__91009,Vvar__5___24Anonymous__91052)
                        & ? [Vvar__6___24Anonymous__91053] :
                            ( cCoq_2emicromega_2eTauto_2eGFormula___24t(Vvar__0__TA__91006,Vvar__1__TX__91007,Vvar__2__AA__91008,Vvar__3__AF__91009,Vvar__6___24Anonymous__91053)
                            & VX91010 = cCoq_2emicromega_2eTauto_2eI___24a7(Vvar__0__TA__91006,Vvar__1__TX__91007,Vvar__2__AA__91008,Vvar__3__AF__91009,Vvar__4___24Anonymous__91051,Vvar__5___24Anonymous__91052,Vvar__6___24Anonymous__91053) ) ) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.micromega.VarMap.t',axiom,
    ! [Vvar__0__A__105293,VX105294] :
      ( cType___24t(Vvar__0__A__105293)
     => ( cCoq_2emicromega_2eVarMap_2et___24t(Vvar__0__A__105293,VX105294)
       => ( VX105294 = cCoq_2emicromega_2eVarMap_2eEmpty___24a1(Vvar__0__A__105293)
          | ? [Vvar__1___24Anonymous__105297] :
              ( t(Vvar__1___24Anonymous__105297,Vvar__0__A__105293)
              & VX105294 = cCoq_2emicromega_2eVarMap_2eElt___24a2(Vvar__0__A__105293,Vvar__1___24Anonymous__105297) )
          | ? [Vvar__1___24Anonymous__105299] :
              ( cCoq_2emicromega_2eVarMap_2et___24t(Vvar__0__A__105293,Vvar__1___24Anonymous__105299)
              & ? [Vvar__2___24Anonymous__105300] :
                  ( t(Vvar__2___24Anonymous__105300,Vvar__0__A__105293)
                  & ? [Vvar__3___24Anonymous__105301] :
                      ( cCoq_2emicromega_2eVarMap_2et___24t(Vvar__0__A__105293,Vvar__3___24Anonymous__105301)
                      & VX105294 = cCoq_2emicromega_2eVarMap_2eBranch___24a4(Vvar__0__A__105293,Vvar__1___24Anonymous__105299,Vvar__2___24Anonymous__105300,Vvar__3___24Anonymous__105301) ) ) ) ) ) ) ).

fof('$_inversion_Coq.micromega.ZMicromega.Vars.Facts.MP.Dec.FSetDecideAuxiliary.FSet_Prop',axiom,
    ! [Vvar__0___24Anonymous__105534] :
      ( cProp___24t(Vvar__0___24Anonymous__105534)
     => ( cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__Prop___24a1(Vvar__0___24Anonymous__105534)
       => ( ? [Vvar__0__P__105536] :
              ( cProp___24t(Vvar__0__P__105536)
              & cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__elt__Prop___24a1(Vvar__0__P__105536)
              & Vvar__0___24Anonymous__105534 = Vvar__0__P__105536 )
          | ? [Vvar__0__s__105538] :
              ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(Vvar__0__s__105538)
              & Vvar__0___24Anonymous__105534 = c_24__prop__105547___24a2(Vvar__0___24Anonymous__105534,Vvar__0__s__105538) )
          | ? [Vvar__0__s1__105540] :
              ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(Vvar__0__s1__105540)
              & ? [Vvar__1__s2__105541] :
                  ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(Vvar__1__s2__105541)
                  & Vvar__0___24Anonymous__105534 = c_24__prop__105548___24a3(Vvar__0___24Anonymous__105534,Vvar__0__s1__105540,Vvar__1__s2__105541) ) )
          | ? [Vvar__0__s1__105544] :
              ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(Vvar__0__s1__105544)
              & ? [Vvar__1__s2__105545] :
                  ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(Vvar__1__s2__105545)
                  & Vvar__0___24Anonymous__105534 = c_24__prop__105549___24a3(Vvar__0___24Anonymous__105534,Vvar__0__s1__105544,Vvar__1__s2__105545) ) ) ) ) ) ).

fof('$_inversion_Coq.micromega.ZMicromega.Vars.Facts.MP.Dec.FSetDecideAuxiliary.FSet_elt_Prop',axiom,
    ! [Vvar__0___24Anonymous__105503] :
      ( cProp___24t(Vvar__0___24Anonymous__105503)
     => ( cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__elt__Prop___24a1(Vvar__0___24Anonymous__105503)
       => ( ? [Vvar__0__S__105505] :
              ( cType___24t(Vvar__0__S__105505)
              & ? [Vvar__1__x__105506] :
                  ( t(Vvar__1__x__105506,Vvar__0__S__105505)
                  & ? [Vvar__2__y__105507] :
                      ( t(Vvar__2__y__105507,Vvar__0__S__105505)
                      & Vvar__0___24Anonymous__105503 = c_24__prop__105527___24a4(Vvar__0___24Anonymous__105503,Vvar__0__S__105505,Vvar__1__x__105506,Vvar__2__y__105507) ) ) )
          | ? [Vvar__0__x__105508] :
              ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0__x__105508)
              & ? [Vvar__1__y__105509] :
                  ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1__y__105509)
                  & Vvar__0___24Anonymous__105503 = c_24__prop__105528___24a3(Vvar__0___24Anonymous__105503,Vvar__0__x__105508,Vvar__1__y__105509) ) )
          | ? [Vvar__0__x__105510] :
              ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(Vvar__0__x__105510)
              & ? [Vvar__1__s__105511] :
                  ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(Vvar__1__s__105511)
                  & Vvar__0___24Anonymous__105503 = c_24__prop__105529___24a3(Vvar__0___24Anonymous__105503,Vvar__0__x__105510,Vvar__1__s__105511) ) )
          | Vvar__0___24Anonymous__105503 = c_24True
          | Vvar__0___24Anonymous__105503 = c_24False
          | ? [Vvar__0__P__105512] :
              ( cProp___24t(Vvar__0__P__105512)
              & ? [Vvar__1__Q__105513] :
                  ( cProp___24t(Vvar__1__Q__105513)
                  & cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__elt__Prop___24a1(Vvar__0__P__105512)
                  & cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__elt__Prop___24a1(Vvar__1__Q__105513)
                  & Vvar__0___24Anonymous__105503 = c_24__prop__105530___24a3(Vvar__0___24Anonymous__105503,Vvar__0__P__105512,Vvar__1__Q__105513) ) )
          | ? [Vvar__0__P__105516] :
              ( cProp___24t(Vvar__0__P__105516)
              & ? [Vvar__1__Q__105517] :
                  ( cProp___24t(Vvar__1__Q__105517)
                  & cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__elt__Prop___24a1(Vvar__0__P__105516)
                  & cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__elt__Prop___24a1(Vvar__1__Q__105517)
                  & Vvar__0___24Anonymous__105503 = c_24__prop__105531___24a3(Vvar__0___24Anonymous__105503,Vvar__0__P__105516,Vvar__1__Q__105517) ) )
          | ? [Vvar__0__P__105520] :
              ( cProp___24t(Vvar__0__P__105520)
              & ? [Vvar__1__Q__105521] :
                  ( cProp___24t(Vvar__1__Q__105521)
                  & cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__elt__Prop___24a1(Vvar__0__P__105520)
                  & cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__elt__Prop___24a1(Vvar__1__Q__105521)
                  & Vvar__0___24Anonymous__105503 = c_24__prop__105532___24a3(Vvar__0___24Anonymous__105503,Vvar__0__P__105520,Vvar__1__Q__105521) ) )
          | ? [Vvar__0__P__105525] :
              ( cProp___24t(Vvar__0__P__105525)
              & cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__elt__Prop___24a1(Vvar__0__P__105525)
              & Vvar__0___24Anonymous__105503 = c_24__prop__105533___24a2(Vvar__0___24Anonymous__105503,Vvar__0__P__105525) ) ) ) ) ).

fof('$_inversion_Coq.micromega.ZMicromega.ZArithProof',axiom,
    ! [VX92849] :
      ( cCoq_2emicromega_2eZMicromega_2eZArithProof___24t(VX92849)
     => ( VX92849 = cCoq_2emicromega_2eZMicromega_2eDoneProof
        | ? [Vvar__0___24Anonymous__92850] :
            ( cCoq_2emicromega_2eZMicromega_2eZWitness___24t(Vvar__0___24Anonymous__92850)
            & ? [Vvar__1___24Anonymous__92851] :
                ( cCoq_2emicromega_2eZMicromega_2eZArithProof___24t(Vvar__1___24Anonymous__92851)
                & VX92849 = cCoq_2emicromega_2eZMicromega_2eRatProof___24a2(Vvar__0___24Anonymous__92850,Vvar__1___24Anonymous__92851) ) )
        | ? [Vvar__0___24Anonymous__92852] :
            ( cCoq_2emicromega_2eZMicromega_2eZWitness___24t(Vvar__0___24Anonymous__92852)
            & ? [Vvar__1___24Anonymous__92853] :
                ( cCoq_2emicromega_2eZMicromega_2eZArithProof___24t(Vvar__1___24Anonymous__92853)
                & VX92849 = cCoq_2emicromega_2eZMicromega_2eCutProof___24a2(Vvar__0___24Anonymous__92852,Vvar__1___24Anonymous__92853) ) )
        | ? [Vvar__0___24Anonymous__92854] :
            ( cCoq_2emicromega_2eZMicromega_2eZWitness___24t(Vvar__0___24Anonymous__92854)
            & ? [Vvar__1___24Anonymous__92855] :
                ( cCoq_2emicromega_2eZMicromega_2eZWitness___24t(Vvar__1___24Anonymous__92855)
                & ? [Vvar__2___24Anonymous__92856] :
                    ( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2emicromega_2eZMicromega_2eZArithProof,Vvar__2___24Anonymous__92856)
                    & VX92849 = cCoq_2emicromega_2eZMicromega_2eEnumProof___24a3(Vvar__0___24Anonymous__92854,Vvar__1___24Anonymous__92855,Vvar__2___24Anonymous__92856) ) ) ) ) ) ).

fof('$_inversion_Coq.micromega.ZMicromega.is_diff_env_elt',axiom,
    ! [Vvar__0__fr__92916,Vvar__1__env__92917,Vvar__2__env_27__92920,Vvar__3__x__92923] :
      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0__fr__92916)
     => ( c_24__type__92944___24t(Vvar__0__fr__92916,Vvar__1__env__92917,Vvar__2__env_27__92920,Vvar__3__x__92923,Vvar__1__env__92917)
       => ( c_24__type__92953___24t(Vvar__0__fr__92916,Vvar__1__env__92917,Vvar__2__env_27__92920,Vvar__3__x__92923,Vvar__2__env_27__92920)
         => ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__3__x__92923)
           => ( cCoq_2emicromega_2eZMicromega_2eis__diff__env__elt___24a4(Vvar__0__fr__92916,Vvar__1__env__92917,Vvar__2__env_27__92920,Vvar__3__x__92923)
             => ( happ(Vvar__1__env__92917,Vvar__3__x__92923) = happ(Vvar__2__env_27__92920,Vvar__3__x__92923)
                & happ(Vvar__1__env__92917,Vvar__3__x__92923) = cCoq_2eZArith_2eBinIntDef_2eZ_2esub___24a2(happ(Vvar__2__env_27__92920,cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(Vvar__0__fr__92916,Vvar__3__x__92923))),happ(Vvar__2__env_27__92920,cCoq_2eNumbers_2eBinNums_2exI___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(Vvar__0__fr__92916,Vvar__3__x__92923))))
                & cCoq_2eZArith_2eBinInt_2eZ_2ege___24a2(happ(Vvar__2__env_27__92920,cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(Vvar__0__fr__92916,Vvar__3__x__92923))),cCoq_2eNumbers_2eBinNums_2eZ0)
                & cCoq_2eZArith_2eBinInt_2eZ_2ege___24a2(happ(Vvar__2__env_27__92920,cCoq_2eNumbers_2eBinNums_2exI___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(Vvar__0__fr__92916,Vvar__3__x__92923))),cCoq_2eNumbers_2eBinNums_2eZ0)
                & p(c_24True) ) ) ) ) ) ) ).

fof('$_inversion_Coq.setoid_ring.Field_theory.FExpr',axiom,
    ! [Vvar__0__C__95219,VX95220] :
      ( cType___24t(Vvar__0__C__95219)
     => ( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__95219,VX95220)
       => ( VX95220 = cCoq_2esetoid__ring_2eField__theory_2eFEO___24a1(Vvar__0__C__95219)
          | VX95220 = cCoq_2esetoid__ring_2eField__theory_2eFEI___24a1(Vvar__0__C__95219)
          | ? [Vvar__1___24Anonymous__95224] :
              ( t(Vvar__1___24Anonymous__95224,Vvar__0__C__95219)
              & VX95220 = cCoq_2esetoid__ring_2eField__theory_2eFEc___24a2(Vvar__0__C__95219,Vvar__1___24Anonymous__95224) )
          | ? [Vvar__1___24Anonymous__95226] :
              ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__95226)
              & VX95220 = cCoq_2esetoid__ring_2eField__theory_2eFEX___24a2(Vvar__0__C__95219,Vvar__1___24Anonymous__95226) )
          | ? [Vvar__1___24Anonymous__95228] :
              ( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__95219,Vvar__1___24Anonymous__95228)
              & ? [Vvar__2___24Anonymous__95229] :
                  ( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__95219,Vvar__2___24Anonymous__95229)
                  & VX95220 = cCoq_2esetoid__ring_2eField__theory_2eFEadd___24a3(Vvar__0__C__95219,Vvar__1___24Anonymous__95228,Vvar__2___24Anonymous__95229) ) )
          | ? [Vvar__1___24Anonymous__95231] :
              ( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__95219,Vvar__1___24Anonymous__95231)
              & ? [Vvar__2___24Anonymous__95232] :
                  ( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__95219,Vvar__2___24Anonymous__95232)
                  & VX95220 = cCoq_2esetoid__ring_2eField__theory_2eFEsub___24a3(Vvar__0__C__95219,Vvar__1___24Anonymous__95231,Vvar__2___24Anonymous__95232) ) )
          | ? [Vvar__1___24Anonymous__95234] :
              ( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__95219,Vvar__1___24Anonymous__95234)
              & ? [Vvar__2___24Anonymous__95235] :
                  ( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__95219,Vvar__2___24Anonymous__95235)
                  & VX95220 = cCoq_2esetoid__ring_2eField__theory_2eFEmul___24a3(Vvar__0__C__95219,Vvar__1___24Anonymous__95234,Vvar__2___24Anonymous__95235) ) )
          | ? [Vvar__1___24Anonymous__95237] :
              ( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__95219,Vvar__1___24Anonymous__95237)
              & VX95220 = cCoq_2esetoid__ring_2eField__theory_2eFEopp___24a2(Vvar__0__C__95219,Vvar__1___24Anonymous__95237) )
          | ? [Vvar__1___24Anonymous__95239] :
              ( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__95219,Vvar__1___24Anonymous__95239)
              & VX95220 = cCoq_2esetoid__ring_2eField__theory_2eFEinv___24a2(Vvar__0__C__95219,Vvar__1___24Anonymous__95239) )
          | ? [Vvar__1___24Anonymous__95241] :
              ( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__95219,Vvar__1___24Anonymous__95241)
              & ? [Vvar__2___24Anonymous__95242] :
                  ( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__95219,Vvar__2___24Anonymous__95242)
                  & VX95220 = cCoq_2esetoid__ring_2eField__theory_2eFEdiv___24a3(Vvar__0__C__95219,Vvar__1___24Anonymous__95241,Vvar__2___24Anonymous__95242) ) )
          | ? [Vvar__1___24Anonymous__95244] :
              ( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__95219,Vvar__1___24Anonymous__95244)
              & ? [Vvar__2___24Anonymous__95245] :
                  ( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__2___24Anonymous__95245)
                  & VX95220 = cCoq_2esetoid__ring_2eField__theory_2eFEpow___24a3(Vvar__0__C__95219,Vvar__1___24Anonymous__95244,Vvar__2___24Anonymous__95245) ) ) ) ) ) ).

fof('$_inversion_Coq.setoid_ring.Field_theory.almost_field_theory',axiom,
    ! [Vvar__0__R__94483,Vvar__1__rO__94484,Vvar__2__rI__94485,Vvar__3__radd__94486,Vvar__4__rmul__94491,Vvar__5__rsub__94496,Vvar__6__ropp__94501,Vvar__7__rdiv__94504,Vvar__8__rinv__94509,Vvar__9__req__94512] :
      ( cType___24t(Vvar__0__R__94483)
     => ( t(Vvar__1__rO__94484,Vvar__0__R__94483)
       => ( t(Vvar__2__rI__94485,Vvar__0__R__94483)
         => ( c_24__type__94677___24t(Vvar__0__R__94483,Vvar__1__rO__94484,Vvar__2__rI__94485,Vvar__3__radd__94486,Vvar__4__rmul__94491,Vvar__5__rsub__94496,Vvar__6__ropp__94501,Vvar__7__rdiv__94504,Vvar__8__rinv__94509,Vvar__9__req__94512,Vvar__3__radd__94486)
           => ( c_24__type__94770___24t(Vvar__0__R__94483,Vvar__1__rO__94484,Vvar__2__rI__94485,Vvar__3__radd__94486,Vvar__4__rmul__94491,Vvar__5__rsub__94496,Vvar__6__ropp__94501,Vvar__7__rdiv__94504,Vvar__8__rinv__94509,Vvar__9__req__94512,Vvar__4__rmul__94491)
             => ( c_24__type__94863___24t(Vvar__0__R__94483,Vvar__1__rO__94484,Vvar__2__rI__94485,Vvar__3__radd__94486,Vvar__4__rmul__94491,Vvar__5__rsub__94496,Vvar__6__ropp__94501,Vvar__7__rdiv__94504,Vvar__8__rinv__94509,Vvar__9__req__94512,Vvar__5__rsub__94496)
               => ( c_24__type__94945___24t(Vvar__0__R__94483,Vvar__1__rO__94484,Vvar__2__rI__94485,Vvar__3__radd__94486,Vvar__4__rmul__94491,Vvar__5__rsub__94496,Vvar__6__ropp__94501,Vvar__7__rdiv__94504,Vvar__8__rinv__94509,Vvar__9__req__94512,Vvar__6__ropp__94501)
                 => ( c_24__type__95038___24t(Vvar__0__R__94483,Vvar__1__rO__94484,Vvar__2__rI__94485,Vvar__3__radd__94486,Vvar__4__rmul__94491,Vvar__5__rsub__94496,Vvar__6__ropp__94501,Vvar__7__rdiv__94504,Vvar__8__rinv__94509,Vvar__9__req__94512,Vvar__7__rdiv__94504)
                   => ( c_24__type__95120___24t(Vvar__0__R__94483,Vvar__1__rO__94484,Vvar__2__rI__94485,Vvar__3__radd__94486,Vvar__4__rmul__94491,Vvar__5__rsub__94496,Vvar__6__ropp__94501,Vvar__7__rdiv__94504,Vvar__8__rinv__94509,Vvar__9__req__94512,Vvar__8__rinv__94509)
                     => ( c_24__type__95213___24t(Vvar__0__R__94483,Vvar__1__rO__94484,Vvar__2__rI__94485,Vvar__3__radd__94486,Vvar__4__rmul__94491,Vvar__5__rsub__94496,Vvar__6__ropp__94501,Vvar__7__rdiv__94504,Vvar__8__rinv__94509,Vvar__9__req__94512,Vvar__9__req__94512)
                       => ( cCoq_2esetoid__ring_2eField__theory_2ealmost__field__theory___24a10(Vvar__0__R__94483,Vvar__1__rO__94484,Vvar__2__rI__94485,Vvar__3__radd__94486,Vvar__4__rmul__94491,Vvar__5__rsub__94496,Vvar__6__ropp__94501,Vvar__7__rdiv__94504,Vvar__8__rinv__94509,Vvar__9__req__94512)
                         => ( cCoq_2esetoid__ring_2eRing__theory_2ealmost__ring__theory___24a8(Vvar__0__R__94483,Vvar__1__rO__94484,Vvar__2__rI__94485,Vvar__3__radd__94486,Vvar__4__rmul__94491,Vvar__5__rsub__94496,Vvar__6__ropp__94501,Vvar__9__req__94512)
                            & ~ p(happ(happ(Vvar__9__req__94512,Vvar__2__rI__94485),Vvar__1__rO__94484))
                            & ! [Vvar__var__var__var__var__var__var__12__p__94555__94557__94564__94566__94568__94570__94572] :
                                ( t(Vvar__var__var__var__var__var__var__12__p__94555__94557__94564__94566__94568__94570__94572,Vvar__0__R__94483)
                               => ! [Vvar__var__var__var__var__var__var__13__q__94556__94558__94565__94567__94569__94571__94573] :
                                    ( t(Vvar__var__var__var__var__var__var__13__q__94556__94558__94565__94567__94569__94571__94573,Vvar__0__R__94483)
                                   => p(happ(happ(Vvar__9__req__94512,happ(happ(Vvar__7__rdiv__94504,Vvar__var__var__var__var__var__var__12__p__94555__94557__94564__94566__94568__94570__94572),Vvar__var__var__var__var__var__var__13__q__94556__94558__94565__94567__94569__94571__94573)),happ(happ(Vvar__4__rmul__94491,Vvar__var__var__var__var__var__var__12__p__94555__94557__94564__94566__94568__94570__94572),happ(Vvar__8__rinv__94509,Vvar__var__var__var__var__var__var__13__q__94556__94558__94565__94567__94569__94571__94573)))) ) )
                            & ! [Vvar__var__var__var__var__var__var__var__13__p__94560__94562__94574__94576__94578__94580__94582__94584] :
                                ( t(Vvar__var__var__var__var__var__var__var__13__p__94560__94562__94574__94576__94578__94580__94582__94584,Vvar__0__R__94483)
                               => ( ~ p(happ(happ(Vvar__9__req__94512,Vvar__var__var__var__var__var__var__var__13__p__94560__94562__94574__94576__94578__94580__94582__94584),Vvar__1__rO__94484))
                                 => p(happ(happ(Vvar__9__req__94512,happ(happ(Vvar__4__rmul__94491,happ(Vvar__8__rinv__94509,Vvar__var__var__var__var__var__var__var__13__p__94560__94562__94574__94576__94578__94580__94582__94584)),Vvar__var__var__var__var__var__var__var__13__p__94560__94562__94574__94576__94578__94580__94582__94584)),Vvar__2__rI__94485)) ) )
                            & p(c_24True) ) ) ) ) ) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.setoid_ring.Field_theory.field_theory',axiom,
    ! [Vvar__0__R__95577,Vvar__1__rO__95578,Vvar__2__rI__95579,Vvar__3__radd__95580,Vvar__4__rmul__95585,Vvar__5__rsub__95590,Vvar__6__ropp__95595,Vvar__7__rdiv__95598,Vvar__8__rinv__95603,Vvar__9__req__95606] :
      ( cType___24t(Vvar__0__R__95577)
     => ( t(Vvar__1__rO__95578,Vvar__0__R__95577)
       => ( t(Vvar__2__rI__95579,Vvar__0__R__95577)
         => ( c_24__type__95771___24t(Vvar__0__R__95577,Vvar__1__rO__95578,Vvar__2__rI__95579,Vvar__3__radd__95580,Vvar__4__rmul__95585,Vvar__5__rsub__95590,Vvar__6__ropp__95595,Vvar__7__rdiv__95598,Vvar__8__rinv__95603,Vvar__9__req__95606,Vvar__3__radd__95580)
           => ( c_24__type__95864___24t(Vvar__0__R__95577,Vvar__1__rO__95578,Vvar__2__rI__95579,Vvar__3__radd__95580,Vvar__4__rmul__95585,Vvar__5__rsub__95590,Vvar__6__ropp__95595,Vvar__7__rdiv__95598,Vvar__8__rinv__95603,Vvar__9__req__95606,Vvar__4__rmul__95585)
             => ( c_24__type__95957___24t(Vvar__0__R__95577,Vvar__1__rO__95578,Vvar__2__rI__95579,Vvar__3__radd__95580,Vvar__4__rmul__95585,Vvar__5__rsub__95590,Vvar__6__ropp__95595,Vvar__7__rdiv__95598,Vvar__8__rinv__95603,Vvar__9__req__95606,Vvar__5__rsub__95590)
               => ( c_24__type__96039___24t(Vvar__0__R__95577,Vvar__1__rO__95578,Vvar__2__rI__95579,Vvar__3__radd__95580,Vvar__4__rmul__95585,Vvar__5__rsub__95590,Vvar__6__ropp__95595,Vvar__7__rdiv__95598,Vvar__8__rinv__95603,Vvar__9__req__95606,Vvar__6__ropp__95595)
                 => ( c_24__type__96132___24t(Vvar__0__R__95577,Vvar__1__rO__95578,Vvar__2__rI__95579,Vvar__3__radd__95580,Vvar__4__rmul__95585,Vvar__5__rsub__95590,Vvar__6__ropp__95595,Vvar__7__rdiv__95598,Vvar__8__rinv__95603,Vvar__9__req__95606,Vvar__7__rdiv__95598)
                   => ( c_24__type__96214___24t(Vvar__0__R__95577,Vvar__1__rO__95578,Vvar__2__rI__95579,Vvar__3__radd__95580,Vvar__4__rmul__95585,Vvar__5__rsub__95590,Vvar__6__ropp__95595,Vvar__7__rdiv__95598,Vvar__8__rinv__95603,Vvar__9__req__95606,Vvar__8__rinv__95603)
                     => ( c_24__type__96307___24t(Vvar__0__R__95577,Vvar__1__rO__95578,Vvar__2__rI__95579,Vvar__3__radd__95580,Vvar__4__rmul__95585,Vvar__5__rsub__95590,Vvar__6__ropp__95595,Vvar__7__rdiv__95598,Vvar__8__rinv__95603,Vvar__9__req__95606,Vvar__9__req__95606)
                       => ( cCoq_2esetoid__ring_2eField__theory_2efield__theory___24a10(Vvar__0__R__95577,Vvar__1__rO__95578,Vvar__2__rI__95579,Vvar__3__radd__95580,Vvar__4__rmul__95585,Vvar__5__rsub__95590,Vvar__6__ropp__95595,Vvar__7__rdiv__95598,Vvar__8__rinv__95603,Vvar__9__req__95606)
                         => ( cCoq_2esetoid__ring_2eRing__theory_2ering__theory___24a8(Vvar__0__R__95577,Vvar__1__rO__95578,Vvar__2__rI__95579,Vvar__3__radd__95580,Vvar__4__rmul__95585,Vvar__5__rsub__95590,Vvar__6__ropp__95595,Vvar__9__req__95606)
                            & ~ p(happ(happ(Vvar__9__req__95606,Vvar__2__rI__95579),Vvar__1__rO__95578))
                            & ! [Vvar__var__var__var__var__var__var__12__p__95649__95651__95658__95660__95662__95664__95666] :
                                ( t(Vvar__var__var__var__var__var__var__12__p__95649__95651__95658__95660__95662__95664__95666,Vvar__0__R__95577)
                               => ! [Vvar__var__var__var__var__var__var__13__q__95650__95652__95659__95661__95663__95665__95667] :
                                    ( t(Vvar__var__var__var__var__var__var__13__q__95650__95652__95659__95661__95663__95665__95667,Vvar__0__R__95577)
                                   => p(happ(happ(Vvar__9__req__95606,happ(happ(Vvar__7__rdiv__95598,Vvar__var__var__var__var__var__var__12__p__95649__95651__95658__95660__95662__95664__95666),Vvar__var__var__var__var__var__var__13__q__95650__95652__95659__95661__95663__95665__95667)),happ(happ(Vvar__4__rmul__95585,Vvar__var__var__var__var__var__var__12__p__95649__95651__95658__95660__95662__95664__95666),happ(Vvar__8__rinv__95603,Vvar__var__var__var__var__var__var__13__q__95650__95652__95659__95661__95663__95665__95667)))) ) )
                            & ! [Vvar__var__var__var__var__var__var__var__13__p__95654__95656__95668__95670__95672__95674__95676__95678] :
                                ( t(Vvar__var__var__var__var__var__var__var__13__p__95654__95656__95668__95670__95672__95674__95676__95678,Vvar__0__R__95577)
                               => ( ~ p(happ(happ(Vvar__9__req__95606,Vvar__var__var__var__var__var__var__var__13__p__95654__95656__95668__95670__95672__95674__95676__95678),Vvar__1__rO__95578))
                                 => p(happ(happ(Vvar__9__req__95606,happ(happ(Vvar__4__rmul__95585,happ(Vvar__8__rinv__95603,Vvar__var__var__var__var__var__var__var__13__p__95654__95656__95668__95670__95672__95674__95676__95678)),Vvar__var__var__var__var__var__var__var__13__p__95654__95656__95668__95670__95672__95674__95676__95678)),Vvar__2__rI__95579)) ) )
                            & p(c_24True) ) ) ) ) ) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.setoid_ring.Field_theory.linear',axiom,
    ! [Vvar__0__C__95549,VX95550] :
      ( cType___24t(Vvar__0__C__95549)
     => ( cCoq_2esetoid__ring_2eField__theory_2elinear___24t(Vvar__0__C__95549,VX95550)
       => ? [Vvar__1__num__95552] :
            ( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__95549,Vvar__1__num__95552)
            & ? [Vvar__2__denum__95553] :
                ( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__95549,Vvar__2__denum__95553)
                & ? [Vvar__3__condition__95554] :
                    ( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(Vvar__0__C__95549),Vvar__3__condition__95554)
                    & VX95550 = cCoq_2esetoid__ring_2eField__theory_2emk__linear___24a4(Vvar__0__C__95549,Vvar__1__num__95552,Vvar__2__denum__95553,Vvar__3__condition__95554) ) ) ) ) ) ).

fof('$_inversion_Coq.setoid_ring.Field_theory.rsplit',axiom,
    ! [Vvar__0__C__95563,VX95564] :
      ( cType___24t(Vvar__0__C__95563)
     => ( cCoq_2esetoid__ring_2eField__theory_2ersplit___24t(Vvar__0__C__95563,VX95564)
       => ? [Vvar__1__rsplit__left__95566] :
            ( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__95563,Vvar__1__rsplit__left__95566)
            & ? [Vvar__2__rsplit__common__95567] :
                ( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__95563,Vvar__2__rsplit__common__95567)
                & ? [Vvar__3__rsplit__right__95568] :
                    ( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__95563,Vvar__3__rsplit__right__95568)
                    & VX95564 = cCoq_2esetoid__ring_2eField__theory_2emk__rsplit___24a4(Vvar__0__C__95563,Vvar__1__rsplit__left__95566,Vvar__2__rsplit__common__95567,Vvar__3__rsplit__right__95568) ) ) ) ) ) ).

fof('$_inversion_Coq.setoid_ring.Field_theory.semi_field_theory',axiom,
    ! [Vvar__0__R__96313,Vvar__1__rO__96314,Vvar__2__rI__96315,Vvar__3__radd__96316,Vvar__4__rmul__96321,Vvar__5__rdiv__96326,Vvar__6__rinv__96331,Vvar__7__req__96334] :
      ( cType___24t(Vvar__0__R__96313)
     => ( t(Vvar__1__rO__96314,Vvar__0__R__96313)
       => ( t(Vvar__2__rI__96315,Vvar__0__R__96313)
         => ( c_24__type__96461___24t(Vvar__0__R__96313,Vvar__1__rO__96314,Vvar__2__rI__96315,Vvar__3__radd__96316,Vvar__4__rmul__96321,Vvar__5__rdiv__96326,Vvar__6__rinv__96331,Vvar__7__req__96334,Vvar__3__radd__96316)
           => ( c_24__type__96524___24t(Vvar__0__R__96313,Vvar__1__rO__96314,Vvar__2__rI__96315,Vvar__3__radd__96316,Vvar__4__rmul__96321,Vvar__5__rdiv__96326,Vvar__6__rinv__96331,Vvar__7__req__96334,Vvar__4__rmul__96321)
             => ( c_24__type__96587___24t(Vvar__0__R__96313,Vvar__1__rO__96314,Vvar__2__rI__96315,Vvar__3__radd__96316,Vvar__4__rmul__96321,Vvar__5__rdiv__96326,Vvar__6__rinv__96331,Vvar__7__req__96334,Vvar__5__rdiv__96326)
               => ( c_24__type__96641___24t(Vvar__0__R__96313,Vvar__1__rO__96314,Vvar__2__rI__96315,Vvar__3__radd__96316,Vvar__4__rmul__96321,Vvar__5__rdiv__96326,Vvar__6__rinv__96331,Vvar__7__req__96334,Vvar__6__rinv__96331)
                 => ( c_24__type__96704___24t(Vvar__0__R__96313,Vvar__1__rO__96314,Vvar__2__rI__96315,Vvar__3__radd__96316,Vvar__4__rmul__96321,Vvar__5__rdiv__96326,Vvar__6__rinv__96331,Vvar__7__req__96334,Vvar__7__req__96334)
                   => ( cCoq_2esetoid__ring_2eField__theory_2esemi__field__theory___24a8(Vvar__0__R__96313,Vvar__1__rO__96314,Vvar__2__rI__96315,Vvar__3__radd__96316,Vvar__4__rmul__96321,Vvar__5__rdiv__96326,Vvar__6__rinv__96331,Vvar__7__req__96334)
                     => ( cCoq_2esetoid__ring_2eRing__theory_2esemi__ring__theory___24a6(Vvar__0__R__96313,Vvar__1__rO__96314,Vvar__2__rI__96315,Vvar__3__radd__96316,Vvar__4__rmul__96321,Vvar__7__req__96334)
                        & ~ p(happ(happ(Vvar__7__req__96334,Vvar__2__rI__96315),Vvar__1__rO__96314))
                        & ! [Vvar__var__var__var__var__var__var__10__p__96369__96371__96378__96380__96382__96384__96386] :
                            ( t(Vvar__var__var__var__var__var__var__10__p__96369__96371__96378__96380__96382__96384__96386,Vvar__0__R__96313)
                           => ! [Vvar__var__var__var__var__var__var__11__q__96370__96372__96379__96381__96383__96385__96387] :
                                ( t(Vvar__var__var__var__var__var__var__11__q__96370__96372__96379__96381__96383__96385__96387,Vvar__0__R__96313)
                               => p(happ(happ(Vvar__7__req__96334,happ(happ(Vvar__5__rdiv__96326,Vvar__var__var__var__var__var__var__10__p__96369__96371__96378__96380__96382__96384__96386),Vvar__var__var__var__var__var__var__11__q__96370__96372__96379__96381__96383__96385__96387)),happ(happ(Vvar__4__rmul__96321,Vvar__var__var__var__var__var__var__10__p__96369__96371__96378__96380__96382__96384__96386),happ(Vvar__6__rinv__96331,Vvar__var__var__var__var__var__var__11__q__96370__96372__96379__96381__96383__96385__96387)))) ) )
                        & ! [Vvar__var__var__var__var__var__var__var__11__p__96374__96376__96388__96390__96392__96394__96396__96398] :
                            ( t(Vvar__var__var__var__var__var__var__var__11__p__96374__96376__96388__96390__96392__96394__96396__96398,Vvar__0__R__96313)
                           => ( ~ p(happ(happ(Vvar__7__req__96334,Vvar__var__var__var__var__var__var__var__11__p__96374__96376__96388__96390__96392__96394__96396__96398),Vvar__1__rO__96314))
                             => p(happ(happ(Vvar__7__req__96334,happ(happ(Vvar__4__rmul__96321,happ(Vvar__6__rinv__96331,Vvar__var__var__var__var__var__var__var__11__p__96374__96376__96388__96390__96392__96394__96396__96398)),Vvar__var__var__var__var__var__var__var__11__p__96374__96376__96388__96390__96392__96394__96396__96398)),Vvar__2__rI__96315)) ) )
                        & p(c_24True) ) ) ) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.setoid_ring.InitialRing.hypo',axiom,
    ! [VX96810] :
      ( cCoq_2esetoid__ring_2eInitialRing_2ehypo___24t(VX96810)
     => ? [Vvar__0__hypo__type__96811] :
          ( cType___24t(Vvar__0__hypo__type__96811)
          & ? [Vvar__1__hypo__proof__96812] :
              ( t(Vvar__1__hypo__proof__96812,Vvar__0__hypo__type__96811)
              & VX96810 = cCoq_2esetoid__ring_2eInitialRing_2emkhypo___24a2(Vvar__0__hypo__type__96811,Vvar__1__hypo__proof__96812) ) ) ) ).

fof('$_inversion_Coq.setoid_ring.Ring_polynom.Mon',axiom,
    ! [VX78227] :
      ( cCoq_2esetoid__ring_2eRing__polynom_2eMon___24t(VX78227)
     => ( VX78227 = cCoq_2esetoid__ring_2eRing__polynom_2emon0
        | ? [Vvar__0___24Anonymous__78228] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__78228)
            & ? [Vvar__1___24Anonymous__78229] :
                ( cCoq_2esetoid__ring_2eRing__polynom_2eMon___24t(Vvar__1___24Anonymous__78229)
                & VX78227 = cCoq_2esetoid__ring_2eRing__polynom_2ezmon___24a2(Vvar__0___24Anonymous__78228,Vvar__1___24Anonymous__78229) ) )
        | ? [Vvar__0___24Anonymous__78230] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__78230)
            & ? [Vvar__1___24Anonymous__78231] :
                ( cCoq_2esetoid__ring_2eRing__polynom_2eMon___24t(Vvar__1___24Anonymous__78231)
                & VX78227 = cCoq_2esetoid__ring_2eRing__polynom_2evmon___24a2(Vvar__0___24Anonymous__78230,Vvar__1___24Anonymous__78231) ) ) ) ) ).

fof('$_inversion_Coq.setoid_ring.Ring_polynom.PExpr',axiom,
    ! [Vvar__0__C__78248,VX78249] :
      ( cType___24t(Vvar__0__C__78248)
     => ( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__78248,VX78249)
       => ( VX78249 = cCoq_2esetoid__ring_2eRing__polynom_2ePEO___24a1(Vvar__0__C__78248)
          | VX78249 = cCoq_2esetoid__ring_2eRing__polynom_2ePEI___24a1(Vvar__0__C__78248)
          | ? [Vvar__1___24Anonymous__78253] :
              ( t(Vvar__1___24Anonymous__78253,Vvar__0__C__78248)
              & VX78249 = cCoq_2esetoid__ring_2eRing__polynom_2ePEc___24a2(Vvar__0__C__78248,Vvar__1___24Anonymous__78253) )
          | ? [Vvar__1___24Anonymous__78255] :
              ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__78255)
              & VX78249 = cCoq_2esetoid__ring_2eRing__polynom_2ePEX___24a2(Vvar__0__C__78248,Vvar__1___24Anonymous__78255) )
          | ? [Vvar__1___24Anonymous__78257] :
              ( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__78248,Vvar__1___24Anonymous__78257)
              & ? [Vvar__2___24Anonymous__78258] :
                  ( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__78248,Vvar__2___24Anonymous__78258)
                  & VX78249 = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(Vvar__0__C__78248,Vvar__1___24Anonymous__78257,Vvar__2___24Anonymous__78258) ) )
          | ? [Vvar__1___24Anonymous__78260] :
              ( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__78248,Vvar__1___24Anonymous__78260)
              & ? [Vvar__2___24Anonymous__78261] :
                  ( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__78248,Vvar__2___24Anonymous__78261)
                  & VX78249 = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(Vvar__0__C__78248,Vvar__1___24Anonymous__78260,Vvar__2___24Anonymous__78261) ) )
          | ? [Vvar__1___24Anonymous__78263] :
              ( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__78248,Vvar__1___24Anonymous__78263)
              & ? [Vvar__2___24Anonymous__78264] :
                  ( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__78248,Vvar__2___24Anonymous__78264)
                  & VX78249 = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(Vvar__0__C__78248,Vvar__1___24Anonymous__78263,Vvar__2___24Anonymous__78264) ) )
          | ? [Vvar__1___24Anonymous__78266] :
              ( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__78248,Vvar__1___24Anonymous__78266)
              & VX78249 = cCoq_2esetoid__ring_2eRing__polynom_2ePEopp___24a2(Vvar__0__C__78248,Vvar__1___24Anonymous__78266) )
          | ? [Vvar__1___24Anonymous__78268] :
              ( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__78248,Vvar__1___24Anonymous__78268)
              & ? [Vvar__2___24Anonymous__78269] :
                  ( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__2___24Anonymous__78269)
                  & VX78249 = cCoq_2esetoid__ring_2eRing__polynom_2ePEpow___24a3(Vvar__0__C__78248,Vvar__1___24Anonymous__78268,Vvar__2___24Anonymous__78269) ) ) ) ) ) ).

fof('$_inversion_Coq.setoid_ring.Ring_polynom.Pol',axiom,
    ! [Vvar__0__C__78046,VX78047] :
      ( cType___24t(Vvar__0__C__78046)
     => ( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vvar__0__C__78046,VX78047)
       => ( ? [Vvar__1___24Anonymous__78049] :
              ( t(Vvar__1___24Anonymous__78049,Vvar__0__C__78046)
              & VX78047 = cCoq_2esetoid__ring_2eRing__polynom_2ePc___24a2(Vvar__0__C__78046,Vvar__1___24Anonymous__78049) )
          | ? [Vvar__1___24Anonymous__78051] :
              ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__78051)
              & ? [Vvar__2___24Anonymous__78052] :
                  ( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vvar__0__C__78046,Vvar__2___24Anonymous__78052)
                  & VX78047 = cCoq_2esetoid__ring_2eRing__polynom_2ePinj___24a3(Vvar__0__C__78046,Vvar__1___24Anonymous__78051,Vvar__2___24Anonymous__78052) ) )
          | ? [Vvar__1___24Anonymous__78054] :
              ( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vvar__0__C__78046,Vvar__1___24Anonymous__78054)
              & ? [Vvar__2___24Anonymous__78055] :
                  ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2___24Anonymous__78055)
                  & ? [Vvar__3___24Anonymous__78056] :
                      ( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vvar__0__C__78046,Vvar__3___24Anonymous__78056)
                      & VX78047 = cCoq_2esetoid__ring_2eRing__polynom_2ePX___24a4(Vvar__0__C__78046,Vvar__1___24Anonymous__78054,Vvar__2___24Anonymous__78055,Vvar__3___24Anonymous__78056) ) ) ) ) ) ) ).

fof('$_inversion_Coq.setoid_ring.Ring_theory.almost_ring_theory',axiom,
    ! [Vvar__0__R__103669,Vvar__1__rO__103670,Vvar__2__rI__103671,Vvar__3__radd__103672,Vvar__4__rmul__103677,Vvar__5__rsub__103682,Vvar__6__ropp__103687,Vvar__7__req__103690] :
      ( cType___24t(Vvar__0__R__103669)
     => ( t(Vvar__1__rO__103670,Vvar__0__R__103669)
       => ( t(Vvar__2__rI__103671,Vvar__0__R__103669)
         => ( c_24__type__103918___24t(Vvar__0__R__103669,Vvar__1__rO__103670,Vvar__2__rI__103671,Vvar__3__radd__103672,Vvar__4__rmul__103677,Vvar__5__rsub__103682,Vvar__6__ropp__103687,Vvar__7__req__103690,Vvar__3__radd__103672)
           => ( c_24__type__103981___24t(Vvar__0__R__103669,Vvar__1__rO__103670,Vvar__2__rI__103671,Vvar__3__radd__103672,Vvar__4__rmul__103677,Vvar__5__rsub__103682,Vvar__6__ropp__103687,Vvar__7__req__103690,Vvar__4__rmul__103677)
             => ( c_24__type__104044___24t(Vvar__0__R__103669,Vvar__1__rO__103670,Vvar__2__rI__103671,Vvar__3__radd__103672,Vvar__4__rmul__103677,Vvar__5__rsub__103682,Vvar__6__ropp__103687,Vvar__7__req__103690,Vvar__5__rsub__103682)
               => ( c_24__type__104098___24t(Vvar__0__R__103669,Vvar__1__rO__103670,Vvar__2__rI__103671,Vvar__3__radd__103672,Vvar__4__rmul__103677,Vvar__5__rsub__103682,Vvar__6__ropp__103687,Vvar__7__req__103690,Vvar__6__ropp__103687)
                 => ( c_24__type__104161___24t(Vvar__0__R__103669,Vvar__1__rO__103670,Vvar__2__rI__103671,Vvar__3__radd__103672,Vvar__4__rmul__103677,Vvar__5__rsub__103682,Vvar__6__ropp__103687,Vvar__7__req__103690,Vvar__7__req__103690)
                   => ( cCoq_2esetoid__ring_2eRing__theory_2ealmost__ring__theory___24a8(Vvar__0__R__103669,Vvar__1__rO__103670,Vvar__2__rI__103671,Vvar__3__radd__103672,Vvar__4__rmul__103677,Vvar__5__rsub__103682,Vvar__6__ropp__103687,Vvar__7__req__103690)
                     => ( ! [Vvar__var__var__var__var__var__8__x__103723__103724__103777__103778__103779__103780] :
                            ( t(Vvar__var__var__var__var__var__8__x__103723__103724__103777__103778__103779__103780,Vvar__0__R__103669)
                           => p(happ(happ(Vvar__7__req__103690,happ(happ(Vvar__3__radd__103672,Vvar__1__rO__103670),Vvar__var__var__var__var__var__8__x__103723__103724__103777__103778__103779__103780)),Vvar__var__var__var__var__var__8__x__103723__103724__103777__103778__103779__103780)) )
                        & ! [Vvar__var__var__var__var__9__x__103726__103728__103781__103783__103785] :
                            ( t(Vvar__var__var__var__var__9__x__103726__103728__103781__103783__103785,Vvar__0__R__103669)
                           => ! [Vvar__var__var__var__var__10__y__103727__103729__103782__103784__103786] :
                                ( t(Vvar__var__var__var__var__10__y__103727__103729__103782__103784__103786,Vvar__0__R__103669)
                               => p(happ(happ(Vvar__7__req__103690,happ(happ(Vvar__3__radd__103672,Vvar__var__var__var__var__9__x__103726__103728__103781__103783__103785),Vvar__var__var__var__var__10__y__103727__103729__103782__103784__103786)),happ(happ(Vvar__3__radd__103672,Vvar__var__var__var__var__10__y__103727__103729__103782__103784__103786),Vvar__var__var__var__var__9__x__103726__103728__103781__103783__103785))) ) )
                        & ! [Vvar__var__var__var__var__10__x__103731__103734__103787__103790__103793] :
                            ( t(Vvar__var__var__var__var__10__x__103731__103734__103787__103790__103793,Vvar__0__R__103669)
                           => ! [Vvar__var__var__var__var__11__y__103732__103735__103788__103791__103794] :
                                ( t(Vvar__var__var__var__var__11__y__103732__103735__103788__103791__103794,Vvar__0__R__103669)
                               => ! [Vvar__var__var__var__var__12__z__103733__103736__103789__103792__103795] :
                                    ( t(Vvar__var__var__var__var__12__z__103733__103736__103789__103792__103795,Vvar__0__R__103669)
                                   => p(happ(happ(Vvar__7__req__103690,happ(happ(Vvar__3__radd__103672,Vvar__var__var__var__var__10__x__103731__103734__103787__103790__103793),happ(happ(Vvar__3__radd__103672,Vvar__var__var__var__var__11__y__103732__103735__103788__103791__103794),Vvar__var__var__var__var__12__z__103733__103736__103789__103792__103795))),happ(happ(Vvar__3__radd__103672,happ(happ(Vvar__3__radd__103672,Vvar__var__var__var__var__10__x__103731__103734__103787__103790__103793),Vvar__var__var__var__var__11__y__103732__103735__103788__103791__103794)),Vvar__var__var__var__var__12__z__103733__103736__103789__103792__103795))) ) ) )
                        & ! [Vvar__var__var__var__var__var__11__x__103738__103739__103796__103797__103798__103799] :
                            ( t(Vvar__var__var__var__var__var__11__x__103738__103739__103796__103797__103798__103799,Vvar__0__R__103669)
                           => p(happ(happ(Vvar__7__req__103690,happ(happ(Vvar__4__rmul__103677,Vvar__2__rI__103671),Vvar__var__var__var__var__var__11__x__103738__103739__103796__103797__103798__103799)),Vvar__var__var__var__var__var__11__x__103738__103739__103796__103797__103798__103799)) )
                        & ! [Vvar__var__var__var__var__var__12__x__103741__103742__103800__103801__103802__103803] :
                            ( t(Vvar__var__var__var__var__var__12__x__103741__103742__103800__103801__103802__103803,Vvar__0__R__103669)
                           => p(happ(happ(Vvar__7__req__103690,happ(happ(Vvar__4__rmul__103677,Vvar__1__rO__103670),Vvar__var__var__var__var__var__12__x__103741__103742__103800__103801__103802__103803)),Vvar__1__rO__103670)) )
                        & ! [Vvar__var__var__var__var__13__x__103744__103746__103804__103806__103808] :
                            ( t(Vvar__var__var__var__var__13__x__103744__103746__103804__103806__103808,Vvar__0__R__103669)
                           => ! [Vvar__var__var__var__var__14__y__103745__103747__103805__103807__103809] :
                                ( t(Vvar__var__var__var__var__14__y__103745__103747__103805__103807__103809,Vvar__0__R__103669)
                               => p(happ(happ(Vvar__7__req__103690,happ(happ(Vvar__4__rmul__103677,Vvar__var__var__var__var__13__x__103744__103746__103804__103806__103808),Vvar__var__var__var__var__14__y__103745__103747__103805__103807__103809)),happ(happ(Vvar__4__rmul__103677,Vvar__var__var__var__var__14__y__103745__103747__103805__103807__103809),Vvar__var__var__var__var__13__x__103744__103746__103804__103806__103808))) ) )
                        & ! [Vvar__var__var__var__var__14__x__103749__103752__103810__103813__103816] :
                            ( t(Vvar__var__var__var__var__14__x__103749__103752__103810__103813__103816,Vvar__0__R__103669)
                           => ! [Vvar__var__var__var__var__15__y__103750__103753__103811__103814__103817] :
                                ( t(Vvar__var__var__var__var__15__y__103750__103753__103811__103814__103817,Vvar__0__R__103669)
                               => ! [Vvar__var__var__var__var__16__z__103751__103754__103812__103815__103818] :
                                    ( t(Vvar__var__var__var__var__16__z__103751__103754__103812__103815__103818,Vvar__0__R__103669)
                                   => p(happ(happ(Vvar__7__req__103690,happ(happ(Vvar__4__rmul__103677,Vvar__var__var__var__var__14__x__103749__103752__103810__103813__103816),happ(happ(Vvar__4__rmul__103677,Vvar__var__var__var__var__15__y__103750__103753__103811__103814__103817),Vvar__var__var__var__var__16__z__103751__103754__103812__103815__103818))),happ(happ(Vvar__4__rmul__103677,happ(happ(Vvar__4__rmul__103677,Vvar__var__var__var__var__14__x__103749__103752__103810__103813__103816),Vvar__var__var__var__var__15__y__103750__103753__103811__103814__103817)),Vvar__var__var__var__var__16__z__103751__103754__103812__103815__103818))) ) ) )
                        & ! [Vvar__var__var__var__var__var__15__x__103756__103759__103819__103822__103825__103828] :
                            ( t(Vvar__var__var__var__var__var__15__x__103756__103759__103819__103822__103825__103828,Vvar__0__R__103669)
                           => ! [Vvar__var__var__var__var__var__16__y__103757__103760__103820__103823__103826__103829] :
                                ( t(Vvar__var__var__var__var__var__16__y__103757__103760__103820__103823__103826__103829,Vvar__0__R__103669)
                               => ! [Vvar__var__var__var__var__var__17__z__103758__103761__103821__103824__103827__103830] :
                                    ( t(Vvar__var__var__var__var__var__17__z__103758__103761__103821__103824__103827__103830,Vvar__0__R__103669)
                                   => p(happ(happ(Vvar__7__req__103690,happ(happ(Vvar__4__rmul__103677,happ(happ(Vvar__3__radd__103672,Vvar__var__var__var__var__var__15__x__103756__103759__103819__103822__103825__103828),Vvar__var__var__var__var__var__16__y__103757__103760__103820__103823__103826__103829)),Vvar__var__var__var__var__var__17__z__103758__103761__103821__103824__103827__103830)),happ(happ(Vvar__3__radd__103672,happ(happ(Vvar__4__rmul__103677,Vvar__var__var__var__var__var__15__x__103756__103759__103819__103822__103825__103828),Vvar__var__var__var__var__var__17__z__103758__103761__103821__103824__103827__103830)),happ(happ(Vvar__4__rmul__103677,Vvar__var__var__var__var__var__16__y__103757__103760__103820__103823__103826__103829),Vvar__var__var__var__var__var__17__z__103758__103761__103821__103824__103827__103830)))) ) ) )
                        & ! [Vvar__var__var__var__var__var__16__x__103763__103765__103831__103833__103835__103837] :
                            ( t(Vvar__var__var__var__var__var__16__x__103763__103765__103831__103833__103835__103837,Vvar__0__R__103669)
                           => ! [Vvar__var__var__var__var__var__17__y__103764__103766__103832__103834__103836__103838] :
                                ( t(Vvar__var__var__var__var__var__17__y__103764__103766__103832__103834__103836__103838,Vvar__0__R__103669)
                               => p(happ(happ(Vvar__7__req__103690,happ(Vvar__6__ropp__103687,happ(happ(Vvar__4__rmul__103677,Vvar__var__var__var__var__var__16__x__103763__103765__103831__103833__103835__103837),Vvar__var__var__var__var__var__17__y__103764__103766__103832__103834__103836__103838))),happ(happ(Vvar__4__rmul__103677,happ(Vvar__6__ropp__103687,Vvar__var__var__var__var__var__16__x__103763__103765__103831__103833__103835__103837)),Vvar__var__var__var__var__var__17__y__103764__103766__103832__103834__103836__103838))) ) )
                        & ! [Vvar__var__var__var__var__var__17__x__103768__103770__103839__103841__103843__103845] :
                            ( t(Vvar__var__var__var__var__var__17__x__103768__103770__103839__103841__103843__103845,Vvar__0__R__103669)
                           => ! [Vvar__var__var__var__var__var__18__y__103769__103771__103840__103842__103844__103846] :
                                ( t(Vvar__var__var__var__var__var__18__y__103769__103771__103840__103842__103844__103846,Vvar__0__R__103669)
                               => p(happ(happ(Vvar__7__req__103690,happ(Vvar__6__ropp__103687,happ(happ(Vvar__3__radd__103672,Vvar__var__var__var__var__var__17__x__103768__103770__103839__103841__103843__103845),Vvar__var__var__var__var__var__18__y__103769__103771__103840__103842__103844__103846))),happ(happ(Vvar__3__radd__103672,happ(Vvar__6__ropp__103687,Vvar__var__var__var__var__var__17__x__103768__103770__103839__103841__103843__103845)),happ(Vvar__6__ropp__103687,Vvar__var__var__var__var__var__18__y__103769__103771__103840__103842__103844__103846)))) ) )
                        & ! [Vvar__var__var__var__var__var__var__18__x__103773__103775__103847__103849__103851__103853__103855] :
                            ( t(Vvar__var__var__var__var__var__var__18__x__103773__103775__103847__103849__103851__103853__103855,Vvar__0__R__103669)
                           => ! [Vvar__var__var__var__var__var__var__19__y__103774__103776__103848__103850__103852__103854__103856] :
                                ( t(Vvar__var__var__var__var__var__var__19__y__103774__103776__103848__103850__103852__103854__103856,Vvar__0__R__103669)
                               => p(happ(happ(Vvar__7__req__103690,happ(happ(Vvar__5__rsub__103682,Vvar__var__var__var__var__var__var__18__x__103773__103775__103847__103849__103851__103853__103855),Vvar__var__var__var__var__var__var__19__y__103774__103776__103848__103850__103852__103854__103856)),happ(happ(Vvar__3__radd__103672,Vvar__var__var__var__var__var__var__18__x__103773__103775__103847__103849__103851__103853__103855),happ(Vvar__6__ropp__103687,Vvar__var__var__var__var__var__var__19__y__103774__103776__103848__103850__103852__103854__103856)))) ) )
                        & p(c_24True) ) ) ) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.setoid_ring.Ring_theory.div_theory',axiom,
    ! [Vvar__0__R__104433,Vvar__1__req__104434,Vvar__2__C__104439,Vvar__3__cadd__104440,Vvar__4__cmul__104445,Vvar__5__phi__104450,Vvar__6__cdiv__104453] :
      ( cType___24t(Vvar__0__R__104433)
     => ( c_24__type__104573___24t(Vvar__0__R__104433,Vvar__1__req__104434,Vvar__2__C__104439,Vvar__3__cadd__104440,Vvar__4__cmul__104445,Vvar__5__phi__104450,Vvar__6__cdiv__104453,Vvar__1__req__104434)
       => ( cType___24t(Vvar__2__C__104439)
         => ( c_24__type__104623___24t(Vvar__0__R__104433,Vvar__1__req__104434,Vvar__2__C__104439,Vvar__3__cadd__104440,Vvar__4__cmul__104445,Vvar__5__phi__104450,Vvar__6__cdiv__104453,Vvar__3__cadd__104440)
           => ( c_24__type__104673___24t(Vvar__0__R__104433,Vvar__1__req__104434,Vvar__2__C__104439,Vvar__3__cadd__104440,Vvar__4__cmul__104445,Vvar__5__phi__104450,Vvar__6__cdiv__104453,Vvar__4__cmul__104445)
             => ( c_24__type__104715___24t(Vvar__0__R__104433,Vvar__1__req__104434,Vvar__2__C__104439,Vvar__3__cadd__104440,Vvar__4__cmul__104445,Vvar__5__phi__104450,Vvar__6__cdiv__104453,Vvar__5__phi__104450)
               => ( c_24__type__104765___24t(Vvar__0__R__104433,Vvar__1__req__104434,Vvar__2__C__104439,Vvar__3__cadd__104440,Vvar__4__cmul__104445,Vvar__5__phi__104450,Vvar__6__cdiv__104453,Vvar__6__cdiv__104453)
                 => ( cCoq_2esetoid__ring_2eRing__theory_2ediv__theory___24a7(Vvar__0__R__104433,Vvar__1__req__104434,Vvar__2__C__104439,Vvar__3__cadd__104440,Vvar__4__cmul__104445,Vvar__5__phi__104450,Vvar__6__cdiv__104453)
                   => ( ! [Vvar__var__var__var__var__var__var__var__7__a__104485__104490__104495__104500__104505__104510__104515__104520] :
                          ( t(Vvar__var__var__var__var__var__var__var__7__a__104485__104490__104495__104500__104505__104510__104515__104520,Vvar__2__C__104439)
                         => ! [Vvar__var__var__var__var__var__var__var__8__b__104486__104491__104496__104501__104506__104511__104516__104521] :
                              ( t(Vvar__var__var__var__var__var__var__var__8__b__104486__104491__104496__104501__104506__104511__104516__104521,Vvar__2__C__104439)
                             => c_24__case__Coq_2eInit_2eDatatypes_2eprod_24104828___24a9(Vvar__0__R__104433,Vvar__1__req__104434,Vvar__2__C__104439,Vvar__3__cadd__104440,Vvar__4__cmul__104445,Vvar__5__phi__104450,Vvar__6__cdiv__104453,Vvar__var__var__var__var__var__var__var__7__a__104485__104490__104495__104500__104505__104510__104515__104520,Vvar__var__var__var__var__var__var__var__8__b__104486__104491__104496__104501__104506__104511__104516__104521) ) )
                      & p(c_24True) ) ) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.setoid_ring.Ring_theory.power_theory',axiom,
    ! [Vvar__0__R__104849,Vvar__1__rI__104850,Vvar__2__rmul__104851,Vvar__3__req__104856,Vvar__4__Cpow__104861,Vvar__5__Cp__phi__104862,Vvar__6__rpow__104865] :
      ( cType___24t(Vvar__0__R__104849)
     => ( t(Vvar__1__rI__104850,Vvar__0__R__104849)
       => ( c_24__type__104951___24t(Vvar__0__R__104849,Vvar__1__rI__104850,Vvar__2__rmul__104851,Vvar__3__req__104856,Vvar__4__Cpow__104861,Vvar__5__Cp__phi__104862,Vvar__6__rpow__104865,Vvar__2__rmul__104851)
         => ( c_24__type__104995___24t(Vvar__0__R__104849,Vvar__1__rI__104850,Vvar__2__rmul__104851,Vvar__3__req__104856,Vvar__4__Cpow__104861,Vvar__5__Cp__phi__104862,Vvar__6__rpow__104865,Vvar__3__req__104856)
           => ( cType___24t(Vvar__4__Cpow__104861)
             => ( c_24__type__105031___24t(Vvar__0__R__104849,Vvar__1__rI__104850,Vvar__2__rmul__104851,Vvar__3__req__104856,Vvar__4__Cpow__104861,Vvar__5__Cp__phi__104862,Vvar__6__rpow__104865,Vvar__5__Cp__phi__104862)
               => ( c_24__type__105075___24t(Vvar__0__R__104849,Vvar__1__rI__104850,Vvar__2__rmul__104851,Vvar__3__req__104856,Vvar__4__Cpow__104861,Vvar__5__Cp__phi__104862,Vvar__6__rpow__104865,Vvar__6__rpow__104865)
                 => ( cCoq_2esetoid__ring_2eRing__theory_2epower__theory___24a7(Vvar__0__R__104849,Vvar__1__rI__104850,Vvar__2__rmul__104851,Vvar__3__req__104856,Vvar__4__Cpow__104861,Vvar__5__Cp__phi__104862,Vvar__6__rpow__104865)
                   => ( ! [Vvar__var__var__var__var__var__var__var__7__r__104893__104895__104897__104899__104901__104903__104905__104907] :
                          ( t(Vvar__var__var__var__var__var__var__var__7__r__104893__104895__104897__104899__104901__104903__104905__104907,Vvar__0__R__104849)
                         => ! [Vvar__var__var__var__var__var__var__var__8__n__104894__104896__104898__104900__104902__104904__104906__104908] :
                              ( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__var__var__var__var__var__var__var__8__n__104894__104896__104898__104900__104902__104904__104906__104908)
                             => p(happ(happ(Vvar__3__req__104856,happ(happ(Vvar__6__rpow__104865,Vvar__var__var__var__var__var__var__var__7__r__104893__104895__104897__104899__104901__104903__104905__104907),happ(Vvar__5__Cp__phi__104862,Vvar__var__var__var__var__var__var__var__8__n__104894__104896__104898__104900__104902__104904__104906__104908))),cCoq_2esetoid__ring_2eRing__theory_2epow__N___24a5(Vvar__0__R__104849,Vvar__1__rI__104850,Vvar__2__rmul__104851,Vvar__var__var__var__var__var__var__var__7__r__104893__104895__104897__104899__104901__104903__104905__104907,Vvar__var__var__var__var__var__var__var__8__n__104894__104896__104898__104900__104902__104904__104906__104908))) ) )
                      & p(c_24True) ) ) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.setoid_ring.Ring_theory.ring_eq_ext',axiom,
    ! [Vvar__0__R__86747,Vvar__1__radd__86748,Vvar__2__rmul__86753,Vvar__3__ropp__86758,Vvar__4__req__86761] :
      ( cType___24t(Vvar__0__R__86747)
     => ( c_24__type__86852___24t(Vvar__0__R__86747,Vvar__1__radd__86748,Vvar__2__rmul__86753,Vvar__3__ropp__86758,Vvar__4__req__86761,Vvar__1__radd__86748)
       => ( c_24__type__86882___24t(Vvar__0__R__86747,Vvar__1__radd__86748,Vvar__2__rmul__86753,Vvar__3__ropp__86758,Vvar__4__req__86761,Vvar__2__rmul__86753)
         => ( c_24__type__86906___24t(Vvar__0__R__86747,Vvar__1__radd__86748,Vvar__2__rmul__86753,Vvar__3__ropp__86758,Vvar__4__req__86761,Vvar__3__ropp__86758)
           => ( c_24__type__86936___24t(Vvar__0__R__86747,Vvar__1__radd__86748,Vvar__2__rmul__86753,Vvar__3__ropp__86758,Vvar__4__req__86761,Vvar__4__req__86761)
             => ( cCoq_2esetoid__ring_2eRing__theory_2ering__eq__ext___24a5(Vvar__0__R__86747,Vvar__1__radd__86748,Vvar__2__rmul__86753,Vvar__3__ropp__86758,Vvar__4__req__86761)
               => ( cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__86966___24a5(Vvar__0__R__86747,Vvar__1__radd__86748,Vvar__2__rmul__86753,Vvar__3__ropp__86758,Vvar__4__req__86761),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(Vvar__0__R__86747,c_24__type__86990___24a5(Vvar__0__R__86747,Vvar__1__radd__86748,Vvar__2__rmul__86753,Vvar__3__ropp__86758,Vvar__4__req__86761),Vvar__4__req__86761,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(Vvar__0__R__86747,Vvar__0__R__86747,Vvar__4__req__86761,Vvar__4__req__86761)),Vvar__1__radd__86748)
                  & cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__87023___24a5(Vvar__0__R__86747,Vvar__1__radd__86748,Vvar__2__rmul__86753,Vvar__3__ropp__86758,Vvar__4__req__86761),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(Vvar__0__R__86747,c_24__type__87047___24a5(Vvar__0__R__86747,Vvar__1__radd__86748,Vvar__2__rmul__86753,Vvar__3__ropp__86758,Vvar__4__req__86761),Vvar__4__req__86761,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(Vvar__0__R__86747,Vvar__0__R__86747,Vvar__4__req__86761,Vvar__4__req__86761)),Vvar__2__rmul__86753)
                  & cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__87074___24a5(Vvar__0__R__86747,Vvar__1__radd__86748,Vvar__2__rmul__86753,Vvar__3__ropp__86758,Vvar__4__req__86761),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(Vvar__0__R__86747,Vvar__0__R__86747,Vvar__4__req__86761,Vvar__4__req__86761),Vvar__3__ropp__86758)
                  & p(c_24True) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.setoid_ring.Ring_theory.ring_kind',axiom,
    ! [VX89662] :
      ( cCoq_2esetoid__ring_2eRing__theory_2ering__kind___24t(VX89662)
     => ( VX89662 = cCoq_2esetoid__ring_2eRing__theory_2eAbstract
        | ? [Vvar__0__R__89663] :
            ( cType___24t(Vvar__0__R__89663)
            & ? [Vvar__1__req__89664] :
                ( c_24__type__78044___24t(Vvar__0__R__89663,Vvar__1__req__89664)
                & ? [Vvar__2__reqb__89669] :
                    ( c_24__type__78211___24t(Vvar__0__R__89663,Vvar__2__reqb__89669)
                    & ! [Vvar__var__3__x__89675__89678] :
                        ( t(Vvar__var__3__x__89675__89678,Vvar__0__R__89663)
                       => ! [Vvar__var__4__y__89676__89679] :
                            ( t(Vvar__var__4__y__89676__89679,Vvar__0__R__89663)
                           => ( happ(happ(Vvar__2__reqb__89669,Vvar__var__3__x__89675__89678),Vvar__var__4__y__89676__89679) = cCoq_2eInit_2eDatatypes_2etrue
                             => p(happ(happ(Vvar__1__req__89664,Vvar__var__3__x__89675__89678),Vvar__var__4__y__89676__89679)) ) ) )
                    & VX89662 = cCoq_2esetoid__ring_2eRing__theory_2eComputational___24a3(Vvar__0__R__89663,Vvar__1__req__89664,Vvar__2__reqb__89669) ) ) )
        | ? [Vvar__0__R__89681] :
            ( cType___24t(Vvar__0__R__89681)
            & ? [Vvar__1__rO__89682] :
                ( t(Vvar__1__rO__89682,Vvar__0__R__89681)
                & ? [Vvar__2__rI__89683] :
                    ( t(Vvar__2__rI__89683,Vvar__0__R__89681)
                    & ? [Vvar__3__radd__89684] :
                        ( c_24__type__1415___24t(Vvar__0__R__89681,Vvar__3__radd__89684)
                        & ? [Vvar__4__rmul__89689] :
                            ( c_24__type__1415___24t(Vvar__0__R__89681,Vvar__4__rmul__89689)
                            & ? [Vvar__5__rsub__89694] :
                                ( c_24__type__1415___24t(Vvar__0__R__89681,Vvar__5__rsub__89694)
                                & ? [Vvar__6__ropp__89699] :
                                    ( c_24__type__78702___24t(Vvar__0__R__89681,Vvar__6__ropp__89699)
                                    & ? [Vvar__7__req__89702] :
                                        ( c_24__type__78044___24t(Vvar__0__R__89681,Vvar__7__req__89702)
                                        & ? [Vvar__8__C__89707] :
                                            ( cType___24t(Vvar__8__C__89707)
                                            & ? [Vvar__9__cO__89708] :
                                                ( t(Vvar__9__cO__89708,Vvar__8__C__89707)
                                                & ? [Vvar__10__cI__89709] :
                                                    ( t(Vvar__10__cI__89709,Vvar__8__C__89707)
                                                    & ? [Vvar__11__cadd__89710] :
                                                        ( c_24__type__82143___24t(Vvar__0__R__89681,Vvar__8__C__89707,Vvar__11__cadd__89710)
                                                        & ? [Vvar__12__cmul__89715] :
                                                            ( c_24__type__82143___24t(Vvar__0__R__89681,Vvar__8__C__89707,Vvar__12__cmul__89715)
                                                            & ? [Vvar__13__csub__89720] :
                                                                ( c_24__type__82143___24t(Vvar__0__R__89681,Vvar__8__C__89707,Vvar__13__csub__89720)
                                                                & ? [Vvar__14__copp__89725] :
                                                                    ( c_24__type__82253___24t(Vvar__0__R__89681,Vvar__8__C__89707,Vvar__14__copp__89725)
                                                                    & ? [Vvar__15__ceqb__89728] :
                                                                        ( c_24__type__82155___24t(Vvar__0__R__89681,Vvar__8__C__89707,Vvar__15__ceqb__89728)
                                                                        & ? [Vvar__16__phi__89733] :
                                                                            ( c_24__type__80805___24t(Vvar__0__R__89681,Vvar__8__C__89707,Vvar__16__phi__89733)
                                                                            & cCoq_2esetoid__ring_2eRing__theory_2ering__morph___24a17(Vvar__0__R__89681,Vvar__1__rO__89682,Vvar__2__rI__89683,Vvar__3__radd__89684,Vvar__4__rmul__89689,Vvar__5__rsub__89694,Vvar__6__ropp__89699,Vvar__7__req__89702,Vvar__8__C__89707,Vvar__9__cO__89708,Vvar__10__cI__89709,Vvar__11__cadd__89710,Vvar__12__cmul__89715,Vvar__13__csub__89720,Vvar__14__copp__89725,Vvar__15__ceqb__89728,Vvar__16__phi__89733)
                                                                            & VX89662 = cCoq_2esetoid__ring_2eRing__theory_2eMorphism___24a17(Vvar__0__R__89681,Vvar__1__rO__89682,Vvar__2__rI__89683,Vvar__3__radd__89684,Vvar__4__rmul__89689,Vvar__5__rsub__89694,Vvar__6__ropp__89699,Vvar__7__req__89702,Vvar__8__C__89707,Vvar__9__cO__89708,Vvar__10__cI__89709,Vvar__11__cadd__89710,Vvar__12__cmul__89715,Vvar__13__csub__89720,Vvar__14__copp__89725,Vvar__15__ceqb__89728,Vvar__16__phi__89733) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.setoid_ring.Ring_theory.ring_morph',axiom,
    ! [Vvar__0__R__87077,Vvar__1__rO__87078,Vvar__2__rI__87079,Vvar__3__radd__87080,Vvar__4__rmul__87085,Vvar__5__rsub__87090,Vvar__6__ropp__87095,Vvar__7__req__87098,Vvar__8__C__87103,Vvar__9__cO__87104,Vvar__10__cI__87105,Vvar__11__cadd__87106,Vvar__12__cmul__87111,Vvar__13__csub__87116,Vvar__14__copp__87121,Vvar__15__ceqb__87124,Vvar__16__phi__87129] :
      ( cType___24t(Vvar__0__R__87077)
     => ( t(Vvar__1__rO__87078,Vvar__0__R__87077)
       => ( t(Vvar__2__rI__87079,Vvar__0__R__87077)
         => ( c_24__type__87473___24t(Vvar__0__R__87077,Vvar__1__rO__87078,Vvar__2__rI__87079,Vvar__3__radd__87080,Vvar__4__rmul__87085,Vvar__5__rsub__87090,Vvar__6__ropp__87095,Vvar__7__req__87098,Vvar__8__C__87103,Vvar__9__cO__87104,Vvar__10__cI__87105,Vvar__11__cadd__87106,Vvar__12__cmul__87111,Vvar__13__csub__87116,Vvar__14__copp__87121,Vvar__15__ceqb__87124,Vvar__16__phi__87129,Vvar__3__radd__87080)
           => ( c_24__type__87686___24t(Vvar__0__R__87077,Vvar__1__rO__87078,Vvar__2__rI__87079,Vvar__3__radd__87080,Vvar__4__rmul__87085,Vvar__5__rsub__87090,Vvar__6__ropp__87095,Vvar__7__req__87098,Vvar__8__C__87103,Vvar__9__cO__87104,Vvar__10__cI__87105,Vvar__11__cadd__87106,Vvar__12__cmul__87111,Vvar__13__csub__87116,Vvar__14__copp__87121,Vvar__15__ceqb__87124,Vvar__16__phi__87129,Vvar__4__rmul__87085)
             => ( c_24__type__87899___24t(Vvar__0__R__87077,Vvar__1__rO__87078,Vvar__2__rI__87079,Vvar__3__radd__87080,Vvar__4__rmul__87085,Vvar__5__rsub__87090,Vvar__6__ropp__87095,Vvar__7__req__87098,Vvar__8__C__87103,Vvar__9__cO__87104,Vvar__10__cI__87105,Vvar__11__cadd__87106,Vvar__12__cmul__87111,Vvar__13__csub__87116,Vvar__14__copp__87121,Vvar__15__ceqb__87124,Vvar__16__phi__87129,Vvar__5__rsub__87090)
               => ( c_24__type__88094___24t(Vvar__0__R__87077,Vvar__1__rO__87078,Vvar__2__rI__87079,Vvar__3__radd__87080,Vvar__4__rmul__87085,Vvar__5__rsub__87090,Vvar__6__ropp__87095,Vvar__7__req__87098,Vvar__8__C__87103,Vvar__9__cO__87104,Vvar__10__cI__87105,Vvar__11__cadd__87106,Vvar__12__cmul__87111,Vvar__13__csub__87116,Vvar__14__copp__87121,Vvar__15__ceqb__87124,Vvar__16__phi__87129,Vvar__6__ropp__87095)
                 => ( c_24__type__88307___24t(Vvar__0__R__87077,Vvar__1__rO__87078,Vvar__2__rI__87079,Vvar__3__radd__87080,Vvar__4__rmul__87085,Vvar__5__rsub__87090,Vvar__6__ropp__87095,Vvar__7__req__87098,Vvar__8__C__87103,Vvar__9__cO__87104,Vvar__10__cI__87105,Vvar__11__cadd__87106,Vvar__12__cmul__87111,Vvar__13__csub__87116,Vvar__14__copp__87121,Vvar__15__ceqb__87124,Vvar__16__phi__87129,Vvar__7__req__87098)
                   => ( cType___24t(Vvar__8__C__87103)
                     => ( t(Vvar__9__cO__87104,Vvar__8__C__87103)
                       => ( t(Vvar__10__cI__87105,Vvar__8__C__87103)
                         => ( c_24__type__88520___24t(Vvar__0__R__87077,Vvar__1__rO__87078,Vvar__2__rI__87079,Vvar__3__radd__87080,Vvar__4__rmul__87085,Vvar__5__rsub__87090,Vvar__6__ropp__87095,Vvar__7__req__87098,Vvar__8__C__87103,Vvar__9__cO__87104,Vvar__10__cI__87105,Vvar__11__cadd__87106,Vvar__12__cmul__87111,Vvar__13__csub__87116,Vvar__14__copp__87121,Vvar__15__ceqb__87124,Vvar__16__phi__87129,Vvar__11__cadd__87106)
                           => ( c_24__type__88733___24t(Vvar__0__R__87077,Vvar__1__rO__87078,Vvar__2__rI__87079,Vvar__3__radd__87080,Vvar__4__rmul__87085,Vvar__5__rsub__87090,Vvar__6__ropp__87095,Vvar__7__req__87098,Vvar__8__C__87103,Vvar__9__cO__87104,Vvar__10__cI__87105,Vvar__11__cadd__87106,Vvar__12__cmul__87111,Vvar__13__csub__87116,Vvar__14__copp__87121,Vvar__15__ceqb__87124,Vvar__16__phi__87129,Vvar__12__cmul__87111)
                             => ( c_24__type__88946___24t(Vvar__0__R__87077,Vvar__1__rO__87078,Vvar__2__rI__87079,Vvar__3__radd__87080,Vvar__4__rmul__87085,Vvar__5__rsub__87090,Vvar__6__ropp__87095,Vvar__7__req__87098,Vvar__8__C__87103,Vvar__9__cO__87104,Vvar__10__cI__87105,Vvar__11__cadd__87106,Vvar__12__cmul__87111,Vvar__13__csub__87116,Vvar__14__copp__87121,Vvar__15__ceqb__87124,Vvar__16__phi__87129,Vvar__13__csub__87116)
                               => ( c_24__type__89141___24t(Vvar__0__R__87077,Vvar__1__rO__87078,Vvar__2__rI__87079,Vvar__3__radd__87080,Vvar__4__rmul__87085,Vvar__5__rsub__87090,Vvar__6__ropp__87095,Vvar__7__req__87098,Vvar__8__C__87103,Vvar__9__cO__87104,Vvar__10__cI__87105,Vvar__11__cadd__87106,Vvar__12__cmul__87111,Vvar__13__csub__87116,Vvar__14__copp__87121,Vvar__15__ceqb__87124,Vvar__16__phi__87129,Vvar__14__copp__87121)
                                 => ( c_24__type__89354___24t(Vvar__0__R__87077,Vvar__1__rO__87078,Vvar__2__rI__87079,Vvar__3__radd__87080,Vvar__4__rmul__87085,Vvar__5__rsub__87090,Vvar__6__ropp__87095,Vvar__7__req__87098,Vvar__8__C__87103,Vvar__9__cO__87104,Vvar__10__cI__87105,Vvar__11__cadd__87106,Vvar__12__cmul__87111,Vvar__13__csub__87116,Vvar__14__copp__87121,Vvar__15__ceqb__87124,Vvar__16__phi__87129,Vvar__15__ceqb__87124)
                                   => ( c_24__type__89549___24t(Vvar__0__R__87077,Vvar__1__rO__87078,Vvar__2__rI__87079,Vvar__3__radd__87080,Vvar__4__rmul__87085,Vvar__5__rsub__87090,Vvar__6__ropp__87095,Vvar__7__req__87098,Vvar__8__C__87103,Vvar__9__cO__87104,Vvar__10__cI__87105,Vvar__11__cadd__87106,Vvar__12__cmul__87111,Vvar__13__csub__87116,Vvar__14__copp__87121,Vvar__15__ceqb__87124,Vvar__16__phi__87129,Vvar__16__phi__87129)
                                     => ( cCoq_2esetoid__ring_2eRing__theory_2ering__morph___24a17(Vvar__0__R__87077,Vvar__1__rO__87078,Vvar__2__rI__87079,Vvar__3__radd__87080,Vvar__4__rmul__87085,Vvar__5__rsub__87090,Vvar__6__ropp__87095,Vvar__7__req__87098,Vvar__8__C__87103,Vvar__9__cO__87104,Vvar__10__cI__87105,Vvar__11__cadd__87106,Vvar__12__cmul__87111,Vvar__13__csub__87116,Vvar__14__copp__87121,Vvar__15__ceqb__87124,Vvar__16__phi__87129)
                                       => ( p(happ(happ(Vvar__7__req__87098,happ(Vvar__16__phi__87129,Vvar__9__cO__87104)),Vvar__1__rO__87078))
                                          & p(happ(happ(Vvar__7__req__87098,happ(Vvar__16__phi__87129,Vvar__10__cI__87105)),Vvar__2__rI__87079))
                                          & ! [Vvar__var__var__var__var__var__var__19__x__87191__87193__87215__87217__87219__87221__87223] :
                                              ( t(Vvar__var__var__var__var__var__var__19__x__87191__87193__87215__87217__87219__87221__87223,Vvar__8__C__87103)
                                             => ! [Vvar__var__var__var__var__var__var__20__y__87192__87194__87216__87218__87220__87222__87224] :
                                                  ( t(Vvar__var__var__var__var__var__var__20__y__87192__87194__87216__87218__87220__87222__87224,Vvar__8__C__87103)
                                                 => p(happ(happ(Vvar__7__req__87098,happ(Vvar__16__phi__87129,happ(happ(Vvar__11__cadd__87106,Vvar__var__var__var__var__var__var__19__x__87191__87193__87215__87217__87219__87221__87223),Vvar__var__var__var__var__var__var__20__y__87192__87194__87216__87218__87220__87222__87224))),happ(happ(Vvar__3__radd__87080,happ(Vvar__16__phi__87129,Vvar__var__var__var__var__var__var__19__x__87191__87193__87215__87217__87219__87221__87223)),happ(Vvar__16__phi__87129,Vvar__var__var__var__var__var__var__20__y__87192__87194__87216__87218__87220__87222__87224)))) ) )
                                          & ! [Vvar__var__var__var__var__var__var__20__x__87196__87198__87225__87227__87229__87231__87233] :
                                              ( t(Vvar__var__var__var__var__var__var__20__x__87196__87198__87225__87227__87229__87231__87233,Vvar__8__C__87103)
                                             => ! [Vvar__var__var__var__var__var__var__21__y__87197__87199__87226__87228__87230__87232__87234] :
                                                  ( t(Vvar__var__var__var__var__var__var__21__y__87197__87199__87226__87228__87230__87232__87234,Vvar__8__C__87103)
                                                 => p(happ(happ(Vvar__7__req__87098,happ(Vvar__16__phi__87129,happ(happ(Vvar__13__csub__87116,Vvar__var__var__var__var__var__var__20__x__87196__87198__87225__87227__87229__87231__87233),Vvar__var__var__var__var__var__var__21__y__87197__87199__87226__87228__87230__87232__87234))),happ(happ(Vvar__5__rsub__87090,happ(Vvar__16__phi__87129,Vvar__var__var__var__var__var__var__20__x__87196__87198__87225__87227__87229__87231__87233)),happ(Vvar__16__phi__87129,Vvar__var__var__var__var__var__var__21__y__87197__87199__87226__87228__87230__87232__87234)))) ) )
                                          & ! [Vvar__var__var__var__var__var__var__21__x__87201__87203__87235__87237__87239__87241__87243] :
                                              ( t(Vvar__var__var__var__var__var__var__21__x__87201__87203__87235__87237__87239__87241__87243,Vvar__8__C__87103)
                                             => ! [Vvar__var__var__var__var__var__var__22__y__87202__87204__87236__87238__87240__87242__87244] :
                                                  ( t(Vvar__var__var__var__var__var__var__22__y__87202__87204__87236__87238__87240__87242__87244,Vvar__8__C__87103)
                                                 => p(happ(happ(Vvar__7__req__87098,happ(Vvar__16__phi__87129,happ(happ(Vvar__12__cmul__87111,Vvar__var__var__var__var__var__var__21__x__87201__87203__87235__87237__87239__87241__87243),Vvar__var__var__var__var__var__var__22__y__87202__87204__87236__87238__87240__87242__87244))),happ(happ(Vvar__4__rmul__87085,happ(Vvar__16__phi__87129,Vvar__var__var__var__var__var__var__21__x__87201__87203__87235__87237__87239__87241__87243)),happ(Vvar__16__phi__87129,Vvar__var__var__var__var__var__var__22__y__87202__87204__87236__87238__87240__87242__87244)))) ) )
                                          & ! [Vvar__var__var__var__var__var__var__22__x__87206__87207__87245__87246__87247__87248__87249] :
                                              ( t(Vvar__var__var__var__var__var__var__22__x__87206__87207__87245__87246__87247__87248__87249,Vvar__8__C__87103)
                                             => p(happ(happ(Vvar__7__req__87098,happ(Vvar__16__phi__87129,happ(Vvar__14__copp__87121,Vvar__var__var__var__var__var__var__22__x__87206__87207__87245__87246__87247__87248__87249))),happ(Vvar__6__ropp__87095,happ(Vvar__16__phi__87129,Vvar__var__var__var__var__var__var__22__x__87206__87207__87245__87246__87247__87248__87249)))) )
                                          & ! [Vvar__var__var__var__var__var__23__x__87209__87212__87250__87253__87256__87259] :
                                              ( t(Vvar__var__var__var__var__var__23__x__87209__87212__87250__87253__87256__87259,Vvar__8__C__87103)
                                             => ! [Vvar__var__var__var__var__var__24__y__87210__87213__87251__87254__87257__87260] :
                                                  ( t(Vvar__var__var__var__var__var__24__y__87210__87213__87251__87254__87257__87260,Vvar__8__C__87103)
                                                 => ( happ(happ(Vvar__15__ceqb__87124,Vvar__var__var__var__var__var__23__x__87209__87212__87250__87253__87256__87259),Vvar__var__var__var__var__var__24__y__87210__87213__87251__87254__87257__87260) = cCoq_2eInit_2eDatatypes_2etrue
                                                   => p(happ(happ(Vvar__7__req__87098,happ(Vvar__16__phi__87129,Vvar__var__var__var__var__var__23__x__87209__87212__87250__87253__87256__87259)),happ(Vvar__16__phi__87129,Vvar__var__var__var__var__var__24__y__87210__87213__87251__87254__87257__87260))) ) ) )
                                          & p(c_24True) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.setoid_ring.Ring_theory.ring_theory',axiom,
    ! [Vvar__0__R__86208,Vvar__1__rO__86209,Vvar__2__rI__86210,Vvar__3__radd__86211,Vvar__4__rmul__86216,Vvar__5__rsub__86221,Vvar__6__ropp__86226,Vvar__7__req__86229] :
      ( cType___24t(Vvar__0__R__86208)
     => ( t(Vvar__1__rO__86209,Vvar__0__R__86208)
       => ( t(Vvar__2__rI__86210,Vvar__0__R__86208)
         => ( c_24__type__86432___24t(Vvar__0__R__86208,Vvar__1__rO__86209,Vvar__2__rI__86210,Vvar__3__radd__86211,Vvar__4__rmul__86216,Vvar__5__rsub__86221,Vvar__6__ropp__86226,Vvar__7__req__86229,Vvar__3__radd__86211)
           => ( c_24__type__86495___24t(Vvar__0__R__86208,Vvar__1__rO__86209,Vvar__2__rI__86210,Vvar__3__radd__86211,Vvar__4__rmul__86216,Vvar__5__rsub__86221,Vvar__6__ropp__86226,Vvar__7__req__86229,Vvar__4__rmul__86216)
             => ( c_24__type__86558___24t(Vvar__0__R__86208,Vvar__1__rO__86209,Vvar__2__rI__86210,Vvar__3__radd__86211,Vvar__4__rmul__86216,Vvar__5__rsub__86221,Vvar__6__ropp__86226,Vvar__7__req__86229,Vvar__5__rsub__86221)
               => ( c_24__type__86612___24t(Vvar__0__R__86208,Vvar__1__rO__86209,Vvar__2__rI__86210,Vvar__3__radd__86211,Vvar__4__rmul__86216,Vvar__5__rsub__86221,Vvar__6__ropp__86226,Vvar__7__req__86229,Vvar__6__ropp__86226)
                 => ( c_24__type__86675___24t(Vvar__0__R__86208,Vvar__1__rO__86209,Vvar__2__rI__86210,Vvar__3__radd__86211,Vvar__4__rmul__86216,Vvar__5__rsub__86221,Vvar__6__ropp__86226,Vvar__7__req__86229,Vvar__7__req__86229)
                   => ( cCoq_2esetoid__ring_2eRing__theory_2ering__theory___24a8(Vvar__0__R__86208,Vvar__1__rO__86209,Vvar__2__rI__86210,Vvar__3__radd__86211,Vvar__4__rmul__86216,Vvar__5__rsub__86221,Vvar__6__ropp__86226,Vvar__7__req__86229)
                     => ( ! [Vvar__var__var__var__var__var__8__x__86262__86263__86306__86307__86308__86309] :
                            ( t(Vvar__var__var__var__var__var__8__x__86262__86263__86306__86307__86308__86309,Vvar__0__R__86208)
                           => p(happ(happ(Vvar__7__req__86229,happ(happ(Vvar__3__radd__86211,Vvar__1__rO__86209),Vvar__var__var__var__var__var__8__x__86262__86263__86306__86307__86308__86309)),Vvar__var__var__var__var__var__8__x__86262__86263__86306__86307__86308__86309)) )
                        & ! [Vvar__var__var__var__var__9__x__86265__86267__86310__86312__86314] :
                            ( t(Vvar__var__var__var__var__9__x__86265__86267__86310__86312__86314,Vvar__0__R__86208)
                           => ! [Vvar__var__var__var__var__10__y__86266__86268__86311__86313__86315] :
                                ( t(Vvar__var__var__var__var__10__y__86266__86268__86311__86313__86315,Vvar__0__R__86208)
                               => p(happ(happ(Vvar__7__req__86229,happ(happ(Vvar__3__radd__86211,Vvar__var__var__var__var__9__x__86265__86267__86310__86312__86314),Vvar__var__var__var__var__10__y__86266__86268__86311__86313__86315)),happ(happ(Vvar__3__radd__86211,Vvar__var__var__var__var__10__y__86266__86268__86311__86313__86315),Vvar__var__var__var__var__9__x__86265__86267__86310__86312__86314))) ) )
                        & ! [Vvar__var__var__var__var__10__x__86270__86273__86316__86319__86322] :
                            ( t(Vvar__var__var__var__var__10__x__86270__86273__86316__86319__86322,Vvar__0__R__86208)
                           => ! [Vvar__var__var__var__var__11__y__86271__86274__86317__86320__86323] :
                                ( t(Vvar__var__var__var__var__11__y__86271__86274__86317__86320__86323,Vvar__0__R__86208)
                               => ! [Vvar__var__var__var__var__12__z__86272__86275__86318__86321__86324] :
                                    ( t(Vvar__var__var__var__var__12__z__86272__86275__86318__86321__86324,Vvar__0__R__86208)
                                   => p(happ(happ(Vvar__7__req__86229,happ(happ(Vvar__3__radd__86211,Vvar__var__var__var__var__10__x__86270__86273__86316__86319__86322),happ(happ(Vvar__3__radd__86211,Vvar__var__var__var__var__11__y__86271__86274__86317__86320__86323),Vvar__var__var__var__var__12__z__86272__86275__86318__86321__86324))),happ(happ(Vvar__3__radd__86211,happ(happ(Vvar__3__radd__86211,Vvar__var__var__var__var__10__x__86270__86273__86316__86319__86322),Vvar__var__var__var__var__11__y__86271__86274__86317__86320__86323)),Vvar__var__var__var__var__12__z__86272__86275__86318__86321__86324))) ) ) )
                        & ! [Vvar__var__var__var__var__var__11__x__86277__86278__86325__86326__86327__86328] :
                            ( t(Vvar__var__var__var__var__var__11__x__86277__86278__86325__86326__86327__86328,Vvar__0__R__86208)
                           => p(happ(happ(Vvar__7__req__86229,happ(happ(Vvar__4__rmul__86216,Vvar__2__rI__86210),Vvar__var__var__var__var__var__11__x__86277__86278__86325__86326__86327__86328)),Vvar__var__var__var__var__var__11__x__86277__86278__86325__86326__86327__86328)) )
                        & ! [Vvar__var__var__var__var__12__x__86280__86282__86329__86331__86333] :
                            ( t(Vvar__var__var__var__var__12__x__86280__86282__86329__86331__86333,Vvar__0__R__86208)
                           => ! [Vvar__var__var__var__var__13__y__86281__86283__86330__86332__86334] :
                                ( t(Vvar__var__var__var__var__13__y__86281__86283__86330__86332__86334,Vvar__0__R__86208)
                               => p(happ(happ(Vvar__7__req__86229,happ(happ(Vvar__4__rmul__86216,Vvar__var__var__var__var__12__x__86280__86282__86329__86331__86333),Vvar__var__var__var__var__13__y__86281__86283__86330__86332__86334)),happ(happ(Vvar__4__rmul__86216,Vvar__var__var__var__var__13__y__86281__86283__86330__86332__86334),Vvar__var__var__var__var__12__x__86280__86282__86329__86331__86333))) ) )
                        & ! [Vvar__var__var__var__var__13__x__86285__86288__86335__86338__86341] :
                            ( t(Vvar__var__var__var__var__13__x__86285__86288__86335__86338__86341,Vvar__0__R__86208)
                           => ! [Vvar__var__var__var__var__14__y__86286__86289__86336__86339__86342] :
                                ( t(Vvar__var__var__var__var__14__y__86286__86289__86336__86339__86342,Vvar__0__R__86208)
                               => ! [Vvar__var__var__var__var__15__z__86287__86290__86337__86340__86343] :
                                    ( t(Vvar__var__var__var__var__15__z__86287__86290__86337__86340__86343,Vvar__0__R__86208)
                                   => p(happ(happ(Vvar__7__req__86229,happ(happ(Vvar__4__rmul__86216,Vvar__var__var__var__var__13__x__86285__86288__86335__86338__86341),happ(happ(Vvar__4__rmul__86216,Vvar__var__var__var__var__14__y__86286__86289__86336__86339__86342),Vvar__var__var__var__var__15__z__86287__86290__86337__86340__86343))),happ(happ(Vvar__4__rmul__86216,happ(happ(Vvar__4__rmul__86216,Vvar__var__var__var__var__13__x__86285__86288__86335__86338__86341),Vvar__var__var__var__var__14__y__86286__86289__86336__86339__86342)),Vvar__var__var__var__var__15__z__86287__86290__86337__86340__86343))) ) ) )
                        & ! [Vvar__var__var__var__var__var__14__x__86292__86295__86344__86347__86350__86353] :
                            ( t(Vvar__var__var__var__var__var__14__x__86292__86295__86344__86347__86350__86353,Vvar__0__R__86208)
                           => ! [Vvar__var__var__var__var__var__15__y__86293__86296__86345__86348__86351__86354] :
                                ( t(Vvar__var__var__var__var__var__15__y__86293__86296__86345__86348__86351__86354,Vvar__0__R__86208)
                               => ! [Vvar__var__var__var__var__var__16__z__86294__86297__86346__86349__86352__86355] :
                                    ( t(Vvar__var__var__var__var__var__16__z__86294__86297__86346__86349__86352__86355,Vvar__0__R__86208)
                                   => p(happ(happ(Vvar__7__req__86229,happ(happ(Vvar__4__rmul__86216,happ(happ(Vvar__3__radd__86211,Vvar__var__var__var__var__var__14__x__86292__86295__86344__86347__86350__86353),Vvar__var__var__var__var__var__15__y__86293__86296__86345__86348__86351__86354)),Vvar__var__var__var__var__var__16__z__86294__86297__86346__86349__86352__86355)),happ(happ(Vvar__3__radd__86211,happ(happ(Vvar__4__rmul__86216,Vvar__var__var__var__var__var__14__x__86292__86295__86344__86347__86350__86353),Vvar__var__var__var__var__var__16__z__86294__86297__86346__86349__86352__86355)),happ(happ(Vvar__4__rmul__86216,Vvar__var__var__var__var__var__15__y__86293__86296__86345__86348__86351__86354),Vvar__var__var__var__var__var__16__z__86294__86297__86346__86349__86352__86355)))) ) ) )
                        & ! [Vvar__var__var__var__var__var__var__15__x__86299__86301__86356__86358__86360__86362__86364] :
                            ( t(Vvar__var__var__var__var__var__var__15__x__86299__86301__86356__86358__86360__86362__86364,Vvar__0__R__86208)
                           => ! [Vvar__var__var__var__var__var__var__16__y__86300__86302__86357__86359__86361__86363__86365] :
                                ( t(Vvar__var__var__var__var__var__var__16__y__86300__86302__86357__86359__86361__86363__86365,Vvar__0__R__86208)
                               => p(happ(happ(Vvar__7__req__86229,happ(happ(Vvar__5__rsub__86221,Vvar__var__var__var__var__var__var__15__x__86299__86301__86356__86358__86360__86362__86364),Vvar__var__var__var__var__var__var__16__y__86300__86302__86357__86359__86361__86363__86365)),happ(happ(Vvar__3__radd__86211,Vvar__var__var__var__var__var__var__15__x__86299__86301__86356__86358__86360__86362__86364),happ(Vvar__6__ropp__86226,Vvar__var__var__var__var__var__var__16__y__86300__86302__86357__86359__86361__86363__86365)))) ) )
                        & ! [Vvar__var__var__var__var__var__var__16__x__86304__86305__86366__86367__86368__86369__86370] :
                            ( t(Vvar__var__var__var__var__var__var__16__x__86304__86305__86366__86367__86368__86369__86370,Vvar__0__R__86208)
                           => p(happ(happ(Vvar__7__req__86229,happ(happ(Vvar__3__radd__86211,Vvar__var__var__var__var__var__var__16__x__86304__86305__86366__86367__86368__86369__86370),happ(Vvar__6__ropp__86226,Vvar__var__var__var__var__var__var__16__x__86304__86305__86366__86367__86368__86369__86370))),Vvar__1__rO__86209)) )
                        & p(c_24True) ) ) ) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.setoid_ring.Ring_theory.semi_morph',axiom,
    ! [Vvar__0__R__81131,Vvar__1__rO__81132,Vvar__2__rI__81133,Vvar__3__radd__81134,Vvar__4__rmul__81139,Vvar__5__req__81144,Vvar__6__C__81149,Vvar__7__cO__81150,Vvar__8__cI__81151,Vvar__9__cadd__81152,Vvar__10__cmul__81157,Vvar__11__ceqb__81162,Vvar__12__phi__81167] :
      ( cType___24t(Vvar__0__R__81131)
     => ( t(Vvar__1__rO__81132,Vvar__0__R__81131)
       => ( t(Vvar__2__rI__81133,Vvar__0__R__81131)
         => ( c_24__type__81384___24t(Vvar__0__R__81131,Vvar__1__rO__81132,Vvar__2__rI__81133,Vvar__3__radd__81134,Vvar__4__rmul__81139,Vvar__5__req__81144,Vvar__6__C__81149,Vvar__7__cO__81150,Vvar__8__cI__81151,Vvar__9__cadd__81152,Vvar__10__cmul__81157,Vvar__11__ceqb__81162,Vvar__12__phi__81167,Vvar__3__radd__81134)
           => ( c_24__type__81509___24t(Vvar__0__R__81131,Vvar__1__rO__81132,Vvar__2__rI__81133,Vvar__3__radd__81134,Vvar__4__rmul__81139,Vvar__5__req__81144,Vvar__6__C__81149,Vvar__7__cO__81150,Vvar__8__cI__81151,Vvar__9__cadd__81152,Vvar__10__cmul__81157,Vvar__11__ceqb__81162,Vvar__12__phi__81167,Vvar__4__rmul__81139)
             => ( c_24__type__81634___24t(Vvar__0__R__81131,Vvar__1__rO__81132,Vvar__2__rI__81133,Vvar__3__radd__81134,Vvar__4__rmul__81139,Vvar__5__req__81144,Vvar__6__C__81149,Vvar__7__cO__81150,Vvar__8__cI__81151,Vvar__9__cadd__81152,Vvar__10__cmul__81157,Vvar__11__ceqb__81162,Vvar__12__phi__81167,Vvar__5__req__81144)
               => ( cType___24t(Vvar__6__C__81149)
                 => ( t(Vvar__7__cO__81150,Vvar__6__C__81149)
                   => ( t(Vvar__8__cI__81151,Vvar__6__C__81149)
                     => ( c_24__type__81759___24t(Vvar__0__R__81131,Vvar__1__rO__81132,Vvar__2__rI__81133,Vvar__3__radd__81134,Vvar__4__rmul__81139,Vvar__5__req__81144,Vvar__6__C__81149,Vvar__7__cO__81150,Vvar__8__cI__81151,Vvar__9__cadd__81152,Vvar__10__cmul__81157,Vvar__11__ceqb__81162,Vvar__12__phi__81167,Vvar__9__cadd__81152)
                       => ( c_24__type__81884___24t(Vvar__0__R__81131,Vvar__1__rO__81132,Vvar__2__rI__81133,Vvar__3__radd__81134,Vvar__4__rmul__81139,Vvar__5__req__81144,Vvar__6__C__81149,Vvar__7__cO__81150,Vvar__8__cI__81151,Vvar__9__cadd__81152,Vvar__10__cmul__81157,Vvar__11__ceqb__81162,Vvar__12__phi__81167,Vvar__10__cmul__81157)
                         => ( c_24__type__82009___24t(Vvar__0__R__81131,Vvar__1__rO__81132,Vvar__2__rI__81133,Vvar__3__radd__81134,Vvar__4__rmul__81139,Vvar__5__req__81144,Vvar__6__C__81149,Vvar__7__cO__81150,Vvar__8__cI__81151,Vvar__9__cadd__81152,Vvar__10__cmul__81157,Vvar__11__ceqb__81162,Vvar__12__phi__81167,Vvar__11__ceqb__81162)
                           => ( c_24__type__82120___24t(Vvar__0__R__81131,Vvar__1__rO__81132,Vvar__2__rI__81133,Vvar__3__radd__81134,Vvar__4__rmul__81139,Vvar__5__req__81144,Vvar__6__C__81149,Vvar__7__cO__81150,Vvar__8__cI__81151,Vvar__9__cadd__81152,Vvar__10__cmul__81157,Vvar__11__ceqb__81162,Vvar__12__phi__81167,Vvar__12__phi__81167)
                             => ( cCoq_2esetoid__ring_2eRing__theory_2esemi__morph___24a13(Vvar__0__R__81131,Vvar__1__rO__81132,Vvar__2__rI__81133,Vvar__3__radd__81134,Vvar__4__rmul__81139,Vvar__5__req__81144,Vvar__6__C__81149,Vvar__7__cO__81150,Vvar__8__cI__81151,Vvar__9__cadd__81152,Vvar__10__cmul__81157,Vvar__11__ceqb__81162,Vvar__12__phi__81167)
                               => ( p(happ(happ(Vvar__5__req__81144,happ(Vvar__12__phi__81167,Vvar__7__cO__81150)),Vvar__1__rO__81132))
                                  & p(happ(happ(Vvar__5__req__81144,happ(Vvar__12__phi__81167,Vvar__8__cI__81151)),Vvar__2__rI__81133))
                                  & ! [Vvar__var__var__var__var__var__var__15__x__81213__81215__81229__81231__81233__81235__81237] :
                                      ( t(Vvar__var__var__var__var__var__var__15__x__81213__81215__81229__81231__81233__81235__81237,Vvar__6__C__81149)
                                     => ! [Vvar__var__var__var__var__var__var__16__y__81214__81216__81230__81232__81234__81236__81238] :
                                          ( t(Vvar__var__var__var__var__var__var__16__y__81214__81216__81230__81232__81234__81236__81238,Vvar__6__C__81149)
                                         => p(happ(happ(Vvar__5__req__81144,happ(Vvar__12__phi__81167,happ(happ(Vvar__9__cadd__81152,Vvar__var__var__var__var__var__var__15__x__81213__81215__81229__81231__81233__81235__81237),Vvar__var__var__var__var__var__var__16__y__81214__81216__81230__81232__81234__81236__81238))),happ(happ(Vvar__3__radd__81134,happ(Vvar__12__phi__81167,Vvar__var__var__var__var__var__var__15__x__81213__81215__81229__81231__81233__81235__81237)),happ(Vvar__12__phi__81167,Vvar__var__var__var__var__var__var__16__y__81214__81216__81230__81232__81234__81236__81238)))) ) )
                                  & ! [Vvar__var__var__var__var__var__var__16__x__81218__81220__81239__81241__81243__81245__81247] :
                                      ( t(Vvar__var__var__var__var__var__var__16__x__81218__81220__81239__81241__81243__81245__81247,Vvar__6__C__81149)
                                     => ! [Vvar__var__var__var__var__var__var__17__y__81219__81221__81240__81242__81244__81246__81248] :
                                          ( t(Vvar__var__var__var__var__var__var__17__y__81219__81221__81240__81242__81244__81246__81248,Vvar__6__C__81149)
                                         => p(happ(happ(Vvar__5__req__81144,happ(Vvar__12__phi__81167,happ(happ(Vvar__10__cmul__81157,Vvar__var__var__var__var__var__var__16__x__81218__81220__81239__81241__81243__81245__81247),Vvar__var__var__var__var__var__var__17__y__81219__81221__81240__81242__81244__81246__81248))),happ(happ(Vvar__4__rmul__81139,happ(Vvar__12__phi__81167,Vvar__var__var__var__var__var__var__16__x__81218__81220__81239__81241__81243__81245__81247)),happ(Vvar__12__phi__81167,Vvar__var__var__var__var__var__var__17__y__81219__81221__81240__81242__81244__81246__81248)))) ) )
                                  & ! [Vvar__var__var__var__var__var__17__x__81223__81226__81249__81252__81255__81258] :
                                      ( t(Vvar__var__var__var__var__var__17__x__81223__81226__81249__81252__81255__81258,Vvar__6__C__81149)
                                     => ! [Vvar__var__var__var__var__var__18__y__81224__81227__81250__81253__81256__81259] :
                                          ( t(Vvar__var__var__var__var__var__18__y__81224__81227__81250__81253__81256__81259,Vvar__6__C__81149)
                                         => ( happ(happ(Vvar__11__ceqb__81162,Vvar__var__var__var__var__var__17__x__81223__81226__81249__81252__81255__81258),Vvar__var__var__var__var__var__18__y__81224__81227__81250__81253__81256__81259) = cCoq_2eInit_2eDatatypes_2etrue
                                           => p(happ(happ(Vvar__5__req__81144,happ(Vvar__12__phi__81167,Vvar__var__var__var__var__var__17__x__81223__81226__81249__81252__81255__81258)),happ(Vvar__12__phi__81167,Vvar__var__var__var__var__var__18__y__81224__81227__81250__81253__81256__81259))) ) ) )
                                  & p(c_24True) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.setoid_ring.Ring_theory.semi_ring_theory',axiom,
    ! [Vvar__0__R__80842,Vvar__1__rO__80843,Vvar__2__rI__80844,Vvar__3__radd__80845,Vvar__4__rmul__80850,Vvar__5__req__80855] :
      ( cType___24t(Vvar__0__R__80842)
     => ( t(Vvar__1__rO__80843,Vvar__0__R__80842)
       => ( t(Vvar__2__rI__80844,Vvar__0__R__80842)
         => ( c_24__type__81010___24t(Vvar__0__R__80842,Vvar__1__rO__80843,Vvar__2__rI__80844,Vvar__3__radd__80845,Vvar__4__rmul__80850,Vvar__5__req__80855,Vvar__3__radd__80845)
           => ( c_24__type__81049___24t(Vvar__0__R__80842,Vvar__1__rO__80843,Vvar__2__rI__80844,Vvar__3__radd__80845,Vvar__4__rmul__80850,Vvar__5__req__80855,Vvar__4__rmul__80850)
             => ( c_24__type__81088___24t(Vvar__0__R__80842,Vvar__1__rO__80843,Vvar__2__rI__80844,Vvar__3__radd__80845,Vvar__4__rmul__80850,Vvar__5__req__80855,Vvar__5__req__80855)
               => ( cCoq_2esetoid__ring_2eRing__theory_2esemi__ring__theory___24a6(Vvar__0__R__80842,Vvar__1__rO__80843,Vvar__2__rI__80844,Vvar__3__radd__80845,Vvar__4__rmul__80850,Vvar__5__req__80855)
                 => ( ! [Vvar__var__var__var__var__var__6__n__80880__80881__80919__80920__80921__80922] :
                        ( t(Vvar__var__var__var__var__var__6__n__80880__80881__80919__80920__80921__80922,Vvar__0__R__80842)
                       => p(happ(happ(Vvar__5__req__80855,happ(happ(Vvar__3__radd__80845,Vvar__1__rO__80843),Vvar__var__var__var__var__var__6__n__80880__80881__80919__80920__80921__80922)),Vvar__var__var__var__var__var__6__n__80880__80881__80919__80920__80921__80922)) )
                    & ! [Vvar__var__var__var__var__7__n__80883__80885__80923__80925__80927] :
                        ( t(Vvar__var__var__var__var__7__n__80883__80885__80923__80925__80927,Vvar__0__R__80842)
                       => ! [Vvar__var__var__var__var__8__m__80884__80886__80924__80926__80928] :
                            ( t(Vvar__var__var__var__var__8__m__80884__80886__80924__80926__80928,Vvar__0__R__80842)
                           => p(happ(happ(Vvar__5__req__80855,happ(happ(Vvar__3__radd__80845,Vvar__var__var__var__var__7__n__80883__80885__80923__80925__80927),Vvar__var__var__var__var__8__m__80884__80886__80924__80926__80928)),happ(happ(Vvar__3__radd__80845,Vvar__var__var__var__var__8__m__80884__80886__80924__80926__80928),Vvar__var__var__var__var__7__n__80883__80885__80923__80925__80927))) ) )
                    & ! [Vvar__var__var__var__var__8__n__80888__80891__80929__80932__80935] :
                        ( t(Vvar__var__var__var__var__8__n__80888__80891__80929__80932__80935,Vvar__0__R__80842)
                       => ! [Vvar__var__var__var__var__9__m__80889__80892__80930__80933__80936] :
                            ( t(Vvar__var__var__var__var__9__m__80889__80892__80930__80933__80936,Vvar__0__R__80842)
                           => ! [Vvar__var__var__var__var__10__p__80890__80893__80931__80934__80937] :
                                ( t(Vvar__var__var__var__var__10__p__80890__80893__80931__80934__80937,Vvar__0__R__80842)
                               => p(happ(happ(Vvar__5__req__80855,happ(happ(Vvar__3__radd__80845,Vvar__var__var__var__var__8__n__80888__80891__80929__80932__80935),happ(happ(Vvar__3__radd__80845,Vvar__var__var__var__var__9__m__80889__80892__80930__80933__80936),Vvar__var__var__var__var__10__p__80890__80893__80931__80934__80937))),happ(happ(Vvar__3__radd__80845,happ(happ(Vvar__3__radd__80845,Vvar__var__var__var__var__8__n__80888__80891__80929__80932__80935),Vvar__var__var__var__var__9__m__80889__80892__80930__80933__80936)),Vvar__var__var__var__var__10__p__80890__80893__80931__80934__80937))) ) ) )
                    & ! [Vvar__var__var__var__var__var__9__n__80895__80896__80938__80939__80940__80941] :
                        ( t(Vvar__var__var__var__var__var__9__n__80895__80896__80938__80939__80940__80941,Vvar__0__R__80842)
                       => p(happ(happ(Vvar__5__req__80855,happ(happ(Vvar__4__rmul__80850,Vvar__2__rI__80844),Vvar__var__var__var__var__var__9__n__80895__80896__80938__80939__80940__80941)),Vvar__var__var__var__var__var__9__n__80895__80896__80938__80939__80940__80941)) )
                    & ! [Vvar__var__var__var__var__var__10__n__80898__80899__80942__80943__80944__80945] :
                        ( t(Vvar__var__var__var__var__var__10__n__80898__80899__80942__80943__80944__80945,Vvar__0__R__80842)
                       => p(happ(happ(Vvar__5__req__80855,happ(happ(Vvar__4__rmul__80850,Vvar__1__rO__80843),Vvar__var__var__var__var__var__10__n__80898__80899__80942__80943__80944__80945)),Vvar__1__rO__80843)) )
                    & ! [Vvar__var__var__var__var__11__n__80901__80903__80946__80948__80950] :
                        ( t(Vvar__var__var__var__var__11__n__80901__80903__80946__80948__80950,Vvar__0__R__80842)
                       => ! [Vvar__var__var__var__var__12__m__80902__80904__80947__80949__80951] :
                            ( t(Vvar__var__var__var__var__12__m__80902__80904__80947__80949__80951,Vvar__0__R__80842)
                           => p(happ(happ(Vvar__5__req__80855,happ(happ(Vvar__4__rmul__80850,Vvar__var__var__var__var__11__n__80901__80903__80946__80948__80950),Vvar__var__var__var__var__12__m__80902__80904__80947__80949__80951)),happ(happ(Vvar__4__rmul__80850,Vvar__var__var__var__var__12__m__80902__80904__80947__80949__80951),Vvar__var__var__var__var__11__n__80901__80903__80946__80948__80950))) ) )
                    & ! [Vvar__var__var__var__var__12__n__80906__80909__80952__80955__80958] :
                        ( t(Vvar__var__var__var__var__12__n__80906__80909__80952__80955__80958,Vvar__0__R__80842)
                       => ! [Vvar__var__var__var__var__13__m__80907__80910__80953__80956__80959] :
                            ( t(Vvar__var__var__var__var__13__m__80907__80910__80953__80956__80959,Vvar__0__R__80842)
                           => ! [Vvar__var__var__var__var__14__p__80908__80911__80954__80957__80960] :
                                ( t(Vvar__var__var__var__var__14__p__80908__80911__80954__80957__80960,Vvar__0__R__80842)
                               => p(happ(happ(Vvar__5__req__80855,happ(happ(Vvar__4__rmul__80850,Vvar__var__var__var__var__12__n__80906__80909__80952__80955__80958),happ(happ(Vvar__4__rmul__80850,Vvar__var__var__var__var__13__m__80907__80910__80953__80956__80959),Vvar__var__var__var__var__14__p__80908__80911__80954__80957__80960))),happ(happ(Vvar__4__rmul__80850,happ(happ(Vvar__4__rmul__80850,Vvar__var__var__var__var__12__n__80906__80909__80952__80955__80958),Vvar__var__var__var__var__13__m__80907__80910__80953__80956__80959)),Vvar__var__var__var__var__14__p__80908__80911__80954__80957__80960))) ) ) )
                    & ! [Vvar__var__var__var__var__var__13__n__80913__80916__80961__80964__80967__80970] :
                        ( t(Vvar__var__var__var__var__var__13__n__80913__80916__80961__80964__80967__80970,Vvar__0__R__80842)
                       => ! [Vvar__var__var__var__var__var__14__m__80914__80917__80962__80965__80968__80971] :
                            ( t(Vvar__var__var__var__var__var__14__m__80914__80917__80962__80965__80968__80971,Vvar__0__R__80842)
                           => ! [Vvar__var__var__var__var__var__15__p__80915__80918__80963__80966__80969__80972] :
                                ( t(Vvar__var__var__var__var__var__15__p__80915__80918__80963__80966__80969__80972,Vvar__0__R__80842)
                               => p(happ(happ(Vvar__5__req__80855,happ(happ(Vvar__4__rmul__80850,happ(happ(Vvar__3__radd__80845,Vvar__var__var__var__var__var__13__n__80913__80916__80961__80964__80967__80970),Vvar__var__var__var__var__var__14__m__80914__80917__80962__80965__80968__80971)),Vvar__var__var__var__var__var__15__p__80915__80918__80963__80966__80969__80972)),happ(happ(Vvar__3__radd__80845,happ(happ(Vvar__4__rmul__80850,Vvar__var__var__var__var__var__13__n__80913__80916__80961__80964__80967__80970),Vvar__var__var__var__var__var__15__p__80915__80918__80963__80966__80969__80972)),happ(happ(Vvar__4__rmul__80850,Vvar__var__var__var__var__var__14__m__80914__80917__80962__80965__80968__80971),Vvar__var__var__var__var__var__15__p__80915__80918__80963__80966__80969__80972)))) ) ) )
                    & p(c_24True) ) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.setoid_ring.Ring_theory.sring_eq_ext',axiom,
    ! [Vvar__0__R__104211,Vvar__1__radd__104212,Vvar__2__rmul__104217,Vvar__3__req__104222] :
      ( cType___24t(Vvar__0__R__104211)
     => ( c_24__type__104297___24t(Vvar__0__R__104211,Vvar__1__radd__104212,Vvar__2__rmul__104217,Vvar__3__req__104222,Vvar__1__radd__104212)
       => ( c_24__type__104320___24t(Vvar__0__R__104211,Vvar__1__radd__104212,Vvar__2__rmul__104217,Vvar__3__req__104222,Vvar__2__rmul__104217)
         => ( c_24__type__104343___24t(Vvar__0__R__104211,Vvar__1__radd__104212,Vvar__2__rmul__104217,Vvar__3__req__104222,Vvar__3__req__104222)
           => ( cCoq_2esetoid__ring_2eRing__theory_2esring__eq__ext___24a4(Vvar__0__R__104211,Vvar__1__radd__104212,Vvar__2__rmul__104217,Vvar__3__req__104222)
             => ( cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__104366___24a4(Vvar__0__R__104211,Vvar__1__radd__104212,Vvar__2__rmul__104217,Vvar__3__req__104222),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(Vvar__0__R__104211,c_24__type__104384___24a4(Vvar__0__R__104211,Vvar__1__radd__104212,Vvar__2__rmul__104217,Vvar__3__req__104222),Vvar__3__req__104222,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(Vvar__0__R__104211,Vvar__0__R__104211,Vvar__3__req__104222,Vvar__3__req__104222)),Vvar__1__radd__104212)
                & cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__104410___24a4(Vvar__0__R__104211,Vvar__1__radd__104212,Vvar__2__rmul__104217,Vvar__3__req__104222),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(Vvar__0__R__104211,c_24__type__104428___24a4(Vvar__0__R__104211,Vvar__1__radd__104212,Vvar__2__rmul__104217,Vvar__3__req__104222),Vvar__3__req__104222,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(Vvar__0__R__104211,Vvar__0__R__104211,Vvar__3__req__104222,Vvar__3__req__104222)),Vvar__2__rmul__104217)
                & p(c_24True) ) ) ) ) ) ) ).

fof('$_inversion_Hammer.Tactics.Reconstr.ReconstrT',axiom,
    ! [VX97381] :
      ( cHammer_2eTactics_2eReconstr_2eReconstrT___24t(VX97381)
     => ( VX97381 = cHammer_2eTactics_2eReconstr_2eEmpty
        | VX97381 = cHammer_2eTactics_2eReconstr_2eAllHyps ) ) ).

fof('$_inversion_IntMap.Map.Map',axiom,
    ! [Vvar__0__A__248,VX249] :
      ( cType___24t(Vvar__0__A__248)
     => ( cIntMap_2eMap_2eMap___24t(Vvar__0__A__248,VX249)
       => ( VX249 = cIntMap_2eMap_2eM0___24a1(Vvar__0__A__248)
          | ? [Vvar__1___24Anonymous__252] :
              ( cIntMap_2eMap_2ead___24t(Vvar__1___24Anonymous__252)
              & ? [Vvar__2___24Anonymous__253] :
                  ( t(Vvar__2___24Anonymous__253,Vvar__0__A__248)
                  & VX249 = cIntMap_2eMap_2eM1___24a3(Vvar__0__A__248,Vvar__1___24Anonymous__252,Vvar__2___24Anonymous__253) ) )
          | ? [Vvar__1___24Anonymous__255] :
              ( cIntMap_2eMap_2eMap___24t(Vvar__0__A__248,Vvar__1___24Anonymous__255)
              & ? [Vvar__2___24Anonymous__256] :
                  ( cIntMap_2eMap_2eMap___24t(Vvar__0__A__248,Vvar__2___24Anonymous__256)
                  & VX249 = cIntMap_2eMap_2eM2___24a3(Vvar__0__A__248,Vvar__1___24Anonymous__255,Vvar__2___24Anonymous__256) ) ) ) ) ) ).

fof('$_inversion_Mapcanon.MapCanon.mapcanon',axiom,
    ! [Vvar__0___24Anonymous__623] :
      ( cIntMap_2eMap_2eMap___24t(cA,Vvar__0___24Anonymous__623)
     => ( cMapcanon_2eMapCanon_2emapcanon___24a1(Vvar__0___24Anonymous__623)
       => ( Vvar__0___24Anonymous__623 = cIntMap_2eMap_2eM0___24a1(cA)
          | ? [Vvar__0__a__625] :
              ( cIntMap_2eMap_2ead___24t(Vvar__0__a__625)
              & ? [Vvar__1__y__626] :
                  ( cA___24t(Vvar__1__y__626)
                  & Vvar__0___24Anonymous__623 = cIntMap_2eMap_2eM1___24a3(cA,Vvar__0__a__625,Vvar__1__y__626) ) )
          | ? [Vvar__0__m1__627] :
              ( cIntMap_2eMap_2eMap___24t(cA,Vvar__0__m1__627)
              & ? [Vvar__1__m2__628] :
                  ( cIntMap_2eMap_2eMap___24t(cA,Vvar__1__m2__628)
                  & cMapcanon_2eMapCanon_2emapcanon___24a1(Vvar__0__m1__627)
                  & cMapcanon_2eMapCanon_2emapcanon___24a1(Vvar__1__m2__628)
                  & cCoq_2eInit_2ePeano_2ele___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO)),cIntMap_2eMap_2eMapCard___24a2(cA,cIntMap_2eMap_2eM2___24a3(cA,Vvar__0__m1__627,Vvar__1__m2__628)))
                  & Vvar__0___24Anonymous__623 = cIntMap_2eMap_2eM2___24a3(cA,Vvar__0__m1__627,Vvar__1__m2__628) ) ) ) ) ) ).

fof('$_lam_105565',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1] : c_24__lam__105565___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = Vv__CANONICAL__0 ).

fof('$_lam_1157',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] : c_24__lam__1157___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_116',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__116___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__120] :
                ( cIntMap_2eMap_2ead___24t(Vvar__1___24Anonymous__120)
                & ? [Vvar__2___24Anonymous__121] :
                    ( t(Vvar__2___24Anonymous__121,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__120)
                           => ( Vv__CANONICAL__5 = cIntMap_2eMap_2eM1___24a3(Vv__CANONICAL__1,Vvar__1___24Anonymous__120,Vvar__2___24Anonymous__121)
                              & ( ? [Vvar__1___24Anonymous__129] :
                                    ( t(Vvar__1___24Anonymous__129,Vv__CANONICAL__0)
                                    & cIntMap_2eMap_2eMapGet___24a3(Vv__CANONICAL__0,Vv__CANONICAL__2,Vvar__1___24Anonymous__120) = cCoq_2eInit_2eDatatypes_2eSome___24a2(Vv__CANONICAL__0,Vvar__1___24Anonymous__129)
                                    & c_24__lam__116___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__120,Vvar__1___24Anonymous__129) )
                                | ( cIntMap_2eMap_2eMapGet___24a3(Vv__CANONICAL__0,Vv__CANONICAL__2,Vvar__1___24Anonymous__120) = cCoq_2eInit_2eDatatypes_2eNone___24a1(Vv__CANONICAL__0)
                                  & c_24__lam__116___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__132] :
                ( cIntMap_2eMap_2eMap___24t(Vv__CANONICAL__1,Vvar__1___24Anonymous__132)
                & ? [Vvar__2___24Anonymous__133] :
                    ( cIntMap_2eMap_2eMap___24t(Vv__CANONICAL__1,Vvar__2___24Anonymous__133)
                    & Vv__CANONICAL__5 = cIntMap_2eMap_2eM2___24a3(Vv__CANONICAL__1,Vvar__1___24Anonymous__132,Vvar__2___24Anonymous__133)
                    & c_24__lam__116___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__132),cIntMap_2eFset_2eMapDomRestrTo___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__4,Vvar__2___24Anonymous__133)) ) ) ) ) ) ) ).

fof('$_lam_1162',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] : c_24__lam__1162___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_1181',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__1181___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__1181___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_1194',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__1194___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = happ(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__1194___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = happ(Vv__CANONICAL__1,cCoq_2eNArith_2eBinNatDef_2eN_2ediv2___24a1(Vv__CANONICAL__3)) ) ) ) ) ).

fof('$_lam_122089',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1] :
      ( c_24__lam__122089___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1)
    <=> ( cIntMap_2eMapaxioms_2eeqmap___24a3(cA,Vv__CANONICAL__0,Vv__CANONICAL__1)
        & cMapcanon_2eMapCanon_2emapcanon___24a1(Vv__CANONICAL__1) ) ) ).

fof('$_lam_1305',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__1305___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__1306] :
                ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__1306)
                & cCoq_2eNArith_2eBinNatDef_2eN_2elxor___24a2(Vv__CANONICAL__2,Vv__CANONICAL__4) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__1306)
                & c_24__lam__1305___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__1306) ) ) ) ) ) ).

fof('$_lam_1342',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__1342___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__1343] :
              ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__1343)
              & ( cType___24t(Vv__CANONICAL__0)
               => ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__1343)
                 => ( Vv__CANONICAL__3 = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__1343)
                    & ( ? [Vvar__0___24Anonymous__1347] :
                          ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__1347)
                          & Vvar__0___24Anonymous__1343 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__1347)
                          & c_24__lam__1342___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__1347),Vv__CANONICAL__4)) )
                      | ? [Vvar__0___24Anonymous__1348] :
                          ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__1348)
                          & Vvar__0___24Anonymous__1343 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__1348)
                          & c_24__lam__1342___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__1348),Vv__CANONICAL__4),Vv__CANONICAL__2) )
                      | ( Vvar__0___24Anonymous__1343 = cCoq_2eNumbers_2eBinNums_2exH
                        & c_24__lam__1342___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_1372',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] : c_24__lam__1372___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO) ).

fof('$_lam_1378',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] : c_24__lam__1378___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = Vv__CANONICAL__2 ).

fof('$_lam_188',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__191] :
                  ( t(Vvar__1___24Anonymous__191,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__191)
                  & c_24__lam__188___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__188___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4) = Vv__CANONICAL__2 ) ) ) ) ) ) ).

fof('$_lam_230',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__230___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__234] :
                ( cIntMap_2eMap_2ead___24t(Vvar__1___24Anonymous__234)
                & ? [Vvar__2___24Anonymous__235] :
                    ( t(Vvar__2___24Anonymous__235,Vv__CANONICAL__1)
                    & Vv__CANONICAL__5 = cIntMap_2eMap_2eM1___24a3(Vv__CANONICAL__1,Vvar__1___24Anonymous__234,Vvar__2___24Anonymous__235)
                    & c_24__lam__230___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__234) ) )
            | ? [Vvar__1___24Anonymous__238] :
                ( cIntMap_2eMap_2eMap___24t(Vv__CANONICAL__1,Vvar__1___24Anonymous__238)
                & ? [Vvar__2___24Anonymous__239] :
                    ( cIntMap_2eMap_2eMap___24t(Vv__CANONICAL__1,Vvar__2___24Anonymous__239)
                    & Vv__CANONICAL__5 = cIntMap_2eMap_2eM2___24a3(Vv__CANONICAL__1,Vvar__1___24Anonymous__238,Vvar__2___24Anonymous__239)
                    & c_24__lam__230___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__238),cIntMap_2eFset_2eMapDomRestrBy___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__4,Vvar__2___24Anonymous__239)) ) ) ) ) ) ) ).

fof('$_lam_43',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] : c_24__lam__43___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = cIntMap_2eMap_2eM0___24a1(Vv__CANONICAL__0) ).

fof('$_lam_449',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__449___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__450] :
                ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__450)
                & cCoq_2eNArith_2eBinNatDef_2eN_2elxor___24a2(Vv__CANONICAL__1,Vv__CANONICAL__3) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__450)
                & c_24__lam__449___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__450) ) ) ) ) ) ).

fof('$_lam_486',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__486___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__487] :
              ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__487)
              & ( cType___24t(Vv__CANONICAL__0)
               => ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__487)
                 => ( Vv__CANONICAL__3 = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__487)
                    & ( ? [Vvar__0___24Anonymous__491] :
                          ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__491)
                          & Vvar__0___24Anonymous__487 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__491)
                          & c_24__lam__486___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__491),Vv__CANONICAL__4)) )
                      | ? [Vvar__0___24Anonymous__492] :
                          ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__492)
                          & Vvar__0___24Anonymous__487 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__492)
                          & c_24__lam__486___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__492),Vv__CANONICAL__4),Vv__CANONICAL__2) )
                      | ( Vvar__0___24Anonymous__487 = cCoq_2eNumbers_2eBinNums_2exH
                        & c_24__lam__486___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_58',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__61] :
                  ( t(Vvar__1___24Anonymous__61,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__61)
                  & c_24__lam__58___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__58___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_67076',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] :
      ( c_24__lam__67076___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_67248',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] :
      ( c_24__lam__67248___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_67269',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] : c_24__lam__67269___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_67275',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] : c_24__lam__67275___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_67335',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] : c_24__lam__67335___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_67379',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__67379___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__67379___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_67459',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__67464] :
              ( cIntMap_2eMap_2ead___24t(Vvar__2___24Anonymous__67464)
              & ? [Vvar__3___24Anonymous__67465] :
                  ( t(Vvar__3___24Anonymous__67465,Vv__CANONICAL__0)
                  & Vv__CANONICAL__4 = cCoq_2eInit_2eDatatypes_2epair___24a4(cIntMap_2eMap_2ead,Vv__CANONICAL__0,Vvar__2___24Anonymous__67464,Vvar__3___24Anonymous__67465)
                  & c_24__lam__67459___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__67464),Vvar__3___24Anonymous__67465)),Vv__CANONICAL__5) ) ) ) ) ) ).

fof('$_lam_703',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] :
      ( c_24__lam__703___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_733',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1] : c_24__lam__733___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = cCoq_2eInit_2eDatatypes_2eNone___24a1(Vv__CANONICAL__0) ).

fof('$_lam_741',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__741___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__741___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = cCoq_2eInit_2eDatatypes_2eNone___24a1(Vv__CANONICAL__0) ) ) ) ) ) ).

fof('$_lam_76154',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__76157] :
                  ( t(Vvar__1___24Anonymous__76157,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__76157)
                  & c_24__lam__76154___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__76154___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_76173',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__76176] :
                  ( t(Vvar__1___24Anonymous__76176,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__76176)
                  & c_24__lam__76173___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__76173___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_76497',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1] : c_24__lam__76497___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = happ(Vv__CANONICAL__0,cCoq_2eNArith_2eBinNatDef_2eN_2edouble___24a1(Vv__CANONICAL__1)) ).

fof('$_lam_76499',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1] : c_24__lam__76499___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = happ(Vv__CANONICAL__0,cCoq_2eNArith_2eBinNatDef_2eN_2esucc__double___24a1(Vv__CANONICAL__1)) ).

fof('$_lam_76551',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__76551___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__76551___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_76584',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__76587] :
                ( t(Vvar__1___24Anonymous__76587,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__76587)
                & c_24__lam__76584___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__76587) )
            | ( 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__76584___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__76584___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_76596',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__76596___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__76596___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_76608',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__76611] :
                ( t(Vvar__1___24Anonymous__76611,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__76611)
                & c_24__lam__76608___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = cCoq_2eInit_2eDatatypes_2eSome___24a2(Vv__CANONICAL__0,Vvar__1___24Anonymous__76611) )
            | ( cIntMap_2eMap_2eMapGet___24a3(Vv__CANONICAL__0,Vv__CANONICAL__2,Vv__CANONICAL__3) = cCoq_2eInit_2eDatatypes_2eNone___24a1(Vv__CANONICAL__0)
              & c_24__lam__76608___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_76658',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__76661] :
                ( t(Vvar__1___24Anonymous__76661,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__76661)
                & c_24__lam__76658___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__76658___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_76708',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__76708___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4) = Vv__CANONICAL__1 )
          | ? [Vvar__1___24Anonymous__76712] :
              ( cIntMap_2eMap_2ead___24t(Vvar__1___24Anonymous__76712)
              & ? [Vvar__2___24Anonymous__76713] :
                  ( t(Vvar__2___24Anonymous__76713,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__76712)
                       => ( Vv__CANONICAL__4 = cIntMap_2eMap_2eM1___24a3(Vv__CANONICAL__0,Vvar__1___24Anonymous__76712,Vvar__2___24Anonymous__76713)
                          & ( ? [Vvar__1___24Anonymous__76721] :
                                ( t(Vvar__1___24Anonymous__76721,Vv__CANONICAL__0)
                                & cIntMap_2eMap_2eMapGet___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__1___24Anonymous__76712) = cCoq_2eInit_2eDatatypes_2eSome___24a2(Vv__CANONICAL__0,Vvar__1___24Anonymous__76721)
                                & c_24__lam__76708___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__76712) )
                            | ( cIntMap_2eMap_2eMapGet___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__1___24Anonymous__76712) = cCoq_2eInit_2eDatatypes_2eNone___24a1(Vv__CANONICAL__0)
                              & c_24__lam__76708___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__76712,Vvar__2___24Anonymous__76713) ) ) ) ) ) ) ) )
          | ? [Vvar__1___24Anonymous__76724] :
              ( cIntMap_2eMap_2eMap___24t(Vv__CANONICAL__0,Vvar__1___24Anonymous__76724)
              & ? [Vvar__2___24Anonymous__76725] :
                  ( cIntMap_2eMap_2eMap___24t(Vv__CANONICAL__0,Vvar__2___24Anonymous__76725)
                  & Vv__CANONICAL__4 = cIntMap_2eMap_2eM2___24a3(Vv__CANONICAL__0,Vvar__1___24Anonymous__76724,Vvar__2___24Anonymous__76725)
                  & c_24__lam__76708___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__76724),cIntMap_2eMap_2eMapDelta___24a3(Vv__CANONICAL__0,Vv__CANONICAL__3,Vvar__2___24Anonymous__76725)) ) ) ) ) ) ).

fof('$_lam_76759',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__76762] :
                ( t(Vvar__1___24Anonymous__76762,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__76762)
                        & ( ? [Vvar__1___24Anonymous__76767] :
                              ( t(Vvar__1___24Anonymous__76767,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__76767)
                              & c_24__lam__76759___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__76759___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = cCoq_2eInit_2eDatatypes_2eSome___24a2(Vv__CANONICAL__0,Vvar__1___24Anonymous__76762) ) ) ) ) ) ) )
            | ( 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__76772] :
                          ( t(Vvar__1___24Anonymous__76772,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__76772)
                          & c_24__lam__76759___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = cCoq_2eInit_2eDatatypes_2eSome___24a2(Vv__CANONICAL__0,Vvar__1___24Anonymous__76772) )
                      | ( cIntMap_2eMap_2eMapGet___24a3(Vv__CANONICAL__0,Vv__CANONICAL__2,Vv__CANONICAL__3) = cCoq_2eInit_2eDatatypes_2eNone___24a1(Vv__CANONICAL__0)
                        & c_24__lam__76759___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = cCoq_2eInit_2eDatatypes_2eNone___24a1(Vv__CANONICAL__0) ) ) ) ) ) ) ) ) ) ) ).

fof('$_lam_768',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__768___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__769] :
              ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__769)
              & ( cType___24t(Vv__CANONICAL__0)
               => ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__769)
                 => ( Vv__CANONICAL__3 = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__769)
                    & ( ? [Vvar__0___24Anonymous__773] :
                          ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__773)
                          & Vvar__0___24Anonymous__769 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__773)
                          & c_24__lam__768___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__773)) )
                      | ? [Vvar__0___24Anonymous__774] :
                          ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__774)
                          & Vvar__0___24Anonymous__769 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__774)
                          & c_24__lam__768___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__774)) )
                      | ( Vvar__0___24Anonymous__769 = cCoq_2eNumbers_2eBinNums_2exH
                        & c_24__lam__768___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_76842',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] : c_24__lam__76842___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_76846',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] : c_24__lam__76846___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_76850',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] : c_24__lam__76850___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_76869',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1] : c_24__lam__76869___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = Vv__CANONICAL__1 ).

fof('$_lam_77113',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] : c_24__lam__77113___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_77119',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] : c_24__lam__77119___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_77275',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4] : c_24__lam__77275___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_77283',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4] : c_24__lam__77283___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_77375',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] : c_24__lam__77375___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = Vv__CANONICAL__3 ).

fof('$_lam_77812',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4] : c_24__lam__77812___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_77846',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4] : c_24__lam__77846___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_77983',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1] :
      ( c_24__lam__77983___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1)
    <=> Vv__CANONICAL__0 = cCoq_2eNArith_2eBinNatDef_2eN_2edouble___24a1(Vv__CANONICAL__1) ) ).

fof('$_lam_77985',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1] :
      ( c_24__lam__77985___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1)
    <=> Vv__CANONICAL__0 = cCoq_2eNArith_2eBinNatDef_2eN_2esucc__double___24a1(Vv__CANONICAL__1) ) ).

fof('$_lam_795',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] : c_24__lam__795___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_800',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] : c_24__lam__800___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_864',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1] : c_24__lam__864___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = cIntMap_2eMap_2eM0___24a1(Vv__CANONICAL__0) ).

fof('$_lam_872',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__872___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__872___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = Vv__CANONICAL__1 ) ) ) ) ) ).

fof('$_lam_880',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__880___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__880___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_912',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1] : c_24__lam__912___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = Vv__CANONICAL__1 ).

fof('$_lam_916',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] : c_24__lam__916___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_948',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__948___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4) = Vv__CANONICAL__1 )
          | ? [Vvar__1___24Anonymous__952] :
              ( cIntMap_2eMap_2ead___24t(Vvar__1___24Anonymous__952)
              & ? [Vvar__2___24Anonymous__953] :
                  ( t(Vvar__2___24Anonymous__953,Vv__CANONICAL__0)
                  & Vv__CANONICAL__4 = cIntMap_2eMap_2eM1___24a3(Vv__CANONICAL__0,Vvar__1___24Anonymous__952,Vvar__2___24Anonymous__953)
                  & c_24__lam__948___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__952,Vvar__2___24Anonymous__953) ) )
          | ? [Vvar__1___24Anonymous__956] :
              ( cIntMap_2eMap_2eMap___24t(Vv__CANONICAL__0,Vvar__1___24Anonymous__956)
              & ? [Vvar__2___24Anonymous__957] :
                  ( cIntMap_2eMap_2eMap___24t(Vv__CANONICAL__0,Vvar__2___24Anonymous__957)
                  & Vv__CANONICAL__4 = cIntMap_2eMap_2eM2___24a3(Vv__CANONICAL__0,Vvar__1___24Anonymous__956,Vvar__2___24Anonymous__957)
                  & c_24__lam__948___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__956),cIntMap_2eMap_2eMapMerge___24a3(Vv__CANONICAL__0,Vv__CANONICAL__3,Vvar__2___24Anonymous__957)) ) ) ) ) ) ).

fof('$_lam_981',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] :
      ( c_24__lam__981___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('$_prop_1020',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__4,Vv__CANONICAL__5] :
      ( p(c_24__prop__1020___24a3(Vv__CANONICAL__0,Vv__CANONICAL__4,Vv__CANONICAL__5))
    <=> Vv__CANONICAL__4 = Vv__CANONICAL__5 ) ).

fof('$_prop_1021',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__4,Vv__CANONICAL__5] :
      ( p(c_24__prop__1021___24a3(Vv__CANONICAL__0,Vv__CANONICAL__4,Vv__CANONICAL__5))
    <=> Vv__CANONICAL__4 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vv__CANONICAL__5) ) ).

fof('$_prop_105527',axiom,
    ! [Vvar__0___24Anonymous__105503,Vvar__0__S__105505,Vvar__1__x__105506,Vvar__2__y__105507] :
      ( p(c_24__prop__105527___24a4(Vvar__0___24Anonymous__105503,Vvar__0__S__105505,Vvar__1__x__105506,Vvar__2__y__105507))
    <=> Vvar__1__x__105506 = Vvar__2__y__105507 ) ).

fof('$_prop_105528',axiom,
    ! [Vvar__0___24Anonymous__105503,Vvar__0__x__105508,Vvar__1__y__105509] :
      ( p(c_24__prop__105528___24a3(Vvar__0___24Anonymous__105503,Vvar__0__x__105508,Vvar__1__y__105509))
    <=> Vvar__0__x__105508 = Vvar__1__y__105509 ) ).

fof('$_prop_105529',axiom,
    ! [Vvar__0___24Anonymous__105503,Vvar__0__x__105510,Vvar__1__s__105511] :
      ( p(c_24__prop__105529___24a3(Vvar__0___24Anonymous__105503,Vvar__0__x__105510,Vvar__1__s__105511))
    <=> cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2emem___24a2(Vvar__0__x__105510,Vvar__1__s__105511) = cCoq_2eInit_2eDatatypes_2etrue ) ).

fof('$_prop_105530',axiom,
    ! [Vvar__0___24Anonymous__105503,Vvar__0__P__105512,Vvar__1__Q__105513] :
      ( p(c_24__prop__105530___24a3(Vvar__0___24Anonymous__105503,Vvar__0__P__105512,Vvar__1__Q__105513))
    <=> ( p(Vvar__0__P__105512)
        & p(Vvar__1__Q__105513) ) ) ).

fof('$_prop_105531',axiom,
    ! [Vvar__0___24Anonymous__105503,Vvar__0__P__105516,Vvar__1__Q__105517] :
      ( p(c_24__prop__105531___24a3(Vvar__0___24Anonymous__105503,Vvar__0__P__105516,Vvar__1__Q__105517))
    <=> ( p(Vvar__0__P__105516)
        | p(Vvar__1__Q__105517) ) ) ).

fof('$_prop_105532',axiom,
    ! [Vvar__0___24Anonymous__105503,Vvar__0__P__105520,Vvar__1__Q__105521] :
      ( p(c_24__prop__105532___24a3(Vvar__0___24Anonymous__105503,Vvar__0__P__105520,Vvar__1__Q__105521))
    <=> ( p(Vvar__0__P__105520)
       => p(Vvar__1__Q__105521) ) ) ).

fof('$_prop_105533',axiom,
    ! [Vvar__0___24Anonymous__105503,Vvar__0__P__105525] :
      ( p(c_24__prop__105533___24a2(Vvar__0___24Anonymous__105503,Vvar__0__P__105525))
    <=> ~ p(Vvar__0__P__105525) ) ).

fof('$_prop_105547',axiom,
    ! [Vvar__0___24Anonymous__105534,Vvar__0__s__105538] :
      ( p(c_24__prop__105547___24a2(Vvar__0___24Anonymous__105534,Vvar__0__s__105538))
    <=> ! [Vvar__1__a__105539] :
          ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(Vvar__1__a__105539)
         => ~ cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eIn___24a2(Vvar__1__a__105539,Vvar__0__s__105538) ) ) ).

fof('$_prop_105548',axiom,
    ! [Vvar__0___24Anonymous__105534,Vvar__0__s1__105540,Vvar__1__s2__105541] :
      ( p(c_24__prop__105548___24a3(Vvar__0___24Anonymous__105534,Vvar__0__s1__105540,Vvar__1__s2__105541))
    <=> ! [Vvar__2__a__105542] :
          ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(Vvar__2__a__105542)
         => ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eIn___24a2(Vvar__2__a__105542,Vvar__0__s1__105540)
           => cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eIn___24a2(Vvar__2__a__105542,Vvar__1__s2__105541) ) ) ) ).

fof('$_prop_105549',axiom,
    ! [Vvar__0___24Anonymous__105534,Vvar__0__s1__105544,Vvar__1__s2__105545] :
      ( p(c_24__prop__105549___24a3(Vvar__0___24Anonymous__105534,Vvar__0__s1__105544,Vvar__1__s2__105545))
    <=> ! [Vvar__2__a__105546] :
          ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(Vvar__2__a__105546)
         => ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eIn___24a2(Vvar__2__a__105546,Vvar__0__s1__105544)
          <=> cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eIn___24a2(Vvar__2__a__105546,Vvar__1__s2__105545) ) ) ) ).

fof('$_prop_1430',axiom,
    ( p(c_24__prop__1430)
  <=> cCoq_2eInit_2eDatatypes_2etrue = cCoq_2eInit_2eDatatypes_2etrue ) ).

fof('$_prop_1431',axiom,
    ( p(c_24__prop__1431)
  <=> cCoq_2eInit_2eDatatypes_2etrue = cCoq_2eInit_2eDatatypes_2efalse ) ).

fof('$_prop_1432',axiom,
    ( p(c_24__prop__1432)
  <=> cCoq_2eInit_2eDatatypes_2efalse = cCoq_2eInit_2eDatatypes_2etrue ) ).

fof('$_prop_1433',axiom,
    ( p(c_24__prop__1433)
  <=> cCoq_2eInit_2eDatatypes_2efalse = cCoq_2eInit_2eDatatypes_2efalse ) ).

fof('$_prop_1436',axiom,
    ! [Vv__CANONICAL__0] :
      ( p(c_24__prop__1436___24a1(Vv__CANONICAL__0))
    <=> Vv__CANONICAL__0 = cCoq_2eInit_2eDatatypes_2etrue ) ).

fof('$_prop_1437',axiom,
    ! [Vv__CANONICAL__0] :
      ( p(c_24__prop__1437___24a1(Vv__CANONICAL__0))
    <=> Vv__CANONICAL__0 = cCoq_2eInit_2eDatatypes_2efalse ) ).

fof('$_prop_562',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__5,Vv__CANONICAL__6] :
      ( p(c_24__prop__562___24a3(Vv__CANONICAL__0,Vv__CANONICAL__5,Vv__CANONICAL__6))
    <=> Vv__CANONICAL__6 = Vv__CANONICAL__5 ) ).

fof('$_prop_563',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__5,Vv__CANONICAL__6] :
      ( p(c_24__prop__563___24a3(Vv__CANONICAL__0,Vv__CANONICAL__5,Vv__CANONICAL__6))
    <=> Vv__CANONICAL__6 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vv__CANONICAL__5) ) ).

fof('$_prop_67217',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__5,Vv__CANONICAL__6] :
      ( p(c_24__prop__67217___24a3(Vv__CANONICAL__0,Vv__CANONICAL__5,Vv__CANONICAL__6))
    <=> Vv__CANONICAL__6 = Vv__CANONICAL__5 ) ).

fof('$_prop_67218',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__5,Vv__CANONICAL__6] :
      ( p(c_24__prop__67218___24a3(Vv__CANONICAL__0,Vv__CANONICAL__5,Vv__CANONICAL__6))
    <=> Vv__CANONICAL__6 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vv__CANONICAL__5) ) ).

fof('$_prop_704',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1] :
      ( p(c_24__prop__704___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1))
    <=> Vv__CANONICAL__1 = cCoq_2eInit_2eDatatypes_2eNone___24a1(Vv__CANONICAL__0) ) ).

fof('$_type_100096',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__100097] :
      ( c_24__type__100096___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__100097)
    <=> ! [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__100097,Vv__CANONICAL__22),Vv__CANONICAL__23)) ) ) ) ).

fof('$_type_100442',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__100443] :
      ( c_24__type__100442___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__100443)
    <=> ! [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__100443,Vv__CANONICAL__22),Vv__CANONICAL__23)) ) ) ) ).

fof('$_type_100788',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__100789] :
      ( c_24__type__100788___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__100789)
    <=> ! [Vv__CANONICAL__22] :
          ( t(Vv__CANONICAL__22,Vv__CANONICAL__9)
         => ! [Vv__CANONICAL__23] :
              ( t(Vv__CANONICAL__23,Vv__CANONICAL__9)
             => t(happ(happ(Vvar__100789,Vv__CANONICAL__22),Vv__CANONICAL__23),Vv__CANONICAL__9) ) ) ) ).

fof('$_type_101134',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__101135] :
      ( c_24__type__101134___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__101135)
    <=> ! [Vv__CANONICAL__22] :
          ( t(Vv__CANONICAL__22,Vv__CANONICAL__9)
         => ! [Vv__CANONICAL__23] :
              ( t(Vv__CANONICAL__23,Vv__CANONICAL__9)
             => t(happ(happ(Vvar__101135,Vv__CANONICAL__22),Vv__CANONICAL__23),Vv__CANONICAL__9) ) ) ) ).

fof('$_type_101480',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__101481] :
      ( c_24__type__101480___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__101481)
    <=> ! [Vv__CANONICAL__22] :
          ( t(Vv__CANONICAL__22,Vv__CANONICAL__9)
         => ! [Vv__CANONICAL__23] :
              ( t(Vv__CANONICAL__23,Vv__CANONICAL__9)
             => t(happ(happ(Vvar__101481,Vv__CANONICAL__22),Vv__CANONICAL__23),Vv__CANONICAL__9) ) ) ) ).

fof('$_type_1018',axiom,
    ! [Vvar__1019] :
      ( c_24__type__1018___24t(Vvar__1019)
    <=> ! [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__1020___24a3(Vv__CANONICAL__0,Vv__CANONICAL__4,Vv__CANONICAL__5),c_24__prop__1021___24a3(Vv__CANONICAL__0,Vv__CANONICAL__4,Vv__CANONICAL__5),happ(happ(happ(happ(happ(happ(Vvar__1019,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5)) ) ) ) ) ) ) ) ) ) ) ).

fof('$_type_101803',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__101804] :
      ( c_24__type__101803___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__101804)
    <=> ! [Vv__CANONICAL__22] :
          ( t(Vv__CANONICAL__22,Vv__CANONICAL__9)
         => t(happ(Vvar__101804,Vv__CANONICAL__22),Vv__CANONICAL__9) ) ) ).

fof('$_type_102149',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__102150] :
      ( c_24__type__102149___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__102150)
    <=> ! [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__102150,Vv__CANONICAL__22),Vv__CANONICAL__23)) ) ) ) ).

fof('$_type_102495',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__102496] :
      ( c_24__type__102495___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__102496)
    <=> ! [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__102496,Vv__CANONICAL__22),Vv__CANONICAL__23)) ) ) ) ).

fof('$_type_1028',axiom,
    ! [Vvar__1029] :
      ( c_24__type__1028___24t(Vvar__1029)
    <=> ! [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__1029,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).

fof('$_type_102818',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__102819] :
      ( c_24__type__102818___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__102819)
    <=> ! [Vv__CANONICAL__22] :
          ( t(Vv__CANONICAL__22,Vv__CANONICAL__9)
         => t(happ(Vvar__102819,Vv__CANONICAL__22),Vv__CANONICAL__0) ) ) ).

fof('$_type_103141',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__103142] :
      ( c_24__type__103141___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__103142)
    <=> ! [Vv__CANONICAL__22] :
          ( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__22)
         => t(happ(Vvar__103142,Vv__CANONICAL__22),Vv__CANONICAL__19) ) ) ).

fof('$_type_103487',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__103488] :
      ( c_24__type__103487___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__103488)
    <=> ! [Vv__CANONICAL__22] :
          ( t(Vv__CANONICAL__22,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__23] :
              ( t(Vv__CANONICAL__23,Vv__CANONICAL__19)
             => t(happ(happ(Vvar__103488,Vv__CANONICAL__22),Vv__CANONICAL__23),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_103644',axiom,
    ! [Vvar__103645] :
      ( c_24__type__103644___24t(Vvar__103645)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
             => cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vv__CANONICAL__0,happ(happ(Vvar__103645,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_103646',axiom,
    ! [Vvar__103647] :
      ( c_24__type__103646___24t(Vvar__103647)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vv__CANONICAL__0,happ(Vvar__103647,Vv__CANONICAL__0)) ) ) ).

fof('$_type_103664',axiom,
    ! [Vvar__103665] :
      ( c_24__type__103664___24t(Vvar__103665)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( c_24__type__1415___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
             => ! [Vv__CANONICAL__2] :
                  ( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
                 => ! [Vv__CANONICAL__3] :
                      ( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
                     => ! [Vv__CANONICAL__4] :
                          ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__4)
                         => t(happ(happ(happ(happ(happ(Vvar__103665,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__0) ) ) ) ) ) ) ).

fof('$_type_103918',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__103919] :
      ( c_24__type__103918___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__103919)
    <=> ! [Vv__CANONICAL__8] :
          ( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__9] :
              ( t(Vv__CANONICAL__9,Vv__CANONICAL__0)
             => t(happ(happ(Vvar__103919,Vv__CANONICAL__8),Vv__CANONICAL__9),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_103981',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__103982] :
      ( c_24__type__103981___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__103982)
    <=> ! [Vv__CANONICAL__8] :
          ( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__9] :
              ( t(Vv__CANONICAL__9,Vv__CANONICAL__0)
             => t(happ(happ(Vvar__103982,Vv__CANONICAL__8),Vv__CANONICAL__9),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_104044',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__104045] :
      ( c_24__type__104044___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__104045)
    <=> ! [Vv__CANONICAL__8] :
          ( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__9] :
              ( t(Vv__CANONICAL__9,Vv__CANONICAL__0)
             => t(happ(happ(Vvar__104045,Vv__CANONICAL__8),Vv__CANONICAL__9),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_104098',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__104099] :
      ( c_24__type__104098___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__104099)
    <=> ! [Vv__CANONICAL__8] :
          ( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
         => t(happ(Vvar__104099,Vv__CANONICAL__8),Vv__CANONICAL__0) ) ) ).

fof('$_type_104161',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__104162] :
      ( c_24__type__104161___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__104162)
    <=> ! [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__104162,Vv__CANONICAL__8),Vv__CANONICAL__9)) ) ) ) ).

fof('$_type_104297',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__104298] :
      ( c_24__type__104297___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__104298)
    <=> ! [Vv__CANONICAL__4] :
          ( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__5] :
              ( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
             => t(happ(happ(Vvar__104298,Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_104320',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__104321] :
      ( c_24__type__104320___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__104321)
    <=> ! [Vv__CANONICAL__4] :
          ( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__5] :
              ( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
             => t(happ(happ(Vvar__104321,Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_104343',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__104344] :
      ( c_24__type__104343___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__104344)
    <=> ! [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__104344,Vv__CANONICAL__4),Vv__CANONICAL__5)) ) ) ) ).

fof('$_type_104366',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__104367] :
      ( c_24__type__104366___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__104367)
    <=> ! [Vv__CANONICAL__4] :
          ( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__5] :
              ( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
             => t(happ(happ(Vvar__104367,Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_104384',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__104385] :
      ( c_24__type__104384___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__104385)
    <=> ! [Vv__CANONICAL__4] :
          ( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
         => t(happ(Vvar__104385,Vv__CANONICAL__4),Vv__CANONICAL__0) ) ) ).

fof('$_type_1044',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__1045] :
      ( c_24__type__1044___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__1045)
    <=> ! [Vv__CANONICAL__2] :
          ( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
         => cProp___24t(happ(Vvar__1045,Vv__CANONICAL__2)) ) ) ).

fof('$_type_104410',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__104411] :
      ( c_24__type__104410___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__104411)
    <=> ! [Vv__CANONICAL__4] :
          ( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__5] :
              ( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
             => t(happ(happ(Vvar__104411,Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_104428',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__104429] :
      ( c_24__type__104428___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__104429)
    <=> ! [Vv__CANONICAL__4] :
          ( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
         => t(happ(Vvar__104429,Vv__CANONICAL__4),Vv__CANONICAL__0) ) ) ).

fof('$_type_104573',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__104574] :
      ( c_24__type__104573___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__104574)
    <=> ! [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__104574,Vv__CANONICAL__7),Vv__CANONICAL__8)) ) ) ) ).

fof('$_type_104623',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__104624] :
      ( c_24__type__104623___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__104624)
    <=> ! [Vv__CANONICAL__7] :
          ( t(Vv__CANONICAL__7,Vv__CANONICAL__2)
         => ! [Vv__CANONICAL__8] :
              ( t(Vv__CANONICAL__8,Vv__CANONICAL__2)
             => t(happ(happ(Vvar__104624,Vv__CANONICAL__7),Vv__CANONICAL__8),Vv__CANONICAL__2) ) ) ) ).

fof('$_type_104673',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__104674] :
      ( c_24__type__104673___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__104674)
    <=> ! [Vv__CANONICAL__7] :
          ( t(Vv__CANONICAL__7,Vv__CANONICAL__2)
         => ! [Vv__CANONICAL__8] :
              ( t(Vv__CANONICAL__8,Vv__CANONICAL__2)
             => t(happ(happ(Vvar__104674,Vv__CANONICAL__7),Vv__CANONICAL__8),Vv__CANONICAL__2) ) ) ) ).

fof('$_type_104715',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__104716] :
      ( c_24__type__104715___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__104716)
    <=> ! [Vv__CANONICAL__7] :
          ( t(Vv__CANONICAL__7,Vv__CANONICAL__2)
         => t(happ(Vvar__104716,Vv__CANONICAL__7),Vv__CANONICAL__0) ) ) ).

fof('$_type_104765',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__104766] :
      ( c_24__type__104765___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__104766)
    <=> ! [Vv__CANONICAL__7] :
          ( t(Vv__CANONICAL__7,Vv__CANONICAL__2)
         => ! [Vv__CANONICAL__8] :
              ( t(Vv__CANONICAL__8,Vv__CANONICAL__2)
             => cCoq_2eInit_2eDatatypes_2eprod___24t(Vv__CANONICAL__2,Vv__CANONICAL__2,happ(happ(Vvar__104766,Vv__CANONICAL__7),Vv__CANONICAL__8)) ) ) ) ).

fof('$_type_1048',axiom,
    ! [Vvar__1049] :
      ( c_24__type__1048___24t(Vvar__1049)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( c_24__type__1051___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
             => cType___24t(happ(happ(Vvar__1049,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_104841',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__104842] :
      ( c_24__type__104841___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__104842)
    <=> ! [Vv__CANONICAL__2] :
          ( t(Vv__CANONICAL__2,Vv__CANONICAL__1)
         => ! [Vv__CANONICAL__3] :
              ( t(Vv__CANONICAL__3,Vv__CANONICAL__1)
             => cCoq_2eInit_2eDatatypes_2eprod___24t(Vv__CANONICAL__1,Vv__CANONICAL__1,happ(happ(Vvar__104842,Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ).

fof('$_type_104951',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__104952] :
      ( c_24__type__104951___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__104952)
    <=> ! [Vv__CANONICAL__7] :
          ( t(Vv__CANONICAL__7,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__8] :
              ( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
             => t(happ(happ(Vvar__104952,Vv__CANONICAL__7),Vv__CANONICAL__8),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_104995',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__104996] :
      ( c_24__type__104995___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__104996)
    <=> ! [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__104996,Vv__CANONICAL__7),Vv__CANONICAL__8)) ) ) ) ).

fof('$_type_105031',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__105032] :
      ( c_24__type__105031___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__105032)
    <=> ! [Vv__CANONICAL__7] :
          ( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__7)
         => t(happ(Vvar__105032,Vv__CANONICAL__7),Vv__CANONICAL__4) ) ) ).

fof('$_type_105075',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__105076] :
      ( c_24__type__105075___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__105076)
    <=> ! [Vv__CANONICAL__7] :
          ( t(Vv__CANONICAL__7,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__8] :
              ( t(Vv__CANONICAL__8,Vv__CANONICAL__4)
             => t(happ(happ(Vvar__105076,Vv__CANONICAL__7),Vv__CANONICAL__8),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_1051',axiom,
    ! [Vv__CANONICAL__0,Vvar__1052] :
      ( c_24__type__1051___24t(Vv__CANONICAL__0,Vvar__1052)
    <=> ! [Vv__CANONICAL__1] :
          ( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
         => cProp___24t(happ(Vvar__1052,Vv__CANONICAL__1)) ) ) ).

fof('$_type_105112',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__105113] :
      ( c_24__type__105112___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__105113)
    <=> ! [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__105113,Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ).

fof('$_type_105145',axiom,
    ! [Vvar__105146] :
      ( c_24__type__105145___24t(Vvar__105146)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cType___24t(Vv__CANONICAL__1)
             => ! [Vv__CANONICAL__2] :
                  ( c_24__type__78044___24t(Vv__CANONICAL__1,Vv__CANONICAL__2)
                 => ! [Vv__CANONICAL__3] :
                      ( c_24__type__105155___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__3)
                     => ! [Vv__CANONICAL__4] :
                          ( c_24__type__82227___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__4)
                         => cProp___24t(happ(happ(happ(happ(happ(Vvar__105146,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ) ) ) ).

fof('$_type_105155',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__105156] :
      ( c_24__type__105155___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__105156)
    <=> ! [Vv__CANONICAL__2] :
          ( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__3] :
              ( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
             => cProp___24t(happ(happ(Vvar__105156,Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ).

fof('$_type_105252',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__105253] :
      ( c_24__type__105252___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__105253)
    <=> ! [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__105253,Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ).

fof('$_type_105287',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__105288] :
      ( c_24__type__105287___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__105288)
    <=> ! [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__105288,Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ).

fof('$_type_105290',axiom,
    ! [Vvar__105291] :
      ( c_24__type__105290___24t(Vvar__105291)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ( p(c_24False)
           => t(happ(Vvar__105291,Vv__CANONICAL__0),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_105337',axiom,
    ! [Vvar__105338] :
      ( c_24__type__105337___24t(Vvar__105338)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( c_24__type__105340___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
             => ! [Vv__CANONICAL__2] :
                  ( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
                 => ! [Vv__CANONICAL__3] :
                      ( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
                     => cProp___24t(happ(happ(happ(happ(Vvar__105338,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).

fof('$_type_105340',axiom,
    ! [Vv__CANONICAL__0,Vvar__105341] :
      ( c_24__type__105340___24t(Vv__CANONICAL__0,Vvar__105341)
    <=> ! [Vv__CANONICAL__1] :
          ( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
         => cCoq_2eInit_2eDatatypes_2enat___24t(happ(Vvar__105341,Vv__CANONICAL__1)) ) ) ).

fof('$_type_105468',axiom,
    ! [Vvar__105469] :
      ( c_24__type__105468___24t(Vvar__105469)
    <=> ! [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__105469,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_105559',axiom,
    ! [Vvar__105560] :
      ( c_24__type__105559___24t(Vvar__105560)
    <=> ! [Vv__CANONICAL__0] :
          ( c_24__type__1454___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( c_24__type__1454___24t(Vv__CANONICAL__1)
             => cProp___24t(happ(happ(Vvar__105560,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_105577',axiom,
    ! [Vvar__105578] :
      ( c_24__type__105577___24t(Vvar__105578)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
             => ! [Vv__CANONICAL__2] :
                  ( c_24__type__105582___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
                 => ! [Vv__CANONICAL__3] :
                      ( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__3)
                     => t(happ(happ(happ(happ(Vvar__105578,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__0) ) ) ) ) ) ).

fof('$_type_105582',axiom,
    ! [Vv__CANONICAL__0,Vvar__105583] :
      ( c_24__type__105582___24t(Vv__CANONICAL__0,Vvar__105583)
    <=> ! [Vv__CANONICAL__1] :
          ( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
         => ! [Vv__CANONICAL__2] :
              ( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
             => t(happ(happ(Vvar__105583,Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_105667',axiom,
    ! [Vvar__105668] :
      ( c_24__type__105667___24t(Vvar__105668)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__0)
         => cType___24t(happ(Vvar__105668,Vv__CANONICAL__0)) ) ) ).

fof('$_type_105712',axiom,
    ! [Vvar__105713] :
      ( c_24__type__105712___24t(Vvar__105713)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__0)
         => cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(Vvar__105713,Vv__CANONICAL__0)) ) ) ).

fof('$_type_105716',axiom,
    ! [Vvar__105717] :
      ( c_24__type__105716___24t(Vvar__105717)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
         => cCoq_2eNumbers_2eBinNums_2epositive___24t(happ(Vvar__105717,Vv__CANONICAL__0)) ) ) ).

fof('$_type_105724',axiom,
    ! [Vvar__105725] :
      ( c_24__type__105724___24t(Vvar__105725)
    <=> ! [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__105725,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_1065',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__1066] :
      ( c_24__type__1065___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__1066)
    <=> ! [Vv__CANONICAL__2] :
          ( cCoq_2eInit_2eSpecif_2esig___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
         => cProp___24t(happ(Vvar__1066,Vv__CANONICAL__2)) ) ) ).

fof('$_type_1079',axiom,
    ! [Vvar__1080] :
      ( c_24__type__1079___24t(Vvar__1080)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cProp___24t(Vv__CANONICAL__1)
             => cType___24t(happ(happ(Vvar__1080,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_1101',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__1102] :
      ( c_24__type__1101___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__1102)
    <=> ! [Vv__CANONICAL__2] :
          ( cCoq_2eInit_2eSpecif_2esumor___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
         => cProp___24t(happ(Vvar__1102,Vv__CANONICAL__2)) ) ) ).

fof('$_type_1106',axiom,
    ! [Vvar__1107] :
      ( c_24__type__1106___24t(Vvar__1107)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__0)
         => cCoq_2eNumbers_2eBinNums_2eN___24t(happ(Vvar__1107,Vv__CANONICAL__0)) ) ) ).

fof('$_type_1119',axiom,
    ! [Vvar__1120] :
      ( c_24__type__1119___24t(Vvar__1120)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__0)
         => cCoq_2eNumbers_2eBinNums_2epositive___24t(happ(Vvar__1120,Vv__CANONICAL__0)) ) ) ).

fof('$_type_1121',axiom,
    ! [Vvar__1122] :
      ( c_24__type__1121___24t(Vvar__1122)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__0)
         => cProp___24t(happ(Vvar__1122,Vv__CANONICAL__0)) ) ) ).

fof('$_type_1132',axiom,
    ! [Vvar__1133] :
      ( c_24__type__1132___24t(Vvar__1133)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__0)
         => cCoq_2eNumbers_2eBinNums_2eN___24t(happ(Vvar__1133,Vv__CANONICAL__0)) ) ) ).

fof('$_type_1134',axiom,
    ! [Vvar__1135] :
      ( c_24__type__1134___24t(Vvar__1135)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__0)
         => cProp___24t(happ(Vvar__1135,Vv__CANONICAL__0)) ) ) ).

fof('$_type_1152',axiom,
    ! [Vvar__1153] :
      ( c_24__type__1152___24t(Vvar__1153)
    <=> ! [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__1153,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_122083',axiom,
    ! [Vvar__122084] :
      ( c_24__type__122083___24t(Vvar__122084)
    <=> ! [Vv__CANONICAL__0] :
          ( cIntMap_2eMap_2eMap___24t(cA,Vv__CANONICAL__0)
         => cIntMap_2eMap_2eMap___24t(cA,happ(Vvar__122084,Vv__CANONICAL__0)) ) ) ).

fof('$_type_122086',axiom,
    ! [Vvar__122087] :
      ( c_24__type__122086___24t(Vvar__122087)
    <=> ! [Vv__CANONICAL__0] :
          ( cIntMap_2eMap_2eMap___24t(cA,Vv__CANONICAL__0)
         => cCoq_2eInit_2eSpecif_2esig___24t(cIntMap_2eMap_2eMap___24a1(cA),c_24__lam__122089___24a1(Vv__CANONICAL__0),happ(Vvar__122087,Vv__CANONICAL__0)) ) ) ).

fof('$_type_1226',axiom,
    ! [Vvar__1227] :
      ( c_24__type__1226___24t(Vvar__1227)
    <=> ! [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__1227,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5)) ) ) ) ) ) ) ) ).

fof('$_type_1364',axiom,
    ! [Vvar__1365] :
      ( c_24__type__1364___24t(Vvar__1365)
    <=> ! [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__1365,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).

fof('$_type_1367',axiom,
    ! [Vv__CANONICAL__0,Vvar__1368] :
      ( c_24__type__1367___24t(Vv__CANONICAL__0,Vvar__1368)
    <=> ! [Vv__CANONICAL__1] :
          ( cIntMap_2eMap_2ead___24t(Vv__CANONICAL__1)
         => cIntMap_2eMap_2ead___24t(happ(Vvar__1368,Vv__CANONICAL__1)) ) ) ).

fof('$_type_141',axiom,
    ! [Vvar__142] :
      ( c_24__type__141___24t(Vvar__142)
    <=> ! [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__142,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).

fof('$_type_1410',axiom,
    ! [Vvar__1411] :
      ( c_24__type__1410___24t(Vvar__1411)
    <=> ! [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__1415___24t(Vv__CANONICAL__1,Vv__CANONICAL__3)
                     => ! [Vv__CANONICAL__4] :
                          ( c_24__type__1422___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__1411,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__1) ) ) ) ) ) ) ) ).

fof('$_type_1415',axiom,
    ! [Vv__CANONICAL__0,Vvar__1416] :
      ( c_24__type__1415___24t(Vv__CANONICAL__0,Vvar__1416)
    <=> ! [Vv__CANONICAL__1] :
          ( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__2] :
              ( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
             => t(happ(happ(Vvar__1416,Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_1422',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__1423] :
      ( c_24__type__1422___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__1423)
    <=> ! [Vv__CANONICAL__2] :
          ( cIntMap_2eMap_2ead___24t(Vv__CANONICAL__2)
         => ! [Vv__CANONICAL__3] :
              ( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
             => t(happ(happ(Vvar__1423,Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__1) ) ) ) ).

fof('$_type_1434',axiom,
    ! [Vvar__1435] :
      ( c_24__type__1434___24t(Vvar__1435)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__0)
         => cCoq_2eInit_2eSpecif_2esumbool___24t(c_24__prop__1436___24a1(Vv__CANONICAL__0),c_24__prop__1437___24a1(Vv__CANONICAL__0),happ(Vvar__1435,Vv__CANONICAL__0)) ) ) ).

fof('$_type_1446',axiom,
    ! [Vvar__1447] :
      ( c_24__type__1446___24t(Vvar__1447)
    <=> ! [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__1447,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_1454',axiom,
    ! [Vvar__1455] :
      ( c_24__type__1454___24t(Vvar__1455)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__0)
         => cCoq_2eInit_2eDatatypes_2ebool___24t(happ(Vvar__1455,Vv__CANONICAL__0)) ) ) ).

fof('$_type_1461',axiom,
    ! [Vvar__1462] :
      ( c_24__type__1461___24t(Vvar__1462)
    <=> ! [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__1462,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_257',axiom,
    ! [Vvar__258] :
      ( c_24__type__257___24t(Vvar__258)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => cType___24t(happ(Vvar__258,Vv__CANONICAL__0)) ) ) ).

fof('$_type_287',axiom,
    ! [Vvar__288] :
      ( c_24__type__287___24t(Vvar__288)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => cIntMap_2eMap_2eMap___24t(Vv__CANONICAL__0,happ(Vvar__288,Vv__CANONICAL__0)) ) ) ).

fof('$_type_292',axiom,
    ! [Vvar__293] :
      ( c_24__type__292___24t(Vvar__293)
    <=> ! [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__293,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).

fof('$_type_297',axiom,
    ! [Vvar__298] :
      ( c_24__type__297___24t(Vvar__298)
    <=> ! [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__298,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).

fof('$_type_313',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__314] :
      ( c_24__type__313___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__314)
    <=> ! [Vv__CANONICAL__2] :
          ( cIntMap_2eMap_2eMap___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
         => cType___24t(happ(Vvar__314,Vv__CANONICAL__2)) ) ) ).

fof('$_type_360',axiom,
    ! [Vvar__361] :
      ( c_24__type__360___24t(Vvar__361)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( c_24__type__363___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__371___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__3)
                     => ! [Vv__CANONICAL__4] :
                          ( c_24__type__388___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__361,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_363',axiom,
    ! [Vv__CANONICAL__0,Vvar__364] :
      ( c_24__type__363___24t(Vv__CANONICAL__0,Vvar__364)
    <=> ! [Vv__CANONICAL__1] :
          ( cIntMap_2eMap_2eMap___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
         => cType___24t(happ(Vvar__364,Vv__CANONICAL__1)) ) ) ).

fof('$_type_371',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__372] :
      ( c_24__type__371___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__372)
    <=> ! [Vv__CANONICAL__2] :
          ( cIntMap_2eMap_2ead___24t(Vv__CANONICAL__2)
         => ! [Vv__CANONICAL__3] :
              ( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
             => t(happ(happ(Vvar__372,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_388',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__389] :
      ( c_24__type__388___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__389)
    <=> ! [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__389,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_391',axiom,
    ! [Vv__CANONICAL__0,Vvar__392] :
      ( c_24__type__391___24t(Vv__CANONICAL__0,Vvar__392)
    <=> ! [Vv__CANONICAL__1] :
          ( cIntMap_2eMap_2eMap___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
         => cProp___24t(happ(Vvar__392,Vv__CANONICAL__1)) ) ) ).

fof('$_type_499',axiom,
    ! [Vvar__500] :
      ( c_24__type__499___24t(Vvar__500)
    <=> ! [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__500,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).

fof('$_type_513',axiom,
    ! [Vvar__514] :
      ( c_24__type__513___24t(Vvar__514)
    <=> ! [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__514,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_560',axiom,
    ! [Vvar__561] :
      ( c_24__type__560___24t(Vvar__561)
    <=> ! [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__562___24a3(Vv__CANONICAL__0,Vv__CANONICAL__5,Vv__CANONICAL__6),c_24__prop__563___24a3(Vv__CANONICAL__0,Vv__CANONICAL__5,Vv__CANONICAL__6),happ(happ(happ(happ(happ(happ(happ(Vvar__561,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__6)) ) ) ) ) ) ) ) ) ) ) ) ).

fof('$_type_567',axiom,
    ! [Vvar__568] :
      ( c_24__type__567___24t(Vvar__568)
    <=> ! [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__568,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_586',axiom,
    ! [Vvar__587] :
      ( c_24__type__586___24t(Vvar__587)
    <=> ! [Vv__CANONICAL__0] :
          ( cProp___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cProp___24t(Vv__CANONICAL__1)
             => cType___24t(happ(happ(Vvar__587,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_6',axiom,
    ! [Vvar__7] :
      ( c_24__type__6___24t(Vvar__7)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
         => cCoq_2eInit_2eDatatypes_2enat___24t(happ(Vvar__7,Vv__CANONICAL__0)) ) ) ).

fof('$_type_608',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__609] :
      ( c_24__type__608___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__609)
    <=> ! [Vv__CANONICAL__2] :
          ( cCoq_2eInit_2eSpecif_2esumbool___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
         => cProp___24t(happ(Vvar__609,Vv__CANONICAL__2)) ) ) ).

fof('$_type_612',axiom,
    ! [Vvar__613] :
      ( c_24__type__612___24t(Vvar__613)
    <=> ! [Vv__CANONICAL__0] :
          ( cIntMap_2eMap_2eMap___24t(cA,Vv__CANONICAL__0)
         => cProp___24t(happ(Vvar__613,Vv__CANONICAL__0)) ) ) ).

fof('$_type_647',axiom,
    ! [Vvar__648] :
      ( c_24__type__647___24t(Vvar__648)
    <=> ! [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__648,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_649',axiom,
    ! [Vvar__650] :
      ( c_24__type__649___24t(Vvar__650)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => cCoq_2eInit_2eDatatypes_2eoption___24t(Vv__CANONICAL__0,happ(Vvar__650,Vv__CANONICAL__0)) ) ) ).

fof('$_type_67032',axiom,
    ! [Vvar__67033] :
      ( c_24__type__67032___24t(Vvar__67033)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cType___24t(Vv__CANONICAL__1)
             => cType___24t(happ(happ(Vvar__67033,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_67050',axiom,
    ! [Vvar__67051] :
      ( c_24__type__67050___24t(Vvar__67051)
    <=> ! [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__67051,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_67059',axiom,
    ! [Vvar__67060] :
      ( c_24__type__67059___24t(Vvar__67060)
    <=> ! [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__67060,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).

fof('$_type_67071',axiom,
    ! [Vvar__67072] :
      ( c_24__type__67071___24t(Vvar__67072)
    <=> ! [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__67076___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2),happ(happ(happ(Vvar__67072,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ) ).

fof('$_type_67099',axiom,
    ! [Vvar__67100] :
      ( c_24__type__67099___24t(Vvar__67100)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cType___24t(Vv__CANONICAL__1)
             => ! [Vv__CANONICAL__2] :
                  ( c_24__type__67106___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__67100,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__0) ) ) ) ) ) ) ).

fof('$_type_67106',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__67107] :
      ( c_24__type__67106___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__67107)
    <=> ! [Vv__CANONICAL__2] :
          ( t(Vv__CANONICAL__2,Vv__CANONICAL__1)
         => ! [Vv__CANONICAL__3] :
              ( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
             => t(happ(happ(Vvar__67107,Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_67165',axiom,
    ! [Vvar__67166] :
      ( c_24__type__67165___24t(Vvar__67166)
    <=> ! [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_2eMapCard___24a2(Vv__CANONICAL__0,cIntMap_2eMap_2eMapPut___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3)) = cIntMap_2eMap_2eMapCard___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1)
                       => cCoq_2eInit_2eSpecif_2esig___24t(Vv__CANONICAL__0,c_24__lam__67076___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2),happ(happ(happ(happ(Vvar__67166,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ) ).

fof('$_type_67215',axiom,
    ! [Vvar__67216] :
      ( c_24__type__67215___24t(Vvar__67216)
    <=> ! [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__67217___24a3(Vv__CANONICAL__0,Vv__CANONICAL__5,Vv__CANONICAL__6),c_24__prop__67218___24a3(Vv__CANONICAL__0,Vv__CANONICAL__5,Vv__CANONICAL__6),happ(happ(happ(happ(happ(happ(happ(Vvar__67216,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__6)) ) ) ) ) ) ) ) ) ) ) ) ).

fof('$_type_67244',axiom,
    ! [Vvar__67245] :
      ( c_24__type__67244___24t(Vvar__67245)
    <=> ! [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__67248___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1),happ(happ(happ(Vvar__67245,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ) ).

fof('$_type_67318',axiom,
    ! [Vvar__67319] :
      ( c_24__type__67318___24t(Vvar__67319)
    <=> ! [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__1415___24t(Vv__CANONICAL__1,Vv__CANONICAL__3)
                     => ! [Vv__CANONICAL__4] :
                          ( c_24__type__1422___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__4)
                         => ! [Vv__CANONICAL__5] :
                              ( c_24__type__67330___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__67319,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_67330',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__67331] :
      ( c_24__type__67330___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__67331)
    <=> ! [Vv__CANONICAL__2] :
          ( cIntMap_2eMap_2ead___24t(Vv__CANONICAL__2)
         => cIntMap_2eMap_2ead___24t(happ(Vvar__67331,Vv__CANONICAL__2)) ) ) ).

fof('$_type_67337',axiom,
    ! [Vvar__67338] :
      ( c_24__type__67337___24t(Vvar__67338)
    <=> ! [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__67338,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_67383',axiom,
    ! [Vvar__67384] :
      ( c_24__type__67383___24t(Vvar__67384)
    <=> ! [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__67384,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).

fof('$_type_67406',axiom,
    ! [Vvar__67407] :
      ( c_24__type__67406___24t(Vvar__67407)
    <=> ! [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__67407,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_67483',axiom,
    ! [Vvar__67484] :
      ( c_24__type__67483___24t(Vvar__67484)
    <=> ! [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__67484,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_67486',axiom,
    ! [Vvar__67487] :
      ( c_24__type__67486___24t(Vvar__67487)
    <=> ! [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__67487,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_67586',axiom,
    ! [Vvar__67587] :
      ( c_24__type__67586___24t(Vvar__67587)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( c_24__type__1051___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__67587,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ) ).

fof('$_type_67609',axiom,
    ! [Vvar__67610] :
      ( c_24__type__67609___24t(Vvar__67610)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( c_24__type__1051___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
             => ! [Vv__CANONICAL__2] :
                  ( c_24__type__67615___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
                 => ! [Vv__CANONICAL__3] :
                      ( c_24__type__67627___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__67610,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),happ(Vv__CANONICAL__2,Vv__CANONICAL__4)) ) ) ) ) ) ) ).

fof('$_type_67615',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__67616] :
      ( c_24__type__67615___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__67616)
    <=> ! [Vv__CANONICAL__2] :
          ( cCoq_2eInit_2eSpecif_2esig___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
         => cType___24t(happ(Vvar__67616,Vv__CANONICAL__2)) ) ) ).

fof('$_type_67627',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__67628] :
      ( c_24__type__67627___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__67628)
    <=> ! [Vv__CANONICAL__3] :
          ( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
         => ( p(happ(Vv__CANONICAL__1,Vv__CANONICAL__3))
           => t(happ(Vvar__67628,Vv__CANONICAL__3),happ(Vv__CANONICAL__2,cCoq_2eInit_2eSpecif_2eexist___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__3))) ) ) ) ).

fof('$_type_67643',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__67644] :
      ( c_24__type__67643___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__67644)
    <=> ! [Vv__CANONICAL__2] :
          ( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
         => cType___24t(happ(Vvar__67644,Vv__CANONICAL__2)) ) ) ).

fof('$_type_67647',axiom,
    ! [Vvar__67648] :
      ( c_24__type__67647___24t(Vvar__67648)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( c_24__type__67650___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
             => cType___24t(happ(happ(Vvar__67648,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_67650',axiom,
    ! [Vv__CANONICAL__0,Vvar__67651] :
      ( c_24__type__67650___24t(Vv__CANONICAL__0,Vvar__67651)
    <=> ! [Vv__CANONICAL__1] :
          ( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
         => cType___24t(happ(Vvar__67651,Vv__CANONICAL__1)) ) ) ).

fof('$_type_67667',axiom,
    ! [Vvar__67668] :
      ( c_24__type__67667___24t(Vvar__67668)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( c_24__type__67650___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__67668,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).

fof('$_type_67686',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__67687] :
      ( c_24__type__67686___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__67687)
    <=> ! [Vv__CANONICAL__3] :
          ( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
         => cType___24t(happ(Vvar__67687,Vv__CANONICAL__3)) ) ) ).

fof('$_type_67694',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__67695] :
      ( c_24__type__67694___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__67695)
    <=> ! [Vv__CANONICAL__3] :
          ( cCoq_2eInit_2eSpecif_2esigT___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__3)
         => cType___24t(happ(Vvar__67695,Vv__CANONICAL__3)) ) ) ).

fof('$_type_67716',axiom,
    ! [Vvar__67717] :
      ( c_24__type__67716___24t(Vvar__67717)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( c_24__type__67650___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
             => ! [Vv__CANONICAL__2] :
                  ( c_24__type__67722___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
                 => ! [Vv__CANONICAL__3] :
                      ( c_24__type__67734___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__67717,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),happ(Vv__CANONICAL__2,Vv__CANONICAL__4)) ) ) ) ) ) ) ).

fof('$_type_67722',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__67723] :
      ( c_24__type__67722___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__67723)
    <=> ! [Vv__CANONICAL__2] :
          ( cCoq_2eInit_2eSpecif_2esigT___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
         => cType___24t(happ(Vvar__67723,Vv__CANONICAL__2)) ) ) ).

fof('$_type_67734',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__67735] :
      ( c_24__type__67734___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__67735)
    <=> ! [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__67735,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_67739',axiom,
    ! [Vvar__67740] :
      ( c_24__type__67739___24t(Vvar__67740)
    <=> ! [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__67740,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ) ).

fof('$_type_67744',axiom,
    ! [Vvar__67745] :
      ( c_24__type__67744___24t(Vvar__67745)
    <=> ! [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__67745,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ) ).

fof('$_type_67759',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__67760] :
      ( c_24__type__67759___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__67760)
    <=> ! [Vv__CANONICAL__3] :
          ( cCoq_2eInit_2eSpecif_2esumbool___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__3)
         => cType___24t(happ(Vvar__67760,Vv__CANONICAL__3)) ) ) ).

fof('$_type_67785',axiom,
    ! [Vvar__67786] :
      ( c_24__type__67785___24t(Vvar__67786)
    <=> ! [Vv__CANONICAL__0] :
          ( cProp___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cProp___24t(Vv__CANONICAL__1)
             => ! [Vv__CANONICAL__2] :
                  ( c_24__type__67789___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
                 => ! [Vv__CANONICAL__3] :
                      ( c_24__type__67796___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3)
                     => ! [Vv__CANONICAL__4] :
                          ( c_24__type__67803___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__67786,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_67789',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__67790] :
      ( c_24__type__67789___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__67790)
    <=> ! [Vv__CANONICAL__2] :
          ( cCoq_2eInit_2eSpecif_2esumbool___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
         => cType___24t(happ(Vvar__67790,Vv__CANONICAL__2)) ) ) ).

fof('$_type_67796',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__67797] :
      ( c_24__type__67796___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__67797)
    <=> ( p(Vv__CANONICAL__0)
       => t(Vvar__67797,happ(Vv__CANONICAL__2,cCoq_2eInit_2eSpecif_2eleft___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1))) ) ) ).

fof('$_type_67803',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__67804] :
      ( c_24__type__67803___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__67804)
    <=> ( p(Vv__CANONICAL__1)
       => t(Vvar__67804,happ(Vv__CANONICAL__2,cCoq_2eInit_2eSpecif_2eright___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1))) ) ) ).

fof('$_type_67853',axiom,
    ! [Vvar__67854] :
      ( c_24__type__67853___24t(Vvar__67854)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cProp___24t(Vv__CANONICAL__1)
             => ! [Vv__CANONICAL__2] :
                  ( c_24__type__67857___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
                 => ! [Vv__CANONICAL__3] :
                      ( c_24__type__67864___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3)
                     => ! [Vv__CANONICAL__4] :
                          ( c_24__type__67871___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__67854,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_67857',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__67858] :
      ( c_24__type__67857___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__67858)
    <=> ! [Vv__CANONICAL__2] :
          ( cCoq_2eInit_2eSpecif_2esumor___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
         => cType___24t(happ(Vvar__67858,Vv__CANONICAL__2)) ) ) ).

fof('$_type_67864',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__67865] :
      ( c_24__type__67864___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__67865)
    <=> ! [Vv__CANONICAL__3] :
          ( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
         => t(happ(Vvar__67865,Vv__CANONICAL__3),happ(Vv__CANONICAL__2,cCoq_2eInit_2eSpecif_2einleft___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__3))) ) ) ).

fof('$_type_67871',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__67872] :
      ( c_24__type__67871___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__67872)
    <=> ( p(Vv__CANONICAL__1)
       => t(Vvar__67872,happ(Vv__CANONICAL__2,cCoq_2eInit_2eSpecif_2einright___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1))) ) ) ).

fof('$_type_67891',axiom,
    ! [Vvar__67892] :
      ( c_24__type__67891___24t(Vvar__67892)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
         => cProp___24t(happ(Vvar__67892,Vv__CANONICAL__0)) ) ) ).

fof('$_type_67955',axiom,
    ! [Vvar__67956] :
      ( c_24__type__67955___24t(Vvar__67956)
    <=> ! [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__67956,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_68063',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__68064] :
      ( c_24__type__68063___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__68064)
    <=> ! [Vv__CANONICAL__3] :
          ( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__3)
         => cProp___24t(happ(Vvar__68064,Vv__CANONICAL__3)) ) ) ).

fof('$_type_68088',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__68089] :
      ( c_24__type__68088___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__68089)
    <=> ! [Vv__CANONICAL__3] :
          ( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__3)
         => cProp___24t(happ(Vvar__68089,Vv__CANONICAL__3)) ) ) ).

fof('$_type_68107',axiom,
    ! [Vvar__68108] :
      ( c_24__type__68107___24t(Vvar__68108)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__0)
         => cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(Vvar__68108,Vv__CANONICAL__0)) ) ) ).

fof('$_type_68135',axiom,
    ! [Vvar__68136] :
      ( c_24__type__68135___24t(Vvar__68136)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
         => cType___24t(happ(Vvar__68136,Vv__CANONICAL__0)) ) ) ).

fof('$_type_699',axiom,
    ! [Vvar__700] :
      ( c_24__type__699___24t(Vvar__700)
    <=> ! [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__703___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1)),c_24__prop__704___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1),happ(happ(Vvar__700,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_75474',axiom,
    ! [Vvar__75475] :
      ( c_24__type__75474___24t(Vvar__75475)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eInit_2eDatatypes_2eunit___24t(Vv__CANONICAL__0)
         => cProp___24t(happ(Vvar__75475,Vv__CANONICAL__0)) ) ) ).

fof('$_type_75476',axiom,
    ! [Vvar__75477] :
      ( c_24__type__75476___24t(Vvar__75477)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__0)
         => cProp___24t(happ(Vvar__75477,Vv__CANONICAL__0)) ) ) ).

fof('$_type_75479',axiom,
    ! [Vvar__75480] :
      ( c_24__type__75479___24t(Vvar__75480)
    <=> ! [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__75480,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_75483',axiom,
    ! [Vvar__75484] :
      ( c_24__type__75483___24t(Vvar__75484)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__0)
         => cCoq_2eInit_2eDatatypes_2ebool___24t(happ(Vvar__75484,Vv__CANONICAL__0)) ) ) ).

fof('$_type_75551',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__75552] :
      ( c_24__type__75551___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__75552)
    <=> ! [Vv__CANONICAL__2] :
          ( cCoq_2eInit_2eDatatypes_2esum___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
         => cProp___24t(happ(Vvar__75552,Vv__CANONICAL__2)) ) ) ).

fof('$_type_75561',axiom,
    ! [Vvar__75562] :
      ( c_24__type__75561___24t(Vvar__75562)
    <=> ! [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__75562,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).

fof('$_type_75574',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__75575] :
      ( c_24__type__75574___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__75575)
    <=> ! [Vv__CANONICAL__3] :
          ( cCoq_2eInit_2eDatatypes_2eprod___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__3)
         => cType___24t(happ(Vvar__75575,Vv__CANONICAL__3)) ) ) ).

fof('$_type_75595',axiom,
    ! [Vvar__75596] :
      ( c_24__type__75595___24t(Vvar__75596)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cType___24t(Vv__CANONICAL__1)
             => ! [Vv__CANONICAL__2] :
                  ( c_24__type__75599___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
                 => ! [Vv__CANONICAL__3] :
                      ( c_24__type__75610___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__75596,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),happ(Vv__CANONICAL__2,Vv__CANONICAL__4)) ) ) ) ) ) ) ).

fof('$_type_75599',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__75600] :
      ( c_24__type__75599___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__75600)
    <=> ! [Vv__CANONICAL__2] :
          ( cCoq_2eInit_2eDatatypes_2eprod___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
         => cType___24t(happ(Vvar__75600,Vv__CANONICAL__2)) ) ) ).

fof('$_type_75610',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__75611] :
      ( c_24__type__75610___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__75611)
    <=> ! [Vv__CANONICAL__3] :
          ( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__4] :
              ( t(Vv__CANONICAL__4,Vv__CANONICAL__1)
             => t(happ(happ(Vvar__75611,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_75614',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__75615] :
      ( c_24__type__75614___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__75615)
    <=> ! [Vv__CANONICAL__2] :
          ( cCoq_2eInit_2eDatatypes_2eprod___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
         => cProp___24t(happ(Vvar__75615,Vv__CANONICAL__2)) ) ) ).

fof('$_type_75628',axiom,
    ! [Vvar__75629] :
      ( c_24__type__75628___24t(Vvar__75629)
    <=> ! [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__75629,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__0) ) ) ) ) ).

fof('$_type_75640',axiom,
    ! [Vvar__75641] :
      ( c_24__type__75640___24t(Vvar__75641)
    <=> ! [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__75641,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__1) ) ) ) ) ).

fof('$_type_75660',axiom,
    ! [Vvar__75661] :
      ( c_24__type__75660___24t(Vvar__75661)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,happ(Vvar__75661,Vv__CANONICAL__0)) ) ) ).

fof('$_type_75665',axiom,
    ! [Vvar__75666] :
      ( c_24__type__75665___24t(Vvar__75666)
    <=> ! [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__75666,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).

fof('$_type_75743',axiom,
    ! [Vvar__75744] :
      ( c_24__type__75743___24t(Vvar__75744)
    <=> ! [Vv__CANONICAL__0] :
          ( cProp___24t(Vv__CANONICAL__0)
         => cProp___24t(happ(Vvar__75744,Vv__CANONICAL__0)) ) ) ).

fof('$_type_76179',axiom,
    ! [Vvar__76180] :
      ( c_24__type__76179___24t(Vvar__76180)
    <=> ! [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__76180,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_76191',axiom,
    ! [Vvar__76192] :
      ( c_24__type__76191___24t(Vvar__76192)
    <=> ! [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__67076___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2),happ(happ(happ(Vvar__76192,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ) ).

fof('$_type_76206',axiom,
    ! [Vvar__76207] :
      ( c_24__type__76206___24t(Vvar__76207)
    <=> ! [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__76207,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).

fof('$_type_76363',axiom,
    ! [Vvar__76364] :
      ( c_24__type__76363___24t(Vvar__76364)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cIntMap_2eMapiter_2ealist___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
             => cCoq_2eInit_2eDatatypes_2ebool___24t(happ(happ(Vvar__76364,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_76397',axiom,
    ! [Vvar__76398] :
      ( c_24__type__76397___24t(Vvar__76398)
    <=> ! [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__76398,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).

fof('$_type_76492',axiom,
    ! [Vvar__76493] :
      ( c_24__type__76492___24t(Vvar__76493)
    <=> ! [Vv__CANONICAL__0] :
          ( c_24__type__76494___24t(Vv__CANONICAL__0)
         => cProp___24t(happ(Vvar__76493,Vv__CANONICAL__0)) ) ) ).

fof('$_type_76494',axiom,
    ! [Vvar__76495] :
      ( c_24__type__76494___24t(Vvar__76495)
    <=> ! [Vv__CANONICAL__0] :
          ( cIntMap_2eMap_2ead___24t(Vv__CANONICAL__0)
         => cIntMap_2eMap_2ead___24t(happ(Vvar__76495,Vv__CANONICAL__0)) ) ) ).

fof('$_type_76785',axiom,
    ! [Vvar__76786] :
      ( c_24__type__76785___24t(Vvar__76786)
    <=> ! [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__76786,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_76796',axiom,
    ! [Vv__CANONICAL__0,Vvar__76797] :
      ( c_24__type__76796___24t(Vv__CANONICAL__0,Vvar__76797)
    <=> ! [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__76797,Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ).

fof('$_type_76807',axiom,
    ! [Vvar__76808] :
      ( c_24__type__76807___24t(Vvar__76808)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( c_24__type__76796___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__76808,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).

fof('$_type_76862',axiom,
    ! [Vvar__76863] :
      ( c_24__type__76862___24t(Vvar__76863)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( c_24__type__76796___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
             => ! [Vv__CANONICAL__2] :
                  ( c_24__type__1367___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__76863,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).

fof('$_type_76876',axiom,
    ! [Vvar__76877] :
      ( c_24__type__76876___24t(Vvar__76877)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( c_24__type__76796___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__76877,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).

fof('$_type_77138',axiom,
    ! [Vvar__77139] :
      ( c_24__type__77138___24t(Vvar__77139)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cType___24t(Vv__CANONICAL__1)
             => ! [Vv__CANONICAL__2] :
                  ( c_24__type__77145___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
                 => ! [Vv__CANONICAL__3] :
                      ( c_24__type__67330___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__77139,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ) ) ) ).

fof('$_type_77145',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__77146] :
      ( c_24__type__77145___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__77146)
    <=> ! [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__77146,Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ).

fof('$_type_77162',axiom,
    ! [Vvar__77163] :
      ( c_24__type__77162___24t(Vvar__77163)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cType___24t(Vv__CANONICAL__1)
             => ! [Vv__CANONICAL__2] :
                  ( c_24__type__77145___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__77163,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).

fof('$_type_77225',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__77226] :
      ( c_24__type__77225___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__77226)
    <=> ! [Vv__CANONICAL__3] :
          ( t(Vv__CANONICAL__3,Vv__CANONICAL__1)
         => ! [Vv__CANONICAL__4] :
              ( t(Vv__CANONICAL__4,Vv__CANONICAL__1)
             => t(happ(happ(Vvar__77226,Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__1) ) ) ) ).

fof('$_type_77239',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__77240] :
      ( c_24__type__77239___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__77240)
    <=> ! [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__77240,Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5)) ) ) ) ) ).

fof('$_type_77244',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__77245] :
      ( c_24__type__77244___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__77245)
    <=> ! [Vv__CANONICAL__3] :
          ( cIntMap_2eMap_2ead___24t(Vv__CANONICAL__3)
         => cIntMap_2eMap_2ead___24t(happ(Vvar__77245,Vv__CANONICAL__3)) ) ) ).

fof('$_type_77352',axiom,
    ! [Vvar__77353] :
      ( c_24__type__77352___24t(Vvar__77353)
    <=> ! [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__1415___24t(Vv__CANONICAL__1,Vv__CANONICAL__3)
                     => ! [Vv__CANONICAL__4] :
                          ( cType___24t(Vv__CANONICAL__4)
                         => ! [Vv__CANONICAL__5] :
                              ( c_24__type__77239___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__77244___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__77353,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_77429',axiom,
    ! [Vvar__77430] :
      ( c_24__type__77429___24t(Vvar__77430)
    <=> ! [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__1415___24t(Vv__CANONICAL__1,Vv__CANONICAL__3)
                     => ! [Vv__CANONICAL__4] :
                          ( cType___24t(Vv__CANONICAL__4)
                         => ! [Vv__CANONICAL__5] :
                              ( c_24__type__77239___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__77430,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_77468',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__77469] :
      ( c_24__type__77468___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__77469)
    <=> ! [Vv__CANONICAL__3] :
          ( cIntMap_2eMap_2ead___24t(Vv__CANONICAL__3)
         => ! [Vv__CANONICAL__4] :
              ( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
             => t(happ(happ(Vvar__77469,Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__1) ) ) ) ).

fof('$_type_77506',axiom,
    ! [Vvar__77507] :
      ( c_24__type__77506___24t(Vvar__77507)
    <=> ! [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__77507,Vv__CANONICAL__0)) ) ) ).

fof('$_type_77511',axiom,
    ! [Vvar__77512] :
      ( c_24__type__77511___24t(Vvar__77512)
    <=> ! [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__77512,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).

fof('$_type_77516',axiom,
    ! [Vvar__77517] :
      ( c_24__type__77516___24t(Vvar__77517)
    <=> ! [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__77517,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).

fof('$_type_778',axiom,
    ! [Vvar__779] :
      ( c_24__type__778___24t(Vvar__779)
    <=> ! [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__779,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).

fof('$_type_77826',axiom,
    ! [Vvar__77827] :
      ( c_24__type__77826___24t(Vvar__77827)
    <=> ! [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__77827,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).

fof('$_type_77893',axiom,
    ! [Vvar__77894] :
      ( c_24__type__77893___24t(Vvar__77894)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
         => cCoq_2eInit_2eDatatypes_2ebool___24t(happ(Vvar__77894,Vv__CANONICAL__0)) ) ) ).

fof('$_type_77980',axiom,
    ! [Vvar__77981] :
      ( c_24__type__77980___24t(Vvar__77981)
    <=> ! [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__77983___24a1(Vv__CANONICAL__0)),cCoq_2eInit_2eSpecif_2esig___24a2(cCoq_2eNumbers_2eBinNums_2eN,c_24__lam__77985___24a1(Vv__CANONICAL__0)),happ(Vvar__77981,Vv__CANONICAL__0)) ) ) ).

fof('$_type_78019',axiom,
    ! [Vvar__78020] :
      ( c_24__type__78019___24t(Vvar__78020)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__0)
         => cCoq_2eReals_2eRdefinitions_2eR___24t(happ(Vvar__78020,Vv__CANONICAL__0)) ) ) ).

fof('$_type_78031',axiom,
    ! [Vvar__78032] :
      ( c_24__type__78031___24t(Vvar__78032)
    <=> ! [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__78032,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_78034',axiom,
    ! [Vvar__78035] :
      ( c_24__type__78034___24t(Vvar__78035)
    <=> ! [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__78035,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_78044',axiom,
    ! [Vv__CANONICAL__0,Vvar__78045] :
      ( c_24__type__78044___24t(Vv__CANONICAL__0,Vvar__78045)
    <=> ! [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__78045,Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ).

fof('$_type_78211',axiom,
    ! [Vv__CANONICAL__0,Vvar__78212] :
      ( c_24__type__78211___24t(Vv__CANONICAL__0,Vvar__78212)
    <=> ! [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__78212,Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ).

fof('$_type_78471',axiom,
    ! [Vvar__78472] :
      ( c_24__type__78471___24t(Vvar__78472)
    <=> ! [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__78472,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_78474',axiom,
    ! [Vvar__78475] :
      ( c_24__type__78474___24t(Vvar__78475)
    <=> ! [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__78475,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_78479',axiom,
    ! [Vvar__78480] :
      ( c_24__type__78479___24t(Vvar__78480)
    <=> ! [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__78480,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).

fof('$_type_786',axiom,
    ! [Vvar__787] :
      ( c_24__type__786___24t(Vvar__787)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( c_24__type__789___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
             => ! [Vv__CANONICAL__2] :
                  ( c_24__type__789___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
                 => cProp___24t(happ(happ(happ(Vvar__787,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).

fof('$_type_78702',axiom,
    ! [Vv__CANONICAL__0,Vvar__78703] :
      ( c_24__type__78702___24t(Vv__CANONICAL__0,Vvar__78703)
    <=> ! [Vv__CANONICAL__1] :
          ( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
         => t(happ(Vvar__78703,Vv__CANONICAL__1),Vv__CANONICAL__0) ) ) ).

fof('$_type_789',axiom,
    ! [Vv__CANONICAL__0,Vvar__790] :
      ( c_24__type__789___24t(Vv__CANONICAL__0,Vvar__790)
    <=> ! [Vv__CANONICAL__1] :
          ( cIntMap_2eMap_2ead___24t(Vv__CANONICAL__1)
         => cCoq_2eInit_2eDatatypes_2eoption___24t(Vv__CANONICAL__0,happ(Vvar__790,Vv__CANONICAL__1)) ) ) ).

fof('$_type_78909',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__78910] :
      ( c_24__type__78909___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__78910)
    <=> ! [Vv__CANONICAL__3] :
          ( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
         => cProp___24t(happ(Vvar__78910,Vv__CANONICAL__3)) ) ) ).

fof('$_type_78917',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__78918] :
      ( c_24__type__78917___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__78918)
    <=> ! [Vv__CANONICAL__3] :
          ( cCoq_2eInit_2eSpecif_2esig___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__3)
         => cType___24t(happ(Vvar__78918,Vv__CANONICAL__3)) ) ) ).

fof('$_type_78986',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__78987] :
      ( c_24__type__78986___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__78987)
    <=> ! [Vv__CANONICAL__3] :
          ( cCoq_2eInit_2eSpecif_2esumor___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__3)
         => cType___24t(happ(Vvar__78987,Vv__CANONICAL__3)) ) ) ).

fof('$_type_79265',axiom,
    ! [Vvar__79266] :
      ( c_24__type__79265___24t(Vvar__79266)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
             => cType___24t(happ(happ(Vvar__79266,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_80212',axiom,
    ! [Vvar__80213] :
      ( c_24__type__80212___24t(Vvar__80213)
    <=> ! [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__80213,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_80245',axiom,
    ! [Vvar__80246] :
      ( c_24__type__80245___24t(Vvar__80246)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__0)
         => cCoq_2eInit_2eDatatypes_2enat___24t(happ(Vvar__80246,Vv__CANONICAL__0)) ) ) ).

fof('$_type_80251',axiom,
    ! [Vvar__80252] :
      ( c_24__type__80251___24t(Vvar__80252)
    <=> ! [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__80252,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_80277',axiom,
    ! [Vvar__80278] :
      ( c_24__type__80277___24t(Vvar__80278)
    <=> ! [Vv__CANONICAL__0] :
          ( c_24__type__77893___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( c_24__type__77893___24t(Vv__CANONICAL__1)
             => cProp___24t(happ(happ(Vvar__80278,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_80300',axiom,
    ! [Vvar__80301] :
      ( c_24__type__80300___24t(Vvar__80301)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( c_24__type__1415___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__80301,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__0) ) ) ) ) ) ).

fof('$_type_80320',axiom,
    ! [Vvar__80321] :
      ( c_24__type__80320___24t(Vvar__80321)
    <=> ! [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__80321,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_80324',axiom,
    ! [Vvar__80325] :
      ( c_24__type__80324___24t(Vvar__80325)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
         => cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(Vvar__80325,Vv__CANONICAL__0)) ) ) ).

fof('$_type_80445',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__80446] :
      ( c_24__type__80445___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__80446)
    <=> ! [Vv__CANONICAL__5] :
          ( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__5)
         => cProp___24t(happ(Vvar__80446,Vv__CANONICAL__5)) ) ) ).

fof('$_type_80453',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__80454] :
      ( c_24__type__80453___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__80454)
    <=> ! [Vv__CANONICAL__5] :
          ( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__5)
         => cProp___24t(happ(Vvar__80454,Vv__CANONICAL__5)) ) ) ).

fof('$_type_80463',axiom,
    ! [Vvar__80464] :
      ( c_24__type__80463___24t(Vvar__80464)
    <=> ! [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__80464,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_80571',axiom,
    ! [Vvar__80572] :
      ( c_24__type__80571___24t(Vvar__80572)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
         => cProp___24t(happ(Vvar__80572,Vv__CANONICAL__0)) ) ) ).

fof('$_type_80805',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__80806] :
      ( c_24__type__80805___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__80806)
    <=> ! [Vv__CANONICAL__2] :
          ( t(Vv__CANONICAL__2,Vv__CANONICAL__1)
         => t(happ(Vvar__80806,Vv__CANONICAL__2),Vv__CANONICAL__0) ) ) ).

fof('$_type_80837',axiom,
    ! [Vvar__80838] :
      ( c_24__type__80837___24t(Vvar__80838)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
             => ! [Vv__CANONICAL__2] :
                  ( c_24__type__1415___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
                 => ! [Vv__CANONICAL__3] :
                      ( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
                     => ! [Vv__CANONICAL__4] :
                          ( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__4)
                         => t(happ(happ(happ(happ(happ(Vvar__80838,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__0) ) ) ) ) ) ) ).

fof('$_type_81010',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__81011] :
      ( c_24__type__81010___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__81011)
    <=> ! [Vv__CANONICAL__6] :
          ( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__7] :
              ( t(Vv__CANONICAL__7,Vv__CANONICAL__0)
             => t(happ(happ(Vvar__81011,Vv__CANONICAL__6),Vv__CANONICAL__7),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_81049',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__81050] :
      ( c_24__type__81049___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__81050)
    <=> ! [Vv__CANONICAL__6] :
          ( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__7] :
              ( t(Vv__CANONICAL__7,Vv__CANONICAL__0)
             => t(happ(happ(Vvar__81050,Vv__CANONICAL__6),Vv__CANONICAL__7),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_81088',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__81089] :
      ( c_24__type__81088___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__81089)
    <=> ! [Vv__CANONICAL__6] :
          ( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__7] :
              ( t(Vv__CANONICAL__7,Vv__CANONICAL__0)
             => cProp___24t(happ(happ(Vvar__81089,Vv__CANONICAL__6),Vv__CANONICAL__7)) ) ) ) ).

fof('$_type_81384',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__81385] :
      ( c_24__type__81384___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__81385)
    <=> ! [Vv__CANONICAL__13] :
          ( t(Vv__CANONICAL__13,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__14] :
              ( t(Vv__CANONICAL__14,Vv__CANONICAL__0)
             => t(happ(happ(Vvar__81385,Vv__CANONICAL__13),Vv__CANONICAL__14),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_81509',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__81510] :
      ( c_24__type__81509___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__81510)
    <=> ! [Vv__CANONICAL__13] :
          ( t(Vv__CANONICAL__13,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__14] :
              ( t(Vv__CANONICAL__14,Vv__CANONICAL__0)
             => t(happ(happ(Vvar__81510,Vv__CANONICAL__13),Vv__CANONICAL__14),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_81634',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__81635] :
      ( c_24__type__81634___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__81635)
    <=> ! [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__81635,Vv__CANONICAL__13),Vv__CANONICAL__14)) ) ) ) ).

fof('$_type_81759',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__81760] :
      ( c_24__type__81759___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__81760)
    <=> ! [Vv__CANONICAL__13] :
          ( t(Vv__CANONICAL__13,Vv__CANONICAL__6)
         => ! [Vv__CANONICAL__14] :
              ( t(Vv__CANONICAL__14,Vv__CANONICAL__6)
             => t(happ(happ(Vvar__81760,Vv__CANONICAL__13),Vv__CANONICAL__14),Vv__CANONICAL__6) ) ) ) ).

fof('$_type_81884',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__81885] :
      ( c_24__type__81884___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__81885)
    <=> ! [Vv__CANONICAL__13] :
          ( t(Vv__CANONICAL__13,Vv__CANONICAL__6)
         => ! [Vv__CANONICAL__14] :
              ( t(Vv__CANONICAL__14,Vv__CANONICAL__6)
             => t(happ(happ(Vvar__81885,Vv__CANONICAL__13),Vv__CANONICAL__14),Vv__CANONICAL__6) ) ) ) ).

fof('$_type_82009',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__82010] :
      ( c_24__type__82009___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__82010)
    <=> ! [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__82010,Vv__CANONICAL__13),Vv__CANONICAL__14)) ) ) ) ).

fof('$_type_82120',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__82121] :
      ( c_24__type__82120___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__82121)
    <=> ! [Vv__CANONICAL__13] :
          ( t(Vv__CANONICAL__13,Vv__CANONICAL__6)
         => t(happ(Vvar__82121,Vv__CANONICAL__13),Vv__CANONICAL__0) ) ) ).

fof('$_type_82143',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__82144] :
      ( c_24__type__82143___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__82144)
    <=> ! [Vv__CANONICAL__2] :
          ( t(Vv__CANONICAL__2,Vv__CANONICAL__1)
         => ! [Vv__CANONICAL__3] :
              ( t(Vv__CANONICAL__3,Vv__CANONICAL__1)
             => t(happ(happ(Vvar__82144,Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__1) ) ) ) ).

fof('$_type_82155',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__82156] :
      ( c_24__type__82155___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__82156)
    <=> ! [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__82156,Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ).

fof('$_type_82174',axiom,
    ! [Vvar__82175] :
      ( c_24__type__82174___24t(Vvar__82175)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
             => t(happ(happ(Vvar__82175,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_82217',axiom,
    ! [Vvar__82218] :
      ( c_24__type__82217___24t(Vvar__82218)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cType___24t(Vv__CANONICAL__1)
             => ! [Vv__CANONICAL__2] :
                  ( c_24__type__78044___24t(Vv__CANONICAL__1,Vv__CANONICAL__2)
                 => ! [Vv__CANONICAL__3] :
                      ( c_24__type__82227___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__3)
                     => cProp___24t(happ(happ(happ(happ(Vvar__82218,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).

fof('$_type_82227',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__82228] :
      ( c_24__type__82227___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__82228)
    <=> ! [Vv__CANONICAL__2] :
          ( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__3] :
              ( t(Vv__CANONICAL__3,Vv__CANONICAL__1)
             => t(happ(happ(Vvar__82228,Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__1) ) ) ) ).

fof('$_type_82253',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__82254] :
      ( c_24__type__82253___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__82254)
    <=> ! [Vv__CANONICAL__2] :
          ( t(Vv__CANONICAL__2,Vv__CANONICAL__1)
         => t(happ(Vvar__82254,Vv__CANONICAL__2),Vv__CANONICAL__1) ) ) ).

fof('$_type_82381',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__82382] :
      ( c_24__type__82381___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__82382)
    <=> ! [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__82382,Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ).

fof('$_type_82394',axiom,
    ! [Vvar__82395] :
      ( c_24__type__82394___24t(Vvar__82395)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( c_24__type__78044___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
             => cProp___24t(happ(happ(Vvar__82395,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_82485',axiom,
    ! [Vvar__82486] :
      ( c_24__type__82485___24t(Vvar__82486)
    <=> ! [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__82486,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_82615',axiom,
    ! [Vvar__82616] :
      ( c_24__type__82615___24t(Vvar__82616)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(Vv__CANONICAL__1)
             => cProp___24t(happ(happ(Vvar__82616,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_82626',axiom,
    ! [Vvar__82627] :
      ( c_24__type__82626___24t(Vvar__82627)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
         => cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(Vvar__82627,Vv__CANONICAL__0)) ) ) ).

fof('$_type_83378',axiom,
    ! [Vvar__83379] :
      ( c_24__type__83378___24t(Vvar__83379)
    <=> ! [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__83379,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).

fof('$_type_83571',axiom,
    ! [Vvar__83572] :
      ( c_24__type__83571___24t(Vvar__83572)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
             => cCoq_2emicromega_2eEnvRing_2ePol___24t(Vv__CANONICAL__0,happ(happ(Vvar__83572,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_84683',axiom,
    ! [Vvar__84684] :
      ( c_24__type__84683___24t(Vvar__84684)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cType___24t(Vv__CANONICAL__1)
             => ! [Vv__CANONICAL__2] :
                  ( c_24__type__84690___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__84684,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__0) ) ) ) ) ) ) ).

fof('$_type_84690',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__84691] :
      ( c_24__type__84690___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__84691)
    <=> ! [Vv__CANONICAL__2] :
          ( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__3] :
              ( t(Vv__CANONICAL__3,Vv__CANONICAL__1)
             => t(happ(happ(Vvar__84691,Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_85136',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__85137] :
      ( c_24__type__85136___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__85137)
    <=> ! [Vv__CANONICAL__10] :
          ( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__11] :
              ( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
             => t(happ(happ(Vvar__85137,Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_85237',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__85238] :
      ( c_24__type__85237___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__85238)
    <=> ! [Vv__CANONICAL__10] :
          ( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__11] :
              ( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
             => t(happ(happ(Vvar__85238,Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_85338',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__85339] :
      ( c_24__type__85338___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__85339)
    <=> ! [Vv__CANONICAL__10] :
          ( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__11] :
              ( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
             => t(happ(happ(Vvar__85339,Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_85428',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__85429] :
      ( c_24__type__85428___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__85429)
    <=> ! [Vv__CANONICAL__10] :
          ( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
         => t(happ(Vvar__85429,Vv__CANONICAL__10),Vv__CANONICAL__0) ) ) ).

fof('$_type_85529',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__85530] :
      ( c_24__type__85529___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__85530)
    <=> ! [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__85530,Vv__CANONICAL__10),Vv__CANONICAL__11)) ) ) ) ).

fof('$_type_85630',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__85631] :
      ( c_24__type__85630___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__85631)
    <=> ! [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__85631,Vv__CANONICAL__10),Vv__CANONICAL__11)) ) ) ) ).

fof('$_type_85731',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__85732] :
      ( c_24__type__85731___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__85732)
    <=> ! [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__85732,Vv__CANONICAL__10),Vv__CANONICAL__11)) ) ) ) ).

fof('$_type_86185',axiom,
    ! [Vvar__86186] :
      ( c_24__type__86185___24t(Vvar__86186)
    <=> ! [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__86186,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_86203',axiom,
    ! [Vvar__86204] :
      ( c_24__type__86203___24t(Vvar__86204)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( c_24__type__1415___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__86204,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__0) ) ) ) ) ) ).

fof('$_type_86432',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__86433] :
      ( c_24__type__86432___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__86433)
    <=> ! [Vv__CANONICAL__8] :
          ( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__9] :
              ( t(Vv__CANONICAL__9,Vv__CANONICAL__0)
             => t(happ(happ(Vvar__86433,Vv__CANONICAL__8),Vv__CANONICAL__9),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_86495',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__86496] :
      ( c_24__type__86495___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__86496)
    <=> ! [Vv__CANONICAL__8] :
          ( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__9] :
              ( t(Vv__CANONICAL__9,Vv__CANONICAL__0)
             => t(happ(happ(Vvar__86496,Vv__CANONICAL__8),Vv__CANONICAL__9),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_86558',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__86559] :
      ( c_24__type__86558___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__86559)
    <=> ! [Vv__CANONICAL__8] :
          ( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__9] :
              ( t(Vv__CANONICAL__9,Vv__CANONICAL__0)
             => t(happ(happ(Vvar__86559,Vv__CANONICAL__8),Vv__CANONICAL__9),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_86612',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__86613] :
      ( c_24__type__86612___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__86613)
    <=> ! [Vv__CANONICAL__8] :
          ( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
         => t(happ(Vvar__86613,Vv__CANONICAL__8),Vv__CANONICAL__0) ) ) ).

fof('$_type_86675',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__86676] :
      ( c_24__type__86675___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__86676)
    <=> ! [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__86676,Vv__CANONICAL__8),Vv__CANONICAL__9)) ) ) ) ).

fof('$_type_86852',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__86853] :
      ( c_24__type__86852___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__86853)
    <=> ! [Vv__CANONICAL__5] :
          ( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__6] :
              ( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
             => t(happ(happ(Vvar__86853,Vv__CANONICAL__5),Vv__CANONICAL__6),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_86882',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__86883] :
      ( c_24__type__86882___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__86883)
    <=> ! [Vv__CANONICAL__5] :
          ( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__6] :
              ( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
             => t(happ(happ(Vvar__86883,Vv__CANONICAL__5),Vv__CANONICAL__6),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_86906',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__86907] :
      ( c_24__type__86906___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__86907)
    <=> ! [Vv__CANONICAL__5] :
          ( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
         => t(happ(Vvar__86907,Vv__CANONICAL__5),Vv__CANONICAL__0) ) ) ).

fof('$_type_86936',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__86937] :
      ( c_24__type__86936___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__86937)
    <=> ! [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__86937,Vv__CANONICAL__5),Vv__CANONICAL__6)) ) ) ) ).

fof('$_type_86966',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__86967] :
      ( c_24__type__86966___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__86967)
    <=> ! [Vv__CANONICAL__5] :
          ( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__6] :
              ( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
             => t(happ(happ(Vvar__86967,Vv__CANONICAL__5),Vv__CANONICAL__6),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_86990',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__86991] :
      ( c_24__type__86990___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__86991)
    <=> ! [Vv__CANONICAL__5] :
          ( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
         => t(happ(Vvar__86991,Vv__CANONICAL__5),Vv__CANONICAL__0) ) ) ).

fof('$_type_87023',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__87024] :
      ( c_24__type__87023___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__87024)
    <=> ! [Vv__CANONICAL__5] :
          ( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__6] :
              ( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
             => t(happ(happ(Vvar__87024,Vv__CANONICAL__5),Vv__CANONICAL__6),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_87047',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__87048] :
      ( c_24__type__87047___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__87048)
    <=> ! [Vv__CANONICAL__5] :
          ( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
         => t(happ(Vvar__87048,Vv__CANONICAL__5),Vv__CANONICAL__0) ) ) ).

fof('$_type_87074',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__87075] :
      ( c_24__type__87074___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__87075)
    <=> ! [Vv__CANONICAL__5] :
          ( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
         => t(happ(Vvar__87075,Vv__CANONICAL__5),Vv__CANONICAL__0) ) ) ).

fof('$_type_87473',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__87474] :
      ( c_24__type__87473___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__87474)
    <=> ! [Vv__CANONICAL__17] :
          ( t(Vv__CANONICAL__17,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__18] :
              ( t(Vv__CANONICAL__18,Vv__CANONICAL__0)
             => t(happ(happ(Vvar__87474,Vv__CANONICAL__17),Vv__CANONICAL__18),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_87686',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__87687] :
      ( c_24__type__87686___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__87687)
    <=> ! [Vv__CANONICAL__17] :
          ( t(Vv__CANONICAL__17,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__18] :
              ( t(Vv__CANONICAL__18,Vv__CANONICAL__0)
             => t(happ(happ(Vvar__87687,Vv__CANONICAL__17),Vv__CANONICAL__18),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_87899',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__87900] :
      ( c_24__type__87899___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__87900)
    <=> ! [Vv__CANONICAL__17] :
          ( t(Vv__CANONICAL__17,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__18] :
              ( t(Vv__CANONICAL__18,Vv__CANONICAL__0)
             => t(happ(happ(Vvar__87900,Vv__CANONICAL__17),Vv__CANONICAL__18),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_88094',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__88095] :
      ( c_24__type__88094___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__88095)
    <=> ! [Vv__CANONICAL__17] :
          ( t(Vv__CANONICAL__17,Vv__CANONICAL__0)
         => t(happ(Vvar__88095,Vv__CANONICAL__17),Vv__CANONICAL__0) ) ) ).

fof('$_type_88307',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__88308] :
      ( c_24__type__88307___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__88308)
    <=> ! [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__88308,Vv__CANONICAL__17),Vv__CANONICAL__18)) ) ) ) ).

fof('$_type_884',axiom,
    ! [Vvar__885] :
      ( c_24__type__884___24t(Vvar__885)
    <=> ! [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__885,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).

fof('$_type_88520',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__88521] :
      ( c_24__type__88520___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__88521)
    <=> ! [Vv__CANONICAL__17] :
          ( t(Vv__CANONICAL__17,Vv__CANONICAL__8)
         => ! [Vv__CANONICAL__18] :
              ( t(Vv__CANONICAL__18,Vv__CANONICAL__8)
             => t(happ(happ(Vvar__88521,Vv__CANONICAL__17),Vv__CANONICAL__18),Vv__CANONICAL__8) ) ) ) ).

fof('$_type_88733',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__88734] :
      ( c_24__type__88733___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__88734)
    <=> ! [Vv__CANONICAL__17] :
          ( t(Vv__CANONICAL__17,Vv__CANONICAL__8)
         => ! [Vv__CANONICAL__18] :
              ( t(Vv__CANONICAL__18,Vv__CANONICAL__8)
             => t(happ(happ(Vvar__88734,Vv__CANONICAL__17),Vv__CANONICAL__18),Vv__CANONICAL__8) ) ) ) ).

fof('$_type_88946',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__88947] :
      ( c_24__type__88946___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__88947)
    <=> ! [Vv__CANONICAL__17] :
          ( t(Vv__CANONICAL__17,Vv__CANONICAL__8)
         => ! [Vv__CANONICAL__18] :
              ( t(Vv__CANONICAL__18,Vv__CANONICAL__8)
             => t(happ(happ(Vvar__88947,Vv__CANONICAL__17),Vv__CANONICAL__18),Vv__CANONICAL__8) ) ) ) ).

fof('$_type_89141',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__89142] :
      ( c_24__type__89141___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__89142)
    <=> ! [Vv__CANONICAL__17] :
          ( t(Vv__CANONICAL__17,Vv__CANONICAL__8)
         => t(happ(Vvar__89142,Vv__CANONICAL__17),Vv__CANONICAL__8) ) ) ).

fof('$_type_89354',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__89355] :
      ( c_24__type__89354___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__89355)
    <=> ! [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__89355,Vv__CANONICAL__17),Vv__CANONICAL__18)) ) ) ) ).

fof('$_type_89549',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__89550] :
      ( c_24__type__89549___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__89550)
    <=> ! [Vv__CANONICAL__17] :
          ( t(Vv__CANONICAL__17,Vv__CANONICAL__8)
         => t(happ(Vvar__89550,Vv__CANONICAL__17),Vv__CANONICAL__0) ) ) ).

fof('$_type_89872',axiom,
    ! [Vvar__89873] :
      ( c_24__type__89872___24t(Vvar__89873)
    <=> ! [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__89873,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_89914',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__89915] :
      ( c_24__type__89914___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__89915)
    <=> ! [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__89915,Vv__CANONICAL__4),Vv__CANONICAL__5)) ) ) ) ).

fof('$_type_89968',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__89969] :
      ( c_24__type__89968___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__89969)
    <=> ! [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__89969,Vv__CANONICAL__4),Vv__CANONICAL__5)) ) ) ) ).

fof('$_type_90026',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__90027] :
      ( c_24__type__90026___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__90027)
    <=> ! [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__90027,Vv__CANONICAL__4),Vv__CANONICAL__5)) ) ) ) ).

fof('$_type_90068',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__90069] :
      ( c_24__type__90068___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__90069)
    <=> ! [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__90069,Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ).

fof('$_type_90094',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__90095] :
      ( c_24__type__90094___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__90095)
    <=> ! [Vv__CANONICAL__3] :
          ( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
         => cProp___24t(happ(Vvar__90095,Vv__CANONICAL__3)) ) ) ).

fof('$_type_90102',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__90103] :
      ( c_24__type__90102___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__90103)
    <=> ! [Vv__CANONICAL__3] :
          ( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
         => cProp___24t(happ(Vvar__90103,Vv__CANONICAL__3)) ) ) ).

fof('$_type_90110',axiom,
    ! [Vvar__90111] :
      ( c_24__type__90110___24t(Vvar__90111)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( c_24__type__1051___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
             => ! [Vv__CANONICAL__2] :
                  ( c_24__type__1051___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
                 => cType___24t(happ(happ(happ(Vvar__90111,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).

fof('$_type_90332',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__90333] :
      ( c_24__type__90332___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__90333)
    <=> ! [Vv__CANONICAL__3] :
          ( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
         => cType___24t(happ(Vvar__90333,Vv__CANONICAL__3)) ) ) ).

fof('$_type_90340',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__90341] :
      ( c_24__type__90340___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__90341)
    <=> ! [Vv__CANONICAL__3] :
          ( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
         => cType___24t(happ(Vvar__90341,Vv__CANONICAL__3)) ) ) ).

fof('$_type_90348',axiom,
    ! [Vvar__90349] :
      ( c_24__type__90348___24t(Vvar__90349)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( c_24__type__67650___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
             => ! [Vv__CANONICAL__2] :
                  ( c_24__type__67650___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
                 => cType___24t(happ(happ(happ(Vvar__90349,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).

fof('$_type_91060',axiom,
    ! [Vvar__91061] :
      ( c_24__type__91060___24t(Vvar__91061)
    <=> ! [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__91061,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).

fof('$_type_92944',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__92945] :
      ( c_24__type__92944___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__92945)
    <=> ! [Vv__CANONICAL__4] :
          ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__4)
         => cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(Vvar__92945,Vv__CANONICAL__4)) ) ) ).

fof('$_type_92953',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__92954] :
      ( c_24__type__92953___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__92954)
    <=> ! [Vv__CANONICAL__4] :
          ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__4)
         => cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(Vvar__92954,Vv__CANONICAL__4)) ) ) ).

fof('$_type_93087',axiom,
    ! [Vvar__93088] :
      ( c_24__type__93087___24t(Vvar__93088)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__0)
         => cCoq_2ePArith_2eBinPosDef_2ePos_2emask___24t(happ(Vvar__93088,Vv__CANONICAL__0)) ) ) ).

fof('$_type_93133',axiom,
    ! [Vvar__93134] :
      ( c_24__type__93133___24t(Vvar__93134)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( c_24__type__78702___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__93134,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__0) ) ) ) ) ) ).

fof('$_type_93138',axiom,
    ! [Vvar__93139] :
      ( c_24__type__93138___24t(Vvar__93139)
    <=> ! [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__93139,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_93209',axiom,
    ! [Vvar__93210] :
      ( c_24__type__93209___24t(Vvar__93210)
    <=> ! [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__93210,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).

fof('$_type_93686',axiom,
    ! [Vvar__93687] :
      ( c_24__type__93686___24t(Vvar__93687)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
         => cCoq_2eInit_2eDatatypes_2ebool___24t(happ(Vvar__93687,Vv__CANONICAL__0)) ) ) ).

fof('$_type_94152',axiom,
    ! [Vvar__94153] :
      ( c_24__type__94152___24t(Vvar__94153)
    <=> ! [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)
                 => cCoq_2eInit_2eDatatypes_2ebool___24t(happ(happ(happ(Vvar__94153,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).

fof('$_type_94162',axiom,
    ! [Vvar__94163] :
      ( c_24__type__94162___24t(Vvar__94163)
    <=> ! [Vv__CANONICAL__0] :
          ( cProp___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__1)
             => cType___24t(happ(happ(Vvar__94163,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_94176',axiom,
    ! [Vvar__94177] :
      ( c_24__type__94176___24t(Vvar__94177)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eInit_2eByte_2ebyte___24t(Vv__CANONICAL__0)
         => cCoq_2eInit_2eByte_2ebyte___24t(happ(Vvar__94177,Vv__CANONICAL__0)) ) ) ).

fof('$_type_94192',axiom,
    ! [Vvar__94193] :
      ( c_24__type__94192___24t(Vvar__94193)
    <=> ! [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__94193,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).

fof('$_type_94244',axiom,
    ! [Vv__CANONICAL__0,Vvar__94245] :
      ( c_24__type__94244___24t(Vv__CANONICAL__0,Vvar__94245)
    <=> ! [Vv__CANONICAL__1] :
          ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__1)
         => t(happ(Vvar__94245,Vv__CANONICAL__1),Vv__CANONICAL__0) ) ) ).

fof('$_type_94453',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__94454] :
      ( c_24__type__94453___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__94454)
    <=> ! [Vv__CANONICAL__6] :
          ( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
         => cType___24t(happ(Vvar__94454,Vv__CANONICAL__6)) ) ) ).

fof('$_type_94481',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__94482] :
      ( c_24__type__94481___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__94482)
    <=> ! [Vv__CANONICAL__6] :
          ( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
         => cType___24t(happ(Vvar__94482,Vv__CANONICAL__6)) ) ) ).

fof('$_type_94677',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__94678] :
      ( c_24__type__94677___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__94678)
    <=> ! [Vv__CANONICAL__10] :
          ( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__11] :
              ( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
             => t(happ(happ(Vvar__94678,Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_94770',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__94771] :
      ( c_24__type__94770___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__94771)
    <=> ! [Vv__CANONICAL__10] :
          ( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__11] :
              ( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
             => t(happ(happ(Vvar__94771,Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_94863',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__94864] :
      ( c_24__type__94863___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__94864)
    <=> ! [Vv__CANONICAL__10] :
          ( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__11] :
              ( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
             => t(happ(happ(Vvar__94864,Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_94945',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__94946] :
      ( c_24__type__94945___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__94946)
    <=> ! [Vv__CANONICAL__10] :
          ( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
         => t(happ(Vvar__94946,Vv__CANONICAL__10),Vv__CANONICAL__0) ) ) ).

fof('$_type_95038',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__95039] :
      ( c_24__type__95038___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__95039)
    <=> ! [Vv__CANONICAL__10] :
          ( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__11] :
              ( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
             => t(happ(happ(Vvar__95039,Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_95120',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__95121] :
      ( c_24__type__95120___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__95121)
    <=> ! [Vv__CANONICAL__10] :
          ( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
         => t(happ(Vvar__95121,Vv__CANONICAL__10),Vv__CANONICAL__0) ) ) ).

fof('$_type_95213',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__95214] :
      ( c_24__type__95213___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__95214)
    <=> ! [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__95214,Vv__CANONICAL__10),Vv__CANONICAL__11)) ) ) ) ).

fof('$_type_95771',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__95772] :
      ( c_24__type__95771___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__95772)
    <=> ! [Vv__CANONICAL__10] :
          ( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__11] :
              ( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
             => t(happ(happ(Vvar__95772,Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_95864',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__95865] :
      ( c_24__type__95864___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__95865)
    <=> ! [Vv__CANONICAL__10] :
          ( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__11] :
              ( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
             => t(happ(happ(Vvar__95865,Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_95957',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__95958] :
      ( c_24__type__95957___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__95958)
    <=> ! [Vv__CANONICAL__10] :
          ( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__11] :
              ( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
             => t(happ(happ(Vvar__95958,Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_96039',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__96040] :
      ( c_24__type__96039___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__96040)
    <=> ! [Vv__CANONICAL__10] :
          ( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
         => t(happ(Vvar__96040,Vv__CANONICAL__10),Vv__CANONICAL__0) ) ) ).

fof('$_type_96132',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__96133] :
      ( c_24__type__96132___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__96133)
    <=> ! [Vv__CANONICAL__10] :
          ( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__11] :
              ( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
             => t(happ(happ(Vvar__96133,Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_96214',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__96215] :
      ( c_24__type__96214___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__96215)
    <=> ! [Vv__CANONICAL__10] :
          ( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
         => t(happ(Vvar__96215,Vv__CANONICAL__10),Vv__CANONICAL__0) ) ) ).

fof('$_type_96307',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__96308] :
      ( c_24__type__96307___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__96308)
    <=> ! [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__96308,Vv__CANONICAL__10),Vv__CANONICAL__11)) ) ) ) ).

fof('$_type_96461',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__96462] :
      ( c_24__type__96461___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__96462)
    <=> ! [Vv__CANONICAL__8] :
          ( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__9] :
              ( t(Vv__CANONICAL__9,Vv__CANONICAL__0)
             => t(happ(happ(Vvar__96462,Vv__CANONICAL__8),Vv__CANONICAL__9),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_96524',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__96525] :
      ( c_24__type__96524___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__96525)
    <=> ! [Vv__CANONICAL__8] :
          ( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__9] :
              ( t(Vv__CANONICAL__9,Vv__CANONICAL__0)
             => t(happ(happ(Vvar__96525,Vv__CANONICAL__8),Vv__CANONICAL__9),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_96587',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__96588] :
      ( c_24__type__96587___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__96588)
    <=> ! [Vv__CANONICAL__8] :
          ( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__9] :
              ( t(Vv__CANONICAL__9,Vv__CANONICAL__0)
             => t(happ(happ(Vvar__96588,Vv__CANONICAL__8),Vv__CANONICAL__9),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_96641',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__96642] :
      ( c_24__type__96641___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__96642)
    <=> ! [Vv__CANONICAL__8] :
          ( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
         => t(happ(Vvar__96642,Vv__CANONICAL__8),Vv__CANONICAL__0) ) ) ).

fof('$_type_96704',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__96705] :
      ( c_24__type__96704___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__96705)
    <=> ! [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__96705,Vv__CANONICAL__8),Vv__CANONICAL__9)) ) ) ) ).

fof('$_type_96713',axiom,
    ! [Vv__CANONICAL__0,Vvar__96714] :
      ( c_24__type__96713___24t(Vv__CANONICAL__0,Vvar__96714)
    <=> ! [Vv__CANONICAL__1] :
          ( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__2] :
              ( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
             => cCoq_2eInit_2eDatatypes_2ecomparison___24t(happ(happ(Vvar__96714,Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ).

fof('$_type_96724',axiom,
    ! [Vvar__96725] :
      ( c_24__type__96724___24t(Vvar__96725)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( c_24__type__96713___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
             => ! [Vv__CANONICAL__2] :
                  ( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
                 => ! [Vv__CANONICAL__3] :
                      ( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
                     => t(happ(happ(happ(happ(Vvar__96725,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__0) ) ) ) ) ) ).

fof('$_type_96766',axiom,
    ! [Vvar__96767] :
      ( c_24__type__96766___24t(Vvar__96767)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
             => ! [Vv__CANONICAL__2] :
                  ( c_24__type__1415___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
                 => ! [Vv__CANONICAL__3] :
                      ( c_24__type__1415___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__96767,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__0) ) ) ) ) ) ) ).

fof('$_type_96826',axiom,
    ! [Vvar__96827] :
      ( c_24__type__96826___24t(Vvar__96827)
    <=> ! [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)
                 => t(happ(happ(happ(Vvar__96827,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__0) ) ) ) ) ).

fof('$_type_96866',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__96867] :
      ( c_24__type__96866___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__96867)
    <=> ! [Vv__CANONICAL__3] :
          ( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
         => cProp___24t(happ(Vvar__96867,Vv__CANONICAL__3)) ) ) ).

fof('$_type_96890',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__96891] :
      ( c_24__type__96890___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__96891)
    <=> ! [Vv__CANONICAL__3] :
          ( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
         => cProp___24t(happ(Vvar__96891,Vv__CANONICAL__3)) ) ) ).

fof('$_type_96937',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__96938] :
      ( c_24__type__96937___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__96938)
    <=> ! [Vv__CANONICAL__5] :
          ( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__6] :
              ( t(Vv__CANONICAL__6,Vv__CANONICAL__1)
             => cProp___24t(happ(happ(Vvar__96938,Vv__CANONICAL__5),Vv__CANONICAL__6)) ) ) ) ).

fof('$_type_96972',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__96973] :
      ( c_24__type__96972___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__96973)
    <=> ! [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__96973,Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ).

fof('$_type_96974',axiom,
    ! [Vvar__96975] :
      ( c_24__type__96974___24t(Vvar__96975)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => cProp___24t(happ(Vvar__96975,Vv__CANONICAL__0)) ) ) ).

fof('$_type_97053',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__97054] :
      ( c_24__type__97053___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__97054)
    <=> ! [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__97054,Vv__CANONICAL__5),Vv__CANONICAL__6)) ) ) ) ).

fof('$_type_97072',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__97073] :
      ( c_24__type__97072___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__97073)
    <=> ! [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__97073,Vv__CANONICAL__5),Vv__CANONICAL__6)) ) ) ) ).

fof('$_type_97092',axiom,
    ! [Vvar__97093] :
      ( c_24__type__97092___24t(Vvar__97093)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( c_24__type__78044___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
             => ! [Vv__CANONICAL__2] :
                  ( c_24__type__78044___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__97093,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ) ) ) ).

fof('$_type_97184',axiom,
    ! [Vvar__97185] :
      ( c_24__type__97184___24t(Vvar__97185)
    <=> ! [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__97185,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_97189',axiom,
    ! [Vvar__97190] :
      ( c_24__type__97189___24t(Vvar__97190)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eQArith_2eQArith__base_2eQ___24t(Vv__CANONICAL__0)
         => cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(Vvar__97190,Vv__CANONICAL__0)) ) ) ).

fof('$_type_97194',axiom,
    ! [Vvar__97195] :
      ( c_24__type__97194___24t(Vvar__97195)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eQArith_2eQArith__base_2eQ___24t(Vv__CANONICAL__0)
         => cCoq_2eNumbers_2eBinNums_2epositive___24t(happ(Vvar__97195,Vv__CANONICAL__0)) ) ) ).

fof('$_type_97376',axiom,
    ! [Vvar__97377] :
      ( c_24__type__97376___24t(Vvar__97377)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
         => cCoq_2emicromega_2eRMicromega_2eRcst___24t(happ(Vvar__97377,Vv__CANONICAL__0)) ) ) ).

fof('$_type_97378',axiom,
    ! [Vvar__97379] :
      ( c_24__type__97378___24t(Vvar__97379)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__0)
         => cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(Vvar__97379,Vv__CANONICAL__0)) ) ) ).

fof('$_type_97383',axiom,
    ! [Vvar__97384] :
      ( c_24__type__97383___24t(Vvar__97384)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
             => cProp___24t(happ(happ(Vvar__97384,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_97401',axiom,
    ! [Vvar__97402] :
      ( c_24__type__97401___24t(Vvar__97402)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( c_24__type__1051___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
             => ! [Vv__CANONICAL__2] :
                  ( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
                 => ! [Vv__CANONICAL__3] :
                      ( cProp___24t(Vv__CANONICAL__3)
                     => cProp___24t(happ(happ(happ(happ(Vvar__97402,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).

fof('$_type_97427',axiom,
    ! [Vvar__97428] :
      ( c_24__type__97427___24t(Vvar__97428)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( c_24__type__1051___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__97428,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).

fof('$_type_97513',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__97514] :
      ( c_24__type__97513___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__97514)
    <=> ! [Vv__CANONICAL__6] :
          ( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__7] :
              ( t(Vv__CANONICAL__7,Vv__CANONICAL__0)
             => cProp___24t(happ(happ(Vvar__97514,Vv__CANONICAL__6),Vv__CANONICAL__7)) ) ) ) ).

fof('$_type_97538',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__97539] :
      ( c_24__type__97538___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__97539)
    <=> ! [Vv__CANONICAL__6] :
          ( t(Vv__CANONICAL__6,Vv__CANONICAL__1)
         => ! [Vv__CANONICAL__7] :
              ( t(Vv__CANONICAL__7,Vv__CANONICAL__1)
             => cProp___24t(happ(happ(Vvar__97539,Vv__CANONICAL__6),Vv__CANONICAL__7)) ) ) ) ).

fof('$_type_97589',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__97590] :
      ( c_24__type__97589___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__97590)
    <=> ! [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__97590,Vv__CANONICAL__4),Vv__CANONICAL__5)) ) ) ) ).

fof('$_type_97687',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__97688] :
      ( c_24__type__97687___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__97688)
    <=> ! [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__97688,Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ).

fof('$_type_977',axiom,
    ! [Vvar__978] :
      ( c_24__type__977___24t(Vvar__978)
    <=> ! [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__981___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1),happ(happ(happ(happ(Vvar__978,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ) ).

fof('$_type_98168',axiom,
    ! [Vvar__98169] :
      ( c_24__type__98168___24t(Vvar__98169)
    <=> ! [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__98169,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_98735',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__98736] :
      ( c_24__type__98735___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__98736)
    <=> ! [Vv__CANONICAL__22] :
          ( t(Vv__CANONICAL__22,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__23] :
              ( t(Vv__CANONICAL__23,Vv__CANONICAL__0)
             => t(happ(happ(Vvar__98736,Vv__CANONICAL__22),Vv__CANONICAL__23),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_99081',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__99082] :
      ( c_24__type__99081___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__99082)
    <=> ! [Vv__CANONICAL__22] :
          ( t(Vv__CANONICAL__22,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__23] :
              ( t(Vv__CANONICAL__23,Vv__CANONICAL__0)
             => t(happ(happ(Vvar__99082,Vv__CANONICAL__22),Vv__CANONICAL__23),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_99427',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__99428] :
      ( c_24__type__99427___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__99428)
    <=> ! [Vv__CANONICAL__22] :
          ( t(Vv__CANONICAL__22,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__23] :
              ( t(Vv__CANONICAL__23,Vv__CANONICAL__0)
             => t(happ(happ(Vvar__99428,Vv__CANONICAL__22),Vv__CANONICAL__23),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_99750',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__99751] :
      ( c_24__type__99750___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__99751)
    <=> ! [Vv__CANONICAL__22] :
          ( t(Vv__CANONICAL__22,Vv__CANONICAL__0)
         => t(happ(Vvar__99751,Vv__CANONICAL__22),Vv__CANONICAL__0) ) ) ).

fof('$_typeof_A',axiom,
    cType___24t(cA) ).

fof('$_typeof_B',axiom,
    cType___24t(cB) ).

fof('$_typeof_Coq.Arith.EqNat.eq_nat',axiom,
    c_24__type__67486___24t(cCoq_2eArith_2eEqNat_2eeq__nat) ).

fof('$_typeof_Coq.Arith.PeanoNat.Nat.eq',axiom,
    c_24__type__67486___24t(cCoq_2eArith_2ePeanoNat_2eNat_2eeq) ).

fof('$_typeof_Coq.Arith.PeanoNat.Nat.eqf',axiom,
    c_24__type__80277___24t(cCoq_2eArith_2ePeanoNat_2eNat_2eeqf) ).

fof('$_typeof_Coq.Arith.PeanoNat.Nat.le',axiom,
    c_24__type__67486___24t(cCoq_2eArith_2ePeanoNat_2eNat_2ele) ).

fof('$_typeof_Coq.Arith.PeanoNat.Nat.lt',axiom,
    c_24__type__67486___24t(cCoq_2eArith_2ePeanoNat_2eNat_2elt) ).

fof('$_typeof_Coq.Arith.PeanoNat.Nat.recursion',axiom,
    c_24__type__105577___24t(cCoq_2eArith_2ePeanoNat_2eNat_2erecursion) ).

fof('$_typeof_Coq.Arith.Plus.tail_plus',axiom,
    c_24__type__567___24t(cCoq_2eArith_2ePlus_2etail__plus) ).

fof('$_typeof_Coq.Arith.Wf_nat.ltof',axiom,
    c_24__type__105337___24t(cCoq_2eArith_2eWf__nat_2eltof) ).

fof('$_typeof_Coq.Bool.Bool.Is_true',axiom,
    c_24__type__75476___24t(cCoq_2eBool_2eBool_2eIs__true) ).

fof('$_typeof_Coq.Bool.Bool.eqb',axiom,
    c_24__type__75479___24t(cCoq_2eBool_2eBool_2eeqb) ).

fof('$_typeof_Coq.Bool.Bool.ifb',axiom,
    c_24__type__94152___24t(cCoq_2eBool_2eBool_2eifb) ).

fof('$_typeof_Coq.Bool.Bool.reflect',axiom,
    c_24__type__94162___24t(cCoq_2eBool_2eBool_2ereflect) ).

fof('$_typeof_Coq.Bool.Sumbool.sumbool_of_bool',axiom,
    c_24__type__1434___24t(cCoq_2eBool_2eSumbool_2esumbool__of__bool) ).

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__93209___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.eq',axiom,
    c_24__type__82615___24t(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eeq) ).

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.byte_of_byte',axiom,
    c_24__type__94176___24t(cCoq_2eInit_2eByte_2ebyte__of__byte) ).

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__83378___24t(cCoq_2eInit_2eDatatypes_2eCompareSpecT) ).

fof('$_typeof_Coq.Init.Datatypes.Empty_set',axiom,
    cType___24t(cCoq_2eInit_2eDatatypes_2eEmpty__set) ).

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.ID',axiom,
    cType___24t(cCoq_2eInit_2eDatatypes_2eID) ).

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__649___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__6___24t(cCoq_2eInit_2eDatatypes_2eS) ).

fof('$_typeof_Coq.Init.Datatypes.Some',axiom,
    c_24__type__647___24t(cCoq_2eInit_2eDatatypes_2eSome) ).

fof('$_typeof_Coq.Init.Datatypes.andb',axiom,
    c_24__type__75479___24t(cCoq_2eInit_2eDatatypes_2eandb) ).

fof('$_typeof_Coq.Init.Datatypes.app',axiom,
    c_24__type__94192___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__75665___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__75628___24t(cCoq_2eInit_2eDatatypes_2efst) ).

fof('$_typeof_Coq.Init.Datatypes.implb',axiom,
    c_24__type__75479___24t(cCoq_2eInit_2eDatatypes_2eimplb) ).

fof('$_typeof_Coq.Init.Datatypes.length',axiom,
    c_24__type__67050___24t(cCoq_2eInit_2eDatatypes_2elength) ).

fof('$_typeof_Coq.Init.Datatypes.list',axiom,
    c_24__type__257___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__75483___24t(cCoq_2eInit_2eDatatypes_2enegb) ).

fof('$_typeof_Coq.Init.Datatypes.nil',axiom,
    c_24__type__75660___24t(cCoq_2eInit_2eDatatypes_2enil) ).

fof('$_typeof_Coq.Init.Datatypes.option',axiom,
    c_24__type__257___24t(cCoq_2eInit_2eDatatypes_2eoption) ).

fof('$_typeof_Coq.Init.Datatypes.orb',axiom,
    c_24__type__75479___24t(cCoq_2eInit_2eDatatypes_2eorb) ).

fof('$_typeof_Coq.Init.Datatypes.pair',axiom,
    c_24__type__75561___24t(cCoq_2eInit_2eDatatypes_2epair) ).

fof('$_typeof_Coq.Init.Datatypes.prod',axiom,
    c_24__type__67032___24t(cCoq_2eInit_2eDatatypes_2eprod) ).

fof('$_typeof_Coq.Init.Datatypes.prod_rect',axiom,
    c_24__type__75595___24t(cCoq_2eInit_2eDatatypes_2eprod__rect) ).

fof('$_typeof_Coq.Init.Datatypes.snd',axiom,
    c_24__type__75640___24t(cCoq_2eInit_2eDatatypes_2esnd) ).

fof('$_typeof_Coq.Init.Datatypes.sum',axiom,
    c_24__type__67032___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__75479___24t(cCoq_2eInit_2eDatatypes_2exorb) ).

fof('$_typeof_Coq.Init.Decimal.Nil',axiom,
    cCoq_2eInit_2eDecimal_2euint___24t(cCoq_2eInit_2eDecimal_2eNil) ).

fof('$_typeof_Coq.Init.Decimal.decimal',axiom,
    cType___24t(cCoq_2eInit_2eDecimal_2edecimal) ).

fof('$_typeof_Coq.Init.Decimal.int',axiom,
    cType___24t(cCoq_2eInit_2eDecimal_2eint) ).

fof('$_typeof_Coq.Init.Decimal.uint',axiom,
    cType___24t(cCoq_2eInit_2eDecimal_2euint) ).

fof('$_typeof_Coq.Init.Logic_Type.notT',axiom,
    c_24__type__96974___24t(cCoq_2eInit_2eLogic__Type_2enotT) ).

fof('$_typeof_Coq.Init.Nat.add',axiom,
    c_24__type__567___24t(cCoq_2eInit_2eNat_2eadd) ).

fof('$_typeof_Coq.Init.Nat.div2',axiom,
    c_24__type__6___24t(cCoq_2eInit_2eNat_2ediv2) ).

fof('$_typeof_Coq.Init.Nat.double',axiom,
    c_24__type__6___24t(cCoq_2eInit_2eNat_2edouble) ).

fof('$_typeof_Coq.Init.Nat.even',axiom,
    c_24__type__77893___24t(cCoq_2eInit_2eNat_2eeven) ).

fof('$_typeof_Coq.Init.Nat.leb',axiom,
    c_24__type__67483___24t(cCoq_2eInit_2eNat_2eleb) ).

fof('$_typeof_Coq.Init.Nat.max',axiom,
    c_24__type__567___24t(cCoq_2eInit_2eNat_2emax) ).

fof('$_typeof_Coq.Init.Nat.min',axiom,
    c_24__type__567___24t(cCoq_2eInit_2eNat_2emin) ).

fof('$_typeof_Coq.Init.Nat.mul',axiom,
    c_24__type__567___24t(cCoq_2eInit_2eNat_2emul) ).

fof('$_typeof_Coq.Init.Nat.pow',axiom,
    c_24__type__567___24t(cCoq_2eInit_2eNat_2epow) ).

fof('$_typeof_Coq.Init.Nat.pred',axiom,
    c_24__type__6___24t(cCoq_2eInit_2eNat_2epred) ).

fof('$_typeof_Coq.Init.Nat.sub',axiom,
    c_24__type__567___24t(cCoq_2eInit_2eNat_2esub) ).

fof('$_typeof_Coq.Init.Nat.succ',axiom,
    c_24__type__6___24t(cCoq_2eInit_2eNat_2esucc) ).

fof('$_typeof_Coq.Init.Nat.t',axiom,
    cType___24t(cCoq_2eInit_2eNat_2et) ).

fof('$_typeof_Coq.Init.Nat.tail_add',axiom,
    c_24__type__567___24t(cCoq_2eInit_2eNat_2etail__add) ).

fof('$_typeof_Coq.Init.Nat.zero',axiom,
    cCoq_2eInit_2eDatatypes_2enat___24t(cCoq_2eInit_2eNat_2ezero) ).

fof('$_typeof_Coq.Init.Peano.IsSucc',axiom,
    c_24__type__67891___24t(cCoq_2eInit_2ePeano_2eIsSucc) ).

fof('$_typeof_Coq.Init.Peano.ge',axiom,
    c_24__type__67486___24t(cCoq_2eInit_2ePeano_2ege) ).

fof('$_typeof_Coq.Init.Peano.gt',axiom,
    c_24__type__67486___24t(cCoq_2eInit_2ePeano_2egt) ).

fof('$_typeof_Coq.Init.Peano.lt',axiom,
    c_24__type__67486___24t(cCoq_2eInit_2ePeano_2elt) ).

fof('$_typeof_Coq.Init.Specif.except',axiom,
    c_24__type__105290___24t(cCoq_2eInit_2eSpecif_2eexcept) ).

fof('$_typeof_Coq.Init.Specif.exist',axiom,
    c_24__type__67586___24t(cCoq_2eInit_2eSpecif_2eexist) ).

fof('$_typeof_Coq.Init.Specif.existT',axiom,
    c_24__type__67667___24t(cCoq_2eInit_2eSpecif_2eexistT) ).

fof('$_typeof_Coq.Init.Specif.left',axiom,
    c_24__type__67739___24t(cCoq_2eInit_2eSpecif_2eleft) ).

fof('$_typeof_Coq.Init.Specif.right',axiom,
    c_24__type__67744___24t(cCoq_2eInit_2eSpecif_2eright) ).

fof('$_typeof_Coq.Init.Specif.sig',axiom,
    c_24__type__1048___24t(cCoq_2eInit_2eSpecif_2esig) ).

fof('$_typeof_Coq.Init.Specif.sig2',axiom,
    c_24__type__90110___24t(cCoq_2eInit_2eSpecif_2esig2) ).

fof('$_typeof_Coq.Init.Specif.sigT',axiom,
    c_24__type__67647___24t(cCoq_2eInit_2eSpecif_2esigT) ).

fof('$_typeof_Coq.Init.Specif.sigT2',axiom,
    c_24__type__90348___24t(cCoq_2eInit_2eSpecif_2esigT2) ).

fof('$_typeof_Coq.Init.Specif.sigT_rect',axiom,
    c_24__type__67716___24t(cCoq_2eInit_2eSpecif_2esigT__rect) ).

fof('$_typeof_Coq.Init.Specif.sig_rec',axiom,
    c_24__type__67609___24t(cCoq_2eInit_2eSpecif_2esig__rec) ).

fof('$_typeof_Coq.Init.Specif.sig_rect',axiom,
    c_24__type__67609___24t(cCoq_2eInit_2eSpecif_2esig__rect) ).

fof('$_typeof_Coq.Init.Specif.sumbool',axiom,
    c_24__type__586___24t(cCoq_2eInit_2eSpecif_2esumbool) ).

fof('$_typeof_Coq.Init.Specif.sumbool_rec',axiom,
    c_24__type__67785___24t(cCoq_2eInit_2eSpecif_2esumbool__rec) ).

fof('$_typeof_Coq.Init.Specif.sumbool_rect',axiom,
    c_24__type__67785___24t(cCoq_2eInit_2eSpecif_2esumbool__rect) ).

fof('$_typeof_Coq.Init.Specif.sumor',axiom,
    c_24__type__1079___24t(cCoq_2eInit_2eSpecif_2esumor) ).

fof('$_typeof_Coq.Init.Specif.sumor_rec',axiom,
    c_24__type__67853___24t(cCoq_2eInit_2eSpecif_2esumor__rec) ).

fof('$_typeof_Coq.Init.Specif.sumor_rect',axiom,
    c_24__type__67853___24t(cCoq_2eInit_2eSpecif_2esumor__rect) ).

fof('$_typeof_Coq.Init.Wf.well_founded',axiom,
    c_24__type__82394___24t(cCoq_2eInit_2eWf_2ewell__founded) ).

fof('$_typeof_Coq.Lists.List.In',axiom,
    c_24__type__76206___24t(cCoq_2eLists_2eList_2eIn) ).

fof('$_typeof_Coq.Lists.List.fold_left',axiom,
    c_24__type__84683___24t(cCoq_2eLists_2eList_2efold__left) ).

fof('$_typeof_Coq.Lists.List.fold_right',axiom,
    c_24__type__67099___24t(cCoq_2eLists_2eList_2efold__right) ).

fof('$_typeof_Coq.Lists.List.hd',axiom,
    c_24__type__96826___24t(cCoq_2eLists_2eList_2ehd) ).

fof('$_typeof_Coq.Lists.SetoidList.transpose',axiom,
    c_24__type__82217___24t(cCoq_2eLists_2eSetoidList_2etranspose) ).

fof('$_typeof_Coq.Lists.SetoidList.transpose2',axiom,
    c_24__type__82217___24t(cCoq_2eLists_2eSetoidList_2etranspose2) ).

fof('$_typeof_Coq.Lists.SetoidList.transpose_restr',axiom,
    c_24__type__105145___24t(cCoq_2eLists_2eSetoidList_2etranspose__restr) ).

fof('$_typeof_Coq.Lists.SetoidList.transpose_restr2',axiom,
    c_24__type__105145___24t(cCoq_2eLists_2eSetoidList_2etranspose__restr2) ).

fof('$_typeof_Coq.Logic.Decidable.decidable',axiom,
    c_24__type__75743___24t(cCoq_2eLogic_2eDecidable_2edecidable) ).

fof('$_typeof_Coq.NArith.BinNat.N.eq',axiom,
    c_24__type__80251___24t(cCoq_2eNArith_2eBinNat_2eN_2eeq) ).

fof('$_typeof_Coq.NArith.BinNat.N.eqf',axiom,
    c_24__type__105559___24t(cCoq_2eNArith_2eBinNat_2eN_2eeqf) ).

fof('$_typeof_Coq.NArith.BinNat.N.le',axiom,
    c_24__type__80251___24t(cCoq_2eNArith_2eBinNat_2eN_2ele) ).

fof('$_typeof_Coq.NArith.BinNat.N.lt',axiom,
    c_24__type__80251___24t(cCoq_2eNArith_2eBinNat_2eN_2elt) ).

fof('$_typeof_Coq.NArith.BinNatDef.N.add',axiom,
    c_24__type__1461___24t(cCoq_2eNArith_2eBinNatDef_2eN_2eadd) ).

fof('$_typeof_Coq.NArith.BinNatDef.N.div2',axiom,
    c_24__type__1106___24t(cCoq_2eNArith_2eBinNatDef_2eN_2ediv2) ).

fof('$_typeof_Coq.NArith.BinNatDef.N.double',axiom,
    c_24__type__1106___24t(cCoq_2eNArith_2eBinNatDef_2eN_2edouble) ).

fof('$_typeof_Coq.NArith.BinNatDef.N.eqb',axiom,
    c_24__type__1446___24t(cCoq_2eNArith_2eBinNatDef_2eN_2eeqb) ).

fof('$_typeof_Coq.NArith.BinNatDef.N.lxor',axiom,
    c_24__type__1461___24t(cCoq_2eNArith_2eBinNatDef_2eN_2elxor) ).

fof('$_typeof_Coq.NArith.BinNatDef.N.min',axiom,
    c_24__type__1461___24t(cCoq_2eNArith_2eBinNatDef_2eN_2emin) ).

fof('$_typeof_Coq.NArith.BinNatDef.N.mul',axiom,
    c_24__type__1461___24t(cCoq_2eNArith_2eBinNatDef_2eN_2emul) ).

fof('$_typeof_Coq.NArith.BinNatDef.N.odd',axiom,
    c_24__type__1454___24t(cCoq_2eNArith_2eBinNatDef_2eN_2eodd) ).

fof('$_typeof_Coq.NArith.BinNatDef.N.succ',axiom,
    c_24__type__1106___24t(cCoq_2eNArith_2eBinNatDef_2eN_2esucc) ).

fof('$_typeof_Coq.NArith.BinNatDef.N.succ_double',axiom,
    c_24__type__1106___24t(cCoq_2eNArith_2eBinNatDef_2eN_2esucc__double) ).

fof('$_typeof_Coq.NArith.BinNatDef.N.t',axiom,
    cType___24t(cCoq_2eNArith_2eBinNatDef_2eN_2et) ).

fof('$_typeof_Coq.NArith.BinNatDef.N.testbit',axiom,
    c_24__type__1446___24t(cCoq_2eNArith_2eBinNatDef_2eN_2etestbit) ).

fof('$_typeof_Coq.NArith.BinNatDef.N.to_nat',axiom,
    c_24__type__80245___24t(cCoq_2eNArith_2eBinNatDef_2eN_2eto__nat) ).

fof('$_typeof_Coq.NArith.BinNatDef.N.zero',axiom,
    cCoq_2eNumbers_2eBinNums_2eN___24t(cCoq_2eNArith_2eBinNatDef_2eN_2ezero) ).

fof('$_typeof_Coq.NArith.Ndec.Ndouble_or_double_plus_un',axiom,
    c_24__type__77980___24t(cCoq_2eNArith_2eNdec_2eNdouble__or__double__plus__un) ).

fof('$_typeof_Coq.NArith.Ndigits.Nless',axiom,
    c_24__type__1446___24t(cCoq_2eNArith_2eNdigits_2eNless) ).

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__1132___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__68107___24t(cCoq_2eNumbers_2eBinNums_2eZneg) ).

fof('$_typeof_Coq.Numbers.BinNums.Zpos',axiom,
    c_24__type__68107___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__1119___24t(cCoq_2eNumbers_2eBinNums_2exI) ).

fof('$_typeof_Coq.Numbers.BinNums.xO',axiom,
    c_24__type__1119___24t(cCoq_2eNumbers_2eBinNums_2exO) ).

fof('$_typeof_Coq.PArith.BinPos.Pos.PeanoView',axiom,
    c_24__type__105667___24t(cCoq_2ePArith_2eBinPos_2ePos_2ePeanoView) ).

fof('$_typeof_Coq.PArith.BinPos.Pos.eq',axiom,
    c_24__type__82485___24t(cCoq_2ePArith_2eBinPos_2ePos_2eeq) ).

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__93087___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2eIsPos) ).

fof('$_typeof_Coq.PArith.BinPosDef.Pos.compare',axiom,
    c_24__type__93138___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare) ).

fof('$_typeof_Coq.PArith.BinPosDef.Pos.div2',axiom,
    c_24__type__1119___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2ediv2) ).

fof('$_typeof_Coq.PArith.BinPosDef.Pos.iter',axiom,
    c_24__type__93133___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2eiter) ).

fof('$_typeof_Coq.PArith.BinPosDef.Pos.iter_op',axiom,
    c_24__type__80300___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.t',axiom,
    cType___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2et) ).

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__97194___24t(cCoq_2eQArith_2eQArith__base_2eQden) ).

fof('$_typeof_Coq.QArith.QArith_base.Qmake',axiom,
    c_24__type__97184___24t(cCoq_2eQArith_2eQArith__base_2eQmake) ).

fof('$_typeof_Coq.QArith.QArith_base.Qnum',axiom,
    c_24__type__97189___24t(cCoq_2eQArith_2eQArith__base_2eQnum) ).

fof('$_typeof_Coq.Reals.RIneq.negreal',axiom,
    cType___24t(cCoq_2eReals_2eRIneq_2enegreal) ).

fof('$_typeof_Coq.Reals.RIneq.nonnegreal',axiom,
    cType___24t(cCoq_2eReals_2eRIneq_2enonnegreal) ).

fof('$_typeof_Coq.Reals.RIneq.nonposreal',axiom,
    cType___24t(cCoq_2eReals_2eRIneq_2enonposreal) ).

fof('$_typeof_Coq.Reals.RIneq.nonzeroreal',axiom,
    cType___24t(cCoq_2eReals_2eRIneq_2enonzeroreal) ).

fof('$_typeof_Coq.Reals.RIneq.posreal',axiom,
    cType___24t(cCoq_2eReals_2eRIneq_2eposreal) ).

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.R1',axiom,
    cCoq_2eReals_2eRdefinitions_2eR___24t(cCoq_2eReals_2eRdefinitions_2eR1) ).

fof('$_typeof_Coq.Reals.Rdefinitions.Rgt',axiom,
    c_24__type__78034___24t(cCoq_2eReals_2eRdefinitions_2eRgt) ).

fof('$_typeof_Coq.Reals.Rdefinitions.Rinv',axiom,
    c_24__type__78019___24t(cCoq_2eReals_2eRdefinitions_2eRinv) ).

fof('$_typeof_Coq.Reals.Rdefinitions.Rle',axiom,
    c_24__type__78034___24t(cCoq_2eReals_2eRdefinitions_2eRle) ).

fof('$_typeof_Coq.Reals.Rdefinitions.Rlt',axiom,
    c_24__type__78034___24t(cCoq_2eReals_2eRdefinitions_2eRlt) ).

fof('$_typeof_Coq.Reals.Rdefinitions.Rmult',axiom,
    c_24__type__78031___24t(cCoq_2eReals_2eRdefinitions_2eRmult) ).

fof('$_typeof_Coq.Reals.Rdefinitions.Ropp',axiom,
    c_24__type__78019___24t(cCoq_2eReals_2eRdefinitions_2eRopp) ).

fof('$_typeof_Coq.Reals.Rdefinitions.Rplus',axiom,
    c_24__type__78031___24t(cCoq_2eReals_2eRdefinitions_2eRplus) ).

fof('$_typeof_Coq.Reals.Rdefinitions.up',axiom,
    c_24__type__97378___24t(cCoq_2eReals_2eRdefinitions_2eup) ).

fof('$_typeof_Coq.Reals.Rfunctions.Z_spec',axiom,
    c_24__type__98168___24t(cCoq_2eReals_2eRfunctions_2eZ__spec) ).

fof('$_typeof_Coq.Relations.Relation_Definitions.relation',axiom,
    c_24__type__257___24t(cCoq_2eRelations_2eRelation__Definitions_2erelation) ).

fof('$_typeof_Coq.Setoids.Setoid.Setoid_Theory',axiom,
    c_24__type__89872___24t(cCoq_2eSetoids_2eSetoid_2eSetoid__Theory) ).

fof('$_typeof_Coq.Sets.Relations_1.Relation',axiom,
    c_24__type__257___24t(cCoq_2eSets_2eRelations__1_2eRelation) ).

fof('$_typeof_Coq.Strings.Ascii.Ascii',axiom,
    c_24__type__67955___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.GenericMinMax.gmax',axiom,
    c_24__type__96724___24t(cCoq_2eStructures_2eGenericMinMax_2egmax) ).

fof('$_typeof_Coq.Structures.GenericMinMax.gmin',axiom,
    c_24__type__96724___24t(cCoq_2eStructures_2eGenericMinMax_2egmin) ).

fof('$_typeof_Coq.Structures.OrderedType.Compare',axiom,
    c_24__type__97092___24t(cCoq_2eStructures_2eOrderedType_2eCompare) ).

fof('$_typeof_Coq.Structures.OrderedTypeEx.N_as_OT.eq',axiom,
    c_24__type__80251___24t(cCoq_2eStructures_2eOrderedTypeEx_2eN__as__OT_2eeq) ).

fof('$_typeof_Coq.Structures.OrderedTypeEx.N_as_OT.lt',axiom,
    c_24__type__80251___24t(cCoq_2eStructures_2eOrderedTypeEx_2eN__as__OT_2elt) ).

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.eq',axiom,
    c_24__type__67486___24t(cCoq_2eStructures_2eOrderedTypeEx_2eNat__as__OT_2eeq) ).

fof('$_typeof_Coq.Structures.OrderedTypeEx.Nat_as_OT.lt',axiom,
    c_24__type__67486___24t(cCoq_2eStructures_2eOrderedTypeEx_2eNat__as__OT_2elt) ).

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.bits_lt',axiom,
    c_24__type__82485___24t(cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2ebits__lt) ).

fof('$_typeof_Coq.Structures.OrderedTypeEx.PositiveOrderedTypeBits.eq',axiom,
    c_24__type__82485___24t(cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2eeq) ).

fof('$_typeof_Coq.Structures.OrderedTypeEx.PositiveOrderedTypeBits.lt',axiom,
    c_24__type__82485___24t(cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2elt) ).

fof('$_typeof_Coq.Structures.OrderedTypeEx.PositiveOrderedTypeBits.t',axiom,
    cType___24t(cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2et) ).

fof('$_typeof_Coq.Structures.OrderedTypeEx.Positive_as_OT.eq',axiom,
    c_24__type__82485___24t(cCoq_2eStructures_2eOrderedTypeEx_2ePositive__as__OT_2eeq) ).

fof('$_typeof_Coq.Structures.OrderedTypeEx.Positive_as_OT.lt',axiom,
    c_24__type__82485___24t(cCoq_2eStructures_2eOrderedTypeEx_2ePositive__as__OT_2elt) ).

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.eq',axiom,
    c_24__type__80463___24t(cCoq_2eStructures_2eOrderedTypeEx_2eZ__as__OT_2eeq) ).

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.OLE',axiom,
    cCoq_2eStructures_2eOrdersTac_2eord___24t(cCoq_2eStructures_2eOrdersTac_2eOLE) ).

fof('$_typeof_Coq.Structures.OrdersTac.OLT',axiom,
    cCoq_2eStructures_2eOrdersTac_2eord___24t(cCoq_2eStructures_2eOrdersTac_2eOLT) ).

fof('$_typeof_Coq.Structures.OrdersTac.ord',axiom,
    cType___24t(cCoq_2eStructures_2eOrdersTac_2eord) ).

fof('$_typeof_Coq.Vectors.Fin.t',axiom,
    c_24__type__68135___24t(cCoq_2eVectors_2eFin_2et) ).

fof('$_typeof_Coq.Vectors.VectorDef.t',axiom,
    c_24__type__79265___24t(cCoq_2eVectors_2eVectorDef_2et) ).

fof('$_typeof_Coq.ZArith.BinInt.Z.Private_Div.Quot2Div.div',axiom,
    c_24__type__80320___24t(cCoq_2eZArith_2eBinInt_2eZ_2ePrivate__Div_2eQuot2Div_2ediv) ).

fof('$_typeof_Coq.ZArith.BinInt.Z.Private_Div.Quot2Div.modulo',axiom,
    c_24__type__80320___24t(cCoq_2eZArith_2eBinInt_2eZ_2ePrivate__Div_2eQuot2Div_2emodulo) ).

fof('$_typeof_Coq.ZArith.BinInt.Z.divide',axiom,
    c_24__type__80463___24t(cCoq_2eZArith_2eBinInt_2eZ_2edivide) ).

fof('$_typeof_Coq.ZArith.BinInt.Z.eq',axiom,
    c_24__type__80463___24t(cCoq_2eZArith_2eBinInt_2eZ_2eeq) ).

fof('$_typeof_Coq.ZArith.BinInt.Z.le',axiom,
    c_24__type__80463___24t(cCoq_2eZArith_2eBinInt_2eZ_2ele) ).

fof('$_typeof_Coq.ZArith.BinInt.Z.lt',axiom,
    c_24__type__80463___24t(cCoq_2eZArith_2eBinInt_2eZ_2elt) ).

fof('$_typeof_Coq.ZArith.BinInt.Zne',axiom,
    c_24__type__80463___24t(cCoq_2eZArith_2eBinInt_2eZne) ).

fof('$_typeof_Coq.ZArith.BinIntDef.Z.abs',axiom,
    c_24__type__80324___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2eabs) ).

fof('$_typeof_Coq.ZArith.BinIntDef.Z.add',axiom,
    c_24__type__80320___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2eadd) ).

fof('$_typeof_Coq.ZArith.BinIntDef.Z.div',axiom,
    c_24__type__80320___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2ediv) ).

fof('$_typeof_Coq.ZArith.BinIntDef.Z.even',axiom,
    c_24__type__93686___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2eeven) ).

fof('$_typeof_Coq.ZArith.BinIntDef.Z.max',axiom,
    c_24__type__80320___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2emax) ).

fof('$_typeof_Coq.ZArith.BinIntDef.Z.min',axiom,
    c_24__type__80320___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2emin) ).

fof('$_typeof_Coq.ZArith.BinIntDef.Z.modulo',axiom,
    c_24__type__80320___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2emodulo) ).

fof('$_typeof_Coq.ZArith.BinIntDef.Z.mul',axiom,
    c_24__type__80320___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2emul) ).

fof('$_typeof_Coq.ZArith.BinIntDef.Z.odd',axiom,
    c_24__type__93686___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2eodd) ).

fof('$_typeof_Coq.ZArith.BinIntDef.Z.of_N',axiom,
    c_24__type__105712___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2eof__N) ).

fof('$_typeof_Coq.ZArith.BinIntDef.Z.opp',axiom,
    c_24__type__80324___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2eopp) ).

fof('$_typeof_Coq.ZArith.BinIntDef.Z.sub',axiom,
    c_24__type__80320___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2esub) ).

fof('$_typeof_Coq.ZArith.BinIntDef.Z.succ',axiom,
    c_24__type__80324___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2esucc) ).

fof('$_typeof_Coq.ZArith.BinIntDef.Z.t',axiom,
    cType___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2et) ).

fof('$_typeof_Coq.ZArith.BinIntDef.Z.to_pos',axiom,
    c_24__type__105716___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2eto__pos) ).

fof('$_typeof_Coq.ZArith.BinIntDef.Z.zero',axiom,
    cCoq_2eNumbers_2eBinNums_2eZ___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2ezero) ).

fof('$_typeof_Coq.ZArith.Zbool.Zeq_bool',axiom,
    c_24__type__80212___24t(cCoq_2eZArith_2eZbool_2eZeq__bool) ).

fof('$_typeof_Coq.ZArith.Zeven.Zeven',axiom,
    c_24__type__80571___24t(cCoq_2eZArith_2eZeven_2eZeven) ).

fof('$_typeof_Coq.ZArith.Zeven.Zodd',axiom,
    c_24__type__80571___24t(cCoq_2eZArith_2eZeven_2eZodd) ).

fof('$_typeof_Coq.ZArith.Zlogarithm.Is_power',axiom,
    c_24__type__1121___24t(cCoq_2eZArith_2eZlogarithm_2eIs__power) ).

fof('$_typeof_Coq.ZArith.Znumtheory.Euclid',axiom,
    c_24__type__98168___24t(cCoq_2eZArith_2eZnumtheory_2eEuclid) ).

fof('$_typeof_Coq.ZArith.Zpower.Zdiv_rest_proofs',axiom,
    c_24__type__105468___24t(cCoq_2eZArith_2eZpower_2eZdiv__rest__proofs) ).

fof('$_typeof_Coq.micromega.Env.Env',axiom,
    c_24__type__257___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__257___24t(cCoq_2emicromega_2eEnvRing_2ePExpr) ).

fof('$_typeof_Coq.micromega.EnvRing.Pc',axiom,
    c_24__type__83571___24t(cCoq_2emicromega_2eEnvRing_2ePc) ).

fof('$_typeof_Coq.micromega.EnvRing.Pol',axiom,
    c_24__type__257___24t(cCoq_2emicromega_2eEnvRing_2ePol) ).

fof('$_typeof_Coq.micromega.EnvRing.mon0',axiom,
    cCoq_2emicromega_2eEnvRing_2eMon___24t(cCoq_2emicromega_2eEnvRing_2emon0) ).

fof('$_typeof_Coq.micromega.RMicromega.C0',axiom,
    cCoq_2emicromega_2eRMicromega_2eRcst___24t(cCoq_2emicromega_2eRMicromega_2eC0) ).

fof('$_typeof_Coq.micromega.RMicromega.C1',axiom,
    cCoq_2emicromega_2eRMicromega_2eRcst___24t(cCoq_2emicromega_2eRMicromega_2eC1) ).

fof('$_typeof_Coq.micromega.RMicromega.CZ',axiom,
    c_24__type__97376___24t(cCoq_2emicromega_2eRMicromega_2eCZ) ).

fof('$_typeof_Coq.micromega.RMicromega.Rcst',axiom,
    cType___24t(cCoq_2emicromega_2eRMicromega_2eRcst) ).

fof('$_typeof_Coq.micromega.Refl.make_conj',axiom,
    c_24__type__97427___24t(cCoq_2emicromega_2eRefl_2emake__conj) ).

fof('$_typeof_Coq.micromega.Refl.make_impl',axiom,
    c_24__type__97401___24t(cCoq_2emicromega_2eRefl_2emake__impl) ).

fof('$_typeof_Coq.micromega.RingMicromega.Equal',axiom,
    cCoq_2emicromega_2eRingMicromega_2eOp1___24t(cCoq_2emicromega_2eRingMicromega_2eEqual) ).

fof('$_typeof_Coq.micromega.RingMicromega.Formula',axiom,
    c_24__type__257___24t(cCoq_2emicromega_2eRingMicromega_2eFormula) ).

fof('$_typeof_Coq.micromega.RingMicromega.NonEqual',axiom,
    cCoq_2emicromega_2eRingMicromega_2eOp1___24t(cCoq_2emicromega_2eRingMicromega_2eNonEqual) ).

fof('$_typeof_Coq.micromega.RingMicromega.NonStrict',axiom,
    cCoq_2emicromega_2eRingMicromega_2eOp1___24t(cCoq_2emicromega_2eRingMicromega_2eNonStrict) ).

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.OpEq',axiom,
    cCoq_2emicromega_2eRingMicromega_2eOp2___24t(cCoq_2emicromega_2eRingMicromega_2eOpEq) ).

fof('$_typeof_Coq.micromega.RingMicromega.OpGe',axiom,
    cCoq_2emicromega_2eRingMicromega_2eOp2___24t(cCoq_2emicromega_2eRingMicromega_2eOpGe) ).

fof('$_typeof_Coq.micromega.RingMicromega.OpGt',axiom,
    cCoq_2emicromega_2eRingMicromega_2eOp2___24t(cCoq_2emicromega_2eRingMicromega_2eOpGt) ).

fof('$_typeof_Coq.micromega.RingMicromega.OpLe',axiom,
    cCoq_2emicromega_2eRingMicromega_2eOp2___24t(cCoq_2emicromega_2eRingMicromega_2eOpLe) ).

fof('$_typeof_Coq.micromega.RingMicromega.OpLt',axiom,
    cCoq_2emicromega_2eRingMicromega_2eOp2___24t(cCoq_2emicromega_2eRingMicromega_2eOpLt) ).

fof('$_typeof_Coq.micromega.RingMicromega.OpNEq',axiom,
    cCoq_2emicromega_2eRingMicromega_2eOp2___24t(cCoq_2emicromega_2eRingMicromega_2eOpNEq) ).

fof('$_typeof_Coq.micromega.RingMicromega.PolC',axiom,
    c_24__type__257___24t(cCoq_2emicromega_2eRingMicromega_2ePolC) ).

fof('$_typeof_Coq.micromega.RingMicromega.PolEnv',axiom,
    c_24__type__257___24t(cCoq_2emicromega_2eRingMicromega_2ePolEnv) ).

fof('$_typeof_Coq.micromega.RingMicromega.Psatz',axiom,
    c_24__type__257___24t(cCoq_2emicromega_2eRingMicromega_2ePsatz) ).

fof('$_typeof_Coq.micromega.RingMicromega.Strict',axiom,
    cCoq_2emicromega_2eRingMicromega_2eOp1___24t(cCoq_2emicromega_2eRingMicromega_2eStrict) ).

fof('$_typeof_Coq.micromega.Tauto.GFormula',axiom,
    c_24__type__91060___24t(cCoq_2emicromega_2eTauto_2eGFormula) ).

fof('$_typeof_Coq.micromega.VarMap.t',axiom,
    c_24__type__257___24t(cCoq_2emicromega_2eVarMap_2et) ).

fof('$_typeof_Coq.micromega.ZMicromega.DoneProof',axiom,
    cCoq_2emicromega_2eZMicromega_2eZArithProof___24t(cCoq_2emicromega_2eZMicromega_2eDoneProof) ).

fof('$_typeof_Coq.micromega.ZMicromega.ZArithProof',axiom,
    cType___24t(cCoq_2emicromega_2eZMicromega_2eZArithProof) ).

fof('$_typeof_Coq.micromega.ZMicromega.coneMember',axiom,
    cType___24t(cCoq_2emicromega_2eZMicromega_2econeMember) ).

fof('$_typeof_Coq.omega.PreOmega.Z_of_nat\'',axiom,
    c_24__type__82626___24t(cCoq_2eomega_2ePreOmega_2eZ__of__nat_27) ).

fof('$_typeof_Coq.omega.PreOmega.Zpos\'',axiom,
    c_24__type__68107___24t(cCoq_2eomega_2ePreOmega_2eZpos_27) ).

fof('$_typeof_Coq.setoid_ring.Field_theory.FExpr',axiom,
    c_24__type__257___24t(cCoq_2esetoid__ring_2eField__theory_2eFExpr) ).

fof('$_typeof_Coq.setoid_ring.Field_theory.linear',axiom,
    c_24__type__257___24t(cCoq_2esetoid__ring_2eField__theory_2elinear) ).

fof('$_typeof_Coq.setoid_ring.Field_theory.rsplit',axiom,
    c_24__type__257___24t(cCoq_2esetoid__ring_2eField__theory_2ersplit) ).

fof('$_typeof_Coq.setoid_ring.InitialRing.NotConstant',axiom,
    cCoq_2eInit_2eDatatypes_2ebool___24t(cCoq_2esetoid__ring_2eInitialRing_2eNotConstant) ).

fof('$_typeof_Coq.setoid_ring.InitialRing.gen_phiPOS',axiom,
    c_24__type__96766___24t(cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS) ).

fof('$_typeof_Coq.setoid_ring.InitialRing.gen_phiPOS1',axiom,
    c_24__type__96766___24t(cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS1) ).

fof('$_typeof_Coq.setoid_ring.InitialRing.hypo',axiom,
    cType___24t(cCoq_2esetoid__ring_2eInitialRing_2ehypo) ).

fof('$_typeof_Coq.setoid_ring.Ring_polynom.Mon',axiom,
    cType___24t(cCoq_2esetoid__ring_2eRing__polynom_2eMon) ).

fof('$_typeof_Coq.setoid_ring.Ring_polynom.PEI',axiom,
    c_24__type__103646___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePEI) ).

fof('$_typeof_Coq.setoid_ring.Ring_polynom.PEO',axiom,
    c_24__type__103646___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePEO) ).

fof('$_typeof_Coq.setoid_ring.Ring_polynom.PEX',axiom,
    c_24__type__78474___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePEX) ).

fof('$_typeof_Coq.setoid_ring.Ring_polynom.PEadd',axiom,
    c_24__type__78479___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePEadd) ).

fof('$_typeof_Coq.setoid_ring.Ring_polynom.PEc',axiom,
    c_24__type__78471___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePEc) ).

fof('$_typeof_Coq.setoid_ring.Ring_polynom.PEmul',axiom,
    c_24__type__78479___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePEmul) ).

fof('$_typeof_Coq.setoid_ring.Ring_polynom.PEopp',axiom,
    c_24__type__86185___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePEopp) ).

fof('$_typeof_Coq.setoid_ring.Ring_polynom.PEsub',axiom,
    c_24__type__78479___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePEsub) ).

fof('$_typeof_Coq.setoid_ring.Ring_polynom.PExpr',axiom,
    c_24__type__257___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr) ).

fof('$_typeof_Coq.setoid_ring.Ring_polynom.Pc',axiom,
    c_24__type__103644___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePc) ).

fof('$_typeof_Coq.setoid_ring.Ring_polynom.Pol',axiom,
    c_24__type__257___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePol) ).

fof('$_typeof_Coq.setoid_ring.Ring_polynom.mkmult_pow',axiom,
    c_24__type__103664___24t(cCoq_2esetoid__ring_2eRing__polynom_2emkmult__pow) ).

fof('$_typeof_Coq.setoid_ring.Ring_polynom.mon0',axiom,
    cCoq_2esetoid__ring_2eRing__polynom_2eMon___24t(cCoq_2esetoid__ring_2eRing__polynom_2emon0) ).

fof('$_typeof_Coq.setoid_ring.Ring_theory.Abstract',axiom,
    cCoq_2esetoid__ring_2eRing__theory_2ering__kind___24t(cCoq_2esetoid__ring_2eRing__theory_2eAbstract) ).

fof('$_typeof_Coq.setoid_ring.Ring_theory.IDphi',axiom,
    c_24__type__82174___24t(cCoq_2esetoid__ring_2eRing__theory_2eIDphi) ).

fof('$_typeof_Coq.setoid_ring.Ring_theory.SRopp',axiom,
    c_24__type__82174___24t(cCoq_2esetoid__ring_2eRing__theory_2eSRopp) ).

fof('$_typeof_Coq.setoid_ring.Ring_theory.id_phi_N',axiom,
    c_24__type__1106___24t(cCoq_2esetoid__ring_2eRing__theory_2eid__phi__N) ).

fof('$_typeof_Coq.setoid_ring.Ring_theory.pow_N',axiom,
    c_24__type__80837___24t(cCoq_2esetoid__ring_2eRing__theory_2epow__N) ).

fof('$_typeof_Coq.setoid_ring.Ring_theory.pow_pos',axiom,
    c_24__type__86203___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_Hammer.Tactics.Reconstr.ReconstrT',axiom,
    cType___24t(cHammer_2eTactics_2eReconstr_2eReconstrT) ).

fof('$_typeof_Hammer.Tactics.Reconstr.rdone',axiom,
    c_24__type__97383___24t(cHammer_2eTactics_2eReconstr_2erdone) ).

fof('$_typeof_Hammer.Tactics.Tactics.rdone',axiom,
    c_24__type__97383___24t(cHammer_2eTactics_2eTactics_2erdone) ).

fof('$_typeof_IntMap.Fset.FSet',axiom,
    cType___24t(cIntMap_2eFset_2eFSet) ).

fof('$_typeof_IntMap.Fset.FSetInter',axiom,
    c_24__type__105724___24t(cIntMap_2eFset_2eFSetInter) ).

fof('$_typeof_IntMap.Fset.MapDom',axiom,
    c_24__type__1152___24t(cIntMap_2eFset_2eMapDom) ).

fof('$_typeof_IntMap.Fset.MapDomRestrBy',axiom,
    c_24__type__141___24t(cIntMap_2eFset_2eMapDomRestrBy) ).

fof('$_typeof_IntMap.Fset.MapDomRestrTo',axiom,
    c_24__type__141___24t(cIntMap_2eFset_2eMapDomRestrTo) ).

fof('$_typeof_IntMap.Fset.MapDom_semantics_2',axiom,
    c_24__type__76191___24t(cIntMap_2eFset_2eMapDom__semantics__2) ).

fof('$_typeof_IntMap.Fset.in_FSet',axiom,
    c_24__type__76179___24t(cIntMap_2eFset_2ein__FSet) ).

fof('$_typeof_IntMap.Fset.in_dom',axiom,
    c_24__type__67059___24t(cIntMap_2eFset_2ein__dom) ).

fof('$_typeof_IntMap.Fset.in_dom_some',axiom,
    c_24__type__67071___24t(cIntMap_2eFset_2ein__dom__some) ).

fof('$_typeof_IntMap.Lsort.ad_monotonic',axiom,
    c_24__type__76492___24t(cIntMap_2eLsort_2ead__monotonic) ).

fof('$_typeof_IntMap.Lsort.alist_nth_ad',axiom,
    c_24__type__76397___24t(cIntMap_2eLsort_2ealist__nth__ad) ).

fof('$_typeof_IntMap.Lsort.alist_sorted',axiom,
    c_24__type__76363___24t(cIntMap_2eLsort_2ealist__sorted) ).

fof('$_typeof_IntMap.Map.M0',axiom,
    c_24__type__287___24t(cIntMap_2eMap_2eM0) ).

fof('$_typeof_IntMap.Map.M1',axiom,
    c_24__type__292___24t(cIntMap_2eMap_2eM1) ).

fof('$_typeof_IntMap.Map.M2',axiom,
    c_24__type__297___24t(cIntMap_2eMap_2eM2) ).

fof('$_typeof_IntMap.Map.Map',axiom,
    c_24__type__257___24t(cIntMap_2eMap_2eMap) ).

fof('$_typeof_IntMap.Map.MapCard',axiom,
    c_24__type__513___24t(cIntMap_2eMap_2eMapCard) ).

fof('$_typeof_IntMap.Map.MapDelta',axiom,
    c_24__type__297___24t(cIntMap_2eMap_2eMapDelta) ).

fof('$_typeof_IntMap.Map.MapEmptyp',axiom,
    c_24__type__76785___24t(cIntMap_2eMap_2eMapEmptyp) ).

fof('$_typeof_IntMap.Map.MapGet',axiom,
    c_24__type__778___24t(cIntMap_2eMap_2eMapGet) ).

fof('$_typeof_IntMap.Map.MapMerge',axiom,
    c_24__type__297___24t(cIntMap_2eMap_2eMapMerge) ).

fof('$_typeof_IntMap.Map.MapPut',axiom,
    c_24__type__499___24t(cIntMap_2eMap_2eMapPut) ).

fof('$_typeof_IntMap.Map.MapPut1',axiom,
    c_24__type__1226___24t(cIntMap_2eMap_2eMapPut1) ).

fof('$_typeof_IntMap.Map.MapPut_behind',axiom,
    c_24__type__499___24t(cIntMap_2eMap_2eMapPut__behind) ).

fof('$_typeof_IntMap.Map.MapRemove',axiom,
    c_24__type__884___24t(cIntMap_2eMap_2eMapRemove) ).

fof('$_typeof_IntMap.Map.MapSingleton',axiom,
    c_24__type__292___24t(cIntMap_2eMap_2eMapSingleton) ).

fof('$_typeof_IntMap.Map.Map_rec',axiom,
    c_24__type__360___24t(cIntMap_2eMap_2eMap__rec) ).

fof('$_typeof_IntMap.Map.Map_rect',axiom,
    c_24__type__360___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__786___24t(cIntMap_2eMap_2eeqm) ).

fof('$_typeof_IntMap.Map.makeM2',axiom,
    c_24__type__297___24t(cIntMap_2eMap_2emakeM2) ).

fof('$_typeof_IntMap.Map.newMap',axiom,
    c_24__type__287___24t(cIntMap_2eMap_2enewMap) ).

fof('$_typeof_IntMap.Map.option_sum',axiom,
    c_24__type__699___24t(cIntMap_2eMap_2eoption__sum) ).

fof('$_typeof_IntMap.Mapaxioms.eqmap',axiom,
    c_24__type__1364___24t(cIntMap_2eMapaxioms_2eeqmap) ).

fof('$_typeof_IntMap.Mapcard.MapCard_Put_1',axiom,
    c_24__type__67165___24t(cIntMap_2eMapcard_2eMapCard__Put__1) ).

fof('$_typeof_IntMap.Mapcard.MapCard_Put_behind_sum',axiom,
    c_24__type__67215___24t(cIntMap_2eMapcard_2eMapCard__Put__behind__sum) ).

fof('$_typeof_IntMap.Mapcard.MapCard_Put_sum',axiom,
    c_24__type__560___24t(cIntMap_2eMapcard_2eMapCard__Put__sum) ).

fof('$_typeof_IntMap.Mapcard.MapCard_Remove_sum',axiom,
    c_24__type__1018___24t(cIntMap_2eMapcard_2eMapCard__Remove__sum) ).

fof('$_typeof_IntMap.Mapcard.MapCard_is_Sn',axiom,
    c_24__type__67244___24t(cIntMap_2eMapcard_2eMapCard__is__Sn) ).

fof('$_typeof_IntMap.Mapcard.MapCard_is_not_O',axiom,
    c_24__type__977___24t(cIntMap_2eMapcard_2eMapCard__is__not__O) ).

fof('$_typeof_IntMap.Mapiter.MapCollect',axiom,
    c_24__type__77162___24t(cIntMap_2eMapiter_2eMapCollect) ).

fof('$_typeof_IntMap.Mapiter.MapCollect1',axiom,
    c_24__type__77138___24t(cIntMap_2eMapiter_2eMapCollect1) ).

fof('$_typeof_IntMap.Mapiter.MapFold',axiom,
    c_24__type__1410___24t(cIntMap_2eMapiter_2eMapFold) ).

fof('$_typeof_IntMap.Mapiter.MapFold1',axiom,
    c_24__type__67318___24t(cIntMap_2eMapiter_2eMapFold1) ).

fof('$_typeof_IntMap.Mapiter.MapFold1_state',axiom,
    c_24__type__77352___24t(cIntMap_2eMapiter_2eMapFold1__state) ).

fof('$_typeof_IntMap.Mapiter.MapFold_state',axiom,
    c_24__type__77429___24t(cIntMap_2eMapiter_2eMapFold__state) ).

fof('$_typeof_IntMap.Mapiter.MapSweep',axiom,
    c_24__type__76876___24t(cIntMap_2eMapiter_2eMapSweep) ).

fof('$_typeof_IntMap.Mapiter.MapSweep1',axiom,
    c_24__type__76862___24t(cIntMap_2eMapiter_2eMapSweep1) ).

fof('$_typeof_IntMap.Mapiter.MapSweep2',axiom,
    c_24__type__76807___24t(cIntMap_2eMapiter_2eMapSweep2) ).

fof('$_typeof_IntMap.Mapiter.Map_of_alist',axiom,
    c_24__type__67406___24t(cIntMap_2eMapiter_2eMap__of__alist) ).

fof('$_typeof_IntMap.Mapiter.aapp',axiom,
    c_24__type__77516___24t(cIntMap_2eMapiter_2eaapp) ).

fof('$_typeof_IntMap.Mapiter.acons',axiom,
    c_24__type__77511___24t(cIntMap_2eMapiter_2eacons) ).

fof('$_typeof_IntMap.Mapiter.ad_inj',axiom,
    c_24__type__76492___24t(cIntMap_2eMapiter_2ead__inj) ).

fof('$_typeof_IntMap.Mapiter.alist',axiom,
    c_24__type__257___24t(cIntMap_2eMapiter_2ealist) ).

fof('$_typeof_IntMap.Mapiter.alist_of_Map',axiom,
    c_24__type__67337___24t(cIntMap_2eMapiter_2ealist__of__Map) ).

fof('$_typeof_IntMap.Mapiter.alist_semantics',axiom,
    c_24__type__67383___24t(cIntMap_2eMapiter_2ealist__semantics) ).

fof('$_typeof_IntMap.Mapiter.anil',axiom,
    c_24__type__77506___24t(cIntMap_2eMapiter_2eanil) ).

fof('$_typeof_IntMap.Mapsubset.MapDisjoint',axiom,
    c_24__type__1028___24t(cIntMap_2eMapsubset_2eMapDisjoint) ).

fof('$_typeof_IntMap.Mapsubset.MapDisjoint_1',axiom,
    c_24__type__77826___24t(cIntMap_2eMapsubset_2eMapDisjoint__1) ).

fof('$_typeof_IntMap.Mapsubset.MapDisjoint_2',axiom,
    c_24__type__1028___24t(cIntMap_2eMapsubset_2eMapDisjoint__2) ).

fof('$_typeof_IntMap.Mapsubset.MapSubset',axiom,
    c_24__type__1028___24t(cIntMap_2eMapsubset_2eMapSubset) ).

fof('$_typeof_IntMap.Mapsubset.MapSubset_1',axiom,
    c_24__type__77826___24t(cIntMap_2eMapsubset_2eMapSubset__1) ).

fof('$_typeof_IntMap.Mapsubset.MapSubset_2',axiom,
    c_24__type__1028___24t(cIntMap_2eMapsubset_2eMapSubset__2) ).

fof('$_typeof_Mapcanon.MapCanon.MapCanonicalize',axiom,
    c_24__type__122083___24t(cMapcanon_2eMapCanon_2eMapCanonicalize) ).

fof('$_typeof_Mapcanon.MapCanon.mapcanon_exists',axiom,
    c_24__type__122086___24t(cMapcanon_2eMapCanon_2emapcanon__exists) ).

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.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_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_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_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.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_equiv',axiom,
    cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(cCoq_2eInit_2eDatatypes_2enat,c_3d___24a1(cCoq_2eInit_2eDatatypes_2enat)) ).

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_ge_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_2ele___24a2(V1__m,V0__n) ) ) ) ).

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_refl',axiom,
    ! [V0__n] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
     => cCoq_2eInit_2ePeano_2ele___24a2(V0__n,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_le_incl',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)
           => cCoq_2eInit_2ePeano_2ele___24a2(V0__n,V1__m) ) ) ) ).

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.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.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_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.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.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__75476___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.idProp',axiom,
    p(cCoq_2eInit_2eDatatypes_2eIDProp) ).

fof('Coq.Init.Datatypes.nat_ind',axiom,
    ! [V0__P] :
      ( c_24__type__67891___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__75614___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.sum_ind',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__B] :
          ( cType___24t(V1__B)
         => ! [V2__P] :
              ( c_24__type__75551___24t(V0__A,V1__B,V2__P)
             => ( ! [V3__a] :
                    ( t(V3__a,V0__A)
                   => p(happ(V2__P,cCoq_2eInit_2eDatatypes_2einl___24a3(V0__A,V1__B,V3__a))) )
               => ( ! [V4__b] :
                      ( t(V4__b,V1__B)
                     => p(happ(V2__P,cCoq_2eInit_2eDatatypes_2einr___24a3(V0__A,V1__B,V4__b))) )
                 => ! [V5__s] :
                      ( cCoq_2eInit_2eDatatypes_2esum___24t(V0__A,V1__B,V5__s)
                     => p(happ(V2__P,V5__s)) ) ) ) ) ) ) ).

fof('Coq.Init.Datatypes.unit_ind',axiom,
    ! [V0__P] :
      ( c_24__type__75474___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.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__1051___24t(V0__A,V1__P)
         => ! [V2__P] :
              ( c_24__type__1065___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__608___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__1101___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.Decidable.not_and_iff',axiom,
    ! [V0__A] :
      ( cProp___24t(V0__A)
     => ! [V1__B] :
          ( cProp___24t(V1__B)
         => ( ( ( p(V0__A)
                & p(V1__B) )
             => p(c_24False) )
          <=> ( p(V0__A)
             => ( p(V1__B)
               => p(c_24False) ) ) ) ) ) ).

fof('Coq.Logic.Decidable.not_or_iff',axiom,
    ! [V0__A] :
      ( cProp___24t(V0__A)
     => ! [V1__B] :
          ( cProp___24t(V1__B)
         => ( ( ( p(V0__A)
                | p(V1__B) )
             => p(c_24False) )
          <=> ( ( p(V0__A)
               => p(c_24False) )
              & ( p(V1__B)
               => p(c_24False) ) ) ) ) ) ).

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_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_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_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.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_equiv',axiom,
    cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(cCoq_2eNumbers_2eBinNums_2eN,c_3d___24a1(cCoq_2eNumbers_2eBinNums_2eN)) ).

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_ge_cases',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) ) ) ) ).

fof('Coq.NArith.BinNat.N.le_refl',axiom,
    ! [V0__n] :
      ( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
     => cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(V0__n,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.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_bit_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_2eeqb___24a2(V0__a,V1__a_27) = cCoq_2eInit_2eDatatypes_2efalse
           => ( cCoq_2eNArith_2eBinNatDef_2eN_2eodd___24a1(V0__a) = cCoq_2eNArith_2eBinNatDef_2eN_2eodd___24a1(V1__a_27)
             => 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_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.Neven_not_double_plus_one',axiom,
    ! [V0__a] :
      ( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__a)
     => ( cCoq_2eNArith_2eNdigits_2eNeven___24a1(V0__a)
       => ! [V2__a0] :
            ( cCoq_2eNumbers_2eBinNums_2eN___24t(V2__a0)
           => cCoq_2eNArith_2eBinNatDef_2eN_2eeqb___24a2(cCoq_2eNArith_2eBinNatDef_2eN_2esucc__double___24a1(V2__a0),V0__a) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ).

fof('Coq.NArith.Ndec.Nodd_not_double',axiom,
    ! [V0__a] :
      ( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__a)
     => ( cCoq_2eNArith_2eNdigits_2eNodd___24a1(V0__a)
       => ! [V2__a0] :
            ( cCoq_2eNumbers_2eBinNums_2eN___24t(V2__a0)
           => cCoq_2eNArith_2eBinNatDef_2eN_2eeqb___24a2(cCoq_2eNArith_2eBinNatDef_2eN_2edouble___24a1(V2__a0),V0__a) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ).

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__1134___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__1121___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.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_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.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_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_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.divide_refl',axiom,
    ! [V0__n] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
     => cCoq_2eZArith_2eBinInt_2eZ_2edivide___24a2(V0__n,V0__n) ) ).

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.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.le_trans',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_2eBinInt_2eZ_2ele___24a2(V0__n,V1__m)
               => ( cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V1__m,V2__p)
                 => cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__n,V2__p) ) ) ) ) ) ).

fof('Coq.ZArith.BinInt.Z.lt_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_2elt___24a2(V0__n,V1__m)
            | cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V1__m,V0__n) ) ) ) ).

fof('Coq.ZArith.BinInt.Z.lt_le_incl',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)
           => cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__n,V1__m) ) ) ) ).

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_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.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.ARmul_1_l',axiom,
    ! [V0__R] :
      ( cType___24t(V0__R)
     => ! [V1__rO] :
          ( t(V1__rO,V0__R)
         => ! [V2__rI] :
              ( t(V2__rI,V0__R)
             => ! [V3__radd] :
                  ( c_24__type__1415___24t(V0__R,V3__radd)
                 => ! [V4__rmul] :
                      ( c_24__type__1415___24t(V0__R,V4__rmul)
                     => ! [V5__rsub] :
                          ( c_24__type__1415___24t(V0__R,V5__rsub)
                         => ! [V6__ropp] :
                              ( c_24__type__78702___24t(V0__R,V6__ropp)
                             => ! [V7__req] :
                                  ( c_24__type__78044___24t(V0__R,V7__req)
                                 => ( cCoq_2esetoid__ring_2eRing__theory_2ealmost__ring__theory___24a8(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__req)
                                   => ! [V9__x] :
                                        ( t(V9__x,V0__R)
                                       => p(happ(happ(V7__req,happ(happ(V4__rmul,V2__rI),V9__x)),V9__x)) ) ) ) ) ) ) ) ) ) ) ).

fof('Coq.setoid_ring.Ring_theory.ARmul_assoc',axiom,
    ! [V0__R] :
      ( cType___24t(V0__R)
     => ! [V1__rO] :
          ( t(V1__rO,V0__R)
         => ! [V2__rI] :
              ( t(V2__rI,V0__R)
             => ! [V3__radd] :
                  ( c_24__type__1415___24t(V0__R,V3__radd)
                 => ! [V4__rmul] :
                      ( c_24__type__1415___24t(V0__R,V4__rmul)
                     => ! [V5__rsub] :
                          ( c_24__type__1415___24t(V0__R,V5__rsub)
                         => ! [V6__ropp] :
                              ( c_24__type__78702___24t(V0__R,V6__ropp)
                             => ! [V7__req] :
                                  ( c_24__type__78044___24t(V0__R,V7__req)
                                 => ( cCoq_2esetoid__ring_2eRing__theory_2ealmost__ring__theory___24a8(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__req)
                                   => ! [V9__x] :
                                        ( t(V9__x,V0__R)
                                       => ! [V10__y] :
                                            ( t(V10__y,V0__R)
                                           => ! [V11__z] :
                                                ( t(V11__z,V0__R)
                                               => p(happ(happ(V7__req,happ(happ(V4__rmul,V9__x),happ(happ(V4__rmul,V10__y),V11__z))),happ(happ(V4__rmul,happ(happ(V4__rmul,V9__x),V10__y)),V11__z))) ) ) ) ) ) ) ) ) ) ) ) ) ).

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__76173___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__76154___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_3',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_2eMapGet___24a3(V0__A,V1__m,V2__a) = cCoq_2eInit_2eDatatypes_2eNone___24a1(V0__A)
               => cIntMap_2eFset_2ein__FSet___24a2(V2__a,cIntMap_2eFset_2eMapDom___24a2(V0__A,V1__m)) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ).

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__76494___24t(V0__pf)
     => ( cIntMap_2eLsort_2ead__monotonic___24a1(V0__pf)
       => cIntMap_2eLsort_2ead__monotonic___24a1(c_24__lam__76497___24a1(V0__pf)) ) ) ).

fof('IntMap.Lsort.ad_comp_double_plus_un_monotonic',axiom,
    ! [V0__pf] :
      ( c_24__type__76494___24t(V0__pf)
     => ( cIntMap_2eLsort_2ead__monotonic___24a1(V0__pf)
       => cIntMap_2eLsort_2ead__monotonic___24a1(c_24__lam__76499___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_2_imp',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__l] :
          ( cIntMap_2eMapiter_2ealist___24t(V0__A,V1__l)
         => ( cIntMap_2eLsort_2ealist__sorted__2___24a2(V0__A,V1__l)
           => cIntMap_2eLsort_2ealist__sorted___24a2(V0__A,V1__l) = cCoq_2eInit_2eDatatypes_2etrue ) ) ) ).

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__1157___24a3(V0__A,V1__m,V2__m_27)) ) ) ) ).

fof('IntMap.Map.Map2_semantics_1_eq',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__f] :
                  ( c_24__type__789___24t(V0__A,V3__f)
                 => ( cIntMap_2eMap_2eeqm___24a3(V0__A,cIntMap_2eMap_2eMapGet___24a2(V0__A,cIntMap_2eMap_2eM2___24a3(V0__A,V1__m,V2__m_27)),V3__f)
                   => cIntMap_2eMap_2eeqm___24a3(V0__A,cIntMap_2eMap_2eMapGet___24a2(V0__A,V1__m),c_24__lam__1162___24a2(V0__A,V3__f)) ) ) ) ) ) ).

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__795___24a3(V0__A,V1__m,V2__m_27)) ) ) ) ).

fof('IntMap.Map.Map2_semantics_2_eq',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__f] :
                  ( c_24__type__789___24t(V0__A,V3__f)
                 => ( cIntMap_2eMap_2eeqm___24a3(V0__A,cIntMap_2eMap_2eMapGet___24a2(V0__A,cIntMap_2eMap_2eM2___24a3(V0__A,V1__m,V2__m_27)),V3__f)
                   => cIntMap_2eMap_2eeqm___24a3(V0__A,cIntMap_2eMap_2eMapGet___24a2(V0__A,V2__m_27),c_24__lam__800___24a2(V0__A,V3__f)) ) ) ) ) ) ).

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__1181___24a3(V0__A,V1__m,V2__m_27)) ) ) ) ).

fof('IntMap.Map.Map2_semantics_3_eq',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__f] :
                  ( c_24__type__789___24t(V0__A,V3__f)
                 => ! [V4__f_27] :
                      ( c_24__type__789___24t(V0__A,V4__f_27)
                     => ( cIntMap_2eMap_2eeqm___24a3(V0__A,cIntMap_2eMap_2eMapGet___24a2(V0__A,V1__m),V3__f)
                       => ( cIntMap_2eMap_2eeqm___24a3(V0__A,cIntMap_2eMap_2eMapGet___24a2(V0__A,V2__m_27),V4__f_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__1194___24a3(V0__A,V3__f,V4__f_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__76759___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_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__a] :
                  ( cIntMap_2eMap_2ead___24t(V3__a)
                 => ! [V4__y] :
                      ( t(V4__y,V0__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_2eSome___24a2(V0__A,V4__y)
                         => cIntMap_2eMap_2eMapGet___24a3(V0__A,cIntMap_2eMap_2eMapDelta___24a3(V0__A,V1__m,V2__m_27),V3__a) = cCoq_2eInit_2eDatatypes_2eSome___24a2(V0__A,V4__y) ) ) ) ) ) ) ) ).

fof('IntMap.Map.MapDelta_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)
             => ! [V3__a] :
                  ( cIntMap_2eMap_2ead___24t(V3__a)
                 => ! [V4__y] :
                      ( t(V4__y,V0__A)
                     => ! [V5__y_27] :
                          ( t(V5__y_27,V0__A)
                         => ( cIntMap_2eMap_2eMapGet___24a3(V0__A,V1__m,V3__a) = cCoq_2eInit_2eDatatypes_2eSome___24a2(V0__A,V4__y)
                           => ( cIntMap_2eMap_2eMapGet___24a3(V0__A,V2__m_27,V3__a) = cCoq_2eInit_2eDatatypes_2eSome___24a2(V0__A,V5__y_27)
                             => 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_241173___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_241244___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_241167___24a4(V0__A,V1__m,V2__m_27,V3__a) ) ) ) ) ).

fof('IntMap.Map.MapGet_M2_both_None',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,cCoq_2eNArith_2eBinNatDef_2eN_2ediv2___24a1(V3__a)) = cCoq_2eInit_2eDatatypes_2eNone___24a1(V0__A)
                   => ( cIntMap_2eMap_2eMapGet___24a3(V0__A,V2__m_27,cCoq_2eNArith_2eBinNatDef_2eN_2ediv2___24a1(V3__a)) = cCoq_2eInit_2eDatatypes_2eNone___24a1(V0__A)
                     => cIntMap_2eMap_2eMapGet___24a3(V0__A,cIntMap_2eMap_2eM2___24a3(V0__A,V1__m,V2__m_27),V3__a) = cCoq_2eInit_2eDatatypes_2eNone___24a1(V0__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_241232___24a4(V0__A,V1__b,V2__m,V3__m_27),V4__a) = c_24__case__Coq_2eInit_2eDatatypes_2ebool_241238___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_2476528___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__76608___24a3(V0__A,V1__m,V2__m_27)) ) ) ) ).

fof('IntMap.Map.MapPut_behind_as_before',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__a0] :
                      ( cIntMap_2eMap_2ead___24t(V4__a0)
                     => ( cCoq_2eNArith_2eBinNatDef_2eN_2eeqb___24a2(V2__a,V4__a0) = cCoq_2eInit_2eDatatypes_2efalse
                       => cIntMap_2eMap_2eMapGet___24a3(V0__A,cIntMap_2eMap_2eMapPut___24a4(V0__A,V1__m,V2__a,V3__y),V4__a0) = cIntMap_2eMap_2eMapGet___24a3(V0__A,cIntMap_2eMap_2eMapPut__behind___24a4(V0__A,V1__m,V2__a,V3__y),V4__a0) ) ) ) ) ) ) ).

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_2476560___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__76584___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_241360___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__76551___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_241250___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__76596___24a3(V0__A,V1__m,V2__a)) ) ) ) ).

fof('IntMap.Map.Map_ind',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__P] :
          ( c_24__type__391___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__789___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__789___24t(V0__A,V1__f)
         => ! [V2__f_27] :
              ( c_24__type__789___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__789___24t(V0__A,V1__f)
         => ! [V2__f_27] :
              ( c_24__type__789___24t(V0__A,V2__f_27)
             => ! [V3__f_27_27] :
                  ( c_24__type__789___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.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_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)
             => ( 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_2eMapRemove___24a3(V0__A,V1__m,V2__a)) = cIntMap_2eMap_2eMapCard___24a2(V0__A,V1__m) ) ) ) ) ).

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__1372___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__1367___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__1372___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.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__1415___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__1422___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__67459___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__1415___24t(V1__M,V3__op)
                 => ! [V4__State] :
                      ( cType___24t(V4__State)
                     => ! [V5__f] :
                          ( c_24__type__77239___24t(V0__A,V1__M,V4__State,V5__f)
                         => ! [V6__g] :
                              ( c_24__type__77468___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__1415___24t(V1__M,V3__op)
                 => ! [V4__State] :
                      ( cType___24t(V4__State)
                     => ! [V5__f] :
                          ( c_24__type__77239___24t(V0__A,V1__M,V4__State,V5__f)
                         => ! [V6__m] :
                              ( cIntMap_2eMap_2eMap___24t(V0__A,V6__m)
                             => ! [V7__g] :
                                  ( c_24__type__77468___24t(V0__A,V1__M,V4__State,V7__g)
                                 => ! [V8__pf] :
                                      ( c_24__type__77244___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__76796___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.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.Map_of_alist_semantics',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__l] :
          ( cIntMap_2eMapiter_2ealist___24t(V0__A,V1__l)
         => cIntMap_2eMap_2eeqm___24a3(V0__A,cIntMap_2eMapiter_2ealist__semantics___24a2(V0__A,V1__l),cIntMap_2eMap_2eMapGet___24a2(V0__A,cIntMap_2eMapiter_2eMap__of__alist___24a2(V0__A,V1__l))) ) ) ).

fof('IntMap.Mapiter.ad_comp_double_inj',axiom,
    ! [V0__pf] :
      ( c_24__type__76494___24t(V0__pf)
     => ( cIntMap_2eMapiter_2ead__inj___24a1(V0__pf)
       => cIntMap_2eMapiter_2ead__inj___24a1(c_24__lam__76497___24a1(V0__pf)) ) ) ).

fof('IntMap.Mapiter.ad_comp_double_plus_un_inj',axiom,
    ! [V0__pf] :
      ( c_24__type__76494___24t(V0__pf)
     => ( cIntMap_2eMapiter_2ead__inj___24a1(V0__pf)
       => cIntMap_2eMapiter_2ead__inj___24a1(c_24__lam__76499___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_2477526___24a4(V0__A,V1__l,V2__l_27,V3__a) ) ) ) ) ).

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('Mapcanon.MapCanon.M0_canon',axiom,
    cMapcanon_2eMapCanon_2emapcanon___24a1(cIntMap_2eMap_2eM0___24a1(cA)) ).

fof('Mapcanon.MapCanon.M1_canon',axiom,
    ! [V0__a] :
      ( cIntMap_2eMap_2ead___24t(V0__a)
     => ! [V1__y] :
          ( cA___24t(V1__y)
         => cMapcanon_2eMapCanon_2emapcanon___24a1(cIntMap_2eMap_2eM1___24a3(cA,V0__a,V1__y)) ) ) ).

fof('Mapcanon.MapCanon.M2_canon',axiom,
    ! [V0__m1] :
      ( cIntMap_2eMap_2eMap___24t(cA,V0__m1)
     => ! [V1__m2] :
          ( cIntMap_2eMap_2eMap___24t(cA,V1__m2)
         => ( cMapcanon_2eMapCanon_2emapcanon___24a1(V0__m1)
           => ( cMapcanon_2eMapCanon_2emapcanon___24a1(V1__m2)
             => ( cCoq_2eInit_2ePeano_2ele___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO)),cIntMap_2eMap_2eMapCard___24a2(cA,cIntMap_2eMap_2eM2___24a3(cA,V0__m1,V1__m2)))
               => cMapcanon_2eMapCanon_2emapcanon___24a1(cIntMap_2eMap_2eM2___24a3(cA,V0__m1,V1__m2)) ) ) ) ) ) ).

fof('Mapcanon.MapCanon.M2_eqmap_1',axiom,
    ! [V0__m0] :
      ( cIntMap_2eMap_2eMap___24t(cA,V0__m0)
     => ! [V1__m1] :
          ( cIntMap_2eMap_2eMap___24t(cA,V1__m1)
         => ! [V2__m2] :
              ( cIntMap_2eMap_2eMap___24t(cA,V2__m2)
             => ! [V3__m3] :
                  ( cIntMap_2eMap_2eMap___24t(cA,V3__m3)
                 => ( cIntMap_2eMapaxioms_2eeqmap___24a3(cA,cIntMap_2eMap_2eM2___24a3(cA,V0__m0,V1__m1),cIntMap_2eMap_2eM2___24a3(cA,V2__m2,V3__m3))
                   => cIntMap_2eMapaxioms_2eeqmap___24a3(cA,V0__m0,V2__m2) ) ) ) ) ) ).

fof('Mapcanon.MapCanon.M2_eqmap_2',axiom,
    ! [V0__m0] :
      ( cIntMap_2eMap_2eMap___24t(cA,V0__m0)
     => ! [V1__m1] :
          ( cIntMap_2eMap_2eMap___24t(cA,V1__m1)
         => ! [V2__m2] :
              ( cIntMap_2eMap_2eMap___24t(cA,V2__m2)
             => ! [V3__m3] :
                  ( cIntMap_2eMap_2eMap___24t(cA,V3__m3)
                 => ( cIntMap_2eMapaxioms_2eeqmap___24a3(cA,cIntMap_2eMap_2eM2___24a3(cA,V0__m0,V1__m1),cIntMap_2eMap_2eM2___24a3(cA,V2__m2,V3__m3))
                   => cIntMap_2eMapaxioms_2eeqmap___24a3(cA,V1__m1,V3__m3) ) ) ) ) ) ).

fof('Mapcanon.MapCanon.MapDelta_canon',axiom,
    ! [V0__m] :
      ( cIntMap_2eMap_2eMap___24t(cA,V0__m)
     => ! [V1__m_27] :
          ( cIntMap_2eMap_2eMap___24t(cA,V1__m_27)
         => ( cMapcanon_2eMapCanon_2emapcanon___24a1(V0__m)
           => ( cMapcanon_2eMapCanon_2emapcanon___24a1(V1__m_27)
             => cMapcanon_2eMapCanon_2emapcanon___24a1(cIntMap_2eMap_2eMapDelta___24a3(cA,V0__m,V1__m_27)) ) ) ) ) ).

fof('Mapcanon.MapCanon.MapMerge_canon',axiom,
    ! [V0__m] :
      ( cIntMap_2eMap_2eMap___24t(cA,V0__m)
     => ! [V1__m_27] :
          ( cIntMap_2eMap_2eMap___24t(cA,V1__m_27)
         => ( cMapcanon_2eMapCanon_2emapcanon___24a1(V0__m)
           => ( cMapcanon_2eMapCanon_2emapcanon___24a1(V1__m_27)
             => cMapcanon_2eMapCanon_2emapcanon___24a1(cIntMap_2eMap_2eMapMerge___24a3(cA,V0__m,V1__m_27)) ) ) ) ) ).

fof('Mapcanon.MapCanon.MapPut1_canon',axiom,
    ! [V0__p] :
      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V0__p)
     => ! [V1__a] :
          ( cIntMap_2eMap_2ead___24t(V1__a)
         => ! [V2__a_27] :
              ( cIntMap_2eMap_2ead___24t(V2__a_27)
             => ! [V3__y] :
                  ( cA___24t(V3__y)
                 => ! [V4__y_27] :
                      ( cA___24t(V4__y_27)
                     => cMapcanon_2eMapCanon_2emapcanon___24a1(cIntMap_2eMap_2eMapPut1___24a6(cA,V1__a,V3__y,V2__a_27,V4__y_27,V0__p)) ) ) ) ) ) ).

fof('Mapcanon.MapCanon.MapPut_behind_canon',axiom,
    ! [V0__m] :
      ( cIntMap_2eMap_2eMap___24t(cA,V0__m)
     => ( cMapcanon_2eMapCanon_2emapcanon___24a1(V0__m)
       => ! [V2__a] :
            ( cIntMap_2eMap_2ead___24t(V2__a)
           => ! [V3__y] :
                ( cA___24t(V3__y)
               => cMapcanon_2eMapCanon_2emapcanon___24a1(cIntMap_2eMap_2eMapPut__behind___24a4(cA,V0__m,V2__a,V3__y)) ) ) ) ) ).

fof('Mapcanon.MapCanon.MapPut_canon',axiom,
    ! [V0__m] :
      ( cIntMap_2eMap_2eMap___24t(cA,V0__m)
     => ( cMapcanon_2eMapCanon_2emapcanon___24a1(V0__m)
       => ! [V2__a] :
            ( cIntMap_2eMap_2ead___24t(V2__a)
           => ! [V3__y] :
                ( cA___24t(V3__y)
               => cMapcanon_2eMapCanon_2emapcanon___24a1(cIntMap_2eMap_2eMapPut___24a4(cA,V0__m,V2__a,V3__y)) ) ) ) ) ).

fof('Mapcanon.MapCanon.MapRemove_canon',axiom,
    ! [V0__m] :
      ( cIntMap_2eMap_2eMap___24t(cA,V0__m)
     => ( cMapcanon_2eMapCanon_2emapcanon___24a1(V0__m)
       => ! [V2__a] :
            ( cIntMap_2eMap_2ead___24t(V2__a)
           => cMapcanon_2eMapCanon_2emapcanon___24a1(cIntMap_2eMap_2eMapRemove___24a3(cA,V0__m,V2__a)) ) ) ) ).

fof('Mapcanon.MapCanon.makeM2_canon',axiom,
    ! [V0__m] :
      ( cIntMap_2eMap_2eMap___24t(cA,V0__m)
     => ! [V1__m_27] :
          ( cIntMap_2eMap_2eMap___24t(cA,V1__m_27)
         => ( cMapcanon_2eMapCanon_2emapcanon___24a1(V0__m)
           => ( cMapcanon_2eMapCanon_2emapcanon___24a1(V1__m_27)
             => cMapcanon_2eMapCanon_2emapcanon___24a1(cIntMap_2eMap_2emakeM2___24a3(cA,V0__m,V1__m_27)) ) ) ) ) ).

fof('Mapcanon.MapCanon.mapcanon_M2',axiom,
    ! [V0__m1] :
      ( cIntMap_2eMap_2eMap___24t(cA,V0__m1)
     => ! [V1__m2] :
          ( cIntMap_2eMap_2eMap___24t(cA,V1__m2)
         => ( cMapcanon_2eMapCanon_2emapcanon___24a1(cIntMap_2eMap_2eM2___24a3(cA,V0__m1,V1__m2))
           => cCoq_2eInit_2ePeano_2ele___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO)),cIntMap_2eMap_2eMapCard___24a2(cA,cIntMap_2eMap_2eM2___24a3(cA,V0__m1,V1__m2))) ) ) ) ).

fof('Mapcanon.MapCanon.mapcanon_M2_1',axiom,
    ! [V0__m1] :
      ( cIntMap_2eMap_2eMap___24t(cA,V0__m1)
     => ! [V1__m2] :
          ( cIntMap_2eMap_2eMap___24t(cA,V1__m2)
         => ( cMapcanon_2eMapCanon_2emapcanon___24a1(cIntMap_2eMap_2eM2___24a3(cA,V0__m1,V1__m2))
           => cMapcanon_2eMapCanon_2emapcanon___24a1(V0__m1) ) ) ) ).

fof('Mapcanon.MapCanon.mapcanon_M2_2',axiom,
    ! [V0__m1] :
      ( cIntMap_2eMap_2eMap___24t(cA,V0__m1)
     => ! [V1__m2] :
          ( cIntMap_2eMap_2eMap___24t(cA,V1__m2)
         => ( cMapcanon_2eMapCanon_2emapcanon___24a1(cIntMap_2eMap_2eM2___24a3(cA,V0__m1,V1__m2))
           => cMapcanon_2eMapCanon_2emapcanon___24a1(V1__m2) ) ) ) ).

fof('Mapcanon.MapCanon.mapcanon_exists_1',axiom,
    ! [V0__m] :
      ( cIntMap_2eMap_2eMap___24t(cA,V0__m)
     => cIntMap_2eMapaxioms_2eeqmap___24a3(cA,V0__m,cMapcanon_2eMapCanon_2eMapCanonicalize___24a1(V0__m)) ) ).

fof('Mapcanon.MapCanon.mapcanon_exists_2',axiom,
    ! [V0__m] :
      ( cIntMap_2eMap_2eMap___24t(cA,V0__m)
     => cMapcanon_2eMapCanon_2emapcanon___24a1(cMapcanon_2eMapCanon_2eMapCanonicalize___24a1(V0__m)) ) ).

fof('Mapcanon.MapCanon.mapcanon_ind',axiom,
    ! [V0__P] :
      ( c_24__type__612___24t(V0__P)
     => ( p(happ(V0__P,cIntMap_2eMap_2eM0___24a1(cA)))
       => ( ! [V2__a] :
              ( cIntMap_2eMap_2ead___24t(V2__a)
             => ! [V3__y] :
                  ( cA___24t(V3__y)
                 => p(happ(V0__P,cIntMap_2eMap_2eM1___24a3(cA,V2__a,V3__y))) ) )
         => ( ! [V3__m1] :
                ( cIntMap_2eMap_2eMap___24t(cA,V3__m1)
               => ! [V4__m2] :
                    ( cIntMap_2eMap_2eMap___24t(cA,V4__m2)
                   => ( cMapcanon_2eMapCanon_2emapcanon___24a1(V3__m1)
                     => ( p(happ(V0__P,V3__m1))
                       => ( cMapcanon_2eMapCanon_2emapcanon___24a1(V4__m2)
                         => ( p(happ(V0__P,V4__m2))
                           => ( cCoq_2eInit_2ePeano_2ele___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO)),cIntMap_2eMap_2eMapCard___24a2(cA,cIntMap_2eMap_2eM2___24a3(cA,V3__m1,V4__m2)))
                             => p(happ(V0__P,cIntMap_2eMap_2eM2___24a3(cA,V3__m1,V4__m2))) ) ) ) ) ) ) )
           => ! [V4__m] :
                ( cIntMap_2eMap_2eMap___24t(cA,V4__m)
               => ( cMapcanon_2eMapCanon_2emapcanon___24a1(V4__m)
                 => p(happ(V0__P,V4__m)) ) ) ) ) ) ) ).

fof('Mapcanon.MapCanon.mapcanon_unique',axiom,
    ! [V0__m] :
      ( cIntMap_2eMap_2eMap___24t(cA,V0__m)
     => ! [V1__m_27] :
          ( cIntMap_2eMap_2eMap___24t(cA,V1__m_27)
         => ( cMapcanon_2eMapCanon_2emapcanon___24a1(V0__m)
           => ( cMapcanon_2eMapCanon_2emapcanon___24a1(V1__m_27)
             => ( cIntMap_2eMapaxioms_2eeqmap___24a3(cA,V0__m,V1__m_27)
               => V0__m = V1__m_27 ) ) ) ) ) ).

fof('$adef_IntMap.Map.M0_$a1',axiom,
    ! [V_24X1] : happ(cIntMap_2eMap_2eM0,V_24X1) = cIntMap_2eMap_2eM0___24a1(V_24X1) ).

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('$adef_$_case_Coq.Init.Datatypes.bool$1238_$a5',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(c_24__case__Coq_2eInit_2eDatatypes_2ebool_241238,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = c_24__case__Coq_2eInit_2eDatatypes_2ebool_241238___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).

fof('$adef_$_prop_563_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__prop__563,V_24X1),V_24X2),V_24X3) = c_24__prop__563___24a3(V_24X1,V_24X2,V_24X3) ).

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('$adef_$_case_Coq.Numbers.BinNums.positive$105648_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(c_24__case__Coq_2eNumbers_2eBinNums_2epositive_24105648,V_24X1),V_24X2) = c_24__case__Coq_2eNumbers_2eBinNums_2epositive_24105648___24a2(V_24X1,V_24X2) ).

fof('$adef_$_lam_864_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(c_24__lam__864,V_24X1),V_24X2) = c_24__lam__864___24a2(V_24X1,V_24X2) ).

fof('$adef_$_lam_76658_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__lam__76658,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__lam__76658___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).

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('$adef_$_lam_77985_$a2',axiom,
    ! [V_24X1,V_24X2] :
      ( p(happ(happ(c_24__lam__77985,V_24X1),V_24X2))
    <=> c_24__lam__77985___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('$adef_$_lam_77375_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__lam__77375,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__lam__77375___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).

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('$adef_Coq.Vectors.VectorDef.cons_$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('$adef_Coq.ZArith.BinIntDef.Z.modulo_$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('$adef_Coq.Init.Datatypes.BoolSpec_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] :
      ( p(happ(happ(happ(cCoq_2eInit_2eDatatypes_2eBoolSpec,V_24X1),V_24X2),V_24X3))
    <=> cCoq_2eInit_2eDatatypes_2eBoolSpec___24a3(V_24X1,V_24X2,V_24X3) ) ).

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('$adef_Coq.micromega.VarMap.t_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2emicromega_2eVarMap_2et,V_24X1) = cCoq_2emicromega_2eVarMap_2et___24a1(V_24X1) ).

fof('$adef_Coq.Lists.List.Exists_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] :
      ( p(happ(happ(happ(cCoq_2eLists_2eList_2eExists,V_24X1),V_24X2),V_24X3))
    <=> cCoq_2eLists_2eList_2eExists___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('$adef_Coq.Init.Specif.sig_rect_$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_67379_$a5',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(c_24__lam__67379,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = c_24__lam__67379___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).

fof('$adef_Coq.micromega.RingMicromega.PsatzMulC_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2emicromega_2eRingMicromega_2ePsatzMulC,V_24X1),V_24X2),V_24X3) = cCoq_2emicromega_2eRingMicromega_2ePsatzMulC___24a3(V_24X1,V_24X2,V_24X3) ).

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('$adef_$_lam_1342_$a5',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(c_24__lam__1342,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = c_24__lam__1342___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).

fof('$adef_$_lam_76173_$a5',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(c_24__lam__76173,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = c_24__lam__76173___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).

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('$adef_$_lam_76499_$a1',axiom,
    ! [V_24X1] : happ(c_24__lam__76499,V_24X1) = c_24__lam__76499___24a1(V_24X1) ).

fof('$adef_Coq.Init.Datatypes.implb_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eDatatypes_2eimplb,V_24X1),V_24X2) = cCoq_2eInit_2eDatatypes_2eimplb___24a2(V_24X1,V_24X2) ).

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('$adef_Coq.Init.Specif.sumor_rect_$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_562_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__prop__562,V_24X1),V_24X2),V_24X3) = c_24__prop__562___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_$_lam_76584_$a5',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(c_24__lam__76584,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = c_24__lam__76584___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).

fof('$adef_$_lam_76551_$a5',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(c_24__lam__76551,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = c_24__lam__76551___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).

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('$adef_Coq.Relations.Relation_Operators.clos_refl_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] :
      ( p(happ(happ(happ(happ(cCoq_2eRelations_2eRelation__Operators_2eclos__refl,V_24X1),V_24X2),V_24X3),V_24X4))
    <=> cCoq_2eRelations_2eRelation__Operators_2eclos__refl___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).

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('$adef_Coq.micromega.RMicromega.CMult_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2emicromega_2eRMicromega_2eCMult,V_24X1),V_24X2) = cCoq_2emicromega_2eRMicromega_2eCMult___24a2(V_24X1,V_24X2) ).

fof('$adef_$_lam_76551_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__lam__76551,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__lam__76551___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).

fof('$adef_$_case_Coq.Init.Datatypes.option$77526_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__case__Coq_2eInit_2eDatatypes_2eoption_2477526,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__case__Coq_2eInit_2eDatatypes_2eoption_2477526___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).

fof('$adef_Coq.micromega.DeclConstant.GT_$a2',axiom,
    ! [V_24X1,V_24X2] :
      ( p(happ(happ(cCoq_2emicromega_2eDeclConstant_2eGT,V_24X1),V_24X2))
    <=> cCoq_2emicromega_2eDeclConstant_2eGT___24a2(V_24X1,V_24X2) ) ).

fof('$adef_$_prop_1021_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__prop__1021,V_24X1),V_24X2),V_24X3) = c_24__prop__1021___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_$_lam_76846_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__76846,V_24X1),V_24X2),V_24X3) = c_24__lam__76846___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_$_prop_105529_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__prop__105529,V_24X1),V_24X2),V_24X3) = c_24__prop__105529___24a3(V_24X1,V_24X2,V_24X3) ).

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('$adef_Coq.Sorting.Sorted.LocallySorted_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] :
      ( p(happ(happ(happ(cCoq_2eSorting_2eSorted_2eLocallySorted,V_24X1),V_24X2),V_24X3))
    <=> cCoq_2eSorting_2eSorted_2eLocallySorted___24a3(V_24X1,V_24X2,V_24X3) ) ).

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_76842_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(c_24__lam__76842,V_24X1),V_24X2) = c_24__lam__76842___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.Init.Decimal.Pos_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eInit_2eDecimal_2ePos,V_24X1) = cCoq_2eInit_2eDecimal_2ePos___24a1(V_24X1) ).

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('$adef_Coq.setoid_ring.Ring_polynom.Pol_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2esetoid__ring_2eRing__polynom_2ePol,V_24X1) = cCoq_2esetoid__ring_2eRing__polynom_2ePol___24a1(V_24X1) ).

fof('$adef_IntMap.Mapsubset.MapSubset_$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('$adef_Coq.Arith.Between.P_nth_$a5',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] :
      ( p(happ(happ(happ(happ(happ(cCoq_2eArith_2eBetween_2eP__nth,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5))
    <=> cCoq_2eArith_2eBetween_2eP__nth___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ) ).

fof('$adef_$_lam_1162_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__1162,V_24X1),V_24X2),V_24X3) = c_24__lam__1162___24a3(V_24X1,V_24X2,V_24X3) ).

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('$adef_$_lam_77846_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__77846,V_24X1),V_24X2),V_24X3) = c_24__lam__77846___24a3(V_24X1,V_24X2,V_24X3) ).

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_77119_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__77119,V_24X1),V_24X2),V_24X3) = c_24__lam__77119___24a3(V_24X1,V_24X2,V_24X3) ).

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('$adef_Coq.setoid_ring.Ring_theory.almost_ring_theory_$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('$adef_Coq.Init.Datatypes.app_$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('$adef_Coq.Init.Decimal.D6_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eInit_2eDecimal_2eD6,V_24X1) = cCoq_2eInit_2eDecimal_2eD6___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('$adef_Coq.Init.Specif.sig_$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_76759_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__76759,V_24X1),V_24X2),V_24X3) = c_24__lam__76759___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('$adef_$_lam_880_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__880,V_24X1),V_24X2),V_24X3) = c_24__lam__880___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('$adef_Coq.micromega.ZMicromega.EnumProof_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2emicromega_2eZMicromega_2eEnumProof,V_24X1),V_24X2),V_24X3) = cCoq_2emicromega_2eZMicromega_2eEnumProof___24a3(V_24X1,V_24X2,V_24X3) ).

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('$adef_Coq.Relations.Relation_Operators.symprod_$a6',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] :
      ( p(happ(happ(happ(happ(happ(happ(cCoq_2eRelations_2eRelation__Operators_2esymprod,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6))
    <=> cCoq_2eRelations_2eRelation__Operators_2esymprod___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ) ).

fof('$adef_Coq.Init.Decimal.D4_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eInit_2eDecimal_2eD4,V_24X1) = cCoq_2eInit_2eDecimal_2eD4___24a1(V_24X1) ).

fof('$adef_Coq.micromega.RingMicromega.Build_Formula_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2emicromega_2eRingMicromega_2eBuild__Formula,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2emicromega_2eRingMicromega_2eBuild__Formula___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).

fof('$adef_$_case_Coq.Init.Datatypes.bool$1232_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__case__Coq_2eInit_2eDatatypes_2ebool_241232,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__case__Coq_2eInit_2eDatatypes_2ebool_241232___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).

fof('$adef_Coq.setoid_ring.Ring_polynom.mkmult_pow_$a5',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2emkmult__pow,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2esetoid__ring_2eRing__polynom_2emkmult__pow___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).

fof('$adef_Mapcanon.MapCanon.mapcanon_$a1',axiom,
    ! [V_24X1] :
      ( p(happ(cMapcanon_2eMapCanon_2emapcanon,V_24X1))
    <=> cMapcanon_2eMapCanon_2emapcanon___24a1(V_24X1) ) ).

fof('$adef_$_lam_122089_$a2',axiom,
    ! [V_24X1,V_24X2] :
      ( p(happ(happ(c_24__lam__122089,V_24X1),V_24X2))
    <=> c_24__lam__122089___24a2(V_24X1,V_24X2) ) ).

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('$adef_$_lam_77275_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__lam__77275,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__lam__77275___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).

fof('$adef_Coq.setoid_ring.Field_theory.mk_rsplit_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2esetoid__ring_2eField__theory_2emk__rsplit,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2esetoid__ring_2eField__theory_2emk__rsplit___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).

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('$adef_Coq.setoid_ring.Ring_theory.semi_ring_theory_$a6',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] :
      ( p(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__theory_2esemi__ring__theory,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6))
    <=> cCoq_2esetoid__ring_2eRing__theory_2esemi__ring__theory___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ) ).

fof('$adef_Coq.Reals.RIneq.mknonposreal_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eReals_2eRIneq_2emknonposreal,V_24X1) = cCoq_2eReals_2eRIneq_2emknonposreal___24a1(V_24X1) ).

fof('$adef_$_lam_77812_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__77812,V_24X1),V_24X2),V_24X3) = c_24__lam__77812___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_Coq.Lists.SetoidList.transpose_restr2_$a5',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] :
      ( p(happ(happ(happ(happ(happ(cCoq_2eLists_2eSetoidList_2etranspose__restr2,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5))
    <=> cCoq_2eLists_2eSetoidList_2etranspose__restr2___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ) ).

fof('$adef_$_lam_76658_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__76658,V_24X1),V_24X2),V_24X3) = c_24__lam__76658___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_$_lam_67459_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__lam__67459,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__lam__67459___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).

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('$adef_$_lam_76497_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(c_24__lam__76497,V_24X1),V_24X2) = c_24__lam__76497___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('$adef_Coq.NArith.Ndigits.Nless_$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('$adef_Coq.FSets.FSetPositive.PositiveSet.ct_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] :
      ( p(happ(happ(happ(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2ect,V_24X1),V_24X2),V_24X3))
    <=> cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2ect___24a3(V_24X1,V_24X2,V_24X3) ) ).

fof('$adef_$_lam_1342_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__1342,V_24X1),V_24X2),V_24X3) = c_24__lam__1342___24a3(V_24X1,V_24X2,V_24X3) ).

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('$adef_$_lam_1305_$a6',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(c_24__lam__1305,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = c_24__lam__1305___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).

fof('$adef_$_let_var_8_m_1200_1203_$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__1200__1203,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = c_24__let__var__8__m__1200__1203___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).

fof('$adef_$_lam_67248_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(c_24__lam__67248,V_24X1),V_24X2) = c_24__lam__67248___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.Lists.List.hd_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eLists_2eList_2ehd,V_24X1),V_24X2),V_24X3) = cCoq_2eLists_2eList_2ehd___24a3(V_24X1,V_24X2,V_24X3) ).

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('$adef_Coq.Relations.Relation_Definitions.relation_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eRelations_2eRelation__Definitions_2erelation,V_24X1) = cCoq_2eRelations_2eRelation__Definitions_2erelation___24a1(V_24X1) ).

fof('$adef_$_lam_77983_$a1',axiom,
    ! [V_24X1] : happ(c_24__lam__77983,V_24X1) = c_24__lam__77983___24a1(V_24X1) ).

fof('$adef_$_lam_1194_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__lam__1194,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__lam__1194___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).

fof('$adef_$_lam_77375_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__77375,V_24X1),V_24X2),V_24X3) = c_24__lam__77375___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_$_lam_67459_$a6',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(c_24__lam__67459,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = c_24__lam__67459___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).

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('$adef_Coq.Vectors.VectorDef.t_$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('$adef_Coq.setoid_ring.Ring_polynom.PExpr_$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('$adef_$_case_Coq.Init.Datatypes.prod$104828_$a9',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9] :
      ( p(happ(happ(happ(happ(happ(happ(happ(happ(happ(c_24__case__Coq_2eInit_2eDatatypes_2eprod_24104828,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9))
    <=> c_24__case__Coq_2eInit_2eDatatypes_2eprod_24104828___24a9(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9) ) ).

fof('$adef_Coq.Arith.Plus.tail_plus_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2eArith_2ePlus_2etail__plus,V_24X1),V_24X2) = cCoq_2eArith_2ePlus_2etail__plus___24a2(V_24X1,V_24X2) ).

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_67248_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] :
      ( p(happ(happ(happ(c_24__lam__67248,V_24X1),V_24X2),V_24X3))
    <=> c_24__lam__67248___24a3(V_24X1,V_24X2,V_24X3) ) ).

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('$adef_Coq.micromega.RingMicromega.SORaddon_$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('$adef_Coq.Arith.Between.exists_between_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] :
      ( p(happ(happ(happ(cCoq_2eArith_2eBetween_2eexists__between,V_24X1),V_24X2),V_24X3))
    <=> cCoq_2eArith_2eBetween_2eexists__between___24a3(V_24X1,V_24X2,V_24X3) ) ).

fof('$adef_$_lam_733_$a1',axiom,
    ! [V_24X1] : happ(c_24__lam__733,V_24X1) = c_24__lam__733___24a1(V_24X1) ).

fof('$adef_$_lam_741_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__741,V_24X1),V_24X2),V_24X3) = c_24__lam__741___24a3(V_24X1,V_24X2,V_24X3) ).

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('$adef_Coq.micromega.RingMicromega.PolEnv_$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('$adef_IntMap.Mapiter.MapFold1_state_$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('$adef_Coq.Init.Datatypes.identity_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] :
      ( p(happ(happ(happ(cCoq_2eInit_2eDatatypes_2eidentity,V_24X1),V_24X2),V_24X3))
    <=> cCoq_2eInit_2eDatatypes_2eidentity___24a3(V_24X1,V_24X2,V_24X3) ) ).

fof('$adef_$_lam_76869_$a1',axiom,
    ! [V_24X1] : happ(c_24__lam__76869,V_24X1) = c_24__lam__76869___24a1(V_24X1) ).

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('$adef_IntMap.Map.Map_rect_$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('$adef_Coq.micromega.EnvRing.zmon_$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('$adef_Coq.Logic.EqdepFacts.eq_dep_$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_1305_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__lam__1305,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__lam__1305___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).

fof('$adef_IntMap.Map.M1_$a1',axiom,
    ! [V_24X1] : happ(cIntMap_2eMap_2eM1,V_24X1) = cIntMap_2eMap_2eM1___24a1(V_24X1) ).

fof('$adef_Coq.setoid_ring.Ring_theory.div_theory_$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_2ediv__theory,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7))
    <=> cCoq_2esetoid__ring_2eRing__theory_2ediv__theory___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7) ) ).

fof('$adef_Coq.Sorting.Sorted.HdRel_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] :
      ( p(happ(happ(happ(happ(cCoq_2eSorting_2eSorted_2eHdRel,V_24X1),V_24X2),V_24X3),V_24X4))
    <=> cCoq_2eSorting_2eSorted_2eHdRel___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).

fof('$adef_Hammer.Tactics.Reconstr.rdone_$a2',axiom,
    ! [V_24X1,V_24X2] :
      ( p(happ(happ(cHammer_2eTactics_2eReconstr_2erdone,V_24X1),V_24X2))
    <=> cHammer_2eTactics_2eReconstr_2erdone___24a2(V_24X1,V_24X2) ) ).

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('$adef_$_lam_76608_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__76608,V_24X1),V_24X2),V_24X3) = c_24__lam__76608___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_Coq.Lists.SetoidList.transpose2_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] :
      ( p(happ(happ(happ(happ(cCoq_2eLists_2eSetoidList_2etranspose2,V_24X1),V_24X2),V_24X3),V_24X4))
    <=> cCoq_2eLists_2eSetoidList_2etranspose2___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).

fof('$adef_$_prop_105533_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(c_24__prop__105533,V_24X1),V_24X2) = c_24__prop__105533___24a2(V_24X1,V_24X2) ).

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('$adef_IntMap.Mapiter.aapp_$a1',axiom,
    ! [V_24X1] : happ(cIntMap_2eMapiter_2eaapp,V_24X1) = cIntMap_2eMapiter_2eaapp___24a1(V_24X1) ).

fof('$adef_$_lam_77985_$a1',axiom,
    ! [V_24X1] : happ(c_24__lam__77985,V_24X1) = c_24__lam__77985___24a1(V_24X1) ).

fof('$adef_Coq.Lists.List.Forall2_$a5',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] :
      ( p(happ(happ(happ(happ(happ(cCoq_2eLists_2eList_2eForall2,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5))
    <=> cCoq_2eLists_2eList_2eForall2___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ) ).

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('$adef_Coq.Init.Datatypes.nil_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eInit_2eDatatypes_2enil,V_24X1) = cCoq_2eInit_2eDatatypes_2enil___24a1(V_24X1) ).

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('$adef_Coq.Init.Datatypes.cons_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eInit_2eDatatypes_2econs,V_24X1) = cCoq_2eInit_2eDatatypes_2econs___24a1(V_24X1) ).

fof('$adef_$_lam_741_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__lam__741,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__lam__741___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).

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('$adef_$_lam_230_$a5',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(c_24__lam__230,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = c_24__lam__230___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).

fof('$adef_$_lam_1157_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__1157,V_24X1),V_24X2),V_24X3) = c_24__lam__1157___24a3(V_24X1,V_24X2,V_24X3) ).

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('$adef_Coq.micromega.Tauto.GFormula_$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('$adef_Coq.setoid_ring.Ring_theory.Morphism_$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('$adef_Coq.setoid_ring.Ring_theory.IDphi_$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('$adef_IntMap.Map.MapPut1_$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('$adef_$_lam_67379_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__lam__67379,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__lam__67379___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).

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('$adef_$_lam_122089_$a1',axiom,
    ! [V_24X1] : happ(c_24__lam__122089,V_24X1) = c_24__lam__122089___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('$adef_Coq.ZArith.Zeven.Zodd_$a1',axiom,
    ! [V_24X1] :
      ( p(happ(cCoq_2eZArith_2eZeven_2eZodd,V_24X1))
    <=> cCoq_2eZArith_2eZeven_2eZodd___24a1(V_24X1) ) ).

fof('$adef_Coq.Structures.GenericMinMax.gmax_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2eStructures_2eGenericMinMax_2egmax,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2eStructures_2eGenericMinMax_2egmax___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).

fof('$adef_Coq.micromega.RMicromega.CPow_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2emicromega_2eRMicromega_2eCPow,V_24X1),V_24X2) = cCoq_2emicromega_2eRMicromega_2eCPow___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.micromega.RMicromega.CPlus_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2emicromega_2eRMicromega_2eCPlus,V_24X1),V_24X2) = cCoq_2emicromega_2eRMicromega_2eCPlus___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.Init.Decimal.D1_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eInit_2eDecimal_2eD1,V_24X1) = cCoq_2eInit_2eDecimal_2eD1___24a1(V_24X1) ).

fof('$adef_$_prop_67218_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__prop__67218,V_24X1),V_24X2),V_24X3) = c_24__prop__67218___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('$adef_Coq.Init.Nat.div2_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eInit_2eNat_2ediv2,V_24X1) = cCoq_2eInit_2eNat_2ediv2___24a1(V_24X1) ).

fof('$adef_Coq.Init.Datatypes.negb_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eInit_2eDatatypes_2enegb,V_24X1) = cCoq_2eInit_2eDatatypes_2enegb___24a1(V_24X1) ).

fof('$adef_Coq.micromega.RMicromega.COpp_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2emicromega_2eRMicromega_2eCOpp,V_24X1) = cCoq_2emicromega_2eRMicromega_2eCOpp___24a1(V_24X1) ).

fof('$adef_Coq.PArith.BinPosDef.Pos.div2_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2ePArith_2eBinPosDef_2ePos_2ediv2,V_24X1) = cCoq_2ePArith_2eBinPosDef_2ePos_2ediv2___24a1(V_24X1) ).

fof('$adef_$_lam_67275_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__67275,V_24X1),V_24X2),V_24X3) = c_24__lam__67275___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_$_lam_77283_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__lam__77283,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__lam__77283___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).

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('$adef_Coq.Lists.List.ForallOrdPairs_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] :
      ( p(happ(happ(happ(cCoq_2eLists_2eList_2eForallOrdPairs,V_24X1),V_24X2),V_24X3))
    <=> cCoq_2eLists_2eList_2eForallOrdPairs___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_67076_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] :
      ( p(happ(happ(happ(happ(c_24__lam__67076,V_24X1),V_24X2),V_24X3),V_24X4))
    <=> c_24__lam__67076___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).

fof('$adef_Coq.Init.Logic_Type.notT_$a1',axiom,
    ! [V_24X1] :
      ( p(happ(cCoq_2eInit_2eLogic__Type_2enotT,V_24X1))
    <=> cCoq_2eInit_2eLogic__Type_2enotT___24a1(V_24X1) ) ).

fof('$adef_$_case_Coq.Init.Datatypes.bool$1167_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__case__Coq_2eInit_2eDatatypes_2ebool_241167,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__case__Coq_2eInit_2eDatatypes_2ebool_241167___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).

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_76846_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(c_24__lam__76846,V_24X1),V_24X2) = c_24__lam__76846___24a2(V_24X1,V_24X2) ).

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('$adef_$_prop_105548_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__prop__105548,V_24X1),V_24X2),V_24X3) = c_24__prop__105548___24a3(V_24X1,V_24X2,V_24X3) ).

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('$adef_$_lam_1162_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(c_24__lam__1162,V_24X1),V_24X2) = c_24__lam__1162___24a2(V_24X1,V_24X2) ).

fof('$adef_$_lam_76608_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__lam__76608,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__lam__76608___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).

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('$adef_$_let_var_6_p_86189_86192_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__let__var__6__p__86189__86192,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__let__var__6__p__86189__86192___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).

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('$adef_$_lam_67269_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__67269,V_24X1),V_24X2),V_24X3) = c_24__lam__67269___24a3(V_24X1,V_24X2,V_24X3) ).

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('$adef_Coq.setoid_ring.Ring_theory.power_theory_$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('$adef_Coq.Lists.List.fold_left_$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('$adef_Coq.setoid_ring.Ring_polynom.Pinj_$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('$adef_Coq.Sorting.Sorted.StronglySorted_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] :
      ( p(happ(happ(happ(cCoq_2eSorting_2eSorted_2eStronglySorted,V_24X1),V_24X2),V_24X3))
    <=> cCoq_2eSorting_2eSorted_2eStronglySorted___24a3(V_24X1,V_24X2,V_24X3) ) ).

fof('$adef_$_lam_105565_$a1',axiom,
    ! [V_24X1] : happ(c_24__lam__105565,V_24X1) = c_24__lam__105565___24a1(V_24X1) ).

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('$adef_Coq.Lists.List.Add_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] :
      ( p(happ(happ(happ(happ(cCoq_2eLists_2eList_2eAdd,V_24X1),V_24X2),V_24X3),V_24X4))
    <=> cCoq_2eLists_2eList_2eAdd___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).

fof('$adef_$_lam_486_$a5',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(c_24__lam__486,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = c_24__lam__486___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).

fof('$adef_Coq.micromega.RMicromega.CMinus_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2emicromega_2eRMicromega_2eCMinus,V_24X1),V_24X2) = cCoq_2emicromega_2eRMicromega_2eCMinus___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.Bool.Bool.ifb_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eBool_2eBool_2eifb,V_24X1),V_24X2),V_24X3) = cCoq_2eBool_2eBool_2eifb___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_$_lam_880_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__lam__880,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__lam__880___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).

fof('$adef_$_lam_76708_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__lam__76708,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__lam__76708___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).

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_916_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__916,V_24X1),V_24X2),V_24X3) = c_24__lam__916___24a3(V_24X1,V_24X2,V_24X3) ).

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('$adef_Coq.Init.Datatypes.S_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eInit_2eDatatypes_2eS,V_24X1) = cCoq_2eInit_2eDatatypes_2eS___24a1(V_24X1) ).

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('$adef_Coq.micromega.EnvRing.PEpow_$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('$adef_Coq.setoid_ring.Ring_theory.semi_morph_$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('$adef_Coq.ZArith.BinIntDef.Z.add_$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('$adef_$_lam_76497_$a1',axiom,
    ! [V_24X1] : happ(c_24__lam__76497,V_24X1) = c_24__lam__76497___24a1(V_24X1) ).

fof('$adef_$_prop_1436_$a1',axiom,
    ! [V_24X1] : happ(c_24__prop__1436,V_24X1) = c_24__prop__1436___24a1(V_24X1) ).

fof('$adef_Coq.micromega.RingMicromega.Formula_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2emicromega_2eRingMicromega_2eFormula,V_24X1) = cCoq_2emicromega_2eRingMicromega_2eFormula___24a1(V_24X1) ).

fof('$adef_Coq.Reals.RIneq.mknegreal_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eReals_2eRIneq_2emknegreal,V_24X1) = cCoq_2eReals_2eRIneq_2emknegreal___24a1(V_24X1) ).

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('$adef_Coq.micromega.ZMicromega.RatProof_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2emicromega_2eZMicromega_2eRatProof,V_24X1),V_24X2) = cCoq_2emicromega_2eZMicromega_2eRatProof___24a2(V_24X1,V_24X2) ).

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('$adef_Coq.micromega.RingMicromega.PolC_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2emicromega_2eRingMicromega_2ePolC,V_24X1) = cCoq_2emicromega_2eRingMicromega_2ePolC___24a1(V_24X1) ).

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('$adef_$_lam_1194_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__1194,V_24X1),V_24X2),V_24X3) = c_24__lam__1194___24a3(V_24X1,V_24X2,V_24X3) ).

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('$adef_$_prop_105547_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(c_24__prop__105547,V_24X1),V_24X2) = c_24__prop__105547___24a2(V_24X1,V_24X2) ).

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('$adef_$_lam_795_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__795,V_24X1),V_24X2),V_24X3) = c_24__lam__795___24a3(V_24X1,V_24X2,V_24X3) ).

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('$adef_Coq.ZArith.BinIntDef.Z.sub_$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('$adef_Coq.setoid_ring.Ring_polynom.PEopp_$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_948_$a5',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(c_24__lam__948,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = c_24__lam__948___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).

fof('$adef_$_lam_795_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__lam__795,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__lam__795___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).

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('$adef_Coq.setoid_ring.Ring_theory.pow_pos_$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('$adef_$_lam_67275_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__lam__67275,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__lam__67275___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).

fof('$adef_Coq.Relations.Relation_Operators.Ltl_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] :
      ( p(happ(happ(happ(happ(cCoq_2eRelations_2eRelation__Operators_2eLtl,V_24X1),V_24X2),V_24X3),V_24X4))
    <=> cCoq_2eRelations_2eRelation__Operators_2eLtl___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('$adef_$_lam_77113_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__lam__77113,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__lam__77113___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('$adef_Coq.micromega.Tauto.I_$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('$adef_$_lam_43_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__43,V_24X1),V_24X2),V_24X3) = c_24__lam__43___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_Coq.ZArith.BinIntDef.Z.even_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eZArith_2eBinIntDef_2eZ_2eeven,V_24X1) = cCoq_2eZArith_2eBinIntDef_2eZ_2eeven___24a1(V_24X1) ).

fof('$adef_$_lam_67076_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__67076,V_24X1),V_24X2),V_24X3) = c_24__lam__67076___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_$_lam_116_$a5',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(c_24__lam__116,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = c_24__lam__116___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).

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('$adef_Coq.setoid_ring.Ring_polynom.PEO_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2esetoid__ring_2eRing__polynom_2ePEO,V_24X1) = cCoq_2esetoid__ring_2eRing__polynom_2ePEO___24a1(V_24X1) ).

fof('$adef_Coq.Bool.Sumbool.sumbool_of_bool_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eBool_2eSumbool_2esumbool__of__bool,V_24X1) = cCoq_2eBool_2eSumbool_2esumbool__of__bool___24a1(V_24X1) ).

fof('$adef_IntMap.Mapiter.alist_semantics_$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('$adef_Coq.Numbers.BinNums.xO_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eNumbers_2eBinNums_2exO,V_24X1) = cCoq_2eNumbers_2eBinNums_2exO___24a1(V_24X1) ).

fof('$adef_$_case_Coq.Init.Datatypes.bool$76528_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__case__Coq_2eInit_2eDatatypes_2ebool_2476528,V_24X1),V_24X2),V_24X3) = c_24__case__Coq_2eInit_2eDatatypes_2ebool_2476528___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_$_lam_116_$a6',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(c_24__lam__116,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = c_24__lam__116___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).

fof('$adef_Coq.Lists.SetoidList.transpose_restr_$a5',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] :
      ( p(happ(happ(happ(happ(happ(cCoq_2eLists_2eSetoidList_2etranspose__restr,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5))
    <=> cCoq_2eLists_2eSetoidList_2etranspose__restr___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ) ).

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('$adef_$_case_Coq.Init.Datatypes.nat$98161_$a1',axiom,
    ! [V_24X1] : happ(c_24__case__Coq_2eInit_2eDatatypes_2enat_2498161,V_24X1) = c_24__case__Coq_2eInit_2eDatatypes_2enat_2498161___24a1(V_24X1) ).

fof('$adef_Coq.setoid_ring.Field_theory.semi_field_theory_$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_2eField__theory_2esemi__field__theory,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8))
    <=> cCoq_2esetoid__ring_2eField__theory_2esemi__field__theory___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8) ) ).

fof('$adef_$_lam_77983_$a2',axiom,
    ! [V_24X1,V_24X2] :
      ( p(happ(happ(c_24__lam__77983,V_24X1),V_24X2))
    <=> c_24__lam__77983___24a2(V_24X1,V_24X2) ) ).

fof('$adef_Coq.Init.Decimal.D8_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eInit_2eDecimal_2eD8,V_24X1) = cCoq_2eInit_2eDecimal_2eD8___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('$adef_Coq.micromega.RMicromega.CQ_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2emicromega_2eRMicromega_2eCQ,V_24X1) = cCoq_2emicromega_2eRMicromega_2eCQ___24a1(V_24X1) ).

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('$adef_Coq.setoid_ring.Ring_polynom.PEX_$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('$adef_Coq.micromega.OrderedRing.SOR_$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_2emicromega_2eOrderedRing_2eSOR,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9),V_24X10))
    <=> cCoq_2emicromega_2eOrderedRing_2eSOR___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10) ) ).

fof('$adef_Coq.Init.Datatypes.sum_$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('$adef_Coq.NArith.BinNatDef.N.min_$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('$adef_$_case_Coq.Init.Datatypes.bool$1360_$a5',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(c_24__case__Coq_2eInit_2eDatatypes_2ebool_241360,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = c_24__case__Coq_2eInit_2eDatatypes_2ebool_241360___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).

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('$adef_Coq.Vectors.Fin.t_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eVectors_2eFin_2et,V_24X1) = cCoq_2eVectors_2eFin_2et___24a1(V_24X1) ).

fof('$adef_Coq.setoid_ring.Field_theory.FEO_$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('$adef_Coq.Lists.List.In_$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('$adef_IntMap.Map.MapPut_behind_$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('$adef_$_lam_981_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(c_24__lam__981,V_24X1),V_24X2) = c_24__lam__981___24a2(V_24X1,V_24X2) ).

fof('$adef_$_lam_188_$a5',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(c_24__lam__188,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = c_24__lam__188___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).

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('$adef_Coq.Init.Datatypes.andb_$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('$adef_$_lam_800_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__800,V_24X1),V_24X2),V_24X3) = c_24__lam__800___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_Coq.micromega.ZMicromega.CutProof_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2emicromega_2eZMicromega_2eCutProof,V_24X1),V_24X2) = cCoq_2emicromega_2eZMicromega_2eCutProof___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('$adef_Coq.Structures.GenericMinMax.gmin_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2eStructures_2eGenericMinMax_2egmin,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2eStructures_2eGenericMinMax_2egmin___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).

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('$adef_Coq.Init.Decimal.D7_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eInit_2eDecimal_2eD7,V_24X1) = cCoq_2eInit_2eDecimal_2eD7___24a1(V_24X1) ).

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('$adef_Coq.setoid_ring.Field_theory.rsplit_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2esetoid__ring_2eField__theory_2ersplit,V_24X1) = cCoq_2esetoid__ring_2eField__theory_2ersplit___24a1(V_24X1) ).

fof('$adef_Coq.Init.Decimal.D2_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eInit_2eDecimal_2eD2,V_24X1) = cCoq_2eInit_2eDecimal_2eD2___24a1(V_24X1) ).

fof('$adef_$_case_Coq.Init.Datatypes.bool$1173_$a5',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(c_24__case__Coq_2eInit_2eDatatypes_2ebool_241173,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = c_24__case__Coq_2eInit_2eDatatypes_2ebool_241173___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('$adef_IntMap.Map.MapSingleton_$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('$adef_$_lam_76850_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(c_24__lam__76850,V_24X1),V_24X2) = c_24__lam__76850___24a2(V_24X1,V_24X2) ).

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('$adef_$_lam_105565_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(c_24__lam__105565,V_24X1),V_24X2) = c_24__lam__105565___24a2(V_24X1,V_24X2) ).

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('$adef_Coq.Init.Datatypes.snd_$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('$adef_IntMap.Fset.in_dom_$a1',axiom,
    ! [V_24X1] : happ(cIntMap_2eFset_2ein__dom,V_24X1) = cIntMap_2eFset_2ein__dom___24a1(V_24X1) ).

fof('$adef_$_lam_76759_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__lam__76759,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__lam__76759___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).

fof('$adef_$_lam_912_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(c_24__lam__912,V_24X1),V_24X2) = c_24__lam__912___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('$adef_Coq.Init.Decimal.D0_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eInit_2eDecimal_2eD0,V_24X1) = cCoq_2eInit_2eDecimal_2eD0___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('$adef_$_lam_916_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__lam__916,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__lam__916___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).

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_76869_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(c_24__lam__76869,V_24X1),V_24X2) = c_24__lam__76869___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_981_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] :
      ( p(happ(happ(happ(c_24__lam__981,V_24X1),V_24X2),V_24X3))
    <=> c_24__lam__981___24a3(V_24X1,V_24X2,V_24X3) ) ).

fof('$adef_Coq.Lists.SetoidList.transpose_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] :
      ( p(happ(happ(happ(happ(cCoq_2eLists_2eSetoidList_2etranspose,V_24X1),V_24X2),V_24X3),V_24X4))
    <=> cCoq_2eLists_2eSetoidList_2etranspose___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).

fof('$adef_Coq.Init.Datatypes.nat_rect_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eInit_2eDatatypes_2enat__rect,V_24X1) = cCoq_2eInit_2eDatatypes_2enat__rect___24a1(V_24X1) ).

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('$adef_Coq.Init.Datatypes.inr_$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_67217_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__prop__67217,V_24X1),V_24X2),V_24X3) = c_24__prop__67217___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_Coq.micromega.VarMap.Branch_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2emicromega_2eVarMap_2eBranch,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2emicromega_2eVarMap_2eBranch___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).

fof('$adef_Coq.Reals.RIneq.mkposreal_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eReals_2eRIneq_2emkposreal,V_24X1) = cCoq_2eReals_2eRIneq_2emkposreal___24a1(V_24X1) ).

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_872_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__lam__872,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__lam__872___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).

fof('$adef_$_lam_768_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__lam__768,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__lam__768___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).

fof('$adef_$_lam_76584_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__lam__76584,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__lam__76584___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).

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('$adef_Coq.Structures.OrderedTypeEx.PositiveOrderedTypeBits.bits_lt_$a2',axiom,
    ! [V_24X1,V_24X2] :
      ( p(happ(happ(cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2ebits__lt,V_24X1),V_24X2))
    <=> cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2ebits__lt___24a2(V_24X1,V_24X2) ) ).

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('$adef_Coq.PArith.BinPosDef.Pos.succ_$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('$adef_$_case_Coq.Init.Datatypes.bool$1250_$a5',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(c_24__case__Coq_2eInit_2eDatatypes_2ebool_241250,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = c_24__case__Coq_2eInit_2eDatatypes_2ebool_241250___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).

fof('$adef_Coq.Relations.Relation_Operators.Desc_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] :
      ( p(happ(happ(happ(cCoq_2eRelations_2eRelation__Operators_2eDesc,V_24X1),V_24X2),V_24X3))
    <=> cCoq_2eRelations_2eRelation__Operators_2eDesc___24a3(V_24X1,V_24X2,V_24X3) ) ).

fof('$adef_$_lam_1372_$a1',axiom,
    ! [V_24X1] : happ(c_24__lam__1372,V_24X1) = c_24__lam__1372___24a1(V_24X1) ).

fof('$adef_$_prop_105527_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__prop__105527,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__prop__105527___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).

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('$adef_$_lam_76596_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__76596,V_24X1),V_24X2),V_24X3) = c_24__lam__76596___24a3(V_24X1,V_24X2,V_24X3) ).

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('$adef_Coq.micromega.DeclConstant.DeclaredConstant_$a2',axiom,
    ! [V_24X1,V_24X2] :
      ( p(happ(happ(cCoq_2emicromega_2eDeclConstant_2eDeclaredConstant,V_24X1),V_24X2))
    <=> cCoq_2emicromega_2eDeclConstant_2eDeclaredConstant___24a2(V_24X1,V_24X2) ) ).

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('$adef_$_prop_105531_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__prop__105531,V_24X1),V_24X2),V_24X3) = c_24__prop__105531___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_$_lam_76154_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__lam__76154,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__lam__76154___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).

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('$adef_IntMap.Mapsubset.MapDisjoint_2_$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('$adef_Coq.setoid_ring.InitialRing.gen_phiPOS_$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('$adef_Coq.Init.Peano.IsSucc_$a1',axiom,
    ! [V_24X1] :
      ( p(happ(cCoq_2eInit_2ePeano_2eIsSucc,V_24X1))
    <=> cCoq_2eInit_2ePeano_2eIsSucc___24a1(V_24X1) ) ).

fof('$adef_$_case_Coq.Init.Datatypes.bool$1210_$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_241210,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = c_24__case__Coq_2eInit_2eDatatypes_2ebool_241210___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).

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('$adef_Coq.Init.Datatypes.eq_true_$a1',axiom,
    ! [V_24X1] :
      ( p(happ(cCoq_2eInit_2eDatatypes_2eeq__true,V_24X1))
    <=> cCoq_2eInit_2eDatatypes_2eeq__true___24a1(V_24X1) ) ).

fof('$adef_Coq.micromega.VarMap.Elt_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2emicromega_2eVarMap_2eElt,V_24X1),V_24X2) = cCoq_2emicromega_2eVarMap_2eElt___24a2(V_24X1,V_24X2) ).

fof('$adef_Mapcanon.MapCanon.MapCanonicalize_$a1',axiom,
    ! [V_24X1] : happ(cMapcanon_2eMapCanon_2eMapCanonicalize,V_24X1) = cMapcanon_2eMapCanon_2eMapCanonicalize___24a1(V_24X1) ).

fof('$adef_Coq.Init.Decimal.Decimal_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eDecimal_2eDecimal,V_24X1),V_24X2) = cCoq_2eInit_2eDecimal_2eDecimal___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.Init.Nat.tail_add_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eNat_2etail__add,V_24X1),V_24X2) = cCoq_2eInit_2eNat_2etail__add___24a2(V_24X1,V_24X2) ).

fof('$adef_$_lam_76154_$a5',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(c_24__lam__76154,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = c_24__lam__76154___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).

fof('$adef_Coq.Strings.Ascii.nat_of_ascii_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eStrings_2eAscii_2enat__of__ascii,V_24X1) = cCoq_2eStrings_2eAscii_2enat__of__ascii___24a1(V_24X1) ).

fof('$adef_$_case_Coq.Numbers.BinNums.Z$98156_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__case__Coq_2eNumbers_2eBinNums_2eZ_2498156,V_24X1),V_24X2),V_24X3) = c_24__case__Coq_2eNumbers_2eBinNums_2eZ_2498156___24a3(V_24X1,V_24X2,V_24X3) ).

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('$adef_Coq.micromega.RMicromega.CZ_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2emicromega_2eRMicromega_2eCZ,V_24X1) = cCoq_2emicromega_2eRMicromega_2eCZ___24a1(V_24X1) ).

fof('$adef_$_case_Coq.Init.Datatypes.option$76560_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__case__Coq_2eInit_2eDatatypes_2eoption_2476560,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__case__Coq_2eInit_2eDatatypes_2eoption_2476560___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).

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('$adef_Coq.setoid_ring.Field_theory.linear_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2esetoid__ring_2eField__theory_2elinear,V_24X1) = cCoq_2esetoid__ring_2eField__theory_2elinear___24a1(V_24X1) ).

fof('$adef_$_lam_948_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__lam__948,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__lam__948___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).

fof('$adef_Coq.Arith.PeanoNat.Nat.recursion_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eArith_2ePeanoNat_2eNat_2erecursion,V_24X1) = cCoq_2eArith_2ePeanoNat_2eNat_2erecursion___24a1(V_24X1) ).

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('$adef_Coq.Structures.OrderedTypeEx.String_as_OT.lts_$a2',axiom,
    ! [V_24X1,V_24X2] :
      ( p(happ(happ(cCoq_2eStructures_2eOrderedTypeEx_2eString__as__OT_2elts,V_24X1),V_24X2))
    <=> cCoq_2eStructures_2eOrderedTypeEx_2eString__as__OT_2elts___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('$adef_Coq.ZArith.BinIntDef.Z.opp_$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('$adef_Coq.Numbers.BinNums.Zneg_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eNumbers_2eBinNums_2eZneg,V_24X1) = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(V_24X1) ).

fof('$adef_Coq.Reals.RIneq.mknonnegreal_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eReals_2eRIneq_2emknonnegreal,V_24X1) = cCoq_2eReals_2eRIneq_2emknonnegreal___24a1(V_24X1) ).

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('$adef_$_case_Coq.Init.Datatypes.list$97885_$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_2elist_2497885,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = c_24__case__Coq_2eInit_2eDatatypes_2elist_2497885___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).

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('$adef_Coq.NArith.BinNatDef.N.to_nat_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eNArith_2eBinNatDef_2eN_2eto__nat,V_24X1) = cCoq_2eNArith_2eBinNatDef_2eN_2eto__nat___24a1(V_24X1) ).

fof('$adef_IntMap.Map.MapEmptyp_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cIntMap_2eMap_2eMapEmptyp,V_24X1),V_24X2) = cIntMap_2eMap_2eMapEmptyp___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.ZArith.Zeven.Zeven_$a1',axiom,
    ! [V_24X1] :
      ( p(happ(cCoq_2eZArith_2eZeven_2eZeven,V_24X1))
    <=> cCoq_2eZArith_2eZeven_2eZeven___24a1(V_24X1) ) ).

fof('$adef_$_lam_77283_$a5',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(c_24__lam__77283,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = c_24__lam__77283___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).

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('$adef_IntMap.Lsort.alist_sorted_1_$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('$adef_IntMap.Mapsubset.MapDisjoint_1_$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('$adef_$_prop_1437_$a1',axiom,
    ! [V_24X1] : happ(c_24__prop__1437,V_24X1) = c_24__prop__1437___24a1(V_24X1) ).

fof('$adef_Coq.Arith.Between.between_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] :
      ( p(happ(happ(happ(cCoq_2eArith_2eBetween_2ebetween,V_24X1),V_24X2),V_24X3))
    <=> cCoq_2eArith_2eBetween_2ebetween___24a3(V_24X1,V_24X2,V_24X3) ) ).

fof('$adef_Coq.micromega.RingMicromega.PsatzIn_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2emicromega_2eRingMicromega_2ePsatzIn,V_24X1),V_24X2) = cCoq_2emicromega_2eRingMicromega_2ePsatzIn___24a2(V_24X1,V_24X2) ).

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('$adef_Coq.setoid_ring.Ring_polynom.PEI_$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('$adef_Coq.NArith.Ndigits.Neven_$a1',axiom,
    ! [V_24X1] :
      ( p(happ(cCoq_2eNArith_2eNdigits_2eNeven,V_24X1))
    <=> cCoq_2eNArith_2eNdigits_2eNeven___24a1(V_24X1) ) ).

fof('$adef_$_lam_230_$a6',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(c_24__lam__230,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = c_24__lam__230___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).

fof('$adef_$_lam_188_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__lam__188,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__lam__188___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).

fof('$adef_$_lam_76596_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__lam__76596,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__lam__76596___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).

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('$adef_Coq.Init.Datatypes.prod_rect_$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('$adef_$_lam_864_$a1',axiom,
    ! [V_24X1] : happ(c_24__lam__864,V_24X1) = c_24__lam__864___24a1(V_24X1) ).

fof('$adef_$_lam_77846_$a5',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(c_24__lam__77846,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = c_24__lam__77846___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).

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('$adef_Coq.setoid_ring.Field_theory.FEopp_$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('$adef_Coq.Lists.SetoidList.eqlistA_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] :
      ( p(happ(happ(happ(happ(cCoq_2eLists_2eSetoidList_2eeqlistA,V_24X1),V_24X2),V_24X3),V_24X4))
    <=> cCoq_2eLists_2eSetoidList_2eeqlistA___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).

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('$adef_IntMap.Map.MapGet_$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('$adef_Coq.ZArith.Znumtheory.Euclid_intro_$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('$adef_Coq.micromega.RingMicromega.PsatzMulE_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2emicromega_2eRingMicromega_2ePsatzMulE,V_24X1),V_24X2),V_24X3) = cCoq_2emicromega_2eRingMicromega_2ePsatzMulE___24a3(V_24X1,V_24X2,V_24X3) ).

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('$adef_Coq.Init.Specif.sumbool_rec_$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('$adef_Coq.micromega.Refl.make_impl_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] :
      ( p(happ(happ(happ(happ(cCoq_2emicromega_2eRefl_2emake__impl,V_24X1),V_24X2),V_24X3),V_24X4))
    <=> cCoq_2emicromega_2eRefl_2emake__impl___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).

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('$adef_Coq.FSets.FSetPositive.PositiveSet.In_$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('$adef_$_lam_1181_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__1181,V_24X1),V_24X2),V_24X3) = c_24__lam__1181___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_Coq.Init.Nat.leb_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eNat_2eleb,V_24X1),V_24X2) = cCoq_2eInit_2eNat_2eleb___24a2(V_24X1,V_24X2) ).

fof('$adef_$_prop_1020_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__prop__1020,V_24X1),V_24X2),V_24X3) = c_24__prop__1020___24a3(V_24X1,V_24X2,V_24X3) ).

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('$adef_Hammer.Tactics.Tactics.rdone_$a2',axiom,
    ! [V_24X1,V_24X2] :
      ( p(happ(happ(cHammer_2eTactics_2eTactics_2erdone,V_24X1),V_24X2))
    <=> cHammer_2eTactics_2eTactics_2erdone___24a2(V_24X1,V_24X2) ) ).

fof('$adef_$_prop_105549_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__prop__105549,V_24X1),V_24X2),V_24X3) = c_24__prop__105549___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_IntMap.Mapiter.alist_$a1',axiom,
    ! [V_24X1] : happ(cIntMap_2eMapiter_2ealist,V_24X1) = cIntMap_2eMapiter_2ealist___24a1(V_24X1) ).

fof('$adef_Coq.setoid_ring.Ring_theory.id_phi_N_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2esetoid__ring_2eRing__theory_2eid__phi__N,V_24X1) = cCoq_2esetoid__ring_2eRing__theory_2eid__phi__N___24a1(V_24X1) ).

fof('$adef_$_prop_704_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(c_24__prop__704,V_24X1),V_24X2) = c_24__prop__704___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('$adef_IntMap.Map.MapMerge_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cIntMap_2eMap_2eMapMerge,V_24X1),V_24X2) = cIntMap_2eMap_2eMapMerge___24a2(V_24X1,V_24X2) ).

fof('$adef_$_lam_1181_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__lam__1181,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__lam__1181___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).

fof('$adef_$_lam_486_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__486,V_24X1),V_24X2),V_24X3) = c_24__lam__486___24a3(V_24X1,V_24X2,V_24X3) ).

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('$adef_Coq.Setoids.Setoid.Setoid_Theory_$a2',axiom,
    ! [V_24X1,V_24X2] :
      ( p(happ(happ(cCoq_2eSetoids_2eSetoid_2eSetoid__Theory,V_24X1),V_24X2))
    <=> cCoq_2eSetoids_2eSetoid_2eSetoid__Theory___24a2(V_24X1,V_24X2) ) ).

fof('$adef_$_lam_912_$a1',axiom,
    ! [V_24X1] : happ(c_24__lam__912,V_24X1) = c_24__lam__912___24a1(V_24X1) ).

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('$adef_IntMap.Lsort.alist_sorted_$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('$adef_Coq.Init.Decimal.Neg_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eInit_2eDecimal_2eNeg,V_24X1) = cCoq_2eInit_2eDecimal_2eNeg___24a1(V_24X1) ).

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('$adef_IntMap.Map.MapRemove_$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('$adef_Coq.Init.Decimal.D9_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eInit_2eDecimal_2eD9,V_24X1) = cCoq_2eInit_2eDecimal_2eD9___24a1(V_24X1) ).

fof('$adef_Coq.Init.Byte.byte_of_byte_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eInit_2eByte_2ebyte__of__byte,V_24X1) = cCoq_2eInit_2eByte_2ebyte__of__byte___24a1(V_24X1) ).

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('$adef_Coq.micromega.Tauto.A_$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('$adef_IntMap.Mapiter.alist_of_Map_$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_1372_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__1372,V_24X1),V_24X2),V_24X3) = c_24__lam__1372___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('$adef_$_lam_449_$a5',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(c_24__lam__449,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = c_24__lam__449___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).

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('$adef_Coq.setoid_ring.Field_theory.almost_field_theory_$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('$adef_Coq.Arith.Wf_nat.ltof_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] :
      ( p(happ(happ(happ(happ(cCoq_2eArith_2eWf__nat_2eltof,V_24X1),V_24X2),V_24X3),V_24X4))
    <=> cCoq_2eArith_2eWf__nat_2eltof___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).

fof('$adef_Coq.Sorting.Sorted.Sorted_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] :
      ( p(happ(happ(happ(cCoq_2eSorting_2eSorted_2eSorted,V_24X1),V_24X2),V_24X3))
    <=> cCoq_2eSorting_2eSorted_2eSorted___24a3(V_24X1,V_24X2,V_24X3) ) ).

fof('$adef_$_lam_58_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__lam__58,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__lam__58___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).

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('$adef_$_lam_67269_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__lam__67269,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__lam__67269___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).

fof('$adef_$_lam_1157_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__lam__1157,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__lam__1157___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).

fof('$adef_Coq.micromega.RMicromega.CInv_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2emicromega_2eRMicromega_2eCInv,V_24X1) = cCoq_2emicromega_2eRMicromega_2eCInv___24a1(V_24X1) ).

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('$adef_Coq.PArith.BinPosDef.Pos.testbit_$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('$adef_IntMap.Map.newMap_$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('$adef_Coq.Init.Specif.exist_$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('$adef_Coq.ZArith.BinInt.Z.le_$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('$adef_$_lam_43_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(c_24__lam__43,V_24X1),V_24X2) = c_24__lam__43___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_76173_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__lam__76173,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__lam__76173___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).

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('$adef_Coq.PArith.BinPosDef.Pos.compare_cont_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare__cont,V_24X1) = cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare__cont___24a1(V_24X1) ).

fof('$adef_$_lam_449_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__449,V_24X1),V_24X2),V_24X3) = c_24__lam__449___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_$_case_Coq.Init.Datatypes.list$97972_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__case__Coq_2eInit_2eDatatypes_2elist_2497972,V_24X1),V_24X2),V_24X3) = c_24__case__Coq_2eInit_2eDatatypes_2elist_2497972___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('$adef_Coq.Init.Wf.well_founded_$a2',axiom,
    ! [V_24X1,V_24X2] :
      ( p(happ(happ(cCoq_2eInit_2eWf_2ewell__founded,V_24X1),V_24X2))
    <=> cCoq_2eInit_2eWf_2ewell__founded___24a2(V_24X1,V_24X2) ) ).

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('$adef_Coq.NArith.Ndigits.Nodd_$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('$adef_Coq.micromega.RingMicromega.PsatzSquare_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2emicromega_2eRingMicromega_2ePsatzSquare,V_24X1),V_24X2) = cCoq_2emicromega_2eRingMicromega_2ePsatzSquare___24a2(V_24X1,V_24X2) ).

fof('$adef_$_lam_76842_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__76842,V_24X1),V_24X2),V_24X3) = c_24__lam__76842___24a3(V_24X1,V_24X2,V_24X3) ).

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('$adef_Coq.Init.Datatypes.pair_$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('$adef_$_lam_872_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__872,V_24X1),V_24X2),V_24X3) = c_24__lam__872___24a3(V_24X1,V_24X2,V_24X3) ).

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('$adef_$_prop_105530_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__prop__105530,V_24X1),V_24X2),V_24X3) = c_24__prop__105530___24a3(V_24X1,V_24X2,V_24X3) ).

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_76708_$a5',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(c_24__lam__76708,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = c_24__lam__76708___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).

fof('$adef_$_lam_1378_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(c_24__lam__1378,V_24X1),V_24X2) = c_24__lam__1378___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.micromega.RingMicromega.Psatz_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2emicromega_2eRingMicromega_2ePsatz,V_24X1) = cCoq_2emicromega_2eRingMicromega_2ePsatz___24a1(V_24X1) ).

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('$adef_Coq.micromega.EnvRing.Pc_$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('$adef_Coq.Structures.OrderedType.EQ_$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('$adef_Coq.Numbers.BinNums.Zpos_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eNumbers_2eBinNums_2eZpos,V_24X1) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(V_24X1) ).

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('$adef_Coq.NArith.BinNatDef.N.double_$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('$adef_Coq.Init.Nat.sub_$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('$adef_Coq.PArith.BinPos.Pos.SubMaskSpec_$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('$adef_Coq.Bool.Bool.ReflectF_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eBool_2eBool_2eReflectF,V_24X1) = cCoq_2eBool_2eBool_2eReflectF___24a1(V_24X1) ).

fof('$adef_Coq.micromega.ZMicromega.Vars.Facts.MP.Dec.FSetDecideAuxiliary.FSet_Prop_$a1',axiom,
    ! [V_24X1] :
      ( p(happ(cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__Prop,V_24X1))
    <=> cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__Prop___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('$adef_Coq.Bool.Bool.ReflectT_$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('$adef_$_case_Coq.Init.Datatypes.nat$98139_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__case__Coq_2eInit_2eDatatypes_2enat_2498139,V_24X1),V_24X2),V_24X3) = c_24__case__Coq_2eInit_2eDatatypes_2enat_2498139___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_$_lam_77275_$a5',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(c_24__lam__77275,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = c_24__lam__77275___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).

fof('$adef_Coq.Lists.List.Forall_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] :
      ( p(happ(happ(happ(cCoq_2eLists_2eList_2eForall,V_24X1),V_24X2),V_24X3))
    <=> cCoq_2eLists_2eList_2eForall___24a3(V_24X1,V_24X2,V_24X3) ) ).

fof('$adef_$_let_var_6_p_86191_86193_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__let__var__6__p__86191__86193,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__let__var__6__p__86191__86193___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).

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('$adef_$_case_Coq.Init.Datatypes.bool$1244_$a5',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(c_24__case__Coq_2eInit_2eDatatypes_2ebool_241244,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = c_24__case__Coq_2eInit_2eDatatypes_2ebool_241244___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).

fof('$adef_Coq.Init.Decimal.D5_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eInit_2eDecimal_2eD5,V_24X1) = cCoq_2eInit_2eDecimal_2eD5___24a1(V_24X1) ).

fof('$adef_$_lam_768_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__768,V_24X1),V_24X2),V_24X3) = c_24__lam__768___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('$adef_Coq.PArith.BinPosDef.Pos.lxor_$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('$adef_Coq.micromega.VarMap.Empty_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2emicromega_2eVarMap_2eEmpty,V_24X1) = cCoq_2emicromega_2eVarMap_2eEmpty___24a1(V_24X1) ).

fof('$adef_Coq.micromega.RingMicromega.PsatzAdd_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2emicromega_2eRingMicromega_2ePsatzAdd,V_24X1),V_24X2),V_24X3) = cCoq_2emicromega_2eRingMicromega_2ePsatzAdd___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_$_lam_703_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(c_24__lam__703,V_24X1),V_24X2) = c_24__lam__703___24a2(V_24X1,V_24X2) ).

fof('$adef_$_lam_58_$a5',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(c_24__lam__58,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = c_24__lam__58___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).

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('$adef_Coq.Init.Decimal.DecimalExp_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eInit_2eDecimal_2eDecimalExp,V_24X1),V_24X2),V_24X3) = cCoq_2eInit_2eDecimal_2eDecimalExp___24a3(V_24X1,V_24X2,V_24X3) ).

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('$adef_$_lam_76499_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(c_24__lam__76499,V_24X1),V_24X2) = c_24__lam__76499___24a2(V_24X1,V_24X2) ).

fof('$adef_$_lam_76850_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__76850,V_24X1),V_24X2),V_24X3) = c_24__lam__76850___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_$_lam_703_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] :
      ( p(happ(happ(happ(c_24__lam__703,V_24X1),V_24X2),V_24X3))
    <=> c_24__lam__703___24a3(V_24X1,V_24X2,V_24X3) ) ).

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('$adef_Coq.micromega.RingMicromega.PsatzC_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2emicromega_2eRingMicromega_2ePsatzC,V_24X1),V_24X2) = cCoq_2emicromega_2eRingMicromega_2ePsatzC___24a2(V_24X1,V_24X2) ).

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('$adef_Coq.setoid_ring.InitialRing.mkhypo_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2esetoid__ring_2eInitialRing_2emkhypo,V_24X1),V_24X2) = cCoq_2esetoid__ring_2eInitialRing_2emkhypo___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('$adef_Coq.ZArith.BinIntDef.Z.div_$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('$adef_IntMap.Mapiter.acons_$a1',axiom,
    ! [V_24X1] : happ(cIntMap_2eMapiter_2eacons,V_24X1) = cIntMap_2eMapiter_2eacons___24a1(V_24X1) ).

fof('$adef_Coq.micromega.RingMicromega.PsatzZ_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2emicromega_2eRingMicromega_2ePsatzZ,V_24X1) = cCoq_2emicromega_2eRingMicromega_2ePsatzZ___24a1(V_24X1) ).

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('$adef_Coq.Lists.List.fold_right_$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('$adef_$_fix_98017_v_CANONICAL_1_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__fix__98017__v__CANONICAL__1,V_24X1),V_24X2),V_24X3) = c_24__fix__98017__v__CANONICAL__1___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_$_lam_67335_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__67335,V_24X1),V_24X2),V_24X3) = c_24__lam__67335___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('$adef_$_lam_77113_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__77113,V_24X1),V_24X2),V_24X3) = c_24__lam__77113___24a3(V_24X1,V_24X2,V_24X3) ).

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('$adef_IntMap.Mapsubset.MapSubset_1_$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('$adef_$_fix_105664_v_CANONICAL_0_$a1',axiom,
    ! [V_24X1] : happ(c_24__fix__105664__v__CANONICAL__0,V_24X1) = c_24__fix__105664__v__CANONICAL__0___24a1(V_24X1) ).

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('$adef_Coq.Init.Specif.left_$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('$adef_Coq.Init.Specif.sigT_$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('$adef_$_lam_77119_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__lam__77119,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__lam__77119___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).

fof('$adef_Coq.Init.Decimal.D3_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eInit_2eDecimal_2eD3,V_24X1) = cCoq_2eInit_2eDecimal_2eD3___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_77812_$a5',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(c_24__lam__77812,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = c_24__lam__77812___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).

fof('$adef_IntMap.Map.Map_$a1',axiom,
    ! [V_24X1] : happ(cIntMap_2eMap_2eMap,V_24X1) = cIntMap_2eMap_2eMap___24a1(V_24X1) ).

fof('$adef_$_lam_800_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(c_24__lam__800,V_24X1),V_24X2) = c_24__lam__800___24a2(V_24X1,V_24X2) ).

fof('$adef_$_lam_67335_$a1',axiom,
    ! [V_24X1] : happ(c_24__lam__67335,V_24X1) = c_24__lam__67335___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('$adef_Coq.micromega.EnvRing.PEadd_$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('$adef_IntMap.Mapiter.MapFold_state_$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('$adef_$_prop_105532_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__prop__105532,V_24X1),V_24X2),V_24X3) = c_24__prop__105532___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_$_prop_105528_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__prop__105528,V_24X1),V_24X2),V_24X3) = c_24__prop__105528___24a3(V_24X1,V_24X2,V_24X3) ).

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('$adef_Coq.NArith.BinNatDef.N.eqb_$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('$adef_Coq.micromega.ZMicromega.is_diff_env_elt_$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('$adef_Coq.NArith.BinNat.N.le_$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('$adef_$_lam_733_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(c_24__lam__733,V_24X1),V_24X2) = c_24__lam__733___24a2(V_24X1,V_24X2) ).

fof('$adef_$_lam_1378_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__1378,V_24X1),V_24X2),V_24X3) = c_24__lam__1378___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('$adef_Coq.ZArith.Zpower.Zdiv_rest_proofs_$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('$adef_Coq.PArith.BinPosDef.Pos.of_succ_nat_$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('$adef_Coq.PArith.BinPosDef.Pos.add_$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('$adef_Coq.Init.Peano.gt_$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_67891',axiom,
    ! [V_24Y] :
      ( c_24__type__67891___24t(V_24Y)
    <=> t(V_24Y,c_24__type__67891) ) ).

fof('$tdef_$_type_67857',axiom,
    ! [V_24X1,V_24X2,V_24Y] :
      ( c_24__type__67857___24t(V_24X1,V_24X2,V_24Y)
    <=> t(V_24Y,c_24__type__67857___24a2(V_24X1,V_24X2)) ) ).

fof('$tdef_$_type_67686',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24Y] :
      ( c_24__type__67686___24t(V_24X1,V_24X2,V_24X3,V_24Y)
    <=> t(V_24Y,c_24__type__67686___24a3(V_24X1,V_24X2,V_24X3)) ) ).

fof('$tdef_$_type_80245',axiom,
    ! [V_24Y] :
      ( c_24__type__80245___24t(V_24Y)
    <=> t(V_24Y,c_24__type__80245) ) ).

fof('$tdef_Coq.micromega.RingMicromega.Psatz',axiom,
    ! [V_24X1,V_24Y] :
      ( cCoq_2emicromega_2eRingMicromega_2ePsatz___24t(V_24X1,V_24Y)
    <=> t(V_24Y,cCoq_2emicromega_2eRingMicromega_2ePsatz___24a1(V_24X1)) ) ).

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('$tdef_$_type_82174',axiom,
    ! [V_24Y] :
      ( c_24__type__82174___24t(V_24Y)
    <=> t(V_24Y,c_24__type__82174) ) ).

fof('$tdef_$_type_95864',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__95864___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__95864___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.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_67796',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24Y] :
      ( c_24__type__67796___24t(V_24X1,V_24X2,V_24X3,V_24Y)
    <=> t(V_24Y,c_24__type__67796___24a3(V_24X1,V_24X2,V_24X3)) ) ).

fof('$tdef_$_type_92953',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
      ( c_24__type__92953___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
    <=> t(V_24Y,c_24__type__92953___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).

fof('$tdef_$_type_103141',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__103141___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__103141___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_85428',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__85428___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__85428___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).

fof('$tdef_$_type_87473',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__87473___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__87473___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_67383',axiom,
    ! [V_24Y] :
      ( c_24__type__67383___24t(V_24Y)
    <=> t(V_24Y,c_24__type__67383) ) ).

fof('$tdef_$_type_68135',axiom,
    ! [V_24Y] :
      ( c_24__type__68135___24t(V_24Y)
    <=> t(V_24Y,c_24__type__68135) ) ).

fof('$tdef_$_type_105577',axiom,
    ! [V_24Y] :
      ( c_24__type__105577___24t(V_24Y)
    <=> t(V_24Y,c_24__type__105577) ) ).

fof('$tdef_$_type_105559',axiom,
    ! [V_24Y] :
      ( c_24__type__105559___24t(V_24Y)
    <=> t(V_24Y,c_24__type__105559) ) ).

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_89914',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
      ( c_24__type__89914___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
    <=> t(V_24Y,c_24__type__89914___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).

fof('$tdef_$_type_67759',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24Y] :
      ( c_24__type__67759___24t(V_24X1,V_24X2,V_24X3,V_24Y)
    <=> t(V_24Y,c_24__type__67759___24a3(V_24X1,V_24X2,V_24X3)) ) ).

fof('$tdef_$_type_86966',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
      ( c_24__type__86966___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
    <=> t(V_24Y,c_24__type__86966___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).

fof('$tdef_$_type_77468',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24Y] :
      ( c_24__type__77468___24t(V_24X1,V_24X2,V_24X3,V_24Y)
    <=> t(V_24Y,c_24__type__77468___24a3(V_24X1,V_24X2,V_24X3)) ) ).

fof('$tdef_$_type_77506',axiom,
    ! [V_24Y] :
      ( c_24__type__77506___24t(V_24Y)
    <=> t(V_24Y,c_24__type__77506) ) ).

fof('$tdef_Coq.micromega.VarMap.t',axiom,
    ! [V_24X1,V_24Y] :
      ( cCoq_2emicromega_2eVarMap_2et___24t(V_24X1,V_24Y)
    <=> t(V_24Y,cCoq_2emicromega_2eVarMap_2et___24a1(V_24X1)) ) ).

fof('$tdef_Coq.Reals.RIneq.nonposreal',axiom,
    ! [V_24Y] :
      ( cCoq_2eReals_2eRIneq_2enonposreal___24t(V_24Y)
    <=> t(V_24Y,cCoq_2eReals_2eRIneq_2enonposreal) ) ).

fof('$tdef_$_type_87047',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
      ( c_24__type__87047___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
    <=> t(V_24Y,c_24__type__87047___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).

fof('$tdef_$_type_81049',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y] :
      ( c_24__type__81049___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y)
    <=> t(V_24Y,c_24__type__81049___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6)) ) ).

fof('$tdef_$_type_82485',axiom,
    ! [V_24Y] :
      ( c_24__type__82485___24t(V_24Y)
    <=> t(V_24Y,c_24__type__82485) ) ).

fof('$tdef_$_type_77352',axiom,
    ! [V_24Y] :
      ( c_24__type__77352___24t(V_24Y)
    <=> t(V_24Y,c_24__type__77352) ) ).

fof('$tdef_$_type_67486',axiom,
    ! [V_24Y] :
      ( c_24__type__67486___24t(V_24Y)
    <=> t(V_24Y,c_24__type__67486) ) ).

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_67106',axiom,
    ! [V_24X1,V_24X2,V_24Y] :
      ( c_24__type__67106___24t(V_24X1,V_24X2,V_24Y)
    <=> t(V_24Y,c_24__type__67106___24a2(V_24X1,V_24X2)) ) ).

fof('$tdef_$_type_95957',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__95957___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__95957___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).

fof('$tdef_$_type_778',axiom,
    ! [V_24Y] :
      ( c_24__type__778___24t(V_24Y)
    <=> t(V_24Y,c_24__type__778) ) ).

fof('$tdef_$_type_77511',axiom,
    ! [V_24Y] :
      ( c_24__type__77511___24t(V_24Y)
    <=> t(V_24Y,c_24__type__77511) ) ).

fof('$tdef_$_type_97376',axiom,
    ! [V_24Y] :
      ( c_24__type__97376___24t(V_24Y)
    <=> t(V_24Y,c_24__type__97376) ) ).

fof('$tdef_$_type_93133',axiom,
    ! [V_24Y] :
      ( c_24__type__93133___24t(V_24Y)
    <=> t(V_24Y,c_24__type__93133) ) ).

fof('$tdef_$_type_83571',axiom,
    ! [V_24Y] :
      ( c_24__type__83571___24t(V_24Y)
    <=> t(V_24Y,c_24__type__83571) ) ).

fof('$tdef_$_type_103487',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__103487___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__103487___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_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('$tdef_$_type_78034',axiom,
    ! [V_24Y] :
      ( c_24__type__78034___24t(V_24Y)
    <=> t(V_24Y,c_24__type__78034) ) ).

fof('$tdef_$_type_86495',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
      ( c_24__type__86495___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__86495___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).

fof('$tdef_Coq.Reals.RIneq.posreal',axiom,
    ! [V_24Y] :
      ( cCoq_2eReals_2eRIneq_2eposreal___24t(V_24Y)
    <=> t(V_24Y,cCoq_2eReals_2eRIneq_2eposreal) ) ).

fof('$tdef_$_type_87023',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
      ( c_24__type__87023___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
    <=> t(V_24Y,c_24__type__87023___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).

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_97092',axiom,
    ! [V_24Y] :
      ( c_24__type__97092___24t(V_24Y)
    <=> t(V_24Y,c_24__type__97092) ) ).

fof('$tdef_$_type_104428',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
      ( c_24__type__104428___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
    <=> t(V_24Y,c_24__type__104428___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).

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_67165',axiom,
    ! [V_24Y] :
      ( c_24__type__67165___24t(V_24Y)
    <=> t(V_24Y,c_24__type__67165) ) ).

fof('$tdef_$_type_80212',axiom,
    ! [V_24Y] :
      ( c_24__type__80212___24t(V_24Y)
    <=> t(V_24Y,c_24__type__80212) ) ).

fof('$tdef_$_type_81088',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y] :
      ( c_24__type__81088___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y)
    <=> t(V_24Y,c_24__type__81088___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6)) ) ).

fof('$tdef_Coq.Init.Decimal.decimal',axiom,
    ! [V_24Y] :
      ( cCoq_2eInit_2eDecimal_2edecimal___24t(V_24Y)
    <=> t(V_24Y,cCoq_2eInit_2eDecimal_2edecimal) ) ).

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_97401',axiom,
    ! [V_24Y] :
      ( c_24__type__97401___24t(V_24Y)
    <=> t(V_24Y,c_24__type__97401) ) ).

fof('$tdef_$_type_75610',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24Y] :
      ( c_24__type__75610___24t(V_24X1,V_24X2,V_24X3,V_24Y)
    <=> t(V_24Y,c_24__type__75610___24a3(V_24X1,V_24X2,V_24X3)) ) ).

fof('$tdef_$_type_67716',axiom,
    ! [V_24Y] :
      ( c_24__type__67716___24t(V_24Y)
    <=> t(V_24Y,c_24__type__67716) ) ).

fof('$tdef_$_type_1106',axiom,
    ! [V_24Y] :
      ( c_24__type__1106___24t(V_24Y)
    <=> t(V_24Y,c_24__type__1106) ) ).

fof('$tdef_$_type_297',axiom,
    ! [V_24Y] :
      ( c_24__type__297___24t(V_24Y)
    <=> t(V_24Y,c_24__type__297) ) ).

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_82626',axiom,
    ! [V_24Y] :
      ( c_24__type__82626___24t(V_24Y)
    <=> t(V_24Y,c_24__type__82626) ) ).

fof('$tdef_$_type_80324',axiom,
    ! [V_24Y] :
      ( c_24__type__80324___24t(V_24Y)
    <=> t(V_24Y,c_24__type__80324) ) ).

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_122083',axiom,
    ! [V_24Y] :
      ( c_24__type__122083___24t(V_24Y)
    <=> t(V_24Y,c_24__type__122083) ) ).

fof('$tdef_$_type_1101',axiom,
    ! [V_24X1,V_24X2,V_24Y] :
      ( c_24__type__1101___24t(V_24X1,V_24X2,V_24Y)
    <=> t(V_24Y,c_24__type__1101___24a2(V_24X1,V_24X2)) ) ).

fof('$tdef_$_type_97383',axiom,
    ! [V_24Y] :
      ( c_24__type__97383___24t(V_24Y)
    <=> t(V_24Y,c_24__type__97383) ) ).

fof('$tdef_Coq.PArith.BinPosDef.Pos.t',axiom,
    ! [V_24Y] :
      ( cCoq_2ePArith_2eBinPosDef_2ePos_2et___24t(V_24Y)
    <=> t(V_24Y,cCoq_2ePArith_2eBinPosDef_2ePos_2et) ) ).

fof('$tdef_$_type_499',axiom,
    ! [V_24Y] :
      ( c_24__type__499___24t(V_24Y)
    <=> t(V_24Y,c_24__type__499) ) ).

fof('$tdef_$_type_77516',axiom,
    ! [V_24Y] :
      ( c_24__type__77516___24t(V_24Y)
    <=> t(V_24Y,c_24__type__77516) ) ).

fof('$tdef_$_type_76876',axiom,
    ! [V_24Y] :
      ( c_24__type__76876___24t(V_24Y)
    <=> t(V_24Y,c_24__type__76876) ) ).

fof('$tdef_$_type_77162',axiom,
    ! [V_24Y] :
      ( c_24__type__77162___24t(V_24Y)
    <=> t(V_24Y,c_24__type__77162) ) ).

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_1132',axiom,
    ! [V_24Y] :
      ( c_24__type__1132___24t(V_24Y)
    <=> t(V_24Y,c_24__type__1132) ) ).

fof('$tdef_$_type_104951',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y] :
      ( c_24__type__104951___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y)
    <=> t(V_24Y,c_24__type__104951___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7)) ) ).

fof('$tdef_$_type_91060',axiom,
    ! [V_24Y] :
      ( c_24__type__91060___24t(V_24Y)
    <=> t(V_24Y,c_24__type__91060) ) ).

fof('$tdef_$_type_97513',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y] :
      ( c_24__type__97513___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y)
    <=> t(V_24Y,c_24__type__97513___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6)) ) ).

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_105252',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24Y] :
      ( c_24__type__105252___24t(V_24X1,V_24X2,V_24X3,V_24Y)
    <=> t(V_24Y,c_24__type__105252___24a3(V_24X1,V_24X2,V_24X3)) ) ).

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_1364',axiom,
    ! [V_24Y] :
      ( c_24__type__1364___24t(V_24Y)
    <=> t(V_24Y,c_24__type__1364) ) ).

fof('$tdef_$_type_586',axiom,
    ! [V_24Y] :
      ( c_24__type__586___24t(V_24Y)
    <=> t(V_24Y,c_24__type__586) ) ).

fof('$tdef_$_type_77893',axiom,
    ! [V_24Y] :
      ( c_24__type__77893___24t(V_24Y)
    <=> t(V_24Y,c_24__type__77893) ) ).

fof('$tdef_$_type_67050',axiom,
    ! [V_24Y] :
      ( c_24__type__67050___24t(V_24Y)
    <=> t(V_24Y,c_24__type__67050) ) ).

fof('$tdef_$_type_82155',axiom,
    ! [V_24X1,V_24X2,V_24Y] :
      ( c_24__type__82155___24t(V_24X1,V_24X2,V_24Y)
    <=> t(V_24Y,c_24__type__82155___24a2(V_24X1,V_24X2)) ) ).

fof('$tdef_$_type_96937',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
      ( c_24__type__96937___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
    <=> t(V_24Y,c_24__type__96937___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).

fof('$tdef_$_type_86990',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
      ( c_24__type__86990___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
    <=> t(V_24Y,c_24__type__86990___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).

fof('$tdef_$_type_75640',axiom,
    ! [V_24Y] :
      ( c_24__type__75640___24t(V_24Y)
    <=> t(V_24Y,c_24__type__75640) ) ).

fof('$tdef_$_type_1119',axiom,
    ! [V_24Y] :
      ( c_24__type__1119___24t(V_24Y)
    <=> t(V_24Y,c_24__type__1119) ) ).

fof('$tdef_$_type_79265',axiom,
    ! [V_24Y] :
      ( c_24__type__79265___24t(V_24Y)
    <=> t(V_24Y,c_24__type__79265) ) ).

fof('$tdef_$_type_649',axiom,
    ! [V_24Y] :
      ( c_24__type__649___24t(V_24Y)
    <=> t(V_24Y,c_24__type__649) ) ).

fof('$tdef_$_type_81509',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__81509___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__81509___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.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_84683',axiom,
    ! [V_24Y] :
      ( c_24__type__84683___24t(V_24Y)
    <=> t(V_24Y,c_24__type__84683) ) ).

fof('$tdef_$_type_86185',axiom,
    ! [V_24Y] :
      ( c_24__type__86185___24t(V_24Y)
    <=> t(V_24Y,c_24__type__86185) ) ).

fof('$tdef_$_type_88946',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__88946___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__88946___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_78986',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24Y] :
      ( c_24__type__78986___24t(V_24X1,V_24X2,V_24X3,V_24Y)
    <=> t(V_24Y,c_24__type__78986___24a3(V_24X1,V_24X2,V_24X3)) ) ).

fof('$tdef_$_type_93209',axiom,
    ! [V_24Y] :
      ( c_24__type__93209___24t(V_24Y)
    <=> t(V_24Y,c_24__type__93209) ) ).

fof('$tdef_$_type_1079',axiom,
    ! [V_24Y] :
      ( c_24__type__1079___24t(V_24Y)
    <=> t(V_24Y,c_24__type__1079) ) ).

fof('$tdef_$_type_96461',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
      ( c_24__type__96461___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__96461___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).

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_Coq.Numbers.BinNums.N',axiom,
    ! [V_24Y] :
      ( cCoq_2eNumbers_2eBinNums_2eN___24t(V_24Y)
    <=> t(V_24Y,cCoq_2eNumbers_2eBinNums_2eN) ) ).

fof('$tdef_$_type_105340',axiom,
    ! [V_24X1,V_24Y] :
      ( c_24__type__105340___24t(V_24X1,V_24Y)
    <=> t(V_24Y,c_24__type__105340___24a1(V_24X1)) ) ).

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_94945',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__94945___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__94945___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).

fof('$tdef_$_type_77138',axiom,
    ! [V_24Y] :
      ( c_24__type__77138___24t(V_24Y)
    <=> t(V_24Y,c_24__type__77138) ) ).

fof('$tdef_$_type_105468',axiom,
    ! [V_24Y] :
      ( c_24__type__105468___24t(V_24Y)
    <=> t(V_24Y,c_24__type__105468) ) ).

fof('$tdef_Coq.ZArith.BinIntDef.Z.t',axiom,
    ! [V_24Y] :
      ( cCoq_2eZArith_2eBinIntDef_2eZ_2et___24t(V_24Y)
    <=> t(V_24Y,cCoq_2eZArith_2eBinIntDef_2eZ_2et) ) ).

fof('$tdef_$_type_97378',axiom,
    ! [V_24Y] :
      ( c_24__type__97378___24t(V_24Y)
    <=> t(V_24Y,c_24__type__97378) ) ).

fof('$tdef_$_type_93138',axiom,
    ! [V_24Y] :
      ( c_24__type__93138___24t(V_24Y)
    <=> t(V_24Y,c_24__type__93138) ) ).

fof('$tdef_$_type_78702',axiom,
    ! [V_24X1,V_24Y] :
      ( c_24__type__78702___24t(V_24X1,V_24Y)
    <=> t(V_24Y,c_24__type__78702___24a1(V_24X1)) ) ).

fof('$tdef_$_type_1134',axiom,
    ! [V_24Y] :
      ( c_24__type__1134___24t(V_24Y)
    <=> t(V_24Y,c_24__type__1134) ) ).

fof('$tdef_$_type_97072',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
      ( c_24__type__97072___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
    <=> t(V_24Y,c_24__type__97072___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).

fof('$tdef_$_type_67330',axiom,
    ! [V_24X1,V_24X2,V_24Y] :
      ( c_24__type__67330___24t(V_24X1,V_24X2,V_24Y)
    <=> t(V_24Y,c_24__type__67330___24a2(V_24X1,V_24X2)) ) ).

fof('$tdef_$_type_78211',axiom,
    ! [V_24X1,V_24Y] :
      ( c_24__type__78211___24t(V_24X1,V_24Y)
    <=> t(V_24Y,c_24__type__78211___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_75628',axiom,
    ! [V_24Y] :
      ( c_24__type__75628___24t(V_24Y)
    <=> t(V_24Y,c_24__type__75628) ) ).

fof('$tdef_$_type_75660',axiom,
    ! [V_24Y] :
      ( c_24__type__75660___24t(V_24Y)
    <=> t(V_24Y,c_24__type__75660) ) ).

fof('$tdef_$_type_81759',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__81759___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__81759___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_94863',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__94863___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__94863___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).

fof('$tdef_$_type_391',axiom,
    ! [V_24X1,V_24Y] :
      ( c_24__type__391___24t(V_24X1,V_24Y)
    <=> t(V_24Y,c_24__type__391___24a1(V_24X1)) ) ).

fof('$tdef_$_type_141',axiom,
    ! [V_24Y] :
      ( c_24__type__141___24t(V_24Y)
    <=> t(V_24Y,c_24__type__141) ) ).

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_76494',axiom,
    ! [V_24Y] :
      ( c_24__type__76494___24t(V_24Y)
    <=> t(V_24Y,c_24__type__76494) ) ).

fof('$tdef_$_type_76397',axiom,
    ! [V_24Y] :
      ( c_24__type__76397___24t(V_24Y)
    <=> t(V_24Y,c_24__type__76397) ) ).

fof('$tdef_$_type_85630',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__85630___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__85630___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).

fof('$tdef_$_type_84690',axiom,
    ! [V_24X1,V_24X2,V_24Y] :
      ( c_24__type__84690___24t(V_24X1,V_24X2,V_24Y)
    <=> t(V_24Y,c_24__type__84690___24a2(V_24X1,V_24X2)) ) ).

fof('$tdef_$_type_75599',axiom,
    ! [V_24X1,V_24X2,V_24Y] :
      ( c_24__type__75599___24t(V_24X1,V_24X2,V_24Y)
    <=> t(V_24Y,c_24__type__75599___24a2(V_24X1,V_24X2)) ) ).

fof('$tdef_Coq.micromega.ZMicromega.ZWitness',axiom,
    ! [V_24Y] :
      ( cCoq_2emicromega_2eZMicromega_2eZWitness___24t(V_24Y)
    <=> t(V_24Y,cCoq_2emicromega_2eZMicromega_2eZWitness) ) ).

fof('$tdef_$_type_76807',axiom,
    ! [V_24Y] :
      ( c_24__type__76807___24t(V_24Y)
    <=> t(V_24Y,c_24__type__76807) ) ).

fof('$tdef_$_type_96972',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24Y] :
      ( c_24__type__96972___24t(V_24X1,V_24X2,V_24X3,V_24Y)
    <=> t(V_24Y,c_24__type__96972___24a3(V_24X1,V_24X2,V_24X3)) ) ).

fof('$tdef_$_type_96890',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24Y] :
      ( c_24__type__96890___24t(V_24X1,V_24X2,V_24X3,V_24Y)
    <=> t(V_24Y,c_24__type__96890___24a3(V_24X1,V_24X2,V_24X3)) ) ).

fof('$tdef_$_type_75476',axiom,
    ! [V_24Y] :
      ( c_24__type__75476___24t(V_24Y)
    <=> t(V_24Y,c_24__type__75476) ) ).

fof('$tdef_$_type_567',axiom,
    ! [V_24Y] :
      ( c_24__type__567___24t(V_24Y)
    <=> t(V_24Y,c_24__type__567) ) ).

fof('$tdef_$_type_90110',axiom,
    ! [V_24Y] :
      ( c_24__type__90110___24t(V_24Y)
    <=> t(V_24Y,c_24__type__90110) ) ).

fof('$tdef_$_type_67032',axiom,
    ! [V_24Y] :
      ( c_24__type__67032___24t(V_24Y)
    <=> t(V_24Y,c_24__type__67032) ) ).

fof('$tdef_$_type_75561',axiom,
    ! [V_24Y] :
      ( c_24__type__75561___24t(V_24Y)
    <=> t(V_24Y,c_24__type__75561) ) ).

fof('$tdef_$_type_104161',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
      ( c_24__type__104161___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__104161___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).

fof('$tdef_$_type_97184',axiom,
    ! [V_24Y] :
      ( c_24__type__97184___24t(V_24Y)
    <=> t(V_24Y,c_24__type__97184) ) ).

fof('$tdef_$_type_78909',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24Y] :
      ( c_24__type__78909___24t(V_24X1,V_24X2,V_24X3,V_24Y)
    <=> t(V_24Y,c_24__type__78909___24a3(V_24X1,V_24X2,V_24X3)) ) ).

fof('$tdef_$_type_513',axiom,
    ! [V_24Y] :
      ( c_24__type__513___24t(V_24Y)
    <=> t(V_24Y,c_24__type__513) ) ).

fof('$tdef_$_type_101480',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__101480___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__101480___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_104673',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y] :
      ( c_24__type__104673___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y)
    <=> t(V_24Y,c_24__type__104673___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7)) ) ).

fof('$tdef_$_type_96132',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__96132___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__96132___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).

fof('$tdef_$_type_786',axiom,
    ! [V_24Y] :
      ( c_24__type__786___24t(V_24Y)
    <=> t(V_24Y,c_24__type__786) ) ).

fof('$tdef_$_type_699',axiom,
    ! [V_24Y] :
      ( c_24__type__699___24t(V_24Y)
    <=> t(V_24Y,c_24__type__699) ) ).

fof('$tdef_$_type_96587',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
      ( c_24__type__96587___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__96587___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).

fof('$tdef_$_type_82253',axiom,
    ! [V_24X1,V_24X2,V_24Y] :
      ( c_24__type__82253___24t(V_24X1,V_24X2,V_24Y)
    <=> t(V_24Y,c_24__type__82253___24a2(V_24X1,V_24X2)) ) ).

fof('$tdef_Coq.micromega.ZMicromega.ZArithProof',axiom,
    ! [V_24Y] :
      ( cCoq_2emicromega_2eZMicromega_2eZArithProof___24t(V_24Y)
    <=> t(V_24Y,cCoq_2emicromega_2eZMicromega_2eZArithProof) ) ).

fof('$tdef_$_type_97687',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24Y] :
      ( c_24__type__97687___24t(V_24X1,V_24X2,V_24X3,V_24Y)
    <=> t(V_24Y,c_24__type__97687___24a3(V_24X1,V_24X2,V_24X3)) ) ).

fof('$tdef_$_type_97194',axiom,
    ! [V_24Y] :
      ( c_24__type__97194___24t(V_24Y)
    <=> t(V_24Y,c_24__type__97194) ) ).

fof('$tdef_$_type_76862',axiom,
    ! [V_24Y] :
      ( c_24__type__76862___24t(V_24Y)
    <=> t(V_24Y,c_24__type__76862) ) ).

fof('$tdef_$_type_103644',axiom,
    ! [V_24Y] :
      ( c_24__type__103644___24t(V_24Y)
    <=> t(V_24Y,c_24__type__103644) ) ).

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('$tdef_$_type_102818',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__102818___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__102818___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.Reals.RIneq.nonnegreal',axiom,
    ! [V_24Y] :
      ( cCoq_2eReals_2eRIneq_2enonnegreal___24t(V_24Y)
    <=> t(V_24Y,cCoq_2eReals_2eRIneq_2enonnegreal) ) ).

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_89872',axiom,
    ! [V_24Y] :
      ( c_24__type__89872___24t(V_24Y)
    <=> t(V_24Y,c_24__type__89872) ) ).

fof('$tdef_$_type_78044',axiom,
    ! [V_24X1,V_24Y] :
      ( c_24__type__78044___24t(V_24X1,V_24Y)
    <=> t(V_24Y,c_24__type__78044___24a1(V_24X1)) ) ).

fof('$tdef_Coq.micromega.RMicromega.Rcst',axiom,
    ! [V_24Y] :
      ( cCoq_2emicromega_2eRMicromega_2eRcst___24t(V_24Y)
    <=> t(V_24Y,cCoq_2emicromega_2eRMicromega_2eRcst) ) ).

fof('$tdef_$_type_94176',axiom,
    ! [V_24Y] :
      ( c_24__type__94176___24t(V_24Y)
    <=> t(V_24Y,c_24__type__94176) ) ).

fof('$tdef_$_type_388',axiom,
    ! [V_24X1,V_24X2,V_24Y] :
      ( c_24__type__388___24t(V_24X1,V_24X2,V_24Y)
    <=> t(V_24Y,c_24__type__388___24a2(V_24X1,V_24X2)) ) ).

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_78474',axiom,
    ! [V_24Y] :
      ( c_24__type__78474___24t(V_24Y)
    <=> t(V_24Y,c_24__type__78474) ) ).

fof('$tdef_$_type_371',axiom,
    ! [V_24X1,V_24X2,V_24Y] :
      ( c_24__type__371___24t(V_24X1,V_24X2,V_24Y)
    <=> t(V_24Y,c_24__type__371___24a2(V_24X1,V_24X2)) ) ).

fof('$tdef_$_type_313',axiom,
    ! [V_24X1,V_24X2,V_24Y] :
      ( c_24__type__313___24t(V_24X1,V_24X2,V_24Y)
    <=> t(V_24Y,c_24__type__313___24a2(V_24X1,V_24X2)) ) ).

fof('$tdef_$_type_77429',axiom,
    ! [V_24Y] :
      ( c_24__type__77429___24t(V_24Y)
    <=> t(V_24Y,c_24__type__77429) ) ).

fof('$tdef_$_type_96214',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__96214___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__96214___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).

fof('$tdef_$_type_97189',axiom,
    ! [V_24Y] :
      ( c_24__type__97189___24t(V_24Y)
    <=> t(V_24Y,c_24__type__97189) ) ).

fof('$tdef_$_type_95771',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__95771___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__95771___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_77239',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24Y] :
      ( c_24__type__77239___24t(V_24X1,V_24X2,V_24X3,V_24Y)
    <=> t(V_24Y,c_24__type__77239___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_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_86203',axiom,
    ! [V_24Y] :
      ( c_24__type__86203___24t(V_24Y)
    <=> t(V_24Y,c_24__type__86203) ) ).

fof('$tdef_$_type_68107',axiom,
    ! [V_24Y] :
      ( c_24__type__68107___24t(V_24Y)
    <=> t(V_24Y,c_24__type__68107) ) ).

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_82217',axiom,
    ! [V_24Y] :
      ( c_24__type__82217___24t(V_24Y)
    <=> t(V_24Y,c_24__type__82217) ) ).

fof('$tdef_$_type_105031',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y] :
      ( c_24__type__105031___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y)
    <=> t(V_24Y,c_24__type__105031___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7)) ) ).

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_87686',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__87686___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__87686___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_67609',axiom,
    ! [V_24Y] :
      ( c_24__type__67609___24t(V_24Y)
    <=> t(V_24Y,c_24__type__67609) ) ).

fof('$tdef_$_type_257',axiom,
    ! [V_24Y] :
      ( c_24__type__257___24t(V_24Y)
    <=> t(V_24Y,c_24__type__257) ) ).

fof('$tdef_$_type_86432',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
      ( c_24__type__86432___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__86432___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).

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_85237',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__85237___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__85237___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).

fof('$tdef_$_type_78479',axiom,
    ! [V_24Y] :
      ( c_24__type__78479___24t(V_24Y)
    <=> t(V_24Y,c_24__type__78479) ) ).

fof('$tdef_$_type_105582',axiom,
    ! [V_24X1,V_24Y] :
      ( c_24__type__105582___24t(V_24X1,V_24Y)
    <=> t(V_24Y,c_24__type__105582___24a1(V_24X1)) ) ).

fof('$tdef_$_type_85529',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__85529___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__85529___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.Nat.t',axiom,
    ! [V_24Y] :
      ( cCoq_2eInit_2eNat_2et___24t(V_24Y)
    <=> t(V_24Y,cCoq_2eInit_2eNat_2et) ) ).

fof('$tdef_$_type_75551',axiom,
    ! [V_24X1,V_24X2,V_24Y] :
      ( c_24__type__75551___24t(V_24X1,V_24X2,V_24Y)
    <=> t(V_24Y,c_24__type__75551___24a2(V_24X1,V_24X2)) ) ).

fof('$tdef_$_type_89354',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__89354___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__89354___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_81634',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__81634___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__81634___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_104623',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y] :
      ( c_24__type__104623___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y)
    <=> t(V_24Y,c_24__type__104623___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7)) ) ).

fof('$tdef_$_type_68088',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24Y] :
      ( c_24__type__68088___24t(V_24X1,V_24X2,V_24X3,V_24Y)
    <=> t(V_24Y,c_24__type__68088___24a3(V_24X1,V_24X2,V_24X3)) ) ).

fof('$tdef_$_type_77244',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24Y] :
      ( c_24__type__77244___24t(V_24X1,V_24X2,V_24X3,V_24Y)
    <=> t(V_24Y,c_24__type__77244___24a3(V_24X1,V_24X2,V_24X3)) ) ).

fof('$tdef_$_type_67337',axiom,
    ! [V_24Y] :
      ( c_24__type__67337___24t(V_24Y)
    <=> t(V_24Y,c_24__type__67337) ) ).

fof('$tdef_$_type_1018',axiom,
    ! [V_24Y] :
      ( c_24__type__1018___24t(V_24Y)
    <=> t(V_24Y,c_24__type__1018) ) ).

fof('$tdef_$_type_75574',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24Y] :
      ( c_24__type__75574___24t(V_24X1,V_24X2,V_24X3,V_24Y)
    <=> t(V_24Y,c_24__type__75574___24a3(V_24X1,V_24X2,V_24X3)) ) ).

fof('$tdef_$_type_96974',axiom,
    ! [V_24Y] :
      ( c_24__type__96974___24t(V_24Y)
    <=> t(V_24Y,c_24__type__96974) ) ).

fof('$tdef_$_type_67871',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24Y] :
      ( c_24__type__67871___24t(V_24X1,V_24X2,V_24X3,V_24Y)
    <=> t(V_24Y,c_24__type__67871___24a3(V_24X1,V_24X2,V_24X3)) ) ).

fof('$tdef_$_type_104320',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
      ( c_24__type__104320___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
    <=> t(V_24Y,c_24__type__104320___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).

fof('$tdef_$_type_1367',axiom,
    ! [V_24X1,V_24Y] :
      ( c_24__type__1367___24t(V_24X1,V_24Y)
    <=> t(V_24Y,c_24__type__1367___24a1(V_24X1)) ) ).

fof('$tdef_$_type_83378',axiom,
    ! [V_24Y] :
      ( c_24__type__83378___24t(V_24Y)
    <=> t(V_24Y,c_24__type__83378) ) ).

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_82381',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24Y] :
      ( c_24__type__82381___24t(V_24X1,V_24X2,V_24X3,V_24Y)
    <=> t(V_24Y,c_24__type__82381___24a3(V_24X1,V_24X2,V_24X3)) ) ).

fof('$tdef_$_type_76796',axiom,
    ! [V_24X1,V_24Y] :
      ( c_24__type__76796___24t(V_24X1,V_24Y)
    <=> t(V_24Y,c_24__type__76796___24a1(V_24X1)) ) ).

fof('$tdef_$_type_67803',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24Y] :
      ( c_24__type__67803___24t(V_24X1,V_24X2,V_24X3,V_24Y)
    <=> t(V_24Y,c_24__type__67803___24a3(V_24X1,V_24X2,V_24X3)) ) ).

fof('$tdef_Coq.Init.Decimal.uint',axiom,
    ! [V_24Y] :
      ( cCoq_2eInit_2eDecimal_2euint___24t(V_24Y)
    <=> t(V_24Y,cCoq_2eInit_2eDecimal_2euint) ) ).

fof('$tdef_Prop',axiom,
    ! [V_24Y] :
      ( cProp___24t(V_24Y)
    <=> t(V_24Y,cProp) ) ).

fof('$tdef_$_type_82120',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__82120___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__82120___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_90094',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24Y] :
      ( c_24__type__90094___24t(V_24X1,V_24X2,V_24X3,V_24Y)
    <=> t(V_24Y,c_24__type__90094___24a3(V_24X1,V_24X2,V_24X3)) ) ).

fof('$tdef_$_type_1048',axiom,
    ! [V_24Y] :
      ( c_24__type__1048___24t(V_24Y)
    <=> t(V_24Y,c_24__type__1048) ) ).

fof('$tdef_Coq.setoid_ring.InitialRing.hypo',axiom,
    ! [V_24Y] :
      ( cCoq_2esetoid__ring_2eInitialRing_2ehypo___24t(V_24Y)
    <=> t(V_24Y,cCoq_2esetoid__ring_2eInitialRing_2ehypo) ) ).

fof('$tdef_$_type_96724',axiom,
    ! [V_24Y] :
      ( c_24__type__96724___24t(V_24Y)
    <=> t(V_24Y,c_24__type__96724) ) ).

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_98168',axiom,
    ! [V_24Y] :
      ( c_24__type__98168___24t(V_24Y)
    <=> t(V_24Y,c_24__type__98168) ) ).

fof('$tdef_$_type_1434',axiom,
    ! [V_24Y] :
      ( c_24__type__1434___24t(V_24Y)
    <=> t(V_24Y,c_24__type__1434) ) ).

fof('$tdef_$_type_1422',axiom,
    ! [V_24X1,V_24X2,V_24Y] :
      ( c_24__type__1422___24t(V_24X1,V_24X2,V_24Y)
    <=> t(V_24Y,c_24__type__1422___24a2(V_24X1,V_24X2)) ) ).

fof('$tdef_$_type_104297',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
      ( c_24__type__104297___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
    <=> t(V_24Y,c_24__type__104297___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).

fof('$tdef_$_type_75483',axiom,
    ! [V_24Y] :
      ( c_24__type__75483___24t(V_24Y)
    <=> t(V_24Y,c_24__type__75483) ) ).

fof('$tdef_$_type_94677',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__94677___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__94677___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.Byte.byte',axiom,
    ! [V_24Y] :
      ( cCoq_2eInit_2eByte_2ebyte___24t(V_24Y)
    <=> t(V_24Y,cCoq_2eInit_2eByte_2ebyte) ) ).

fof('$tdef_$_type_78471',axiom,
    ! [V_24Y] :
      ( c_24__type__78471___24t(V_24Y)
    <=> t(V_24Y,c_24__type__78471) ) ).

fof('$tdef_$_type_76363',axiom,
    ! [V_24Y] :
      ( c_24__type__76363___24t(V_24Y)
    <=> t(V_24Y,c_24__type__76363) ) ).

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_104343',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
      ( c_24__type__104343___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
    <=> t(V_24Y,c_24__type__104343___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).

fof('$tdef_Coq.Init.Decimal.int',axiom,
    ! [V_24Y] :
      ( cCoq_2eInit_2eDecimal_2eint___24t(V_24Y)
    <=> t(V_24Y,cCoq_2eInit_2eDecimal_2eint) ) ).

fof('$tdef_$_type_77225',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24Y] :
      ( c_24__type__77225___24t(V_24X1,V_24X2,V_24X3,V_24Y)
    <=> t(V_24Y,c_24__type__77225___24a3(V_24X1,V_24X2,V_24X3)) ) ).

fof('$tdef_$_type_81884',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__81884___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__81884___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_80277',axiom,
    ! [V_24Y] :
      ( c_24__type__80277___24t(V_24Y)
    <=> t(V_24Y,c_24__type__80277) ) ).

fof('$tdef_$_type_88307',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__88307___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__88307___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_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_86936',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
      ( c_24__type__86936___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
    <=> t(V_24Y,c_24__type__86936___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).

fof('$tdef_$_type_104044',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
      ( c_24__type__104044___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__104044___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).

fof('$tdef_$_type_1454',axiom,
    ! [V_24Y] :
      ( c_24__type__1454___24t(V_24Y)
    <=> t(V_24Y,c_24__type__1454) ) ).

fof('$tdef_$_type_99427',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__99427___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__99427___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_85136',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__85136___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__85136___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).

fof('$tdef_$_type_101134',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__101134___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__101134___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_67643',axiom,
    ! [V_24X1,V_24X2,V_24Y] :
      ( c_24__type__67643___24t(V_24X1,V_24X2,V_24Y)
    <=> t(V_24Y,c_24__type__67643___24a2(V_24X1,V_24X2)) ) ).

fof('$tdef_IntMap.Map.ad',axiom,
    ! [V_24Y] :
      ( cIntMap_2eMap_2ead___24t(V_24Y)
    <=> t(V_24Y,cIntMap_2eMap_2ead) ) ).

fof('$tdef_$_type_75614',axiom,
    ! [V_24X1,V_24X2,V_24Y] :
      ( c_24__type__75614___24t(V_24X1,V_24X2,V_24Y)
    <=> t(V_24Y,c_24__type__75614___24a2(V_24X1,V_24X2)) ) ).

fof('$tdef_$_type_1065',axiom,
    ! [V_24X1,V_24X2,V_24Y] :
      ( c_24__type__1065___24t(V_24X1,V_24X2,V_24Y)
    <=> t(V_24Y,c_24__type__1065___24a2(V_24X1,V_24X2)) ) ).

fof('$tdef_$_type_105716',axiom,
    ! [V_24Y] :
      ( c_24__type__105716___24t(V_24Y)
    <=> t(V_24Y,c_24__type__105716) ) ).

fof('$tdef_$_type_104995',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y] :
      ( c_24__type__104995___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y)
    <=> t(V_24Y,c_24__type__104995___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7)) ) ).

fof('$tdef_$_type_67406',axiom,
    ! [V_24Y] :
      ( c_24__type__67406___24t(V_24Y)
    <=> t(V_24Y,c_24__type__67406) ) ).

fof('$tdef_$_type_97589',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
      ( c_24__type__97589___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
    <=> t(V_24Y,c_24__type__97589___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).

fof('$tdef_$_type_647',axiom,
    ! [V_24Y] :
      ( c_24__type__647___24t(V_24Y)
    <=> t(V_24Y,c_24__type__647) ) ).

fof('$tdef_$_type_608',axiom,
    ! [V_24X1,V_24X2,V_24Y] :
      ( c_24__type__608___24t(V_24X1,V_24X2,V_24Y)
    <=> t(V_24Y,c_24__type__608___24a2(V_24X1,V_24X2)) ) ).

fof('$tdef_$_type_105724',axiom,
    ! [V_24Y] :
      ( c_24__type__105724___24t(V_24Y)
    <=> t(V_24Y,c_24__type__105724) ) ).

fof('$tdef_$_type_96524',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
      ( c_24__type__96524___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__96524___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).

fof('$tdef_Coq.micromega.RingMicromega.Op1',axiom,
    ! [V_24Y] :
      ( cCoq_2emicromega_2eRingMicromega_2eOp1___24t(V_24Y)
    <=> t(V_24Y,cCoq_2emicromega_2eRingMicromega_2eOp1) ) ).

fof('$tdef_$_type_105287',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24Y] :
      ( c_24__type__105287___24t(V_24X1,V_24X2,V_24X3,V_24Y)
    <=> t(V_24Y,c_24__type__105287___24a3(V_24X1,V_24X2,V_24X3)) ) ).

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_67650',axiom,
    ! [V_24X1,V_24Y] :
      ( c_24__type__67650___24t(V_24X1,V_24Y)
    <=> t(V_24Y,c_24__type__67650___24a1(V_24X1)) ) ).

fof('$tdef_Coq.micromega.ZMicromega.coneMember',axiom,
    ! [V_24Y] :
      ( cCoq_2emicromega_2eZMicromega_2econeMember___24t(V_24Y)
    <=> t(V_24Y,cCoq_2emicromega_2eZMicromega_2econeMember) ) ).

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_93686',axiom,
    ! [V_24Y] :
      ( c_24__type__93686___24t(V_24Y)
    <=> t(V_24Y,c_24__type__93686) ) ).

fof('$tdef_$_type_80320',axiom,
    ! [V_24Y] :
      ( c_24__type__80320___24t(V_24Y)
    <=> t(V_24Y,c_24__type__80320) ) ).

fof('$tdef_$_type_99081',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__99081___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__99081___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_80463',axiom,
    ! [V_24Y] :
      ( c_24__type__80463___24t(V_24Y)
    <=> t(V_24Y,c_24__type__80463) ) ).

fof('$tdef_$_type_67734',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24Y] :
      ( c_24__type__67734___24t(V_24X1,V_24X2,V_24X3,V_24Y)
    <=> t(V_24Y,c_24__type__67734___24a3(V_24X1,V_24X2,V_24X3)) ) ).

fof('$tdef_$_type_102149',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__102149___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__102149___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_A',axiom,
    ! [V_24Y] :
      ( cA___24t(V_24Y)
    <=> t(V_24Y,cA) ) ).

fof('$tdef_$_type_105145',axiom,
    ! [V_24Y] :
      ( c_24__type__105145___24t(V_24Y)
    <=> t(V_24Y,c_24__type__105145) ) ).

fof('$tdef_Coq.setoid_ring.Field_theory.rsplit',axiom,
    ! [V_24X1,V_24Y] :
      ( cCoq_2esetoid__ring_2eField__theory_2ersplit___24t(V_24X1,V_24Y)
    <=> t(V_24Y,cCoq_2esetoid__ring_2eField__theory_2ersplit___24a1(V_24X1)) ) ).

fof('$tdef_$_type_67739',axiom,
    ! [V_24Y] :
      ( c_24__type__67739___24t(V_24Y)
    <=> t(V_24Y,c_24__type__67739) ) ).

fof('$tdef_$_type_86906',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
      ( c_24__type__86906___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
    <=> t(V_24Y,c_24__type__86906___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).

fof('$tdef_$_type_82009',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__82009___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__82009___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.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_96826',axiom,
    ! [V_24Y] :
      ( c_24__type__96826___24t(V_24Y)
    <=> t(V_24Y,c_24__type__96826) ) ).

fof('$tdef_$_type_67615',axiom,
    ! [V_24X1,V_24X2,V_24Y] :
      ( c_24__type__67615___24t(V_24X1,V_24X2,V_24Y)
    <=> t(V_24Y,c_24__type__67615___24a2(V_24X1,V_24X2)) ) ).

fof('$tdef_$_type_105667',axiom,
    ! [V_24Y] :
      ( c_24__type__105667___24t(V_24Y)
    <=> t(V_24Y,c_24__type__105667) ) ).

fof('$tdef_$_type_89549',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__89549___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__89549___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_80453',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
      ( c_24__type__80453___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
    <=> t(V_24Y,c_24__type__80453___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).

fof('$tdef_$_type_80300',axiom,
    ! [V_24Y] :
      ( c_24__type__80300___24t(V_24Y)
    <=> t(V_24Y,c_24__type__80300) ) ).

fof('$tdef_$_type_67244',axiom,
    ! [V_24Y] :
      ( c_24__type__67244___24t(V_24Y)
    <=> t(V_24Y,c_24__type__67244) ) ).

fof('$tdef_$_type_1051',axiom,
    ! [V_24X1,V_24Y] :
      ( c_24__type__1051___24t(V_24X1,V_24Y)
    <=> t(V_24Y,c_24__type__1051___24a1(V_24X1)) ) ).

fof('$tdef_$_type_67483',axiom,
    ! [V_24Y] :
      ( c_24__type__67483___24t(V_24Y)
    <=> t(V_24Y,c_24__type__67483) ) ).

fof('$tdef_$_type_1121',axiom,
    ! [V_24Y] :
      ( c_24__type__1121___24t(V_24Y)
    <=> t(V_24Y,c_24__type__1121) ) ).

fof('$tdef_$_type_1446',axiom,
    ! [V_24Y] :
      ( c_24__type__1446___24t(V_24Y)
    <=> t(V_24Y,c_24__type__1446) ) ).

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_67586',axiom,
    ! [V_24Y] :
      ( c_24__type__67586___24t(V_24Y)
    <=> t(V_24Y,c_24__type__67586) ) ).

fof('$tdef_$_type_789',axiom,
    ! [V_24X1,V_24Y] :
      ( c_24__type__789___24t(V_24X1,V_24Y)
    <=> t(V_24Y,c_24__type__789___24a1(V_24X1)) ) ).

fof('$tdef_$_type_76179',axiom,
    ! [V_24Y] :
      ( c_24__type__76179___24t(V_24Y)
    <=> t(V_24Y,c_24__type__76179) ) ).

fof('$tdef_$_type_76785',axiom,
    ! [V_24Y] :
      ( c_24__type__76785___24t(V_24Y)
    <=> t(V_24Y,c_24__type__76785) ) ).

fof('$tdef_$_type_67955',axiom,
    ! [V_24Y] :
      ( c_24__type__67955___24t(V_24Y)
    <=> t(V_24Y,c_24__type__67955) ) ).

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_67647',axiom,
    ! [V_24Y] :
      ( c_24__type__67647___24t(V_24Y)
    <=> t(V_24Y,c_24__type__67647) ) ).

fof('$tdef_$_type_103918',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
      ( c_24__type__103918___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__103918___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).

fof('$tdef_$_type_96039',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__96039___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__96039___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).

fof('$tdef_$_type_101803',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__101803___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__101803___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_76206',axiom,
    ! [V_24Y] :
      ( c_24__type__76206___24t(V_24Y)
    <=> t(V_24Y,c_24__type__76206) ) ).

fof('$tdef_$_type_97538',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y] :
      ( c_24__type__97538___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y)
    <=> t(V_24Y,c_24__type__97538___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6)) ) ).

fof('$tdef_$_type_80251',axiom,
    ! [V_24Y] :
      ( c_24__type__80251___24t(V_24Y)
    <=> t(V_24Y,c_24__type__80251) ) ).

fof('$tdef_$_type_122086',axiom,
    ! [V_24Y] :
      ( c_24__type__122086___24t(V_24Y)
    <=> t(V_24Y,c_24__type__122086) ) ).

fof('$tdef_$_type_102495',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__102495___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__102495___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.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_287',axiom,
    ! [V_24Y] :
      ( c_24__type__287___24t(V_24Y)
    <=> t(V_24Y,c_24__type__287) ) ).

fof('$tdef_$_type_90340',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24Y] :
      ( c_24__type__90340___24t(V_24X1,V_24X2,V_24X3,V_24Y)
    <=> t(V_24Y,c_24__type__90340___24a3(V_24X1,V_24X2,V_24X3)) ) ).

fof('$tdef_$_type_67059',axiom,
    ! [V_24Y] :
      ( c_24__type__67059___24t(V_24Y)
    <=> t(V_24Y,c_24__type__67059) ) ).

fof('$tdef_$_type_884',axiom,
    ! [V_24Y] :
      ( c_24__type__884___24t(V_24Y)
    <=> t(V_24Y,c_24__type__884) ) ).

fof('$tdef_$_type_104098',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
      ( c_24__type__104098___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__104098___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).

fof('$tdef_$_type_67789',axiom,
    ! [V_24X1,V_24X2,V_24Y] :
      ( c_24__type__67789___24t(V_24X1,V_24X2,V_24Y)
    <=> t(V_24Y,c_24__type__67789___24a2(V_24X1,V_24X2)) ) ).

fof('$tdef_$_type_96866',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24Y] :
      ( c_24__type__96866___24t(V_24X1,V_24X2,V_24X3,V_24Y)
    <=> t(V_24Y,c_24__type__96866___24a3(V_24X1,V_24X2,V_24X3)) ) ).

fof('$tdef_$_type_1152',axiom,
    ! [V_24Y] :
      ( c_24__type__1152___24t(V_24Y)
    <=> t(V_24Y,c_24__type__1152) ) ).

fof('$tdef_$_type_88094',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__88094___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__88094___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_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_67099',axiom,
    ! [V_24Y] :
      ( c_24__type__67099___24t(V_24Y)
    <=> t(V_24Y,c_24__type__67099) ) ).

fof('$tdef_$_type_86852',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
      ( c_24__type__86852___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
    <=> t(V_24Y,c_24__type__86852___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).

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_6',axiom,
    ! [V_24Y] :
      ( c_24__type__6___24t(V_24Y)
    <=> t(V_24Y,c_24__type__6) ) ).

fof('$tdef_$_type_94481',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y] :
      ( c_24__type__94481___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y)
    <=> t(V_24Y,c_24__type__94481___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6)) ) ).

fof('$tdef_$_type_68063',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24Y] :
      ( c_24__type__68063___24t(V_24X1,V_24X2,V_24X3,V_24Y)
    <=> t(V_24Y,c_24__type__68063___24a3(V_24X1,V_24X2,V_24X3)) ) ).

fof('$tdef_$_type_100442',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__100442___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__100442___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_1226',axiom,
    ! [V_24Y] :
      ( c_24__type__1226___24t(V_24Y)
    <=> t(V_24Y,c_24__type__1226) ) ).

fof('$tdef_$_type_97053',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
      ( c_24__type__97053___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
    <=> t(V_24Y,c_24__type__97053___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).

fof('$tdef_$_type_360',axiom,
    ! [V_24Y] :
      ( c_24__type__360___24t(V_24Y)
    <=> t(V_24Y,c_24__type__360) ) ).

fof('$tdef_$_type_104384',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
      ( c_24__type__104384___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
    <=> t(V_24Y,c_24__type__104384___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).

fof('$tdef_$_type_67853',axiom,
    ! [V_24Y] :
      ( c_24__type__67853___24t(V_24Y)
    <=> t(V_24Y,c_24__type__67853) ) ).

fof('$tdef_$_type_67744',axiom,
    ! [V_24Y] :
      ( c_24__type__67744___24t(V_24Y)
    <=> t(V_24Y,c_24__type__67744) ) ).

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_80837',axiom,
    ! [V_24Y] :
      ( c_24__type__80837___24t(V_24Y)
    <=> t(V_24Y,c_24__type__80837) ) ).

fof('$tdef_$_type_292',axiom,
    ! [V_24Y] :
      ( c_24__type__292___24t(V_24Y)
    <=> t(V_24Y,c_24__type__292) ) ).

fof('$tdef_$_type_99750',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__99750___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__99750___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.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_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_95038',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__95038___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__95038___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.nat',axiom,
    ! [V_24Y] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(V_24Y)
    <=> t(V_24Y,cCoq_2eInit_2eDatatypes_2enat) ) ).

fof('$tdef_$_type_67627',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24Y] :
      ( c_24__type__67627___24t(V_24X1,V_24X2,V_24X3,V_24Y)
    <=> t(V_24Y,c_24__type__67627___24a3(V_24X1,V_24X2,V_24X3)) ) ).

fof('$tdef_$_type_94162',axiom,
    ! [V_24Y] :
      ( c_24__type__94162___24t(V_24Y)
    <=> t(V_24Y,c_24__type__94162) ) ).

fof('$tdef_$_type_93087',axiom,
    ! [V_24Y] :
      ( c_24__type__93087___24t(V_24Y)
    <=> t(V_24Y,c_24__type__93087) ) ).

fof('$tdef_$_type_67864',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24Y] :
      ( c_24__type__67864___24t(V_24X1,V_24X2,V_24X3,V_24Y)
    <=> t(V_24Y,c_24__type__67864___24a3(V_24X1,V_24X2,V_24X3)) ) ).

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_67785',axiom,
    ! [V_24Y] :
      ( c_24__type__67785___24t(V_24Y)
    <=> t(V_24Y,c_24__type__67785) ) ).

fof('$tdef_$_type_87899',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__87899___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__87899___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_104765',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y] :
      ( c_24__type__104765___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y)
    <=> t(V_24Y,c_24__type__104765___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7)) ) ).

fof('$tdef_$_type_96307',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__96307___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__96307___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_105155',axiom,
    ! [V_24X1,V_24X2,V_24Y] :
      ( c_24__type__105155___24t(V_24X1,V_24X2,V_24Y)
    <=> t(V_24Y,c_24__type__105155___24a2(V_24X1,V_24X2)) ) ).

fof('$tdef_$_type_86675',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
      ( c_24__type__86675___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__86675___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).

fof('$tdef_Coq.micromega.RingMicromega.Formula',axiom,
    ! [V_24X1,V_24Y] :
      ( cCoq_2emicromega_2eRingMicromega_2eFormula___24t(V_24X1,V_24Y)
    <=> t(V_24Y,cCoq_2emicromega_2eRingMicromega_2eFormula___24a1(V_24X1)) ) ).

fof('$tdef_$_type_105712',axiom,
    ! [V_24Y] :
      ( c_24__type__105712___24t(V_24Y)
    <=> t(V_24Y,c_24__type__105712) ) ).

fof('$tdef_$_type_105290',axiom,
    ! [V_24Y] :
      ( c_24__type__105290___24t(V_24Y)
    <=> t(V_24Y,c_24__type__105290) ) ).

fof('$tdef_$_type_1028',axiom,
    ! [V_24Y] :
      ( c_24__type__1028___24t(V_24Y)
    <=> t(V_24Y,c_24__type__1028) ) ).

fof('$tdef_$_type_86882',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
      ( c_24__type__86882___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
    <=> t(V_24Y,c_24__type__86882___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).

fof('$tdef_$_type_86558',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
      ( c_24__type__86558___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__86558___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).

fof('$tdef_$_type_1410',axiom,
    ! [V_24Y] :
      ( c_24__type__1410___24t(V_24Y)
    <=> t(V_24Y,c_24__type__1410) ) ).

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_Coq.micromega.RingMicromega.PolC',axiom,
    ! [V_24X1,V_24Y] :
      ( cCoq_2emicromega_2eRingMicromega_2ePolC___24t(V_24X1,V_24Y)
    <=> t(V_24Y,cCoq_2emicromega_2eRingMicromega_2ePolC___24a1(V_24X1)) ) ).

fof('$tdef_$_type_92944',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
      ( c_24__type__92944___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
    <=> t(V_24Y,c_24__type__92944___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).

fof('$tdef_$_type_104841',axiom,
    ! [V_24X1,V_24X2,V_24Y] :
      ( c_24__type__104841___24t(V_24X1,V_24X2,V_24Y)
    <=> t(V_24Y,c_24__type__104841___24a2(V_24X1,V_24X2)) ) ).

fof('$tdef_$_type_82143',axiom,
    ! [V_24X1,V_24X2,V_24Y] :
      ( c_24__type__82143___24t(V_24X1,V_24X2,V_24Y)
    <=> t(V_24Y,c_24__type__82143___24a2(V_24X1,V_24X2)) ) ).

fof('$tdef_$_type_105112',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24Y] :
      ( c_24__type__105112___24t(V_24X1,V_24X2,V_24X3,V_24Y)
    <=> t(V_24Y,c_24__type__105112___24a3(V_24X1,V_24X2,V_24X3)) ) ).

fof('$tdef_Coq.NArith.BinNatDef.N.t',axiom,
    ! [V_24Y] :
      ( cCoq_2eNArith_2eBinNatDef_2eN_2et___24t(V_24Y)
    <=> t(V_24Y,cCoq_2eNArith_2eBinNatDef_2eN_2et) ) ).

fof('$tdef_Coq.Init.Datatypes.ID',axiom,
    ! [V_24Y] :
      ( cCoq_2eInit_2eDatatypes_2eID___24t(V_24Y)
    <=> t(V_24Y,cCoq_2eInit_2eDatatypes_2eID) ) ).

fof('$tdef_$_type_82615',axiom,
    ! [V_24Y] :
      ( c_24__type__82615___24t(V_24Y)
    <=> t(V_24Y,c_24__type__82615) ) ).

fof('$tdef_Hammer.Tactics.Reconstr.ReconstrT',axiom,
    ! [V_24Y] :
      ( cHammer_2eTactics_2eReconstr_2eReconstrT___24t(V_24Y)
    <=> t(V_24Y,cHammer_2eTactics_2eReconstr_2eReconstrT) ) ).

fof('$tdef_$_type_94192',axiom,
    ! [V_24Y] :
      ( c_24__type__94192___24t(V_24Y)
    <=> t(V_24Y,c_24__type__94192) ) ).

fof('$tdef_$_type_88733',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__88733___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__88733___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_104715',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y] :
      ( c_24__type__104715___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y)
    <=> t(V_24Y,c_24__type__104715___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7)) ) ).

fof('$tdef_$_type_78019',axiom,
    ! [V_24Y] :
      ( c_24__type__78019___24t(V_24Y)
    <=> t(V_24Y,c_24__type__78019) ) ).

fof('$tdef_$_type_75474',axiom,
    ! [V_24Y] :
      ( c_24__type__75474___24t(V_24Y)
    <=> t(V_24Y,c_24__type__75474) ) ).

fof('$tdef_$_type_80805',axiom,
    ! [V_24X1,V_24X2,V_24Y] :
      ( c_24__type__80805___24t(V_24X1,V_24X2,V_24Y)
    <=> t(V_24Y,c_24__type__80805___24a2(V_24X1,V_24X2)) ) ).

fof('$tdef_$_type_100096',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__100096___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__100096___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_1415',axiom,
    ! [V_24X1,V_24Y] :
      ( c_24__type__1415___24t(V_24X1,V_24Y)
    <=> t(V_24Y,c_24__type__1415___24a1(V_24X1)) ) ).

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_97427',axiom,
    ! [V_24Y] :
      ( c_24__type__97427___24t(V_24Y)
    <=> t(V_24Y,c_24__type__97427) ) ).

fof('$tdef_$_type_104573',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y] :
      ( c_24__type__104573___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y)
    <=> t(V_24Y,c_24__type__104573___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7)) ) ).

fof('$tdef_$_type_89968',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
      ( c_24__type__89968___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
    <=> t(V_24Y,c_24__type__89968___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).

fof('$tdef_$_type_75479',axiom,
    ! [V_24Y] :
      ( c_24__type__75479___24t(V_24Y)
    <=> t(V_24Y,c_24__type__75479) ) ).

fof('$tdef_$_type_75743',axiom,
    ! [V_24Y] :
      ( c_24__type__75743___24t(V_24Y)
    <=> t(V_24Y,c_24__type__75743) ) ).

fof('$tdef_$_type_75665',axiom,
    ! [V_24Y] :
      ( c_24__type__75665___24t(V_24Y)
    <=> t(V_24Y,c_24__type__75665) ) ).

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_87074',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
      ( c_24__type__87074___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
    <=> t(V_24Y,c_24__type__87074___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).

fof('$tdef_$_type_67215',axiom,
    ! [V_24Y] :
      ( c_24__type__67215___24t(V_24Y)
    <=> t(V_24Y,c_24__type__67215) ) ).

fof('$tdef_$_type_67071',axiom,
    ! [V_24Y] :
      ( c_24__type__67071___24t(V_24Y)
    <=> t(V_24Y,c_24__type__67071) ) ).

fof('$tdef_$_type_103646',axiom,
    ! [V_24Y] :
      ( c_24__type__103646___24t(V_24Y)
    <=> t(V_24Y,c_24__type__103646) ) ).

fof('$tdef_$_type_82394',axiom,
    ! [V_24Y] :
      ( c_24__type__82394___24t(V_24Y)
    <=> t(V_24Y,c_24__type__82394) ) ).

fof('$tdef_$_type_90332',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24Y] :
      ( c_24__type__90332___24t(V_24X1,V_24X2,V_24X3,V_24Y)
    <=> t(V_24Y,c_24__type__90332___24a3(V_24X1,V_24X2,V_24X3)) ) ).

fof('$tdef_$_type_76492',axiom,
    ! [V_24Y] :
      ( c_24__type__76492___24t(V_24Y)
    <=> t(V_24Y,c_24__type__76492) ) ).

fof('$tdef_$_type_88520',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__88520___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__88520___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_96704',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
      ( c_24__type__96704___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__96704___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).

fof('$tdef_$_type_363',axiom,
    ! [V_24X1,V_24Y] :
      ( c_24__type__363___24t(V_24X1,V_24Y)
    <=> t(V_24Y,c_24__type__363___24a1(V_24X1)) ) ).

fof('$tdef_$_type_105075',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y] :
      ( c_24__type__105075___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y)
    <=> t(V_24Y,c_24__type__105075___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7)) ) ).

fof('$tdef_$_type_85731',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__85731___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__85731___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).

fof('$tdef_Type',axiom,
    ! [V_24Y] :
      ( cType___24t(V_24Y)
    <=> t(V_24Y,cType) ) ).

fof('$tdef_$_type_80571',axiom,
    ! [V_24Y] :
      ( c_24__type__80571___24t(V_24Y)
    <=> t(V_24Y,c_24__type__80571) ) ).

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_90102',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24Y] :
      ( c_24__type__90102___24t(V_24X1,V_24X2,V_24X3,V_24Y)
    <=> t(V_24Y,c_24__type__90102___24a3(V_24X1,V_24X2,V_24X3)) ) ).

fof('$tdef_$_type_100788',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__100788___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__100788___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_90026',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
      ( c_24__type__90026___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
    <=> t(V_24Y,c_24__type__90026___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).

fof('$tdef_$_type_80445',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
      ( c_24__type__80445___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
    <=> t(V_24Y,c_24__type__80445___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).

fof('$tdef_$_type_90348',axiom,
    ! [V_24Y] :
      ( c_24__type__90348___24t(V_24Y)
    <=> t(V_24Y,c_24__type__90348) ) ).

fof('$tdef_$_type_81010',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y] :
      ( c_24__type__81010___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y)
    <=> t(V_24Y,c_24__type__81010___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6)) ) ).

fof('$tdef_$_type_103664',axiom,
    ! [V_24Y] :
      ( c_24__type__103664___24t(V_24Y)
    <=> t(V_24Y,c_24__type__103664) ) ).

fof('$tdef_$_type_95120',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__95120___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__95120___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).

fof('$tdef_$_type_104366',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
      ( c_24__type__104366___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
    <=> t(V_24Y,c_24__type__104366___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).

fof('$tdef_$_type_78917',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24Y] :
      ( c_24__type__78917___24t(V_24X1,V_24X2,V_24X3,V_24Y)
    <=> t(V_24Y,c_24__type__78917___24a3(V_24X1,V_24X2,V_24X3)) ) ).

fof('$tdef_$_type_82227',axiom,
    ! [V_24X1,V_24X2,V_24Y] :
      ( c_24__type__82227___24t(V_24X1,V_24X2,V_24Y)
    <=> t(V_24Y,c_24__type__82227___24a2(V_24X1,V_24X2)) ) ).

fof('$tdef_$_type_76191',axiom,
    ! [V_24Y] :
      ( c_24__type__76191___24t(V_24Y)
    <=> t(V_24Y,c_24__type__76191) ) ).

fof('$tdef_$_type_104410',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
      ( c_24__type__104410___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
    <=> t(V_24Y,c_24__type__104410___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).

fof('$tdef_$_type_94770',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__94770___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__94770___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).

fof('$tdef_$_type_96766',axiom,
    ! [V_24Y] :
      ( c_24__type__96766___24t(V_24Y)
    <=> t(V_24Y,c_24__type__96766) ) ).

fof('$tdef_$_type_94244',axiom,
    ! [V_24X1,V_24Y] :
      ( c_24__type__94244___24t(V_24X1,V_24Y)
    <=> t(V_24Y,c_24__type__94244___24a1(V_24X1)) ) ).

fof('$tdef_$_type_67722',axiom,
    ! [V_24X1,V_24X2,V_24Y] :
      ( c_24__type__67722___24t(V_24X1,V_24X2,V_24Y)
    <=> t(V_24Y,c_24__type__67722___24a2(V_24X1,V_24X2)) ) ).

fof('$tdef_$_type_560',axiom,
    ! [V_24Y] :
      ( c_24__type__560___24t(V_24Y)
    <=> t(V_24Y,c_24__type__560) ) ).

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_86612',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
      ( c_24__type__86612___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__86612___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).

fof('$tdef_$_type_1044',axiom,
    ! [V_24X1,V_24X2,V_24Y] :
      ( c_24__type__1044___24t(V_24X1,V_24X2,V_24Y)
    <=> t(V_24Y,c_24__type__1044___24a2(V_24X1,V_24X2)) ) ).

fof('$tdef_$_type_94152',axiom,
    ! [V_24Y] :
      ( c_24__type__94152___24t(V_24Y)
    <=> t(V_24Y,c_24__type__94152) ) ).

fof('$tdef_$_type_612',axiom,
    ! [V_24Y] :
      ( c_24__type__612___24t(V_24Y)
    <=> t(V_24Y,c_24__type__612) ) ).

fof('$tdef_$_type_98735',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__98735___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__98735___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_95213',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__95213___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__95213___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).

fof('$tdef_$_type_977',axiom,
    ! [V_24Y] :
      ( c_24__type__977___24t(V_24Y)
    <=> t(V_24Y,c_24__type__977) ) ).

fof('$tdef_$_type_67694',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24Y] :
      ( c_24__type__67694___24t(V_24X1,V_24X2,V_24X3,V_24Y)
    <=> t(V_24Y,c_24__type__67694___24a3(V_24X1,V_24X2,V_24X3)) ) ).

fof('$tdef_$_type_94453',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y] :
      ( c_24__type__94453___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y)
    <=> t(V_24Y,c_24__type__94453___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6)) ) ).

fof('$tdef_$_type_77980',axiom,
    ! [V_24Y] :
      ( c_24__type__77980___24t(V_24Y)
    <=> t(V_24Y,c_24__type__77980) ) ).

fof('$tdef_$_type_85338',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__85338___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__85338___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.RIneq.negreal',axiom,
    ! [V_24Y] :
      ( cCoq_2eReals_2eRIneq_2enegreal___24t(V_24Y)
    <=> t(V_24Y,cCoq_2eReals_2eRIneq_2enegreal) ) ).

fof('$tdef_$_type_105337',axiom,
    ! [V_24Y] :
      ( c_24__type__105337___24t(V_24Y)
    <=> t(V_24Y,c_24__type__105337) ) ).

fof('$tdef_$_type_103981',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
      ( c_24__type__103981___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__103981___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).

fof('$tdef_$_type_90068',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24Y] :
      ( c_24__type__90068___24t(V_24X1,V_24X2,V_24X3,V_24Y)
    <=> t(V_24Y,c_24__type__90068___24a3(V_24X1,V_24X2,V_24X3)) ) ).

fof('$tdef_$_type_77145',axiom,
    ! [V_24X1,V_24X2,V_24Y] :
      ( c_24__type__77145___24t(V_24X1,V_24X2,V_24Y)
    <=> t(V_24Y,c_24__type__77145___24a2(V_24X1,V_24X2)) ) ).

fof('$tdef_$_type_67318',axiom,
    ! [V_24Y] :
      ( c_24__type__67318___24t(V_24Y)
    <=> t(V_24Y,c_24__type__67318) ) ).

fof('$tdef_$_type_77826',axiom,
    ! [V_24Y] :
      ( c_24__type__77826___24t(V_24Y)
    <=> t(V_24Y,c_24__type__77826) ) ).

fof('$tdef_$_type_81384',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__81384___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__81384___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_89141',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__89141___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__89141___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_78031',axiom,
    ! [V_24Y] :
      ( c_24__type__78031___24t(V_24Y)
    <=> t(V_24Y,c_24__type__78031) ) ).

fof('$tdef_$_type_96641',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
      ( c_24__type__96641___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__96641___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).

fof('$tdef_$_type_75595',axiom,
    ! [V_24Y] :
      ( c_24__type__75595___24t(V_24Y)
    <=> t(V_24Y,c_24__type__75595) ) ).

fof('$tdef_$_type_67667',axiom,
    ! [V_24Y] :
      ( c_24__type__67667___24t(V_24Y)
    <=> t(V_24Y,c_24__type__67667) ) ).

fof('$tdef_$_type_96713',axiom,
    ! [V_24X1,V_24Y] :
      ( c_24__type__96713___24t(V_24X1,V_24Y)
    <=> t(V_24Y,c_24__type__96713___24a1(V_24X1)) ) ).

fof('$tdef_$_type_1461',axiom,
    ! [V_24Y] :
      ( c_24__type__1461___24t(V_24Y)
    <=> t(V_24Y,c_24__type__1461) ) ).

fof('_HAMMER_GOAL',conjecture,
    ! [V0__m] :
      ( cIntMap_2eMap_2eMap___24t(cA,V0__m)
     => ( cMapcanon_2eMapCanon_2emapcanon___24a1(V0__m)
       => ! [V2__m_27] :
            ( cIntMap_2eMap_2eMap___24t(cB,V2__m_27)
           => cMapcanon_2eMapCanon_2emapcanon___24a1(cIntMap_2eFset_2eMapDomRestrTo___24a4(cA,cB,V0__m,V2__m_27)) ) ) ) ).

%------------------------------------------------------------------------------