TPTP Problem File: SEV646+1.p

View Solutions - Solve Problem

%------------------------------------------------------------------------------
% File     : SEV646+1 : TPTP v9.3.1. Released v9.3.0.
% Domain   : Set theory
% Problem  : CoqHammer - Mapaxioms FSetUnion assoc
% 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    : Mapaxioms.FSetUnion.assoc.p [Kal26]

% Status   : Theorem
% Rating   : 0.52 v9.3.0
% Syntax   : Number of formulae    : 3068 (1329 unt;   0 def)
%            Number of atoms       : 10111 (2850 equ)
%            Maximal formula atoms :  257 (   3 avg)
%            Number of connectives : 7129 (  86   ~; 802   |;1827   &)
%                                         (1144 <=>;3270  =>;   0  <=;   0 <~>)
%            Maximal formula depth :  258 (   6 avg)
%            Maximal term depth    :   23 (   1 avg)
%            Number of predicates  :  618 ( 617 usr;   0 prp; 1-23 aty)
%            Number of functors    : 1810 (1810 usr;1166 con; 0-22 aty)
%            Number of variables   : 9950 (9220   !; 730   ?)
% SPC      : FOF_THM_RFO_SEQ

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

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

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

fof('$_case_Coq.Init.Datatypes.list$110186',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_24110273___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_24110186___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__110190] :
                ( t(Vvar__1___24Anonymous__110190,Vv__CANONICAL__0)
                & ? [Vvar__2___24Anonymous__110191] :
                    ( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vvar__2___24Anonymous__110191)
                    & c_24__case__Coq_2eInit_2eDatatypes_2elist_24110273___24a3(Vv__CANONICAL__0,Vv__CANONICAL__4,Vv__CANONICAL__5) = cCoq_2eInit_2eDatatypes_2econs___24a3(Vv__CANONICAL__0,Vvar__1___24Anonymous__110190,Vvar__2___24Anonymous__110191)
                    & c_24__case__Coq_2eInit_2eDatatypes_2elist_24110186___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__110190,c_24__fix__110318__v__CANONICAL__1___24a3(Vv__CANONICAL__0,Vvar__2___24Anonymous__110191,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$110273',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_24110273___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__110277] :
              ( t(Vvar__1___24Anonymous__110277,Vv__CANONICAL__0)
              & ? [Vvar__2___24Anonymous__110278] :
                  ( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vvar__2___24Anonymous__110278)
                  & Vv__CANONICAL__2 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vv__CANONICAL__0,Vvar__1___24Anonymous__110277,Vvar__2___24Anonymous__110278)
                  & c_24__case__Coq_2eInit_2eDatatypes_2elist_24110273___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = cCoq_2eInit_2eDatatypes_2econs___24a3(Vv__CANONICAL__0,Vvar__1___24Anonymous__110277,c_24__fix__110318__v__CANONICAL__1___24a3(Vv__CANONICAL__0,Vvar__2___24Anonymous__110278,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$110440',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_24110440___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = cCoq_2eNumbers_2eBinNums_2eZ0 )
        | ? [Vvar__0___24Anonymous__110441] :
            ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__110441)
            & Vv__CANONICAL__2 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__110441)
            & c_24__case__Coq_2eInit_2eDatatypes_2enat_24110440___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__110441)) ) ) ) ).

fof('$_case_Coq.Init.Datatypes.nat$110462',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_24110462___24a1(Vv__CANONICAL__0) = cCoq_2eNumbers_2eBinNums_2eZ0 )
        | ? [Vvar__0___24Anonymous__110463] :
            ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__110463)
            & Vv__CANONICAL__0 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__110463)
            & c_24__case__Coq_2eInit_2eDatatypes_2enat_24110462___24a1(Vv__CANONICAL__0) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eof__succ__nat___24a1(Vvar__0___24Anonymous__110463)) ) ) ) ).

fof('$_case_Coq.Init.Datatypes.prod$11718',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__11731___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__11723] :
                  ( t(Vvar__2___24Anonymous__11723,Vv__CANONICAL__2)
                  & ? [Vvar__3___24Anonymous__11724] :
                      ( t(Vvar__3___24Anonymous__11724,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__11723,Vvar__3___24Anonymous__11724)
                      & ( c_24__case__Coq_2eInit_2eDatatypes_2eprod_2411718___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__11723)),Vvar__3___24Anonymous__11724)))) ) ) ) ) ) ) ) ) ).

fof('$_case_Coq.Numbers.BinNums.Z$110457',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_24110462___24a1(Vv__CANONICAL__2) = cCoq_2eNumbers_2eBinNums_2eZ0
          & c_24__case__Coq_2eNumbers_2eBinNums_2eZ_24110457___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = cCoq_2eNumbers_2eBinNums_2eZ0 )
        | ? [Vvar__0___24Anonymous__110458] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__110458)
            & c_24__case__Coq_2eInit_2eDatatypes_2enat_24110462___24a1(Vv__CANONICAL__2) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__110458)
            & c_24__case__Coq_2eNumbers_2eBinNums_2eZ_24110457___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__110458) )
        | ? [Vvar__0___24Anonymous__110459] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__110459)
            & c_24__case__Coq_2eInit_2eDatatypes_2enat_24110462___24a1(Vv__CANONICAL__2) = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__110459)
            & c_24__case__Coq_2eNumbers_2eBinNums_2eZ_24110457___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__110459) ) ) ) ).

fof('$_case_Coq.Numbers.BinNums.positive$113672',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1] :
      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__1)
     => ( ? [Vvar__0___24Anonymous__113673] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__113673)
            & Vv__CANONICAL__1 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__113673)
            & c_24__case__Coq_2eNumbers_2eBinNums_2epositive_24113672___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = cCoq_2eNumbers_2eBinNums_2exO___24a1(c_24__fix__113688__v__CANONICAL__0___24a1(Vvar__0___24Anonymous__113673)) )
        | ? [Vvar__0___24Anonymous__113680] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__113680)
            & Vv__CANONICAL__1 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__113680)
            & c_24__case__Coq_2eNumbers_2eBinNums_2epositive_24113672___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__113680) )
        | ( Vv__CANONICAL__1 = cCoq_2eNumbers_2eBinNums_2exH
          & c_24__case__Coq_2eNumbers_2eBinNums_2epositive_24113672___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2eNumbers_2eBinNums_2exH) ) ) ) ).

fof('$_def_$_let_var_6_p_7626_7629',axiom,
    ! [V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__7625] : c_24__let__var__6__p__7626__7629___24a4(V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__7625) = cCoq_2esetoid__ring_2eRing__theory_2epow__pos___24a4(V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__7625) ).

fof('$_def_$_let_var_6_p_7628_7630',axiom,
    ! [V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__7627] : c_24__let__var__6__p__7628__7630___24a4(V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__7627) = cCoq_2esetoid__ring_2eRing__theory_2epow__pos___24a4(V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__7627) ).

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__107714] :
                  ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__107714)
                  & V2__m = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__107714)
                  & ( cCoq_2eArith_2eEqNat_2eeq__nat___24a2(V1__n,V2__m)
                  <=> p(c_24False) ) ) ) ) )
        | ? [Vvar__0___24Anonymous__107715] :
            ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__107715)
            & ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__m)
             => ( V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__107715)
                & ( ( V2__m = cCoq_2eInit_2eDatatypes_2eO
                    & ( cCoq_2eArith_2eEqNat_2eeq__nat___24a2(V1__n,V2__m)
                    <=> p(c_24False) ) )
                  | ? [Vvar__0___24Anonymous__107718] :
                      ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__107718)
                      & V2__m = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__107718)
                      & ( cCoq_2eArith_2eEqNat_2eeq__nat___24a2(V1__n,V2__m)
                      <=> cCoq_2eArith_2eEqNat_2eeq__nat___24a2(Vvar__0___24Anonymous__107715,Vvar__0___24Anonymous__107718) ) ) ) ) ) ) ) ) ).

fof('$_def_Coq.Arith.PeanoNat.Nat.b2n',axiom,
    ! [V0__b] :
      ( cCoq_2eInit_2eDatatypes_2ebool___24t(V0__b)
     => ( ( V0__b = cCoq_2eInit_2eDatatypes_2etrue
          & cCoq_2eArith_2ePeanoNat_2eNat_2eb2n___24a1(V0__b) = cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO) )
        | ( V0__b = cCoq_2eInit_2eDatatypes_2efalse
          & cCoq_2eArith_2ePeanoNat_2eNat_2eb2n___24a1(V0__b) = cCoq_2eInit_2eDatatypes_2eO ) ) ) ).

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

fof('$_def_Coq.Arith.PeanoNat.Nat.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__120322___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__121345] :
            ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__121345)
            & V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__121345)
            & cCoq_2eArith_2ePlus_2etail__plus___24a2(V1__n,V2__m) = cCoq_2eArith_2ePlus_2etail__plus___24a2(Vvar__0___24Anonymous__121345,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.Bvector.Bvector',axiom,
    cCoq_2eBool_2eBvector_2eBvector = cCoq_2eVectors_2eVectorDef_2et___24a1(cCoq_2eInit_2eDatatypes_2ebool) ).

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__286,c_24__prop__287,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__288,c_24__prop__289,cCoq_2eInit_2eLogic_2eeq__refl___24a2(cCoq_2eInit_2eDatatypes_2ebool,cCoq_2eInit_2eDatatypes_2efalse)) ) ) ) ).

fof('$_def_Coq.Bool.Zerob.zerob',axiom,
    ! [V0__n] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
     => ( ( V0__n = cCoq_2eInit_2eDatatypes_2eO
          & cCoq_2eBool_2eZerob_2ezerob___24a1(V0__n) = cCoq_2eInit_2eDatatypes_2etrue )
        | ? [Vvar__0___24Anonymous__118413] :
            ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__118413)
            & V0__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__118413)
            & cCoq_2eBool_2eZerob_2ezerob___24a1(V0__n) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ).

fof('$_def_Coq.FSets.FSetPositive.PositiveSet.Equal',axiom,
    ! [V0__s,V1__s_27] :
      ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eEqual___24a2(V0__s,V1__s_27)
    <=> ! [V2__a] :
          ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(V2__a)
         => ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eIn___24a2(V2__a,V0__s)
          <=> cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eIn___24a2(V2__a,V1__s_27) ) ) ) ).

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

fof('$_def_Coq.FSets.FSetPositive.PositiveSet.elements',axiom,
    ! [V0__m] : cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelements___24a1(V0__m) = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2exelements___24a3(V0__m,cCoq_2eNumbers_2eBinNums_2exH,cCoq_2eInit_2eDatatypes_2enil___24a1(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt)) ).

fof('$_def_Coq.FSets.FSetPositive.PositiveSet.elt',axiom,
    ! [Vvar__107100] :
      ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(Vvar__107100)
    <=> cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__107100) ) ).

fof('$_def_Coq.FSets.FSetPositive.PositiveSet.empty',axiom,
    cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eempty = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eLeaf ).

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

fof('$_def_Coq.FSets.FSetPositive.PositiveSet.fold',axiom,
    ! [V0__B,V1__f,V2__m,V3__i] : cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2efold___24a4(V0__B,V1__f,V2__m,V3__i) = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2exfold___24a5(V0__B,V1__f,V2__m,V3__i,cCoq_2eNumbers_2eBinNums_2exH) ).

fof('$_def_Coq.FSets.FSetPositive.PositiveSet.mem',axiom,
    ! [V1__i,V2__m] :
      ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(V2__m)
     => ( ( V2__m = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eLeaf
          & cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2emem___24a2(V1__i,V2__m) = cCoq_2eInit_2eDatatypes_2efalse )
        | ? [Vvar__0___24Anonymous__107148] :
            ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree___24t(Vvar__0___24Anonymous__107148)
            & ? [Vvar__1___24Anonymous__107149] :
                ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__1___24Anonymous__107149)
                & ? [Vvar__2___24Anonymous__107150] :
                    ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree___24t(Vvar__2___24Anonymous__107150)
                    & ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(V1__i)
                     => ( V2__m = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eNode___24a3(Vvar__0___24Anonymous__107148,Vvar__1___24Anonymous__107149,Vvar__2___24Anonymous__107150)
                        & ( ? [Vvar__0___24Anonymous__107163] :
                              ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__107163)
                              & V1__i = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__107163)
                              & cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2emem___24a2(V1__i,V2__m) = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2emem___24a2(Vvar__0___24Anonymous__107163,Vvar__2___24Anonymous__107150) )
                          | ? [Vvar__0___24Anonymous__107164] :
                              ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__107164)
                              & V1__i = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__107164)
                              & cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2emem___24a2(V1__i,V2__m) = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2emem___24a2(Vvar__0___24Anonymous__107164,Vvar__0___24Anonymous__107148) )
                          | ( V1__i = cCoq_2eNumbers_2eBinNums_2exH
                            & cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2emem___24a2(V1__i,V2__m) = Vvar__1___24Anonymous__107149 ) ) ) ) ) ) ) ) ) ).

fof('$_def_Coq.FSets.FSetPositive.PositiveSet.t',axiom,
    ! [Vvar__107126] :
      ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(Vvar__107126)
    <=> cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree___24t(Vvar__107126) ) ).

fof('$_def_Coq.FSets.FSetPositive.PositiveSet.union',axiom,
    ! [V1__m,V2__m_27] :
      ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(V1__m)
     => ( ( V1__m = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eLeaf
          & cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eunion___24a2(V1__m,V2__m_27) = V2__m_27 )
        | ? [Vvar__0___24Anonymous__107169] :
            ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree___24t(Vvar__0___24Anonymous__107169)
            & ? [Vvar__1___24Anonymous__107170] :
                ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__1___24Anonymous__107170)
                & ? [Vvar__2___24Anonymous__107171] :
                    ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree___24t(Vvar__2___24Anonymous__107171)
                    & ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(V2__m_27)
                     => ( V1__m = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eNode___24a3(Vvar__0___24Anonymous__107169,Vvar__1___24Anonymous__107170,Vvar__2___24Anonymous__107171)
                        & ( ( V2__m_27 = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eLeaf
                            & cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eunion___24a2(V1__m,V2__m_27) = V1__m )
                          | ? [Vvar__0___24Anonymous__107187] :
                              ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree___24t(Vvar__0___24Anonymous__107187)
                              & ? [Vvar__1___24Anonymous__107188] :
                                  ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__1___24Anonymous__107188)
                                  & ? [Vvar__2___24Anonymous__107189] :
                                      ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree___24t(Vvar__2___24Anonymous__107189)
                                      & V2__m_27 = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eNode___24a3(Vvar__0___24Anonymous__107187,Vvar__1___24Anonymous__107188,Vvar__2___24Anonymous__107189)
                                      & cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eunion___24a2(V1__m,V2__m_27) = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eNode___24a3(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eunion___24a2(Vvar__0___24Anonymous__107169,Vvar__0___24Anonymous__107187),cCoq_2eInit_2eDatatypes_2eorb___24a2(Vvar__1___24Anonymous__107170,Vvar__1___24Anonymous__107188),cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eunion___24a2(Vvar__2___24Anonymous__107171,Vvar__2___24Anonymous__107189)) ) ) ) ) ) ) ) ) ) ) ) ).

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.CompOpp',axiom,
    ! [V0__r] :
      ( cCoq_2eInit_2eDatatypes_2ecomparison___24t(V0__r)
     => ( ( V0__r = cCoq_2eInit_2eDatatypes_2eEq
          & cCoq_2eInit_2eDatatypes_2eCompOpp___24a1(V0__r) = cCoq_2eInit_2eDatatypes_2eEq )
        | ( V0__r = cCoq_2eInit_2eDatatypes_2eLt
          & cCoq_2eInit_2eDatatypes_2eCompOpp___24a1(V0__r) = cCoq_2eInit_2eDatatypes_2eGt )
        | ( V0__r = cCoq_2eInit_2eDatatypes_2eGt
          & cCoq_2eInit_2eDatatypes_2eCompOpp___24a1(V0__r) = cCoq_2eInit_2eDatatypes_2eLt ) ) ) ).

fof('$_def_Coq.Init.Datatypes.ID',axiom,
    ! [Vvar__107637] :
      ( cCoq_2eInit_2eDatatypes_2eID___24t(Vvar__107637)
    <=> ! [V0__A] :
          ( cType___24t(V0__A)
         => ! [V1___24Anonymous] :
              ( t(V1___24Anonymous,V0__A)
             => t(happ(happ(Vvar__107637,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__2657] :
              ( t(Vvar__1___24Anonymous__2657,V0__A)
              & ? [Vvar__2___24Anonymous__2658] :
                  ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__2658)
                  & V2__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__2657,Vvar__2___24Anonymous__2658)
                  & cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V2__l,V3__m) = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__2657,cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,Vvar__2___24Anonymous__2658,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__85552] :
              ( t(Vvar__2___24Anonymous__85552,V0__A)
              & ? [Vvar__3___24Anonymous__85553] :
                  ( t(Vvar__3___24Anonymous__85553,V1__B)
                  & V2__p = cCoq_2eInit_2eDatatypes_2epair___24a4(V0__A,V1__B,Vvar__2___24Anonymous__85552,Vvar__3___24Anonymous__85553)
                  & cCoq_2eInit_2eDatatypes_2efst___24a3(V0__A,V1__B,V2__p) = Vvar__2___24Anonymous__85552 ) ) ) ) ) ).

fof('$_def_Coq.Init.Datatypes.id',axiom,
    ! [V0__A,V1__x] : cCoq_2eInit_2eDatatypes_2eid___24a2(V0__A,V1__x) = V1__x ).

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__2647] :
              ( t(Vvar__1___24Anonymous__2647,V0__A)
              & ? [Vvar__2___24Anonymous__2648] :
                  ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__2648)
                  & V2__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__2647,Vvar__2___24Anonymous__2648)
                  & cCoq_2eInit_2eDatatypes_2elength___24a2(V0__A,V2__l) = cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2elength___24a2(V0__A,Vvar__2___24Anonymous__2648)) ) ) ) ) ) ).

fof('$_def_Coq.Init.Datatypes.nat_rect',axiom,
    ! [V0__P,V1__f,V2__f,V4__n] :
      ( c_24__type__116798___24t(V0__P,V0__P)
     => ( cCoq_2eInit_2eDatatypes_2enat___24t(V4__n)
       => ( ( V4__n = cCoq_2eInit_2eDatatypes_2eO
            & cCoq_2eInit_2eDatatypes_2enat__rect___24a4(V0__P,V1__f,V2__f,V4__n) = V1__f )
          | ? [Vvar__0___24Anonymous__116796] :
              ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__116796)
              & V4__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__116796)
              & cCoq_2eInit_2eDatatypes_2enat__rect___24a4(V0__P,V1__f,V2__f,V4__n) = happ(happ(V2__f,Vvar__0___24Anonymous__116796),cCoq_2eInit_2eDatatypes_2enat__rect___24a4(V0__P,V1__f,V2__f,Vvar__0___24Anonymous__116796)) ) ) ) ) ).

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.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__85564] :
              ( t(Vvar__2___24Anonymous__85564,V0__A)
              & ? [Vvar__3___24Anonymous__85565] :
                  ( t(Vvar__3___24Anonymous__85565,V1__B)
                  & V2__p = cCoq_2eInit_2eDatatypes_2epair___24a4(V0__A,V1__B,Vvar__2___24Anonymous__85564,Vvar__3___24Anonymous__85565)
                  & cCoq_2eInit_2eDatatypes_2esnd___24a3(V0__A,V1__B,V2__p) = Vvar__3___24Anonymous__85565 ) ) ) ) ) ).

fof('$_def_Coq.Init.Datatypes.unit_rec',axiom,
    ! [V0__P] : cCoq_2eInit_2eDatatypes_2eunit__rec___24a1(V0__P) = cCoq_2eInit_2eDatatypes_2eunit__rect___24a1(V0__P) ).

fof('$_def_Coq.Init.Datatypes.unit_rect',axiom,
    ! [V0__P,V1__f,V2__u] :
      ( c_24__type__172555___24t(V0__P,V0__P)
     => ( cCoq_2eInit_2eDatatypes_2eunit___24t(V2__u)
       => ( V2__u = cCoq_2eInit_2eDatatypes_2ett
          & cCoq_2eInit_2eDatatypes_2eunit__rect___24a3(V0__P,V1__f,V2__u) = V1__f ) ) ) ).

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.Decimal.int_of_int',axiom,
    ! [V0__i] : cCoq_2eInit_2eDecimal_2eint__of__int___24a1(V0__i) = V0__i ).

fof('$_def_Coq.Init.Decimal.nzhead',axiom,
    ! [V1__d] :
      ( cCoq_2eInit_2eDecimal_2euint___24t(V1__d)
     => ( ( V1__d = cCoq_2eInit_2eDecimal_2eNil
          & cCoq_2eInit_2eDecimal_2enzhead___24a1(V1__d) = V1__d )
        | ? [Vvar__0___24Anonymous__120885] :
            ( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0___24Anonymous__120885)
            & V1__d = cCoq_2eInit_2eDecimal_2eD0___24a1(Vvar__0___24Anonymous__120885)
            & cCoq_2eInit_2eDecimal_2enzhead___24a1(V1__d) = cCoq_2eInit_2eDecimal_2enzhead___24a1(Vvar__0___24Anonymous__120885) )
        | ? [Vvar__0___24Anonymous__120886] :
            ( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0___24Anonymous__120886)
            & V1__d = cCoq_2eInit_2eDecimal_2eD1___24a1(Vvar__0___24Anonymous__120886)
            & cCoq_2eInit_2eDecimal_2enzhead___24a1(V1__d) = V1__d )
        | ? [Vvar__0___24Anonymous__120887] :
            ( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0___24Anonymous__120887)
            & V1__d = cCoq_2eInit_2eDecimal_2eD2___24a1(Vvar__0___24Anonymous__120887)
            & cCoq_2eInit_2eDecimal_2enzhead___24a1(V1__d) = V1__d )
        | ? [Vvar__0___24Anonymous__120888] :
            ( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0___24Anonymous__120888)
            & V1__d = cCoq_2eInit_2eDecimal_2eD3___24a1(Vvar__0___24Anonymous__120888)
            & cCoq_2eInit_2eDecimal_2enzhead___24a1(V1__d) = V1__d )
        | ? [Vvar__0___24Anonymous__120889] :
            ( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0___24Anonymous__120889)
            & V1__d = cCoq_2eInit_2eDecimal_2eD4___24a1(Vvar__0___24Anonymous__120889)
            & cCoq_2eInit_2eDecimal_2enzhead___24a1(V1__d) = V1__d )
        | ? [Vvar__0___24Anonymous__120890] :
            ( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0___24Anonymous__120890)
            & V1__d = cCoq_2eInit_2eDecimal_2eD5___24a1(Vvar__0___24Anonymous__120890)
            & cCoq_2eInit_2eDecimal_2enzhead___24a1(V1__d) = V1__d )
        | ? [Vvar__0___24Anonymous__120891] :
            ( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0___24Anonymous__120891)
            & V1__d = cCoq_2eInit_2eDecimal_2eD6___24a1(Vvar__0___24Anonymous__120891)
            & cCoq_2eInit_2eDecimal_2enzhead___24a1(V1__d) = V1__d )
        | ? [Vvar__0___24Anonymous__120892] :
            ( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0___24Anonymous__120892)
            & V1__d = cCoq_2eInit_2eDecimal_2eD7___24a1(Vvar__0___24Anonymous__120892)
            & cCoq_2eInit_2eDecimal_2enzhead___24a1(V1__d) = V1__d )
        | ? [Vvar__0___24Anonymous__120893] :
            ( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0___24Anonymous__120893)
            & V1__d = cCoq_2eInit_2eDecimal_2eD8___24a1(Vvar__0___24Anonymous__120893)
            & cCoq_2eInit_2eDecimal_2enzhead___24a1(V1__d) = V1__d )
        | ? [Vvar__0___24Anonymous__120894] :
            ( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0___24Anonymous__120894)
            & V1__d = cCoq_2eInit_2eDecimal_2eD9___24a1(Vvar__0___24Anonymous__120894)
            & cCoq_2eInit_2eDecimal_2enzhead___24a1(V1__d) = V1__d ) ) ) ).

fof('$_def_Coq.Init.Decimal.uint_of_uint',axiom,
    ! [V0__i] : cCoq_2eInit_2eDecimal_2euint__of__uint___24a1(V0__i) = V0__i ).

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__1932] :
            ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__1932)
            & V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__1932)
            & cCoq_2eInit_2eNat_2eadd___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eNat_2eadd___24a2(Vvar__0___24Anonymous__1932,V2__m)) ) ) ) ).

fof('$_def_Coq.Init.Nat.compare',axiom,
    ! [V1__n,V2__m] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
     => ( ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__m)
         => ( V1__n = cCoq_2eInit_2eDatatypes_2eO
            & ( ( V2__m = cCoq_2eInit_2eDatatypes_2eO
                & cCoq_2eInit_2eNat_2ecompare___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2eEq )
              | ? [Vvar__0___24Anonymous__109412] :
                  ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__109412)
                  & V2__m = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__109412)
                  & cCoq_2eInit_2eNat_2ecompare___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2eLt ) ) ) )
        | ? [Vvar__0___24Anonymous__109413] :
            ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__109413)
            & ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__m)
             => ( V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__109413)
                & ( ( V2__m = cCoq_2eInit_2eDatatypes_2eO
                    & cCoq_2eInit_2eNat_2ecompare___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2eGt )
                  | ? [Vvar__0___24Anonymous__109416] :
                      ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__109416)
                      & V2__m = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__109416)
                      & cCoq_2eInit_2eNat_2ecompare___24a2(V1__n,V2__m) = cCoq_2eInit_2eNat_2ecompare___24a2(Vvar__0___24Anonymous__109413,Vvar__0___24Anonymous__109416) ) ) ) ) ) ) ) ).

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__120988] :
            ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__120988)
            & ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__120988)
             => ( V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__120988)
                & ( ( Vvar__0___24Anonymous__120988 = cCoq_2eInit_2eDatatypes_2eO
                    & cCoq_2eInit_2eNat_2ediv2___24a1(V1__n) = cCoq_2eInit_2eDatatypes_2eO )
                  | ? [Vvar__0___24Anonymous__120991] :
                      ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__120991)
                      & Vvar__0___24Anonymous__120988 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__120991)
                      & cCoq_2eInit_2eNat_2ediv2___24a1(V1__n) = cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eNat_2ediv2___24a1(Vvar__0___24Anonymous__120991)) ) ) ) ) ) ) ) ).

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

fof('$_def_Coq.Init.Nat.eqb',axiom,
    ! [V1__n,V2__m] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
     => ( ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__m)
         => ( V1__n = cCoq_2eInit_2eDatatypes_2eO
            & ( ( V2__m = cCoq_2eInit_2eDatatypes_2eO
                & cCoq_2eInit_2eNat_2eeqb___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2etrue )
              | ? [Vvar__0___24Anonymous__120965] :
                  ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__120965)
                  & V2__m = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__120965)
                  & cCoq_2eInit_2eNat_2eeqb___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) )
        | ? [Vvar__0___24Anonymous__120966] :
            ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__120966)
            & ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__m)
             => ( V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__120966)
                & ( ( V2__m = cCoq_2eInit_2eDatatypes_2eO
                    & cCoq_2eInit_2eNat_2eeqb___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2efalse )
                  | ? [Vvar__0___24Anonymous__120969] :
                      ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__120969)
                      & V2__m = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__120969)
                      & cCoq_2eInit_2eNat_2eeqb___24a2(V1__n,V2__m) = cCoq_2eInit_2eNat_2eeqb___24a2(Vvar__0___24Anonymous__120966,Vvar__0___24Anonymous__120969) ) ) ) ) ) ) ) ).

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__109433] :
            ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__109433)
            & ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__109433)
             => ( V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__109433)
                & ( ( Vvar__0___24Anonymous__109433 = cCoq_2eInit_2eDatatypes_2eO
                    & cCoq_2eInit_2eNat_2eeven___24a1(V1__n) = cCoq_2eInit_2eDatatypes_2efalse )
                  | ? [Vvar__0___24Anonymous__109436] :
                      ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__109436)
                      & Vvar__0___24Anonymous__109433 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__109436)
                      & cCoq_2eInit_2eNat_2eeven___24a1(V1__n) = cCoq_2eInit_2eNat_2eeven___24a1(Vvar__0___24Anonymous__109436) ) ) ) ) ) ) ) ).

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__89835] :
            ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__89835)
            & ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__m)
             => ( V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__89835)
                & ( ( V2__m = cCoq_2eInit_2eDatatypes_2eO
                    & cCoq_2eInit_2eNat_2eleb___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2efalse )
                  | ? [Vvar__0___24Anonymous__89838] :
                      ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__89838)
                      & V2__m = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__89838)
                      & cCoq_2eInit_2eNat_2eleb___24a2(V1__n,V2__m) = cCoq_2eInit_2eNat_2eleb___24a2(Vvar__0___24Anonymous__89835,Vvar__0___24Anonymous__89838) ) ) ) ) ) ) ) ).

fof('$_def_Coq.Init.Nat.log2_iter',axiom,
    ! [V1__k,V2__p,V3__q,V4__r] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(V1__k)
     => ( ( V1__k = cCoq_2eInit_2eDatatypes_2eO
          & cCoq_2eInit_2eNat_2elog2__iter___24a4(V1__k,V2__p,V3__q,V4__r) = V2__p )
        | ? [Vvar__0___24Anonymous__120975] :
            ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__120975)
            & ( cCoq_2eInit_2eDatatypes_2enat___24t(V4__r)
             => ( V1__k = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__120975)
                & ( ( V4__r = cCoq_2eInit_2eDatatypes_2eO
                    & cCoq_2eInit_2eNat_2elog2__iter___24a4(V1__k,V2__p,V3__q,V4__r) = cCoq_2eInit_2eNat_2elog2__iter___24a4(Vvar__0___24Anonymous__120975,cCoq_2eInit_2eDatatypes_2eS___24a1(V2__p),cCoq_2eInit_2eDatatypes_2eS___24a1(V3__q),V3__q) )
                  | ? [Vvar__0___24Anonymous__120978] :
                      ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__120978)
                      & V4__r = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__120978)
                      & cCoq_2eInit_2eNat_2elog2__iter___24a4(V1__k,V2__p,V3__q,V4__r) = cCoq_2eInit_2eNat_2elog2__iter___24a4(Vvar__0___24Anonymous__120975,V2__p,cCoq_2eInit_2eDatatypes_2eS___24a1(V3__q),Vvar__0___24Anonymous__120978) ) ) ) ) ) ) ) ).

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__109421] :
            ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__109421)
            & ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__m)
             => ( V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__109421)
                & ( ( V2__m = cCoq_2eInit_2eDatatypes_2eO
                    & cCoq_2eInit_2eNat_2emax___24a2(V1__n,V2__m) = V1__n )
                  | ? [Vvar__0___24Anonymous__109424] :
                      ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__109424)
                      & V2__m = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__109424)
                      & cCoq_2eInit_2eNat_2emax___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eNat_2emax___24a2(Vvar__0___24Anonymous__109421,Vvar__0___24Anonymous__109424)) ) ) ) ) ) ) ) ).

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__109427] :
            ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__109427)
            & ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__m)
             => ( V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__109427)
                & ( ( V2__m = cCoq_2eInit_2eDatatypes_2eO
                    & cCoq_2eInit_2eNat_2emin___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2eO )
                  | ? [Vvar__0___24Anonymous__109430] :
                      ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__109430)
                      & V2__m = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__109430)
                      & cCoq_2eInit_2eNat_2emin___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eNat_2emin___24a2(Vvar__0___24Anonymous__109427,Vvar__0___24Anonymous__109430)) ) ) ) ) ) ) ) ).

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__109409] :
            ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__109409)
            & V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__109409)
            & cCoq_2eInit_2eNat_2emul___24a2(V1__n,V2__m) = cCoq_2eInit_2eNat_2eadd___24a2(V2__m,cCoq_2eInit_2eNat_2emul___24a2(Vvar__0___24Anonymous__109409,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__115731] :
            ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__115731)
            & V2__m = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__115731)
            & 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__115731)) ) ) ) ).

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__109407] :
            ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__109407)
            & V0__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__109407)
            & cCoq_2eInit_2eNat_2epred___24a1(V0__n) = Vvar__0___24Anonymous__109407 ) ) ) ).

fof('$_def_Coq.Init.Nat.square',axiom,
    ! [V0__n] : cCoq_2eInit_2eNat_2esquare___24a1(V0__n) = cCoq_2eInit_2eNat_2emul___24a2(V0__n,V0__n) ).

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__89829] :
            ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__89829)
            & ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__m)
             => ( V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__89829)
                & ( ( V2__m = cCoq_2eInit_2eDatatypes_2eO
                    & cCoq_2eInit_2eNat_2esub___24a2(V1__n,V2__m) = V1__n )
                  | ? [Vvar__0___24Anonymous__89832] :
                      ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__89832)
                      & V2__m = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__89832)
                      & cCoq_2eInit_2eNat_2esub___24a2(V1__n,V2__m) = cCoq_2eInit_2eNat_2esub___24a2(Vvar__0___24Anonymous__89829,Vvar__0___24Anonymous__89832) ) ) ) ) ) ) ) ).

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

fof('$_def_Coq.Init.Nat.t',axiom,
    ! [Vvar__109406] :
      ( cCoq_2eInit_2eNat_2et___24t(Vvar__109406)
    <=> cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__109406) ) ).

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__120972] :
            ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__120972)
            & V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__120972)
            & cCoq_2eInit_2eNat_2etail__add___24a2(V1__n,V2__m) = cCoq_2eInit_2eNat_2etail__add___24a2(Vvar__0___24Anonymous__120972,cCoq_2eInit_2eDatatypes_2eS___24a1(V2__m)) ) ) ) ).

fof('$_def_Coq.Init.Nat.testbit',axiom,
    ! [V1__a,V2__n] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__n)
     => ( ( V2__n = cCoq_2eInit_2eDatatypes_2eO
          & cCoq_2eInit_2eNat_2etestbit___24a2(V1__a,V2__n) = cCoq_2eInit_2eNat_2eodd___24a1(V1__a) )
        | ? [Vvar__0___24Anonymous__120993] :
            ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__120993)
            & V2__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__120993)
            & cCoq_2eInit_2eNat_2etestbit___24a2(V1__a,V2__n) = cCoq_2eInit_2eNat_2etestbit___24a2(cCoq_2eInit_2eNat_2ediv2___24a1(V1__a),Vvar__0___24Anonymous__120993) ) ) ) ).

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__109632] :
            ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__109632)
            & V0__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__109632)
            & ( 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.Exc',axiom,
    ! [V0__A] : cCoq_2eInit_2eSpecif_2eExc___24a1(V0__A) = cCoq_2eInit_2eDatatypes_2eoption___24a1(V0__A) ).

fof('$_def_Coq.Init.Specif.except',axiom,
    cCoq_2eInit_2eSpecif_2eexcept = cCoq_2eInit_2eLogic_2eFalse__rec ).

fof('$_def_Coq.Init.Specif.proj1_sig',axiom,
    ! [V0__A,V1__P,V2__e] :
      ( cType___24t(V0__A)
     => ( c_24__type__121886___24t(V0__A,V1__P,V1__P)
       => ( cCoq_2eInit_2eSpecif_2esig___24t(V0__A,V1__P,V2__e)
         => ? [Vvar__2__x__121880] :
              ( t(Vvar__2__x__121880,V0__A)
              & p(happ(V1__P,Vvar__2__x__121880))
              & V2__e = cCoq_2eInit_2eSpecif_2eexist___24a3(V0__A,V1__P,Vvar__2__x__121880)
              & cCoq_2eInit_2eSpecif_2eproj1__sig___24a3(V0__A,V1__P,V2__e) = Vvar__2__x__121880 ) ) ) ) ).

fof('$_def_Coq.Init.Specif.projT1',axiom,
    ! [V0__A,V1__P,V2__x] :
      ( cType___24t(V0__A)
     => ( c_24__type__121909___24t(V0__A,V1__P,V1__P)
       => ( cCoq_2eInit_2eSpecif_2esigT___24t(V0__A,V1__P,V2__x)
         => ? [Vvar__2__x__121903] :
              ( t(Vvar__2__x__121903,V0__A)
              & ? [Vvar__3___24Anonymous__121904] :
                  ( t(Vvar__3___24Anonymous__121904,happ(V1__P,Vvar__2__x__121903))
                  & V2__x = cCoq_2eInit_2eSpecif_2eexistT___24a4(V0__A,V1__P,Vvar__2__x__121903,Vvar__3___24Anonymous__121904)
                  & cCoq_2eInit_2eSpecif_2eprojT1___24a3(V0__A,V1__P,V2__x) = Vvar__2__x__121903 ) ) ) ) ) ).

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.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__4986] :
              ( t(Vvar__1___24Anonymous__4986,V0__A)
              & ? [Vvar__2___24Anonymous__4987] :
                  ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__4987)
                  & V3__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__4986,Vvar__2___24Anonymous__4987)
                  & ( cCoq_2eLists_2eList_2eIn___24a3(V0__A,V2__a,V3__l)
                  <=> ( Vvar__1___24Anonymous__4986 = V2__a
                      | cCoq_2eLists_2eList_2eIn___24a3(V0__A,V2__a,Vvar__2___24Anonymous__4987) ) ) ) ) ) ) ) ).

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__109247] :
                ( t(Vvar__1___24Anonymous__109247,V1__B)
                & ? [Vvar__2___24Anonymous__109248] :
                    ( cCoq_2eInit_2eDatatypes_2elist___24t(V1__B,Vvar__2___24Anonymous__109248)
                    & V4__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V1__B,Vvar__1___24Anonymous__109247,Vvar__2___24Anonymous__109248)
                    & 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__109248,happ(happ(V2__f,V5__a0),Vvar__1___24Anonymous__109247)) ) ) ) ) ) ) ).

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__5020] :
                ( t(Vvar__1___24Anonymous__5020,V1__B)
                & ? [Vvar__2___24Anonymous__5021] :
                    ( cCoq_2eInit_2eDatatypes_2elist___24t(V1__B,Vvar__2___24Anonymous__5021)
                    & V5__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V1__B,Vvar__1___24Anonymous__5020,Vvar__2___24Anonymous__5021)
                    & cCoq_2eLists_2eList_2efold__right___24a5(V0__A,V1__B,V2__f,V3__a0,V5__l) = happ(happ(V2__f,Vvar__1___24Anonymous__5020),cCoq_2eLists_2eList_2efold__right___24a5(V0__A,V1__B,V2__f,V3__a0,Vvar__2___24Anonymous__5021)) ) ) ) ) ) ) ).

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__89684] :
              ( t(Vvar__1___24Anonymous__89684,V0__A)
              & ? [Vvar__2___24Anonymous__89685] :
                  ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__89685)
                  & V2__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__89684,Vvar__2___24Anonymous__89685)
                  & cCoq_2eLists_2eList_2ehd___24a3(V0__A,V1__default,V2__l) = Vvar__1___24Anonymous__89684 ) ) ) ) ) ).

fof('$_def_Coq.Lists.List.last',axiom,
    ! [V0__A,V2__l,V3__d] :
      ( 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_2elast___24a3(V0__A,V2__l,V3__d) = V3__d )
          | ? [Vvar__1___24Anonymous__117888] :
              ( t(Vvar__1___24Anonymous__117888,V0__A)
              & ? [Vvar__2___24Anonymous__117889] :
                  ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__117889)
                  & ( cType___24t(V0__A)
                   => ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__117889)
                     => ( V2__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__117888,Vvar__2___24Anonymous__117889)
                        & ( ( Vvar__2___24Anonymous__117889 = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)
                            & cCoq_2eLists_2eList_2elast___24a3(V0__A,V2__l,V3__d) = Vvar__1___24Anonymous__117888 )
                          | ? [Vvar__1___24Anonymous__117900] :
                              ( t(Vvar__1___24Anonymous__117900,V0__A)
                              & ? [Vvar__2___24Anonymous__117901] :
                                  ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__117901)
                                  & Vvar__2___24Anonymous__117889 = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__117900,Vvar__2___24Anonymous__117901)
                                  & cCoq_2eLists_2eList_2elast___24a3(V0__A,V2__l,V3__d) = cCoq_2eLists_2eList_2elast___24a3(V0__A,Vvar__2___24Anonymous__117889,V3__d) ) ) ) ) ) ) ) ) ) ) ) ).

fof('$_def_Coq.Lists.List.map',axiom,
    ! [V0__A,V1__B,V2__f,V4__l] :
      ( cType___24t(V0__A)
     => ( cType___24t(V1__B)
       => ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V4__l)
         => ( ( V4__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)
              & cCoq_2eLists_2eList_2emap___24a4(V0__A,V1__B,V2__f,V4__l) = cCoq_2eInit_2eDatatypes_2enil___24a1(V1__B) )
            | ? [Vvar__1___24Anonymous__89761] :
                ( t(Vvar__1___24Anonymous__89761,V0__A)
                & ? [Vvar__2___24Anonymous__89762] :
                    ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__89762)
                    & V4__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__89761,Vvar__2___24Anonymous__89762)
                    & cCoq_2eLists_2eList_2emap___24a4(V0__A,V1__B,V2__f,V4__l) = cCoq_2eInit_2eDatatypes_2econs___24a3(V1__B,happ(V2__f,Vvar__1___24Anonymous__89761),cCoq_2eLists_2eList_2emap___24a4(V0__A,V1__B,V2__f,Vvar__2___24Anonymous__89762)) ) ) ) ) ) ) ).

fof('$_def_Coq.Lists.List.nth',axiom,
    ! [V0__A,V2__n,V3__l,V4__default] :
      ( cType___24t(V0__A)
     => ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__n)
       => ( ( cType___24t(V0__A)
           => ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l)
             => ( V2__n = cCoq_2eInit_2eDatatypes_2eO
                & ( ( V3__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)
                    & cCoq_2eLists_2eList_2enth___24a4(V0__A,V2__n,V3__l,V4__default) = V4__default )
                  | ? [Vvar__1___24Anonymous__89714] :
                      ( t(Vvar__1___24Anonymous__89714,V0__A)
                      & ? [Vvar__2___24Anonymous__89715] :
                          ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__89715)
                          & V3__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__89714,Vvar__2___24Anonymous__89715)
                          & cCoq_2eLists_2eList_2enth___24a4(V0__A,V2__n,V3__l,V4__default) = Vvar__1___24Anonymous__89714 ) ) ) ) ) )
          | ? [Vvar__0___24Anonymous__89717] :
              ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__89717)
              & ( cType___24t(V0__A)
               => ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l)
                 => ( V2__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__89717)
                    & ( ( V3__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)
                        & cCoq_2eLists_2eList_2enth___24a4(V0__A,V2__n,V3__l,V4__default) = V4__default )
                      | ? [Vvar__1___24Anonymous__89724] :
                          ( t(Vvar__1___24Anonymous__89724,V0__A)
                          & ? [Vvar__2___24Anonymous__89725] :
                              ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__89725)
                              & V3__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__89724,Vvar__2___24Anonymous__89725)
                              & cCoq_2eLists_2eList_2enth___24a4(V0__A,V2__n,V3__l,V4__default) = cCoq_2eLists_2eList_2enth___24a4(V0__A,Vvar__0___24Anonymous__89717,Vvar__2___24Anonymous__89725,V4__default) ) ) ) ) ) ) ) ) ) ) ).

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

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

fof('$_def_Coq.NArith.BinNat.N.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.BinNat.N.recursion',axiom,
    ! [V0__A] : cCoq_2eNArith_2eBinNat_2eN_2erecursion___24a1(V0__A) = cCoq_2eNArith_2eBinNat_2eN_2epeano__rect___24a1(c_24__lam__122197___24a1(V0__A)) ).

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__107022] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__107022)
            & ( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
             => ( V0__n = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__107022)
                & ( ( V1__m = cCoq_2eNumbers_2eBinNums_2eN0
                    & cCoq_2eNArith_2eBinNatDef_2eN_2eadd___24a2(V0__n,V1__m) = V0__n )
                  | ? [Vvar__0___24Anonymous__107025] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__107025)
                      & V1__m = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__107025)
                      & cCoq_2eNArith_2eBinNatDef_2eN_2eadd___24a2(V0__n,V1__m) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(Vvar__0___24Anonymous__107022,Vvar__0___24Anonymous__107025)) ) ) ) ) ) ) ) ).

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__307] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__307)
            & ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__307)
             => ( V0__n = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__307)
                & ( ? [Vvar__0___24Anonymous__311] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__311)
                      & Vvar__0___24Anonymous__307 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__311)
                      & cCoq_2eNArith_2eBinNatDef_2eN_2ediv2___24a1(V0__n) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__311) )
                  | ? [Vvar__0___24Anonymous__312] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__312)
                      & Vvar__0___24Anonymous__307 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__312)
                      & cCoq_2eNArith_2eBinNatDef_2eN_2ediv2___24a1(V0__n) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__312) )
                  | ( Vvar__0___24Anonymous__307 = 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__297] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__297)
            & V0__n = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__297)
            & cCoq_2eNArith_2eBinNatDef_2eN_2edouble___24a1(V0__n) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__297)) ) ) ) ).

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__299] :
                  ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__299)
                  & V2__m = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__299)
                  & cCoq_2eNArith_2eBinNatDef_2eN_2eeqb___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) )
        | ? [Vvar__0___24Anonymous__300] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__300)
            & ( cCoq_2eNumbers_2eBinNums_2eN___24t(V2__m)
             => ( V1__n = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__300)
                & ( ( V2__m = cCoq_2eNumbers_2eBinNums_2eN0
                    & cCoq_2eNArith_2eBinNatDef_2eN_2eeqb___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2efalse )
                  | ? [Vvar__0___24Anonymous__303] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__303)
                      & V2__m = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__303)
                      & cCoq_2eNArith_2eBinNatDef_2eN_2eeqb___24a2(V1__n,V2__m) = cCoq_2ePArith_2eBinPosDef_2ePos_2eeqb___24a2(Vvar__0___24Anonymous__300,Vvar__0___24Anonymous__303) ) ) ) ) ) ) ) ).

fof('$_def_Coq.NArith.BinNatDef.N.even',axiom,
    ! [V0__n] :
      ( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
     => ( ( V0__n = cCoq_2eNumbers_2eBinNums_2eN0
          & cCoq_2eNArith_2eBinNatDef_2eN_2eeven___24a1(V0__n) = cCoq_2eInit_2eDatatypes_2etrue )
        | ? [Vvar__0___24Anonymous__120006] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__120006)
            & ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__120006)
             => ( V0__n = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__120006)
                & ( ? [Vvar__0___24Anonymous__120010] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__120010)
                      & Vvar__0___24Anonymous__120006 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__120010)
                      & cCoq_2eNArith_2eBinNatDef_2eN_2eeven___24a1(V0__n) = cCoq_2eInit_2eDatatypes_2efalse )
                  | ? [Vvar__0___24Anonymous__120011] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__120011)
                      & Vvar__0___24Anonymous__120006 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__120011)
                      & cCoq_2eNArith_2eBinNatDef_2eN_2eeven___24a1(V0__n) = cCoq_2eInit_2eDatatypes_2etrue )
                  | ( Vvar__0___24Anonymous__120006 = cCoq_2eNumbers_2eBinNums_2exH
                    & cCoq_2eNArith_2eBinNatDef_2eN_2eeven___24a1(V0__n) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ) ) ) ).

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__976] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__976)
            & ( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
             => ( V0__n = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__976)
                & ( ( V1__m = cCoq_2eNumbers_2eBinNums_2eN0
                    & cCoq_2eNArith_2eBinNatDef_2eN_2elxor___24a2(V0__n,V1__m) = V0__n )
                  | ? [Vvar__0___24Anonymous__979] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__979)
                      & V1__m = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__979)
                      & cCoq_2eNArith_2eBinNatDef_2eN_2elxor___24a2(V0__n,V1__m) = cCoq_2ePArith_2eBinPosDef_2ePos_2elxor___24a2(Vvar__0___24Anonymous__976,Vvar__0___24Anonymous__979) ) ) ) ) ) ) ) ).

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

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

fof('$_def_Coq.NArith.BinNatDef.N.mul',axiom,
    ! [V0__n,V1__m] :
      ( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
     => ( ( V0__n = cCoq_2eNumbers_2eBinNums_2eN0
          & cCoq_2eNArith_2eBinNatDef_2eN_2emul___24a2(V0__n,V1__m) = cCoq_2eNumbers_2eBinNums_2eN0 )
        | ? [Vvar__0___24Anonymous__113550] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__113550)
            & ( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
             => ( V0__n = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__113550)
                & ( ( V1__m = cCoq_2eNumbers_2eBinNums_2eN0
                    & cCoq_2eNArith_2eBinNatDef_2eN_2emul___24a2(V0__n,V1__m) = cCoq_2eNumbers_2eBinNums_2eN0 )
                  | ? [Vvar__0___24Anonymous__113553] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__113553)
                      & V1__m = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__113553)
                      & cCoq_2eNArith_2eBinNatDef_2eN_2emul___24a2(V0__n,V1__m) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2emul___24a2(Vvar__0___24Anonymous__113550,Vvar__0___24Anonymous__113553)) ) ) ) ) ) ) ) ).

fof('$_def_Coq.NArith.BinNatDef.N.pred',axiom,
    ! [V0__n] :
      ( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
     => ( ( V0__n = cCoq_2eNumbers_2eBinNums_2eN0
          & cCoq_2eNArith_2eBinNatDef_2eN_2epred___24a1(V0__n) = cCoq_2eNumbers_2eBinNums_2eN0 )
        | ? [Vvar__0___24Anonymous__119993] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__119993)
            & V0__n = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__119993)
            & cCoq_2eNArith_2eBinNatDef_2eN_2epred___24a1(V0__n) = cCoq_2ePArith_2eBinPosDef_2ePos_2epred__N___24a1(Vvar__0___24Anonymous__119993) ) ) ) ).

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__119992] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__119992)
            & V0__n = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__119992)
            & cCoq_2eNArith_2eBinNatDef_2eN_2esucc___24a1(V0__n) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2esucc___24a1(Vvar__0___24Anonymous__119992)) ) ) ) ).

fof('$_def_Coq.NArith.BinNatDef.N.t',axiom,
    ! [Vvar__113549] :
      ( cCoq_2eNArith_2eBinNatDef_2eN_2et___24t(Vvar__113549)
    <=> cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__113549) ) ).

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__120116] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__120116)
            & V0__a = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__120116)
            & cCoq_2eNArith_2eBinNatDef_2eN_2etestbit___24a2(V0__a,V1__n) = cCoq_2ePArith_2eBinPosDef_2ePos_2etestbit___24a2(Vvar__0___24Anonymous__120116,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__113564] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__113564)
            & V0__a = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__113564)
            & cCoq_2eNArith_2eBinNatDef_2eN_2eto__nat___24a1(V0__a) = cCoq_2ePArith_2eBinPosDef_2ePos_2eto__nat___24a1(Vvar__0___24Anonymous__113564) ) ) ) ).

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

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

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

fof('$_def_Coq.PArith.BinPos.Pos.le',axiom,
    ! [V0__x,V1__y] :
      ( cCoq_2ePArith_2eBinPos_2ePos_2ele___24a2(V0__x,V1__y)
    <=> cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare___24a2(V0__x,V1__y) != cCoq_2eInit_2eDatatypes_2eGt ) ).

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

fof('$_def_Coq.PArith.BinPos.Pos.switch_Eq',axiom,
    ! [V0__c,V1__c_27] :
      ( cCoq_2eInit_2eDatatypes_2ecomparison___24t(V1__c_27)
     => ( ( V1__c_27 = cCoq_2eInit_2eDatatypes_2eEq
          & cCoq_2ePArith_2eBinPos_2ePos_2eswitch__Eq___24a2(V0__c,V1__c_27) = V0__c )
        | ( V1__c_27 = cCoq_2eInit_2eDatatypes_2eLt
          & cCoq_2ePArith_2eBinPos_2ePos_2eswitch__Eq___24a2(V0__c,V1__c_27) = cCoq_2eInit_2eDatatypes_2eLt )
        | ( V1__c_27 = cCoq_2eInit_2eDatatypes_2eGt
          & cCoq_2ePArith_2eBinPos_2ePos_2eswitch__Eq___24a2(V0__c,V1__c_27) = cCoq_2eInit_2eDatatypes_2eGt ) ) ) ).

fof('$_def_Coq.PArith.BinPosDef.Pos.add',axiom,
    ! [V2__x,V3__y] :
      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V2__x)
     => ( ? [Vvar__0___24Anonymous__107046] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__107046)
            & ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V3__y)
             => ( V2__x = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__107046)
                & ( ? [Vvar__0___24Anonymous__107050] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__107050)
                      & V3__y = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__107050)
                      & cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exO___24a1(c_24__fix__107045__1__add__carry___24a2(Vvar__0___24Anonymous__107046,Vvar__0___24Anonymous__107050)) )
                  | ? [Vvar__0___24Anonymous__107051] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__107051)
                      & V3__y = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__107051)
                      & cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exI___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(Vvar__0___24Anonymous__107046,Vvar__0___24Anonymous__107051)) )
                  | ( V3__y = cCoq_2eNumbers_2eBinNums_2exH
                    & cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2esucc___24a1(Vvar__0___24Anonymous__107046)) ) ) ) ) )
        | ? [Vvar__0___24Anonymous__107052] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__107052)
            & ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V3__y)
             => ( V2__x = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__107052)
                & ( ? [Vvar__0___24Anonymous__107056] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__107056)
                      & V3__y = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__107056)
                      & cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exI___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(Vvar__0___24Anonymous__107052,Vvar__0___24Anonymous__107056)) )
                  | ? [Vvar__0___24Anonymous__107057] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__107057)
                      & V3__y = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__107057)
                      & cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(Vvar__0___24Anonymous__107052,Vvar__0___24Anonymous__107057)) )
                  | ( V3__y = cCoq_2eNumbers_2eBinNums_2exH
                    & cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__107052) ) ) ) ) )
        | ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V3__y)
         => ( V2__x = cCoq_2eNumbers_2eBinNums_2exH
            & ( ? [Vvar__0___24Anonymous__107058] :
                  ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__107058)
                  & V3__y = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__107058)
                  & cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2esucc___24a1(Vvar__0___24Anonymous__107058)) )
              | ? [Vvar__0___24Anonymous__107059] :
                  ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__107059)
                  & V3__y = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__107059)
                  & cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__107059) )
              | ( V3__y = cCoq_2eNumbers_2eBinNums_2exH
                & cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2eNumbers_2eBinNums_2exH) ) ) ) ) ) ) ).

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__113610] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__113610)
            & V0__p = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__113610)
            & cCoq_2ePArith_2eBinPosDef_2ePos_2ediv2___24a1(V0__p) = Vvar__0___24Anonymous__113610 )
        | ? [Vvar__0___24Anonymous__113611] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__113611)
            & V0__p = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__113611)
            & cCoq_2ePArith_2eBinPosDef_2ePos_2ediv2___24a1(V0__p) = Vvar__0___24Anonymous__113611 )
        | ( V0__p = cCoq_2eNumbers_2eBinNums_2exH
          & cCoq_2ePArith_2eBinPosDef_2ePos_2ediv2___24a1(V0__p) = cCoq_2eNumbers_2eBinNums_2exH ) ) ) ).

fof('$_def_Coq.PArith.BinPosDef.Pos.eqb',axiom,
    ! [V1__p,V2__q] :
      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__p)
     => ( ? [Vvar__0___24Anonymous__122231] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__122231)
            & ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V2__q)
             => ( V1__p = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__122231)
                & ( ? [Vvar__0___24Anonymous__122235] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__122235)
                      & V2__q = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__122235)
                      & cCoq_2ePArith_2eBinPosDef_2ePos_2eeqb___24a2(V1__p,V2__q) = cCoq_2ePArith_2eBinPosDef_2ePos_2eeqb___24a2(Vvar__0___24Anonymous__122231,Vvar__0___24Anonymous__122235) )
                  | ? [Vvar__0___24Anonymous__122236] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__122236)
                      & V2__q = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__122236)
                      & cCoq_2ePArith_2eBinPosDef_2ePos_2eeqb___24a2(V1__p,V2__q) = cCoq_2eInit_2eDatatypes_2efalse )
                  | ( V2__q = cCoq_2eNumbers_2eBinNums_2exH
                    & cCoq_2ePArith_2eBinPosDef_2ePos_2eeqb___24a2(V1__p,V2__q) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) )
        | ? [Vvar__0___24Anonymous__122237] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__122237)
            & ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V2__q)
             => ( V1__p = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__122237)
                & ( ? [Vvar__0___24Anonymous__122241] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__122241)
                      & V2__q = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__122241)
                      & cCoq_2ePArith_2eBinPosDef_2ePos_2eeqb___24a2(V1__p,V2__q) = cCoq_2eInit_2eDatatypes_2efalse )
                  | ? [Vvar__0___24Anonymous__122242] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__122242)
                      & V2__q = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__122242)
                      & cCoq_2ePArith_2eBinPosDef_2ePos_2eeqb___24a2(V1__p,V2__q) = cCoq_2ePArith_2eBinPosDef_2ePos_2eeqb___24a2(Vvar__0___24Anonymous__122237,Vvar__0___24Anonymous__122242) )
                  | ( V2__q = cCoq_2eNumbers_2eBinNums_2exH
                    & cCoq_2ePArith_2eBinPosDef_2ePos_2eeqb___24a2(V1__p,V2__q) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) )
        | ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V2__q)
         => ( V1__p = cCoq_2eNumbers_2eBinNums_2exH
            & ( ? [Vvar__0___24Anonymous__122243] :
                  ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__122243)
                  & V2__q = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__122243)
                  & cCoq_2ePArith_2eBinPosDef_2ePos_2eeqb___24a2(V1__p,V2__q) = cCoq_2eInit_2eDatatypes_2efalse )
              | ? [Vvar__0___24Anonymous__122244] :
                  ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__122244)
                  & V2__q = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__122244)
                  & cCoq_2ePArith_2eBinPosDef_2ePos_2eeqb___24a2(V1__p,V2__q) = cCoq_2eInit_2eDatatypes_2efalse )
              | ( V2__q = cCoq_2eNumbers_2eBinNums_2exH
                & cCoq_2ePArith_2eBinPosDef_2ePos_2eeqb___24a2(V1__p,V2__q) = cCoq_2eInit_2eDatatypes_2etrue ) ) ) ) ) ) ).

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__113598] :
              ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__113598)
              & V4__n = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__113598)
              & 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__113598),Vvar__0___24Anonymous__113598)) )
          | ? [Vvar__0___24Anonymous__113599] :
              ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__113599)
              & V4__n = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__113599)
              & 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__113599),Vvar__0___24Anonymous__113599) )
          | ( 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__113616] :
              ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__113616)
              & V3__p = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__113616)
              & 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__113616,happ(happ(V1__op,V4__a),V4__a))) )
          | ? [Vvar__0___24Anonymous__113617] :
              ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__113617)
              & V3__p = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__113617)
              & 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__113617,happ(happ(V1__op,V4__a),V4__a)) )
          | ( V3__p = cCoq_2eNumbers_2eBinNums_2exH
            & cCoq_2ePArith_2eBinPosDef_2ePos_2eiter__op___24a4(V0__A,V1__op,V3__p,V4__a) = V4__a ) ) ) ) ).

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

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

fof('$_def_Coq.PArith.BinPosDef.Pos.mul',axiom,
    ! [V1__x,V2__y] :
      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__x)
     => ( ? [Vvar__0___24Anonymous__113594] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__113594)
            & V1__x = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__113594)
            & cCoq_2ePArith_2eBinPosDef_2ePos_2emul___24a2(V1__x,V2__y) = cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(V2__y,cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2emul___24a2(Vvar__0___24Anonymous__113594,V2__y))) )
        | ? [Vvar__0___24Anonymous__113595] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__113595)
            & V1__x = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__113595)
            & cCoq_2ePArith_2eBinPosDef_2ePos_2emul___24a2(V1__x,V2__y) = cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2emul___24a2(Vvar__0___24Anonymous__113595,V2__y)) )
        | ( V1__x = cCoq_2eNumbers_2eBinNums_2exH
          & cCoq_2ePArith_2eBinPosDef_2ePos_2emul___24a2(V1__x,V2__y) = V2__y ) ) ) ).

fof('$_def_Coq.PArith.BinPosDef.Pos.of_nat',axiom,
    ! [V1__n] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
     => ( ( V1__n = cCoq_2eInit_2eDatatypes_2eO
          & cCoq_2ePArith_2eBinPosDef_2ePos_2eof__nat___24a1(V1__n) = cCoq_2eNumbers_2eBinNums_2exH )
        | ? [Vvar__0___24Anonymous__122277] :
            ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__122277)
            & ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__122277)
             => ( V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__122277)
                & ( ( Vvar__0___24Anonymous__122277 = cCoq_2eInit_2eDatatypes_2eO
                    & cCoq_2ePArith_2eBinPosDef_2ePos_2eof__nat___24a1(V1__n) = cCoq_2eNumbers_2eBinNums_2exH )
                  | ? [Vvar__0___24Anonymous__122280] :
                      ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__122280)
                      & Vvar__0___24Anonymous__122277 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__122280)
                      & cCoq_2ePArith_2eBinPosDef_2ePos_2eof__nat___24a1(V1__n) = cCoq_2ePArith_2eBinPosDef_2ePos_2esucc___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eof__nat___24a1(Vvar__0___24Anonymous__122277)) ) ) ) ) ) ) ) ).

fof('$_def_Coq.PArith.BinPosDef.Pos.of_succ_nat',axiom,
    ! [V1__n] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
     => ( ( V1__n = cCoq_2eInit_2eDatatypes_2eO
          & cCoq_2ePArith_2eBinPosDef_2ePos_2eof__succ__nat___24a1(V1__n) = cCoq_2eNumbers_2eBinNums_2exH )
        | ? [Vvar__0___24Anonymous__122284] :
            ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__122284)
            & V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__122284)
            & cCoq_2ePArith_2eBinPosDef_2ePos_2eof__succ__nat___24a1(V1__n) = cCoq_2ePArith_2eBinPosDef_2ePos_2esucc___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eof__succ__nat___24a1(Vvar__0___24Anonymous__122284)) ) ) ) ).

fof('$_def_Coq.PArith.BinPosDef.Pos.size_nat',axiom,
    ! [V1__p] :
      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__p)
     => ( ? [Vvar__0___24Anonymous__122223] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__122223)
            & V1__p = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__122223)
            & cCoq_2ePArith_2eBinPosDef_2ePos_2esize__nat___24a1(V1__p) = cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2esize__nat___24a1(Vvar__0___24Anonymous__122223)) )
        | ? [Vvar__0___24Anonymous__122224] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__122224)
            & V1__p = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__122224)
            & cCoq_2ePArith_2eBinPosDef_2ePos_2esize__nat___24a1(V1__p) = cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2esize__nat___24a1(Vvar__0___24Anonymous__122224)) )
        | ( V1__p = cCoq_2eNumbers_2eBinNums_2exH
          & cCoq_2ePArith_2eBinPosDef_2ePos_2esize__nat___24a1(V1__p) = cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO) ) ) ) ).

fof('$_def_Coq.PArith.BinPosDef.Pos.sub',axiom,
    ! [V0__x,V1__y] :
      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V0__x)
     => ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__y)
       => ( ( cCoq_2ePArith_2eBinPosDef_2ePos_2esub__mask___24a2(V0__x,V1__y) = cCoq_2ePArith_2eBinPosDef_2ePos_2eIsNul
            & cCoq_2ePArith_2eBinPosDef_2ePos_2esub___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2exH )
          | ? [Vvar__0___24Anonymous__113591] :
              ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__113591)
              & cCoq_2ePArith_2eBinPosDef_2ePos_2esub__mask___24a2(V0__x,V1__y) = cCoq_2ePArith_2eBinPosDef_2ePos_2eIsPos___24a1(Vvar__0___24Anonymous__113591)
              & cCoq_2ePArith_2eBinPosDef_2ePos_2esub___24a2(V0__x,V1__y) = Vvar__0___24Anonymous__113591 )
          | ( cCoq_2ePArith_2eBinPosDef_2ePos_2esub__mask___24a2(V0__x,V1__y) = cCoq_2ePArith_2eBinPosDef_2ePos_2eIsNeg
            & cCoq_2ePArith_2eBinPosDef_2ePos_2esub___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2exH ) ) ) ) ).

fof('$_def_Coq.PArith.BinPosDef.Pos.succ',axiom,
    ! [V1__x] :
      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__x)
     => ( ? [Vvar__0___24Anonymous__107043] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__107043)
            & V1__x = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__107043)
            & cCoq_2ePArith_2eBinPosDef_2ePos_2esucc___24a1(V1__x) = cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2esucc___24a1(Vvar__0___24Anonymous__107043)) )
        | ? [Vvar__0___24Anonymous__107044] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__107044)
            & V1__x = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__107044)
            & cCoq_2ePArith_2eBinPosDef_2ePos_2esucc___24a1(V1__x) = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__107044) )
        | ( V1__x = cCoq_2eNumbers_2eBinNums_2exH
          & cCoq_2ePArith_2eBinPosDef_2ePos_2esucc___24a1(V1__x) = cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2eNumbers_2eBinNums_2exH) ) ) ) ).

fof('$_def_Coq.PArith.BinPosDef.Pos.t',axiom,
    ! [Vvar__113582] :
      ( cCoq_2ePArith_2eBinPosDef_2ePos_2et___24t(Vvar__113582)
    <=> cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__113582) ) ).

fof('$_def_Coq.PArith.BinPosDef.Pos.testbit_nat',axiom,
    ! [V1__p] :
      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__p)
     => ( ? [Vvar__0___24Anonymous__122247] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__122247)
            & V1__p = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__122247)
            & cCoq_2ePArith_2eBinPosDef_2ePos_2etestbit__nat___24a1(V1__p) = c_24__lam__122260___24a1(Vvar__0___24Anonymous__122247) )
        | ? [Vvar__0___24Anonymous__122251] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__122251)
            & V1__p = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__122251)
            & cCoq_2ePArith_2eBinPosDef_2ePos_2etestbit__nat___24a1(V1__p) = c_24__lam__122267___24a1(Vvar__0___24Anonymous__122251) )
        | ( V1__p = cCoq_2eNumbers_2eBinNums_2exH
          & cCoq_2ePArith_2eBinPosDef_2ePos_2etestbit__nat___24a1(V1__p) = c_24__lam__122271 ) ) ) ).

fof('$_def_Coq.QArith.QArith_base.Qden',axiom,
    ! [V0__q] :
      ( cCoq_2eQArith_2eQArith__base_2eQ___24t(V0__q)
     => ? [Vvar__0__Qnum__109638] :
          ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__0__Qnum__109638)
          & ? [Vvar__1__Qden__109639] :
              ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1__Qden__109639)
              & V0__q = cCoq_2eQArith_2eQArith__base_2eQmake___24a2(Vvar__0__Qnum__109638,Vvar__1__Qden__109639)
              & cCoq_2eQArith_2eQArith__base_2eQden___24a1(V0__q) = Vvar__1__Qden__109639 ) ) ) ).

fof('$_def_Coq.QArith.QArith_base.Qnum',axiom,
    ! [V0__q] :
      ( cCoq_2eQArith_2eQArith__base_2eQ___24t(V0__q)
     => ? [Vvar__0__Qnum__109633] :
          ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__0__Qnum__109633)
          & ? [Vvar__1__Qden__109634] :
              ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1__Qden__109634)
              & V0__q = cCoq_2eQArith_2eQArith__base_2eQmake___24a2(Vvar__0__Qnum__109633,Vvar__1__Qden__109634)
              & cCoq_2eQArith_2eQArith__base_2eQnum___24a1(V0__q) = Vvar__0__Qnum__109633 ) ) ) ).

fof('$_def_Coq.Reals.RIneq.Rsqr',axiom,
    ! [V0__r] : cCoq_2eReals_2eRIneq_2eRsqr___24a1(V0__r) = cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V0__r,V0__r) ).

fof('$_def_Coq.Reals.Rdefinitions.IZR',axiom,
    ! [V0__z] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__z)
     => ( ( V0__z = cCoq_2eNumbers_2eBinNums_2eZ0
          & cCoq_2eReals_2eRdefinitions_2eIZR___24a1(V0__z) = cCoq_2eReals_2eRdefinitions_2eR0 )
        | ? [Vvar__0___24Anonymous__118011] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__118011)
            & V0__z = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__118011)
            & cCoq_2eReals_2eRdefinitions_2eIZR___24a1(V0__z) = cCoq_2eReals_2eRdefinitions_2eIPR___24a1(Vvar__0___24Anonymous__118011) )
        | ? [Vvar__0___24Anonymous__118012] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__118012)
            & V0__z = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__118012)
            & cCoq_2eReals_2eRdefinitions_2eIZR___24a1(V0__z) = cCoq_2eReals_2eRdefinitions_2eRopp___24a1(cCoq_2eReals_2eRdefinitions_2eIPR___24a1(Vvar__0___24Anonymous__118012)) ) ) ) ).

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

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

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

fof('$_def_Coq.Relations.Relation_Definitions.relation',axiom,
    ! [V0__A] : cCoq_2eRelations_2eRelation__Definitions_2erelation___24a1(V0__A) = c_24__type__1300___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__1300___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__120918___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__120918___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__113575] :
      ( cCoq_2eStructures_2eOrderedTypeEx_2eN__as__OT_2et___24t(Vvar__113575)
    <=> cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__113575) ) ).

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__113579] :
      ( cCoq_2eStructures_2eOrderedTypeEx_2eNat__as__OT_2et___24t(Vvar__113579)
    <=> cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__113579) ) ).

fof('$_def_Coq.Structures.OrderedTypeEx.PositiveOrderedTypeBits.bits_lt',axiom,
    ! [V1__p,V2__q] :
      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__p)
     => ( ? [Vvar__0___24Anonymous__113487] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__113487)
            & ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V2__q)
             => ( V1__p = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__113487)
                & ( ? [Vvar__0___24Anonymous__113491] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__113491)
                      & V2__q = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__113491)
                      & ( cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2ebits__lt___24a2(V1__p,V2__q)
                      <=> cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2ebits__lt___24a2(Vvar__0___24Anonymous__113487,Vvar__0___24Anonymous__113491) ) )
                  | ? [Vvar__0___24Anonymous__113492] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__113492)
                      & V2__q = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__113492)
                      & ( 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__113493] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__113493)
            & ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V2__q)
             => ( V1__p = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__113493)
                & ( ? [Vvar__0___24Anonymous__113497] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__113497)
                      & V2__q = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__113497)
                      & ( cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2ebits__lt___24a2(V1__p,V2__q)
                      <=> p(c_24True) ) )
                  | ? [Vvar__0___24Anonymous__113498] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__113498)
                      & V2__q = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__113498)
                      & ( cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2ebits__lt___24a2(V1__p,V2__q)
                      <=> cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2ebits__lt___24a2(Vvar__0___24Anonymous__113493,Vvar__0___24Anonymous__113498) ) )
                  | ( 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__113499] :
                  ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__113499)
                  & V2__q = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__113499)
                  & ( cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2ebits__lt___24a2(V1__p,V2__q)
                  <=> p(c_24True) ) )
              | ? [Vvar__0___24Anonymous__113500] :
                  ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__113500)
                  & V2__q = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__113500)
                  & ( 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__113485] :
      ( cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2et___24t(Vvar__113485)
    <=> cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__113485) ) ).

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__113758] :
      ( cCoq_2eStructures_2eOrderedTypeEx_2ePositive__as__OT_2et___24t(Vvar__113758)
    <=> cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__113758) ) ).

fof('$_def_Coq.Structures.OrderedTypeEx.String_as_OT.lt',axiom,
    cCoq_2eStructures_2eOrderedTypeEx_2eString__as__OT_2elt = cCoq_2eStructures_2eOrderedTypeEx_2eString__as__OT_2elts ).

fof('$_def_Coq.Structures.OrderedTypeEx.String_as_OT.t',axiom,
    ! [Vvar__113759] :
      ( cCoq_2eStructures_2eOrderedTypeEx_2eString__as__OT_2et___24t(Vvar__113759)
    <=> cCoq_2eStrings_2eString_2estring___24t(Vvar__113759) ) ).

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.lt',axiom,
    ! [V0__x,V1__y] :
      ( cCoq_2eStructures_2eOrderedTypeEx_2eZ__as__OT_2elt___24a2(V0__x,V1__y)
    <=> p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__x,V1__y)) ) ).

fof('$_def_Coq.Structures.OrderedTypeEx.Z_as_OT.t',axiom,
    ! [Vvar__113785] :
      ( cCoq_2eStructures_2eOrderedTypeEx_2eZ__as__OT_2et___24t(Vvar__113785)
    <=> cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__113785) ) ).

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.eqf',axiom,
    ! [V0__f,V1__g] :
      ( cCoq_2eZArith_2eBinInt_2eZ_2eeqf___24a2(V0__f,V1__g)
    <=> ! [V2__n] :
          ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__n)
         => happ(V0__f,V2__n) = happ(V1__g,V2__n) ) ) ).

fof('$_def_Coq.ZArith.BinInt.Z.ge',axiom,
    ! [V0__x,V1__y] :
      ( cCoq_2eZArith_2eBinInt_2eZ_2ege___24a2(V0__x,V1__y)
    <=> cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) != cCoq_2eInit_2eDatatypes_2eLt ) ).

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

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

fof('$_def_Coq.ZArith.BinInt.Z.lt',axiom,
    ! [V0__x,V1__y] :
      ( p(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__113775] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__113775)
            & V0__z = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__113775)
            & cCoq_2eZArith_2eBinIntDef_2eZ_2eabs___24a1(V0__z) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__113775) )
        | ? [Vvar__0___24Anonymous__113776] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__113776)
            & V0__z = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__113776)
            & cCoq_2eZArith_2eBinIntDef_2eZ_2eabs___24a1(V0__z) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__113776) ) ) ) ).

fof('$_def_Coq.ZArith.BinIntDef.Z.abs_N',axiom,
    ! [V0__z] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__z)
     => ( ( V0__z = cCoq_2eNumbers_2eBinNums_2eZ0
          & cCoq_2eZArith_2eBinIntDef_2eZ_2eabs__N___24a1(V0__z) = cCoq_2eNumbers_2eBinNums_2eN0 )
        | ? [Vvar__0___24Anonymous__120716] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__120716)
            & V0__z = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__120716)
            & cCoq_2eZArith_2eBinIntDef_2eZ_2eabs__N___24a1(V0__z) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__120716) )
        | ? [Vvar__0___24Anonymous__120717] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__120717)
            & V0__z = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__120717)
            & cCoq_2eZArith_2eBinIntDef_2eZ_2eabs__N___24a1(V0__z) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__120717) ) ) ) ).

fof('$_def_Coq.ZArith.BinIntDef.Z.abs_nat',axiom,
    ! [V0__z] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__z)
     => ( ( V0__z = cCoq_2eNumbers_2eBinNums_2eZ0
          & cCoq_2eZArith_2eBinIntDef_2eZ_2eabs__nat___24a1(V0__z) = cCoq_2eInit_2eDatatypes_2eO )
        | ? [Vvar__0___24Anonymous__122311] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__122311)
            & V0__z = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__122311)
            & cCoq_2eZArith_2eBinIntDef_2eZ_2eabs__nat___24a1(V0__z) = cCoq_2ePArith_2eBinPosDef_2ePos_2eto__nat___24a1(Vvar__0___24Anonymous__122311) )
        | ? [Vvar__0___24Anonymous__122312] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__122312)
            & V0__z = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__122312)
            & cCoq_2eZArith_2eBinIntDef_2eZ_2eabs__nat___24a1(V0__z) = cCoq_2ePArith_2eBinPosDef_2ePos_2eto__nat___24a1(Vvar__0___24Anonymous__122312) ) ) ) ).

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__107311] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__107311)
            & ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
             => ( V0__x = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__107311)
                & ( ( V1__y = cCoq_2eNumbers_2eBinNums_2eZ0
                    & cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__x,V1__y) = V0__x )
                  | ? [Vvar__0___24Anonymous__107315] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__107315)
                      & V1__y = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__107315)
                      & cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(Vvar__0___24Anonymous__107311,Vvar__0___24Anonymous__107315)) )
                  | ? [Vvar__0___24Anonymous__107316] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__107316)
                      & V1__y = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__107316)
                      & cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__x,V1__y) = cCoq_2eZArith_2eBinIntDef_2eZ_2epos__sub___24a2(Vvar__0___24Anonymous__107311,Vvar__0___24Anonymous__107316) ) ) ) ) )
        | ? [Vvar__0___24Anonymous__107317] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__107317)
            & ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
             => ( V0__x = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__107317)
                & ( ( V1__y = cCoq_2eNumbers_2eBinNums_2eZ0
                    & cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__x,V1__y) = V0__x )
                  | ? [Vvar__0___24Anonymous__107321] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__107321)
                      & V1__y = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__107321)
                      & cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__x,V1__y) = cCoq_2eZArith_2eBinIntDef_2eZ_2epos__sub___24a2(Vvar__0___24Anonymous__107321,Vvar__0___24Anonymous__107317) )
                  | ? [Vvar__0___24Anonymous__107322] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__107322)
                      & V1__y = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__107322)
                      & cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(Vvar__0___24Anonymous__107317,Vvar__0___24Anonymous__107322)) ) ) ) ) ) ) ) ).

fof('$_def_Coq.ZArith.BinIntDef.Z.compare',axiom,
    ! [V0__x,V1__y] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
     => ( ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
         => ( V0__x = cCoq_2eNumbers_2eBinNums_2eZ0
            & ( ( V1__y = cCoq_2eNumbers_2eBinNums_2eZ0
                & cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eEq )
              | ? [Vvar__0___24Anonymous__107345] :
                  ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__107345)
                  & V1__y = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__107345)
                  & cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eLt )
              | ? [Vvar__0___24Anonymous__107346] :
                  ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__107346)
                  & V1__y = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__107346)
                  & cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eGt ) ) ) )
        | ? [Vvar__0___24Anonymous__107347] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__107347)
            & ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
             => ( V0__x = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__107347)
                & ( ( V1__y = cCoq_2eNumbers_2eBinNums_2eZ0
                    & cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eGt )
                  | ? [Vvar__0___24Anonymous__107351] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__107351)
                      & V1__y = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__107351)
                      & cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare___24a2(Vvar__0___24Anonymous__107347,Vvar__0___24Anonymous__107351) )
                  | ? [Vvar__0___24Anonymous__107352] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__107352)
                      & V1__y = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__107352)
                      & cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eGt ) ) ) ) )
        | ? [Vvar__0___24Anonymous__107353] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__107353)
            & ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
             => ( V0__x = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__107353)
                & ( ( V1__y = cCoq_2eNumbers_2eBinNums_2eZ0
                    & cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eLt )
                  | ? [Vvar__0___24Anonymous__107357] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__107357)
                      & V1__y = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__107357)
                      & cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eLt )
                  | ? [Vvar__0___24Anonymous__107358] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__107358)
                      & V1__y = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__107358)
                      & cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eCompOpp___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare___24a2(Vvar__0___24Anonymous__107353,Vvar__0___24Anonymous__107358)) ) ) ) ) ) ) ) ).

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__107371] :
            ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__2___24Anonymous__107371)
            & ? [Vvar__3___24Anonymous__107372] :
                ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__3___24Anonymous__107372)
                & 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__107371,Vvar__3___24Anonymous__107372)
                & cCoq_2eZArith_2eBinIntDef_2eZ_2ediv___24a2(V0__a,V1__b) = Vvar__2___24Anonymous__107371 ) ) ) ) ).

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__120795] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__120795)
            & ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__120795)
             => ( V0__z = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__120795)
                & ( ? [Vvar__0___24Anonymous__120799] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__120799)
                      & Vvar__0___24Anonymous__120795 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__120799)
                      & cCoq_2eZArith_2eBinIntDef_2eZ_2eeven___24a1(V0__z) = cCoq_2eInit_2eDatatypes_2efalse )
                  | ? [Vvar__0___24Anonymous__120800] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__120800)
                      & Vvar__0___24Anonymous__120795 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__120800)
                      & cCoq_2eZArith_2eBinIntDef_2eZ_2eeven___24a1(V0__z) = cCoq_2eInit_2eDatatypes_2etrue )
                  | ( Vvar__0___24Anonymous__120795 = cCoq_2eNumbers_2eBinNums_2exH
                    & cCoq_2eZArith_2eBinIntDef_2eZ_2eeven___24a1(V0__z) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) )
        | ? [Vvar__0___24Anonymous__120801] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__120801)
            & ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__120801)
             => ( V0__z = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__120801)
                & ( ? [Vvar__0___24Anonymous__120805] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__120805)
                      & Vvar__0___24Anonymous__120801 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__120805)
                      & cCoq_2eZArith_2eBinIntDef_2eZ_2eeven___24a1(V0__z) = cCoq_2eInit_2eDatatypes_2efalse )
                  | ? [Vvar__0___24Anonymous__120806] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__120806)
                      & Vvar__0___24Anonymous__120801 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__120806)
                      & cCoq_2eZArith_2eBinIntDef_2eZ_2eeven___24a1(V0__z) = cCoq_2eInit_2eDatatypes_2etrue )
                  | ( Vvar__0___24Anonymous__120801 = cCoq_2eNumbers_2eBinNums_2exH
                    & cCoq_2eZArith_2eBinIntDef_2eZ_2eeven___24a1(V0__z) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ) ) ) ).

fof('$_def_Coq.ZArith.BinIntDef.Z.leb',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_2eBinIntDef_2eZ_2eleb___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_2eBinIntDef_2eZ_2eleb___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2etrue )
          | ( cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eGt
            & cCoq_2eZArith_2eBinIntDef_2eZ_2eleb___24a2(V0__x,V1__y) = 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__120722] :
            ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__2___24Anonymous__120722)
            & ? [Vvar__3___24Anonymous__120723] :
                ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__3___24Anonymous__120723)
                & 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__120722,Vvar__3___24Anonymous__120723)
                & cCoq_2eZArith_2eBinIntDef_2eZ_2emodulo___24a2(V0__a,V1__b) = Vvar__3___24Anonymous__120723 ) ) ) ) ).

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__107329] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__107329)
            & ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
             => ( V0__x = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__107329)
                & ( ( V1__y = cCoq_2eNumbers_2eBinNums_2eZ0
                    & cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZ0 )
                  | ? [Vvar__0___24Anonymous__107333] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__107333)
                      & V1__y = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__107333)
                      & cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2emul___24a2(Vvar__0___24Anonymous__107329,Vvar__0___24Anonymous__107333)) )
                  | ? [Vvar__0___24Anonymous__107334] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__107334)
                      & V1__y = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__107334)
                      & cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2emul___24a2(Vvar__0___24Anonymous__107329,Vvar__0___24Anonymous__107334)) ) ) ) ) )
        | ? [Vvar__0___24Anonymous__107335] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__107335)
            & ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
             => ( V0__x = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__107335)
                & ( ( V1__y = cCoq_2eNumbers_2eBinNums_2eZ0
                    & cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZ0 )
                  | ? [Vvar__0___24Anonymous__107339] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__107339)
                      & V1__y = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__107339)
                      & cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2emul___24a2(Vvar__0___24Anonymous__107335,Vvar__0___24Anonymous__107339)) )
                  | ? [Vvar__0___24Anonymous__107340] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__107340)
                      & V1__y = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__107340)
                      & cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2emul___24a2(Vvar__0___24Anonymous__107335,Vvar__0___24Anonymous__107340)) ) ) ) ) ) ) ) ).

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__115921] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__115921)
            & ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__115921)
             => ( V0__z = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__115921)
                & ( ? [Vvar__0___24Anonymous__115925] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__115925)
                      & Vvar__0___24Anonymous__115921 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__115925)
                      & cCoq_2eZArith_2eBinIntDef_2eZ_2eodd___24a1(V0__z) = cCoq_2eInit_2eDatatypes_2etrue )
                  | ? [Vvar__0___24Anonymous__115926] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__115926)
                      & Vvar__0___24Anonymous__115921 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__115926)
                      & cCoq_2eZArith_2eBinIntDef_2eZ_2eodd___24a1(V0__z) = cCoq_2eInit_2eDatatypes_2efalse )
                  | ( Vvar__0___24Anonymous__115921 = cCoq_2eNumbers_2eBinNums_2exH
                    & cCoq_2eZArith_2eBinIntDef_2eZ_2eodd___24a1(V0__z) = cCoq_2eInit_2eDatatypes_2etrue ) ) ) ) )
        | ? [Vvar__0___24Anonymous__115927] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__115927)
            & ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__115927)
             => ( V0__z = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__115927)
                & ( ? [Vvar__0___24Anonymous__115931] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__115931)
                      & Vvar__0___24Anonymous__115927 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__115931)
                      & cCoq_2eZArith_2eBinIntDef_2eZ_2eodd___24a1(V0__z) = cCoq_2eInit_2eDatatypes_2etrue )
                  | ? [Vvar__0___24Anonymous__115932] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__115932)
                      & Vvar__0___24Anonymous__115927 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__115932)
                      & cCoq_2eZArith_2eBinIntDef_2eZ_2eodd___24a1(V0__z) = cCoq_2eInit_2eDatatypes_2efalse )
                  | ( Vvar__0___24Anonymous__115927 = 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__107364] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__107364)
            & V0__n = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__107364)
            & cCoq_2eZArith_2eBinIntDef_2eZ_2eof__N___24a1(V0__n) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__107364) ) ) ) ).

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__107324] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__107324)
            & V0__x = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__107324)
            & cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V0__x) = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__107324) )
        | ? [Vvar__0___24Anonymous__107325] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__107325)
            & V0__x = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__107325)
            & cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V0__x) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__107325) ) ) ) ).

fof('$_def_Coq.ZArith.BinIntDef.Z.pow',axiom,
    ! [V0__x,V1__y] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
     => ( ( V1__y = cCoq_2eNumbers_2eBinNums_2eZ0
          & cCoq_2eZArith_2eBinIntDef_2eZ_2epow___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH) )
        | ? [Vvar__0___24Anonymous__107342] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__107342)
            & V1__y = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__107342)
            & cCoq_2eZArith_2eBinIntDef_2eZ_2epow___24a2(V0__x,V1__y) = cCoq_2eZArith_2eBinIntDef_2eZ_2epow__pos___24a2(V0__x,Vvar__0___24Anonymous__107342) )
        | ? [Vvar__0___24Anonymous__107343] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__107343)
            & V1__y = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__107343)
            & cCoq_2eZArith_2eBinIntDef_2eZ_2epow___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZ0 ) ) ) ).

fof('$_def_Coq.ZArith.BinIntDef.Z.pred',axiom,
    ! [V0__x] : cCoq_2eZArith_2eBinIntDef_2eZ_2epred___24a1(V0__x) = cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__x,cCoq_2eNumbers_2eBinNums_2eZneg___24a1(cCoq_2eNumbers_2eBinNums_2exH)) ).

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__113774] :
      ( cCoq_2eZArith_2eBinIntDef_2eZ_2et___24t(Vvar__113774)
    <=> cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__113774) ) ).

fof('$_def_Coq.ZArith.BinIntDef.Z.to_N',axiom,
    ! [V0__z] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__z)
     => ( ( V0__z = cCoq_2eNumbers_2eBinNums_2eZ0
          & cCoq_2eZArith_2eBinIntDef_2eZ_2eto__N___24a1(V0__z) = cCoq_2eNumbers_2eBinNums_2eN0 )
        | ? [Vvar__0___24Anonymous__115919] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__115919)
            & V0__z = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__115919)
            & cCoq_2eZArith_2eBinIntDef_2eZ_2eto__N___24a1(V0__z) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__115919) )
        | ? [Vvar__0___24Anonymous__115920] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__115920)
            & V0__z = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__115920)
            & cCoq_2eZArith_2eBinIntDef_2eZ_2eto__N___24a1(V0__z) = cCoq_2eNumbers_2eBinNums_2eN0 ) ) ) ).

fof('$_def_Coq.ZArith.BinIntDef.Z.to_nat',axiom,
    ! [V0__z] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__z)
     => ( ( V0__z = cCoq_2eNumbers_2eBinNums_2eZ0
          & cCoq_2eZArith_2eBinIntDef_2eZ_2eto__nat___24a1(V0__z) = cCoq_2eInit_2eDatatypes_2eO )
        | ? [Vvar__0___24Anonymous__122315] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__122315)
            & V0__z = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__122315)
            & cCoq_2eZArith_2eBinIntDef_2eZ_2eto__nat___24a1(V0__z) = cCoq_2ePArith_2eBinPosDef_2ePos_2eto__nat___24a1(Vvar__0___24Anonymous__122315) )
        | ? [Vvar__0___24Anonymous__122316] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__122316)
            & V0__z = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__122316)
            & cCoq_2eZArith_2eBinIntDef_2eZ_2eto__nat___24a1(V0__z) = cCoq_2eInit_2eDatatypes_2eO ) ) ) ).

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__113780] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__113780)
            & V0__z = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__113780)
            & cCoq_2eZArith_2eBinIntDef_2eZ_2eto__pos___24a1(V0__z) = Vvar__0___24Anonymous__113780 )
        | ? [Vvar__0___24Anonymous__113781] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__113781)
            & V0__z = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__113781)
            & 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__113372] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__113372)
            & ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__113372)
             => ( V0__z = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__113372)
                & ( ? [Vvar__0___24Anonymous__113376] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__113376)
                      & Vvar__0___24Anonymous__113372 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__113376)
                      & ( cCoq_2eZArith_2eZeven_2eZeven___24a1(V0__z)
                      <=> p(c_24False) ) )
                  | ? [Vvar__0___24Anonymous__113377] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__113377)
                      & Vvar__0___24Anonymous__113372 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__113377)
                      & ( cCoq_2eZArith_2eZeven_2eZeven___24a1(V0__z)
                      <=> p(c_24True) ) )
                  | ( Vvar__0___24Anonymous__113372 = cCoq_2eNumbers_2eBinNums_2exH
                    & ( cCoq_2eZArith_2eZeven_2eZeven___24a1(V0__z)
                    <=> p(c_24False) ) ) ) ) ) )
        | ? [Vvar__0___24Anonymous__113378] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__113378)
            & ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__113378)
             => ( V0__z = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__113378)
                & ( ? [Vvar__0___24Anonymous__113382] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__113382)
                      & Vvar__0___24Anonymous__113378 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__113382)
                      & ( cCoq_2eZArith_2eZeven_2eZeven___24a1(V0__z)
                      <=> p(c_24False) ) )
                  | ? [Vvar__0___24Anonymous__113383] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__113383)
                      & Vvar__0___24Anonymous__113378 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__113383)
                      & ( cCoq_2eZArith_2eZeven_2eZeven___24a1(V0__z)
                      <=> p(c_24True) ) )
                  | ( Vvar__0___24Anonymous__113378 = 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__113384] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__113384)
            & ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__113384)
             => ( V0__z = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__113384)
                & ( ? [Vvar__0___24Anonymous__113388] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__113388)
                      & Vvar__0___24Anonymous__113384 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__113388)
                      & ( cCoq_2eZArith_2eZeven_2eZodd___24a1(V0__z)
                      <=> p(c_24True) ) )
                  | ? [Vvar__0___24Anonymous__113389] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__113389)
                      & Vvar__0___24Anonymous__113384 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__113389)
                      & ( cCoq_2eZArith_2eZeven_2eZodd___24a1(V0__z)
                      <=> p(c_24False) ) )
                  | ( Vvar__0___24Anonymous__113384 = cCoq_2eNumbers_2eBinNums_2exH
                    & ( cCoq_2eZArith_2eZeven_2eZodd___24a1(V0__z)
                    <=> p(c_24True) ) ) ) ) ) )
        | ? [Vvar__0___24Anonymous__113390] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__113390)
            & ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__113390)
             => ( V0__z = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__113390)
                & ( ? [Vvar__0___24Anonymous__113394] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__113394)
                      & Vvar__0___24Anonymous__113390 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__113394)
                      & ( cCoq_2eZArith_2eZeven_2eZodd___24a1(V0__z)
                      <=> p(c_24True) ) )
                  | ? [Vvar__0___24Anonymous__113395] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__113395)
                      & Vvar__0___24Anonymous__113390 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__113395)
                      & ( cCoq_2eZArith_2eZeven_2eZodd___24a1(V0__z)
                      <=> p(c_24False) ) )
                  | ( Vvar__0___24Anonymous__113390 = 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__113397] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__113397)
            & V1__p = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__113397)
            & ( cCoq_2eZArith_2eZlogarithm_2eIs__power___24a1(V1__p)
            <=> p(c_24False) ) )
        | ? [Vvar__0___24Anonymous__113398] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__113398)
            & V1__p = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__113398)
            & ( cCoq_2eZArith_2eZlogarithm_2eIs__power___24a1(V1__p)
            <=> cCoq_2eZArith_2eZlogarithm_2eIs__power___24a1(Vvar__0___24Anonymous__113398) ) )
        | ( V1__p = cCoq_2eNumbers_2eBinNums_2exH
          & ( cCoq_2eZArith_2eZlogarithm_2eIs__power___24a1(V1__p)
          <=> p(c_24True) ) ) ) ) ).

fof('$_def_Coq.ZArith.Zlogarithm.log_inf',axiom,
    ! [V1__p] :
      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__p)
     => ( ? [Vvar__0___24Anonymous__122186] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__122186)
            & V1__p = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__122186)
            & cCoq_2eZArith_2eZlogarithm_2elog__inf___24a1(V1__p) = cCoq_2eZArith_2eBinIntDef_2eZ_2esucc___24a1(cCoq_2eZArith_2eZlogarithm_2elog__inf___24a1(Vvar__0___24Anonymous__122186)) )
        | ? [Vvar__0___24Anonymous__122187] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__122187)
            & V1__p = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__122187)
            & cCoq_2eZArith_2eZlogarithm_2elog__inf___24a1(V1__p) = cCoq_2eZArith_2eBinIntDef_2eZ_2esucc___24a1(cCoq_2eZArith_2eZlogarithm_2elog__inf___24a1(Vvar__0___24Anonymous__122187)) )
        | ( V1__p = cCoq_2eNumbers_2eBinNums_2exH
          & cCoq_2eZArith_2eZlogarithm_2elog__inf___24a1(V1__p) = cCoq_2eNumbers_2eBinNums_2eZ0 ) ) ) ).

fof('$_def_Coq.micromega.Env.Env',axiom,
    ! [V0__D] : cCoq_2emicromega_2eEnv_2eEnv___24a1(V0__D) = c_24__type__85706___24a1(V0__D) ).

fof('$_def_Coq.micromega.QMicromega.QWitness',axiom,
    ! [Vvar__172695] :
      ( cCoq_2emicromega_2eQMicromega_2eQWitness___24t(Vvar__172695)
    <=> cCoq_2emicromega_2eRingMicromega_2ePsatz___24t(cCoq_2eQArith_2eQArith__base_2eQ,Vvar__172695) ) ).

fof('$_def_Coq.micromega.RMicromega.RWitness',axiom,
    ! [Vvar__172733] :
      ( cCoq_2emicromega_2eRMicromega_2eRWitness___24t(Vvar__172733)
    <=> cCoq_2emicromega_2eRingMicromega_2ePsatz___24t(cCoq_2eQArith_2eQArith__base_2eQ,Vvar__172733) ) ).

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__5098] :
              ( t(Vvar__1___24Anonymous__5098,V1__A)
              & ? [Vvar__2___24Anonymous__5099] :
                  ( cCoq_2eInit_2eDatatypes_2elist___24t(V1__A,Vvar__2___24Anonymous__5099)
                  & ( cType___24t(V1__A)
                   => ( cCoq_2eInit_2eDatatypes_2elist___24t(V1__A,Vvar__2___24Anonymous__5099)
                     => ( V3__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V1__A,Vvar__1___24Anonymous__5098,Vvar__2___24Anonymous__5099)
                        & ( ( Vvar__2___24Anonymous__5099 = 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__5098)) ) )
                          | ? [Vvar__1___24Anonymous__5110] :
                              ( t(Vvar__1___24Anonymous__5110,V1__A)
                              & ? [Vvar__2___24Anonymous__5111] :
                                  ( cCoq_2eInit_2eDatatypes_2elist___24t(V1__A,Vvar__2___24Anonymous__5111)
                                  & Vvar__2___24Anonymous__5099 = cCoq_2eInit_2eDatatypes_2econs___24a3(V1__A,Vvar__1___24Anonymous__5110,Vvar__2___24Anonymous__5111)
                                  & ( cCoq_2emicromega_2eRefl_2emake__conj___24a3(V1__A,V2__eval,V3__l)
                                  <=> ( p(happ(V2__eval,Vvar__1___24Anonymous__5098))
                                      & cCoq_2emicromega_2eRefl_2emake__conj___24a3(V1__A,V2__eval,Vvar__2___24Anonymous__5099) ) ) ) ) ) ) ) ) ) ) ) ) ) ).

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__91233] :
              ( t(Vvar__1___24Anonymous__91233,V1__A)
              & ? [Vvar__2___24Anonymous__91234] :
                  ( cCoq_2eInit_2eDatatypes_2elist___24t(V1__A,Vvar__2___24Anonymous__91234)
                  & V3__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V1__A,Vvar__1___24Anonymous__91233,Vvar__2___24Anonymous__91234)
                  & ( cCoq_2emicromega_2eRefl_2emake__impl___24a4(V1__A,V2__eval,V3__l,V4__goal)
                  <=> ( p(happ(V2__eval,Vvar__1___24Anonymous__91233))
                     => cCoq_2emicromega_2eRefl_2emake__impl___24a4(V1__A,V2__eval,Vvar__2___24Anonymous__91234,V4__goal) ) ) ) ) ) ) ) ).

fof('$_def_Coq.micromega.RingMicromega.NFormula',axiom,
    ! [V0__C] : cCoq_2emicromega_2eRingMicromega_2eNFormula___24a1(V0__C) = cCoq_2eInit_2eDatatypes_2eprod___24a2(cCoq_2emicromega_2eRingMicromega_2ePolC___24a1(V0__C),cCoq_2emicromega_2eRingMicromega_2eOp1) ).

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.RingMicromega.eval_op1',axiom,
    ! [V0__R,V1__rO,V2__req,V3__rle,V4__rlt,V5__o] :
      ( cType___24t(V0__R)
     => ( cCoq_2emicromega_2eRingMicromega_2eOp1___24t(V5__o)
       => ( ( V5__o = cCoq_2emicromega_2eRingMicromega_2eEqual
            & cCoq_2emicromega_2eRingMicromega_2eeval__op1___24a6(V0__R,V1__rO,V2__req,V3__rle,V4__rlt,V5__o) = c_24__lam__96901___24a3(V0__R,V1__rO,V2__req) )
          | ( V5__o = cCoq_2emicromega_2eRingMicromega_2eNonEqual
            & cCoq_2emicromega_2eRingMicromega_2eeval__op1___24a6(V0__R,V1__rO,V2__req,V3__rle,V4__rlt,V5__o) = c_24__lam__96909___24a3(V0__R,V1__rO,V2__req) )
          | ( V5__o = cCoq_2emicromega_2eRingMicromega_2eStrict
            & cCoq_2emicromega_2eRingMicromega_2eeval__op1___24a6(V0__R,V1__rO,V2__req,V3__rle,V4__rlt,V5__o) = c_24__lam__96917___24a3(V0__R,V1__rO,V4__rlt) )
          | ( V5__o = cCoq_2emicromega_2eRingMicromega_2eNonStrict
            & cCoq_2emicromega_2eRingMicromega_2eeval__op1___24a6(V0__R,V1__rO,V2__req,V3__rle,V4__rlt,V5__o) = c_24__lam__96925___24a3(V0__R,V1__rO,V3__rle) ) ) ) ) ).

fof('$_def_Coq.micromega.RingMicromega.eval_pol',axiom,
    ! [V0__R,V1__rplus,V2__rtimes,V3__C,V4__phi] : cCoq_2emicromega_2eRingMicromega_2eeval__pol___24a5(V0__R,V1__rplus,V2__rtimes,V3__C,V4__phi) = cCoq_2emicromega_2eEnvRing_2ePphi___24a5(V0__R,V1__rplus,V2__rtimes,V3__C,V4__phi) ).

fof('$_def_Coq.micromega.RingMicromega.ge_bool',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_2emicromega_2eRingMicromega_2ege__bool___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2etrue )
              | ? [Vvar__0___24Anonymous__121776] :
                  ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__121776)
                  & V2__m = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__121776)
                  & cCoq_2emicromega_2eRingMicromega_2ege__bool___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) )
        | ? [Vvar__0___24Anonymous__121777] :
            ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__121777)
            & ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__m)
             => ( V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__121777)
                & ( ( V2__m = cCoq_2eInit_2eDatatypes_2eO
                    & cCoq_2emicromega_2eRingMicromega_2ege__bool___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2etrue )
                  | ? [Vvar__0___24Anonymous__121780] :
                      ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__121780)
                      & V2__m = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__121780)
                      & cCoq_2emicromega_2eRingMicromega_2ege__bool___24a2(V1__n,V2__m) = cCoq_2emicromega_2eRingMicromega_2ege__bool___24a2(Vvar__0___24Anonymous__121777,Vvar__0___24Anonymous__121780) ) ) ) ) ) ) ) ).

fof('$_def_Coq.micromega.Tauto.BFormula',axiom,
    ! [V0__A] : cCoq_2emicromega_2eTauto_2eBFormula___24a1(V0__A) = cCoq_2emicromega_2eTauto_2eGFormula___24a4(V0__A,cProp,cCoq_2eInit_2eDatatypes_2eunit,cCoq_2eInit_2eDatatypes_2eunit) ).

fof('$_def_Coq.micromega.Tauto.TFormula',axiom,
    ! [V0__Term,V1__Annot,V2__TX,V3__AF] : cCoq_2emicromega_2eTauto_2eTFormula___24a4(V0__Term,V1__Annot,V2__TX,V3__AF) = cCoq_2emicromega_2eTauto_2eGFormula___24a4(V0__Term,V2__TX,V1__Annot,V3__AF) ).

fof('$_def_Coq.micromega.Tauto.and_cnf',axiom,
    ! [V0__Term_27,V1__Annot,V2__f1,V3__f2] : cCoq_2emicromega_2eTauto_2eand__cnf___24a4(V0__Term_27,V1__Annot,V2__f1,V3__f2) = cCoq_2eInit_2eDatatypes_2eapp___24a3(cCoq_2emicromega_2eTauto_2eclause___24a2(V0__Term_27,V1__Annot),V2__f1,V3__f2) ).

fof('$_def_Coq.micromega.Tauto.clause',axiom,
    ! [V0__Term_27,V1__Annot] : cCoq_2emicromega_2eTauto_2eclause___24a2(V0__Term_27,V1__Annot) = cCoq_2eInit_2eDatatypes_2elist___24a1(cCoq_2eInit_2eDatatypes_2eprod___24a2(V0__Term_27,V1__Annot)) ).

fof('$_def_Coq.micromega.Tauto.cnf',axiom,
    ! [V0__Term_27,V1__Annot] : cCoq_2emicromega_2eTauto_2ecnf___24a2(V0__Term_27,V1__Annot) = cCoq_2eInit_2eDatatypes_2elist___24a1(cCoq_2emicromega_2eTauto_2eclause___24a2(V0__Term_27,V1__Annot)) ).

fof('$_def_Coq.micromega.Tauto.cnf_ff',axiom,
    ! [V0__Term_27,V1__Annot] : cCoq_2emicromega_2eTauto_2ecnf__ff___24a2(V0__Term_27,V1__Annot) = cCoq_2eInit_2eDatatypes_2econs___24a3(cCoq_2eInit_2eDatatypes_2elist___24a1(cCoq_2eInit_2eDatatypes_2eprod___24a2(V0__Term_27,V1__Annot)),cCoq_2eInit_2eDatatypes_2enil___24a1(cCoq_2eInit_2eDatatypes_2eprod___24a2(V0__Term_27,V1__Annot)),cCoq_2eInit_2eDatatypes_2enil___24a1(cCoq_2eInit_2eDatatypes_2elist___24a1(cCoq_2eInit_2eDatatypes_2eprod___24a2(V0__Term_27,V1__Annot)))) ).

fof('$_def_Coq.micromega.Tauto.cnf_tt',axiom,
    ! [V0__Term_27,V1__Annot] : cCoq_2emicromega_2eTauto_2ecnf__tt___24a2(V0__Term_27,V1__Annot) = cCoq_2eInit_2eDatatypes_2enil___24a1(cCoq_2emicromega_2eTauto_2eclause___24a2(V0__Term_27,V1__Annot)) ).

fof('$_def_Coq.micromega.Tauto.eval_bf',axiom,
    ! [V0__A,V1__ea,V2__f] :
      ( p(cCoq_2emicromega_2eTauto_2eeval__bf___24a3(V0__A,V1__ea,V2__f))
    <=> cCoq_2emicromega_2eTauto_2eeval__f___24a7(V0__A,cProp,cCoq_2eInit_2eDatatypes_2eunit,cCoq_2eInit_2eDatatypes_2eunit,c_24__lam__113894___24a1(V0__A),V1__ea,V2__f) ) ).

fof('$_def_Coq.micromega.Tauto.eval_clause',axiom,
    ! [V0__Env,V1__Term_27,V2__Annot,V3__eval_27,V4__env,V5__cl] :
      ( cCoq_2emicromega_2eTauto_2eeval__clause___24a6(V0__Env,V1__Term_27,V2__Annot,V3__eval_27,V4__env,V5__cl)
    <=> ~ cCoq_2emicromega_2eRefl_2emake__conj___24a3(cCoq_2eInit_2eDatatypes_2eprod___24a2(V1__Term_27,V2__Annot),cCoq_2emicromega_2eTauto_2eeval__tt___24a5(V0__Env,V1__Term_27,V2__Annot,V3__eval_27,V4__env),V5__cl) ) ).

fof('$_def_Coq.micromega.Tauto.eval_cnf',axiom,
    ! [V0__Env,V1__Term_27,V2__Annot,V3__eval_27,V4__env,V5__f] :
      ( cCoq_2emicromega_2eTauto_2eeval__cnf___24a6(V0__Env,V1__Term_27,V2__Annot,V3__eval_27,V4__env,V5__f)
    <=> cCoq_2emicromega_2eRefl_2emake__conj___24a3(cCoq_2emicromega_2eTauto_2eclause___24a2(V1__Term_27,V2__Annot),cCoq_2emicromega_2eTauto_2eeval__clause___24a5(V0__Env,V1__Term_27,V2__Annot,V3__eval_27,V4__env),V5__f) ) ).

fof('$_def_Coq.micromega.Tauto.eval_f',axiom,
    ! [V0__TA,V1__TX,V2__AA,V3__AF,V4__ex,V5__ea,V7__f] :
      ( cType___24t(V0__TA)
     => ( cType___24t(V1__TX)
       => ( cType___24t(V2__AA)
         => ( cType___24t(V3__AF)
           => ( cCoq_2emicromega_2eTauto_2eGFormula___24t(V0__TA,V1__TX,V2__AA,V3__AF,V7__f)
             => ( ( V7__f = cCoq_2emicromega_2eTauto_2eTT___24a4(V0__TA,V1__TX,V2__AA,V3__AF)
                  & ( cCoq_2emicromega_2eTauto_2eeval__f___24a7(V0__TA,V1__TX,V2__AA,V3__AF,V4__ex,V5__ea,V7__f)
                  <=> p(c_24True) ) )
                | ( V7__f = cCoq_2emicromega_2eTauto_2eFF___24a4(V0__TA,V1__TX,V2__AA,V3__AF)
                  & ( cCoq_2emicromega_2eTauto_2eeval__f___24a7(V0__TA,V1__TX,V2__AA,V3__AF,V4__ex,V5__ea,V7__f)
                  <=> p(c_24False) ) )
                | ? [Vvar__4___24Anonymous__105061] :
                    ( t(Vvar__4___24Anonymous__105061,V1__TX)
                    & V7__f = cCoq_2emicromega_2eTauto_2eX___24a5(V0__TA,V1__TX,V2__AA,V3__AF,Vvar__4___24Anonymous__105061)
                    & ( cCoq_2emicromega_2eTauto_2eeval__f___24a7(V0__TA,V1__TX,V2__AA,V3__AF,V4__ex,V5__ea,V7__f)
                    <=> p(happ(V4__ex,Vvar__4___24Anonymous__105061)) ) )
                | ? [Vvar__4___24Anonymous__105066] :
                    ( t(Vvar__4___24Anonymous__105066,V0__TA)
                    & ? [Vvar__5___24Anonymous__105067] :
                        ( t(Vvar__5___24Anonymous__105067,V2__AA)
                        & V7__f = cCoq_2emicromega_2eTauto_2eA___24a6(V0__TA,V1__TX,V2__AA,V3__AF,Vvar__4___24Anonymous__105066,Vvar__5___24Anonymous__105067)
                        & ( cCoq_2emicromega_2eTauto_2eeval__f___24a7(V0__TA,V1__TX,V2__AA,V3__AF,V4__ex,V5__ea,V7__f)
                        <=> p(happ(V5__ea,Vvar__4___24Anonymous__105066)) ) ) )
                | ? [Vvar__4___24Anonymous__105073] :
                    ( cCoq_2emicromega_2eTauto_2eGFormula___24t(V0__TA,V1__TX,V2__AA,V3__AF,Vvar__4___24Anonymous__105073)
                    & ? [Vvar__5___24Anonymous__105074] :
                        ( cCoq_2emicromega_2eTauto_2eGFormula___24t(V0__TA,V1__TX,V2__AA,V3__AF,Vvar__5___24Anonymous__105074)
                        & V7__f = cCoq_2emicromega_2eTauto_2eCj___24a6(V0__TA,V1__TX,V2__AA,V3__AF,Vvar__4___24Anonymous__105073,Vvar__5___24Anonymous__105074)
                        & ( cCoq_2emicromega_2eTauto_2eeval__f___24a7(V0__TA,V1__TX,V2__AA,V3__AF,V4__ex,V5__ea,V7__f)
                        <=> ( cCoq_2emicromega_2eTauto_2eeval__f___24a7(V0__TA,V1__TX,V2__AA,V3__AF,V4__ex,V5__ea,Vvar__4___24Anonymous__105073)
                            & cCoq_2emicromega_2eTauto_2eeval__f___24a7(V0__TA,V1__TX,V2__AA,V3__AF,V4__ex,V5__ea,Vvar__5___24Anonymous__105074) ) ) ) )
                | ? [Vvar__4___24Anonymous__105080] :
                    ( cCoq_2emicromega_2eTauto_2eGFormula___24t(V0__TA,V1__TX,V2__AA,V3__AF,Vvar__4___24Anonymous__105080)
                    & ? [Vvar__5___24Anonymous__105081] :
                        ( cCoq_2emicromega_2eTauto_2eGFormula___24t(V0__TA,V1__TX,V2__AA,V3__AF,Vvar__5___24Anonymous__105081)
                        & V7__f = cCoq_2emicromega_2eTauto_2eD___24a6(V0__TA,V1__TX,V2__AA,V3__AF,Vvar__4___24Anonymous__105080,Vvar__5___24Anonymous__105081)
                        & ( cCoq_2emicromega_2eTauto_2eeval__f___24a7(V0__TA,V1__TX,V2__AA,V3__AF,V4__ex,V5__ea,V7__f)
                        <=> ( cCoq_2emicromega_2eTauto_2eeval__f___24a7(V0__TA,V1__TX,V2__AA,V3__AF,V4__ex,V5__ea,Vvar__4___24Anonymous__105080)
                            | cCoq_2emicromega_2eTauto_2eeval__f___24a7(V0__TA,V1__TX,V2__AA,V3__AF,V4__ex,V5__ea,Vvar__5___24Anonymous__105081) ) ) ) )
                | ? [Vvar__4___24Anonymous__105087] :
                    ( cCoq_2emicromega_2eTauto_2eGFormula___24t(V0__TA,V1__TX,V2__AA,V3__AF,Vvar__4___24Anonymous__105087)
                    & V7__f = cCoq_2emicromega_2eTauto_2eN___24a5(V0__TA,V1__TX,V2__AA,V3__AF,Vvar__4___24Anonymous__105087)
                    & ( cCoq_2emicromega_2eTauto_2eeval__f___24a7(V0__TA,V1__TX,V2__AA,V3__AF,V4__ex,V5__ea,V7__f)
                    <=> ~ cCoq_2emicromega_2eTauto_2eeval__f___24a7(V0__TA,V1__TX,V2__AA,V3__AF,V4__ex,V5__ea,Vvar__4___24Anonymous__105087) ) )
                | ? [Vvar__4___24Anonymous__105092] :
                    ( cCoq_2emicromega_2eTauto_2eGFormula___24t(V0__TA,V1__TX,V2__AA,V3__AF,Vvar__4___24Anonymous__105092)
                    & ? [Vvar__5___24Anonymous__105093] :
                        ( cCoq_2eInit_2eDatatypes_2eoption___24t(V3__AF,Vvar__5___24Anonymous__105093)
                        & ? [Vvar__6___24Anonymous__105094] :
                            ( cCoq_2emicromega_2eTauto_2eGFormula___24t(V0__TA,V1__TX,V2__AA,V3__AF,Vvar__6___24Anonymous__105094)
                            & V7__f = cCoq_2emicromega_2eTauto_2eI___24a7(V0__TA,V1__TX,V2__AA,V3__AF,Vvar__4___24Anonymous__105092,Vvar__5___24Anonymous__105093,Vvar__6___24Anonymous__105094)
                            & ( cCoq_2emicromega_2eTauto_2eeval__f___24a7(V0__TA,V1__TX,V2__AA,V3__AF,V4__ex,V5__ea,V7__f)
                            <=> ( cCoq_2emicromega_2eTauto_2eeval__f___24a7(V0__TA,V1__TX,V2__AA,V3__AF,V4__ex,V5__ea,Vvar__4___24Anonymous__105092)
                               => cCoq_2emicromega_2eTauto_2eeval__f___24a7(V0__TA,V1__TX,V2__AA,V3__AF,V4__ex,V5__ea,Vvar__6___24Anonymous__105094) ) ) ) ) ) ) ) ) ) ) ) ).

fof('$_def_Coq.micromega.Tauto.eval_tt',axiom,
    ! [V0__Env,V1__Term_27,V2__Annot,V3__eval_27,V4__env,V5__tt] :
      ( cCoq_2emicromega_2eTauto_2eeval__tt___24a6(V0__Env,V1__Term_27,V2__Annot,V3__eval_27,V4__env,V5__tt)
    <=> p(happ(happ(V3__eval_27,V4__env),cCoq_2eInit_2eDatatypes_2efst___24a3(V1__Term_27,V2__Annot,V5__tt))) ) ).

fof('$_def_Coq.micromega.ZMicromega.Vars.Facts.Add',axiom,
    cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eAdd = cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eAdd ).

fof('$_def_Coq.micromega.ZMicromega.Vars.max_element',axiom,
    ! [V0__vars] : cCoq_2emicromega_2eZMicromega_2eVars_2emax__element___24a1(V0__vars) = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2efold___24a4(cCoq_2eNumbers_2eBinNums_2epositive,cCoq_2ePArith_2eBinPosDef_2ePos_2emax,V0__vars,cCoq_2eNumbers_2eBinNums_2exH) ).

fof('$_def_Coq.micromega.ZMicromega.ZWitness',axiom,
    ! [Vvar__106522] :
      ( cCoq_2emicromega_2eZMicromega_2eZWitness___24t(Vvar__106522)
    <=> cCoq_2emicromega_2eRingMicromega_2ePsatz___24t(cCoq_2eNumbers_2eBinNums_2eZ,Vvar__106522) ) ).

fof('$_def_Coq.micromega.ZMicromega.Zeval_op2',axiom,
    ! [V0__o] :
      ( cCoq_2emicromega_2eRingMicromega_2eOp2___24t(V0__o)
     => ( ( V0__o = cCoq_2emicromega_2eRingMicromega_2eOpEq
          & cCoq_2emicromega_2eZMicromega_2eZeval__op2___24a1(V0__o) = c_3d___24a1(cCoq_2eNumbers_2eBinNums_2eZ) )
        | ( V0__o = cCoq_2emicromega_2eRingMicromega_2eOpNEq
          & cCoq_2emicromega_2eZMicromega_2eZeval__op2___24a1(V0__o) = c_24__lam__173584 )
        | ( V0__o = cCoq_2emicromega_2eRingMicromega_2eOpLe
          & cCoq_2emicromega_2eZMicromega_2eZeval__op2___24a1(V0__o) = cCoq_2eZArith_2eBinInt_2eZ_2ele )
        | ( V0__o = cCoq_2emicromega_2eRingMicromega_2eOpGe
          & cCoq_2emicromega_2eZMicromega_2eZeval__op2___24a1(V0__o) = cCoq_2eZArith_2eBinInt_2eZ_2ege )
        | ( V0__o = cCoq_2emicromega_2eRingMicromega_2eOpLt
          & cCoq_2emicromega_2eZMicromega_2eZeval__op2___24a1(V0__o) = cCoq_2eZArith_2eBinInt_2eZ_2elt )
        | ( V0__o = cCoq_2emicromega_2eRingMicromega_2eOpGt
          & cCoq_2emicromega_2eZMicromega_2eZeval__op2___24a1(V0__o) = cCoq_2eZArith_2eBinInt_2eZ_2egt ) ) ) ).

fof('$_def_Coq.micromega.ZMicromega.Zunsat',axiom,
    cCoq_2emicromega_2eZMicromega_2eZunsat = cCoq_2emicromega_2eRingMicromega_2echeck__inconsistent___24a4(cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eNumbers_2eBinNums_2eZ0,cCoq_2eZArith_2eZbool_2eZeq__bool,cCoq_2eZArith_2eBinIntDef_2eZ_2eleb) ).

fof('$_def_Coq.micromega.ZMicromega.agree_env',axiom,
    ! [V0__v,V1__env,V2__env_27] :
      ( cCoq_2emicromega_2eZMicromega_2eagree__env___24a3(V0__v,V1__env,V2__env_27)
    <=> ! [V3__x] :
          ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(V3__x)
         => ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2emem___24a2(V3__x,V0__v) = cCoq_2eInit_2eDatatypes_2etrue
           => happ(V1__env,V3__x) = happ(V2__env_27,V3__x) ) ) ) ).

fof('$_def_Coq.micromega.ZMicromega.coneMember',axiom,
    ! [Vvar__122184] :
      ( cCoq_2emicromega_2eZMicromega_2econeMember___24t(Vvar__122184)
    <=> cCoq_2emicromega_2eZMicromega_2eZWitness___24t(Vvar__122184) ) ).

fof('$_def_Coq.omega.PreOmega.Z_of_N\'',axiom,
    cCoq_2eomega_2ePreOmega_2eZ__of__N_27 = cCoq_2eZArith_2eBinIntDef_2eZ_2eof__N ).

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.Zneg\'',axiom,
    cCoq_2eomega_2ePreOmega_2eZneg_27 = cCoq_2eNumbers_2eBinNums_2eZneg ).

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

fof('$_def_Coq.setoid_ring.ArithRing.protected_to_nat',axiom,
    cCoq_2esetoid__ring_2eArithRing_2eprotected__to__nat = cCoq_2eNArith_2eBinNatDef_2eN_2eto__nat ).

fof('$_def_Coq.setoid_ring.InitialRing.Nopp',axiom,
    cCoq_2esetoid__ring_2eInitialRing_2eNopp = cCoq_2esetoid__ring_2eRing__theory_2eSRopp___24a1(cCoq_2eNumbers_2eBinNums_2eN) ).

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

fof('$_def_Coq.setoid_ring.InitialRing.Nword',axiom,
    ! [Vvar__120946] :
      ( cCoq_2esetoid__ring_2eInitialRing_2eNword___24t(Vvar__120946)
    <=> cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eNumbers_2eBinNums_2eN,Vvar__120946) ) ).

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__109201] :
              ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__109201)
              & ( cType___24t(V0__R)
               => ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__109201)
                 => ( V5__p = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__109201)
                    & ( ? [Vvar__0___24Anonymous__109205] :
                          ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__109205)
                          & Vvar__0___24Anonymous__109201 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__109205)
                          & 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__109201))) )
                      | ? [Vvar__0___24Anonymous__109206] :
                          ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__109206)
                          & Vvar__0___24Anonymous__109201 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__109206)
                          & 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__109201))) )
                      | ( Vvar__0___24Anonymous__109201 = 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__109207] :
              ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__109207)
              & ( cType___24t(V0__R)
               => ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__109207)
                 => ( V5__p = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__109207)
                    & ( ? [Vvar__0___24Anonymous__109211] :
                          ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__109211)
                          & Vvar__0___24Anonymous__109207 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__109211)
                          & 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__109207)) )
                      | ? [Vvar__0___24Anonymous__109212] :
                          ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__109212)
                          & Vvar__0___24Anonymous__109207 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__109212)
                          & 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__109207)) )
                      | ( Vvar__0___24Anonymous__109207 = 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__109168] :
              ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__109168)
              & V5__p = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__109168)
              & 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__109168))) )
          | ? [Vvar__0___24Anonymous__109169] :
              ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__109169)
              & V5__p = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__109169)
              & 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__109169)) )
          | ( 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.Peq',axiom,
    ! [V0__C,V1__ceqb,V3__P,V4__P_27] :
      ( cType___24t(V0__C)
     => ( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,V3__P)
       => ( ? [Vvar__1___24Anonymous__98302] :
              ( t(Vvar__1___24Anonymous__98302,V0__C)
              & ( cType___24t(V0__C)
               => ( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,V4__P_27)
                 => ( V3__P = cCoq_2esetoid__ring_2eRing__polynom_2ePc___24a2(V0__C,Vvar__1___24Anonymous__98302)
                    & ( ? [Vvar__1___24Anonymous__98312] :
                          ( t(Vvar__1___24Anonymous__98312,V0__C)
                          & V4__P_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePc___24a2(V0__C,Vvar__1___24Anonymous__98312)
                          & cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,V3__P,V4__P_27) = happ(happ(V1__ceqb,Vvar__1___24Anonymous__98302),Vvar__1___24Anonymous__98312) )
                      | ? [Vvar__1___24Anonymous__98314] :
                          ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__98314)
                          & ? [Vvar__2___24Anonymous__98315] :
                              ( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__2___24Anonymous__98315)
                              & V4__P_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePinj___24a3(V0__C,Vvar__1___24Anonymous__98314,Vvar__2___24Anonymous__98315)
                              & cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,V3__P,V4__P_27) = cCoq_2eInit_2eDatatypes_2efalse ) )
                      | ? [Vvar__1___24Anonymous__98318] :
                          ( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__1___24Anonymous__98318)
                          & ? [Vvar__2___24Anonymous__98319] :
                              ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2___24Anonymous__98319)
                              & ? [Vvar__3___24Anonymous__98320] :
                                  ( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__3___24Anonymous__98320)
                                  & V4__P_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePX___24a4(V0__C,Vvar__1___24Anonymous__98318,Vvar__2___24Anonymous__98319,Vvar__3___24Anonymous__98320)
                                  & cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,V3__P,V4__P_27) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ) ) ) )
          | ? [Vvar__1___24Anonymous__98325] :
              ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__98325)
              & ? [Vvar__2___24Anonymous__98326] :
                  ( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__2___24Anonymous__98326)
                  & ( cType___24t(V0__C)
                   => ( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,V4__P_27)
                     => ( V3__P = cCoq_2esetoid__ring_2eRing__polynom_2ePinj___24a3(V0__C,Vvar__1___24Anonymous__98325,Vvar__2___24Anonymous__98326)
                        & ( ? [Vvar__1___24Anonymous__98346] :
                              ( t(Vvar__1___24Anonymous__98346,V0__C)
                              & V4__P_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePc___24a2(V0__C,Vvar__1___24Anonymous__98346)
                              & cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,V3__P,V4__P_27) = cCoq_2eInit_2eDatatypes_2efalse )
                          | ? [Vvar__1___24Anonymous__98348] :
                              ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__98348)
                              & ? [Vvar__2___24Anonymous__98349] :
                                  ( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__2___24Anonymous__98349)
                                  & ( cType___24t(V0__C)
                                   => ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__98325)
                                     => ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__98348)
                                       => ( V4__P_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePinj___24a3(V0__C,Vvar__1___24Anonymous__98348,Vvar__2___24Anonymous__98349)
                                          & ( ( cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare___24a2(Vvar__1___24Anonymous__98325,Vvar__1___24Anonymous__98348) = cCoq_2eInit_2eDatatypes_2eEq
                                              & cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,V3__P,V4__P_27) = cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,Vvar__2___24Anonymous__98326,Vvar__2___24Anonymous__98349) )
                                            | ( cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare___24a2(Vvar__1___24Anonymous__98325,Vvar__1___24Anonymous__98348) = cCoq_2eInit_2eDatatypes_2eLt
                                              & cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,V3__P,V4__P_27) = cCoq_2eInit_2eDatatypes_2efalse )
                                            | ( cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare___24a2(Vvar__1___24Anonymous__98325,Vvar__1___24Anonymous__98348) = cCoq_2eInit_2eDatatypes_2eGt
                                              & cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,V3__P,V4__P_27) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ) ) ) )
                          | ? [Vvar__1___24Anonymous__98354] :
                              ( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__1___24Anonymous__98354)
                              & ? [Vvar__2___24Anonymous__98355] :
                                  ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2___24Anonymous__98355)
                                  & ? [Vvar__3___24Anonymous__98356] :
                                      ( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__3___24Anonymous__98356)
                                      & V4__P_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePX___24a4(V0__C,Vvar__1___24Anonymous__98354,Vvar__2___24Anonymous__98355,Vvar__3___24Anonymous__98356)
                                      & cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,V3__P,V4__P_27) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ) ) ) ) )
          | ? [Vvar__1___24Anonymous__98361] :
              ( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__1___24Anonymous__98361)
              & ? [Vvar__2___24Anonymous__98362] :
                  ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2___24Anonymous__98362)
                  & ? [Vvar__3___24Anonymous__98363] :
                      ( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__3___24Anonymous__98363)
                      & ( cType___24t(V0__C)
                       => ( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,V4__P_27)
                         => ( V3__P = cCoq_2esetoid__ring_2eRing__polynom_2ePX___24a4(V0__C,Vvar__1___24Anonymous__98361,Vvar__2___24Anonymous__98362,Vvar__3___24Anonymous__98363)
                            & ( ? [Vvar__1___24Anonymous__98396] :
                                  ( t(Vvar__1___24Anonymous__98396,V0__C)
                                  & V4__P_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePc___24a2(V0__C,Vvar__1___24Anonymous__98396)
                                  & cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,V3__P,V4__P_27) = cCoq_2eInit_2eDatatypes_2efalse )
                              | ? [Vvar__1___24Anonymous__98398] :
                                  ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__98398)
                                  & ? [Vvar__2___24Anonymous__98399] :
                                      ( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__2___24Anonymous__98399)
                                      & V4__P_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePinj___24a3(V0__C,Vvar__1___24Anonymous__98398,Vvar__2___24Anonymous__98399)
                                      & cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,V3__P,V4__P_27) = cCoq_2eInit_2eDatatypes_2efalse ) )
                              | ? [Vvar__1___24Anonymous__98402] :
                                  ( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__1___24Anonymous__98402)
                                  & ? [Vvar__2___24Anonymous__98403] :
                                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2___24Anonymous__98403)
                                      & ? [Vvar__3___24Anonymous__98404] :
                                          ( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__3___24Anonymous__98404)
                                          & ( cType___24t(V0__C)
                                           => ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2___24Anonymous__98362)
                                             => ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2___24Anonymous__98403)
                                               => ( V4__P_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePX___24a4(V0__C,Vvar__1___24Anonymous__98402,Vvar__2___24Anonymous__98403,Vvar__3___24Anonymous__98404)
                                                  & ( ( cType___24t(V0__C)
                                                     => ( c_24__type__1063___24t(V0__C,V1__ceqb)
                                                       => ( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__1___24Anonymous__98361)
                                                         => ( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__1___24Anonymous__98402)
                                                           => ( cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare___24a2(Vvar__2___24Anonymous__98362,Vvar__2___24Anonymous__98403) = cCoq_2eInit_2eDatatypes_2eEq
                                                              & ( ( cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,Vvar__1___24Anonymous__98361,Vvar__1___24Anonymous__98402) = cCoq_2eInit_2eDatatypes_2etrue
                                                                  & cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,V3__P,V4__P_27) = cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,Vvar__3___24Anonymous__98363,Vvar__3___24Anonymous__98404) )
                                                                | ( cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,Vvar__1___24Anonymous__98361,Vvar__1___24Anonymous__98402) = cCoq_2eInit_2eDatatypes_2efalse
                                                                  & cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,V3__P,V4__P_27) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ) ) )
                                                    | ( cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare___24a2(Vvar__2___24Anonymous__98362,Vvar__2___24Anonymous__98403) = cCoq_2eInit_2eDatatypes_2eLt
                                                      & cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,V3__P,V4__P_27) = cCoq_2eInit_2eDatatypes_2efalse )
                                                    | ( cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare___24a2(Vvar__2___24Anonymous__98362,Vvar__2___24Anonymous__98403) = cCoq_2eInit_2eDatatypes_2eGt
                                                      & cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,V3__P,V4__P_27) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).

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__103696] :
              ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__103696)
              & V5__p = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__103696)
              & 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__103696),V4__x,Vvar__0___24Anonymous__103696) )
          | ? [Vvar__0___24Anonymous__103697] :
              ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__103697)
              & V5__p = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__103697)
              & 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__103697),V4__x,Vvar__0___24Anonymous__103697) )
          | ( 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_tac.ring_subst_niter',axiom,
    cCoq_2esetoid__ring_2eRing__tac_2ering__subst__niter = cCoq_2eInit_2eNat_2emul___24a2(cCoq_2eInit_2eNat_2emul___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO)))))))))),cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO))))))))))),cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO))))))))))) ).

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

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

fof('$_def_Coq.setoid_ring.Ring_theory.SRsub',axiom,
    ! [V0__R,V1__radd,V2__x,V3__y] : cCoq_2esetoid__ring_2eRing__theory_2eSRsub___24a4(V0__R,V1__radd,V2__x,V3__y) = happ(happ(V1__radd,V2__x),cCoq_2esetoid__ring_2eRing__theory_2eSRopp___24a2(V0__R,V3__y)) ).

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__7645] :
              ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__7645)
              & V4__p = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__7645)
              & 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__7645) ) ) ) ) ).

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__7625] :
              ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__7625)
              & V4__i = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__7625)
              & 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__7626__7629___24a4(V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__7625)),c_24__let__var__6__p__7626__7629___24a4(V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__7625))) )
          | ? [Vvar__0___24Anonymous__7627] :
              ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__7627)
              & V4__i = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__7627)
              & 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__7628__7630___24a4(V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__7627)),c_24__let__var__6__p__7628__7630___24a4(V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__7627)) )
          | ( 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.default',axiom,
    cHammer_2eTactics_2eTactics_2edefault = cCoq_2eInit_2eDatatypes_2ett ).

fof('$_def_Hammer.Tactics.Tactics.hints',axiom,
    cHammer_2eTactics_2eTactics_2ehints = cCoq_2eInit_2eDatatypes_2ett ).

fof('$_def_Hammer.Tactics.Tactics.logic',axiom,
    cHammer_2eTactics_2eTactics_2elogic = cCoq_2eInit_2eDatatypes_2ett ).

fof('$_def_Hammer.Tactics.Tactics.nohints',axiom,
    cHammer_2eTactics_2eTactics_2enohints = cCoq_2eInit_2eDatatypes_2ett ).

fof('$_def_Hammer.Tactics.Tactics.none',axiom,
    cHammer_2eTactics_2eTactics_2enone = cCoq_2eInit_2eDatatypes_2ett ).

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__1428] :
      ( cIntMap_2eFset_2eFSet___24t(Vvar__1428)
    <=> cIntMap_2eMap_2eMap___24t(cCoq_2eInit_2eDatatypes_2eunit,Vvar__1428) ) ).

fof('$_def_IntMap.Fset.FSetDelta',axiom,
    ! [V0__s,V1__s_27] : cIntMap_2eFset_2eFSetDelta___24a2(V0__s,V1__s_27) = cIntMap_2eMap_2eMapDelta___24a3(cCoq_2eInit_2eDatatypes_2eunit,V0__s,V1__s_27) ).

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

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

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

fof('$_def_IntMap.Fset.MapDom',axiom,
    ! [V0__A,V2__m] :
      ( cType___24t(V0__A)
     => ( cIntMap_2eMap_2eMap___24t(V0__A,V2__m)
       => ( ( V2__m = cIntMap_2eMap_2eM0___24a1(V0__A)
            & cIntMap_2eFset_2eMapDom___24a2(V0__A,V2__m) = cIntMap_2eMap_2eM0___24a1(cCoq_2eInit_2eDatatypes_2eunit) )
          | ? [Vvar__1___24Anonymous__1436] :
              ( cIntMap_2eMap_2ead___24t(Vvar__1___24Anonymous__1436)
              & ? [Vvar__2___24Anonymous__1437] :
                  ( t(Vvar__2___24Anonymous__1437,V0__A)
                  & V2__m = cIntMap_2eMap_2eM1___24a3(V0__A,Vvar__1___24Anonymous__1436,Vvar__2___24Anonymous__1437)
                  & cIntMap_2eFset_2eMapDom___24a2(V0__A,V2__m) = cIntMap_2eMap_2eM1___24a3(cCoq_2eInit_2eDatatypes_2eunit,Vvar__1___24Anonymous__1436,cCoq_2eInit_2eDatatypes_2ett) ) )
          | ? [Vvar__1___24Anonymous__1440] :
              ( cIntMap_2eMap_2eMap___24t(V0__A,Vvar__1___24Anonymous__1440)
              & ? [Vvar__2___24Anonymous__1441] :
                  ( cIntMap_2eMap_2eMap___24t(V0__A,Vvar__2___24Anonymous__1441)
                  & V2__m = cIntMap_2eMap_2eM2___24a3(V0__A,Vvar__1___24Anonymous__1440,Vvar__2___24Anonymous__1441)
                  & 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__1440),cIntMap_2eFset_2eMapDom___24a2(V0__A,Vvar__2___24Anonymous__1441)) ) ) ) ) ) ).

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__363___24a2(V0__A,V1__B) )
          | ? [Vvar__1___24Anonymous__486] :
              ( cIntMap_2eMap_2ead___24t(Vvar__1___24Anonymous__486)
              & ? [Vvar__2___24Anonymous__487] :
                  ( t(Vvar__2___24Anonymous__487,V0__A)
                  & V3__m = cIntMap_2eMap_2eM1___24a3(V0__A,Vvar__1___24Anonymous__486,Vvar__2___24Anonymous__487)
                  & cIntMap_2eFset_2eMapDomRestrBy___24a3(V0__A,V1__B,V3__m) = c_24__lam__527___24a4(V0__A,V1__B,V3__m,Vvar__1___24Anonymous__486) ) )
          | ? [Vvar__1___24Anonymous__496] :
              ( cIntMap_2eMap_2eMap___24t(V0__A,Vvar__1___24Anonymous__496)
              & ? [Vvar__2___24Anonymous__497] :
                  ( cIntMap_2eMap_2eMap___24t(V0__A,Vvar__2___24Anonymous__497)
                  & V3__m = cIntMap_2eMap_2eM2___24a3(V0__A,Vvar__1___24Anonymous__496,Vvar__2___24Anonymous__497)
                  & cIntMap_2eFset_2eMapDomRestrBy___24a3(V0__A,V1__B,V3__m) = c_24__lam__569___24a5(V0__A,V1__B,V3__m,Vvar__1___24Anonymous__496,Vvar__2___24Anonymous__497) ) ) ) ) ) ).

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__363___24a2(V0__A,V1__B) )
          | ? [Vvar__1___24Anonymous__332] :
              ( cIntMap_2eMap_2ead___24t(Vvar__1___24Anonymous__332)
              & ? [Vvar__2___24Anonymous__333] :
                  ( t(Vvar__2___24Anonymous__333,V0__A)
                  & V3__m = cIntMap_2eMap_2eM1___24a3(V0__A,Vvar__1___24Anonymous__332,Vvar__2___24Anonymous__333)
                  & cIntMap_2eFset_2eMapDomRestrTo___24a3(V0__A,V1__B,V3__m) = c_24__lam__378___24a4(V0__A,V1__B,V3__m,Vvar__1___24Anonymous__332) ) )
          | ? [Vvar__1___24Anonymous__342] :
              ( cIntMap_2eMap_2eMap___24t(V0__A,Vvar__1___24Anonymous__342)
              & ? [Vvar__2___24Anonymous__343] :
                  ( cIntMap_2eMap_2eMap___24t(V0__A,Vvar__2___24Anonymous__343)
                  & V3__m = cIntMap_2eMap_2eM2___24a3(V0__A,Vvar__1___24Anonymous__342,Vvar__2___24Anonymous__343)
                  & cIntMap_2eFset_2eMapDomRestrTo___24a3(V0__A,V1__B,V3__m) = c_24__lam__436___24a5(V0__A,V1__B,V3__m,Vvar__1___24Anonymous__342,Vvar__2___24Anonymous__343) ) ) ) ) ) ).

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__1421] :
                ( t(Vvar__1___24Anonymous__1421,V0__A)
                & cIntMap_2eMap_2eMapGet___24a3(V0__A,V2__m,V1__a) = cCoq_2eInit_2eDatatypes_2eSome___24a2(V0__A,Vvar__1___24Anonymous__1421)
                & 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.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__910___24a1(V0__A) )
          | ? [Vvar__1___24Anonymous__1761] :
              ( cIntMap_2eMap_2ead___24t(Vvar__1___24Anonymous__1761)
              & ? [Vvar__2___24Anonymous__1762] :
                  ( t(Vvar__2___24Anonymous__1762,V0__A)
                  & V2__m = cIntMap_2eMap_2eM1___24a3(V0__A,Vvar__1___24Anonymous__1761,Vvar__2___24Anonymous__1762)
                  & cIntMap_2eMap_2eMapDelta___24a2(V0__A,V2__m) = c_24__lam__1802___24a3(V0__A,Vvar__1___24Anonymous__1761,Vvar__2___24Anonymous__1762) ) )
          | ? [Vvar__1___24Anonymous__1771] :
              ( cIntMap_2eMap_2eMap___24t(V0__A,Vvar__1___24Anonymous__1771)
              & ? [Vvar__2___24Anonymous__1772] :
                  ( cIntMap_2eMap_2eMap___24t(V0__A,Vvar__2___24Anonymous__1772)
                  & V2__m = cIntMap_2eMap_2eM2___24a3(V0__A,Vvar__1___24Anonymous__1771,Vvar__2___24Anonymous__1772)
                  & cIntMap_2eMap_2eMapDelta___24a2(V0__A,V2__m) = c_24__lam__1852___24a4(V0__A,V2__m,Vvar__1___24Anonymous__1771,Vvar__2___24Anonymous__1772) ) ) ) ) ) ).

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__101___24a1(V0__A) )
          | ? [Vvar__1___24Anonymous__77] :
              ( cIntMap_2eMap_2ead___24t(Vvar__1___24Anonymous__77)
              & ? [Vvar__2___24Anonymous__78] :
                  ( t(Vvar__2___24Anonymous__78,V0__A)
                  & V2__m = cIntMap_2eMap_2eM1___24a3(V0__A,Vvar__1___24Anonymous__77,Vvar__2___24Anonymous__78)
                  & cIntMap_2eMap_2eMapGet___24a2(V0__A,V2__m) = c_24__lam__109___24a3(V0__A,Vvar__1___24Anonymous__77,Vvar__2___24Anonymous__78) ) )
          | ? [Vvar__1___24Anonymous__85] :
              ( cIntMap_2eMap_2eMap___24t(V0__A,Vvar__1___24Anonymous__85)
              & ? [Vvar__2___24Anonymous__86] :
                  ( cIntMap_2eMap_2eMap___24t(V0__A,Vvar__2___24Anonymous__86)
                  & V2__m = cIntMap_2eMap_2eM2___24a3(V0__A,Vvar__1___24Anonymous__85,Vvar__2___24Anonymous__86)
                  & cIntMap_2eMap_2eMapGet___24a2(V0__A,V2__m) = c_24__lam__136___24a3(V0__A,Vvar__1___24Anonymous__85,Vvar__2___24Anonymous__86) ) ) ) ) ) ).

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__910___24a1(V0__A) )
          | ? [Vvar__1___24Anonymous__888] :
              ( cIntMap_2eMap_2ead___24t(Vvar__1___24Anonymous__888)
              & ? [Vvar__2___24Anonymous__889] :
                  ( t(Vvar__2___24Anonymous__889,V0__A)
                  & V2__m = cIntMap_2eMap_2eM1___24a3(V0__A,Vvar__1___24Anonymous__888,Vvar__2___24Anonymous__889)
                  & cIntMap_2eMap_2eMapMerge___24a2(V0__A,V2__m) = c_24__lam__914___24a3(V0__A,Vvar__1___24Anonymous__888,Vvar__2___24Anonymous__889) ) )
          | ? [Vvar__1___24Anonymous__894] :
              ( cIntMap_2eMap_2eMap___24t(V0__A,Vvar__1___24Anonymous__894)
              & ? [Vvar__2___24Anonymous__895] :
                  ( cIntMap_2eMap_2eMap___24t(V0__A,Vvar__2___24Anonymous__895)
                  & V2__m = cIntMap_2eMap_2eM2___24a3(V0__A,Vvar__1___24Anonymous__894,Vvar__2___24Anonymous__895)
                  & cIntMap_2eMap_2eMapMerge___24a2(V0__A,V2__m) = c_24__lam__946___24a4(V0__A,V2__m,Vvar__1___24Anonymous__894,Vvar__2___24Anonymous__895) ) ) ) ) ) ).

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__640] :
              ( cIntMap_2eMap_2ead___24t(Vvar__1___24Anonymous__640)
              & ? [Vvar__2___24Anonymous__641] :
                  ( t(Vvar__2___24Anonymous__641,V0__A)
                  & V2__m = cIntMap_2eMap_2eM1___24a3(V0__A,Vvar__1___24Anonymous__640,Vvar__2___24Anonymous__641)
                  & cIntMap_2eMap_2eMapPut___24a2(V0__A,V2__m) = c_24__lam__686___24a3(V0__A,Vvar__1___24Anonymous__640,Vvar__2___24Anonymous__641) ) )
          | ? [Vvar__1___24Anonymous__652] :
              ( cIntMap_2eMap_2eMap___24t(V0__A,Vvar__1___24Anonymous__652)
              & ? [Vvar__2___24Anonymous__653] :
                  ( cIntMap_2eMap_2eMap___24t(V0__A,Vvar__2___24Anonymous__653)
                  & V2__m = cIntMap_2eMap_2eM2___24a3(V0__A,Vvar__1___24Anonymous__652,Vvar__2___24Anonymous__653)
                  & cIntMap_2eMap_2eMapPut___24a2(V0__A,V2__m) = c_24__lam__723___24a3(V0__A,Vvar__1___24Anonymous__652,Vvar__2___24Anonymous__653) ) ) ) ) ) ).

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__854___24a1(V0__A) )
          | ? [Vvar__1___24Anonymous__838] :
              ( cIntMap_2eMap_2ead___24t(Vvar__1___24Anonymous__838)
              & ? [Vvar__2___24Anonymous__839] :
                  ( t(Vvar__2___24Anonymous__839,V0__A)
                  & V2__m = cIntMap_2eMap_2eM1___24a3(V0__A,Vvar__1___24Anonymous__838,Vvar__2___24Anonymous__839)
                  & cIntMap_2eMap_2eMapRemove___24a2(V0__A,V2__m) = c_24__lam__862___24a3(V0__A,V2__m,Vvar__1___24Anonymous__838) ) )
          | ? [Vvar__1___24Anonymous__846] :
              ( cIntMap_2eMap_2eMap___24t(V0__A,Vvar__1___24Anonymous__846)
              & ? [Vvar__2___24Anonymous__847] :
                  ( cIntMap_2eMap_2eMap___24t(V0__A,Vvar__2___24Anonymous__847)
                  & V2__m = cIntMap_2eMap_2eM2___24a3(V0__A,Vvar__1___24Anonymous__846,Vvar__2___24Anonymous__847)
                  & cIntMap_2eMap_2eMapRemove___24a2(V0__A,V2__m) = c_24__lam__870___24a3(V0__A,Vvar__1___24Anonymous__846,Vvar__2___24Anonymous__847) ) ) ) ) ) ).

fof('$_def_IntMap.Map.ad',axiom,
    ! [Vvar__30] :
      ( cIntMap_2eMap_2ead___24t(Vvar__30)
    <=> cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__30) ) ).

fof('$_def_Mapaxioms.eqmap',axiom,
    ! [V0__A,V1__m,V2__m_27] :
      ( cMapaxioms_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('$_discrim_Coq.Bool.Bool.ReflectT$Coq.Bool.Bool.ReflectF',axiom,
    ! [Vvar__0__P__107526,Vvar__1___24Anonymous__107527,Vvar__0__P__107528,Vvar__1___24Anonymous__107529] : cCoq_2eBool_2eBool_2eReflectT___24a1(Vvar__0__P__107526) != cCoq_2eBool_2eBool_2eReflectF___24a1(Vvar__0__P__107528) ).

fof('$_discrim_Coq.FSets.FSetPositive.PositiveSet.Leaf$Coq.FSets.FSetPositive.PositiveSet.Node',axiom,
    ! [Vvar__0___24Anonymous__107105,Vvar__1___24Anonymous__107106,Vvar__2___24Anonymous__107107] : cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eLeaf != cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eNode___24a3(Vvar__0___24Anonymous__107105,Vvar__1___24Anonymous__107106,Vvar__2___24Anonymous__107107) ).

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__107599,Vvar__1__Plt__107600,Vvar__2__Pgt__107601,Vvar__3___24Anonymous__107602,Vvar__0__Peq__107603,Vvar__1__Plt__107604,Vvar__2__Pgt__107605,Vvar__3___24Anonymous__107606] : cCoq_2eInit_2eDatatypes_2eCompEqT___24a3(Vvar__0__Peq__107599,Vvar__1__Plt__107600,Vvar__2__Pgt__107601) != cCoq_2eInit_2eDatatypes_2eCompLtT___24a3(Vvar__0__Peq__107603,Vvar__1__Plt__107604,Vvar__2__Pgt__107605) ).

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__997] : cCoq_2eInit_2eDatatypes_2eO != cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__997) ).

fof('$_discrim_Coq.Init.Datatypes.Some$Coq.Init.Datatypes.None',axiom,
    ! [Vvar__0__A__16,Vvar__1___24Anonymous__17,Vvar__0__A__18] : cCoq_2eInit_2eDatatypes_2eSome___24a2(Vvar__0__A__16,Vvar__1___24Anonymous__17) != cCoq_2eInit_2eDatatypes_2eNone___24a1(Vvar__0__A__18) ).

fof('$_discrim_Coq.Init.Datatypes.inl$Coq.Init.Datatypes.inr',axiom,
    ! [Vvar__0__A__2570,Vvar__1__B__2571,Vvar__2___24Anonymous__2572,Vvar__0__A__2573,Vvar__1__B__2574,Vvar__2___24Anonymous__2575] : cCoq_2eInit_2eDatatypes_2einl___24a3(Vvar__0__A__2570,Vvar__1__B__2571,Vvar__2___24Anonymous__2572) != cCoq_2eInit_2eDatatypes_2einr___24a3(Vvar__0__A__2573,Vvar__1__B__2574,Vvar__2___24Anonymous__2575) ).

fof('$_discrim_Coq.Init.Datatypes.nil$Coq.Init.Datatypes.cons',axiom,
    ! [Vvar__0__A__2618,Vvar__0__A__2619,Vvar__1___24Anonymous__2620,Vvar__2___24Anonymous__2621] : cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__2618) != cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__2619,Vvar__1___24Anonymous__2620,Vvar__2___24Anonymous__2621) ).

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__107655,Vvar__1__f__107656,Vvar__0__i__107657,Vvar__1__f__107658,Vvar__2__e__107659] : cCoq_2eInit_2eDecimal_2eDecimal___24a2(Vvar__0__i__107655,Vvar__1__f__107656) != cCoq_2eInit_2eDecimal_2eDecimalExp___24a3(Vvar__0__i__107657,Vvar__1__f__107658,Vvar__2__e__107659) ).

fof('$_discrim_Coq.Init.Decimal.Nil$Coq.Init.Decimal.D0',axiom,
    ! [Vvar__0___24Anonymous__85684] : cCoq_2eInit_2eDecimal_2eNil != cCoq_2eInit_2eDecimal_2eD0___24a1(Vvar__0___24Anonymous__85684) ).

fof('$_discrim_Coq.Init.Decimal.Pos$Coq.Init.Decimal.Neg',axiom,
    ! [Vvar__0__d__107643,Vvar__0__d__107644] : cCoq_2eInit_2eDecimal_2ePos___24a1(Vvar__0__d__107643) != cCoq_2eInit_2eDecimal_2eNeg___24a1(Vvar__0__d__107644) ).

fof('$_discrim_Coq.Init.Specif.inleft$Coq.Init.Specif.inright',axiom,
    ! [Vvar__0__A__2030,Vvar__1__B__2031,Vvar__2___24Anonymous__2032,Vvar__0__A__2033,Vvar__1__B__2034,Vvar__2___24Anonymous__2035] : cCoq_2eInit_2eSpecif_2einleft___24a3(Vvar__0__A__2030,Vvar__1__B__2031,Vvar__2___24Anonymous__2032) != cCoq_2eInit_2eSpecif_2einright___24a2(Vvar__0__A__2033,Vvar__1__B__2034) ).

fof('$_discrim_Coq.Init.Specif.left$Coq.Init.Specif.right',axiom,
    ! [Vvar__0__A__262,Vvar__1__B__263,Vvar__2___24Anonymous__264,Vvar__0__A__265,Vvar__1__B__266,Vvar__2___24Anonymous__267] : cCoq_2eInit_2eSpecif_2eleft___24a2(Vvar__0__A__262,Vvar__1__B__263) != cCoq_2eInit_2eSpecif_2eright___24a2(Vvar__0__A__265,Vvar__1__B__266) ).

fof('$_discrim_Coq.Numbers.BinNums.N0$Coq.Numbers.BinNums.Npos',axiom,
    ! [Vvar__0___24Anonymous__5] : cCoq_2eNumbers_2eBinNums_2eN0 != cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__5) ).

fof('$_discrim_Coq.Numbers.BinNums.Z0$Coq.Numbers.BinNums.Zpos',axiom,
    ! [Vvar__0___24Anonymous__14030] : cCoq_2eNumbers_2eBinNums_2eZ0 != cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__14030) ).

fof('$_discrim_Coq.Numbers.BinNums.xI$Coq.Numbers.BinNums.xO',axiom,
    ! [Vvar__0___24Anonymous__320,Vvar__0___24Anonymous__321] : cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__320) != cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__321) ).

fof('$_discrim_Coq.PArith.BinPos.Pos.PeanoOne$Coq.PArith.BinPos.Pos.PeanoSucc',axiom,
    ! [Vvar__0__p__113693,Vvar__1___24Anonymous__113694] : cCoq_2ePArith_2eBinPos_2ePos_2ePeanoOne != cCoq_2ePArith_2eBinPos_2ePos_2ePeanoSucc___24a2(Vvar__0__p__113693,Vvar__1___24Anonymous__113694) ).

fof('$_discrim_Coq.PArith.BinPosDef.Pos.IsNul$Coq.PArith.BinPosDef.Pos.IsPos',axiom,
    ! [Vvar__0___24Anonymous__113586] : cCoq_2ePArith_2eBinPosDef_2ePos_2eIsNul != cCoq_2ePArith_2eBinPosDef_2ePos_2eIsPos___24a1(Vvar__0___24Anonymous__113586) ).

fof('$_discrim_Coq.Reals.Rfunctions.ZintNull$Coq.Reals.Rfunctions.ZintPos',axiom,
    ! [Vvar__0__x__110482,Vvar__1___24Anonymous__110483,Vvar__0__x__110484,Vvar__1__n__110485,Vvar__2___24Anonymous__110486] : cCoq_2eReals_2eRfunctions_2eZintNull___24a1(Vvar__0__x__110482) != cCoq_2eReals_2eRfunctions_2eZintPos___24a2(Vvar__0__x__110484,Vvar__1__n__110485) ).

fof('$_discrim_Coq.Strings.String.EmptyString$Coq.Strings.String.String',axiom,
    ! [Vvar__0___24Anonymous__104285,Vvar__1___24Anonymous__104286] : cCoq_2eStrings_2eString_2eEmptyString != cCoq_2eStrings_2eString_2eString___24a2(Vvar__0___24Anonymous__104285,Vvar__1___24Anonymous__104286) ).

fof('$_discrim_Coq.Structures.OrderedType.LT$Coq.Structures.OrderedType.EQ',axiom,
    ! [Vvar__0__X__109583,Vvar__1__lt__109584,Vvar__2__eq__109585,Vvar__3__x__109586,Vvar__4__y__109587,Vvar__5___24Anonymous__109588,Vvar__0__X__109589,Vvar__1__lt__109590,Vvar__2__eq__109591,Vvar__3__x__109592,Vvar__4__y__109593,Vvar__5___24Anonymous__109594] : cCoq_2eStructures_2eOrderedType_2eLT___24a5(Vvar__0__X__109583,Vvar__1__lt__109584,Vvar__2__eq__109585,Vvar__3__x__109586,Vvar__4__y__109587) != cCoq_2eStructures_2eOrderedType_2eEQ___24a5(Vvar__0__X__109589,Vvar__1__lt__109590,Vvar__2__eq__109591,Vvar__3__x__109592,Vvar__4__y__109593) ).

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__109158,Vvar__0__n__109159,Vvar__1___24Anonymous__109160] : cCoq_2eVectors_2eFin_2eF1___24a1(Vvar__0__n__109158) != cCoq_2eVectors_2eFin_2eFS___24a2(Vvar__0__n__109159,Vvar__1___24Anonymous__109160) ).

fof('$_discrim_Coq.Vectors.VectorDef.nil$Coq.Vectors.VectorDef.cons',axiom,
    ! [Vvar__0__A__113234,Vvar__0__A__113235,Vvar__1__h__113236,Vvar__2__n__113237,Vvar__3___24Anonymous__113238] : cCoq_2eVectors_2eVectorDef_2enil___24a1(Vvar__0__A__113234) != cCoq_2eVectors_2eVectorDef_2econs___24a4(Vvar__0__A__113235,Vvar__1__h__113236,Vvar__2__n__113237,Vvar__3___24Anonymous__113238) ).

fof('$_discrim_Coq.micromega.EnvRing.PEc$Coq.micromega.EnvRing.PEX',axiom,
    ! [Vvar__0__C__85832,Vvar__1___24Anonymous__85833,Vvar__0__C__85834,Vvar__1___24Anonymous__85835] : cCoq_2emicromega_2eEnvRing_2ePEc___24a2(Vvar__0__C__85832,Vvar__1___24Anonymous__85833) != cCoq_2emicromega_2eEnvRing_2ePEX___24a2(Vvar__0__C__85834,Vvar__1___24Anonymous__85835) ).

fof('$_discrim_Coq.micromega.EnvRing.Pc$Coq.micromega.EnvRing.Pinj',axiom,
    ! [Vvar__0__C__85896,Vvar__1___24Anonymous__85897,Vvar__0__C__85898,Vvar__1___24Anonymous__85899,Vvar__2___24Anonymous__85900] : cCoq_2emicromega_2eEnvRing_2ePc___24a2(Vvar__0__C__85896,Vvar__1___24Anonymous__85897) != cCoq_2emicromega_2eEnvRing_2ePinj___24a3(Vvar__0__C__85898,Vvar__1___24Anonymous__85899,Vvar__2___24Anonymous__85900) ).

fof('$_discrim_Coq.micromega.EnvRing.mon0$Coq.micromega.EnvRing.zmon',axiom,
    ! [Vvar__0___24Anonymous__86838,Vvar__1___24Anonymous__86839] : cCoq_2emicromega_2eEnvRing_2emon0 != cCoq_2emicromega_2eEnvRing_2ezmon___24a2(Vvar__0___24Anonymous__86838,Vvar__1___24Anonymous__86839) ).

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__97265,Vvar__1___24Anonymous__97266,Vvar__0__C__97267,Vvar__1___24Anonymous__97268] : cCoq_2emicromega_2eRingMicromega_2ePsatzIn___24a2(Vvar__0__C__97265,Vvar__1___24Anonymous__97266) != cCoq_2emicromega_2eRingMicromega_2ePsatzSquare___24a2(Vvar__0__C__97267,Vvar__1___24Anonymous__97268) ).

fof('$_discrim_Coq.micromega.Tauto.TT$Coq.micromega.Tauto.FF',axiom,
    ! [Vvar__0__TA__2403,Vvar__1__TX__2404,Vvar__2__AA__2405,Vvar__3__AF__2406,Vvar__0__TA__2407,Vvar__1__TX__2408,Vvar__2__AA__2409,Vvar__3__AF__2410] : cCoq_2emicromega_2eTauto_2eTT___24a4(Vvar__0__TA__2403,Vvar__1__TX__2404,Vvar__2__AA__2405,Vvar__3__AF__2406) != cCoq_2emicromega_2eTauto_2eFF___24a4(Vvar__0__TA__2407,Vvar__1__TX__2408,Vvar__2__AA__2409,Vvar__3__AF__2410) ).

fof('$_discrim_Coq.micromega.VarMap.Empty$Coq.micromega.VarMap.Elt',axiom,
    ! [Vvar__0__A__113206,Vvar__0__A__113207,Vvar__1___24Anonymous__113208] : cCoq_2emicromega_2eVarMap_2eEmpty___24a1(Vvar__0__A__113206) != cCoq_2emicromega_2eVarMap_2eElt___24a2(Vvar__0__A__113207,Vvar__1___24Anonymous__113208) ).

fof('$_discrim_Coq.micromega.ZMicromega.DoneProof$Coq.micromega.ZMicromega.RatProof',axiom,
    ! [Vvar__0___24Anonymous__113315,Vvar__1___24Anonymous__113316] : cCoq_2emicromega_2eZMicromega_2eDoneProof != cCoq_2emicromega_2eZMicromega_2eRatProof___24a2(Vvar__0___24Anonymous__113315,Vvar__1___24Anonymous__113316) ).

fof('$_discrim_Coq.setoid_ring.Field_theory.FEO$Coq.setoid_ring.Field_theory.FEI',axiom,
    ! [Vvar__0__C__3744,Vvar__0__C__3745] : cCoq_2esetoid__ring_2eField__theory_2eFEO___24a1(Vvar__0__C__3744) != cCoq_2esetoid__ring_2eField__theory_2eFEI___24a1(Vvar__0__C__3745) ).

fof('$_discrim_Coq.setoid_ring.Ring_polynom.PEO$Coq.setoid_ring.Ring_polynom.PEI',axiom,
    ! [Vvar__0__C__5478,Vvar__0__C__5479] : cCoq_2esetoid__ring_2eRing__polynom_2ePEO___24a1(Vvar__0__C__5478) != cCoq_2esetoid__ring_2eRing__polynom_2ePEI___24a1(Vvar__0__C__5479) ).

fof('$_discrim_Coq.setoid_ring.Ring_polynom.Pc$Coq.setoid_ring.Ring_polynom.Pinj',axiom,
    ! [Vvar__0__C__5184,Vvar__1___24Anonymous__5185,Vvar__0__C__5186,Vvar__1___24Anonymous__5187,Vvar__2___24Anonymous__5188] : cCoq_2esetoid__ring_2eRing__polynom_2ePc___24a2(Vvar__0__C__5184,Vvar__1___24Anonymous__5185) != cCoq_2esetoid__ring_2eRing__polynom_2ePinj___24a3(Vvar__0__C__5186,Vvar__1___24Anonymous__5187,Vvar__2___24Anonymous__5188) ).

fof('$_discrim_Coq.setoid_ring.Ring_polynom.mon0$Coq.setoid_ring.Ring_polynom.zmon',axiom,
    ! [Vvar__0___24Anonymous__5218,Vvar__1___24Anonymous__5219] : cCoq_2esetoid__ring_2eRing__polynom_2emon0 != cCoq_2esetoid__ring_2eRing__polynom_2ezmon___24a2(Vvar__0___24Anonymous__5218,Vvar__1___24Anonymous__5219) ).

fof('$_discrim_Coq.setoid_ring.Ring_theory.Abstract$Coq.setoid_ring.Ring_theory.Computational',axiom,
    ! [Vvar__0__R__112662,Vvar__1__req__112663,Vvar__2__reqb__112664,Vvar__3___24Anonymous__112665] : cCoq_2esetoid__ring_2eRing__theory_2eAbstract != cCoq_2esetoid__ring_2eRing__theory_2eComputational___24a3(Vvar__0__R__112662,Vvar__1__req__112663,Vvar__2__reqb__112664) ).

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__50,Vvar__0__A__51,Vvar__1___24Anonymous__52,Vvar__2___24Anonymous__53] : cIntMap_2eMap_2eM0___24a1(Vvar__0__A__50) != cIntMap_2eMap_2eM1___24a3(Vvar__0__A__51,Vvar__1___24Anonymous__52,Vvar__2___24Anonymous__53) ).

fof('$_fix_107045_1_add_carry',axiom,
    ! [V2__x,V3__y] :
      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V2__x)
     => ( ? [Vvar__0___24Anonymous__107060] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__107060)
            & ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V3__y)
             => ( V2__x = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__107060)
                & ( ? [Vvar__0___24Anonymous__107064] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__107064)
                      & V3__y = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__107064)
                      & c_24__fix__107045__1__add__carry___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exI___24a1(c_24__fix__107045__1__add__carry___24a2(Vvar__0___24Anonymous__107060,Vvar__0___24Anonymous__107064)) )
                  | ? [Vvar__0___24Anonymous__107065] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__107065)
                      & V3__y = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__107065)
                      & c_24__fix__107045__1__add__carry___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exO___24a1(c_24__fix__107045__1__add__carry___24a2(Vvar__0___24Anonymous__107060,Vvar__0___24Anonymous__107065)) )
                  | ( V3__y = cCoq_2eNumbers_2eBinNums_2exH
                    & c_24__fix__107045__1__add__carry___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exI___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2esucc___24a1(Vvar__0___24Anonymous__107060)) ) ) ) ) )
        | ? [Vvar__0___24Anonymous__107066] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__107066)
            & ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V3__y)
             => ( V2__x = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__107066)
                & ( ? [Vvar__0___24Anonymous__107070] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__107070)
                      & V3__y = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__107070)
                      & c_24__fix__107045__1__add__carry___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exO___24a1(c_24__fix__107045__1__add__carry___24a2(Vvar__0___24Anonymous__107066,Vvar__0___24Anonymous__107070)) )
                  | ? [Vvar__0___24Anonymous__107071] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__107071)
                      & V3__y = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__107071)
                      & c_24__fix__107045__1__add__carry___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exI___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(Vvar__0___24Anonymous__107066,Vvar__0___24Anonymous__107071)) )
                  | ( V3__y = cCoq_2eNumbers_2eBinNums_2exH
                    & c_24__fix__107045__1__add__carry___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2esucc___24a1(Vvar__0___24Anonymous__107066)) ) ) ) ) )
        | ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V3__y)
         => ( V2__x = cCoq_2eNumbers_2eBinNums_2exH
            & ( ? [Vvar__0___24Anonymous__107072] :
                  ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__107072)
                  & V3__y = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__107072)
                  & c_24__fix__107045__1__add__carry___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exI___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2esucc___24a1(Vvar__0___24Anonymous__107072)) )
              | ? [Vvar__0___24Anonymous__107073] :
                  ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__107073)
                  & V3__y = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__107073)
                  & c_24__fix__107045__1__add__carry___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2esucc___24a1(Vvar__0___24Anonymous__107073)) )
              | ( V3__y = cCoq_2eNumbers_2eBinNums_2exH
                & c_24__fix__107045__1__add__carry___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exI___24a1(cCoq_2eNumbers_2eBinNums_2exH) ) ) ) ) ) ) ).

fof('$_fix_110318_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__110318__v__CANONICAL__1___24a3(Vv__CANONICAL__0,Vv__CANONICAL__2,Vv__CANONICAL__3) = Vv__CANONICAL__3 )
          | ? [Vvar__1___24Anonymous__110322] :
              ( t(Vvar__1___24Anonymous__110322,Vv__CANONICAL__0)
              & ? [Vvar__2___24Anonymous__110323] :
                  ( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vvar__2___24Anonymous__110323)
                  & Vv__CANONICAL__2 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vv__CANONICAL__0,Vvar__1___24Anonymous__110322,Vvar__2___24Anonymous__110323)
                  & c_24__fix__110318__v__CANONICAL__1___24a3(Vv__CANONICAL__0,Vv__CANONICAL__2,Vv__CANONICAL__3) = cCoq_2eInit_2eDatatypes_2econs___24a3(Vv__CANONICAL__0,Vvar__1___24Anonymous__110322,c_24__fix__110318__v__CANONICAL__1___24a3(Vv__CANONICAL__0,Vvar__2___24Anonymous__110323,Vv__CANONICAL__3)) ) ) ) ) ) ).

fof('$_fix_113688_v_CANONICAL_0',axiom,
    ! [Vv__CANONICAL__1] :
      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__1)
     => ( ? [Vvar__0___24Anonymous__113689] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__113689)
            & Vv__CANONICAL__1 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__113689)
            & c_24__fix__113688__v__CANONICAL__0___24a1(Vv__CANONICAL__1) = cCoq_2eNumbers_2eBinNums_2exO___24a1(c_24__fix__113688__v__CANONICAL__0___24a1(Vvar__0___24Anonymous__113689)) )
        | ? [Vvar__0___24Anonymous__113690] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__113690)
            & Vv__CANONICAL__1 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__113690)
            & c_24__fix__113688__v__CANONICAL__0___24a1(Vv__CANONICAL__1) = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__113690) )
        | ( Vv__CANONICAL__1 = cCoq_2eNumbers_2eBinNums_2exH
          & c_24__fix__113688__v__CANONICAL__0___24a1(Vv__CANONICAL__1) = cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2eNumbers_2eBinNums_2exH) ) ) ) ).

fof('$_inj_Coq.Bool.Bool.ReflectF',axiom,
    ! [Vvar__0__P__107534,Vvar__0__P__107535,Vvar__1___24Anonymous__107536,Vvar__1___24Anonymous__107537] :
      ( cCoq_2eBool_2eBool_2eReflectF___24a1(Vvar__0__P__107534) = cCoq_2eBool_2eBool_2eReflectF___24a1(Vvar__0__P__107535)
     => ( c_24Proof = c_24Proof
        & Vvar__0__P__107534 = Vvar__0__P__107535 ) ) ).

fof('$_inj_Coq.Bool.Bool.ReflectT',axiom,
    ! [Vvar__0__P__107530,Vvar__0__P__107531,Vvar__1___24Anonymous__107532,Vvar__1___24Anonymous__107533] :
      ( cCoq_2eBool_2eBool_2eReflectT___24a1(Vvar__0__P__107530) = cCoq_2eBool_2eBool_2eReflectT___24a1(Vvar__0__P__107531)
     => ( c_24Proof = c_24Proof
        & Vvar__0__P__107530 = Vvar__0__P__107531 ) ) ).

fof('$_inj_Coq.FSets.FSetPositive.PositiveSet.Node',axiom,
    ! [Vvar__0___24Anonymous__107108,Vvar__0___24Anonymous__107109,Vvar__1___24Anonymous__107110,Vvar__1___24Anonymous__107111,Vvar__2___24Anonymous__107112,Vvar__2___24Anonymous__107113] :
      ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eNode___24a3(Vvar__0___24Anonymous__107108,Vvar__1___24Anonymous__107110,Vvar__2___24Anonymous__107112) = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eNode___24a3(Vvar__0___24Anonymous__107109,Vvar__1___24Anonymous__107111,Vvar__2___24Anonymous__107113)
     => ( Vvar__2___24Anonymous__107112 = Vvar__2___24Anonymous__107113
        & Vvar__1___24Anonymous__107110 = Vvar__1___24Anonymous__107111
        & Vvar__0___24Anonymous__107108 = Vvar__0___24Anonymous__107109 ) ) ).

fof('$_inj_Coq.Init.Datatypes.CompEqT',axiom,
    ! [Vvar__0__Peq__107607,Vvar__0__Peq__107608,Vvar__1__Plt__107609,Vvar__1__Plt__107610,Vvar__2__Pgt__107611,Vvar__2__Pgt__107612,Vvar__3___24Anonymous__107613,Vvar__3___24Anonymous__107614] :
      ( cCoq_2eInit_2eDatatypes_2eCompEqT___24a3(Vvar__0__Peq__107607,Vvar__1__Plt__107609,Vvar__2__Pgt__107611) = cCoq_2eInit_2eDatatypes_2eCompEqT___24a3(Vvar__0__Peq__107608,Vvar__1__Plt__107610,Vvar__2__Pgt__107612)
     => ( c_24Proof = c_24Proof
        & Vvar__2__Pgt__107611 = Vvar__2__Pgt__107612
        & Vvar__1__Plt__107609 = Vvar__1__Plt__107610
        & Vvar__0__Peq__107607 = Vvar__0__Peq__107608 ) ) ).

fof('$_inj_Coq.Init.Datatypes.CompGtT',axiom,
    ! [Vvar__0__Peq__107623,Vvar__0__Peq__107624,Vvar__1__Plt__107625,Vvar__1__Plt__107626,Vvar__2__Pgt__107627,Vvar__2__Pgt__107628,Vvar__3___24Anonymous__107629,Vvar__3___24Anonymous__107630] :
      ( cCoq_2eInit_2eDatatypes_2eCompGtT___24a3(Vvar__0__Peq__107623,Vvar__1__Plt__107625,Vvar__2__Pgt__107627) = cCoq_2eInit_2eDatatypes_2eCompGtT___24a3(Vvar__0__Peq__107624,Vvar__1__Plt__107626,Vvar__2__Pgt__107628)
     => ( c_24Proof = c_24Proof
        & Vvar__2__Pgt__107627 = Vvar__2__Pgt__107628
        & Vvar__1__Plt__107625 = Vvar__1__Plt__107626
        & Vvar__0__Peq__107623 = Vvar__0__Peq__107624 ) ) ).

fof('$_inj_Coq.Init.Datatypes.CompLtT',axiom,
    ! [Vvar__0__Peq__107615,Vvar__0__Peq__107616,Vvar__1__Plt__107617,Vvar__1__Plt__107618,Vvar__2__Pgt__107619,Vvar__2__Pgt__107620,Vvar__3___24Anonymous__107621,Vvar__3___24Anonymous__107622] :
      ( cCoq_2eInit_2eDatatypes_2eCompLtT___24a3(Vvar__0__Peq__107615,Vvar__1__Plt__107617,Vvar__2__Pgt__107619) = cCoq_2eInit_2eDatatypes_2eCompLtT___24a3(Vvar__0__Peq__107616,Vvar__1__Plt__107618,Vvar__2__Pgt__107620)
     => ( c_24Proof = c_24Proof
        & Vvar__2__Pgt__107619 = Vvar__2__Pgt__107620
        & Vvar__1__Plt__107617 = Vvar__1__Plt__107618
        & Vvar__0__Peq__107615 = Vvar__0__Peq__107616 ) ) ).

fof('$_inj_Coq.Init.Datatypes.None',axiom,
    ! [Vvar__0__A__23,Vvar__0__A__24] :
      ( cCoq_2eInit_2eDatatypes_2eNone___24a1(Vvar__0__A__23) = cCoq_2eInit_2eDatatypes_2eNone___24a1(Vvar__0__A__24)
     => Vvar__0__A__23 = Vvar__0__A__24 ) ).

fof('$_inj_Coq.Init.Datatypes.S',axiom,
    ! [Vvar__0___24Anonymous__998,Vvar__0___24Anonymous__999] :
      ( cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__998) = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__999)
     => Vvar__0___24Anonymous__998 = Vvar__0___24Anonymous__999 ) ).

fof('$_inj_Coq.Init.Datatypes.Some',axiom,
    ! [Vvar__0__A__19,Vvar__0__A__20,Vvar__1___24Anonymous__21,Vvar__1___24Anonymous__22] :
      ( cCoq_2eInit_2eDatatypes_2eSome___24a2(Vvar__0__A__19,Vvar__1___24Anonymous__21) = cCoq_2eInit_2eDatatypes_2eSome___24a2(Vvar__0__A__20,Vvar__1___24Anonymous__22)
     => ( Vvar__1___24Anonymous__21 = Vvar__1___24Anonymous__22
        & Vvar__0__A__19 = Vvar__0__A__20 ) ) ).

fof('$_inj_Coq.Init.Datatypes.cons',axiom,
    ! [Vvar__0__A__2624,Vvar__0__A__2625,Vvar__1___24Anonymous__2626,Vvar__1___24Anonymous__2627,Vvar__2___24Anonymous__2628,Vvar__2___24Anonymous__2629] :
      ( cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__2624,Vvar__1___24Anonymous__2626,Vvar__2___24Anonymous__2628) = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__2625,Vvar__1___24Anonymous__2627,Vvar__2___24Anonymous__2629)
     => ( Vvar__2___24Anonymous__2628 = Vvar__2___24Anonymous__2629
        & Vvar__1___24Anonymous__2626 = Vvar__1___24Anonymous__2627
        & Vvar__0__A__2624 = Vvar__0__A__2625 ) ) ).

fof('$_inj_Coq.Init.Datatypes.inl',axiom,
    ! [Vvar__0__A__2576,Vvar__0__A__2577,Vvar__1__B__2578,Vvar__1__B__2579,Vvar__2___24Anonymous__2580,Vvar__2___24Anonymous__2581] :
      ( cCoq_2eInit_2eDatatypes_2einl___24a3(Vvar__0__A__2576,Vvar__1__B__2578,Vvar__2___24Anonymous__2580) = cCoq_2eInit_2eDatatypes_2einl___24a3(Vvar__0__A__2577,Vvar__1__B__2579,Vvar__2___24Anonymous__2581)
     => ( Vvar__2___24Anonymous__2580 = Vvar__2___24Anonymous__2581
        & Vvar__1__B__2578 = Vvar__1__B__2579
        & Vvar__0__A__2576 = Vvar__0__A__2577 ) ) ).

fof('$_inj_Coq.Init.Datatypes.inr',axiom,
    ! [Vvar__0__A__2582,Vvar__0__A__2583,Vvar__1__B__2584,Vvar__1__B__2585,Vvar__2___24Anonymous__2586,Vvar__2___24Anonymous__2587] :
      ( cCoq_2eInit_2eDatatypes_2einr___24a3(Vvar__0__A__2582,Vvar__1__B__2584,Vvar__2___24Anonymous__2586) = cCoq_2eInit_2eDatatypes_2einr___24a3(Vvar__0__A__2583,Vvar__1__B__2585,Vvar__2___24Anonymous__2587)
     => ( Vvar__2___24Anonymous__2586 = Vvar__2___24Anonymous__2587
        & Vvar__1__B__2584 = Vvar__1__B__2585
        & Vvar__0__A__2582 = Vvar__0__A__2583 ) ) ).

fof('$_inj_Coq.Init.Datatypes.nil',axiom,
    ! [Vvar__0__A__2622,Vvar__0__A__2623] :
      ( cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__2622) = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__2623)
     => Vvar__0__A__2622 = Vvar__0__A__2623 ) ).

fof('$_inj_Coq.Init.Datatypes.pair',axiom,
    ! [Vvar__0__A__2596,Vvar__0__A__2597,Vvar__1__B__2598,Vvar__1__B__2599,Vvar__2___24Anonymous__2600,Vvar__2___24Anonymous__2601,Vvar__3___24Anonymous__2602,Vvar__3___24Anonymous__2603] :
      ( cCoq_2eInit_2eDatatypes_2epair___24a4(Vvar__0__A__2596,Vvar__1__B__2598,Vvar__2___24Anonymous__2600,Vvar__3___24Anonymous__2602) = cCoq_2eInit_2eDatatypes_2epair___24a4(Vvar__0__A__2597,Vvar__1__B__2599,Vvar__2___24Anonymous__2601,Vvar__3___24Anonymous__2603)
     => ( Vvar__3___24Anonymous__2602 = Vvar__3___24Anonymous__2603
        & Vvar__2___24Anonymous__2600 = Vvar__2___24Anonymous__2601
        & Vvar__1__B__2598 = Vvar__1__B__2599
        & Vvar__0__A__2596 = Vvar__0__A__2597 ) ) ).

fof('$_inj_Coq.Init.Decimal.D0',axiom,
    ! [Vvar__0___24Anonymous__85685,Vvar__0___24Anonymous__85686] :
      ( cCoq_2eInit_2eDecimal_2eD0___24a1(Vvar__0___24Anonymous__85685) = cCoq_2eInit_2eDecimal_2eD0___24a1(Vvar__0___24Anonymous__85686)
     => Vvar__0___24Anonymous__85685 = Vvar__0___24Anonymous__85686 ) ).

fof('$_inj_Coq.Init.Decimal.D1',axiom,
    ! [Vvar__0___24Anonymous__85687,Vvar__0___24Anonymous__85688] :
      ( cCoq_2eInit_2eDecimal_2eD1___24a1(Vvar__0___24Anonymous__85687) = cCoq_2eInit_2eDecimal_2eD1___24a1(Vvar__0___24Anonymous__85688)
     => Vvar__0___24Anonymous__85687 = Vvar__0___24Anonymous__85688 ) ).

fof('$_inj_Coq.Init.Decimal.D2',axiom,
    ! [Vvar__0___24Anonymous__85689,Vvar__0___24Anonymous__85690] :
      ( cCoq_2eInit_2eDecimal_2eD2___24a1(Vvar__0___24Anonymous__85689) = cCoq_2eInit_2eDecimal_2eD2___24a1(Vvar__0___24Anonymous__85690)
     => Vvar__0___24Anonymous__85689 = Vvar__0___24Anonymous__85690 ) ).

fof('$_inj_Coq.Init.Decimal.D3',axiom,
    ! [Vvar__0___24Anonymous__85691,Vvar__0___24Anonymous__85692] :
      ( cCoq_2eInit_2eDecimal_2eD3___24a1(Vvar__0___24Anonymous__85691) = cCoq_2eInit_2eDecimal_2eD3___24a1(Vvar__0___24Anonymous__85692)
     => Vvar__0___24Anonymous__85691 = Vvar__0___24Anonymous__85692 ) ).

fof('$_inj_Coq.Init.Decimal.D4',axiom,
    ! [Vvar__0___24Anonymous__85693,Vvar__0___24Anonymous__85694] :
      ( cCoq_2eInit_2eDecimal_2eD4___24a1(Vvar__0___24Anonymous__85693) = cCoq_2eInit_2eDecimal_2eD4___24a1(Vvar__0___24Anonymous__85694)
     => Vvar__0___24Anonymous__85693 = Vvar__0___24Anonymous__85694 ) ).

fof('$_inj_Coq.Init.Decimal.D5',axiom,
    ! [Vvar__0___24Anonymous__85695,Vvar__0___24Anonymous__85696] :
      ( cCoq_2eInit_2eDecimal_2eD5___24a1(Vvar__0___24Anonymous__85695) = cCoq_2eInit_2eDecimal_2eD5___24a1(Vvar__0___24Anonymous__85696)
     => Vvar__0___24Anonymous__85695 = Vvar__0___24Anonymous__85696 ) ).

fof('$_inj_Coq.Init.Decimal.D6',axiom,
    ! [Vvar__0___24Anonymous__85697,Vvar__0___24Anonymous__85698] :
      ( cCoq_2eInit_2eDecimal_2eD6___24a1(Vvar__0___24Anonymous__85697) = cCoq_2eInit_2eDecimal_2eD6___24a1(Vvar__0___24Anonymous__85698)
     => Vvar__0___24Anonymous__85697 = Vvar__0___24Anonymous__85698 ) ).

fof('$_inj_Coq.Init.Decimal.D7',axiom,
    ! [Vvar__0___24Anonymous__85699,Vvar__0___24Anonymous__85700] :
      ( cCoq_2eInit_2eDecimal_2eD7___24a1(Vvar__0___24Anonymous__85699) = cCoq_2eInit_2eDecimal_2eD7___24a1(Vvar__0___24Anonymous__85700)
     => Vvar__0___24Anonymous__85699 = Vvar__0___24Anonymous__85700 ) ).

fof('$_inj_Coq.Init.Decimal.D8',axiom,
    ! [Vvar__0___24Anonymous__85701,Vvar__0___24Anonymous__85702] :
      ( cCoq_2eInit_2eDecimal_2eD8___24a1(Vvar__0___24Anonymous__85701) = cCoq_2eInit_2eDecimal_2eD8___24a1(Vvar__0___24Anonymous__85702)
     => Vvar__0___24Anonymous__85701 = Vvar__0___24Anonymous__85702 ) ).

fof('$_inj_Coq.Init.Decimal.D9',axiom,
    ! [Vvar__0___24Anonymous__85703,Vvar__0___24Anonymous__85704] :
      ( cCoq_2eInit_2eDecimal_2eD9___24a1(Vvar__0___24Anonymous__85703) = cCoq_2eInit_2eDecimal_2eD9___24a1(Vvar__0___24Anonymous__85704)
     => Vvar__0___24Anonymous__85703 = Vvar__0___24Anonymous__85704 ) ).

fof('$_inj_Coq.Init.Decimal.Decimal',axiom,
    ! [Vvar__0__i__107660,Vvar__0__i__107661,Vvar__1__f__107662,Vvar__1__f__107663] :
      ( cCoq_2eInit_2eDecimal_2eDecimal___24a2(Vvar__0__i__107660,Vvar__1__f__107662) = cCoq_2eInit_2eDecimal_2eDecimal___24a2(Vvar__0__i__107661,Vvar__1__f__107663)
     => ( Vvar__1__f__107662 = Vvar__1__f__107663
        & Vvar__0__i__107660 = Vvar__0__i__107661 ) ) ).

fof('$_inj_Coq.Init.Decimal.DecimalExp',axiom,
    ! [Vvar__0__i__107664,Vvar__0__i__107665,Vvar__1__f__107666,Vvar__1__f__107667,Vvar__2__e__107668,Vvar__2__e__107669] :
      ( cCoq_2eInit_2eDecimal_2eDecimalExp___24a3(Vvar__0__i__107664,Vvar__1__f__107666,Vvar__2__e__107668) = cCoq_2eInit_2eDecimal_2eDecimalExp___24a3(Vvar__0__i__107665,Vvar__1__f__107667,Vvar__2__e__107669)
     => ( Vvar__2__e__107668 = Vvar__2__e__107669
        & Vvar__1__f__107666 = Vvar__1__f__107667
        & Vvar__0__i__107664 = Vvar__0__i__107665 ) ) ).

fof('$_inj_Coq.Init.Decimal.Neg',axiom,
    ! [Vvar__0__d__107647,Vvar__0__d__107648] :
      ( cCoq_2eInit_2eDecimal_2eNeg___24a1(Vvar__0__d__107647) = cCoq_2eInit_2eDecimal_2eNeg___24a1(Vvar__0__d__107648)
     => Vvar__0__d__107647 = Vvar__0__d__107648 ) ).

fof('$_inj_Coq.Init.Decimal.Pos',axiom,
    ! [Vvar__0__d__107645,Vvar__0__d__107646] :
      ( cCoq_2eInit_2eDecimal_2ePos___24a1(Vvar__0__d__107645) = cCoq_2eInit_2eDecimal_2ePos___24a1(Vvar__0__d__107646)
     => Vvar__0__d__107645 = Vvar__0__d__107646 ) ).

fof('$_inj_Coq.Init.Specif.exist',axiom,
    ! [Vvar__0__A__2002,Vvar__0__A__2003,Vvar__1__P__2004,Vvar__1__P__2005,Vvar__2__x__2006,Vvar__2__x__2007,Vvar__3___24Anonymous__2008,Vvar__3___24Anonymous__2009] :
      ( cCoq_2eInit_2eSpecif_2eexist___24a3(Vvar__0__A__2002,Vvar__1__P__2004,Vvar__2__x__2006) = cCoq_2eInit_2eSpecif_2eexist___24a3(Vvar__0__A__2003,Vvar__1__P__2005,Vvar__2__x__2007)
     => ( c_24Proof = c_24Proof
        & Vvar__2__x__2006 = Vvar__2__x__2007
        & Vvar__1__P__2004 = Vvar__1__P__2005
        & Vvar__0__A__2002 = Vvar__0__A__2003 ) ) ).

fof('$_inj_Coq.Init.Specif.exist2',axiom,
    ! [Vvar__0__A__113076,Vvar__0__A__113077,Vvar__1__P__113078,Vvar__1__P__113079,Vvar__2__Q__113080,Vvar__2__Q__113081,Vvar__3__x__113082,Vvar__3__x__113083,Vvar__4___24Anonymous__113084,Vvar__4___24Anonymous__113085,Vvar__5___24Anonymous__113086,Vvar__5___24Anonymous__113087] :
      ( cCoq_2eInit_2eSpecif_2eexist2___24a4(Vvar__0__A__113076,Vvar__1__P__113078,Vvar__2__Q__113080,Vvar__3__x__113082) = cCoq_2eInit_2eSpecif_2eexist2___24a4(Vvar__0__A__113077,Vvar__1__P__113079,Vvar__2__Q__113081,Vvar__3__x__113083)
     => ( c_24Proof = c_24Proof
        & c_24Proof = c_24Proof
        & Vvar__3__x__113082 = Vvar__3__x__113083
        & Vvar__2__Q__113080 = Vvar__2__Q__113081
        & Vvar__1__P__113078 = Vvar__1__P__113079
        & Vvar__0__A__113076 = Vvar__0__A__113077 ) ) ).

fof('$_inj_Coq.Init.Specif.existT',axiom,
    ! [Vvar__0__A__113111,Vvar__0__A__113112,Vvar__1__P__113113,Vvar__1__P__113114,Vvar__2__x__113115,Vvar__2__x__113116,Vvar__3___24Anonymous__113117,Vvar__3___24Anonymous__113118] :
      ( cCoq_2eInit_2eSpecif_2eexistT___24a4(Vvar__0__A__113111,Vvar__1__P__113113,Vvar__2__x__113115,Vvar__3___24Anonymous__113117) = cCoq_2eInit_2eSpecif_2eexistT___24a4(Vvar__0__A__113112,Vvar__1__P__113114,Vvar__2__x__113116,Vvar__3___24Anonymous__113118)
     => ( Vvar__3___24Anonymous__113117 = Vvar__3___24Anonymous__113118
        & Vvar__2__x__113115 = Vvar__2__x__113116
        & Vvar__1__P__113113 = Vvar__1__P__113114
        & Vvar__0__A__113111 = Vvar__0__A__113112 ) ) ).

fof('$_inj_Coq.Init.Specif.existT2',axiom,
    ! [Vvar__0__A__113163,Vvar__0__A__113164,Vvar__1__P__113165,Vvar__1__P__113166,Vvar__2__Q__113167,Vvar__2__Q__113168,Vvar__3__x__113169,Vvar__3__x__113170,Vvar__4___24Anonymous__113171,Vvar__4___24Anonymous__113172,Vvar__5___24Anonymous__113173,Vvar__5___24Anonymous__113174] :
      ( cCoq_2eInit_2eSpecif_2eexistT2___24a6(Vvar__0__A__113163,Vvar__1__P__113165,Vvar__2__Q__113167,Vvar__3__x__113169,Vvar__4___24Anonymous__113171,Vvar__5___24Anonymous__113173) = cCoq_2eInit_2eSpecif_2eexistT2___24a6(Vvar__0__A__113164,Vvar__1__P__113166,Vvar__2__Q__113168,Vvar__3__x__113170,Vvar__4___24Anonymous__113172,Vvar__5___24Anonymous__113174)
     => ( Vvar__5___24Anonymous__113173 = Vvar__5___24Anonymous__113174
        & Vvar__4___24Anonymous__113171 = Vvar__4___24Anonymous__113172
        & Vvar__3__x__113169 = Vvar__3__x__113170
        & Vvar__2__Q__113167 = Vvar__2__Q__113168
        & Vvar__1__P__113165 = Vvar__1__P__113166
        & Vvar__0__A__113163 = Vvar__0__A__113164 ) ) ).

fof('$_inj_Coq.Init.Specif.inleft',axiom,
    ! [Vvar__0__A__2036,Vvar__0__A__2037,Vvar__1__B__2038,Vvar__1__B__2039,Vvar__2___24Anonymous__2040,Vvar__2___24Anonymous__2041] :
      ( cCoq_2eInit_2eSpecif_2einleft___24a3(Vvar__0__A__2036,Vvar__1__B__2038,Vvar__2___24Anonymous__2040) = cCoq_2eInit_2eSpecif_2einleft___24a3(Vvar__0__A__2037,Vvar__1__B__2039,Vvar__2___24Anonymous__2041)
     => ( Vvar__2___24Anonymous__2040 = Vvar__2___24Anonymous__2041
        & Vvar__1__B__2038 = Vvar__1__B__2039
        & Vvar__0__A__2036 = Vvar__0__A__2037 ) ) ).

fof('$_inj_Coq.Init.Specif.inright',axiom,
    ! [Vvar__0__A__2042,Vvar__0__A__2043,Vvar__1__B__2044,Vvar__1__B__2045,Vvar__2___24Anonymous__2046,Vvar__2___24Anonymous__2047] :
      ( cCoq_2eInit_2eSpecif_2einright___24a2(Vvar__0__A__2042,Vvar__1__B__2044) = cCoq_2eInit_2eSpecif_2einright___24a2(Vvar__0__A__2043,Vvar__1__B__2045)
     => ( c_24Proof = c_24Proof
        & Vvar__1__B__2044 = Vvar__1__B__2045
        & Vvar__0__A__2042 = Vvar__0__A__2043 ) ) ).

fof('$_inj_Coq.Init.Specif.left',axiom,
    ! [Vvar__0__A__268,Vvar__0__A__269,Vvar__1__B__270,Vvar__1__B__271,Vvar__2___24Anonymous__272,Vvar__2___24Anonymous__273] :
      ( cCoq_2eInit_2eSpecif_2eleft___24a2(Vvar__0__A__268,Vvar__1__B__270) = cCoq_2eInit_2eSpecif_2eleft___24a2(Vvar__0__A__269,Vvar__1__B__271)
     => ( c_24Proof = c_24Proof
        & Vvar__1__B__270 = Vvar__1__B__271
        & Vvar__0__A__268 = Vvar__0__A__269 ) ) ).

fof('$_inj_Coq.Init.Specif.right',axiom,
    ! [Vvar__0__A__274,Vvar__0__A__275,Vvar__1__B__276,Vvar__1__B__277,Vvar__2___24Anonymous__278,Vvar__2___24Anonymous__279] :
      ( cCoq_2eInit_2eSpecif_2eright___24a2(Vvar__0__A__274,Vvar__1__B__276) = cCoq_2eInit_2eSpecif_2eright___24a2(Vvar__0__A__275,Vvar__1__B__277)
     => ( c_24Proof = c_24Proof
        & Vvar__1__B__276 = Vvar__1__B__277
        & Vvar__0__A__274 = Vvar__0__A__275 ) ) ).

fof('$_inj_Coq.Numbers.BinNums.Npos',axiom,
    ! [Vvar__0___24Anonymous__6,Vvar__0___24Anonymous__7] :
      ( cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__6) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__7)
     => Vvar__0___24Anonymous__6 = Vvar__0___24Anonymous__7 ) ).

fof('$_inj_Coq.Numbers.BinNums.Zneg',axiom,
    ! [Vvar__0___24Anonymous__14033,Vvar__0___24Anonymous__14034] :
      ( cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__14033) = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__14034)
     => Vvar__0___24Anonymous__14033 = Vvar__0___24Anonymous__14034 ) ).

fof('$_inj_Coq.Numbers.BinNums.Zpos',axiom,
    ! [Vvar__0___24Anonymous__14031,Vvar__0___24Anonymous__14032] :
      ( cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__14031) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__14032)
     => Vvar__0___24Anonymous__14031 = Vvar__0___24Anonymous__14032 ) ).

fof('$_inj_Coq.Numbers.BinNums.xI',axiom,
    ! [Vvar__0___24Anonymous__322,Vvar__0___24Anonymous__323] :
      ( cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__322) = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__323)
     => Vvar__0___24Anonymous__322 = Vvar__0___24Anonymous__323 ) ).

fof('$_inj_Coq.Numbers.BinNums.xO',axiom,
    ! [Vvar__0___24Anonymous__324,Vvar__0___24Anonymous__325] :
      ( cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__324) = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__325)
     => Vvar__0___24Anonymous__324 = Vvar__0___24Anonymous__325 ) ).

fof('$_inj_Coq.PArith.BinPos.Pos.PeanoSucc',axiom,
    ! [Vvar__0__p__113695,Vvar__0__p__113696,Vvar__1___24Anonymous__113697,Vvar__1___24Anonymous__113698] :
      ( cCoq_2ePArith_2eBinPos_2ePos_2ePeanoSucc___24a2(Vvar__0__p__113695,Vvar__1___24Anonymous__113697) = cCoq_2ePArith_2eBinPos_2ePos_2ePeanoSucc___24a2(Vvar__0__p__113696,Vvar__1___24Anonymous__113698)
     => ( Vvar__1___24Anonymous__113697 = Vvar__1___24Anonymous__113698
        & Vvar__0__p__113695 = Vvar__0__p__113696 ) ) ).

fof('$_inj_Coq.PArith.BinPosDef.Pos.IsPos',axiom,
    ! [Vvar__0___24Anonymous__113587,Vvar__0___24Anonymous__113588] :
      ( cCoq_2ePArith_2eBinPosDef_2ePos_2eIsPos___24a1(Vvar__0___24Anonymous__113587) = cCoq_2ePArith_2eBinPosDef_2ePos_2eIsPos___24a1(Vvar__0___24Anonymous__113588)
     => Vvar__0___24Anonymous__113587 = Vvar__0___24Anonymous__113588 ) ).

fof('$_inj_Coq.QArith.QArith_base.Qmake',axiom,
    ! [Vvar__0__Qnum__91213,Vvar__0__Qnum__91214,Vvar__1__Qden__91215,Vvar__1__Qden__91216] :
      ( cCoq_2eQArith_2eQArith__base_2eQmake___24a2(Vvar__0__Qnum__91213,Vvar__1__Qden__91215) = cCoq_2eQArith_2eQArith__base_2eQmake___24a2(Vvar__0__Qnum__91214,Vvar__1__Qden__91216)
     => ( Vvar__1__Qden__91215 = Vvar__1__Qden__91216
        & Vvar__0__Qnum__91213 = Vvar__0__Qnum__91214 ) ) ).

fof('$_inj_Coq.Reals.RIneq.mknegreal',axiom,
    ! [Vvar__0__neg__109667,Vvar__0__neg__109668,Vvar__1__cond__neg__109669,Vvar__1__cond__neg__109670] :
      ( cCoq_2eReals_2eRIneq_2emknegreal___24a1(Vvar__0__neg__109667) = cCoq_2eReals_2eRIneq_2emknegreal___24a1(Vvar__0__neg__109668)
     => ( c_24Proof = c_24Proof
        & Vvar__0__neg__109667 = Vvar__0__neg__109668 ) ) ).

fof('$_inj_Coq.Reals.RIneq.mknonnegreal',axiom,
    ! [Vvar__0__nonneg__109646,Vvar__0__nonneg__109647,Vvar__1__cond__nonneg__109648,Vvar__1__cond__nonneg__109649] :
      ( cCoq_2eReals_2eRIneq_2emknonnegreal___24a1(Vvar__0__nonneg__109646) = cCoq_2eReals_2eRIneq_2emknonnegreal___24a1(Vvar__0__nonneg__109647)
     => ( c_24Proof = c_24Proof
        & Vvar__0__nonneg__109646 = Vvar__0__nonneg__109647 ) ) ).

fof('$_inj_Coq.Reals.RIneq.mknonposreal',axiom,
    ! [Vvar__0__nonpos__109660,Vvar__0__nonpos__109661,Vvar__1__cond__nonpos__109662,Vvar__1__cond__nonpos__109663] :
      ( cCoq_2eReals_2eRIneq_2emknonposreal___24a1(Vvar__0__nonpos__109660) = cCoq_2eReals_2eRIneq_2emknonposreal___24a1(Vvar__0__nonpos__109661)
     => ( c_24Proof = c_24Proof
        & Vvar__0__nonpos__109660 = Vvar__0__nonpos__109661 ) ) ).

fof('$_inj_Coq.Reals.RIneq.mknonzeroreal',axiom,
    ! [Vvar__0__nonzero__109674,Vvar__0__nonzero__109675,Vvar__1__cond__nonzero__109676,Vvar__1__cond__nonzero__109677] :
      ( cCoq_2eReals_2eRIneq_2emknonzeroreal___24a1(Vvar__0__nonzero__109674) = cCoq_2eReals_2eRIneq_2emknonzeroreal___24a1(Vvar__0__nonzero__109675)
     => ( c_24Proof = c_24Proof
        & Vvar__0__nonzero__109674 = Vvar__0__nonzero__109675 ) ) ).

fof('$_inj_Coq.Reals.RIneq.mkposreal',axiom,
    ! [Vvar__0__pos__109653,Vvar__0__pos__109654,Vvar__1__cond__pos__109655,Vvar__1__cond__pos__109656] :
      ( cCoq_2eReals_2eRIneq_2emkposreal___24a1(Vvar__0__pos__109653) = cCoq_2eReals_2eRIneq_2emkposreal___24a1(Vvar__0__pos__109654)
     => ( c_24Proof = c_24Proof
        & Vvar__0__pos__109653 = Vvar__0__pos__109654 ) ) ).

fof('$_inj_Coq.Reals.Rfunctions.ZintNeg',axiom,
    ! [Vvar__0__x__110497,Vvar__0__x__110498,Vvar__1__n__110499,Vvar__1__n__110500,Vvar__2___24Anonymous__110501,Vvar__2___24Anonymous__110502] :
      ( cCoq_2eReals_2eRfunctions_2eZintNeg___24a2(Vvar__0__x__110497,Vvar__1__n__110499) = cCoq_2eReals_2eRfunctions_2eZintNeg___24a2(Vvar__0__x__110498,Vvar__1__n__110500)
     => ( c_24Proof = c_24Proof
        & Vvar__1__n__110499 = Vvar__1__n__110500
        & Vvar__0__x__110497 = Vvar__0__x__110498 ) ) ).

fof('$_inj_Coq.Reals.Rfunctions.ZintNull',axiom,
    ! [Vvar__0__x__110487,Vvar__0__x__110488,Vvar__1___24Anonymous__110489,Vvar__1___24Anonymous__110490] :
      ( cCoq_2eReals_2eRfunctions_2eZintNull___24a1(Vvar__0__x__110487) = cCoq_2eReals_2eRfunctions_2eZintNull___24a1(Vvar__0__x__110488)
     => ( c_24Proof = c_24Proof
        & Vvar__0__x__110487 = Vvar__0__x__110488 ) ) ).

fof('$_inj_Coq.Reals.Rfunctions.ZintPos',axiom,
    ! [Vvar__0__x__110491,Vvar__0__x__110492,Vvar__1__n__110493,Vvar__1__n__110494,Vvar__2___24Anonymous__110495,Vvar__2___24Anonymous__110496] :
      ( cCoq_2eReals_2eRfunctions_2eZintPos___24a2(Vvar__0__x__110491,Vvar__1__n__110493) = cCoq_2eReals_2eRfunctions_2eZintPos___24a2(Vvar__0__x__110492,Vvar__1__n__110494)
     => ( c_24Proof = c_24Proof
        & Vvar__1__n__110493 = Vvar__1__n__110494
        & Vvar__0__x__110491 = Vvar__0__x__110492 ) ) ).

fof('$_inj_Coq.Strings.Ascii.Ascii',axiom,
    ! [Vvar__0___24Anonymous__13744,Vvar__0___24Anonymous__13745,Vvar__1___24Anonymous__13746,Vvar__1___24Anonymous__13747,Vvar__2___24Anonymous__13748,Vvar__2___24Anonymous__13749,Vvar__3___24Anonymous__13750,Vvar__3___24Anonymous__13751,Vvar__4___24Anonymous__13752,Vvar__4___24Anonymous__13753,Vvar__5___24Anonymous__13754,Vvar__5___24Anonymous__13755,Vvar__6___24Anonymous__13756,Vvar__6___24Anonymous__13757,Vvar__7___24Anonymous__13758,Vvar__7___24Anonymous__13759] :
      ( cCoq_2eStrings_2eAscii_2eAscii___24a8(Vvar__0___24Anonymous__13744,Vvar__1___24Anonymous__13746,Vvar__2___24Anonymous__13748,Vvar__3___24Anonymous__13750,Vvar__4___24Anonymous__13752,Vvar__5___24Anonymous__13754,Vvar__6___24Anonymous__13756,Vvar__7___24Anonymous__13758) = cCoq_2eStrings_2eAscii_2eAscii___24a8(Vvar__0___24Anonymous__13745,Vvar__1___24Anonymous__13747,Vvar__2___24Anonymous__13749,Vvar__3___24Anonymous__13751,Vvar__4___24Anonymous__13753,Vvar__5___24Anonymous__13755,Vvar__6___24Anonymous__13757,Vvar__7___24Anonymous__13759)
     => ( Vvar__7___24Anonymous__13758 = Vvar__7___24Anonymous__13759
        & Vvar__6___24Anonymous__13756 = Vvar__6___24Anonymous__13757
        & Vvar__5___24Anonymous__13754 = Vvar__5___24Anonymous__13755
        & Vvar__4___24Anonymous__13752 = Vvar__4___24Anonymous__13753
        & Vvar__3___24Anonymous__13750 = Vvar__3___24Anonymous__13751
        & Vvar__2___24Anonymous__13748 = Vvar__2___24Anonymous__13749
        & Vvar__1___24Anonymous__13746 = Vvar__1___24Anonymous__13747
        & Vvar__0___24Anonymous__13744 = Vvar__0___24Anonymous__13745 ) ) ).

fof('$_inj_Coq.Strings.String.String',axiom,
    ! [Vvar__0___24Anonymous__104287,Vvar__0___24Anonymous__104288,Vvar__1___24Anonymous__104289,Vvar__1___24Anonymous__104290] :
      ( cCoq_2eStrings_2eString_2eString___24a2(Vvar__0___24Anonymous__104287,Vvar__1___24Anonymous__104289) = cCoq_2eStrings_2eString_2eString___24a2(Vvar__0___24Anonymous__104288,Vvar__1___24Anonymous__104290)
     => ( Vvar__1___24Anonymous__104289 = Vvar__1___24Anonymous__104290
        & Vvar__0___24Anonymous__104287 = Vvar__0___24Anonymous__104288 ) ) ).

fof('$_inj_Coq.Structures.OrderedType.EQ',axiom,
    ! [Vvar__0__X__109607,Vvar__0__X__109608,Vvar__1__lt__109609,Vvar__1__lt__109610,Vvar__2__eq__109611,Vvar__2__eq__109612,Vvar__3__x__109613,Vvar__3__x__109614,Vvar__4__y__109615,Vvar__4__y__109616,Vvar__5___24Anonymous__109617,Vvar__5___24Anonymous__109618] :
      ( cCoq_2eStructures_2eOrderedType_2eEQ___24a5(Vvar__0__X__109607,Vvar__1__lt__109609,Vvar__2__eq__109611,Vvar__3__x__109613,Vvar__4__y__109615) = cCoq_2eStructures_2eOrderedType_2eEQ___24a5(Vvar__0__X__109608,Vvar__1__lt__109610,Vvar__2__eq__109612,Vvar__3__x__109614,Vvar__4__y__109616)
     => ( c_24Proof = c_24Proof
        & Vvar__4__y__109615 = Vvar__4__y__109616
        & Vvar__3__x__109613 = Vvar__3__x__109614
        & Vvar__2__eq__109611 = Vvar__2__eq__109612
        & Vvar__1__lt__109609 = Vvar__1__lt__109610
        & Vvar__0__X__109607 = Vvar__0__X__109608 ) ) ).

fof('$_inj_Coq.Structures.OrderedType.GT',axiom,
    ! [Vvar__0__X__109619,Vvar__0__X__109620,Vvar__1__lt__109621,Vvar__1__lt__109622,Vvar__2__eq__109623,Vvar__2__eq__109624,Vvar__3__x__109625,Vvar__3__x__109626,Vvar__4__y__109627,Vvar__4__y__109628,Vvar__5___24Anonymous__109629,Vvar__5___24Anonymous__109630] :
      ( cCoq_2eStructures_2eOrderedType_2eGT___24a5(Vvar__0__X__109619,Vvar__1__lt__109621,Vvar__2__eq__109623,Vvar__3__x__109625,Vvar__4__y__109627) = cCoq_2eStructures_2eOrderedType_2eGT___24a5(Vvar__0__X__109620,Vvar__1__lt__109622,Vvar__2__eq__109624,Vvar__3__x__109626,Vvar__4__y__109628)
     => ( c_24Proof = c_24Proof
        & Vvar__4__y__109627 = Vvar__4__y__109628
        & Vvar__3__x__109625 = Vvar__3__x__109626
        & Vvar__2__eq__109623 = Vvar__2__eq__109624
        & Vvar__1__lt__109621 = Vvar__1__lt__109622
        & Vvar__0__X__109619 = Vvar__0__X__109620 ) ) ).

fof('$_inj_Coq.Structures.OrderedType.LT',axiom,
    ! [Vvar__0__X__109595,Vvar__0__X__109596,Vvar__1__lt__109597,Vvar__1__lt__109598,Vvar__2__eq__109599,Vvar__2__eq__109600,Vvar__3__x__109601,Vvar__3__x__109602,Vvar__4__y__109603,Vvar__4__y__109604,Vvar__5___24Anonymous__109605,Vvar__5___24Anonymous__109606] :
      ( cCoq_2eStructures_2eOrderedType_2eLT___24a5(Vvar__0__X__109595,Vvar__1__lt__109597,Vvar__2__eq__109599,Vvar__3__x__109601,Vvar__4__y__109603) = cCoq_2eStructures_2eOrderedType_2eLT___24a5(Vvar__0__X__109596,Vvar__1__lt__109598,Vvar__2__eq__109600,Vvar__3__x__109602,Vvar__4__y__109604)
     => ( c_24Proof = c_24Proof
        & Vvar__4__y__109603 = Vvar__4__y__109604
        & Vvar__3__x__109601 = Vvar__3__x__109602
        & Vvar__2__eq__109599 = Vvar__2__eq__109600
        & Vvar__1__lt__109597 = Vvar__1__lt__109598
        & Vvar__0__X__109595 = Vvar__0__X__109596 ) ) ).

fof('$_inj_Coq.Vectors.Fin.F1',axiom,
    ! [Vvar__0__n__109161,Vvar__0__n__109162] :
      ( cCoq_2eVectors_2eFin_2eF1___24a1(Vvar__0__n__109161) = cCoq_2eVectors_2eFin_2eF1___24a1(Vvar__0__n__109162)
     => Vvar__0__n__109161 = Vvar__0__n__109162 ) ).

fof('$_inj_Coq.Vectors.Fin.FS',axiom,
    ! [Vvar__0__n__109163,Vvar__0__n__109164,Vvar__1___24Anonymous__109165,Vvar__1___24Anonymous__109166] :
      ( cCoq_2eVectors_2eFin_2eFS___24a2(Vvar__0__n__109163,Vvar__1___24Anonymous__109165) = cCoq_2eVectors_2eFin_2eFS___24a2(Vvar__0__n__109164,Vvar__1___24Anonymous__109166)
     => ( Vvar__1___24Anonymous__109165 = Vvar__1___24Anonymous__109166
        & Vvar__0__n__109163 = Vvar__0__n__109164 ) ) ).

fof('$_inj_Coq.Vectors.VectorDef.cons',axiom,
    ! [Vvar__0__A__113241,Vvar__0__A__113242,Vvar__1__h__113243,Vvar__1__h__113244,Vvar__2__n__113245,Vvar__2__n__113246,Vvar__3___24Anonymous__113247,Vvar__3___24Anonymous__113248] :
      ( cCoq_2eVectors_2eVectorDef_2econs___24a4(Vvar__0__A__113241,Vvar__1__h__113243,Vvar__2__n__113245,Vvar__3___24Anonymous__113247) = cCoq_2eVectors_2eVectorDef_2econs___24a4(Vvar__0__A__113242,Vvar__1__h__113244,Vvar__2__n__113246,Vvar__3___24Anonymous__113248)
     => ( Vvar__3___24Anonymous__113247 = Vvar__3___24Anonymous__113248
        & Vvar__2__n__113245 = Vvar__2__n__113246
        & Vvar__1__h__113243 = Vvar__1__h__113244
        & Vvar__0__A__113241 = Vvar__0__A__113242 ) ) ).

fof('$_inj_Coq.Vectors.VectorDef.nil',axiom,
    ! [Vvar__0__A__113239,Vvar__0__A__113240] :
      ( cCoq_2eVectors_2eVectorDef_2enil___24a1(Vvar__0__A__113239) = cCoq_2eVectors_2eVectorDef_2enil___24a1(Vvar__0__A__113240)
     => Vvar__0__A__113239 = Vvar__0__A__113240 ) ).

fof('$_inj_Coq.ZArith.Znumtheory.Euclid_intro',axiom,
    ! [Vvar__0__a__113410,Vvar__0__a__113411,Vvar__1__b__113412,Vvar__1__b__113413,Vvar__2__u__113414,Vvar__2__u__113415,Vvar__3__v__113416,Vvar__3__v__113417,Vvar__4__d__113418,Vvar__4__d__113419,Vvar__5___24Anonymous__113420,Vvar__5___24Anonymous__113421,Vvar__6___24Anonymous__113422,Vvar__6___24Anonymous__113423] :
      ( cCoq_2eZArith_2eZnumtheory_2eEuclid__intro___24a5(Vvar__0__a__113410,Vvar__1__b__113412,Vvar__2__u__113414,Vvar__3__v__113416,Vvar__4__d__113418) = cCoq_2eZArith_2eZnumtheory_2eEuclid__intro___24a5(Vvar__0__a__113411,Vvar__1__b__113413,Vvar__2__u__113415,Vvar__3__v__113417,Vvar__4__d__113419)
     => ( c_24Proof = c_24Proof
        & c_24Proof = c_24Proof
        & Vvar__4__d__113418 = Vvar__4__d__113419
        & Vvar__3__v__113416 = Vvar__3__v__113417
        & Vvar__2__u__113414 = Vvar__2__u__113415
        & Vvar__1__b__113412 = Vvar__1__b__113413
        & Vvar__0__a__113410 = Vvar__0__a__113411 ) ) ).

fof('$_inj_Coq.ZArith.Zpower.Zdiv_rest_proof',axiom,
    ! [Vvar__0__x__113471,Vvar__0__x__113472,Vvar__1__p__113473,Vvar__1__p__113474,Vvar__2__q__113475,Vvar__2__q__113476,Vvar__3__r__113477,Vvar__3__r__113478,Vvar__4___24Anonymous__113479,Vvar__4___24Anonymous__113480,Vvar__5___24Anonymous__113481,Vvar__5___24Anonymous__113482,Vvar__6___24Anonymous__113483,Vvar__6___24Anonymous__113484] :
      ( cCoq_2eZArith_2eZpower_2eZdiv__rest__proof___24a4(Vvar__0__x__113471,Vvar__1__p__113473,Vvar__2__q__113475,Vvar__3__r__113477) = cCoq_2eZArith_2eZpower_2eZdiv__rest__proof___24a4(Vvar__0__x__113472,Vvar__1__p__113474,Vvar__2__q__113476,Vvar__3__r__113478)
     => ( c_24Proof = c_24Proof
        & c_24Proof = c_24Proof
        & c_24Proof = c_24Proof
        & Vvar__3__r__113477 = Vvar__3__r__113478
        & Vvar__2__q__113475 = Vvar__2__q__113476
        & Vvar__1__p__113473 = Vvar__1__p__113474
        & Vvar__0__x__113471 = Vvar__0__x__113472 ) ) ).

fof('$_inj_Coq.micromega.EnvRing.PEX',axiom,
    ! [Vvar__0__C__85840,Vvar__0__C__85841,Vvar__1___24Anonymous__85842,Vvar__1___24Anonymous__85843] :
      ( cCoq_2emicromega_2eEnvRing_2ePEX___24a2(Vvar__0__C__85840,Vvar__1___24Anonymous__85842) = cCoq_2emicromega_2eEnvRing_2ePEX___24a2(Vvar__0__C__85841,Vvar__1___24Anonymous__85843)
     => ( Vvar__1___24Anonymous__85842 = Vvar__1___24Anonymous__85843
        & Vvar__0__C__85840 = Vvar__0__C__85841 ) ) ).

fof('$_inj_Coq.micromega.EnvRing.PEadd',axiom,
    ! [Vvar__0__C__85844,Vvar__0__C__85845,Vvar__1___24Anonymous__85846,Vvar__1___24Anonymous__85847,Vvar__2___24Anonymous__85848,Vvar__2___24Anonymous__85849] :
      ( cCoq_2emicromega_2eEnvRing_2ePEadd___24a3(Vvar__0__C__85844,Vvar__1___24Anonymous__85846,Vvar__2___24Anonymous__85848) = cCoq_2emicromega_2eEnvRing_2ePEadd___24a3(Vvar__0__C__85845,Vvar__1___24Anonymous__85847,Vvar__2___24Anonymous__85849)
     => ( Vvar__2___24Anonymous__85848 = Vvar__2___24Anonymous__85849
        & Vvar__1___24Anonymous__85846 = Vvar__1___24Anonymous__85847
        & Vvar__0__C__85844 = Vvar__0__C__85845 ) ) ).

fof('$_inj_Coq.micromega.EnvRing.PEc',axiom,
    ! [Vvar__0__C__85836,Vvar__0__C__85837,Vvar__1___24Anonymous__85838,Vvar__1___24Anonymous__85839] :
      ( cCoq_2emicromega_2eEnvRing_2ePEc___24a2(Vvar__0__C__85836,Vvar__1___24Anonymous__85838) = cCoq_2emicromega_2eEnvRing_2ePEc___24a2(Vvar__0__C__85837,Vvar__1___24Anonymous__85839)
     => ( Vvar__1___24Anonymous__85838 = Vvar__1___24Anonymous__85839
        & Vvar__0__C__85836 = Vvar__0__C__85837 ) ) ).

fof('$_inj_Coq.micromega.EnvRing.PEmul',axiom,
    ! [Vvar__0__C__85856,Vvar__0__C__85857,Vvar__1___24Anonymous__85858,Vvar__1___24Anonymous__85859,Vvar__2___24Anonymous__85860,Vvar__2___24Anonymous__85861] :
      ( cCoq_2emicromega_2eEnvRing_2ePEmul___24a3(Vvar__0__C__85856,Vvar__1___24Anonymous__85858,Vvar__2___24Anonymous__85860) = cCoq_2emicromega_2eEnvRing_2ePEmul___24a3(Vvar__0__C__85857,Vvar__1___24Anonymous__85859,Vvar__2___24Anonymous__85861)
     => ( Vvar__2___24Anonymous__85860 = Vvar__2___24Anonymous__85861
        & Vvar__1___24Anonymous__85858 = Vvar__1___24Anonymous__85859
        & Vvar__0__C__85856 = Vvar__0__C__85857 ) ) ).

fof('$_inj_Coq.micromega.EnvRing.PEopp',axiom,
    ! [Vvar__0__C__85862,Vvar__0__C__85863,Vvar__1___24Anonymous__85864,Vvar__1___24Anonymous__85865] :
      ( cCoq_2emicromega_2eEnvRing_2ePEopp___24a2(Vvar__0__C__85862,Vvar__1___24Anonymous__85864) = cCoq_2emicromega_2eEnvRing_2ePEopp___24a2(Vvar__0__C__85863,Vvar__1___24Anonymous__85865)
     => ( Vvar__1___24Anonymous__85864 = Vvar__1___24Anonymous__85865
        & Vvar__0__C__85862 = Vvar__0__C__85863 ) ) ).

fof('$_inj_Coq.micromega.EnvRing.PEpow',axiom,
    ! [Vvar__0__C__85866,Vvar__0__C__85867,Vvar__1___24Anonymous__85868,Vvar__1___24Anonymous__85869,Vvar__2___24Anonymous__85870,Vvar__2___24Anonymous__85871] :
      ( cCoq_2emicromega_2eEnvRing_2ePEpow___24a3(Vvar__0__C__85866,Vvar__1___24Anonymous__85868,Vvar__2___24Anonymous__85870) = cCoq_2emicromega_2eEnvRing_2ePEpow___24a3(Vvar__0__C__85867,Vvar__1___24Anonymous__85869,Vvar__2___24Anonymous__85871)
     => ( Vvar__2___24Anonymous__85870 = Vvar__2___24Anonymous__85871
        & Vvar__1___24Anonymous__85868 = Vvar__1___24Anonymous__85869
        & Vvar__0__C__85866 = Vvar__0__C__85867 ) ) ).

fof('$_inj_Coq.micromega.EnvRing.PEsub',axiom,
    ! [Vvar__0__C__85850,Vvar__0__C__85851,Vvar__1___24Anonymous__85852,Vvar__1___24Anonymous__85853,Vvar__2___24Anonymous__85854,Vvar__2___24Anonymous__85855] :
      ( cCoq_2emicromega_2eEnvRing_2ePEsub___24a3(Vvar__0__C__85850,Vvar__1___24Anonymous__85852,Vvar__2___24Anonymous__85854) = cCoq_2emicromega_2eEnvRing_2ePEsub___24a3(Vvar__0__C__85851,Vvar__1___24Anonymous__85853,Vvar__2___24Anonymous__85855)
     => ( Vvar__2___24Anonymous__85854 = Vvar__2___24Anonymous__85855
        & Vvar__1___24Anonymous__85852 = Vvar__1___24Anonymous__85853
        & Vvar__0__C__85850 = Vvar__0__C__85851 ) ) ).

fof('$_inj_Coq.micromega.EnvRing.PX',axiom,
    ! [Vvar__0__C__85911,Vvar__0__C__85912,Vvar__1___24Anonymous__85913,Vvar__1___24Anonymous__85914,Vvar__2___24Anonymous__85915,Vvar__2___24Anonymous__85916,Vvar__3___24Anonymous__85917,Vvar__3___24Anonymous__85918] :
      ( cCoq_2emicromega_2eEnvRing_2ePX___24a4(Vvar__0__C__85911,Vvar__1___24Anonymous__85913,Vvar__2___24Anonymous__85915,Vvar__3___24Anonymous__85917) = cCoq_2emicromega_2eEnvRing_2ePX___24a4(Vvar__0__C__85912,Vvar__1___24Anonymous__85914,Vvar__2___24Anonymous__85916,Vvar__3___24Anonymous__85918)
     => ( Vvar__3___24Anonymous__85917 = Vvar__3___24Anonymous__85918
        & Vvar__2___24Anonymous__85915 = Vvar__2___24Anonymous__85916
        & Vvar__1___24Anonymous__85913 = Vvar__1___24Anonymous__85914
        & Vvar__0__C__85911 = Vvar__0__C__85912 ) ) ).

fof('$_inj_Coq.micromega.EnvRing.Pc',axiom,
    ! [Vvar__0__C__85901,Vvar__0__C__85902,Vvar__1___24Anonymous__85903,Vvar__1___24Anonymous__85904] :
      ( cCoq_2emicromega_2eEnvRing_2ePc___24a2(Vvar__0__C__85901,Vvar__1___24Anonymous__85903) = cCoq_2emicromega_2eEnvRing_2ePc___24a2(Vvar__0__C__85902,Vvar__1___24Anonymous__85904)
     => ( Vvar__1___24Anonymous__85903 = Vvar__1___24Anonymous__85904
        & Vvar__0__C__85901 = Vvar__0__C__85902 ) ) ).

fof('$_inj_Coq.micromega.EnvRing.Pinj',axiom,
    ! [Vvar__0__C__85905,Vvar__0__C__85906,Vvar__1___24Anonymous__85907,Vvar__1___24Anonymous__85908,Vvar__2___24Anonymous__85909,Vvar__2___24Anonymous__85910] :
      ( cCoq_2emicromega_2eEnvRing_2ePinj___24a3(Vvar__0__C__85905,Vvar__1___24Anonymous__85907,Vvar__2___24Anonymous__85909) = cCoq_2emicromega_2eEnvRing_2ePinj___24a3(Vvar__0__C__85906,Vvar__1___24Anonymous__85908,Vvar__2___24Anonymous__85910)
     => ( Vvar__2___24Anonymous__85909 = Vvar__2___24Anonymous__85910
        & Vvar__1___24Anonymous__85907 = Vvar__1___24Anonymous__85908
        & Vvar__0__C__85905 = Vvar__0__C__85906 ) ) ).

fof('$_inj_Coq.micromega.EnvRing.vmon',axiom,
    ! [Vvar__0___24Anonymous__86844,Vvar__0___24Anonymous__86845,Vvar__1___24Anonymous__86846,Vvar__1___24Anonymous__86847] :
      ( cCoq_2emicromega_2eEnvRing_2evmon___24a2(Vvar__0___24Anonymous__86844,Vvar__1___24Anonymous__86846) = cCoq_2emicromega_2eEnvRing_2evmon___24a2(Vvar__0___24Anonymous__86845,Vvar__1___24Anonymous__86847)
     => ( Vvar__1___24Anonymous__86846 = Vvar__1___24Anonymous__86847
        & Vvar__0___24Anonymous__86844 = Vvar__0___24Anonymous__86845 ) ) ).

fof('$_inj_Coq.micromega.EnvRing.zmon',axiom,
    ! [Vvar__0___24Anonymous__86840,Vvar__0___24Anonymous__86841,Vvar__1___24Anonymous__86842,Vvar__1___24Anonymous__86843] :
      ( cCoq_2emicromega_2eEnvRing_2ezmon___24a2(Vvar__0___24Anonymous__86840,Vvar__1___24Anonymous__86842) = cCoq_2emicromega_2eEnvRing_2ezmon___24a2(Vvar__0___24Anonymous__86841,Vvar__1___24Anonymous__86843)
     => ( Vvar__1___24Anonymous__86842 = Vvar__1___24Anonymous__86843
        & Vvar__0___24Anonymous__86840 = Vvar__0___24Anonymous__86841 ) ) ).

fof('$_inj_Coq.micromega.RMicromega.CInv',axiom,
    ! [Vvar__0__r__109819,Vvar__0__r__109820] :
      ( cCoq_2emicromega_2eRMicromega_2eCInv___24a1(Vvar__0__r__109819) = cCoq_2emicromega_2eRMicromega_2eCInv___24a1(Vvar__0__r__109820)
     => Vvar__0__r__109819 = Vvar__0__r__109820 ) ).

fof('$_inj_Coq.micromega.RMicromega.CMinus',axiom,
    ! [Vvar__0__r1__109807,Vvar__0__r1__109808,Vvar__1__r2__109809,Vvar__1__r2__109810] :
      ( cCoq_2emicromega_2eRMicromega_2eCMinus___24a2(Vvar__0__r1__109807,Vvar__1__r2__109809) = cCoq_2emicromega_2eRMicromega_2eCMinus___24a2(Vvar__0__r1__109808,Vvar__1__r2__109810)
     => ( Vvar__1__r2__109809 = Vvar__1__r2__109810
        & Vvar__0__r1__109807 = Vvar__0__r1__109808 ) ) ).

fof('$_inj_Coq.micromega.RMicromega.CMult',axiom,
    ! [Vvar__0__r1__109811,Vvar__0__r1__109812,Vvar__1__r2__109813,Vvar__1__r2__109814] :
      ( cCoq_2emicromega_2eRMicromega_2eCMult___24a2(Vvar__0__r1__109811,Vvar__1__r2__109813) = cCoq_2emicromega_2eRMicromega_2eCMult___24a2(Vvar__0__r1__109812,Vvar__1__r2__109814)
     => ( Vvar__1__r2__109813 = Vvar__1__r2__109814
        & Vvar__0__r1__109811 = Vvar__0__r1__109812 ) ) ).

fof('$_inj_Coq.micromega.RMicromega.COpp',axiom,
    ! [Vvar__0__r__109821,Vvar__0__r__109822] :
      ( cCoq_2emicromega_2eRMicromega_2eCOpp___24a1(Vvar__0__r__109821) = cCoq_2emicromega_2eRMicromega_2eCOpp___24a1(Vvar__0__r__109822)
     => Vvar__0__r__109821 = Vvar__0__r__109822 ) ).

fof('$_inj_Coq.micromega.RMicromega.CPlus',axiom,
    ! [Vvar__0__r1__109803,Vvar__0__r1__109804,Vvar__1__r2__109805,Vvar__1__r2__109806] :
      ( cCoq_2emicromega_2eRMicromega_2eCPlus___24a2(Vvar__0__r1__109803,Vvar__1__r2__109805) = cCoq_2emicromega_2eRMicromega_2eCPlus___24a2(Vvar__0__r1__109804,Vvar__1__r2__109806)
     => ( Vvar__1__r2__109805 = Vvar__1__r2__109806
        & Vvar__0__r1__109803 = Vvar__0__r1__109804 ) ) ).

fof('$_inj_Coq.micromega.RMicromega.CPow',axiom,
    ! [Vvar__0__r1__109815,Vvar__0__r1__109816,Vvar__1__z__109817,Vvar__1__z__109818] :
      ( cCoq_2emicromega_2eRMicromega_2eCPow___24a2(Vvar__0__r1__109815,Vvar__1__z__109817) = cCoq_2emicromega_2eRMicromega_2eCPow___24a2(Vvar__0__r1__109816,Vvar__1__z__109818)
     => ( Vvar__1__z__109817 = Vvar__1__z__109818
        & Vvar__0__r1__109815 = Vvar__0__r1__109816 ) ) ).

fof('$_inj_Coq.micromega.RMicromega.CQ',axiom,
    ! [Vvar__0__r__109799,Vvar__0__r__109800] :
      ( cCoq_2emicromega_2eRMicromega_2eCQ___24a1(Vvar__0__r__109799) = cCoq_2emicromega_2eRMicromega_2eCQ___24a1(Vvar__0__r__109800)
     => Vvar__0__r__109799 = Vvar__0__r__109800 ) ).

fof('$_inj_Coq.micromega.RMicromega.CZ',axiom,
    ! [Vvar__0__r__109801,Vvar__0__r__109802] :
      ( cCoq_2emicromega_2eRMicromega_2eCZ___24a1(Vvar__0__r__109801) = cCoq_2emicromega_2eRMicromega_2eCZ___24a1(Vvar__0__r__109802)
     => Vvar__0__r__109801 = Vvar__0__r__109802 ) ).

fof('$_inj_Coq.micromega.RingMicromega.Build_Formula',axiom,
    ! [Vvar__0__T__98177,Vvar__0__T__98178,Vvar__1__Flhs__98179,Vvar__1__Flhs__98180,Vvar__2__Fop__98181,Vvar__2__Fop__98182,Vvar__3__Frhs__98183,Vvar__3__Frhs__98184] :
      ( cCoq_2emicromega_2eRingMicromega_2eBuild__Formula___24a4(Vvar__0__T__98177,Vvar__1__Flhs__98179,Vvar__2__Fop__98181,Vvar__3__Frhs__98183) = cCoq_2emicromega_2eRingMicromega_2eBuild__Formula___24a4(Vvar__0__T__98178,Vvar__1__Flhs__98180,Vvar__2__Fop__98182,Vvar__3__Frhs__98184)
     => ( Vvar__3__Frhs__98183 = Vvar__3__Frhs__98184
        & Vvar__2__Fop__98181 = Vvar__2__Fop__98182
        & Vvar__1__Flhs__98179 = Vvar__1__Flhs__98180
        & Vvar__0__T__98177 = Vvar__0__T__98178 ) ) ).

fof('$_inj_Coq.micromega.RingMicromega.PsatzAdd',axiom,
    ! [Vvar__0__C__97289,Vvar__0__C__97290,Vvar__1___24Anonymous__97291,Vvar__1___24Anonymous__97292,Vvar__2___24Anonymous__97293,Vvar__2___24Anonymous__97294] :
      ( cCoq_2emicromega_2eRingMicromega_2ePsatzAdd___24a3(Vvar__0__C__97289,Vvar__1___24Anonymous__97291,Vvar__2___24Anonymous__97293) = cCoq_2emicromega_2eRingMicromega_2ePsatzAdd___24a3(Vvar__0__C__97290,Vvar__1___24Anonymous__97292,Vvar__2___24Anonymous__97294)
     => ( Vvar__2___24Anonymous__97293 = Vvar__2___24Anonymous__97294
        & Vvar__1___24Anonymous__97291 = Vvar__1___24Anonymous__97292
        & Vvar__0__C__97289 = Vvar__0__C__97290 ) ) ).

fof('$_inj_Coq.micromega.RingMicromega.PsatzC',axiom,
    ! [Vvar__0__C__97295,Vvar__0__C__97296,Vvar__1___24Anonymous__97297,Vvar__1___24Anonymous__97298] :
      ( cCoq_2emicromega_2eRingMicromega_2ePsatzC___24a2(Vvar__0__C__97295,Vvar__1___24Anonymous__97297) = cCoq_2emicromega_2eRingMicromega_2ePsatzC___24a2(Vvar__0__C__97296,Vvar__1___24Anonymous__97298)
     => ( Vvar__1___24Anonymous__97297 = Vvar__1___24Anonymous__97298
        & Vvar__0__C__97295 = Vvar__0__C__97296 ) ) ).

fof('$_inj_Coq.micromega.RingMicromega.PsatzIn',axiom,
    ! [Vvar__0__C__97269,Vvar__0__C__97270,Vvar__1___24Anonymous__97271,Vvar__1___24Anonymous__97272] :
      ( cCoq_2emicromega_2eRingMicromega_2ePsatzIn___24a2(Vvar__0__C__97269,Vvar__1___24Anonymous__97271) = cCoq_2emicromega_2eRingMicromega_2ePsatzIn___24a2(Vvar__0__C__97270,Vvar__1___24Anonymous__97272)
     => ( Vvar__1___24Anonymous__97271 = Vvar__1___24Anonymous__97272
        & Vvar__0__C__97269 = Vvar__0__C__97270 ) ) ).

fof('$_inj_Coq.micromega.RingMicromega.PsatzMulC',axiom,
    ! [Vvar__0__C__97277,Vvar__0__C__97278,Vvar__1___24Anonymous__97279,Vvar__1___24Anonymous__97280,Vvar__2___24Anonymous__97281,Vvar__2___24Anonymous__97282] :
      ( cCoq_2emicromega_2eRingMicromega_2ePsatzMulC___24a3(Vvar__0__C__97277,Vvar__1___24Anonymous__97279,Vvar__2___24Anonymous__97281) = cCoq_2emicromega_2eRingMicromega_2ePsatzMulC___24a3(Vvar__0__C__97278,Vvar__1___24Anonymous__97280,Vvar__2___24Anonymous__97282)
     => ( Vvar__2___24Anonymous__97281 = Vvar__2___24Anonymous__97282
        & Vvar__1___24Anonymous__97279 = Vvar__1___24Anonymous__97280
        & Vvar__0__C__97277 = Vvar__0__C__97278 ) ) ).

fof('$_inj_Coq.micromega.RingMicromega.PsatzMulE',axiom,
    ! [Vvar__0__C__97283,Vvar__0__C__97284,Vvar__1___24Anonymous__97285,Vvar__1___24Anonymous__97286,Vvar__2___24Anonymous__97287,Vvar__2___24Anonymous__97288] :
      ( cCoq_2emicromega_2eRingMicromega_2ePsatzMulE___24a3(Vvar__0__C__97283,Vvar__1___24Anonymous__97285,Vvar__2___24Anonymous__97287) = cCoq_2emicromega_2eRingMicromega_2ePsatzMulE___24a3(Vvar__0__C__97284,Vvar__1___24Anonymous__97286,Vvar__2___24Anonymous__97288)
     => ( Vvar__2___24Anonymous__97287 = Vvar__2___24Anonymous__97288
        & Vvar__1___24Anonymous__97285 = Vvar__1___24Anonymous__97286
        & Vvar__0__C__97283 = Vvar__0__C__97284 ) ) ).

fof('$_inj_Coq.micromega.RingMicromega.PsatzSquare',axiom,
    ! [Vvar__0__C__97273,Vvar__0__C__97274,Vvar__1___24Anonymous__97275,Vvar__1___24Anonymous__97276] :
      ( cCoq_2emicromega_2eRingMicromega_2ePsatzSquare___24a2(Vvar__0__C__97273,Vvar__1___24Anonymous__97275) = cCoq_2emicromega_2eRingMicromega_2ePsatzSquare___24a2(Vvar__0__C__97274,Vvar__1___24Anonymous__97276)
     => ( Vvar__1___24Anonymous__97275 = Vvar__1___24Anonymous__97276
        & Vvar__0__C__97273 = Vvar__0__C__97274 ) ) ).

fof('$_inj_Coq.micromega.RingMicromega.PsatzZ',axiom,
    ! [Vvar__0__C__97299,Vvar__0__C__97300] :
      ( cCoq_2emicromega_2eRingMicromega_2ePsatzZ___24a1(Vvar__0__C__97299) = cCoq_2emicromega_2eRingMicromega_2ePsatzZ___24a1(Vvar__0__C__97300)
     => Vvar__0__C__97299 = Vvar__0__C__97300 ) ).

fof('$_inj_Coq.micromega.Tauto.A',axiom,
    ! [Vvar__0__TA__2437,Vvar__0__TA__2438,Vvar__1__TX__2439,Vvar__1__TX__2440,Vvar__2__AA__2441,Vvar__2__AA__2442,Vvar__3__AF__2443,Vvar__3__AF__2444,Vvar__4___24Anonymous__2445,Vvar__4___24Anonymous__2446,Vvar__5___24Anonymous__2447,Vvar__5___24Anonymous__2448] :
      ( cCoq_2emicromega_2eTauto_2eA___24a6(Vvar__0__TA__2437,Vvar__1__TX__2439,Vvar__2__AA__2441,Vvar__3__AF__2443,Vvar__4___24Anonymous__2445,Vvar__5___24Anonymous__2447) = cCoq_2emicromega_2eTauto_2eA___24a6(Vvar__0__TA__2438,Vvar__1__TX__2440,Vvar__2__AA__2442,Vvar__3__AF__2444,Vvar__4___24Anonymous__2446,Vvar__5___24Anonymous__2448)
     => ( Vvar__5___24Anonymous__2447 = Vvar__5___24Anonymous__2448
        & Vvar__4___24Anonymous__2445 = Vvar__4___24Anonymous__2446
        & Vvar__3__AF__2443 = Vvar__3__AF__2444
        & Vvar__2__AA__2441 = Vvar__2__AA__2442
        & Vvar__1__TX__2439 = Vvar__1__TX__2440
        & Vvar__0__TA__2437 = Vvar__0__TA__2438 ) ) ).

fof('$_inj_Coq.micromega.Tauto.Cj',axiom,
    ! [Vvar__0__TA__2449,Vvar__0__TA__2450,Vvar__1__TX__2451,Vvar__1__TX__2452,Vvar__2__AA__2453,Vvar__2__AA__2454,Vvar__3__AF__2455,Vvar__3__AF__2456,Vvar__4___24Anonymous__2457,Vvar__4___24Anonymous__2458,Vvar__5___24Anonymous__2459,Vvar__5___24Anonymous__2460] :
      ( cCoq_2emicromega_2eTauto_2eCj___24a6(Vvar__0__TA__2449,Vvar__1__TX__2451,Vvar__2__AA__2453,Vvar__3__AF__2455,Vvar__4___24Anonymous__2457,Vvar__5___24Anonymous__2459) = cCoq_2emicromega_2eTauto_2eCj___24a6(Vvar__0__TA__2450,Vvar__1__TX__2452,Vvar__2__AA__2454,Vvar__3__AF__2456,Vvar__4___24Anonymous__2458,Vvar__5___24Anonymous__2460)
     => ( Vvar__5___24Anonymous__2459 = Vvar__5___24Anonymous__2460
        & Vvar__4___24Anonymous__2457 = Vvar__4___24Anonymous__2458
        & Vvar__3__AF__2455 = Vvar__3__AF__2456
        & Vvar__2__AA__2453 = Vvar__2__AA__2454
        & Vvar__1__TX__2451 = Vvar__1__TX__2452
        & Vvar__0__TA__2449 = Vvar__0__TA__2450 ) ) ).

fof('$_inj_Coq.micromega.Tauto.D',axiom,
    ! [Vvar__0__TA__2461,Vvar__0__TA__2462,Vvar__1__TX__2463,Vvar__1__TX__2464,Vvar__2__AA__2465,Vvar__2__AA__2466,Vvar__3__AF__2467,Vvar__3__AF__2468,Vvar__4___24Anonymous__2469,Vvar__4___24Anonymous__2470,Vvar__5___24Anonymous__2471,Vvar__5___24Anonymous__2472] :
      ( cCoq_2emicromega_2eTauto_2eD___24a6(Vvar__0__TA__2461,Vvar__1__TX__2463,Vvar__2__AA__2465,Vvar__3__AF__2467,Vvar__4___24Anonymous__2469,Vvar__5___24Anonymous__2471) = cCoq_2emicromega_2eTauto_2eD___24a6(Vvar__0__TA__2462,Vvar__1__TX__2464,Vvar__2__AA__2466,Vvar__3__AF__2468,Vvar__4___24Anonymous__2470,Vvar__5___24Anonymous__2472)
     => ( Vvar__5___24Anonymous__2471 = Vvar__5___24Anonymous__2472
        & Vvar__4___24Anonymous__2469 = Vvar__4___24Anonymous__2470
        & Vvar__3__AF__2467 = Vvar__3__AF__2468
        & Vvar__2__AA__2465 = Vvar__2__AA__2466
        & Vvar__1__TX__2463 = Vvar__1__TX__2464
        & Vvar__0__TA__2461 = Vvar__0__TA__2462 ) ) ).

fof('$_inj_Coq.micromega.Tauto.FF',axiom,
    ! [Vvar__0__TA__2419,Vvar__0__TA__2420,Vvar__1__TX__2421,Vvar__1__TX__2422,Vvar__2__AA__2423,Vvar__2__AA__2424,Vvar__3__AF__2425,Vvar__3__AF__2426] :
      ( cCoq_2emicromega_2eTauto_2eFF___24a4(Vvar__0__TA__2419,Vvar__1__TX__2421,Vvar__2__AA__2423,Vvar__3__AF__2425) = cCoq_2emicromega_2eTauto_2eFF___24a4(Vvar__0__TA__2420,Vvar__1__TX__2422,Vvar__2__AA__2424,Vvar__3__AF__2426)
     => ( Vvar__3__AF__2425 = Vvar__3__AF__2426
        & Vvar__2__AA__2423 = Vvar__2__AA__2424
        & Vvar__1__TX__2421 = Vvar__1__TX__2422
        & Vvar__0__TA__2419 = Vvar__0__TA__2420 ) ) ).

fof('$_inj_Coq.micromega.Tauto.I',axiom,
    ! [Vvar__0__TA__2483,Vvar__0__TA__2484,Vvar__1__TX__2485,Vvar__1__TX__2486,Vvar__2__AA__2487,Vvar__2__AA__2488,Vvar__3__AF__2489,Vvar__3__AF__2490,Vvar__4___24Anonymous__2491,Vvar__4___24Anonymous__2492,Vvar__5___24Anonymous__2493,Vvar__5___24Anonymous__2494,Vvar__6___24Anonymous__2495,Vvar__6___24Anonymous__2496] :
      ( cCoq_2emicromega_2eTauto_2eI___24a7(Vvar__0__TA__2483,Vvar__1__TX__2485,Vvar__2__AA__2487,Vvar__3__AF__2489,Vvar__4___24Anonymous__2491,Vvar__5___24Anonymous__2493,Vvar__6___24Anonymous__2495) = cCoq_2emicromega_2eTauto_2eI___24a7(Vvar__0__TA__2484,Vvar__1__TX__2486,Vvar__2__AA__2488,Vvar__3__AF__2490,Vvar__4___24Anonymous__2492,Vvar__5___24Anonymous__2494,Vvar__6___24Anonymous__2496)
     => ( Vvar__6___24Anonymous__2495 = Vvar__6___24Anonymous__2496
        & Vvar__5___24Anonymous__2493 = Vvar__5___24Anonymous__2494
        & Vvar__4___24Anonymous__2491 = Vvar__4___24Anonymous__2492
        & Vvar__3__AF__2489 = Vvar__3__AF__2490
        & Vvar__2__AA__2487 = Vvar__2__AA__2488
        & Vvar__1__TX__2485 = Vvar__1__TX__2486
        & Vvar__0__TA__2483 = Vvar__0__TA__2484 ) ) ).

fof('$_inj_Coq.micromega.Tauto.N',axiom,
    ! [Vvar__0__TA__2473,Vvar__0__TA__2474,Vvar__1__TX__2475,Vvar__1__TX__2476,Vvar__2__AA__2477,Vvar__2__AA__2478,Vvar__3__AF__2479,Vvar__3__AF__2480,Vvar__4___24Anonymous__2481,Vvar__4___24Anonymous__2482] :
      ( cCoq_2emicromega_2eTauto_2eN___24a5(Vvar__0__TA__2473,Vvar__1__TX__2475,Vvar__2__AA__2477,Vvar__3__AF__2479,Vvar__4___24Anonymous__2481) = cCoq_2emicromega_2eTauto_2eN___24a5(Vvar__0__TA__2474,Vvar__1__TX__2476,Vvar__2__AA__2478,Vvar__3__AF__2480,Vvar__4___24Anonymous__2482)
     => ( Vvar__4___24Anonymous__2481 = Vvar__4___24Anonymous__2482
        & Vvar__3__AF__2479 = Vvar__3__AF__2480
        & Vvar__2__AA__2477 = Vvar__2__AA__2478
        & Vvar__1__TX__2475 = Vvar__1__TX__2476
        & Vvar__0__TA__2473 = Vvar__0__TA__2474 ) ) ).

fof('$_inj_Coq.micromega.Tauto.TT',axiom,
    ! [Vvar__0__TA__2411,Vvar__0__TA__2412,Vvar__1__TX__2413,Vvar__1__TX__2414,Vvar__2__AA__2415,Vvar__2__AA__2416,Vvar__3__AF__2417,Vvar__3__AF__2418] :
      ( cCoq_2emicromega_2eTauto_2eTT___24a4(Vvar__0__TA__2411,Vvar__1__TX__2413,Vvar__2__AA__2415,Vvar__3__AF__2417) = cCoq_2emicromega_2eTauto_2eTT___24a4(Vvar__0__TA__2412,Vvar__1__TX__2414,Vvar__2__AA__2416,Vvar__3__AF__2418)
     => ( Vvar__3__AF__2417 = Vvar__3__AF__2418
        & Vvar__2__AA__2415 = Vvar__2__AA__2416
        & Vvar__1__TX__2413 = Vvar__1__TX__2414
        & Vvar__0__TA__2411 = Vvar__0__TA__2412 ) ) ).

fof('$_inj_Coq.micromega.Tauto.X',axiom,
    ! [Vvar__0__TA__2427,Vvar__0__TA__2428,Vvar__1__TX__2429,Vvar__1__TX__2430,Vvar__2__AA__2431,Vvar__2__AA__2432,Vvar__3__AF__2433,Vvar__3__AF__2434,Vvar__4___24Anonymous__2435,Vvar__4___24Anonymous__2436] :
      ( cCoq_2emicromega_2eTauto_2eX___24a5(Vvar__0__TA__2427,Vvar__1__TX__2429,Vvar__2__AA__2431,Vvar__3__AF__2433,Vvar__4___24Anonymous__2435) = cCoq_2emicromega_2eTauto_2eX___24a5(Vvar__0__TA__2428,Vvar__1__TX__2430,Vvar__2__AA__2432,Vvar__3__AF__2434,Vvar__4___24Anonymous__2436)
     => ( Vvar__4___24Anonymous__2435 = Vvar__4___24Anonymous__2436
        & Vvar__3__AF__2433 = Vvar__3__AF__2434
        & Vvar__2__AA__2431 = Vvar__2__AA__2432
        & Vvar__1__TX__2429 = Vvar__1__TX__2430
        & Vvar__0__TA__2427 = Vvar__0__TA__2428 ) ) ).

fof('$_inj_Coq.micromega.VarMap.Branch',axiom,
    ! [Vvar__0__A__113215,Vvar__0__A__113216,Vvar__1___24Anonymous__113217,Vvar__1___24Anonymous__113218,Vvar__2___24Anonymous__113219,Vvar__2___24Anonymous__113220,Vvar__3___24Anonymous__113221,Vvar__3___24Anonymous__113222] :
      ( cCoq_2emicromega_2eVarMap_2eBranch___24a4(Vvar__0__A__113215,Vvar__1___24Anonymous__113217,Vvar__2___24Anonymous__113219,Vvar__3___24Anonymous__113221) = cCoq_2emicromega_2eVarMap_2eBranch___24a4(Vvar__0__A__113216,Vvar__1___24Anonymous__113218,Vvar__2___24Anonymous__113220,Vvar__3___24Anonymous__113222)
     => ( Vvar__3___24Anonymous__113221 = Vvar__3___24Anonymous__113222
        & Vvar__2___24Anonymous__113219 = Vvar__2___24Anonymous__113220
        & Vvar__1___24Anonymous__113217 = Vvar__1___24Anonymous__113218
        & Vvar__0__A__113215 = Vvar__0__A__113216 ) ) ).

fof('$_inj_Coq.micromega.VarMap.Elt',axiom,
    ! [Vvar__0__A__113211,Vvar__0__A__113212,Vvar__1___24Anonymous__113213,Vvar__1___24Anonymous__113214] :
      ( cCoq_2emicromega_2eVarMap_2eElt___24a2(Vvar__0__A__113211,Vvar__1___24Anonymous__113213) = cCoq_2emicromega_2eVarMap_2eElt___24a2(Vvar__0__A__113212,Vvar__1___24Anonymous__113214)
     => ( Vvar__1___24Anonymous__113213 = Vvar__1___24Anonymous__113214
        & Vvar__0__A__113211 = Vvar__0__A__113212 ) ) ).

fof('$_inj_Coq.micromega.VarMap.Empty',axiom,
    ! [Vvar__0__A__113209,Vvar__0__A__113210] :
      ( cCoq_2emicromega_2eVarMap_2eEmpty___24a1(Vvar__0__A__113209) = cCoq_2emicromega_2eVarMap_2eEmpty___24a1(Vvar__0__A__113210)
     => Vvar__0__A__113209 = Vvar__0__A__113210 ) ).

fof('$_inj_Coq.micromega.ZMicromega.CutProof',axiom,
    ! [Vvar__0___24Anonymous__113321,Vvar__0___24Anonymous__113322,Vvar__1___24Anonymous__113323,Vvar__1___24Anonymous__113324] :
      ( cCoq_2emicromega_2eZMicromega_2eCutProof___24a2(Vvar__0___24Anonymous__113321,Vvar__1___24Anonymous__113323) = cCoq_2emicromega_2eZMicromega_2eCutProof___24a2(Vvar__0___24Anonymous__113322,Vvar__1___24Anonymous__113324)
     => ( Vvar__1___24Anonymous__113323 = Vvar__1___24Anonymous__113324
        & Vvar__0___24Anonymous__113321 = Vvar__0___24Anonymous__113322 ) ) ).

fof('$_inj_Coq.micromega.ZMicromega.EnumProof',axiom,
    ! [Vvar__0___24Anonymous__113325,Vvar__0___24Anonymous__113326,Vvar__1___24Anonymous__113327,Vvar__1___24Anonymous__113328,Vvar__2___24Anonymous__113329,Vvar__2___24Anonymous__113330] :
      ( cCoq_2emicromega_2eZMicromega_2eEnumProof___24a3(Vvar__0___24Anonymous__113325,Vvar__1___24Anonymous__113327,Vvar__2___24Anonymous__113329) = cCoq_2emicromega_2eZMicromega_2eEnumProof___24a3(Vvar__0___24Anonymous__113326,Vvar__1___24Anonymous__113328,Vvar__2___24Anonymous__113330)
     => ( Vvar__2___24Anonymous__113329 = Vvar__2___24Anonymous__113330
        & Vvar__1___24Anonymous__113327 = Vvar__1___24Anonymous__113328
        & Vvar__0___24Anonymous__113325 = Vvar__0___24Anonymous__113326 ) ) ).

fof('$_inj_Coq.micromega.ZMicromega.RatProof',axiom,
    ! [Vvar__0___24Anonymous__113317,Vvar__0___24Anonymous__113318,Vvar__1___24Anonymous__113319,Vvar__1___24Anonymous__113320] :
      ( cCoq_2emicromega_2eZMicromega_2eRatProof___24a2(Vvar__0___24Anonymous__113317,Vvar__1___24Anonymous__113319) = cCoq_2emicromega_2eZMicromega_2eRatProof___24a2(Vvar__0___24Anonymous__113318,Vvar__1___24Anonymous__113320)
     => ( Vvar__1___24Anonymous__113319 = Vvar__1___24Anonymous__113320
        & Vvar__0___24Anonymous__113317 = Vvar__0___24Anonymous__113318 ) ) ).

fof('$_inj_Coq.setoid_ring.Field_theory.FEI',axiom,
    ! [Vvar__0__C__3748,Vvar__0__C__3749] :
      ( cCoq_2esetoid__ring_2eField__theory_2eFEI___24a1(Vvar__0__C__3748) = cCoq_2esetoid__ring_2eField__theory_2eFEI___24a1(Vvar__0__C__3749)
     => Vvar__0__C__3748 = Vvar__0__C__3749 ) ).

fof('$_inj_Coq.setoid_ring.Field_theory.FEO',axiom,
    ! [Vvar__0__C__3746,Vvar__0__C__3747] :
      ( cCoq_2esetoid__ring_2eField__theory_2eFEO___24a1(Vvar__0__C__3746) = cCoq_2esetoid__ring_2eField__theory_2eFEO___24a1(Vvar__0__C__3747)
     => Vvar__0__C__3746 = Vvar__0__C__3747 ) ).

fof('$_inj_Coq.setoid_ring.Field_theory.FEX',axiom,
    ! [Vvar__0__C__3754,Vvar__0__C__3755,Vvar__1___24Anonymous__3756,Vvar__1___24Anonymous__3757] :
      ( cCoq_2esetoid__ring_2eField__theory_2eFEX___24a2(Vvar__0__C__3754,Vvar__1___24Anonymous__3756) = cCoq_2esetoid__ring_2eField__theory_2eFEX___24a2(Vvar__0__C__3755,Vvar__1___24Anonymous__3757)
     => ( Vvar__1___24Anonymous__3756 = Vvar__1___24Anonymous__3757
        & Vvar__0__C__3754 = Vvar__0__C__3755 ) ) ).

fof('$_inj_Coq.setoid_ring.Field_theory.FEadd',axiom,
    ! [Vvar__0__C__3758,Vvar__0__C__3759,Vvar__1___24Anonymous__3760,Vvar__1___24Anonymous__3761,Vvar__2___24Anonymous__3762,Vvar__2___24Anonymous__3763] :
      ( cCoq_2esetoid__ring_2eField__theory_2eFEadd___24a3(Vvar__0__C__3758,Vvar__1___24Anonymous__3760,Vvar__2___24Anonymous__3762) = cCoq_2esetoid__ring_2eField__theory_2eFEadd___24a3(Vvar__0__C__3759,Vvar__1___24Anonymous__3761,Vvar__2___24Anonymous__3763)
     => ( Vvar__2___24Anonymous__3762 = Vvar__2___24Anonymous__3763
        & Vvar__1___24Anonymous__3760 = Vvar__1___24Anonymous__3761
        & Vvar__0__C__3758 = Vvar__0__C__3759 ) ) ).

fof('$_inj_Coq.setoid_ring.Field_theory.FEc',axiom,
    ! [Vvar__0__C__3750,Vvar__0__C__3751,Vvar__1___24Anonymous__3752,Vvar__1___24Anonymous__3753] :
      ( cCoq_2esetoid__ring_2eField__theory_2eFEc___24a2(Vvar__0__C__3750,Vvar__1___24Anonymous__3752) = cCoq_2esetoid__ring_2eField__theory_2eFEc___24a2(Vvar__0__C__3751,Vvar__1___24Anonymous__3753)
     => ( Vvar__1___24Anonymous__3752 = Vvar__1___24Anonymous__3753
        & Vvar__0__C__3750 = Vvar__0__C__3751 ) ) ).

fof('$_inj_Coq.setoid_ring.Field_theory.FEdiv',axiom,
    ! [Vvar__0__C__3784,Vvar__0__C__3785,Vvar__1___24Anonymous__3786,Vvar__1___24Anonymous__3787,Vvar__2___24Anonymous__3788,Vvar__2___24Anonymous__3789] :
      ( cCoq_2esetoid__ring_2eField__theory_2eFEdiv___24a3(Vvar__0__C__3784,Vvar__1___24Anonymous__3786,Vvar__2___24Anonymous__3788) = cCoq_2esetoid__ring_2eField__theory_2eFEdiv___24a3(Vvar__0__C__3785,Vvar__1___24Anonymous__3787,Vvar__2___24Anonymous__3789)
     => ( Vvar__2___24Anonymous__3788 = Vvar__2___24Anonymous__3789
        & Vvar__1___24Anonymous__3786 = Vvar__1___24Anonymous__3787
        & Vvar__0__C__3784 = Vvar__0__C__3785 ) ) ).

fof('$_inj_Coq.setoid_ring.Field_theory.FEinv',axiom,
    ! [Vvar__0__C__3780,Vvar__0__C__3781,Vvar__1___24Anonymous__3782,Vvar__1___24Anonymous__3783] :
      ( cCoq_2esetoid__ring_2eField__theory_2eFEinv___24a2(Vvar__0__C__3780,Vvar__1___24Anonymous__3782) = cCoq_2esetoid__ring_2eField__theory_2eFEinv___24a2(Vvar__0__C__3781,Vvar__1___24Anonymous__3783)
     => ( Vvar__1___24Anonymous__3782 = Vvar__1___24Anonymous__3783
        & Vvar__0__C__3780 = Vvar__0__C__3781 ) ) ).

fof('$_inj_Coq.setoid_ring.Field_theory.FEmul',axiom,
    ! [Vvar__0__C__3770,Vvar__0__C__3771,Vvar__1___24Anonymous__3772,Vvar__1___24Anonymous__3773,Vvar__2___24Anonymous__3774,Vvar__2___24Anonymous__3775] :
      ( cCoq_2esetoid__ring_2eField__theory_2eFEmul___24a3(Vvar__0__C__3770,Vvar__1___24Anonymous__3772,Vvar__2___24Anonymous__3774) = cCoq_2esetoid__ring_2eField__theory_2eFEmul___24a3(Vvar__0__C__3771,Vvar__1___24Anonymous__3773,Vvar__2___24Anonymous__3775)
     => ( Vvar__2___24Anonymous__3774 = Vvar__2___24Anonymous__3775
        & Vvar__1___24Anonymous__3772 = Vvar__1___24Anonymous__3773
        & Vvar__0__C__3770 = Vvar__0__C__3771 ) ) ).

fof('$_inj_Coq.setoid_ring.Field_theory.FEopp',axiom,
    ! [Vvar__0__C__3776,Vvar__0__C__3777,Vvar__1___24Anonymous__3778,Vvar__1___24Anonymous__3779] :
      ( cCoq_2esetoid__ring_2eField__theory_2eFEopp___24a2(Vvar__0__C__3776,Vvar__1___24Anonymous__3778) = cCoq_2esetoid__ring_2eField__theory_2eFEopp___24a2(Vvar__0__C__3777,Vvar__1___24Anonymous__3779)
     => ( Vvar__1___24Anonymous__3778 = Vvar__1___24Anonymous__3779
        & Vvar__0__C__3776 = Vvar__0__C__3777 ) ) ).

fof('$_inj_Coq.setoid_ring.Field_theory.FEpow',axiom,
    ! [Vvar__0__C__3790,Vvar__0__C__3791,Vvar__1___24Anonymous__3792,Vvar__1___24Anonymous__3793,Vvar__2___24Anonymous__3794,Vvar__2___24Anonymous__3795] :
      ( cCoq_2esetoid__ring_2eField__theory_2eFEpow___24a3(Vvar__0__C__3790,Vvar__1___24Anonymous__3792,Vvar__2___24Anonymous__3794) = cCoq_2esetoid__ring_2eField__theory_2eFEpow___24a3(Vvar__0__C__3791,Vvar__1___24Anonymous__3793,Vvar__2___24Anonymous__3795)
     => ( Vvar__2___24Anonymous__3794 = Vvar__2___24Anonymous__3795
        & Vvar__1___24Anonymous__3792 = Vvar__1___24Anonymous__3793
        & Vvar__0__C__3790 = Vvar__0__C__3791 ) ) ).

fof('$_inj_Coq.setoid_ring.Field_theory.FEsub',axiom,
    ! [Vvar__0__C__3764,Vvar__0__C__3765,Vvar__1___24Anonymous__3766,Vvar__1___24Anonymous__3767,Vvar__2___24Anonymous__3768,Vvar__2___24Anonymous__3769] :
      ( cCoq_2esetoid__ring_2eField__theory_2eFEsub___24a3(Vvar__0__C__3764,Vvar__1___24Anonymous__3766,Vvar__2___24Anonymous__3768) = cCoq_2esetoid__ring_2eField__theory_2eFEsub___24a3(Vvar__0__C__3765,Vvar__1___24Anonymous__3767,Vvar__2___24Anonymous__3769)
     => ( Vvar__2___24Anonymous__3768 = Vvar__2___24Anonymous__3769
        & Vvar__1___24Anonymous__3766 = Vvar__1___24Anonymous__3767
        & Vvar__0__C__3764 = Vvar__0__C__3765 ) ) ).

fof('$_inj_Coq.setoid_ring.Field_theory.mk_linear',axiom,
    ! [Vvar__0__C__4087,Vvar__0__C__4088,Vvar__1__num__4089,Vvar__1__num__4090,Vvar__2__denum__4091,Vvar__2__denum__4092,Vvar__3__condition__4093,Vvar__3__condition__4094] :
      ( cCoq_2esetoid__ring_2eField__theory_2emk__linear___24a4(Vvar__0__C__4087,Vvar__1__num__4089,Vvar__2__denum__4091,Vvar__3__condition__4093) = cCoq_2esetoid__ring_2eField__theory_2emk__linear___24a4(Vvar__0__C__4088,Vvar__1__num__4090,Vvar__2__denum__4092,Vvar__3__condition__4094)
     => ( Vvar__3__condition__4093 = Vvar__3__condition__4094
        & Vvar__2__denum__4091 = Vvar__2__denum__4092
        & Vvar__1__num__4089 = Vvar__1__num__4090
        & Vvar__0__C__4087 = Vvar__0__C__4088 ) ) ).

fof('$_inj_Coq.setoid_ring.Field_theory.mk_rsplit',axiom,
    ! [Vvar__0__C__1008,Vvar__0__C__1009,Vvar__1__rsplit__left__1010,Vvar__1__rsplit__left__1011,Vvar__2__rsplit__common__1012,Vvar__2__rsplit__common__1013,Vvar__3__rsplit__right__1014,Vvar__3__rsplit__right__1015] :
      ( cCoq_2esetoid__ring_2eField__theory_2emk__rsplit___24a4(Vvar__0__C__1008,Vvar__1__rsplit__left__1010,Vvar__2__rsplit__common__1012,Vvar__3__rsplit__right__1014) = cCoq_2esetoid__ring_2eField__theory_2emk__rsplit___24a4(Vvar__0__C__1009,Vvar__1__rsplit__left__1011,Vvar__2__rsplit__common__1013,Vvar__3__rsplit__right__1015)
     => ( Vvar__3__rsplit__right__1014 = Vvar__3__rsplit__right__1015
        & Vvar__2__rsplit__common__1012 = Vvar__2__rsplit__common__1013
        & Vvar__1__rsplit__left__1010 = Vvar__1__rsplit__left__1011
        & Vvar__0__C__1008 = Vvar__0__C__1009 ) ) ).

fof('$_inj_Coq.setoid_ring.InitialRing.mkhypo',axiom,
    ! [Vvar__0__hypo__type__109239,Vvar__0__hypo__type__109240,Vvar__1__hypo__proof__109241,Vvar__1__hypo__proof__109242] :
      ( cCoq_2esetoid__ring_2eInitialRing_2emkhypo___24a2(Vvar__0__hypo__type__109239,Vvar__1__hypo__proof__109241) = cCoq_2esetoid__ring_2eInitialRing_2emkhypo___24a2(Vvar__0__hypo__type__109240,Vvar__1__hypo__proof__109242)
     => ( Vvar__1__hypo__proof__109241 = Vvar__1__hypo__proof__109242
        & Vvar__0__hypo__type__109239 = Vvar__0__hypo__type__109240 ) ) ).

fof('$_inj_Coq.setoid_ring.Ring_polynom.PEI',axiom,
    ! [Vvar__0__C__5482,Vvar__0__C__5483] :
      ( cCoq_2esetoid__ring_2eRing__polynom_2ePEI___24a1(Vvar__0__C__5482) = cCoq_2esetoid__ring_2eRing__polynom_2ePEI___24a1(Vvar__0__C__5483)
     => Vvar__0__C__5482 = Vvar__0__C__5483 ) ).

fof('$_inj_Coq.setoid_ring.Ring_polynom.PEO',axiom,
    ! [Vvar__0__C__5480,Vvar__0__C__5481] :
      ( cCoq_2esetoid__ring_2eRing__polynom_2ePEO___24a1(Vvar__0__C__5480) = cCoq_2esetoid__ring_2eRing__polynom_2ePEO___24a1(Vvar__0__C__5481)
     => Vvar__0__C__5480 = Vvar__0__C__5481 ) ).

fof('$_inj_Coq.setoid_ring.Ring_polynom.PEX',axiom,
    ! [Vvar__0__C__5488,Vvar__0__C__5489,Vvar__1___24Anonymous__5490,Vvar__1___24Anonymous__5491] :
      ( cCoq_2esetoid__ring_2eRing__polynom_2ePEX___24a2(Vvar__0__C__5488,Vvar__1___24Anonymous__5490) = cCoq_2esetoid__ring_2eRing__polynom_2ePEX___24a2(Vvar__0__C__5489,Vvar__1___24Anonymous__5491)
     => ( Vvar__1___24Anonymous__5490 = Vvar__1___24Anonymous__5491
        & Vvar__0__C__5488 = Vvar__0__C__5489 ) ) ).

fof('$_inj_Coq.setoid_ring.Ring_polynom.PEadd',axiom,
    ! [Vvar__0__C__5492,Vvar__0__C__5493,Vvar__1___24Anonymous__5494,Vvar__1___24Anonymous__5495,Vvar__2___24Anonymous__5496,Vvar__2___24Anonymous__5497] :
      ( cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(Vvar__0__C__5492,Vvar__1___24Anonymous__5494,Vvar__2___24Anonymous__5496) = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(Vvar__0__C__5493,Vvar__1___24Anonymous__5495,Vvar__2___24Anonymous__5497)
     => ( Vvar__2___24Anonymous__5496 = Vvar__2___24Anonymous__5497
        & Vvar__1___24Anonymous__5494 = Vvar__1___24Anonymous__5495
        & Vvar__0__C__5492 = Vvar__0__C__5493 ) ) ).

fof('$_inj_Coq.setoid_ring.Ring_polynom.PEc',axiom,
    ! [Vvar__0__C__5484,Vvar__0__C__5485,Vvar__1___24Anonymous__5486,Vvar__1___24Anonymous__5487] :
      ( cCoq_2esetoid__ring_2eRing__polynom_2ePEc___24a2(Vvar__0__C__5484,Vvar__1___24Anonymous__5486) = cCoq_2esetoid__ring_2eRing__polynom_2ePEc___24a2(Vvar__0__C__5485,Vvar__1___24Anonymous__5487)
     => ( Vvar__1___24Anonymous__5486 = Vvar__1___24Anonymous__5487
        & Vvar__0__C__5484 = Vvar__0__C__5485 ) ) ).

fof('$_inj_Coq.setoid_ring.Ring_polynom.PEmul',axiom,
    ! [Vvar__0__C__5504,Vvar__0__C__5505,Vvar__1___24Anonymous__5506,Vvar__1___24Anonymous__5507,Vvar__2___24Anonymous__5508,Vvar__2___24Anonymous__5509] :
      ( cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(Vvar__0__C__5504,Vvar__1___24Anonymous__5506,Vvar__2___24Anonymous__5508) = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(Vvar__0__C__5505,Vvar__1___24Anonymous__5507,Vvar__2___24Anonymous__5509)
     => ( Vvar__2___24Anonymous__5508 = Vvar__2___24Anonymous__5509
        & Vvar__1___24Anonymous__5506 = Vvar__1___24Anonymous__5507
        & Vvar__0__C__5504 = Vvar__0__C__5505 ) ) ).

fof('$_inj_Coq.setoid_ring.Ring_polynom.PEopp',axiom,
    ! [Vvar__0__C__5510,Vvar__0__C__5511,Vvar__1___24Anonymous__5512,Vvar__1___24Anonymous__5513] :
      ( cCoq_2esetoid__ring_2eRing__polynom_2ePEopp___24a2(Vvar__0__C__5510,Vvar__1___24Anonymous__5512) = cCoq_2esetoid__ring_2eRing__polynom_2ePEopp___24a2(Vvar__0__C__5511,Vvar__1___24Anonymous__5513)
     => ( Vvar__1___24Anonymous__5512 = Vvar__1___24Anonymous__5513
        & Vvar__0__C__5510 = Vvar__0__C__5511 ) ) ).

fof('$_inj_Coq.setoid_ring.Ring_polynom.PEpow',axiom,
    ! [Vvar__0__C__5514,Vvar__0__C__5515,Vvar__1___24Anonymous__5516,Vvar__1___24Anonymous__5517,Vvar__2___24Anonymous__5518,Vvar__2___24Anonymous__5519] :
      ( cCoq_2esetoid__ring_2eRing__polynom_2ePEpow___24a3(Vvar__0__C__5514,Vvar__1___24Anonymous__5516,Vvar__2___24Anonymous__5518) = cCoq_2esetoid__ring_2eRing__polynom_2ePEpow___24a3(Vvar__0__C__5515,Vvar__1___24Anonymous__5517,Vvar__2___24Anonymous__5519)
     => ( Vvar__2___24Anonymous__5518 = Vvar__2___24Anonymous__5519
        & Vvar__1___24Anonymous__5516 = Vvar__1___24Anonymous__5517
        & Vvar__0__C__5514 = Vvar__0__C__5515 ) ) ).

fof('$_inj_Coq.setoid_ring.Ring_polynom.PEsub',axiom,
    ! [Vvar__0__C__5498,Vvar__0__C__5499,Vvar__1___24Anonymous__5500,Vvar__1___24Anonymous__5501,Vvar__2___24Anonymous__5502,Vvar__2___24Anonymous__5503] :
      ( cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(Vvar__0__C__5498,Vvar__1___24Anonymous__5500,Vvar__2___24Anonymous__5502) = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(Vvar__0__C__5499,Vvar__1___24Anonymous__5501,Vvar__2___24Anonymous__5503)
     => ( Vvar__2___24Anonymous__5502 = Vvar__2___24Anonymous__5503
        & Vvar__1___24Anonymous__5500 = Vvar__1___24Anonymous__5501
        & Vvar__0__C__5498 = Vvar__0__C__5499 ) ) ).

fof('$_inj_Coq.setoid_ring.Ring_polynom.PX',axiom,
    ! [Vvar__0__C__5199,Vvar__0__C__5200,Vvar__1___24Anonymous__5201,Vvar__1___24Anonymous__5202,Vvar__2___24Anonymous__5203,Vvar__2___24Anonymous__5204,Vvar__3___24Anonymous__5205,Vvar__3___24Anonymous__5206] :
      ( cCoq_2esetoid__ring_2eRing__polynom_2ePX___24a4(Vvar__0__C__5199,Vvar__1___24Anonymous__5201,Vvar__2___24Anonymous__5203,Vvar__3___24Anonymous__5205) = cCoq_2esetoid__ring_2eRing__polynom_2ePX___24a4(Vvar__0__C__5200,Vvar__1___24Anonymous__5202,Vvar__2___24Anonymous__5204,Vvar__3___24Anonymous__5206)
     => ( Vvar__3___24Anonymous__5205 = Vvar__3___24Anonymous__5206
        & Vvar__2___24Anonymous__5203 = Vvar__2___24Anonymous__5204
        & Vvar__1___24Anonymous__5201 = Vvar__1___24Anonymous__5202
        & Vvar__0__C__5199 = Vvar__0__C__5200 ) ) ).

fof('$_inj_Coq.setoid_ring.Ring_polynom.Pc',axiom,
    ! [Vvar__0__C__5189,Vvar__0__C__5190,Vvar__1___24Anonymous__5191,Vvar__1___24Anonymous__5192] :
      ( cCoq_2esetoid__ring_2eRing__polynom_2ePc___24a2(Vvar__0__C__5189,Vvar__1___24Anonymous__5191) = cCoq_2esetoid__ring_2eRing__polynom_2ePc___24a2(Vvar__0__C__5190,Vvar__1___24Anonymous__5192)
     => ( Vvar__1___24Anonymous__5191 = Vvar__1___24Anonymous__5192
        & Vvar__0__C__5189 = Vvar__0__C__5190 ) ) ).

fof('$_inj_Coq.setoid_ring.Ring_polynom.Pinj',axiom,
    ! [Vvar__0__C__5193,Vvar__0__C__5194,Vvar__1___24Anonymous__5195,Vvar__1___24Anonymous__5196,Vvar__2___24Anonymous__5197,Vvar__2___24Anonymous__5198] :
      ( cCoq_2esetoid__ring_2eRing__polynom_2ePinj___24a3(Vvar__0__C__5193,Vvar__1___24Anonymous__5195,Vvar__2___24Anonymous__5197) = cCoq_2esetoid__ring_2eRing__polynom_2ePinj___24a3(Vvar__0__C__5194,Vvar__1___24Anonymous__5196,Vvar__2___24Anonymous__5198)
     => ( Vvar__2___24Anonymous__5197 = Vvar__2___24Anonymous__5198
        & Vvar__1___24Anonymous__5195 = Vvar__1___24Anonymous__5196
        & Vvar__0__C__5193 = Vvar__0__C__5194 ) ) ).

fof('$_inj_Coq.setoid_ring.Ring_polynom.vmon',axiom,
    ! [Vvar__0___24Anonymous__5224,Vvar__0___24Anonymous__5225,Vvar__1___24Anonymous__5226,Vvar__1___24Anonymous__5227] :
      ( cCoq_2esetoid__ring_2eRing__polynom_2evmon___24a2(Vvar__0___24Anonymous__5224,Vvar__1___24Anonymous__5226) = cCoq_2esetoid__ring_2eRing__polynom_2evmon___24a2(Vvar__0___24Anonymous__5225,Vvar__1___24Anonymous__5227)
     => ( Vvar__1___24Anonymous__5226 = Vvar__1___24Anonymous__5227
        & Vvar__0___24Anonymous__5224 = Vvar__0___24Anonymous__5225 ) ) ).

fof('$_inj_Coq.setoid_ring.Ring_polynom.zmon',axiom,
    ! [Vvar__0___24Anonymous__5220,Vvar__0___24Anonymous__5221,Vvar__1___24Anonymous__5222,Vvar__1___24Anonymous__5223] :
      ( cCoq_2esetoid__ring_2eRing__polynom_2ezmon___24a2(Vvar__0___24Anonymous__5220,Vvar__1___24Anonymous__5222) = cCoq_2esetoid__ring_2eRing__polynom_2ezmon___24a2(Vvar__0___24Anonymous__5221,Vvar__1___24Anonymous__5223)
     => ( Vvar__1___24Anonymous__5222 = Vvar__1___24Anonymous__5223
        & Vvar__0___24Anonymous__5220 = Vvar__0___24Anonymous__5221 ) ) ).

fof('$_inj_Coq.setoid_ring.Ring_theory.Computational',axiom,
    ! [Vvar__0__R__112666,Vvar__0__R__112667,Vvar__1__req__112668,Vvar__1__req__112669,Vvar__2__reqb__112670,Vvar__2__reqb__112671,Vvar__3___24Anonymous__112672,Vvar__3___24Anonymous__112673] :
      ( cCoq_2esetoid__ring_2eRing__theory_2eComputational___24a3(Vvar__0__R__112666,Vvar__1__req__112668,Vvar__2__reqb__112670) = cCoq_2esetoid__ring_2eRing__theory_2eComputational___24a3(Vvar__0__R__112667,Vvar__1__req__112669,Vvar__2__reqb__112671)
     => ( c_24Proof = c_24Proof
        & Vvar__2__reqb__112670 = Vvar__2__reqb__112671
        & Vvar__1__req__112668 = Vvar__1__req__112669
        & Vvar__0__R__112666 = Vvar__0__R__112667 ) ) ).

fof('$_inj_Coq.setoid_ring.Ring_theory.Morphism',axiom,
    ! [Vvar__0__R__112674,Vvar__0__R__112675,Vvar__1__rO__112676,Vvar__1__rO__112677,Vvar__2__rI__112678,Vvar__2__rI__112679,Vvar__3__radd__112680,Vvar__3__radd__112681,Vvar__4__rmul__112682,Vvar__4__rmul__112683,Vvar__5__rsub__112684,Vvar__5__rsub__112685,Vvar__6__ropp__112686,Vvar__6__ropp__112687,Vvar__7__req__112688,Vvar__7__req__112689,Vvar__8__C__112690,Vvar__8__C__112691,Vvar__9__cO__112692,Vvar__9__cO__112693,Vvar__10__cI__112694,Vvar__10__cI__112695,Vvar__11__cadd__112696,Vvar__11__cadd__112697,Vvar__12__cmul__112698,Vvar__12__cmul__112699,Vvar__13__csub__112700,Vvar__13__csub__112701,Vvar__14__copp__112702,Vvar__14__copp__112703,Vvar__15__ceqb__112704,Vvar__15__ceqb__112705,Vvar__16__phi__112706,Vvar__16__phi__112707,Vvar__17___24Anonymous__112708,Vvar__17___24Anonymous__112709] :
      ( cCoq_2esetoid__ring_2eRing__theory_2eMorphism___24a17(Vvar__0__R__112674,Vvar__1__rO__112676,Vvar__2__rI__112678,Vvar__3__radd__112680,Vvar__4__rmul__112682,Vvar__5__rsub__112684,Vvar__6__ropp__112686,Vvar__7__req__112688,Vvar__8__C__112690,Vvar__9__cO__112692,Vvar__10__cI__112694,Vvar__11__cadd__112696,Vvar__12__cmul__112698,Vvar__13__csub__112700,Vvar__14__copp__112702,Vvar__15__ceqb__112704,Vvar__16__phi__112706) = cCoq_2esetoid__ring_2eRing__theory_2eMorphism___24a17(Vvar__0__R__112675,Vvar__1__rO__112677,Vvar__2__rI__112679,Vvar__3__radd__112681,Vvar__4__rmul__112683,Vvar__5__rsub__112685,Vvar__6__ropp__112687,Vvar__7__req__112689,Vvar__8__C__112691,Vvar__9__cO__112693,Vvar__10__cI__112695,Vvar__11__cadd__112697,Vvar__12__cmul__112699,Vvar__13__csub__112701,Vvar__14__copp__112703,Vvar__15__ceqb__112705,Vvar__16__phi__112707)
     => ( c_24Proof = c_24Proof
        & Vvar__16__phi__112706 = Vvar__16__phi__112707
        & Vvar__15__ceqb__112704 = Vvar__15__ceqb__112705
        & Vvar__14__copp__112702 = Vvar__14__copp__112703
        & Vvar__13__csub__112700 = Vvar__13__csub__112701
        & Vvar__12__cmul__112698 = Vvar__12__cmul__112699
        & Vvar__11__cadd__112696 = Vvar__11__cadd__112697
        & Vvar__10__cI__112694 = Vvar__10__cI__112695
        & Vvar__9__cO__112692 = Vvar__9__cO__112693
        & Vvar__8__C__112690 = Vvar__8__C__112691
        & Vvar__7__req__112688 = Vvar__7__req__112689
        & Vvar__6__ropp__112686 = Vvar__6__ropp__112687
        & Vvar__5__rsub__112684 = Vvar__5__rsub__112685
        & Vvar__4__rmul__112682 = Vvar__4__rmul__112683
        & Vvar__3__radd__112680 = Vvar__3__radd__112681
        & Vvar__2__rI__112678 = Vvar__2__rI__112679
        & Vvar__1__rO__112676 = Vvar__1__rO__112677
        & Vvar__0__R__112674 = Vvar__0__R__112675 ) ) ).

fof('$_inj_IntMap.Map.M0',axiom,
    ! [Vvar__0__A__54,Vvar__0__A__55] :
      ( cIntMap_2eMap_2eM0___24a1(Vvar__0__A__54) = cIntMap_2eMap_2eM0___24a1(Vvar__0__A__55)
     => Vvar__0__A__54 = Vvar__0__A__55 ) ).

fof('$_inj_IntMap.Map.M1',axiom,
    ! [Vvar__0__A__56,Vvar__0__A__57,Vvar__1___24Anonymous__58,Vvar__1___24Anonymous__59,Vvar__2___24Anonymous__60,Vvar__2___24Anonymous__61] :
      ( cIntMap_2eMap_2eM1___24a3(Vvar__0__A__56,Vvar__1___24Anonymous__58,Vvar__2___24Anonymous__60) = cIntMap_2eMap_2eM1___24a3(Vvar__0__A__57,Vvar__1___24Anonymous__59,Vvar__2___24Anonymous__61)
     => ( Vvar__2___24Anonymous__60 = Vvar__2___24Anonymous__61
        & Vvar__1___24Anonymous__58 = Vvar__1___24Anonymous__59
        & Vvar__0__A__56 = Vvar__0__A__57 ) ) ).

fof('$_inj_IntMap.Map.M2',axiom,
    ! [Vvar__0__A__62,Vvar__0__A__63,Vvar__1___24Anonymous__64,Vvar__1___24Anonymous__65,Vvar__2___24Anonymous__66,Vvar__2___24Anonymous__67] :
      ( cIntMap_2eMap_2eM2___24a3(Vvar__0__A__62,Vvar__1___24Anonymous__64,Vvar__2___24Anonymous__66) = cIntMap_2eMap_2eM2___24a3(Vvar__0__A__63,Vvar__1___24Anonymous__65,Vvar__2___24Anonymous__67)
     => ( Vvar__2___24Anonymous__66 = Vvar__2___24Anonymous__67
        & Vvar__1___24Anonymous__64 = Vvar__1___24Anonymous__65
        & Vvar__0__A__62 = Vvar__0__A__63 ) ) ).

fof('$_inversion_Coq.Arith.Between.P_nth',axiom,
    ! [Vvar__0__P__107464,Vvar__1__Q__107466,Vvar__2__init__107469,Vvar__3___24Anonymous__107470,Vvar__4___24Anonymous__107471] :
      ( c_24__type__107497___24t(Vvar__0__P__107464,Vvar__1__Q__107466,Vvar__2__init__107469,Vvar__3___24Anonymous__107470,Vvar__4___24Anonymous__107471,Vvar__0__P__107464)
     => ( c_24__type__107505___24t(Vvar__0__P__107464,Vvar__1__Q__107466,Vvar__2__init__107469,Vvar__3___24Anonymous__107470,Vvar__4___24Anonymous__107471,Vvar__1__Q__107466)
       => ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__2__init__107469)
         => ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__3___24Anonymous__107470)
           => ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__4___24Anonymous__107471)
             => ( cCoq_2eArith_2eBetween_2eP__nth___24a5(Vvar__0__P__107464,Vvar__1__Q__107466,Vvar__2__init__107469,Vvar__3___24Anonymous__107470,Vvar__4___24Anonymous__107471)
               => ( ( Vvar__4___24Anonymous__107471 = cCoq_2eInit_2eDatatypes_2eO
                    & Vvar__3___24Anonymous__107470 = Vvar__2__init__107469 )
                  | ? [Vvar__3__k__107485] :
                      ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__3__k__107485)
                      & ? [Vvar__4__l__107486] :
                          ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__4__l__107486)
                          & ? [Vvar__5__n__107487] :
                              ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__5__n__107487)
                              & cCoq_2eArith_2eBetween_2eP__nth___24a5(Vvar__0__P__107464,Vvar__1__Q__107466,Vvar__2__init__107469,Vvar__3__k__107485,Vvar__5__n__107487)
                              & cCoq_2eArith_2eBetween_2ebetween___24a3(Vvar__0__P__107464,cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__3__k__107485),Vvar__4__l__107486)
                              & p(happ(Vvar__1__Q__107466,Vvar__4__l__107486))
                              & Vvar__4___24Anonymous__107471 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__5__n__107487)
                              & Vvar__3___24Anonymous__107470 = Vvar__4__l__107486 ) ) ) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.Arith.Between.between',axiom,
    ! [Vvar__0__P__107424,Vvar__1__k__107426,Vvar__2___24Anonymous__107427] :
      ( c_24__type__107441___24t(Vvar__0__P__107424,Vvar__1__k__107426,Vvar__2___24Anonymous__107427,Vvar__0__P__107424)
     => ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__1__k__107426)
       => ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__2___24Anonymous__107427)
         => ( cCoq_2eArith_2eBetween_2ebetween___24a3(Vvar__0__P__107424,Vvar__1__k__107426,Vvar__2___24Anonymous__107427)
           => ( Vvar__2___24Anonymous__107427 = Vvar__1__k__107426
              | ? [Vvar__2__l__107435] :
                  ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__2__l__107435)
                  & cCoq_2eArith_2eBetween_2ebetween___24a3(Vvar__0__P__107424,Vvar__1__k__107426,Vvar__2__l__107435)
                  & p(happ(Vvar__0__P__107424,Vvar__2__l__107435))
                  & Vvar__2___24Anonymous__107427 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__2__l__107435) ) ) ) ) ) ) ).

fof('$_inversion_Coq.Arith.Between.exists_between',axiom,
    ! [Vvar__0__Q__107443,Vvar__1__k__107445,Vvar__2___24Anonymous__107446] :
      ( c_24__type__107462___24t(Vvar__0__Q__107443,Vvar__1__k__107445,Vvar__2___24Anonymous__107446,Vvar__0__Q__107443)
     => ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__1__k__107445)
       => ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__2___24Anonymous__107446)
         => ( cCoq_2eArith_2eBetween_2eexists__between___24a3(Vvar__0__Q__107443,Vvar__1__k__107445,Vvar__2___24Anonymous__107446)
           => ( ? [Vvar__2__l__107451] :
                  ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__2__l__107451)
                  & cCoq_2eArith_2eBetween_2eexists__between___24a3(Vvar__0__Q__107443,Vvar__1__k__107445,Vvar__2__l__107451)
                  & Vvar__2___24Anonymous__107446 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__2__l__107451) )
              | ? [Vvar__2__l__107456] :
                  ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__2__l__107456)
                  & cCoq_2eInit_2ePeano_2ele___24a2(Vvar__1__k__107445,Vvar__2__l__107456)
                  & p(happ(Vvar__0__Q__107443,Vvar__2__l__107456))
                  & Vvar__2___24Anonymous__107446 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__2__l__107456) ) ) ) ) ) ) ).

fof('$_inversion_Coq.Arith.Even.even',axiom,
    ! [Vvar__0___24Anonymous__107772] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__107772)
     => ( cCoq_2eArith_2eEven_2eeven___24a1(Vvar__0___24Anonymous__107772)
       => ( Vvar__0___24Anonymous__107772 = cCoq_2eInit_2eDatatypes_2eO
          | ? [Vvar__0__n__107774] :
              ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0__n__107774)
              & cCoq_2eArith_2eEven_2eodd___24a1(Vvar__0__n__107774)
              & Vvar__0___24Anonymous__107772 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0__n__107774) ) ) ) ) ).

fof('$_inversion_Coq.Arith.Even.odd',axiom,
    ! [Vvar__0___24Anonymous__107776] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__107776)
     => ( cCoq_2eArith_2eEven_2eodd___24a1(Vvar__0___24Anonymous__107776)
       => ? [Vvar__0__n__107778] :
            ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0__n__107778)
            & cCoq_2eArith_2eEven_2eeven___24a1(Vvar__0__n__107778)
            & Vvar__0___24Anonymous__107776 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0__n__107778) ) ) ) ).

fof('$_inversion_Coq.Bool.Bool.reflect',axiom,
    ! [Vvar__0__P__107516,Vvar__1___24Anonymous__107517,VX107518] :
      ( cProp___24t(Vvar__0__P__107516)
     => ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__1___24Anonymous__107517)
       => ( cCoq_2eBool_2eBool_2ereflect___24t(Vvar__0__P__107516,Vvar__1___24Anonymous__107517,VX107518)
         => ( ( p(Vvar__0__P__107516)
              & Vvar__1___24Anonymous__107517 = cCoq_2eInit_2eDatatypes_2etrue
              & VX107518 = cCoq_2eBool_2eBool_2eReflectT___24a1(Vvar__0__P__107516) )
            | ( ~ p(Vvar__0__P__107516)
              & Vvar__1___24Anonymous__107517 = cCoq_2eInit_2eDatatypes_2efalse
              & VX107518 = cCoq_2eBool_2eBool_2eReflectF___24a1(Vvar__0__P__107516) ) ) ) ) ) ).

fof('$_inversion_Coq.FSets.FSetPositive.PositiveSet.ct',axiom,
    ! [Vvar__0___24Anonymous__113749,Vvar__1___24Anonymous__113750,Vvar__2___24Anonymous__113751] :
      ( cCoq_2eInit_2eDatatypes_2ecomparison___24t(Vvar__0___24Anonymous__113749)
     => ( cCoq_2eInit_2eDatatypes_2ecomparison___24t(Vvar__1___24Anonymous__113750)
       => ( cCoq_2eInit_2eDatatypes_2ecomparison___24t(Vvar__2___24Anonymous__113751)
         => ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2ect___24a3(Vvar__0___24Anonymous__113749,Vvar__1___24Anonymous__113750,Vvar__2___24Anonymous__113751)
           => ( ? [Vvar__0__x__113753] :
                  ( cCoq_2eInit_2eDatatypes_2ecomparison___24t(Vvar__0__x__113753)
                  & Vvar__2___24Anonymous__113751 = Vvar__0__x__113753
                  & Vvar__1___24Anonymous__113750 = Vvar__0__x__113753
                  & Vvar__0___24Anonymous__113749 = Vvar__0__x__113753 )
              | ? [Vvar__0__x__113754] :
                  ( cCoq_2eInit_2eDatatypes_2ecomparison___24t(Vvar__0__x__113754)
                  & Vvar__2___24Anonymous__113751 = Vvar__0__x__113754
                  & Vvar__1___24Anonymous__113750 = cCoq_2eInit_2eDatatypes_2eEq
                  & Vvar__0___24Anonymous__113749 = Vvar__0__x__113754 )
              | ? [Vvar__0__x__113755] :
                  ( cCoq_2eInit_2eDatatypes_2ecomparison___24t(Vvar__0__x__113755)
                  & Vvar__2___24Anonymous__113751 = Vvar__0__x__113755
                  & Vvar__1___24Anonymous__113750 = Vvar__0__x__113755
                  & Vvar__0___24Anonymous__113749 = cCoq_2eInit_2eDatatypes_2eEq )
              | ? [Vvar__0__x__113756] :
                  ( cCoq_2eInit_2eDatatypes_2ecomparison___24t(Vvar__0__x__113756)
                  & Vvar__2___24Anonymous__113751 = Vvar__0__x__113756
                  & Vvar__1___24Anonymous__113750 = cCoq_2eInit_2eDatatypes_2eLt
                  & Vvar__0___24Anonymous__113749 = cCoq_2eInit_2eDatatypes_2eGt )
              | ? [Vvar__0__x__113757] :
                  ( cCoq_2eInit_2eDatatypes_2ecomparison___24t(Vvar__0__x__113757)
                  & Vvar__2___24Anonymous__113751 = Vvar__0__x__113757
                  & Vvar__1___24Anonymous__113750 = cCoq_2eInit_2eDatatypes_2eGt
                  & Vvar__0___24Anonymous__113749 = cCoq_2eInit_2eDatatypes_2eLt ) ) ) ) ) ) ).

fof('$_inversion_Coq.FSets.FSetPositive.PositiveSet.tree',axiom,
    ! [VX107101] :
      ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree___24t(VX107101)
     => ( VX107101 = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eLeaf
        | ? [Vvar__0___24Anonymous__107102] :
            ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree___24t(Vvar__0___24Anonymous__107102)
            & ? [Vvar__1___24Anonymous__107103] :
                ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__1___24Anonymous__107103)
                & ? [Vvar__2___24Anonymous__107104] :
                    ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree___24t(Vvar__2___24Anonymous__107104)
                    & VX107101 = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eNode___24a3(Vvar__0___24Anonymous__107102,Vvar__1___24Anonymous__107103,Vvar__2___24Anonymous__107104) ) ) ) ) ) ).

fof('$_inversion_Coq.Init.Byte.byte',axiom,
    ! [VX14047] :
      ( cCoq_2eInit_2eByte_2ebyte___24t(VX14047)
     => ( VX14047 = cCoq_2eInit_2eByte_2ex00
        | VX14047 = cCoq_2eInit_2eByte_2ex01
        | VX14047 = cCoq_2eInit_2eByte_2ex02
        | VX14047 = cCoq_2eInit_2eByte_2ex03
        | VX14047 = cCoq_2eInit_2eByte_2ex04
        | VX14047 = cCoq_2eInit_2eByte_2ex05
        | VX14047 = cCoq_2eInit_2eByte_2ex06
        | VX14047 = cCoq_2eInit_2eByte_2ex07
        | VX14047 = cCoq_2eInit_2eByte_2ex08
        | VX14047 = cCoq_2eInit_2eByte_2ex09
        | VX14047 = cCoq_2eInit_2eByte_2ex0a
        | VX14047 = cCoq_2eInit_2eByte_2ex0b
        | VX14047 = cCoq_2eInit_2eByte_2ex0c
        | VX14047 = cCoq_2eInit_2eByte_2ex0d
        | VX14047 = cCoq_2eInit_2eByte_2ex0e
        | VX14047 = cCoq_2eInit_2eByte_2ex0f
        | VX14047 = cCoq_2eInit_2eByte_2ex10
        | VX14047 = cCoq_2eInit_2eByte_2ex11
        | VX14047 = cCoq_2eInit_2eByte_2ex12
        | VX14047 = cCoq_2eInit_2eByte_2ex13
        | VX14047 = cCoq_2eInit_2eByte_2ex14
        | VX14047 = cCoq_2eInit_2eByte_2ex15
        | VX14047 = cCoq_2eInit_2eByte_2ex16
        | VX14047 = cCoq_2eInit_2eByte_2ex17
        | VX14047 = cCoq_2eInit_2eByte_2ex18
        | VX14047 = cCoq_2eInit_2eByte_2ex19
        | VX14047 = cCoq_2eInit_2eByte_2ex1a
        | VX14047 = cCoq_2eInit_2eByte_2ex1b
        | VX14047 = cCoq_2eInit_2eByte_2ex1c
        | VX14047 = cCoq_2eInit_2eByte_2ex1d
        | VX14047 = cCoq_2eInit_2eByte_2ex1e
        | VX14047 = cCoq_2eInit_2eByte_2ex1f
        | VX14047 = cCoq_2eInit_2eByte_2ex20
        | VX14047 = cCoq_2eInit_2eByte_2ex21
        | VX14047 = cCoq_2eInit_2eByte_2ex22
        | VX14047 = cCoq_2eInit_2eByte_2ex23
        | VX14047 = cCoq_2eInit_2eByte_2ex24
        | VX14047 = cCoq_2eInit_2eByte_2ex25
        | VX14047 = cCoq_2eInit_2eByte_2ex26
        | VX14047 = cCoq_2eInit_2eByte_2ex27
        | VX14047 = cCoq_2eInit_2eByte_2ex28
        | VX14047 = cCoq_2eInit_2eByte_2ex29
        | VX14047 = cCoq_2eInit_2eByte_2ex2a
        | VX14047 = cCoq_2eInit_2eByte_2ex2b
        | VX14047 = cCoq_2eInit_2eByte_2ex2c
        | VX14047 = cCoq_2eInit_2eByte_2ex2d
        | VX14047 = cCoq_2eInit_2eByte_2ex2e
        | VX14047 = cCoq_2eInit_2eByte_2ex2f
        | VX14047 = cCoq_2eInit_2eByte_2ex30
        | VX14047 = cCoq_2eInit_2eByte_2ex31
        | VX14047 = cCoq_2eInit_2eByte_2ex32
        | VX14047 = cCoq_2eInit_2eByte_2ex33
        | VX14047 = cCoq_2eInit_2eByte_2ex34
        | VX14047 = cCoq_2eInit_2eByte_2ex35
        | VX14047 = cCoq_2eInit_2eByte_2ex36
        | VX14047 = cCoq_2eInit_2eByte_2ex37
        | VX14047 = cCoq_2eInit_2eByte_2ex38
        | VX14047 = cCoq_2eInit_2eByte_2ex39
        | VX14047 = cCoq_2eInit_2eByte_2ex3a
        | VX14047 = cCoq_2eInit_2eByte_2ex3b
        | VX14047 = cCoq_2eInit_2eByte_2ex3c
        | VX14047 = cCoq_2eInit_2eByte_2ex3d
        | VX14047 = cCoq_2eInit_2eByte_2ex3e
        | VX14047 = cCoq_2eInit_2eByte_2ex3f
        | VX14047 = cCoq_2eInit_2eByte_2ex40
        | VX14047 = cCoq_2eInit_2eByte_2ex41
        | VX14047 = cCoq_2eInit_2eByte_2ex42
        | VX14047 = cCoq_2eInit_2eByte_2ex43
        | VX14047 = cCoq_2eInit_2eByte_2ex44
        | VX14047 = cCoq_2eInit_2eByte_2ex45
        | VX14047 = cCoq_2eInit_2eByte_2ex46
        | VX14047 = cCoq_2eInit_2eByte_2ex47
        | VX14047 = cCoq_2eInit_2eByte_2ex48
        | VX14047 = cCoq_2eInit_2eByte_2ex49
        | VX14047 = cCoq_2eInit_2eByte_2ex4a
        | VX14047 = cCoq_2eInit_2eByte_2ex4b
        | VX14047 = cCoq_2eInit_2eByte_2ex4c
        | VX14047 = cCoq_2eInit_2eByte_2ex4d
        | VX14047 = cCoq_2eInit_2eByte_2ex4e
        | VX14047 = cCoq_2eInit_2eByte_2ex4f
        | VX14047 = cCoq_2eInit_2eByte_2ex50
        | VX14047 = cCoq_2eInit_2eByte_2ex51
        | VX14047 = cCoq_2eInit_2eByte_2ex52
        | VX14047 = cCoq_2eInit_2eByte_2ex53
        | VX14047 = cCoq_2eInit_2eByte_2ex54
        | VX14047 = cCoq_2eInit_2eByte_2ex55
        | VX14047 = cCoq_2eInit_2eByte_2ex56
        | VX14047 = cCoq_2eInit_2eByte_2ex57
        | VX14047 = cCoq_2eInit_2eByte_2ex58
        | VX14047 = cCoq_2eInit_2eByte_2ex59
        | VX14047 = cCoq_2eInit_2eByte_2ex5a
        | VX14047 = cCoq_2eInit_2eByte_2ex5b
        | VX14047 = cCoq_2eInit_2eByte_2ex5c
        | VX14047 = cCoq_2eInit_2eByte_2ex5d
        | VX14047 = cCoq_2eInit_2eByte_2ex5e
        | VX14047 = cCoq_2eInit_2eByte_2ex5f
        | VX14047 = cCoq_2eInit_2eByte_2ex60
        | VX14047 = cCoq_2eInit_2eByte_2ex61
        | VX14047 = cCoq_2eInit_2eByte_2ex62
        | VX14047 = cCoq_2eInit_2eByte_2ex63
        | VX14047 = cCoq_2eInit_2eByte_2ex64
        | VX14047 = cCoq_2eInit_2eByte_2ex65
        | VX14047 = cCoq_2eInit_2eByte_2ex66
        | VX14047 = cCoq_2eInit_2eByte_2ex67
        | VX14047 = cCoq_2eInit_2eByte_2ex68
        | VX14047 = cCoq_2eInit_2eByte_2ex69
        | VX14047 = cCoq_2eInit_2eByte_2ex6a
        | VX14047 = cCoq_2eInit_2eByte_2ex6b
        | VX14047 = cCoq_2eInit_2eByte_2ex6c
        | VX14047 = cCoq_2eInit_2eByte_2ex6d
        | VX14047 = cCoq_2eInit_2eByte_2ex6e
        | VX14047 = cCoq_2eInit_2eByte_2ex6f
        | VX14047 = cCoq_2eInit_2eByte_2ex70
        | VX14047 = cCoq_2eInit_2eByte_2ex71
        | VX14047 = cCoq_2eInit_2eByte_2ex72
        | VX14047 = cCoq_2eInit_2eByte_2ex73
        | VX14047 = cCoq_2eInit_2eByte_2ex74
        | VX14047 = cCoq_2eInit_2eByte_2ex75
        | VX14047 = cCoq_2eInit_2eByte_2ex76
        | VX14047 = cCoq_2eInit_2eByte_2ex77
        | VX14047 = cCoq_2eInit_2eByte_2ex78
        | VX14047 = cCoq_2eInit_2eByte_2ex79
        | VX14047 = cCoq_2eInit_2eByte_2ex7a
        | VX14047 = cCoq_2eInit_2eByte_2ex7b
        | VX14047 = cCoq_2eInit_2eByte_2ex7c
        | VX14047 = cCoq_2eInit_2eByte_2ex7d
        | VX14047 = cCoq_2eInit_2eByte_2ex7e
        | VX14047 = cCoq_2eInit_2eByte_2ex7f
        | VX14047 = cCoq_2eInit_2eByte_2ex80
        | VX14047 = cCoq_2eInit_2eByte_2ex81
        | VX14047 = cCoq_2eInit_2eByte_2ex82
        | VX14047 = cCoq_2eInit_2eByte_2ex83
        | VX14047 = cCoq_2eInit_2eByte_2ex84
        | VX14047 = cCoq_2eInit_2eByte_2ex85
        | VX14047 = cCoq_2eInit_2eByte_2ex86
        | VX14047 = cCoq_2eInit_2eByte_2ex87
        | VX14047 = cCoq_2eInit_2eByte_2ex88
        | VX14047 = cCoq_2eInit_2eByte_2ex89
        | VX14047 = cCoq_2eInit_2eByte_2ex8a
        | VX14047 = cCoq_2eInit_2eByte_2ex8b
        | VX14047 = cCoq_2eInit_2eByte_2ex8c
        | VX14047 = cCoq_2eInit_2eByte_2ex8d
        | VX14047 = cCoq_2eInit_2eByte_2ex8e
        | VX14047 = cCoq_2eInit_2eByte_2ex8f
        | VX14047 = cCoq_2eInit_2eByte_2ex90
        | VX14047 = cCoq_2eInit_2eByte_2ex91
        | VX14047 = cCoq_2eInit_2eByte_2ex92
        | VX14047 = cCoq_2eInit_2eByte_2ex93
        | VX14047 = cCoq_2eInit_2eByte_2ex94
        | VX14047 = cCoq_2eInit_2eByte_2ex95
        | VX14047 = cCoq_2eInit_2eByte_2ex96
        | VX14047 = cCoq_2eInit_2eByte_2ex97
        | VX14047 = cCoq_2eInit_2eByte_2ex98
        | VX14047 = cCoq_2eInit_2eByte_2ex99
        | VX14047 = cCoq_2eInit_2eByte_2ex9a
        | VX14047 = cCoq_2eInit_2eByte_2ex9b
        | VX14047 = cCoq_2eInit_2eByte_2ex9c
        | VX14047 = cCoq_2eInit_2eByte_2ex9d
        | VX14047 = cCoq_2eInit_2eByte_2ex9e
        | VX14047 = cCoq_2eInit_2eByte_2ex9f
        | VX14047 = cCoq_2eInit_2eByte_2exa0
        | VX14047 = cCoq_2eInit_2eByte_2exa1
        | VX14047 = cCoq_2eInit_2eByte_2exa2
        | VX14047 = cCoq_2eInit_2eByte_2exa3
        | VX14047 = cCoq_2eInit_2eByte_2exa4
        | VX14047 = cCoq_2eInit_2eByte_2exa5
        | VX14047 = cCoq_2eInit_2eByte_2exa6
        | VX14047 = cCoq_2eInit_2eByte_2exa7
        | VX14047 = cCoq_2eInit_2eByte_2exa8
        | VX14047 = cCoq_2eInit_2eByte_2exa9
        | VX14047 = cCoq_2eInit_2eByte_2exaa
        | VX14047 = cCoq_2eInit_2eByte_2exab
        | VX14047 = cCoq_2eInit_2eByte_2exac
        | VX14047 = cCoq_2eInit_2eByte_2exad
        | VX14047 = cCoq_2eInit_2eByte_2exae
        | VX14047 = cCoq_2eInit_2eByte_2exaf
        | VX14047 = cCoq_2eInit_2eByte_2exb0
        | VX14047 = cCoq_2eInit_2eByte_2exb1
        | VX14047 = cCoq_2eInit_2eByte_2exb2
        | VX14047 = cCoq_2eInit_2eByte_2exb3
        | VX14047 = cCoq_2eInit_2eByte_2exb4
        | VX14047 = cCoq_2eInit_2eByte_2exb5
        | VX14047 = cCoq_2eInit_2eByte_2exb6
        | VX14047 = cCoq_2eInit_2eByte_2exb7
        | VX14047 = cCoq_2eInit_2eByte_2exb8
        | VX14047 = cCoq_2eInit_2eByte_2exb9
        | VX14047 = cCoq_2eInit_2eByte_2exba
        | VX14047 = cCoq_2eInit_2eByte_2exbb
        | VX14047 = cCoq_2eInit_2eByte_2exbc
        | VX14047 = cCoq_2eInit_2eByte_2exbd
        | VX14047 = cCoq_2eInit_2eByte_2exbe
        | VX14047 = cCoq_2eInit_2eByte_2exbf
        | VX14047 = cCoq_2eInit_2eByte_2exc0
        | VX14047 = cCoq_2eInit_2eByte_2exc1
        | VX14047 = cCoq_2eInit_2eByte_2exc2
        | VX14047 = cCoq_2eInit_2eByte_2exc3
        | VX14047 = cCoq_2eInit_2eByte_2exc4
        | VX14047 = cCoq_2eInit_2eByte_2exc5
        | VX14047 = cCoq_2eInit_2eByte_2exc6
        | VX14047 = cCoq_2eInit_2eByte_2exc7
        | VX14047 = cCoq_2eInit_2eByte_2exc8
        | VX14047 = cCoq_2eInit_2eByte_2exc9
        | VX14047 = cCoq_2eInit_2eByte_2exca
        | VX14047 = cCoq_2eInit_2eByte_2excb
        | VX14047 = cCoq_2eInit_2eByte_2excc
        | VX14047 = cCoq_2eInit_2eByte_2excd
        | VX14047 = cCoq_2eInit_2eByte_2exce
        | VX14047 = cCoq_2eInit_2eByte_2excf
        | VX14047 = cCoq_2eInit_2eByte_2exd0
        | VX14047 = cCoq_2eInit_2eByte_2exd1
        | VX14047 = cCoq_2eInit_2eByte_2exd2
        | VX14047 = cCoq_2eInit_2eByte_2exd3
        | VX14047 = cCoq_2eInit_2eByte_2exd4
        | VX14047 = cCoq_2eInit_2eByte_2exd5
        | VX14047 = cCoq_2eInit_2eByte_2exd6
        | VX14047 = cCoq_2eInit_2eByte_2exd7
        | VX14047 = cCoq_2eInit_2eByte_2exd8
        | VX14047 = cCoq_2eInit_2eByte_2exd9
        | VX14047 = cCoq_2eInit_2eByte_2exda
        | VX14047 = cCoq_2eInit_2eByte_2exdb
        | VX14047 = cCoq_2eInit_2eByte_2exdc
        | VX14047 = cCoq_2eInit_2eByte_2exdd
        | VX14047 = cCoq_2eInit_2eByte_2exde
        | VX14047 = cCoq_2eInit_2eByte_2exdf
        | VX14047 = cCoq_2eInit_2eByte_2exe0
        | VX14047 = cCoq_2eInit_2eByte_2exe1
        | VX14047 = cCoq_2eInit_2eByte_2exe2
        | VX14047 = cCoq_2eInit_2eByte_2exe3
        | VX14047 = cCoq_2eInit_2eByte_2exe4
        | VX14047 = cCoq_2eInit_2eByte_2exe5
        | VX14047 = cCoq_2eInit_2eByte_2exe6
        | VX14047 = cCoq_2eInit_2eByte_2exe7
        | VX14047 = cCoq_2eInit_2eByte_2exe8
        | VX14047 = cCoq_2eInit_2eByte_2exe9
        | VX14047 = cCoq_2eInit_2eByte_2exea
        | VX14047 = cCoq_2eInit_2eByte_2exeb
        | VX14047 = cCoq_2eInit_2eByte_2exec
        | VX14047 = cCoq_2eInit_2eByte_2exed
        | VX14047 = cCoq_2eInit_2eByte_2exee
        | VX14047 = cCoq_2eInit_2eByte_2exef
        | VX14047 = cCoq_2eInit_2eByte_2exf0
        | VX14047 = cCoq_2eInit_2eByte_2exf1
        | VX14047 = cCoq_2eInit_2eByte_2exf2
        | VX14047 = cCoq_2eInit_2eByte_2exf3
        | VX14047 = cCoq_2eInit_2eByte_2exf4
        | VX14047 = cCoq_2eInit_2eByte_2exf5
        | VX14047 = cCoq_2eInit_2eByte_2exf6
        | VX14047 = cCoq_2eInit_2eByte_2exf7
        | VX14047 = cCoq_2eInit_2eByte_2exf8
        | VX14047 = cCoq_2eInit_2eByte_2exf9
        | VX14047 = cCoq_2eInit_2eByte_2exfa
        | VX14047 = cCoq_2eInit_2eByte_2exfb
        | VX14047 = cCoq_2eInit_2eByte_2exfc
        | VX14047 = cCoq_2eInit_2eByte_2exfd
        | VX14047 = cCoq_2eInit_2eByte_2exfe
        | VX14047 = cCoq_2eInit_2eByte_2exff ) ) ).

fof('$_inversion_Coq.Init.Datatypes.BoolSpec',axiom,
    ! [Vvar__0__P__85491,Vvar__1__Q__85492,Vvar__2___24Anonymous__85493] :
      ( cProp___24t(Vvar__0__P__85491)
     => ( cProp___24t(Vvar__1__Q__85492)
       => ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__2___24Anonymous__85493)
         => ( cCoq_2eInit_2eDatatypes_2eBoolSpec___24a3(Vvar__0__P__85491,Vvar__1__Q__85492,Vvar__2___24Anonymous__85493)
           => ( ( p(Vvar__0__P__85491)
                & Vvar__2___24Anonymous__85493 = cCoq_2eInit_2eDatatypes_2etrue )
              | ( p(Vvar__1__Q__85492)
                & Vvar__2___24Anonymous__85493 = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ) ) ).

fof('$_inversion_Coq.Init.Datatypes.CompareSpec',axiom,
    ! [Vvar__0__Peq__107541,Vvar__1__Plt__107542,Vvar__2__Pgt__107543,Vvar__3___24Anonymous__107544] :
      ( cProp___24t(Vvar__0__Peq__107541)
     => ( cProp___24t(Vvar__1__Plt__107542)
       => ( cProp___24t(Vvar__2__Pgt__107543)
         => ( cCoq_2eInit_2eDatatypes_2ecomparison___24t(Vvar__3___24Anonymous__107544)
           => ( cCoq_2eInit_2eDatatypes_2eCompareSpec___24a4(Vvar__0__Peq__107541,Vvar__1__Plt__107542,Vvar__2__Pgt__107543,Vvar__3___24Anonymous__107544)
             => ( ( p(Vvar__0__Peq__107541)
                  & Vvar__3___24Anonymous__107544 = cCoq_2eInit_2eDatatypes_2eEq )
                | ( p(Vvar__1__Plt__107542)
                  & Vvar__3___24Anonymous__107544 = cCoq_2eInit_2eDatatypes_2eLt )
                | ( p(Vvar__2__Pgt__107543)
                  & Vvar__3___24Anonymous__107544 = cCoq_2eInit_2eDatatypes_2eGt ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.Init.Datatypes.CompareSpecT',axiom,
    ! [Vvar__0__Peq__107558,Vvar__1__Plt__107559,Vvar__2__Pgt__107560,Vvar__3___24Anonymous__107561,VX107562] :
      ( cProp___24t(Vvar__0__Peq__107558)
     => ( cProp___24t(Vvar__1__Plt__107559)
       => ( cProp___24t(Vvar__2__Pgt__107560)
         => ( cCoq_2eInit_2eDatatypes_2ecomparison___24t(Vvar__3___24Anonymous__107561)
           => ( cCoq_2eInit_2eDatatypes_2eCompareSpecT___24t(Vvar__0__Peq__107558,Vvar__1__Plt__107559,Vvar__2__Pgt__107560,Vvar__3___24Anonymous__107561,VX107562)
             => ( ( p(Vvar__0__Peq__107558)
                  & Vvar__3___24Anonymous__107561 = cCoq_2eInit_2eDatatypes_2eEq
                  & VX107562 = cCoq_2eInit_2eDatatypes_2eCompEqT___24a3(Vvar__0__Peq__107558,Vvar__1__Plt__107559,Vvar__2__Pgt__107560) )
                | ( p(Vvar__1__Plt__107559)
                  & Vvar__3___24Anonymous__107561 = cCoq_2eInit_2eDatatypes_2eLt
                  & VX107562 = cCoq_2eInit_2eDatatypes_2eCompLtT___24a3(Vvar__0__Peq__107558,Vvar__1__Plt__107559,Vvar__2__Pgt__107560) )
                | ( p(Vvar__2__Pgt__107560)
                  & Vvar__3___24Anonymous__107561 = cCoq_2eInit_2eDatatypes_2eGt
                  & VX107562 = cCoq_2eInit_2eDatatypes_2eCompGtT___24a3(Vvar__0__Peq__107558,Vvar__1__Plt__107559,Vvar__2__Pgt__107560) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.Init.Datatypes.bool',axiom,
    ! [VX8] :
      ( cCoq_2eInit_2eDatatypes_2ebool___24t(VX8)
     => ( VX8 = cCoq_2eInit_2eDatatypes_2etrue
        | VX8 = cCoq_2eInit_2eDatatypes_2efalse ) ) ).

fof('$_inversion_Coq.Init.Datatypes.comparison',axiom,
    ! [VX85572] :
      ( cCoq_2eInit_2eDatatypes_2ecomparison___24t(VX85572)
     => ( VX85572 = cCoq_2eInit_2eDatatypes_2eEq
        | VX85572 = cCoq_2eInit_2eDatatypes_2eLt
        | VX85572 = cCoq_2eInit_2eDatatypes_2eGt ) ) ).

fof('$_inversion_Coq.Init.Datatypes.eq_true',axiom,
    ! [Vvar__0___24Anonymous__107539] :
      ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__0___24Anonymous__107539)
     => ( cCoq_2eInit_2eDatatypes_2eeq__true___24a1(Vvar__0___24Anonymous__107539)
       => Vvar__0___24Anonymous__107539 = cCoq_2eInit_2eDatatypes_2etrue ) ) ).

fof('$_inversion_Coq.Init.Datatypes.identity',axiom,
    ! [Vvar__0__A__107631,Vvar__1__a__107632,Vvar__2___24Anonymous__107633] :
      ( cType___24t(Vvar__0__A__107631)
     => ( t(Vvar__1__a__107632,Vvar__0__A__107631)
       => ( t(Vvar__2___24Anonymous__107633,Vvar__0__A__107631)
         => ( cCoq_2eInit_2eDatatypes_2eidentity___24a3(Vvar__0__A__107631,Vvar__1__a__107632,Vvar__2___24Anonymous__107633)
           => Vvar__2___24Anonymous__107633 = Vvar__1__a__107632 ) ) ) ) ).

fof('$_inversion_Coq.Init.Datatypes.list',axiom,
    ! [Vvar__0__A__2612,VX2613] :
      ( cType___24t(Vvar__0__A__2612)
     => ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__2612,VX2613)
       => ( VX2613 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__2612)
          | ? [Vvar__1___24Anonymous__2616] :
              ( t(Vvar__1___24Anonymous__2616,Vvar__0__A__2612)
              & ? [Vvar__2___24Anonymous__2617] :
                  ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__2612,Vvar__2___24Anonymous__2617)
                  & VX2613 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__2612,Vvar__1___24Anonymous__2616,Vvar__2___24Anonymous__2617) ) ) ) ) ) ).

fof('$_inversion_Coq.Init.Datatypes.nat',axiom,
    ! [VX995] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(VX995)
     => ( VX995 = cCoq_2eInit_2eDatatypes_2eO
        | ? [Vvar__0___24Anonymous__996] :
            ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__996)
            & VX995 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__996) ) ) ) ).

fof('$_inversion_Coq.Init.Datatypes.option',axiom,
    ! [Vvar__0__A__9,VX10] :
      ( cType___24t(Vvar__0__A__9)
     => ( cCoq_2eInit_2eDatatypes_2eoption___24t(Vvar__0__A__9,VX10)
       => ( ? [Vvar__1___24Anonymous__12] :
              ( t(Vvar__1___24Anonymous__12,Vvar__0__A__9)
              & VX10 = cCoq_2eInit_2eDatatypes_2eSome___24a2(Vvar__0__A__9,Vvar__1___24Anonymous__12) )
          | VX10 = cCoq_2eInit_2eDatatypes_2eNone___24a1(Vvar__0__A__9) ) ) ) ).

fof('$_inversion_Coq.Init.Datatypes.prod',axiom,
    ! [Vvar__0__A__2588,Vvar__1__B__2589,VX2590] :
      ( cType___24t(Vvar__0__A__2588)
     => ( cType___24t(Vvar__1__B__2589)
       => ( cCoq_2eInit_2eDatatypes_2eprod___24t(Vvar__0__A__2588,Vvar__1__B__2589,VX2590)
         => ? [Vvar__2___24Anonymous__2593] :
              ( t(Vvar__2___24Anonymous__2593,Vvar__0__A__2588)
              & ? [Vvar__3___24Anonymous__2594] :
                  ( t(Vvar__3___24Anonymous__2594,Vvar__1__B__2589)
                  & VX2590 = cCoq_2eInit_2eDatatypes_2epair___24a4(Vvar__0__A__2588,Vvar__1__B__2589,Vvar__2___24Anonymous__2593,Vvar__3___24Anonymous__2594) ) ) ) ) ) ).

fof('$_inversion_Coq.Init.Datatypes.sum',axiom,
    ! [Vvar__0__A__2558,Vvar__1__B__2559,VX2560] :
      ( cType___24t(Vvar__0__A__2558)
     => ( cType___24t(Vvar__1__B__2559)
       => ( cCoq_2eInit_2eDatatypes_2esum___24t(Vvar__0__A__2558,Vvar__1__B__2559,VX2560)
         => ( ? [Vvar__2___24Anonymous__2563] :
                ( t(Vvar__2___24Anonymous__2563,Vvar__0__A__2558)
                & VX2560 = cCoq_2eInit_2eDatatypes_2einl___24a3(Vvar__0__A__2558,Vvar__1__B__2559,Vvar__2___24Anonymous__2563) )
            | ? [Vvar__2___24Anonymous__2566] :
                ( t(Vvar__2___24Anonymous__2566,Vvar__1__B__2559)
                & VX2560 = cCoq_2eInit_2eDatatypes_2einr___24a3(Vvar__0__A__2558,Vvar__1__B__2559,Vvar__2___24Anonymous__2566) ) ) ) ) ) ).

fof('$_inversion_Coq.Init.Datatypes.unit',axiom,
    ! [VX994] :
      ( cCoq_2eInit_2eDatatypes_2eunit___24t(VX994)
     => VX994 = cCoq_2eInit_2eDatatypes_2ett ) ).

fof('$_inversion_Coq.Init.Decimal.decimal',axiom,
    ! [VX107649] :
      ( cCoq_2eInit_2eDecimal_2edecimal___24t(VX107649)
     => ( ? [Vvar__0__i__107650] :
            ( cCoq_2eInit_2eDecimal_2eint___24t(Vvar__0__i__107650)
            & ? [Vvar__1__f__107651] :
                ( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__1__f__107651)
                & VX107649 = cCoq_2eInit_2eDecimal_2eDecimal___24a2(Vvar__0__i__107650,Vvar__1__f__107651) ) )
        | ? [Vvar__0__i__107652] :
            ( cCoq_2eInit_2eDecimal_2eint___24t(Vvar__0__i__107652)
            & ? [Vvar__1__f__107653] :
                ( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__1__f__107653)
                & ? [Vvar__2__e__107654] :
                    ( cCoq_2eInit_2eDecimal_2eint___24t(Vvar__2__e__107654)
                    & VX107649 = cCoq_2eInit_2eDecimal_2eDecimalExp___24a3(Vvar__0__i__107652,Vvar__1__f__107653,Vvar__2__e__107654) ) ) ) ) ) ).

fof('$_inversion_Coq.Init.Decimal.int',axiom,
    ! [VX107640] :
      ( cCoq_2eInit_2eDecimal_2eint___24t(VX107640)
     => ( ? [Vvar__0__d__107641] :
            ( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0__d__107641)
            & VX107640 = cCoq_2eInit_2eDecimal_2ePos___24a1(Vvar__0__d__107641) )
        | ? [Vvar__0__d__107642] :
            ( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0__d__107642)
            & VX107640 = cCoq_2eInit_2eDecimal_2eNeg___24a1(Vvar__0__d__107642) ) ) ) ).

fof('$_inversion_Coq.Init.Decimal.uint',axiom,
    ! [VX85574] :
      ( cCoq_2eInit_2eDecimal_2euint___24t(VX85574)
     => ( VX85574 = cCoq_2eInit_2eDecimal_2eNil
        | ? [Vvar__0___24Anonymous__85575] :
            ( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0___24Anonymous__85575)
            & VX85574 = cCoq_2eInit_2eDecimal_2eD0___24a1(Vvar__0___24Anonymous__85575) )
        | ? [Vvar__0___24Anonymous__85576] :
            ( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0___24Anonymous__85576)
            & VX85574 = cCoq_2eInit_2eDecimal_2eD1___24a1(Vvar__0___24Anonymous__85576) )
        | ? [Vvar__0___24Anonymous__85577] :
            ( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0___24Anonymous__85577)
            & VX85574 = cCoq_2eInit_2eDecimal_2eD2___24a1(Vvar__0___24Anonymous__85577) )
        | ? [Vvar__0___24Anonymous__85578] :
            ( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0___24Anonymous__85578)
            & VX85574 = cCoq_2eInit_2eDecimal_2eD3___24a1(Vvar__0___24Anonymous__85578) )
        | ? [Vvar__0___24Anonymous__85579] :
            ( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0___24Anonymous__85579)
            & VX85574 = cCoq_2eInit_2eDecimal_2eD4___24a1(Vvar__0___24Anonymous__85579) )
        | ? [Vvar__0___24Anonymous__85580] :
            ( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0___24Anonymous__85580)
            & VX85574 = cCoq_2eInit_2eDecimal_2eD5___24a1(Vvar__0___24Anonymous__85580) )
        | ? [Vvar__0___24Anonymous__85581] :
            ( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0___24Anonymous__85581)
            & VX85574 = cCoq_2eInit_2eDecimal_2eD6___24a1(Vvar__0___24Anonymous__85581) )
        | ? [Vvar__0___24Anonymous__85582] :
            ( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0___24Anonymous__85582)
            & VX85574 = cCoq_2eInit_2eDecimal_2eD7___24a1(Vvar__0___24Anonymous__85582) )
        | ? [Vvar__0___24Anonymous__85583] :
            ( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0___24Anonymous__85583)
            & VX85574 = cCoq_2eInit_2eDecimal_2eD8___24a1(Vvar__0___24Anonymous__85583) )
        | ? [Vvar__0___24Anonymous__85584] :
            ( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0___24Anonymous__85584)
            & VX85574 = cCoq_2eInit_2eDecimal_2eD9___24a1(Vvar__0___24Anonymous__85584) ) ) ) ).

fof('$_inversion_Coq.Init.Peano.le',axiom,
    ! [Vvar__0__n__5083,Vvar__1___24Anonymous__5084] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0__n__5083)
     => ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__1___24Anonymous__5084)
       => ( cCoq_2eInit_2ePeano_2ele___24a2(Vvar__0__n__5083,Vvar__1___24Anonymous__5084)
         => ( Vvar__1___24Anonymous__5084 = Vvar__0__n__5083
            | ? [Vvar__1__m__5088] :
                ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__1__m__5088)
                & cCoq_2eInit_2ePeano_2ele___24a2(Vvar__0__n__5083,Vvar__1__m__5088)
                & Vvar__1___24Anonymous__5084 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__1__m__5088) ) ) ) ) ) ).

fof('$_inversion_Coq.Init.Specif.sig',axiom,
    ! [Vvar__0__A__1979,Vvar__1__P__1980,VX1983] :
      ( cType___24t(Vvar__0__A__1979)
     => ( c_24__type__1993___24t(Vvar__0__A__1979,Vvar__1__P__1980,Vvar__1__P__1980)
       => ( cCoq_2eInit_2eSpecif_2esig___24t(Vvar__0__A__1979,Vvar__1__P__1980,VX1983)
         => ? [Vvar__2__x__1988] :
              ( t(Vvar__2__x__1988,Vvar__0__A__1979)
              & p(happ(Vvar__1__P__1980,Vvar__2__x__1988))
              & VX1983 = cCoq_2eInit_2eSpecif_2eexist___24a3(Vvar__0__A__1979,Vvar__1__P__1980,Vvar__2__x__1988) ) ) ) ) ).

fof('$_inversion_Coq.Init.Specif.sig2',axiom,
    ! [Vvar__0__A__113032,Vvar__1__P__113033,Vvar__2__Q__113036,VX113039] :
      ( cType___24t(Vvar__0__A__113032)
     => ( c_24__type__113056___24t(Vvar__0__A__113032,Vvar__1__P__113033,Vvar__2__Q__113036,Vvar__1__P__113033)
       => ( c_24__type__113064___24t(Vvar__0__A__113032,Vvar__1__P__113033,Vvar__2__Q__113036,Vvar__2__Q__113036)
         => ( cCoq_2eInit_2eSpecif_2esig2___24t(Vvar__0__A__113032,Vvar__1__P__113033,Vvar__2__Q__113036,VX113039)
           => ? [Vvar__3__x__113047] :
                ( t(Vvar__3__x__113047,Vvar__0__A__113032)
                & p(happ(Vvar__1__P__113033,Vvar__3__x__113047))
                & p(happ(Vvar__2__Q__113036,Vvar__3__x__113047))
                & VX113039 = cCoq_2eInit_2eSpecif_2eexist2___24a4(Vvar__0__A__113032,Vvar__1__P__113033,Vvar__2__Q__113036,Vvar__3__x__113047) ) ) ) ) ) ).

fof('$_inversion_Coq.Init.Specif.sigT',axiom,
    ! [Vvar__0__A__113088,Vvar__1__P__113089,VX113092] :
      ( cType___24t(Vvar__0__A__113088)
     => ( c_24__type__113102___24t(Vvar__0__A__113088,Vvar__1__P__113089,Vvar__1__P__113089)
       => ( cCoq_2eInit_2eSpecif_2esigT___24t(Vvar__0__A__113088,Vvar__1__P__113089,VX113092)
         => ? [Vvar__2__x__113097] :
              ( t(Vvar__2__x__113097,Vvar__0__A__113088)
              & ? [Vvar__3___24Anonymous__113098] :
                  ( t(Vvar__3___24Anonymous__113098,happ(Vvar__1__P__113089,Vvar__2__x__113097))
                  & VX113092 = cCoq_2eInit_2eSpecif_2eexistT___24a4(Vvar__0__A__113088,Vvar__1__P__113089,Vvar__2__x__113097,Vvar__3___24Anonymous__113098) ) ) ) ) ) ).

fof('$_inversion_Coq.Init.Specif.sigT2',axiom,
    ! [Vvar__0__A__113119,Vvar__1__P__113120,Vvar__2__Q__113123,VX113126] :
      ( cType___24t(Vvar__0__A__113119)
     => ( c_24__type__113143___24t(Vvar__0__A__113119,Vvar__1__P__113120,Vvar__2__Q__113123,Vvar__1__P__113120)
       => ( c_24__type__113151___24t(Vvar__0__A__113119,Vvar__1__P__113120,Vvar__2__Q__113123,Vvar__2__Q__113123)
         => ( cCoq_2eInit_2eSpecif_2esigT2___24t(Vvar__0__A__113119,Vvar__1__P__113120,Vvar__2__Q__113123,VX113126)
           => ? [Vvar__3__x__113134] :
                ( t(Vvar__3__x__113134,Vvar__0__A__113119)
                & ? [Vvar__4___24Anonymous__113135] :
                    ( t(Vvar__4___24Anonymous__113135,happ(Vvar__1__P__113120,Vvar__3__x__113134))
                    & ? [Vvar__5___24Anonymous__113136] :
                        ( t(Vvar__5___24Anonymous__113136,happ(Vvar__2__Q__113123,Vvar__3__x__113134))
                        & VX113126 = cCoq_2eInit_2eSpecif_2eexistT2___24a6(Vvar__0__A__113119,Vvar__1__P__113120,Vvar__2__Q__113123,Vvar__3__x__113134,Vvar__4___24Anonymous__113135,Vvar__5___24Anonymous__113136) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.Init.Specif.sumbool',axiom,
    ! [Vvar__0__A__250,Vvar__1__B__251,VX252] :
      ( cProp___24t(Vvar__0__A__250)
     => ( cProp___24t(Vvar__1__B__251)
       => ( cCoq_2eInit_2eSpecif_2esumbool___24t(Vvar__0__A__250,Vvar__1__B__251,VX252)
         => ( ( p(Vvar__0__A__250)
              & VX252 = cCoq_2eInit_2eSpecif_2eleft___24a2(Vvar__0__A__250,Vvar__1__B__251) )
            | ( p(Vvar__1__B__251)
              & VX252 = cCoq_2eInit_2eSpecif_2eright___24a2(Vvar__0__A__250,Vvar__1__B__251) ) ) ) ) ) ).

fof('$_inversion_Coq.Init.Specif.sumor',axiom,
    ! [Vvar__0__A__2018,Vvar__1__B__2019,VX2020] :
      ( cType___24t(Vvar__0__A__2018)
     => ( cProp___24t(Vvar__1__B__2019)
       => ( cCoq_2eInit_2eSpecif_2esumor___24t(Vvar__0__A__2018,Vvar__1__B__2019,VX2020)
         => ( ? [Vvar__2___24Anonymous__2023] :
                ( t(Vvar__2___24Anonymous__2023,Vvar__0__A__2018)
                & VX2020 = cCoq_2eInit_2eSpecif_2einleft___24a3(Vvar__0__A__2018,Vvar__1__B__2019,Vvar__2___24Anonymous__2023) )
            | ( p(Vvar__1__B__2019)
              & VX2020 = cCoq_2eInit_2eSpecif_2einright___24a2(Vvar__0__A__2018,Vvar__1__B__2019) ) ) ) ) ) ).

fof('$_inversion_Coq.Init.Wf.Acc',axiom,
    ! [Vvar__0__A__113249,Vvar__1__R__113250,Vvar__2__x__113255] :
      ( cType___24t(Vvar__0__A__113249)
     => ( c_24__type__113284___24t(Vvar__0__A__113249,Vvar__1__R__113250,Vvar__2__x__113255,Vvar__1__R__113250)
       => ( t(Vvar__2__x__113255,Vvar__0__A__113249)
         => ( cCoq_2eInit_2eWf_2eAcc___24a3(Vvar__0__A__113249,Vvar__1__R__113250,Vvar__2__x__113255)
           => ( ! [Vvar__var__var__var__var__3__y__113265__113267__113269__113271__113273] :
                  ( t(Vvar__var__var__var__var__3__y__113265__113267__113269__113271__113273,Vvar__0__A__113249)
                 => ( p(happ(happ(Vvar__1__R__113250,Vvar__var__var__var__var__3__y__113265__113267__113269__113271__113273),Vvar__2__x__113255))
                   => cCoq_2eInit_2eWf_2eAcc___24a3(Vvar__0__A__113249,Vvar__1__R__113250,Vvar__var__var__var__var__3__y__113265__113267__113269__113271__113273) ) )
              & p(c_24True) ) ) ) ) ) ).

fof('$_inversion_Coq.Lists.List.Add',axiom,
    ! [Vvar__0__A__120950,Vvar__1__a__120951,Vvar__2___24Anonymous__120952,Vvar__3___24Anonymous__120953] :
      ( cType___24t(Vvar__0__A__120950)
     => ( t(Vvar__1__a__120951,Vvar__0__A__120950)
       => ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__120950,Vvar__2___24Anonymous__120952)
         => ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__120950,Vvar__3___24Anonymous__120953)
           => ( cCoq_2eLists_2eList_2eAdd___24a4(Vvar__0__A__120950,Vvar__1__a__120951,Vvar__2___24Anonymous__120952,Vvar__3___24Anonymous__120953)
             => ( ? [Vvar__2__l__120957] :
                    ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__120950,Vvar__2__l__120957)
                    & Vvar__3___24Anonymous__120953 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__120950,Vvar__1__a__120951,Vvar__2__l__120957)
                    & Vvar__2___24Anonymous__120952 = Vvar__2__l__120957 )
                | ? [Vvar__2__x__120960] :
                    ( t(Vvar__2__x__120960,Vvar__0__A__120950)
                    & ? [Vvar__3__l__120961] :
                        ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__120950,Vvar__3__l__120961)
                        & ? [Vvar__4__l_27__120962] :
                            ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__120950,Vvar__4__l_27__120962)
                            & cCoq_2eLists_2eList_2eAdd___24a4(Vvar__0__A__120950,Vvar__1__a__120951,Vvar__3__l__120961,Vvar__4__l_27__120962)
                            & Vvar__3___24Anonymous__120953 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__120950,Vvar__2__x__120960,Vvar__4__l_27__120962)
                            & Vvar__2___24Anonymous__120952 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__120950,Vvar__2__x__120960,Vvar__3__l__120961) ) ) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.Lists.List.Exists',axiom,
    ! [Vvar__0__A__109272,Vvar__1__P__109273,Vvar__2___24Anonymous__109276] :
      ( cType___24t(Vvar__0__A__109272)
     => ( c_24__type__109296___24t(Vvar__0__A__109272,Vvar__1__P__109273,Vvar__2___24Anonymous__109276,Vvar__1__P__109273)
       => ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__109272,Vvar__2___24Anonymous__109276)
         => ( cCoq_2eLists_2eList_2eExists___24a3(Vvar__0__A__109272,Vvar__1__P__109273,Vvar__2___24Anonymous__109276)
           => ( ? [Vvar__2__x__109282] :
                  ( t(Vvar__2__x__109282,Vvar__0__A__109272)
                  & ? [Vvar__3__l__109283] :
                      ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__109272,Vvar__3__l__109283)
                      & p(happ(Vvar__1__P__109273,Vvar__2__x__109282))
                      & Vvar__2___24Anonymous__109276 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__109272,Vvar__2__x__109282,Vvar__3__l__109283) ) )
              | ? [Vvar__2__x__109289] :
                  ( t(Vvar__2__x__109289,Vvar__0__A__109272)
                  & ? [Vvar__3__l__109290] :
                      ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__109272,Vvar__3__l__109290)
                      & cCoq_2eLists_2eList_2eExists___24a3(Vvar__0__A__109272,Vvar__1__P__109273,Vvar__3__l__109290)
                      & Vvar__2___24Anonymous__109276 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__109272,Vvar__2__x__109289,Vvar__3__l__109290) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.Lists.List.Forall',axiom,
    ! [Vvar__0__A__109298,Vvar__1__P__109299,Vvar__2___24Anonymous__109302] :
      ( cType___24t(Vvar__0__A__109298)
     => ( c_24__type__109320___24t(Vvar__0__A__109298,Vvar__1__P__109299,Vvar__2___24Anonymous__109302,Vvar__1__P__109299)
       => ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__109298,Vvar__2___24Anonymous__109302)
         => ( cCoq_2eLists_2eList_2eForall___24a3(Vvar__0__A__109298,Vvar__1__P__109299,Vvar__2___24Anonymous__109302)
           => ( Vvar__2___24Anonymous__109302 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__109298)
              | ? [Vvar__2__x__109312] :
                  ( t(Vvar__2__x__109312,Vvar__0__A__109298)
                  & ? [Vvar__3__l__109313] :
                      ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__109298,Vvar__3__l__109313)
                      & p(happ(Vvar__1__P__109299,Vvar__2__x__109312))
                      & cCoq_2eLists_2eList_2eForall___24a3(Vvar__0__A__109298,Vvar__1__P__109299,Vvar__3__l__109313)
                      & Vvar__2___24Anonymous__109302 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__109298,Vvar__2__x__109312,Vvar__3__l__109313) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.Lists.List.Forall2',axiom,
    ! [Vvar__0__A__109322,Vvar__1__B__109323,Vvar__2__R__109324,Vvar__3___24Anonymous__109329,Vvar__4___24Anonymous__109330] :
      ( cType___24t(Vvar__0__A__109322)
     => ( cType___24t(Vvar__1__B__109323)
       => ( c_24__type__109367___24t(Vvar__0__A__109322,Vvar__1__B__109323,Vvar__2__R__109324,Vvar__3___24Anonymous__109329,Vvar__4___24Anonymous__109330,Vvar__2__R__109324)
         => ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__109322,Vvar__3___24Anonymous__109329)
           => ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__1__B__109323,Vvar__4___24Anonymous__109330)
             => ( cCoq_2eLists_2eList_2eForall2___24a5(Vvar__0__A__109322,Vvar__1__B__109323,Vvar__2__R__109324,Vvar__3___24Anonymous__109329,Vvar__4___24Anonymous__109330)
               => ( ( Vvar__4___24Anonymous__109330 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__1__B__109323)
                    & Vvar__3___24Anonymous__109329 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__109322) )
                  | ? [Vvar__3__x__109346] :
                      ( t(Vvar__3__x__109346,Vvar__0__A__109322)
                      & ? [Vvar__4__y__109347] :
                          ( t(Vvar__4__y__109347,Vvar__1__B__109323)
                          & ? [Vvar__5__l__109348] :
                              ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__109322,Vvar__5__l__109348)
                              & ? [Vvar__6__l_27__109349] :
                                  ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__1__B__109323,Vvar__6__l_27__109349)
                                  & p(happ(happ(Vvar__2__R__109324,Vvar__3__x__109346),Vvar__4__y__109347))
                                  & cCoq_2eLists_2eList_2eForall2___24a5(Vvar__0__A__109322,Vvar__1__B__109323,Vvar__2__R__109324,Vvar__5__l__109348,Vvar__6__l_27__109349)
                                  & Vvar__4___24Anonymous__109330 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__1__B__109323,Vvar__4__y__109347,Vvar__6__l_27__109349)
                                  & Vvar__3___24Anonymous__109329 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__109322,Vvar__3__x__109346,Vvar__5__l__109348) ) ) ) ) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.Lists.List.ForallOrdPairs',axiom,
    ! [Vvar__0__A__109369,Vvar__1__R__109370,Vvar__2___24Anonymous__109375] :
      ( cType___24t(Vvar__0__A__109369)
     => ( c_24__type__109402___24t(Vvar__0__A__109369,Vvar__1__R__109370,Vvar__2___24Anonymous__109375,Vvar__1__R__109370)
       => ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__109369,Vvar__2___24Anonymous__109375)
         => ( cCoq_2eLists_2eList_2eForallOrdPairs___24a3(Vvar__0__A__109369,Vvar__1__R__109370,Vvar__2___24Anonymous__109375)
           => ( Vvar__2___24Anonymous__109375 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__109369)
              | ? [Vvar__2__a__109389] :
                  ( t(Vvar__2__a__109389,Vvar__0__A__109369)
                  & ? [Vvar__3__l__109390] :
                      ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__109369,Vvar__3__l__109390)
                      & cCoq_2eLists_2eList_2eForall___24a3(Vvar__0__A__109369,happ(Vvar__1__R__109370,Vvar__2__a__109389),Vvar__3__l__109390)
                      & cCoq_2eLists_2eList_2eForallOrdPairs___24a3(Vvar__0__A__109369,Vvar__1__R__109370,Vvar__3__l__109390)
                      & Vvar__2___24Anonymous__109375 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__109369,Vvar__2__a__109389,Vvar__3__l__109390) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.Lists.List.NoDup',axiom,
    ! [Vvar__0__A__5068,Vvar__1___24Anonymous__5069] :
      ( cType___24t(Vvar__0__A__5068)
     => ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__5068,Vvar__1___24Anonymous__5069)
       => ( cCoq_2eLists_2eList_2eNoDup___24a2(Vvar__0__A__5068,Vvar__1___24Anonymous__5069)
         => ( Vvar__1___24Anonymous__5069 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__5068)
            | ? [Vvar__1__x__5073] :
                ( t(Vvar__1__x__5073,Vvar__0__A__5068)
                & ? [Vvar__2__l__5074] :
                    ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__5068,Vvar__2__l__5074)
                    & ~ cCoq_2eLists_2eList_2eIn___24a3(Vvar__0__A__5068,Vvar__1__x__5073,Vvar__2__l__5074)
                    & cCoq_2eLists_2eList_2eNoDup___24a2(Vvar__0__A__5068,Vvar__2__l__5074)
                    & Vvar__1___24Anonymous__5069 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__5068,Vvar__1__x__5073,Vvar__2__l__5074) ) ) ) ) ) ) ).

fof('$_inversion_Coq.Lists.SetoidList.InA',axiom,
    ! [Vvar__0__A__104000,Vvar__1__eqA__104001,Vvar__2__x__104006,Vvar__3___24Anonymous__104007] :
      ( cType___24t(Vvar__0__A__104000)
     => ( c_24__type__104040___24t(Vvar__0__A__104000,Vvar__1__eqA__104001,Vvar__2__x__104006,Vvar__3___24Anonymous__104007,Vvar__1__eqA__104001)
       => ( t(Vvar__2__x__104006,Vvar__0__A__104000)
         => ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__104000,Vvar__3___24Anonymous__104007)
           => ( cCoq_2eLists_2eSetoidList_2eInA___24a4(Vvar__0__A__104000,Vvar__1__eqA__104001,Vvar__2__x__104006,Vvar__3___24Anonymous__104007)
             => ( ? [Vvar__3__y__104016] :
                    ( t(Vvar__3__y__104016,Vvar__0__A__104000)
                    & ? [Vvar__4__l__104017] :
                        ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__104000,Vvar__4__l__104017)
                        & p(happ(happ(Vvar__1__eqA__104001,Vvar__2__x__104006),Vvar__3__y__104016))
                        & Vvar__3___24Anonymous__104007 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__104000,Vvar__3__y__104016,Vvar__4__l__104017) ) )
                | ? [Vvar__3__y__104026] :
                    ( t(Vvar__3__y__104026,Vvar__0__A__104000)
                    & ? [Vvar__4__l__104027] :
                        ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__104000,Vvar__4__l__104027)
                        & cCoq_2eLists_2eSetoidList_2eInA___24a4(Vvar__0__A__104000,Vvar__1__eqA__104001,Vvar__2__x__104006,Vvar__4__l__104027)
                        & Vvar__3___24Anonymous__104007 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__104000,Vvar__3__y__104026,Vvar__4__l__104027) ) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.Lists.SetoidList.NoDupA',axiom,
    ! [Vvar__0__A__104048,Vvar__1__eqA__104049,Vvar__2___24Anonymous__104054] :
      ( cType___24t(Vvar__0__A__104048)
     => ( c_24__type__104081___24t(Vvar__0__A__104048,Vvar__1__eqA__104049,Vvar__2___24Anonymous__104054,Vvar__1__eqA__104049)
       => ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__104048,Vvar__2___24Anonymous__104054)
         => ( cCoq_2eLists_2eSetoidList_2eNoDupA___24a3(Vvar__0__A__104048,Vvar__1__eqA__104049,Vvar__2___24Anonymous__104054)
           => ( Vvar__2___24Anonymous__104054 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__104048)
              | ? [Vvar__2__x__104068] :
                  ( t(Vvar__2__x__104068,Vvar__0__A__104048)
                  & ? [Vvar__3__l__104069] :
                      ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__104048,Vvar__3__l__104069)
                      & ~ cCoq_2eLists_2eSetoidList_2eInA___24a4(Vvar__0__A__104048,Vvar__1__eqA__104049,Vvar__2__x__104068,Vvar__3__l__104069)
                      & cCoq_2eLists_2eSetoidList_2eNoDupA___24a3(Vvar__0__A__104048,Vvar__1__eqA__104049,Vvar__3__l__104069)
                      & Vvar__2___24Anonymous__104054 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__104048,Vvar__2__x__104068,Vvar__3__l__104069) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.Lists.SetoidList.eqlistA',axiom,
    ! [Vvar__0__A__112713,Vvar__1__eqA__112714,Vvar__2___24Anonymous__112719,Vvar__3___24Anonymous__112720] :
      ( cType___24t(Vvar__0__A__112713)
     => ( c_24__type__112751___24t(Vvar__0__A__112713,Vvar__1__eqA__112714,Vvar__2___24Anonymous__112719,Vvar__3___24Anonymous__112720,Vvar__1__eqA__112714)
       => ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__112713,Vvar__2___24Anonymous__112719)
         => ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__112713,Vvar__3___24Anonymous__112720)
           => ( cCoq_2eLists_2eSetoidList_2eeqlistA___24a4(Vvar__0__A__112713,Vvar__1__eqA__112714,Vvar__2___24Anonymous__112719,Vvar__3___24Anonymous__112720)
             => ( ( Vvar__3___24Anonymous__112720 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__112713)
                  & Vvar__2___24Anonymous__112719 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__112713) )
                | ? [Vvar__2__x__112734] :
                    ( t(Vvar__2__x__112734,Vvar__0__A__112713)
                    & ? [Vvar__3__x_27__112735] :
                        ( t(Vvar__3__x_27__112735,Vvar__0__A__112713)
                        & ? [Vvar__4__l__112736] :
                            ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__112713,Vvar__4__l__112736)
                            & ? [Vvar__5__l_27__112737] :
                                ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__112713,Vvar__5__l_27__112737)
                                & p(happ(happ(Vvar__1__eqA__112714,Vvar__2__x__112734),Vvar__3__x_27__112735))
                                & cCoq_2eLists_2eSetoidList_2eeqlistA___24a4(Vvar__0__A__112713,Vvar__1__eqA__112714,Vvar__4__l__112736,Vvar__5__l_27__112737)
                                & Vvar__3___24Anonymous__112720 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__112713,Vvar__3__x_27__112735,Vvar__5__l_27__112737)
                                & Vvar__2___24Anonymous__112719 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__112713,Vvar__2__x__112734,Vvar__4__l__112736) ) ) ) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.Logic.EqdepFacts.eq_dep',axiom,
    ! [Vvar__0__U__107720,Vvar__1__P__107721,Vvar__2__p__107724,Vvar__3__x__107725,Vvar__4__q__107726,Vvar__5___24Anonymous__107727] :
      ( cType___24t(Vvar__0__U__107720)
     => ( c_24__type__107742___24t(Vvar__0__U__107720,Vvar__1__P__107721,Vvar__2__p__107724,Vvar__3__x__107725,Vvar__4__q__107726,Vvar__5___24Anonymous__107727,Vvar__1__P__107721)
       => ( t(Vvar__2__p__107724,Vvar__0__U__107720)
         => ( t(Vvar__3__x__107725,happ(Vvar__1__P__107721,Vvar__2__p__107724))
           => ( t(Vvar__4__q__107726,Vvar__0__U__107720)
             => ( t(Vvar__5___24Anonymous__107727,happ(Vvar__1__P__107721,Vvar__4__q__107726))
               => ( cCoq_2eLogic_2eEqdepFacts_2eeq__dep___24a6(Vvar__0__U__107720,Vvar__1__P__107721,Vvar__2__p__107724,Vvar__3__x__107725,Vvar__4__q__107726,Vvar__5___24Anonymous__107727)
                 => ( Vvar__5___24Anonymous__107727 = Vvar__3__x__107725
                    & Vvar__4__q__107726 = Vvar__2__p__107724 ) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.Logic.EqdepFacts.eq_dep1',axiom,
    ! [Vvar__0__U__107744,Vvar__1__P__107745,Vvar__2__p__107748,Vvar__3__x__107749,Vvar__4__q__107750,Vvar__5__y__107751] :
      ( cType___24t(Vvar__0__U__107744)
     => ( c_24__type__107770___24t(Vvar__0__U__107744,Vvar__1__P__107745,Vvar__2__p__107748,Vvar__3__x__107749,Vvar__4__q__107750,Vvar__5__y__107751,Vvar__1__P__107745)
       => ( t(Vvar__2__p__107748,Vvar__0__U__107744)
         => ( t(Vvar__3__x__107749,happ(Vvar__1__P__107745,Vvar__2__p__107748))
           => ( t(Vvar__4__q__107750,Vvar__0__U__107744)
             => ( t(Vvar__5__y__107751,happ(Vvar__1__P__107745,Vvar__4__q__107750))
               => ( cCoq_2eLogic_2eEqdepFacts_2eeq__dep1___24a6(Vvar__0__U__107744,Vvar__1__P__107745,Vvar__2__p__107748,Vvar__3__x__107749,Vvar__4__q__107750,Vvar__5__y__107751)
                 => ( Vvar__4__q__107750 = Vvar__2__p__107748
                    & Vvar__3__x__107749 = cCoq_2eInit_2eLogic_2eeq__rect___24a5(Vvar__0__U__107744,Vvar__4__q__107750,Vvar__1__P__107745,Vvar__5__y__107751,Vvar__2__p__107748)
                    & p(c_24True) ) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.Numbers.BinNums.N',axiom,
    ! [VX3] :
      ( cCoq_2eNumbers_2eBinNums_2eN___24t(VX3)
     => ( VX3 = cCoq_2eNumbers_2eBinNums_2eN0
        | ? [Vvar__0___24Anonymous__4] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__4)
            & VX3 = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__4) ) ) ) ).

fof('$_inversion_Coq.Numbers.BinNums.Z',axiom,
    ! [VX14024] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(VX14024)
     => ( VX14024 = cCoq_2eNumbers_2eBinNums_2eZ0
        | ? [Vvar__0___24Anonymous__14025] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__14025)
            & VX14024 = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__14025) )
        | ? [Vvar__0___24Anonymous__14026] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__14026)
            & VX14024 = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__14026) ) ) ) ).

fof('$_inversion_Coq.Numbers.BinNums.positive',axiom,
    ! [VX315] :
      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(VX315)
     => ( ? [Vvar__0___24Anonymous__316] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__316)
            & VX315 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__316) )
        | ? [Vvar__0___24Anonymous__317] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__317)
            & VX315 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__317) )
        | VX315 = cCoq_2eNumbers_2eBinNums_2exH ) ) ).

fof('$_inversion_Coq.PArith.BinPos.Pos.PeanoView',axiom,
    ! [Vvar__0___24Anonymous__113634,VX113635] :
      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__113634)
     => ( cCoq_2ePArith_2eBinPos_2ePos_2ePeanoView___24t(Vvar__0___24Anonymous__113634,VX113635)
       => ( ( Vvar__0___24Anonymous__113634 = cCoq_2eNumbers_2eBinNums_2exH
            & VX113635 = cCoq_2ePArith_2eBinPos_2ePos_2ePeanoOne )
          | ? [Vvar__0__p__113636] :
              ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0__p__113636)
              & ? [Vvar__1___24Anonymous__113637] :
                  ( cCoq_2ePArith_2eBinPos_2ePos_2ePeanoView___24t(Vvar__0__p__113636,Vvar__1___24Anonymous__113637)
                  & Vvar__0___24Anonymous__113634 = c_24__case__Coq_2eNumbers_2eBinNums_2epositive_24113672___24a2(Vvar__0___24Anonymous__113634,Vvar__0__p__113636)
                  & VX113635 = cCoq_2ePArith_2eBinPos_2ePos_2ePeanoSucc___24a2(Vvar__0__p__113636,Vvar__1___24Anonymous__113637) ) ) ) ) ) ).

fof('$_inversion_Coq.PArith.BinPos.Pos.SubMaskSpec',axiom,
    ! [Vvar__0__p__122286,Vvar__1__q__122287,Vvar__2___24Anonymous__122288] :
      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0__p__122286)
     => ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1__q__122287)
       => ( cCoq_2ePArith_2eBinPosDef_2ePos_2emask___24t(Vvar__2___24Anonymous__122288)
         => ( cCoq_2ePArith_2eBinPos_2ePos_2eSubMaskSpec___24a3(Vvar__0__p__122286,Vvar__1__q__122287,Vvar__2___24Anonymous__122288)
           => ( ( Vvar__0__p__122286 = Vvar__1__q__122287
                & Vvar__2___24Anonymous__122288 = cCoq_2ePArith_2eBinPosDef_2ePos_2eIsNul )
              | ? [Vvar__2__r__122295] :
                  ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2__r__122295)
                  & cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(Vvar__1__q__122287,Vvar__2__r__122295) = Vvar__0__p__122286
                  & Vvar__2___24Anonymous__122288 = cCoq_2ePArith_2eBinPosDef_2ePos_2eIsPos___24a1(Vvar__2__r__122295) )
              | ? [Vvar__2__r__122299] :
                  ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2__r__122299)
                  & cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(Vvar__0__p__122286,Vvar__2__r__122299) = Vvar__1__q__122287
                  & Vvar__2___24Anonymous__122288 = cCoq_2ePArith_2eBinPosDef_2ePos_2eIsNeg ) ) ) ) ) ) ).

fof('$_inversion_Coq.PArith.BinPosDef.Pos.mask',axiom,
    ! [VX113583] :
      ( cCoq_2ePArith_2eBinPosDef_2ePos_2emask___24t(VX113583)
     => ( VX113583 = cCoq_2ePArith_2eBinPosDef_2ePos_2eIsNul
        | ? [Vvar__0___24Anonymous__113584] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__113584)
            & VX113583 = cCoq_2ePArith_2eBinPosDef_2ePos_2eIsPos___24a1(Vvar__0___24Anonymous__113584) )
        | VX113583 = cCoq_2ePArith_2eBinPosDef_2ePos_2eIsNeg ) ) ).

fof('$_inversion_Coq.QArith.QArith_base.Q',axiom,
    ! [VX91210] :
      ( cCoq_2eQArith_2eQArith__base_2eQ___24t(VX91210)
     => ? [Vvar__0__Qnum__91211] :
          ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__0__Qnum__91211)
          & ? [Vvar__1__Qden__91212] :
              ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1__Qden__91212)
              & VX91210 = cCoq_2eQArith_2eQArith__base_2eQmake___24a2(Vvar__0__Qnum__91211,Vvar__1__Qden__91212) ) ) ) ).

fof('$_inversion_Coq.Reals.RIneq.negreal',axiom,
    ! [VX109664] :
      ( cCoq_2eReals_2eRIneq_2enegreal___24t(VX109664)
     => ? [Vvar__0__neg__109665] :
          ( cCoq_2eReals_2eRdefinitions_2eR___24t(Vvar__0__neg__109665)
          & cCoq_2eReals_2eRdefinitions_2eRlt___24a2(Vvar__0__neg__109665,cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0))
          & VX109664 = cCoq_2eReals_2eRIneq_2emknegreal___24a1(Vvar__0__neg__109665) ) ) ).

fof('$_inversion_Coq.Reals.RIneq.nonnegreal',axiom,
    ! [VX109643] :
      ( cCoq_2eReals_2eRIneq_2enonnegreal___24t(VX109643)
     => ? [Vvar__0__nonneg__109644] :
          ( cCoq_2eReals_2eRdefinitions_2eR___24t(Vvar__0__nonneg__109644)
          & cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),Vvar__0__nonneg__109644)
          & VX109643 = cCoq_2eReals_2eRIneq_2emknonnegreal___24a1(Vvar__0__nonneg__109644) ) ) ).

fof('$_inversion_Coq.Reals.RIneq.nonposreal',axiom,
    ! [VX109657] :
      ( cCoq_2eReals_2eRIneq_2enonposreal___24t(VX109657)
     => ? [Vvar__0__nonpos__109658] :
          ( cCoq_2eReals_2eRdefinitions_2eR___24t(Vvar__0__nonpos__109658)
          & cCoq_2eReals_2eRdefinitions_2eRle___24a2(Vvar__0__nonpos__109658,cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0))
          & VX109657 = cCoq_2eReals_2eRIneq_2emknonposreal___24a1(Vvar__0__nonpos__109658) ) ) ).

fof('$_inversion_Coq.Reals.RIneq.nonzeroreal',axiom,
    ! [VX109671] :
      ( cCoq_2eReals_2eRIneq_2enonzeroreal___24t(VX109671)
     => ? [Vvar__0__nonzero__109672] :
          ( cCoq_2eReals_2eRdefinitions_2eR___24t(Vvar__0__nonzero__109672)
          & Vvar__0__nonzero__109672 != cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)
          & VX109671 = cCoq_2eReals_2eRIneq_2emknonzeroreal___24a1(Vvar__0__nonzero__109672) ) ) ).

fof('$_inversion_Coq.Reals.RIneq.posreal',axiom,
    ! [VX109650] :
      ( cCoq_2eReals_2eRIneq_2eposreal___24t(VX109650)
     => ? [Vvar__0__pos__109651] :
          ( cCoq_2eReals_2eRdefinitions_2eR___24t(Vvar__0__pos__109651)
          & cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),Vvar__0__pos__109651)
          & VX109650 = cCoq_2eReals_2eRIneq_2emkposreal___24a1(Vvar__0__pos__109651) ) ) ).

fof('$_inversion_Coq.Reals.Rfunctions.Z_spec',axiom,
    ! [Vvar__0__x__110414,Vvar__1___24Anonymous__110415,VX110416] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__0__x__110414)
     => ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__1___24Anonymous__110415)
       => ( cCoq_2eReals_2eRfunctions_2eZ__spec___24t(Vvar__0__x__110414,Vvar__1___24Anonymous__110415,VX110416)
         => ( ( Vvar__0__x__110414 = cCoq_2eNumbers_2eBinNums_2eZ0
              & Vvar__1___24Anonymous__110415 = cCoq_2eNumbers_2eBinNums_2eZ0
              & VX110416 = cCoq_2eReals_2eRfunctions_2eZintNull___24a1(Vvar__0__x__110414) )
            | ? [Vvar__1__n__110420] :
                ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__1__n__110420)
                & Vvar__0__x__110414 = cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat___24a1(Vvar__1__n__110420)
                & Vvar__1___24Anonymous__110415 = c_24__case__Coq_2eInit_2eDatatypes_2enat_24110440___24a3(Vvar__0__x__110414,Vvar__1___24Anonymous__110415,Vvar__1__n__110420)
                & VX110416 = cCoq_2eReals_2eRfunctions_2eZintPos___24a2(Vvar__0__x__110414,Vvar__1__n__110420) )
            | ? [Vvar__1__n__110425] :
                ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__1__n__110425)
                & Vvar__0__x__110414 = cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat___24a1(Vvar__1__n__110425))
                & Vvar__1___24Anonymous__110415 = c_24__case__Coq_2eNumbers_2eBinNums_2eZ_24110457___24a3(Vvar__0__x__110414,Vvar__1___24Anonymous__110415,Vvar__1__n__110425)
                & VX110416 = cCoq_2eReals_2eRfunctions_2eZintNeg___24a2(Vvar__0__x__110414,Vvar__1__n__110425) ) ) ) ) ) ).

fof('$_inversion_Coq.Relations.Relation_Definitions.PER',axiom,
    ! [Vvar__0__A__121371,Vvar__1__R__121372] :
      ( cType___24t(Vvar__0__A__121371)
     => ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vvar__0__A__121371,Vvar__1__R__121372)
       => ( cCoq_2eRelations_2eRelation__Definitions_2ePER___24a2(Vvar__0__A__121371,Vvar__1__R__121372)
         => ( cCoq_2eRelations_2eRelation__Definitions_2esymmetric___24a2(Vvar__0__A__121371,Vvar__1__R__121372)
            & cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2(Vvar__0__A__121371,Vvar__1__R__121372)
            & p(c_24True) ) ) ) ) ).

fof('$_inversion_Coq.Relations.Relation_Definitions.equivalence',axiom,
    ! [Vvar__0__A__118033,Vvar__1__R__118034] :
      ( cType___24t(Vvar__0__A__118033)
     => ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vvar__0__A__118033,Vvar__1__R__118034)
       => ( cCoq_2eRelations_2eRelation__Definitions_2eequivalence___24a2(Vvar__0__A__118033,Vvar__1__R__118034)
         => ( cCoq_2eRelations_2eRelation__Definitions_2ereflexive___24a2(Vvar__0__A__118033,Vvar__1__R__118034)
            & cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2(Vvar__0__A__118033,Vvar__1__R__118034)
            & cCoq_2eRelations_2eRelation__Definitions_2esymmetric___24a2(Vvar__0__A__118033,Vvar__1__R__118034)
            & p(c_24True) ) ) ) ) ).

fof('$_inversion_Coq.Relations.Relation_Definitions.order',axiom,
    ! [Vvar__0__A__121363,Vvar__1__R__121364] :
      ( cType___24t(Vvar__0__A__121363)
     => ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vvar__0__A__121363,Vvar__1__R__121364)
       => ( cCoq_2eRelations_2eRelation__Definitions_2eorder___24a2(Vvar__0__A__121363,Vvar__1__R__121364)
         => ( cCoq_2eRelations_2eRelation__Definitions_2ereflexive___24a2(Vvar__0__A__121363,Vvar__1__R__121364)
            & cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2(Vvar__0__A__121363,Vvar__1__R__121364)
            & cCoq_2eRelations_2eRelation__Definitions_2eantisymmetric___24a2(Vvar__0__A__121363,Vvar__1__R__121364)
            & p(c_24True) ) ) ) ) ).

fof('$_inversion_Coq.Relations.Relation_Definitions.preorder',axiom,
    ! [Vvar__0__A__121356,Vvar__1__R__121357] :
      ( cType___24t(Vvar__0__A__121356)
     => ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vvar__0__A__121356,Vvar__1__R__121357)
       => ( cCoq_2eRelations_2eRelation__Definitions_2epreorder___24a2(Vvar__0__A__121356,Vvar__1__R__121357)
         => ( cCoq_2eRelations_2eRelation__Definitions_2ereflexive___24a2(Vvar__0__A__121356,Vvar__1__R__121357)
            & cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2(Vvar__0__A__121356,Vvar__1__R__121357)
            & p(c_24True) ) ) ) ) ).

fof('$_inversion_Coq.Relations.Relation_Operators.Desc',axiom,
    ! [Vvar__0__A__109892,Vvar__1__leA__109893,Vvar__2___24Anonymous__109898] :
      ( cType___24t(Vvar__0__A__109892)
     => ( c_24__type__109988___24t(Vvar__0__A__109892,Vvar__1__leA__109893,Vvar__2___24Anonymous__109898,Vvar__1__leA__109893)
       => ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__109892,Vvar__2___24Anonymous__109898)
         => ( cCoq_2eRelations_2eRelation__Operators_2eDesc___24a3(Vvar__0__A__109892,Vvar__1__leA__109893,Vvar__2___24Anonymous__109898)
           => ( Vvar__2___24Anonymous__109898 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__109892)
              | ? [Vvar__2__x__109912] :
                  ( t(Vvar__2__x__109912,Vvar__0__A__109892)
                  & Vvar__2___24Anonymous__109898 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__109892,Vvar__2__x__109912,cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__109892)) )
              | ? [Vvar__2__x__109919] :
                  ( t(Vvar__2__x__109919,Vvar__0__A__109892)
                  & ? [Vvar__3__y__109920] :
                      ( t(Vvar__3__y__109920,Vvar__0__A__109892)
                      & ? [Vvar__4__l__109921] :
                          ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__109892,Vvar__4__l__109921)
                          & cCoq_2eRelations_2eRelation__Operators_2eclos__refl___24a4(Vvar__0__A__109892,Vvar__1__leA__109893,Vvar__2__x__109919,Vvar__3__y__109920)
                          & cCoq_2eRelations_2eRelation__Operators_2eDesc___24a3(Vvar__0__A__109892,Vvar__1__leA__109893,cCoq_2eInit_2eDatatypes_2eapp___24a3(Vvar__0__A__109892,Vvar__4__l__109921,cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__109892,Vvar__3__y__109920,cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__109892))))
                          & Vvar__2___24Anonymous__109898 = c_24__case__Coq_2eInit_2eDatatypes_2elist_24110186___24a6(Vvar__0__A__109892,Vvar__1__leA__109893,Vvar__2___24Anonymous__109898,Vvar__2__x__109919,Vvar__3__y__109920,Vvar__4__l__109921) ) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.Relations.Relation_Operators.Ltl',axiom,
    ! [Vvar__0__A__109841,Vvar__1__leA__109842,Vvar__2___24Anonymous__109847,Vvar__3___24Anonymous__109848] :
      ( cType___24t(Vvar__0__A__109841)
     => ( c_24__type__109890___24t(Vvar__0__A__109841,Vvar__1__leA__109842,Vvar__2___24Anonymous__109847,Vvar__3___24Anonymous__109848,Vvar__1__leA__109842)
       => ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__109841,Vvar__2___24Anonymous__109847)
         => ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__109841,Vvar__3___24Anonymous__109848)
           => ( cCoq_2eRelations_2eRelation__Operators_2eLtl___24a4(Vvar__0__A__109841,Vvar__1__leA__109842,Vvar__2___24Anonymous__109847,Vvar__3___24Anonymous__109848)
             => ( ? [Vvar__2__a__109856] :
                    ( t(Vvar__2__a__109856,Vvar__0__A__109841)
                    & ? [Vvar__3__x__109857] :
                        ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__109841,Vvar__3__x__109857)
                        & Vvar__3___24Anonymous__109848 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__109841,Vvar__2__a__109856,Vvar__3__x__109857)
                        & Vvar__2___24Anonymous__109847 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__109841) ) )
                | ? [Vvar__2__a__109864] :
                    ( t(Vvar__2__a__109864,Vvar__0__A__109841)
                    & ? [Vvar__3__b__109865] :
                        ( t(Vvar__3__b__109865,Vvar__0__A__109841)
                        & p(happ(happ(Vvar__1__leA__109842,Vvar__2__a__109864),Vvar__3__b__109865))
                        & ? [Vvar__5__x__109867] :
                            ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__109841,Vvar__5__x__109867)
                            & ? [Vvar__6__y__109868] :
                                ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__109841,Vvar__6__y__109868)
                                & Vvar__3___24Anonymous__109848 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__109841,Vvar__3__b__109865,Vvar__6__y__109868)
                                & Vvar__2___24Anonymous__109847 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__109841,Vvar__2__a__109864,Vvar__5__x__109867) ) ) ) )
                | ? [Vvar__2__a__109875] :
                    ( t(Vvar__2__a__109875,Vvar__0__A__109841)
                    & ? [Vvar__3__x__109876] :
                        ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__109841,Vvar__3__x__109876)
                        & ? [Vvar__4__y__109877] :
                            ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__109841,Vvar__4__y__109877)
                            & cCoq_2eRelations_2eRelation__Operators_2eLtl___24a4(Vvar__0__A__109841,Vvar__1__leA__109842,Vvar__3__x__109876,Vvar__4__y__109877)
                            & Vvar__3___24Anonymous__109848 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__109841,Vvar__2__a__109875,Vvar__4__y__109877)
                            & Vvar__2___24Anonymous__109847 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__109841,Vvar__2__a__109875,Vvar__3__x__109876) ) ) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.Relations.Relation_Operators.clos_refl',axiom,
    ! [Vvar__0__A__118041,Vvar__1__R__118042,Vvar__2__x__118043,Vvar__3___24Anonymous__118044] :
      ( cType___24t(Vvar__0__A__118041)
     => ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vvar__0__A__118041,Vvar__1__R__118042)
       => ( t(Vvar__2__x__118043,Vvar__0__A__118041)
         => ( t(Vvar__3___24Anonymous__118044,Vvar__0__A__118041)
           => ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl___24a4(Vvar__0__A__118041,Vvar__1__R__118042,Vvar__2__x__118043,Vvar__3___24Anonymous__118044)
             => ( ? [Vvar__3__y__118049] :
                    ( t(Vvar__3__y__118049,Vvar__0__A__118041)
                    & p(happ(happ(Vvar__1__R__118042,Vvar__2__x__118043),Vvar__3__y__118049))
                    & Vvar__3___24Anonymous__118044 = Vvar__3__y__118049 )
                | Vvar__3___24Anonymous__118044 = Vvar__2__x__118043 ) ) ) ) ) ) ).

fof('$_inversion_Coq.Relations.Relation_Operators.clos_refl_sym_trans_1n',axiom,
    ! [Vvar__0__A__121444,Vvar__1__R__121445,Vvar__2__x__121446,Vvar__3___24Anonymous__121447] :
      ( cType___24t(Vvar__0__A__121444)
     => ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vvar__0__A__121444,Vvar__1__R__121445)
       => ( t(Vvar__2__x__121446,Vvar__0__A__121444)
         => ( t(Vvar__3___24Anonymous__121447,Vvar__0__A__121444)
           => ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans__1n___24a4(Vvar__0__A__121444,Vvar__1__R__121445,Vvar__2__x__121446,Vvar__3___24Anonymous__121447)
             => ( Vvar__3___24Anonymous__121447 = Vvar__2__x__121446
                | ? [Vvar__3__y__121455] :
                    ( t(Vvar__3__y__121455,Vvar__0__A__121444)
                    & ? [Vvar__4__z__121456] :
                        ( t(Vvar__4__z__121456,Vvar__0__A__121444)
                        & ( p(happ(happ(Vvar__1__R__121445,Vvar__2__x__121446),Vvar__3__y__121455))
                          | p(happ(happ(Vvar__1__R__121445,Vvar__3__y__121455),Vvar__2__x__121446)) )
                        & cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans__1n___24a4(Vvar__0__A__121444,Vvar__1__R__121445,Vvar__3__y__121455,Vvar__4__z__121456)
                        & Vvar__3___24Anonymous__121447 = Vvar__4__z__121456 ) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.Relations.Relation_Operators.clos_refl_sym_trans_n1',axiom,
    ! [Vvar__0__A__121459,Vvar__1__R__121460,Vvar__2__x__121461,Vvar__3___24Anonymous__121462] :
      ( cType___24t(Vvar__0__A__121459)
     => ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vvar__0__A__121459,Vvar__1__R__121460)
       => ( t(Vvar__2__x__121461,Vvar__0__A__121459)
         => ( t(Vvar__3___24Anonymous__121462,Vvar__0__A__121459)
           => ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans__n1___24a4(Vvar__0__A__121459,Vvar__1__R__121460,Vvar__2__x__121461,Vvar__3___24Anonymous__121462)
             => ( Vvar__3___24Anonymous__121462 = Vvar__2__x__121461
                | ? [Vvar__3__y__121470] :
                    ( t(Vvar__3__y__121470,Vvar__0__A__121459)
                    & ? [Vvar__4__z__121471] :
                        ( t(Vvar__4__z__121471,Vvar__0__A__121459)
                        & ( p(happ(happ(Vvar__1__R__121460,Vvar__3__y__121470),Vvar__4__z__121471))
                          | p(happ(happ(Vvar__1__R__121460,Vvar__4__z__121471),Vvar__3__y__121470)) )
                        & cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans__n1___24a4(Vvar__0__A__121459,Vvar__1__R__121460,Vvar__2__x__121461,Vvar__3__y__121470)
                        & Vvar__3___24Anonymous__121462 = Vvar__4__z__121471 ) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.Relations.Relation_Operators.clos_refl_trans',axiom,
    ! [Vvar__0__A__118054,Vvar__1__R__118055,Vvar__2__x__118056,Vvar__3___24Anonymous__118057] :
      ( cType___24t(Vvar__0__A__118054)
     => ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vvar__0__A__118054,Vvar__1__R__118055)
       => ( t(Vvar__2__x__118056,Vvar__0__A__118054)
         => ( t(Vvar__3___24Anonymous__118057,Vvar__0__A__118054)
           => ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a4(Vvar__0__A__118054,Vvar__1__R__118055,Vvar__2__x__118056,Vvar__3___24Anonymous__118057)
             => ( ? [Vvar__3__y__118062] :
                    ( t(Vvar__3__y__118062,Vvar__0__A__118054)
                    & p(happ(happ(Vvar__1__R__118055,Vvar__2__x__118056),Vvar__3__y__118062))
                    & Vvar__3___24Anonymous__118057 = Vvar__3__y__118062 )
                | Vvar__3___24Anonymous__118057 = Vvar__2__x__118056
                | ? [Vvar__3__y__118070] :
                    ( t(Vvar__3__y__118070,Vvar__0__A__118054)
                    & ? [Vvar__4__z__118071] :
                        ( t(Vvar__4__z__118071,Vvar__0__A__118054)
                        & cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a4(Vvar__0__A__118054,Vvar__1__R__118055,Vvar__2__x__118056,Vvar__3__y__118070)
                        & cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a4(Vvar__0__A__118054,Vvar__1__R__118055,Vvar__3__y__118070,Vvar__4__z__118071)
                        & Vvar__3___24Anonymous__118057 = Vvar__4__z__118071 ) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.Relations.Relation_Operators.clos_refl_trans_1n',axiom,
    ! [Vvar__0__A__121429,Vvar__1__R__121430,Vvar__2__x__121431,Vvar__3___24Anonymous__121432] :
      ( cType___24t(Vvar__0__A__121429)
     => ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vvar__0__A__121429,Vvar__1__R__121430)
       => ( t(Vvar__2__x__121431,Vvar__0__A__121429)
         => ( t(Vvar__3___24Anonymous__121432,Vvar__0__A__121429)
           => ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans__1n___24a4(Vvar__0__A__121429,Vvar__1__R__121430,Vvar__2__x__121431,Vvar__3___24Anonymous__121432)
             => ( Vvar__3___24Anonymous__121432 = Vvar__2__x__121431
                | ? [Vvar__3__y__121440] :
                    ( t(Vvar__3__y__121440,Vvar__0__A__121429)
                    & ? [Vvar__4__z__121441] :
                        ( t(Vvar__4__z__121441,Vvar__0__A__121429)
                        & p(happ(happ(Vvar__1__R__121430,Vvar__2__x__121431),Vvar__3__y__121440))
                        & cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans__1n___24a4(Vvar__0__A__121429,Vvar__1__R__121430,Vvar__3__y__121440,Vvar__4__z__121441)
                        & Vvar__3___24Anonymous__121432 = Vvar__4__z__121441 ) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.Relations.Relation_Operators.clos_refl_trans_n1',axiom,
    ! [Vvar__0__A__118074,Vvar__1__R__118075,Vvar__2__x__118076,Vvar__3___24Anonymous__118077] :
      ( cType___24t(Vvar__0__A__118074)
     => ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vvar__0__A__118074,Vvar__1__R__118075)
       => ( t(Vvar__2__x__118076,Vvar__0__A__118074)
         => ( t(Vvar__3___24Anonymous__118077,Vvar__0__A__118074)
           => ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans__n1___24a4(Vvar__0__A__118074,Vvar__1__R__118075,Vvar__2__x__118076,Vvar__3___24Anonymous__118077)
             => ( Vvar__3___24Anonymous__118077 = Vvar__2__x__118076
                | ? [Vvar__3__y__118085] :
                    ( t(Vvar__3__y__118085,Vvar__0__A__118074)
                    & ? [Vvar__4__z__118086] :
                        ( t(Vvar__4__z__118086,Vvar__0__A__118074)
                        & p(happ(happ(Vvar__1__R__118075,Vvar__3__y__118085),Vvar__4__z__118086))
                        & cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans__n1___24a4(Vvar__0__A__118074,Vvar__1__R__118075,Vvar__2__x__118076,Vvar__3__y__118085)
                        & Vvar__3___24Anonymous__118077 = Vvar__4__z__118086 ) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.Relations.Relation_Operators.clos_trans',axiom,
    ! [Vvar__0__A__121378,Vvar__1__R__121379,Vvar__2__x__121380,Vvar__3___24Anonymous__121381] :
      ( cType___24t(Vvar__0__A__121378)
     => ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vvar__0__A__121378,Vvar__1__R__121379)
       => ( t(Vvar__2__x__121380,Vvar__0__A__121378)
         => ( t(Vvar__3___24Anonymous__121381,Vvar__0__A__121378)
           => ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a4(Vvar__0__A__121378,Vvar__1__R__121379,Vvar__2__x__121380,Vvar__3___24Anonymous__121381)
             => ( ? [Vvar__3__y__121386] :
                    ( t(Vvar__3__y__121386,Vvar__0__A__121378)
                    & p(happ(happ(Vvar__1__R__121379,Vvar__2__x__121380),Vvar__3__y__121386))
                    & Vvar__3___24Anonymous__121381 = Vvar__3__y__121386 )
                | ? [Vvar__3__y__121391] :
                    ( t(Vvar__3__y__121391,Vvar__0__A__121378)
                    & ? [Vvar__4__z__121392] :
                        ( t(Vvar__4__z__121392,Vvar__0__A__121378)
                        & cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a4(Vvar__0__A__121378,Vvar__1__R__121379,Vvar__2__x__121380,Vvar__3__y__121391)
                        & cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a4(Vvar__0__A__121378,Vvar__1__R__121379,Vvar__3__y__121391,Vvar__4__z__121392)
                        & Vvar__3___24Anonymous__121381 = Vvar__4__z__121392 ) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.Relations.Relation_Operators.clos_trans_1n',axiom,
    ! [Vvar__0__A__121395,Vvar__1__R__121396,Vvar__2__x__121397,Vvar__3___24Anonymous__121398] :
      ( cType___24t(Vvar__0__A__121395)
     => ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vvar__0__A__121395,Vvar__1__R__121396)
       => ( t(Vvar__2__x__121397,Vvar__0__A__121395)
         => ( t(Vvar__3___24Anonymous__121398,Vvar__0__A__121395)
           => ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans__1n___24a4(Vvar__0__A__121395,Vvar__1__R__121396,Vvar__2__x__121397,Vvar__3___24Anonymous__121398)
             => ( ? [Vvar__3__y__121403] :
                    ( t(Vvar__3__y__121403,Vvar__0__A__121395)
                    & p(happ(happ(Vvar__1__R__121396,Vvar__2__x__121397),Vvar__3__y__121403))
                    & Vvar__3___24Anonymous__121398 = Vvar__3__y__121403 )
                | ? [Vvar__3__y__121408] :
                    ( t(Vvar__3__y__121408,Vvar__0__A__121395)
                    & ? [Vvar__4__z__121409] :
                        ( t(Vvar__4__z__121409,Vvar__0__A__121395)
                        & p(happ(happ(Vvar__1__R__121396,Vvar__2__x__121397),Vvar__3__y__121408))
                        & cCoq_2eRelations_2eRelation__Operators_2eclos__trans__1n___24a4(Vvar__0__A__121395,Vvar__1__R__121396,Vvar__3__y__121408,Vvar__4__z__121409)
                        & Vvar__3___24Anonymous__121398 = Vvar__4__z__121409 ) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.Relations.Relation_Operators.clos_trans_n1',axiom,
    ! [Vvar__0__A__121412,Vvar__1__R__121413,Vvar__2__x__121414,Vvar__3___24Anonymous__121415] :
      ( cType___24t(Vvar__0__A__121412)
     => ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vvar__0__A__121412,Vvar__1__R__121413)
       => ( t(Vvar__2__x__121414,Vvar__0__A__121412)
         => ( t(Vvar__3___24Anonymous__121415,Vvar__0__A__121412)
           => ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans__n1___24a4(Vvar__0__A__121412,Vvar__1__R__121413,Vvar__2__x__121414,Vvar__3___24Anonymous__121415)
             => ( ? [Vvar__3__y__121420] :
                    ( t(Vvar__3__y__121420,Vvar__0__A__121412)
                    & p(happ(happ(Vvar__1__R__121413,Vvar__2__x__121414),Vvar__3__y__121420))
                    & Vvar__3___24Anonymous__121415 = Vvar__3__y__121420 )
                | ? [Vvar__3__y__121425] :
                    ( t(Vvar__3__y__121425,Vvar__0__A__121412)
                    & ? [Vvar__4__z__121426] :
                        ( t(Vvar__4__z__121426,Vvar__0__A__121412)
                        & p(happ(happ(Vvar__1__R__121413,Vvar__3__y__121425),Vvar__4__z__121426))
                        & cCoq_2eRelations_2eRelation__Operators_2eclos__trans__n1___24a4(Vvar__0__A__121412,Vvar__1__R__121413,Vvar__2__x__121414,Vvar__3__y__121425)
                        & Vvar__3___24Anonymous__121415 = Vvar__4__z__121426 ) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.Relations.Relation_Operators.lexprod',axiom,
    ! [Vvar__0__A__121474,Vvar__1__B__121475,Vvar__2__leA__121478,Vvar__3__leB__121483,Vvar__4___24Anonymous__121490,Vvar__5___24Anonymous__121491] :
      ( cType___24t(Vvar__0__A__121474)
     => ( c_24__type__121554___24t(Vvar__0__A__121474,Vvar__1__B__121475,Vvar__2__leA__121478,Vvar__3__leB__121483,Vvar__4___24Anonymous__121490,Vvar__5___24Anonymous__121491,Vvar__1__B__121475)
       => ( c_24__type__121583___24t(Vvar__0__A__121474,Vvar__1__B__121475,Vvar__2__leA__121478,Vvar__3__leB__121483,Vvar__4___24Anonymous__121490,Vvar__5___24Anonymous__121491,Vvar__2__leA__121478)
         => ( c_24__type__121620___24t(Vvar__0__A__121474,Vvar__1__B__121475,Vvar__2__leA__121478,Vvar__3__leB__121483,Vvar__4___24Anonymous__121490,Vvar__5___24Anonymous__121491,Vvar__3__leB__121483)
           => ( cCoq_2eInit_2eSpecif_2esigT___24t(Vvar__0__A__121474,Vvar__1__B__121475,Vvar__4___24Anonymous__121490)
             => ( cCoq_2eInit_2eSpecif_2esigT___24t(Vvar__0__A__121474,Vvar__1__B__121475,Vvar__5___24Anonymous__121491)
               => ( cCoq_2eRelations_2eRelation__Operators_2elexprod___24a6(Vvar__0__A__121474,Vvar__1__B__121475,Vvar__2__leA__121478,Vvar__3__leB__121483,Vvar__4___24Anonymous__121490,Vvar__5___24Anonymous__121491)
                 => ( ? [Vvar__4__x__121509] :
                        ( t(Vvar__4__x__121509,Vvar__0__A__121474)
                        & ? [Vvar__5__x_27__121510] :
                            ( t(Vvar__5__x_27__121510,Vvar__0__A__121474)
                            & ? [Vvar__6__y__121511] :
                                ( t(Vvar__6__y__121511,happ(Vvar__1__B__121475,Vvar__4__x__121509))
                                & ? [Vvar__7__y_27__121512] :
                                    ( t(Vvar__7__y_27__121512,happ(Vvar__1__B__121475,Vvar__5__x_27__121510))
                                    & p(happ(happ(Vvar__2__leA__121478,Vvar__4__x__121509),Vvar__5__x_27__121510))
                                    & Vvar__5___24Anonymous__121491 = cCoq_2eInit_2eSpecif_2eexistT___24a4(Vvar__0__A__121474,Vvar__1__B__121475,Vvar__5__x_27__121510,Vvar__7__y_27__121512)
                                    & Vvar__4___24Anonymous__121490 = cCoq_2eInit_2eSpecif_2eexistT___24a4(Vvar__0__A__121474,Vvar__1__B__121475,Vvar__4__x__121509,Vvar__6__y__121511) ) ) ) )
                    | ? [Vvar__4__x__121530] :
                        ( t(Vvar__4__x__121530,Vvar__0__A__121474)
                        & ? [Vvar__5__y__121531] :
                            ( t(Vvar__5__y__121531,happ(Vvar__1__B__121475,Vvar__4__x__121530))
                            & ? [Vvar__6__y_27__121532] :
                                ( t(Vvar__6__y_27__121532,happ(Vvar__1__B__121475,Vvar__4__x__121530))
                                & p(happ(happ(happ(Vvar__3__leB__121483,Vvar__4__x__121530),Vvar__5__y__121531),Vvar__6__y_27__121532))
                                & Vvar__5___24Anonymous__121491 = cCoq_2eInit_2eSpecif_2eexistT___24a4(Vvar__0__A__121474,Vvar__1__B__121475,Vvar__4__x__121530,Vvar__6__y_27__121532)
                                & Vvar__4___24Anonymous__121490 = cCoq_2eInit_2eSpecif_2eexistT___24a4(Vvar__0__A__121474,Vvar__1__B__121475,Vvar__4__x__121530,Vvar__5__y__121531) ) ) ) ) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.Relations.Relation_Operators.swapprod',axiom,
    ! [Vvar__0__A__121719,Vvar__1__R__121720,Vvar__2___24Anonymous__121725,Vvar__3___24Anonymous__121726] :
      ( cType___24t(Vvar__0__A__121719)
     => ( c_24__type__121759___24t(Vvar__0__A__121719,Vvar__1__R__121720,Vvar__2___24Anonymous__121725,Vvar__3___24Anonymous__121726,Vvar__1__R__121720)
       => ( cCoq_2eInit_2eDatatypes_2eprod___24t(Vvar__0__A__121719,Vvar__0__A__121719,Vvar__2___24Anonymous__121725)
         => ( cCoq_2eInit_2eDatatypes_2eprod___24t(Vvar__0__A__121719,Vvar__0__A__121719,Vvar__3___24Anonymous__121726)
           => ( cCoq_2eRelations_2eRelation__Operators_2eswapprod___24a4(Vvar__0__A__121719,Vvar__1__R__121720,Vvar__2___24Anonymous__121725,Vvar__3___24Anonymous__121726)
             => ( ? [Vvar__2__x__121734] :
                    ( t(Vvar__2__x__121734,Vvar__0__A__121719)
                    & ? [Vvar__3__y__121735] :
                        ( t(Vvar__3__y__121735,Vvar__0__A__121719)
                        & ? [Vvar__4__p__121736] :
                            ( cCoq_2eInit_2eDatatypes_2eprod___24t(Vvar__0__A__121719,Vvar__0__A__121719,Vvar__4__p__121736)
                            & cCoq_2eRelations_2eRelation__Operators_2esymprod___24a6(Vvar__0__A__121719,Vvar__0__A__121719,Vvar__1__R__121720,Vvar__1__R__121720,cCoq_2eInit_2eDatatypes_2epair___24a4(Vvar__0__A__121719,Vvar__0__A__121719,Vvar__2__x__121734,Vvar__3__y__121735),Vvar__4__p__121736)
                            & Vvar__3___24Anonymous__121726 = Vvar__4__p__121736
                            & Vvar__2___24Anonymous__121725 = cCoq_2eInit_2eDatatypes_2epair___24a4(Vvar__0__A__121719,Vvar__0__A__121719,Vvar__2__x__121734,Vvar__3__y__121735) ) ) )
                | ? [Vvar__2__x__121744] :
                    ( t(Vvar__2__x__121744,Vvar__0__A__121719)
                    & ? [Vvar__3__y__121745] :
                        ( t(Vvar__3__y__121745,Vvar__0__A__121719)
                        & ? [Vvar__4__p__121746] :
                            ( cCoq_2eInit_2eDatatypes_2eprod___24t(Vvar__0__A__121719,Vvar__0__A__121719,Vvar__4__p__121746)
                            & cCoq_2eRelations_2eRelation__Operators_2esymprod___24a6(Vvar__0__A__121719,Vvar__0__A__121719,Vvar__1__R__121720,Vvar__1__R__121720,cCoq_2eInit_2eDatatypes_2epair___24a4(Vvar__0__A__121719,Vvar__0__A__121719,Vvar__2__x__121744,Vvar__3__y__121745),Vvar__4__p__121746)
                            & Vvar__3___24Anonymous__121726 = Vvar__4__p__121746
                            & Vvar__2___24Anonymous__121725 = cCoq_2eInit_2eDatatypes_2epair___24a4(Vvar__0__A__121719,Vvar__0__A__121719,Vvar__3__y__121745,Vvar__2__x__121744) ) ) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.Relations.Relation_Operators.symprod',axiom,
    ! [Vvar__0__A__121622,Vvar__1__B__121623,Vvar__2__leA__121624,Vvar__3__leB__121629,Vvar__4___24Anonymous__121634,Vvar__5___24Anonymous__121635] :
      ( cType___24t(Vvar__0__A__121622)
     => ( cType___24t(Vvar__1__B__121623)
       => ( c_24__type__121692___24t(Vvar__0__A__121622,Vvar__1__B__121623,Vvar__2__leA__121624,Vvar__3__leB__121629,Vvar__4___24Anonymous__121634,Vvar__5___24Anonymous__121635,Vvar__2__leA__121624)
         => ( c_24__type__121717___24t(Vvar__0__A__121622,Vvar__1__B__121623,Vvar__2__leA__121624,Vvar__3__leB__121629,Vvar__4___24Anonymous__121634,Vvar__5___24Anonymous__121635,Vvar__3__leB__121629)
           => ( cCoq_2eInit_2eDatatypes_2eprod___24t(Vvar__0__A__121622,Vvar__1__B__121623,Vvar__4___24Anonymous__121634)
             => ( cCoq_2eInit_2eDatatypes_2eprod___24t(Vvar__0__A__121622,Vvar__1__B__121623,Vvar__5___24Anonymous__121635)
               => ( cCoq_2eRelations_2eRelation__Operators_2esymprod___24a6(Vvar__0__A__121622,Vvar__1__B__121623,Vvar__2__leA__121624,Vvar__3__leB__121629,Vvar__4___24Anonymous__121634,Vvar__5___24Anonymous__121635)
                 => ( ? [Vvar__4__x__121649] :
                        ( t(Vvar__4__x__121649,Vvar__0__A__121622)
                        & ? [Vvar__5__x_27__121650] :
                            ( t(Vvar__5__x_27__121650,Vvar__0__A__121622)
                            & p(happ(happ(Vvar__2__leA__121624,Vvar__4__x__121649),Vvar__5__x_27__121650))
                            & ? [Vvar__7__y__121652] :
                                ( t(Vvar__7__y__121652,Vvar__1__B__121623)
                                & Vvar__5___24Anonymous__121635 = cCoq_2eInit_2eDatatypes_2epair___24a4(Vvar__0__A__121622,Vvar__1__B__121623,Vvar__5__x_27__121650,Vvar__7__y__121652)
                                & Vvar__4___24Anonymous__121634 = cCoq_2eInit_2eDatatypes_2epair___24a4(Vvar__0__A__121622,Vvar__1__B__121623,Vvar__4__x__121649,Vvar__7__y__121652) ) ) )
                    | ? [Vvar__4__y__121665] :
                        ( t(Vvar__4__y__121665,Vvar__1__B__121623)
                        & ? [Vvar__5__y_27__121666] :
                            ( t(Vvar__5__y_27__121666,Vvar__1__B__121623)
                            & p(happ(happ(Vvar__3__leB__121629,Vvar__4__y__121665),Vvar__5__y_27__121666))
                            & ? [Vvar__7__x__121668] :
                                ( t(Vvar__7__x__121668,Vvar__0__A__121622)
                                & Vvar__5___24Anonymous__121635 = cCoq_2eInit_2eDatatypes_2epair___24a4(Vvar__0__A__121622,Vvar__1__B__121623,Vvar__7__x__121668,Vvar__5__y_27__121666)
                                & Vvar__4___24Anonymous__121634 = cCoq_2eInit_2eDatatypes_2epair___24a4(Vvar__0__A__121622,Vvar__1__B__121623,Vvar__7__x__121668,Vvar__4__y__121665) ) ) ) ) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.Sorting.Sorted.HdRel',axiom,
    ! [Vvar__0__A__112923,Vvar__1__R__112924,Vvar__2__a__112929,Vvar__3___24Anonymous__112930] :
      ( cType___24t(Vvar__0__A__112923)
     => ( c_24__type__112960___24t(Vvar__0__A__112923,Vvar__1__R__112924,Vvar__2__a__112929,Vvar__3___24Anonymous__112930,Vvar__1__R__112924)
       => ( t(Vvar__2__a__112929,Vvar__0__A__112923)
         => ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__112923,Vvar__3___24Anonymous__112930)
           => ( cCoq_2eSorting_2eSorted_2eHdRel___24a4(Vvar__0__A__112923,Vvar__1__R__112924,Vvar__2__a__112929,Vvar__3___24Anonymous__112930)
             => ( Vvar__3___24Anonymous__112930 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__112923)
                | ? [Vvar__3__b__112946] :
                    ( t(Vvar__3__b__112946,Vvar__0__A__112923)
                    & ? [Vvar__4__l__112947] :
                        ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__112923,Vvar__4__l__112947)
                        & p(happ(happ(Vvar__1__R__112924,Vvar__2__a__112929),Vvar__3__b__112946))
                        & Vvar__3___24Anonymous__112930 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__112923,Vvar__3__b__112946,Vvar__4__l__112947) ) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.Sorting.Sorted.LocallySorted',axiom,
    ! [Vvar__0__A__112880,Vvar__1__R__112881,Vvar__2___24Anonymous__112886] :
      ( cType___24t(Vvar__0__A__112880)
     => ( c_24__type__112921___24t(Vvar__0__A__112880,Vvar__1__R__112881,Vvar__2___24Anonymous__112886,Vvar__1__R__112881)
       => ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__112880,Vvar__2___24Anonymous__112886)
         => ( cCoq_2eSorting_2eSorted_2eLocallySorted___24a3(Vvar__0__A__112880,Vvar__1__R__112881,Vvar__2___24Anonymous__112886)
           => ( Vvar__2___24Anonymous__112886 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__112880)
              | ? [Vvar__2__a__112900] :
                  ( t(Vvar__2__a__112900,Vvar__0__A__112880)
                  & Vvar__2___24Anonymous__112886 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__112880,Vvar__2__a__112900,cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__112880)) )
              | ? [Vvar__2__a__112907] :
                  ( t(Vvar__2__a__112907,Vvar__0__A__112880)
                  & ? [Vvar__3__b__112908] :
                      ( t(Vvar__3__b__112908,Vvar__0__A__112880)
                      & ? [Vvar__4__l__112909] :
                          ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__112880,Vvar__4__l__112909)
                          & cCoq_2eSorting_2eSorted_2eLocallySorted___24a3(Vvar__0__A__112880,Vvar__1__R__112881,cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__112880,Vvar__3__b__112908,Vvar__4__l__112909))
                          & p(happ(happ(Vvar__1__R__112881,Vvar__2__a__112907),Vvar__3__b__112908))
                          & Vvar__2___24Anonymous__112886 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__112880,Vvar__2__a__112907,cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__112880,Vvar__3__b__112908,Vvar__4__l__112909)) ) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.Sorting.Sorted.Sorted',axiom,
    ! [Vvar__0__A__112962,Vvar__1__R__112963,Vvar__2___24Anonymous__112968] :
      ( cType___24t(Vvar__0__A__112962)
     => ( c_24__type__112995___24t(Vvar__0__A__112962,Vvar__1__R__112963,Vvar__2___24Anonymous__112968,Vvar__1__R__112963)
       => ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__112962,Vvar__2___24Anonymous__112968)
         => ( cCoq_2eSorting_2eSorted_2eSorted___24a3(Vvar__0__A__112962,Vvar__1__R__112963,Vvar__2___24Anonymous__112968)
           => ( Vvar__2___24Anonymous__112968 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__112962)
              | ? [Vvar__2__a__112982] :
                  ( t(Vvar__2__a__112982,Vvar__0__A__112962)
                  & ? [Vvar__3__l__112983] :
                      ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__112962,Vvar__3__l__112983)
                      & cCoq_2eSorting_2eSorted_2eSorted___24a3(Vvar__0__A__112962,Vvar__1__R__112963,Vvar__3__l__112983)
                      & cCoq_2eSorting_2eSorted_2eHdRel___24a4(Vvar__0__A__112962,Vvar__1__R__112963,Vvar__2__a__112982,Vvar__3__l__112983)
                      & Vvar__2___24Anonymous__112968 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__112962,Vvar__2__a__112982,Vvar__3__l__112983) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.Sorting.Sorted.StronglySorted',axiom,
    ! [Vvar__0__A__112997,Vvar__1__R__112998,Vvar__2___24Anonymous__113003] :
      ( cType___24t(Vvar__0__A__112997)
     => ( c_24__type__113030___24t(Vvar__0__A__112997,Vvar__1__R__112998,Vvar__2___24Anonymous__113003,Vvar__1__R__112998)
       => ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__112997,Vvar__2___24Anonymous__113003)
         => ( cCoq_2eSorting_2eSorted_2eStronglySorted___24a3(Vvar__0__A__112997,Vvar__1__R__112998,Vvar__2___24Anonymous__113003)
           => ( Vvar__2___24Anonymous__113003 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__112997)
              | ? [Vvar__2__a__113017] :
                  ( t(Vvar__2__a__113017,Vvar__0__A__112997)
                  & ? [Vvar__3__l__113018] :
                      ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__112997,Vvar__3__l__113018)
                      & cCoq_2eSorting_2eSorted_2eStronglySorted___24a3(Vvar__0__A__112997,Vvar__1__R__112998,Vvar__3__l__113018)
                      & cCoq_2eLists_2eList_2eForall___24a3(Vvar__0__A__112997,happ(Vvar__1__R__112998,Vvar__2__a__113017),Vvar__3__l__113018)
                      & Vvar__2___24Anonymous__113003 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__112997,Vvar__2__a__113017,Vvar__3__l__113018) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.Strings.Ascii.ascii',axiom,
    ! [VX13735] :
      ( cCoq_2eStrings_2eAscii_2eascii___24t(VX13735)
     => ? [Vvar__0___24Anonymous__13736] :
          ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__0___24Anonymous__13736)
          & ? [Vvar__1___24Anonymous__13737] :
              ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__1___24Anonymous__13737)
              & ? [Vvar__2___24Anonymous__13738] :
                  ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__2___24Anonymous__13738)
                  & ? [Vvar__3___24Anonymous__13739] :
                      ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__3___24Anonymous__13739)
                      & ? [Vvar__4___24Anonymous__13740] :
                          ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__4___24Anonymous__13740)
                          & ? [Vvar__5___24Anonymous__13741] :
                              ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__5___24Anonymous__13741)
                              & ? [Vvar__6___24Anonymous__13742] :
                                  ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__6___24Anonymous__13742)
                                  & ? [Vvar__7___24Anonymous__13743] :
                                      ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__7___24Anonymous__13743)
                                      & VX13735 = cCoq_2eStrings_2eAscii_2eAscii___24a8(Vvar__0___24Anonymous__13736,Vvar__1___24Anonymous__13737,Vvar__2___24Anonymous__13738,Vvar__3___24Anonymous__13739,Vvar__4___24Anonymous__13740,Vvar__5___24Anonymous__13741,Vvar__6___24Anonymous__13742,Vvar__7___24Anonymous__13743) ) ) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.Strings.String.string',axiom,
    ! [VX104282] :
      ( cCoq_2eStrings_2eString_2estring___24t(VX104282)
     => ( VX104282 = cCoq_2eStrings_2eString_2eEmptyString
        | ? [Vvar__0___24Anonymous__104283] :
            ( cCoq_2eStrings_2eAscii_2eascii___24t(Vvar__0___24Anonymous__104283)
            & ? [Vvar__1___24Anonymous__104284] :
                ( cCoq_2eStrings_2eString_2estring___24t(Vvar__1___24Anonymous__104284)
                & VX104282 = cCoq_2eStrings_2eString_2eString___24a2(Vvar__0___24Anonymous__104283,Vvar__1___24Anonymous__104284) ) ) ) ) ).

fof('$_inversion_Coq.Structures.OrderedType.Compare',axiom,
    ! [Vvar__0__X__109439,Vvar__1__lt__109440,Vvar__2__eq__109445,Vvar__3__x__109450,Vvar__4__y__109451,VX109452] :
      ( cType___24t(Vvar__0__X__109439)
     => ( c_24__type__109512___24t(Vvar__0__X__109439,Vvar__1__lt__109440,Vvar__2__eq__109445,Vvar__3__x__109450,Vvar__4__y__109451,Vvar__1__lt__109440)
       => ( c_24__type__109531___24t(Vvar__0__X__109439,Vvar__1__lt__109440,Vvar__2__eq__109445,Vvar__3__x__109450,Vvar__4__y__109451,Vvar__2__eq__109445)
         => ( t(Vvar__3__x__109450,Vvar__0__X__109439)
           => ( t(Vvar__4__y__109451,Vvar__0__X__109439)
             => ( cCoq_2eStructures_2eOrderedType_2eCompare___24t(Vvar__0__X__109439,Vvar__1__lt__109440,Vvar__2__eq__109445,Vvar__3__x__109450,Vvar__4__y__109451,VX109452)
               => ( ( p(happ(happ(Vvar__1__lt__109440,Vvar__3__x__109450),Vvar__4__y__109451))
                    & VX109452 = cCoq_2eStructures_2eOrderedType_2eLT___24a5(Vvar__0__X__109439,Vvar__1__lt__109440,Vvar__2__eq__109445,Vvar__3__x__109450,Vvar__4__y__109451) )
                  | ( p(happ(happ(Vvar__2__eq__109445,Vvar__3__x__109450),Vvar__4__y__109451))
                    & VX109452 = cCoq_2eStructures_2eOrderedType_2eEQ___24a5(Vvar__0__X__109439,Vvar__1__lt__109440,Vvar__2__eq__109445,Vvar__3__x__109450,Vvar__4__y__109451) )
                  | ( p(happ(happ(Vvar__1__lt__109440,Vvar__4__y__109451),Vvar__3__x__109450))
                    & VX109452 = cCoq_2eStructures_2eOrderedType_2eGT___24a5(Vvar__0__X__109439,Vvar__1__lt__109440,Vvar__2__eq__109445,Vvar__3__x__109450,Vvar__4__y__109451) ) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.Structures.OrderedTypeEx.String_as_OT.lts',axiom,
    ! [Vvar__0___24Anonymous__113760,Vvar__1___24Anonymous__113761] :
      ( cCoq_2eStrings_2eString_2estring___24t(Vvar__0___24Anonymous__113760)
     => ( cCoq_2eStrings_2eString_2estring___24t(Vvar__1___24Anonymous__113761)
       => ( cCoq_2eStructures_2eOrderedTypeEx_2eString__as__OT_2elts___24a2(Vvar__0___24Anonymous__113760,Vvar__1___24Anonymous__113761)
         => ( ? [Vvar__0__a__113763] :
                ( cCoq_2eStrings_2eAscii_2eascii___24t(Vvar__0__a__113763)
                & ? [Vvar__1__s__113764] :
                    ( cCoq_2eStrings_2eString_2estring___24t(Vvar__1__s__113764)
                    & Vvar__1___24Anonymous__113761 = cCoq_2eStrings_2eString_2eString___24a2(Vvar__0__a__113763,Vvar__1__s__113764)
                    & Vvar__0___24Anonymous__113760 = cCoq_2eStrings_2eString_2eEmptyString ) )
            | ? [Vvar__0__a__113765] :
                ( cCoq_2eStrings_2eAscii_2eascii___24t(Vvar__0__a__113765)
                & ? [Vvar__1__s1__113766] :
                    ( cCoq_2eStrings_2eString_2estring___24t(Vvar__1__s1__113766)
                    & ? [Vvar__2__s2__113767] :
                        ( cCoq_2eStrings_2eString_2estring___24t(Vvar__2__s2__113767)
                        & cCoq_2eStructures_2eOrderedTypeEx_2eString__as__OT_2elts___24a2(Vvar__1__s1__113766,Vvar__2__s2__113767)
                        & Vvar__1___24Anonymous__113761 = cCoq_2eStrings_2eString_2eString___24a2(Vvar__0__a__113765,Vvar__2__s2__113767)
                        & Vvar__0___24Anonymous__113760 = cCoq_2eStrings_2eString_2eString___24a2(Vvar__0__a__113765,Vvar__1__s1__113766) ) ) )
            | ? [Vvar__0__a__113769] :
                ( cCoq_2eStrings_2eAscii_2eascii___24t(Vvar__0__a__113769)
                & ? [Vvar__1__b__113770] :
                    ( cCoq_2eStrings_2eAscii_2eascii___24t(Vvar__1__b__113770)
                    & ? [Vvar__2__s1__113771] :
                        ( cCoq_2eStrings_2eString_2estring___24t(Vvar__2__s1__113771)
                        & ? [Vvar__3__s2__113772] :
                            ( cCoq_2eStrings_2eString_2estring___24t(Vvar__3__s2__113772)
                            & cCoq_2eInit_2ePeano_2elt___24a2(cCoq_2eStrings_2eAscii_2enat__of__ascii___24a1(Vvar__0__a__113769),cCoq_2eStrings_2eAscii_2enat__of__ascii___24a1(Vvar__1__b__113770))
                            & Vvar__1___24Anonymous__113761 = cCoq_2eStrings_2eString_2eString___24a2(Vvar__1__b__113770,Vvar__3__s2__113772)
                            & Vvar__0___24Anonymous__113760 = cCoq_2eStrings_2eString_2eString___24a2(Vvar__0__a__113769,Vvar__2__s1__113771) ) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.Structures.OrdersTac.ord',axiom,
    ! [VX109631] :
      ( cCoq_2eStructures_2eOrdersTac_2eord___24t(VX109631)
     => ( VX109631 = cCoq_2eStructures_2eOrdersTac_2eOEQ
        | VX109631 = cCoq_2eStructures_2eOrdersTac_2eOLT
        | VX109631 = cCoq_2eStructures_2eOrdersTac_2eOLE ) ) ).

fof('$_inversion_Coq.Vectors.Fin.t',axiom,
    ! [Vvar__0___24Anonymous__109151,VX109152] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__109151)
     => ( cCoq_2eVectors_2eFin_2et___24t(Vvar__0___24Anonymous__109151,VX109152)
       => ( ? [Vvar__0__n__109153] :
              ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0__n__109153)
              & Vvar__0___24Anonymous__109151 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0__n__109153)
              & VX109152 = cCoq_2eVectors_2eFin_2eF1___24a1(Vvar__0__n__109153) )
          | ? [Vvar__0__n__109154] :
              ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0__n__109154)
              & ? [Vvar__1___24Anonymous__109155] :
                  ( cCoq_2eVectors_2eFin_2et___24t(Vvar__0__n__109154,Vvar__1___24Anonymous__109155)
                  & Vvar__0___24Anonymous__109151 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0__n__109154)
                  & VX109152 = cCoq_2eVectors_2eFin_2eFS___24a2(Vvar__0__n__109154,Vvar__1___24Anonymous__109155) ) ) ) ) ) ).

fof('$_inversion_Coq.Vectors.VectorDef.Forall',axiom,
    ! [Vvar__0__A__121920,Vvar__1__P__121921,Vvar__2__n__121924,Vvar__3__v__121925] :
      ( cType___24t(Vvar__0__A__121920)
     => ( c_24__type__121945___24t(Vvar__0__A__121920,Vvar__1__P__121921,Vvar__2__n__121924,Vvar__3__v__121925,Vvar__1__P__121921)
       => ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__2__n__121924)
         => ( cCoq_2eVectors_2eVectorDef_2et___24t(Vvar__0__A__121920,Vvar__2__n__121924,Vvar__3__v__121925)
           => ( cCoq_2eVectors_2eVectorDef_2eForall___24a4(Vvar__0__A__121920,Vvar__1__P__121921,Vvar__2__n__121924,Vvar__3__v__121925)
             => ( ( Vvar__3__v__121925 = cCoq_2eVectors_2eVectorDef_2enil___24a1(Vvar__0__A__121920)
                  & Vvar__2__n__121924 = cCoq_2eInit_2eDatatypes_2eO )
                | ? [Vvar__2__n__121935] :
                    ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__2__n__121935)
                    & ? [Vvar__3__x__121936] :
                        ( t(Vvar__3__x__121936,Vvar__0__A__121920)
                        & ? [Vvar__4__v__121937] :
                            ( cCoq_2eVectors_2eVectorDef_2et___24t(Vvar__0__A__121920,Vvar__2__n__121935,Vvar__4__v__121937)
                            & p(happ(Vvar__1__P__121921,Vvar__3__x__121936))
                            & cCoq_2eVectors_2eVectorDef_2eForall___24a4(Vvar__0__A__121920,Vvar__1__P__121921,Vvar__2__n__121935,Vvar__4__v__121937)
                            & Vvar__3__v__121925 = cCoq_2eVectors_2eVectorDef_2econs___24a4(Vvar__0__A__121920,Vvar__3__x__121936,Vvar__2__n__121935,Vvar__4__v__121937)
                            & Vvar__2__n__121924 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__2__n__121935) ) ) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.Vectors.VectorDef.Forall2',axiom,
    ! [Vvar__0__A__121992,Vvar__1__B__121993,Vvar__2__P__121994,Vvar__3__n__121999,Vvar__4___24Anonymous__122000,Vvar__5___24Anonymous__122001] :
      ( cType___24t(Vvar__0__A__121992)
     => ( cType___24t(Vvar__1__B__121993)
       => ( c_24__type__122041___24t(Vvar__0__A__121992,Vvar__1__B__121993,Vvar__2__P__121994,Vvar__3__n__121999,Vvar__4___24Anonymous__122000,Vvar__5___24Anonymous__122001,Vvar__2__P__121994)
         => ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__3__n__121999)
           => ( cCoq_2eVectors_2eVectorDef_2et___24t(Vvar__0__A__121992,Vvar__3__n__121999,Vvar__4___24Anonymous__122000)
             => ( cCoq_2eVectors_2eVectorDef_2et___24t(Vvar__1__B__121993,Vvar__3__n__121999,Vvar__5___24Anonymous__122001)
               => ( cCoq_2eVectors_2eVectorDef_2eForall2___24a6(Vvar__0__A__121992,Vvar__1__B__121993,Vvar__2__P__121994,Vvar__3__n__121999,Vvar__4___24Anonymous__122000,Vvar__5___24Anonymous__122001)
                 => ( ( Vvar__5___24Anonymous__122001 = cCoq_2eVectors_2eVectorDef_2enil___24a1(Vvar__1__B__121993)
                      & Vvar__4___24Anonymous__122000 = cCoq_2eVectors_2eVectorDef_2enil___24a1(Vvar__0__A__121992)
                      & Vvar__3__n__121999 = cCoq_2eInit_2eDatatypes_2eO )
                    | ? [Vvar__3__m__122017] :
                        ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__3__m__122017)
                        & ? [Vvar__4__x1__122018] :
                            ( t(Vvar__4__x1__122018,Vvar__0__A__121992)
                            & ? [Vvar__5__x2__122019] :
                                ( t(Vvar__5__x2__122019,Vvar__1__B__121993)
                                & ? [Vvar__6__v1__122020] :
                                    ( cCoq_2eVectors_2eVectorDef_2et___24t(Vvar__0__A__121992,Vvar__3__m__122017,Vvar__6__v1__122020)
                                    & ? [Vvar__7__v2__122021] :
                                        ( cCoq_2eVectors_2eVectorDef_2et___24t(Vvar__1__B__121993,Vvar__3__m__122017,Vvar__7__v2__122021)
                                        & p(happ(happ(Vvar__2__P__121994,Vvar__4__x1__122018),Vvar__5__x2__122019))
                                        & cCoq_2eVectors_2eVectorDef_2eForall2___24a6(Vvar__0__A__121992,Vvar__1__B__121993,Vvar__2__P__121994,Vvar__3__m__122017,Vvar__6__v1__122020,Vvar__7__v2__122021)
                                        & Vvar__5___24Anonymous__122001 = cCoq_2eVectors_2eVectorDef_2econs___24a4(Vvar__1__B__121993,Vvar__5__x2__122019,Vvar__3__m__122017,Vvar__7__v2__122021)
                                        & Vvar__4___24Anonymous__122000 = cCoq_2eVectors_2eVectorDef_2econs___24a4(Vvar__0__A__121992,Vvar__4__x1__122018,Vvar__3__m__122017,Vvar__6__v1__122020)
                                        & Vvar__3__n__121999 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__3__m__122017) ) ) ) ) ) ) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.Vectors.VectorDef.t',axiom,
    ! [Vvar__0__A__113223,Vvar__1___24Anonymous__113224,VX113225] :
      ( cType___24t(Vvar__0__A__113223)
     => ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__1___24Anonymous__113224)
       => ( cCoq_2eVectors_2eVectorDef_2et___24t(Vvar__0__A__113223,Vvar__1___24Anonymous__113224,VX113225)
         => ( ( Vvar__1___24Anonymous__113224 = cCoq_2eInit_2eDatatypes_2eO
              & VX113225 = cCoq_2eVectors_2eVectorDef_2enil___24a1(Vvar__0__A__113223) )
            | ? [Vvar__1__h__113228] :
                ( t(Vvar__1__h__113228,Vvar__0__A__113223)
                & ? [Vvar__2__n__113229] :
                    ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__2__n__113229)
                    & ? [Vvar__3___24Anonymous__113230] :
                        ( cCoq_2eVectors_2eVectorDef_2et___24t(Vvar__0__A__113223,Vvar__2__n__113229,Vvar__3___24Anonymous__113230)
                        & Vvar__1___24Anonymous__113224 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__2__n__113229)
                        & VX113225 = cCoq_2eVectors_2eVectorDef_2econs___24a4(Vvar__0__A__113223,Vvar__1__h__113228,Vvar__2__n__113229,Vvar__3___24Anonymous__113230) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.ZArith.Znumtheory.Bezout',axiom,
    ! [Vvar__0__a__113424,Vvar__1__b__113425,Vvar__2__d__113426] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__0__a__113424)
     => ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__1__b__113425)
       => ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__2__d__113426)
         => ( cCoq_2eZArith_2eZnumtheory_2eBezout___24a3(Vvar__0__a__113424,Vvar__1__b__113425,Vvar__2__d__113426)
           => ? [Vvar__3__u__113431] :
                ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__3__u__113431)
                & ? [Vvar__4__v__113432] :
                    ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__4__v__113432)
                    & cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(Vvar__3__u__113431,Vvar__0__a__113424),cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(Vvar__4__v__113432,Vvar__1__b__113425)) = Vvar__2__d__113426
                    & p(c_24True) ) ) ) ) ) ) ).

fof('$_inversion_Coq.ZArith.Znumtheory.Euclid',axiom,
    ! [Vvar__0__a__113399,Vvar__1__b__113400,VX113401] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__0__a__113399)
     => ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__1__b__113400)
       => ( cCoq_2eZArith_2eZnumtheory_2eEuclid___24t(Vvar__0__a__113399,Vvar__1__b__113400,VX113401)
         => ? [Vvar__2__u__113404] :
              ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__2__u__113404)
              & ? [Vvar__3__v__113405] :
                  ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__3__v__113405)
                  & ? [Vvar__4__d__113406] :
                      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__4__d__113406)
                      & cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(Vvar__2__u__113404,Vvar__0__a__113399),cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(Vvar__3__v__113405,Vvar__1__b__113400)) = Vvar__4__d__113406
                      & cCoq_2eZArith_2eZnumtheory_2eZis__gcd___24a3(Vvar__0__a__113399,Vvar__1__b__113400,Vvar__4__d__113406)
                      & VX113401 = cCoq_2eZArith_2eZnumtheory_2eEuclid__intro___24a5(Vvar__0__a__113399,Vvar__1__b__113400,Vvar__2__u__113404,Vvar__3__v__113405,Vvar__4__d__113406) ) ) ) ) ) ) ).

fof('$_inversion_Coq.ZArith.Znumtheory.Zis_gcd',axiom,
    ! [Vvar__0__a__106987,Vvar__1__b__106988,Vvar__2__g__106989] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__0__a__106987)
     => ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__1__b__106988)
       => ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__2__g__106989)
         => ( cCoq_2eZArith_2eZnumtheory_2eZis__gcd___24a3(Vvar__0__a__106987,Vvar__1__b__106988,Vvar__2__g__106989)
           => ( cCoq_2eZArith_2eBinInt_2eZ_2edivide___24a2(Vvar__2__g__106989,Vvar__0__a__106987)
              & cCoq_2eZArith_2eBinInt_2eZ_2edivide___24a2(Vvar__2__g__106989,Vvar__1__b__106988)
              & ! [Vvar__var__var__var__var__5__x__106997__107000__107003__107006__107009] :
                  ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__var__var__var__var__5__x__106997__107000__107003__107006__107009)
                 => ( cCoq_2eZArith_2eBinInt_2eZ_2edivide___24a2(Vvar__var__var__var__var__5__x__106997__107000__107003__107006__107009,Vvar__0__a__106987)
                   => ( cCoq_2eZArith_2eBinInt_2eZ_2edivide___24a2(Vvar__var__var__var__var__5__x__106997__107000__107003__107006__107009,Vvar__1__b__106988)
                     => cCoq_2eZArith_2eBinInt_2eZ_2edivide___24a2(Vvar__var__var__var__var__5__x__106997__107000__107003__107006__107009,Vvar__2__g__106989) ) ) )
              & p(c_24True) ) ) ) ) ) ).

fof('$_inversion_Coq.ZArith.Znumtheory.prime',axiom,
    ! [Vvar__0__p__113434] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__0__p__113434)
     => ( cCoq_2eZArith_2eZnumtheory_2eprime___24a1(Vvar__0__p__113434)
       => ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH),Vvar__0__p__113434))
          & ! [Vvar__var__var__2__n__113439__113441__113443] :
              ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__var__var__2__n__113439__113441__113443)
             => ( ( cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH),Vvar__var__var__2__n__113439__113441__113443)
                  & p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(Vvar__var__var__2__n__113439__113441__113443,Vvar__0__p__113434)) )
               => cCoq_2eZArith_2eZnumtheory_2erel__prime___24a2(Vvar__var__var__2__n__113439__113441__113443,Vvar__0__p__113434) ) )
          & p(c_24True) ) ) ) ).

fof('$_inversion_Coq.ZArith.Zpower.Zdiv_rest_proofs',axiom,
    ! [Vvar__0__x__113447,Vvar__1__p__113448,VX113449] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__0__x__113447)
     => ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1__p__113448)
       => ( cCoq_2eZArith_2eZpower_2eZdiv__rest__proofs___24t(Vvar__0__x__113447,Vvar__1__p__113448,VX113449)
         => ? [Vvar__2__q__113452] :
              ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__2__q__113452)
              & ? [Vvar__3__r__113453] :
                  ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__3__r__113453)
                  & Vvar__0__x__113447 = cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(Vvar__2__q__113452,cCoq_2eZArith_2eZpower_2etwo__power__pos___24a1(Vvar__1__p__113448)),Vvar__3__r__113453)
                  & cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,Vvar__3__r__113453)
                  & p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(Vvar__3__r__113453,cCoq_2eZArith_2eZpower_2etwo__power__pos___24a1(Vvar__1__p__113448)))
                  & VX113449 = cCoq_2eZArith_2eZpower_2eZdiv__rest__proof___24a4(Vvar__0__x__113447,Vvar__1__p__113448,Vvar__2__q__113452,Vvar__3__r__113453) ) ) ) ) ) ).

fof('$_inversion_Coq.micromega.DeclConstant.DeclaredConstant',axiom,
    ! [Vvar__0__T__107678,Vvar__1__F__107679] :
      ( cType___24t(Vvar__0__T__107678)
     => ( t(Vvar__1__F__107679,Vvar__0__T__107678)
       => ( cCoq_2emicromega_2eDeclConstant_2eDeclaredConstant___24a2(Vvar__0__T__107678,Vvar__1__F__107679)
         => p(c_24True) ) ) ) ).

fof('$_inversion_Coq.micromega.DeclConstant.GT',axiom,
    ! [Vvar__0__T__107683,Vvar__1__F__107684] :
      ( cType___24t(Vvar__0__T__107683)
     => ( t(Vvar__1__F__107684,Vvar__0__T__107683)
       => ( cCoq_2emicromega_2eDeclConstant_2eGT___24a2(Vvar__0__T__107683,Vvar__1__F__107684)
         => p(c_24True) ) ) ) ).

fof('$_inversion_Coq.micromega.EnvRing.Mon',axiom,
    ! [VX86827] :
      ( cCoq_2emicromega_2eEnvRing_2eMon___24t(VX86827)
     => ( VX86827 = cCoq_2emicromega_2eEnvRing_2emon0
        | ? [Vvar__0___24Anonymous__86828] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__86828)
            & ? [Vvar__1___24Anonymous__86829] :
                ( cCoq_2emicromega_2eEnvRing_2eMon___24t(Vvar__1___24Anonymous__86829)
                & VX86827 = cCoq_2emicromega_2eEnvRing_2ezmon___24a2(Vvar__0___24Anonymous__86828,Vvar__1___24Anonymous__86829) ) )
        | ? [Vvar__0___24Anonymous__86830] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__86830)
            & ? [Vvar__1___24Anonymous__86831] :
                ( cCoq_2emicromega_2eEnvRing_2eMon___24t(Vvar__1___24Anonymous__86831)
                & VX86827 = cCoq_2emicromega_2eEnvRing_2evmon___24a2(Vvar__0___24Anonymous__86830,Vvar__1___24Anonymous__86831) ) ) ) ) ).

fof('$_inversion_Coq.micromega.EnvRing.PExpr',axiom,
    ! [Vvar__0__C__85708,VX85709] :
      ( cType___24t(Vvar__0__C__85708)
     => ( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__C__85708,VX85709)
       => ( ? [Vvar__1___24Anonymous__85711] :
              ( t(Vvar__1___24Anonymous__85711,Vvar__0__C__85708)
              & VX85709 = cCoq_2emicromega_2eEnvRing_2ePEc___24a2(Vvar__0__C__85708,Vvar__1___24Anonymous__85711) )
          | ? [Vvar__1___24Anonymous__85713] :
              ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__85713)
              & VX85709 = cCoq_2emicromega_2eEnvRing_2ePEX___24a2(Vvar__0__C__85708,Vvar__1___24Anonymous__85713) )
          | ? [Vvar__1___24Anonymous__85715] :
              ( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__C__85708,Vvar__1___24Anonymous__85715)
              & ? [Vvar__2___24Anonymous__85716] :
                  ( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__C__85708,Vvar__2___24Anonymous__85716)
                  & VX85709 = cCoq_2emicromega_2eEnvRing_2ePEadd___24a3(Vvar__0__C__85708,Vvar__1___24Anonymous__85715,Vvar__2___24Anonymous__85716) ) )
          | ? [Vvar__1___24Anonymous__85718] :
              ( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__C__85708,Vvar__1___24Anonymous__85718)
              & ? [Vvar__2___24Anonymous__85719] :
                  ( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__C__85708,Vvar__2___24Anonymous__85719)
                  & VX85709 = cCoq_2emicromega_2eEnvRing_2ePEsub___24a3(Vvar__0__C__85708,Vvar__1___24Anonymous__85718,Vvar__2___24Anonymous__85719) ) )
          | ? [Vvar__1___24Anonymous__85721] :
              ( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__C__85708,Vvar__1___24Anonymous__85721)
              & ? [Vvar__2___24Anonymous__85722] :
                  ( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__C__85708,Vvar__2___24Anonymous__85722)
                  & VX85709 = cCoq_2emicromega_2eEnvRing_2ePEmul___24a3(Vvar__0__C__85708,Vvar__1___24Anonymous__85721,Vvar__2___24Anonymous__85722) ) )
          | ? [Vvar__1___24Anonymous__85724] :
              ( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__C__85708,Vvar__1___24Anonymous__85724)
              & VX85709 = cCoq_2emicromega_2eEnvRing_2ePEopp___24a2(Vvar__0__C__85708,Vvar__1___24Anonymous__85724) )
          | ? [Vvar__1___24Anonymous__85726] :
              ( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__C__85708,Vvar__1___24Anonymous__85726)
              & ? [Vvar__2___24Anonymous__85727] :
                  ( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__2___24Anonymous__85727)
                  & VX85709 = cCoq_2emicromega_2eEnvRing_2ePEpow___24a3(Vvar__0__C__85708,Vvar__1___24Anonymous__85726,Vvar__2___24Anonymous__85727) ) ) ) ) ) ).

fof('$_inversion_Coq.micromega.EnvRing.Pol',axiom,
    ! [Vvar__0__C__85872,VX85873] :
      ( cType___24t(Vvar__0__C__85872)
     => ( cCoq_2emicromega_2eEnvRing_2ePol___24t(Vvar__0__C__85872,VX85873)
       => ( ? [Vvar__1___24Anonymous__85875] :
              ( t(Vvar__1___24Anonymous__85875,Vvar__0__C__85872)
              & VX85873 = cCoq_2emicromega_2eEnvRing_2ePc___24a2(Vvar__0__C__85872,Vvar__1___24Anonymous__85875) )
          | ? [Vvar__1___24Anonymous__85877] :
              ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__85877)
              & ? [Vvar__2___24Anonymous__85878] :
                  ( cCoq_2emicromega_2eEnvRing_2ePol___24t(Vvar__0__C__85872,Vvar__2___24Anonymous__85878)
                  & VX85873 = cCoq_2emicromega_2eEnvRing_2ePinj___24a3(Vvar__0__C__85872,Vvar__1___24Anonymous__85877,Vvar__2___24Anonymous__85878) ) )
          | ? [Vvar__1___24Anonymous__85880] :
              ( cCoq_2emicromega_2eEnvRing_2ePol___24t(Vvar__0__C__85872,Vvar__1___24Anonymous__85880)
              & ? [Vvar__2___24Anonymous__85881] :
                  ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2___24Anonymous__85881)
                  & ? [Vvar__3___24Anonymous__85882] :
                      ( cCoq_2emicromega_2eEnvRing_2ePol___24t(Vvar__0__C__85872,Vvar__3___24Anonymous__85882)
                      & VX85873 = cCoq_2emicromega_2eEnvRing_2ePX___24a4(Vvar__0__C__85872,Vvar__1___24Anonymous__85880,Vvar__2___24Anonymous__85881,Vvar__3___24Anonymous__85882) ) ) ) ) ) ) ).

fof('$_inversion_Coq.micromega.OrderedRing.SOR',axiom,
    ! [Vvar__0__R__89844,Vvar__1__rO__89845,Vvar__2__rI__89846,Vvar__3__rplus__89847,Vvar__4__rtimes__89852,Vvar__5__rminus__89857,Vvar__6__ropp__89862,Vvar__7__req__89865,Vvar__8__rle__89870,Vvar__9__rlt__89875] :
      ( cType___24t(Vvar__0__R__89844)
     => ( t(Vvar__1__rO__89845,Vvar__0__R__89844)
       => ( t(Vvar__2__rI__89846,Vvar__0__R__89844)
         => ( c_24__type__90276___24t(Vvar__0__R__89844,Vvar__1__rO__89845,Vvar__2__rI__89846,Vvar__3__rplus__89847,Vvar__4__rtimes__89852,Vvar__5__rminus__89857,Vvar__6__ropp__89862,Vvar__7__req__89865,Vvar__8__rle__89870,Vvar__9__rlt__89875,Vvar__3__rplus__89847)
           => ( c_24__type__90377___24t(Vvar__0__R__89844,Vvar__1__rO__89845,Vvar__2__rI__89846,Vvar__3__rplus__89847,Vvar__4__rtimes__89852,Vvar__5__rminus__89857,Vvar__6__ropp__89862,Vvar__7__req__89865,Vvar__8__rle__89870,Vvar__9__rlt__89875,Vvar__4__rtimes__89852)
             => ( c_24__type__90478___24t(Vvar__0__R__89844,Vvar__1__rO__89845,Vvar__2__rI__89846,Vvar__3__rplus__89847,Vvar__4__rtimes__89852,Vvar__5__rminus__89857,Vvar__6__ropp__89862,Vvar__7__req__89865,Vvar__8__rle__89870,Vvar__9__rlt__89875,Vvar__5__rminus__89857)
               => ( c_24__type__90568___24t(Vvar__0__R__89844,Vvar__1__rO__89845,Vvar__2__rI__89846,Vvar__3__rplus__89847,Vvar__4__rtimes__89852,Vvar__5__rminus__89857,Vvar__6__ropp__89862,Vvar__7__req__89865,Vvar__8__rle__89870,Vvar__9__rlt__89875,Vvar__6__ropp__89862)
                 => ( c_24__type__90669___24t(Vvar__0__R__89844,Vvar__1__rO__89845,Vvar__2__rI__89846,Vvar__3__rplus__89847,Vvar__4__rtimes__89852,Vvar__5__rminus__89857,Vvar__6__ropp__89862,Vvar__7__req__89865,Vvar__8__rle__89870,Vvar__9__rlt__89875,Vvar__7__req__89865)
                   => ( c_24__type__90770___24t(Vvar__0__R__89844,Vvar__1__rO__89845,Vvar__2__rI__89846,Vvar__3__rplus__89847,Vvar__4__rtimes__89852,Vvar__5__rminus__89857,Vvar__6__ropp__89862,Vvar__7__req__89865,Vvar__8__rle__89870,Vvar__9__rlt__89875,Vvar__8__rle__89870)
                     => ( c_24__type__90871___24t(Vvar__0__R__89844,Vvar__1__rO__89845,Vvar__2__rI__89846,Vvar__3__rplus__89847,Vvar__4__rtimes__89852,Vvar__5__rminus__89857,Vvar__6__ropp__89862,Vvar__7__req__89865,Vvar__8__rle__89870,Vvar__9__rlt__89875,Vvar__9__rlt__89875)
                       => ( cCoq_2emicromega_2eOrderedRing_2eSOR___24a10(Vvar__0__R__89844,Vvar__1__rO__89845,Vvar__2__rI__89846,Vvar__3__rplus__89847,Vvar__4__rtimes__89852,Vvar__5__rminus__89857,Vvar__6__ropp__89862,Vvar__7__req__89865,Vvar__8__rle__89870,Vvar__9__rlt__89875)
                         => ( cCoq_2eSetoids_2eSetoid_2eSetoid__Theory___24a2(Vvar__0__R__89844,Vvar__7__req__89865)
                            & ! [Vvar__var__var__var__var__11__x1__89919__89925__90030__90036__90042] :
                                ( t(Vvar__var__var__var__var__11__x1__89919__89925__90030__90036__90042,Vvar__0__R__89844)
                               => ! [Vvar__var__var__var__var__12__x2__89920__89926__90031__90037__90043] :
                                    ( t(Vvar__var__var__var__var__12__x2__89920__89926__90031__90037__90043,Vvar__0__R__89844)
                                   => ( p(happ(happ(Vvar__7__req__89865,Vvar__var__var__var__var__11__x1__89919__89925__90030__90036__90042),Vvar__var__var__var__var__12__x2__89920__89926__90031__90037__90043))
                                     => ! [Vvar__var__var__var__var__14__y1__89921__89927__90032__90038__90044] :
                                          ( t(Vvar__var__var__var__var__14__y1__89921__89927__90032__90038__90044,Vvar__0__R__89844)
                                         => ! [Vvar__var__var__var__var__15__y2__89922__89928__90033__90039__90045] :
                                              ( t(Vvar__var__var__var__var__15__y2__89922__89928__90033__90039__90045,Vvar__0__R__89844)
                                             => ( p(happ(happ(Vvar__7__req__89865,Vvar__var__var__var__var__14__y1__89921__89927__90032__90038__90044),Vvar__var__var__var__var__15__y2__89922__89928__90033__90039__90045))
                                               => p(happ(happ(Vvar__7__req__89865,happ(happ(Vvar__3__rplus__89847,Vvar__var__var__var__var__11__x1__89919__89925__90030__90036__90042),Vvar__var__var__var__var__14__y1__89921__89927__90032__90038__90044)),happ(happ(Vvar__3__rplus__89847,Vvar__var__var__var__var__12__x2__89920__89926__90031__90037__90043),Vvar__var__var__var__var__15__y2__89922__89928__90033__90039__90045))) ) ) ) ) ) )
                            & ! [Vvar__var__var__var__var__12__x1__89932__89938__90048__90054__90060] :
                                ( t(Vvar__var__var__var__var__12__x1__89932__89938__90048__90054__90060,Vvar__0__R__89844)
                               => ! [Vvar__var__var__var__var__13__x2__89933__89939__90049__90055__90061] :
                                    ( t(Vvar__var__var__var__var__13__x2__89933__89939__90049__90055__90061,Vvar__0__R__89844)
                                   => ( p(happ(happ(Vvar__7__req__89865,Vvar__var__var__var__var__12__x1__89932__89938__90048__90054__90060),Vvar__var__var__var__var__13__x2__89933__89939__90049__90055__90061))
                                     => ! [Vvar__var__var__var__var__15__y1__89934__89940__90050__90056__90062] :
                                          ( t(Vvar__var__var__var__var__15__y1__89934__89940__90050__90056__90062,Vvar__0__R__89844)
                                         => ! [Vvar__var__var__var__var__16__y2__89935__89941__90051__90057__90063] :
                                              ( t(Vvar__var__var__var__var__16__y2__89935__89941__90051__90057__90063,Vvar__0__R__89844)
                                             => ( p(happ(happ(Vvar__7__req__89865,Vvar__var__var__var__var__15__y1__89934__89940__90050__90056__90062),Vvar__var__var__var__var__16__y2__89935__89941__90051__90057__90063))
                                               => p(happ(happ(Vvar__7__req__89865,happ(happ(Vvar__4__rtimes__89852,Vvar__var__var__var__var__12__x1__89932__89938__90048__90054__90060),Vvar__var__var__var__var__15__y1__89934__89940__90050__90056__90062)),happ(happ(Vvar__4__rtimes__89852,Vvar__var__var__var__var__13__x2__89933__89939__90049__90055__90061),Vvar__var__var__var__var__16__y2__89935__89941__90051__90057__90063))) ) ) ) ) ) )
                            & ! [Vvar__var__var__var__var__13__x1__89945__89948__90066__90069__90072] :
                                ( t(Vvar__var__var__var__var__13__x1__89945__89948__90066__90069__90072,Vvar__0__R__89844)
                               => ! [Vvar__var__var__var__var__14__x2__89946__89949__90067__90070__90073] :
                                    ( t(Vvar__var__var__var__var__14__x2__89946__89949__90067__90070__90073,Vvar__0__R__89844)
                                   => ( p(happ(happ(Vvar__7__req__89865,Vvar__var__var__var__var__13__x1__89945__89948__90066__90069__90072),Vvar__var__var__var__var__14__x2__89946__89949__90067__90070__90073))
                                     => p(happ(happ(Vvar__7__req__89865,happ(Vvar__6__ropp__89862,Vvar__var__var__var__var__13__x1__89945__89948__90066__90069__90072)),happ(Vvar__6__ropp__89862,Vvar__var__var__var__var__14__x2__89946__89949__90067__90070__90073))) ) ) )
                            & ! [Vvar__var__var__var__var__14__x1__89952__89958__90075__90081__90087] :
                                ( t(Vvar__var__var__var__var__14__x1__89952__89958__90075__90081__90087,Vvar__0__R__89844)
                               => ! [Vvar__var__var__var__var__15__x2__89953__89959__90076__90082__90088] :
                                    ( t(Vvar__var__var__var__var__15__x2__89953__89959__90076__90082__90088,Vvar__0__R__89844)
                                   => ( p(happ(happ(Vvar__7__req__89865,Vvar__var__var__var__var__14__x1__89952__89958__90075__90081__90087),Vvar__var__var__var__var__15__x2__89953__89959__90076__90082__90088))
                                     => ! [Vvar__var__var__var__var__17__y1__89954__89960__90077__90083__90089] :
                                          ( t(Vvar__var__var__var__var__17__y1__89954__89960__90077__90083__90089,Vvar__0__R__89844)
                                         => ! [Vvar__var__var__var__var__18__y2__89955__89961__90078__90084__90090] :
                                              ( t(Vvar__var__var__var__var__18__y2__89955__89961__90078__90084__90090,Vvar__0__R__89844)
                                             => ( p(happ(happ(Vvar__7__req__89865,Vvar__var__var__var__var__17__y1__89954__89960__90077__90083__90089),Vvar__var__var__var__var__18__y2__89955__89961__90078__90084__90090))
                                               => ( p(happ(happ(Vvar__8__rle__89870,Vvar__var__var__var__var__14__x1__89952__89958__90075__90081__90087),Vvar__var__var__var__var__17__y1__89954__89960__90077__90083__90089))
                                                <=> p(happ(happ(Vvar__8__rle__89870,Vvar__var__var__var__var__15__x2__89953__89959__90076__90082__90088),Vvar__var__var__var__var__18__y2__89955__89961__90078__90084__90090)) ) ) ) ) ) ) )
                            & ! [Vvar__var__var__var__var__15__x1__89965__89971__90093__90099__90105] :
                                ( t(Vvar__var__var__var__var__15__x1__89965__89971__90093__90099__90105,Vvar__0__R__89844)
                               => ! [Vvar__var__var__var__var__16__x2__89966__89972__90094__90100__90106] :
                                    ( t(Vvar__var__var__var__var__16__x2__89966__89972__90094__90100__90106,Vvar__0__R__89844)
                                   => ( p(happ(happ(Vvar__7__req__89865,Vvar__var__var__var__var__15__x1__89965__89971__90093__90099__90105),Vvar__var__var__var__var__16__x2__89966__89972__90094__90100__90106))
                                     => ! [Vvar__var__var__var__var__18__y1__89967__89973__90095__90101__90107] :
                                          ( t(Vvar__var__var__var__var__18__y1__89967__89973__90095__90101__90107,Vvar__0__R__89844)
                                         => ! [Vvar__var__var__var__var__19__y2__89968__89974__90096__90102__90108] :
                                              ( t(Vvar__var__var__var__var__19__y2__89968__89974__90096__90102__90108,Vvar__0__R__89844)
                                             => ( p(happ(happ(Vvar__7__req__89865,Vvar__var__var__var__var__18__y1__89967__89973__90095__90101__90107),Vvar__var__var__var__var__19__y2__89968__89974__90096__90102__90108))
                                               => ( p(happ(happ(Vvar__9__rlt__89875,Vvar__var__var__var__var__15__x1__89965__89971__90093__90099__90105),Vvar__var__var__var__var__18__y1__89967__89973__90095__90101__90107))
                                                <=> p(happ(happ(Vvar__9__rlt__89875,Vvar__var__var__var__var__16__x2__89966__89972__90094__90100__90106),Vvar__var__var__var__var__19__y2__89968__89974__90096__90102__90108)) ) ) ) ) ) ) )
                            & cCoq_2esetoid__ring_2eRing__theory_2ering__theory___24a8(Vvar__0__R__89844,Vvar__1__rO__89845,Vvar__2__rI__89846,Vvar__3__rplus__89847,Vvar__4__rtimes__89852,Vvar__5__rminus__89857,Vvar__6__ropp__89862,Vvar__7__req__89865)
                            & ! [Vvar__var__var__var__17__n__89979__89980__90111__90112] :
                                ( t(Vvar__var__var__var__17__n__89979__89980__90111__90112,Vvar__0__R__89844)
                               => p(happ(happ(Vvar__8__rle__89870,Vvar__var__var__var__17__n__89979__89980__90111__90112),Vvar__var__var__var__17__n__89979__89980__90111__90112)) )
                            & ! [Vvar__var__var__var__var__18__n__89982__89986__90113__90117__90121] :
                                ( t(Vvar__var__var__var__var__18__n__89982__89986__90113__90117__90121,Vvar__0__R__89844)
                               => ! [Vvar__var__var__var__var__19__m__89983__89987__90114__90118__90122] :
                                    ( t(Vvar__var__var__var__var__19__m__89983__89987__90114__90118__90122,Vvar__0__R__89844)
                                   => ( p(happ(happ(Vvar__8__rle__89870,Vvar__var__var__var__var__18__n__89982__89986__90113__90117__90121),Vvar__var__var__var__var__19__m__89983__89987__90114__90118__90122))
                                     => ( p(happ(happ(Vvar__8__rle__89870,Vvar__var__var__var__var__19__m__89983__89987__90114__90118__90122),Vvar__var__var__var__var__18__n__89982__89986__90113__90117__90121))
                                       => p(happ(happ(Vvar__7__req__89865,Vvar__var__var__var__var__18__n__89982__89986__90113__90117__90121),Vvar__var__var__var__var__19__m__89983__89987__90114__90118__90122)) ) ) ) )
                            & ! [Vvar__var__var__var__19__n__89991__89996__90125__90130] :
                                ( t(Vvar__var__var__var__19__n__89991__89996__90125__90130,Vvar__0__R__89844)
                               => ! [Vvar__var__var__var__20__m__89992__89997__90126__90131] :
                                    ( t(Vvar__var__var__var__20__m__89992__89997__90126__90131,Vvar__0__R__89844)
                                   => ! [Vvar__var__var__var__21__p__89993__89998__90127__90132] :
                                        ( t(Vvar__var__var__var__21__p__89993__89998__90127__90132,Vvar__0__R__89844)
                                       => ( p(happ(happ(Vvar__8__rle__89870,Vvar__var__var__var__19__n__89991__89996__90125__90130),Vvar__var__var__var__20__m__89992__89997__90126__90131))
                                         => ( p(happ(happ(Vvar__8__rle__89870,Vvar__var__var__var__20__m__89992__89997__90126__90131),Vvar__var__var__var__21__p__89993__89998__90127__90132))
                                           => p(happ(happ(Vvar__8__rle__89870,Vvar__var__var__var__19__n__89991__89996__90125__90130),Vvar__var__var__var__21__p__89993__89998__90127__90132)) ) ) ) ) )
                            & ! [Vvar__var__var__var__var__var__20__n__90002__90004__90135__90137__90139__90141] :
                                ( t(Vvar__var__var__var__var__var__20__n__90002__90004__90135__90137__90139__90141,Vvar__0__R__89844)
                               => ! [Vvar__var__var__var__var__var__21__m__90003__90005__90136__90138__90140__90142] :
                                    ( t(Vvar__var__var__var__var__var__21__m__90003__90005__90136__90138__90140__90142,Vvar__0__R__89844)
                                   => ( p(happ(happ(Vvar__9__rlt__89875,Vvar__var__var__var__var__var__20__n__90002__90004__90135__90137__90139__90141),Vvar__var__var__var__var__var__21__m__90003__90005__90136__90138__90140__90142))
                                    <=> ( p(happ(happ(Vvar__8__rle__89870,Vvar__var__var__var__var__var__20__n__90002__90004__90135__90137__90139__90141),Vvar__var__var__var__var__var__21__m__90003__90005__90136__90138__90140__90142))
                                        & ~ p(happ(happ(Vvar__7__req__89865,Vvar__var__var__var__var__var__20__n__90002__90004__90135__90137__90139__90141),Vvar__var__var__var__var__var__21__m__90003__90005__90136__90138__90140__90142)) ) ) ) )
                            & ! [Vvar__var__var__var__var__21__n__90007__90009__90143__90145__90147] :
                                ( t(Vvar__var__var__var__var__21__n__90007__90009__90143__90145__90147,Vvar__0__R__89844)
                               => ! [Vvar__var__var__var__var__22__m__90008__90010__90144__90146__90148] :
                                    ( t(Vvar__var__var__var__var__22__m__90008__90010__90144__90146__90148,Vvar__0__R__89844)
                                   => ( p(happ(happ(Vvar__9__rlt__89875,Vvar__var__var__var__var__21__n__90007__90009__90143__90145__90147),Vvar__var__var__var__var__22__m__90008__90010__90144__90146__90148))
                                      | p(happ(happ(Vvar__7__req__89865,Vvar__var__var__var__var__21__n__90007__90009__90143__90145__90147),Vvar__var__var__var__var__22__m__90008__90010__90144__90146__90148))
                                      | p(happ(happ(Vvar__9__rlt__89875,Vvar__var__var__var__var__22__m__90008__90010__90144__90146__90148),Vvar__var__var__var__var__21__n__90007__90009__90143__90145__90147)) ) ) )
                            & ! [Vvar__var__var__var__var__22__n__90012__90016__90149__90153__90157] :
                                ( t(Vvar__var__var__var__var__22__n__90012__90016__90149__90153__90157,Vvar__0__R__89844)
                               => ! [Vvar__var__var__var__var__23__m__90013__90017__90150__90154__90158] :
                                    ( t(Vvar__var__var__var__var__23__m__90013__90017__90150__90154__90158,Vvar__0__R__89844)
                                   => ! [Vvar__var__var__var__var__24__p__90014__90018__90151__90155__90159] :
                                        ( t(Vvar__var__var__var__var__24__p__90014__90018__90151__90155__90159,Vvar__0__R__89844)
                                       => ( p(happ(happ(Vvar__8__rle__89870,Vvar__var__var__var__var__22__n__90012__90016__90149__90153__90157),Vvar__var__var__var__var__23__m__90013__90017__90150__90154__90158))
                                         => p(happ(happ(Vvar__8__rle__89870,happ(happ(Vvar__3__rplus__89847,Vvar__var__var__var__var__24__p__90014__90018__90151__90155__90159),Vvar__var__var__var__var__22__n__90012__90016__90149__90153__90157)),happ(happ(Vvar__3__rplus__89847,Vvar__var__var__var__var__24__p__90014__90018__90151__90155__90159),Vvar__var__var__var__var__23__m__90013__90017__90150__90154__90158))) ) ) ) )
                            & ! [Vvar__var__var__var__var__var__23__n__90021__90025__90161__90165__90169__90173] :
                                ( t(Vvar__var__var__var__var__var__23__n__90021__90025__90161__90165__90169__90173,Vvar__0__R__89844)
                               => ! [Vvar__var__var__var__var__var__24__m__90022__90026__90162__90166__90170__90174] :
                                    ( t(Vvar__var__var__var__var__var__24__m__90022__90026__90162__90166__90170__90174,Vvar__0__R__89844)
                                   => ( p(happ(happ(Vvar__9__rlt__89875,Vvar__1__rO__89845),Vvar__var__var__var__var__var__23__n__90021__90025__90161__90165__90169__90173))
                                     => ( p(happ(happ(Vvar__9__rlt__89875,Vvar__1__rO__89845),Vvar__var__var__var__var__var__24__m__90022__90026__90162__90166__90170__90174))
                                       => p(happ(happ(Vvar__9__rlt__89875,Vvar__1__rO__89845),happ(happ(Vvar__4__rtimes__89852,Vvar__var__var__var__var__var__23__n__90021__90025__90161__90165__90169__90173),Vvar__var__var__var__var__var__24__m__90022__90026__90162__90166__90170__90174))) ) ) ) )
                            & ~ p(happ(happ(Vvar__7__req__89865,Vvar__1__rO__89845),Vvar__2__rI__89846))
                            & p(c_24True) ) ) ) ) ) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.micromega.RMicromega.Rcst',axiom,
    ! [VX109678] :
      ( cCoq_2emicromega_2eRMicromega_2eRcst___24t(VX109678)
     => ( VX109678 = cCoq_2emicromega_2eRMicromega_2eC0
        | VX109678 = cCoq_2emicromega_2eRMicromega_2eC1
        | ? [Vvar__0__r__109679] :
            ( cCoq_2eQArith_2eQArith__base_2eQ___24t(Vvar__0__r__109679)
            & VX109678 = cCoq_2emicromega_2eRMicromega_2eCQ___24a1(Vvar__0__r__109679) )
        | ? [Vvar__0__r__109680] :
            ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__0__r__109680)
            & VX109678 = cCoq_2emicromega_2eRMicromega_2eCZ___24a1(Vvar__0__r__109680) )
        | ? [Vvar__0__r1__109681] :
            ( cCoq_2emicromega_2eRMicromega_2eRcst___24t(Vvar__0__r1__109681)
            & ? [Vvar__1__r2__109682] :
                ( cCoq_2emicromega_2eRMicromega_2eRcst___24t(Vvar__1__r2__109682)
                & VX109678 = cCoq_2emicromega_2eRMicromega_2eCPlus___24a2(Vvar__0__r1__109681,Vvar__1__r2__109682) ) )
        | ? [Vvar__0__r1__109683] :
            ( cCoq_2emicromega_2eRMicromega_2eRcst___24t(Vvar__0__r1__109683)
            & ? [Vvar__1__r2__109684] :
                ( cCoq_2emicromega_2eRMicromega_2eRcst___24t(Vvar__1__r2__109684)
                & VX109678 = cCoq_2emicromega_2eRMicromega_2eCMinus___24a2(Vvar__0__r1__109683,Vvar__1__r2__109684) ) )
        | ? [Vvar__0__r1__109685] :
            ( cCoq_2emicromega_2eRMicromega_2eRcst___24t(Vvar__0__r1__109685)
            & ? [Vvar__1__r2__109686] :
                ( cCoq_2emicromega_2eRMicromega_2eRcst___24t(Vvar__1__r2__109686)
                & VX109678 = cCoq_2emicromega_2eRMicromega_2eCMult___24a2(Vvar__0__r1__109685,Vvar__1__r2__109686) ) )
        | ? [Vvar__0__r1__109687] :
            ( cCoq_2emicromega_2eRMicromega_2eRcst___24t(Vvar__0__r1__109687)
            & ? [Vvar__1__z__109688] :
                ( cCoq_2eInit_2eDatatypes_2esum___24t(cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eInit_2eDatatypes_2enat,Vvar__1__z__109688)
                & VX109678 = cCoq_2emicromega_2eRMicromega_2eCPow___24a2(Vvar__0__r1__109687,Vvar__1__z__109688) ) )
        | ? [Vvar__0__r__109689] :
            ( cCoq_2emicromega_2eRMicromega_2eRcst___24t(Vvar__0__r__109689)
            & VX109678 = cCoq_2emicromega_2eRMicromega_2eCInv___24a1(Vvar__0__r__109689) )
        | ? [Vvar__0__r__109690] :
            ( cCoq_2emicromega_2eRMicromega_2eRcst___24t(Vvar__0__r__109690)
            & VX109678 = cCoq_2emicromega_2eRMicromega_2eCOpp___24a1(Vvar__0__r__109690) ) ) ) ).

fof('$_inversion_Coq.micromega.RingMicromega.Formula',axiom,
    ! [Vvar__0__T__98171,VX98172] :
      ( cType___24t(Vvar__0__T__98171)
     => ( cCoq_2emicromega_2eRingMicromega_2eFormula___24t(Vvar__0__T__98171,VX98172)
       => ? [Vvar__1__Flhs__98174] :
            ( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__T__98171,Vvar__1__Flhs__98174)
            & ? [Vvar__2__Fop__98175] :
                ( cCoq_2emicromega_2eRingMicromega_2eOp2___24t(Vvar__2__Fop__98175)
                & ? [Vvar__3__Frhs__98176] :
                    ( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__T__98171,Vvar__3__Frhs__98176)
                    & VX98172 = cCoq_2emicromega_2eRingMicromega_2eBuild__Formula___24a4(Vvar__0__T__98171,Vvar__1__Flhs__98174,Vvar__2__Fop__98175,Vvar__3__Frhs__98176) ) ) ) ) ) ).

fof('$_inversion_Coq.micromega.RingMicromega.Op1',axiom,
    ! [VX96893] :
      ( cCoq_2emicromega_2eRingMicromega_2eOp1___24t(VX96893)
     => ( VX96893 = cCoq_2emicromega_2eRingMicromega_2eEqual
        | VX96893 = cCoq_2emicromega_2eRingMicromega_2eNonEqual
        | VX96893 = cCoq_2emicromega_2eRingMicromega_2eStrict
        | VX96893 = cCoq_2emicromega_2eRingMicromega_2eNonStrict ) ) ).

fof('$_inversion_Coq.micromega.RingMicromega.Op2',axiom,
    ! [VX110503] :
      ( cCoq_2emicromega_2eRingMicromega_2eOp2___24t(VX110503)
     => ( VX110503 = cCoq_2emicromega_2eRingMicromega_2eOpEq
        | VX110503 = cCoq_2emicromega_2eRingMicromega_2eOpNEq
        | VX110503 = cCoq_2emicromega_2eRingMicromega_2eOpLe
        | VX110503 = cCoq_2emicromega_2eRingMicromega_2eOpGe
        | VX110503 = cCoq_2emicromega_2eRingMicromega_2eOpLt
        | VX110503 = cCoq_2emicromega_2eRingMicromega_2eOpGt ) ) ).

fof('$_inversion_Coq.micromega.RingMicromega.Psatz',axiom,
    ! [Vvar__0__C__97155,VX97156] :
      ( cType___24t(Vvar__0__C__97155)
     => ( cCoq_2emicromega_2eRingMicromega_2ePsatz___24t(Vvar__0__C__97155,VX97156)
       => ( ? [Vvar__1___24Anonymous__97158] :
              ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__1___24Anonymous__97158)
              & VX97156 = cCoq_2emicromega_2eRingMicromega_2ePsatzIn___24a2(Vvar__0__C__97155,Vvar__1___24Anonymous__97158) )
          | ? [Vvar__1___24Anonymous__97160] :
              ( cCoq_2emicromega_2eRingMicromega_2ePolC___24t(Vvar__0__C__97155,Vvar__1___24Anonymous__97160)
              & VX97156 = cCoq_2emicromega_2eRingMicromega_2ePsatzSquare___24a2(Vvar__0__C__97155,Vvar__1___24Anonymous__97160) )
          | ? [Vvar__1___24Anonymous__97162] :
              ( cCoq_2emicromega_2eRingMicromega_2ePolC___24t(Vvar__0__C__97155,Vvar__1___24Anonymous__97162)
              & ? [Vvar__2___24Anonymous__97163] :
                  ( cCoq_2emicromega_2eRingMicromega_2ePsatz___24t(Vvar__0__C__97155,Vvar__2___24Anonymous__97163)
                  & VX97156 = cCoq_2emicromega_2eRingMicromega_2ePsatzMulC___24a3(Vvar__0__C__97155,Vvar__1___24Anonymous__97162,Vvar__2___24Anonymous__97163) ) )
          | ? [Vvar__1___24Anonymous__97165] :
              ( cCoq_2emicromega_2eRingMicromega_2ePsatz___24t(Vvar__0__C__97155,Vvar__1___24Anonymous__97165)
              & ? [Vvar__2___24Anonymous__97166] :
                  ( cCoq_2emicromega_2eRingMicromega_2ePsatz___24t(Vvar__0__C__97155,Vvar__2___24Anonymous__97166)
                  & VX97156 = cCoq_2emicromega_2eRingMicromega_2ePsatzMulE___24a3(Vvar__0__C__97155,Vvar__1___24Anonymous__97165,Vvar__2___24Anonymous__97166) ) )
          | ? [Vvar__1___24Anonymous__97168] :
              ( cCoq_2emicromega_2eRingMicromega_2ePsatz___24t(Vvar__0__C__97155,Vvar__1___24Anonymous__97168)
              & ? [Vvar__2___24Anonymous__97169] :
                  ( cCoq_2emicromega_2eRingMicromega_2ePsatz___24t(Vvar__0__C__97155,Vvar__2___24Anonymous__97169)
                  & VX97156 = cCoq_2emicromega_2eRingMicromega_2ePsatzAdd___24a3(Vvar__0__C__97155,Vvar__1___24Anonymous__97168,Vvar__2___24Anonymous__97169) ) )
          | ? [Vvar__1___24Anonymous__97171] :
              ( t(Vvar__1___24Anonymous__97171,Vvar__0__C__97155)
              & VX97156 = cCoq_2emicromega_2eRingMicromega_2ePsatzC___24a2(Vvar__0__C__97155,Vvar__1___24Anonymous__97171) )
          | VX97156 = cCoq_2emicromega_2eRingMicromega_2ePsatzZ___24a1(Vvar__0__C__97155) ) ) ) ).

fof('$_inversion_Coq.micromega.RingMicromega.SORaddon',axiom,
    ! [Vvar__0__R__91250,Vvar__1__rO__91251,Vvar__2__rI__91252,Vvar__3__rplus__91253,Vvar__4__rtimes__91258,Vvar__5__rminus__91263,Vvar__6__ropp__91268,Vvar__7__req__91271,Vvar__8__rle__91276,Vvar__9__C__91281,Vvar__10__cO__91282,Vvar__11__cI__91283,Vvar__12__cplus__91284,Vvar__13__ctimes__91289,Vvar__14__cminus__91294,Vvar__15__copp__91299,Vvar__16__ceqb__91302,Vvar__17__cleb__91307,Vvar__18__phi__91312,Vvar__19__E__91315,Vvar__20__pow__phi__91316,Vvar__21__rpow__91319] :
      ( cType___24t(Vvar__0__R__91250)
     => ( t(Vvar__1__rO__91251,Vvar__0__R__91250)
       => ( t(Vvar__2__rI__91252,Vvar__0__R__91250)
         => ( c_24__type__91783___24t(Vvar__0__R__91250,Vvar__1__rO__91251,Vvar__2__rI__91252,Vvar__3__rplus__91253,Vvar__4__rtimes__91258,Vvar__5__rminus__91263,Vvar__6__ropp__91268,Vvar__7__req__91271,Vvar__8__rle__91276,Vvar__9__C__91281,Vvar__10__cO__91282,Vvar__11__cI__91283,Vvar__12__cplus__91284,Vvar__13__ctimes__91289,Vvar__14__cminus__91294,Vvar__15__copp__91299,Vvar__16__ceqb__91302,Vvar__17__cleb__91307,Vvar__18__phi__91312,Vvar__19__E__91315,Vvar__20__pow__phi__91316,Vvar__21__rpow__91319,Vvar__3__rplus__91253)
           => ( c_24__type__92129___24t(Vvar__0__R__91250,Vvar__1__rO__91251,Vvar__2__rI__91252,Vvar__3__rplus__91253,Vvar__4__rtimes__91258,Vvar__5__rminus__91263,Vvar__6__ropp__91268,Vvar__7__req__91271,Vvar__8__rle__91276,Vvar__9__C__91281,Vvar__10__cO__91282,Vvar__11__cI__91283,Vvar__12__cplus__91284,Vvar__13__ctimes__91289,Vvar__14__cminus__91294,Vvar__15__copp__91299,Vvar__16__ceqb__91302,Vvar__17__cleb__91307,Vvar__18__phi__91312,Vvar__19__E__91315,Vvar__20__pow__phi__91316,Vvar__21__rpow__91319,Vvar__4__rtimes__91258)
             => ( c_24__type__92475___24t(Vvar__0__R__91250,Vvar__1__rO__91251,Vvar__2__rI__91252,Vvar__3__rplus__91253,Vvar__4__rtimes__91258,Vvar__5__rminus__91263,Vvar__6__ropp__91268,Vvar__7__req__91271,Vvar__8__rle__91276,Vvar__9__C__91281,Vvar__10__cO__91282,Vvar__11__cI__91283,Vvar__12__cplus__91284,Vvar__13__ctimes__91289,Vvar__14__cminus__91294,Vvar__15__copp__91299,Vvar__16__ceqb__91302,Vvar__17__cleb__91307,Vvar__18__phi__91312,Vvar__19__E__91315,Vvar__20__pow__phi__91316,Vvar__21__rpow__91319,Vvar__5__rminus__91263)
               => ( c_24__type__92798___24t(Vvar__0__R__91250,Vvar__1__rO__91251,Vvar__2__rI__91252,Vvar__3__rplus__91253,Vvar__4__rtimes__91258,Vvar__5__rminus__91263,Vvar__6__ropp__91268,Vvar__7__req__91271,Vvar__8__rle__91276,Vvar__9__C__91281,Vvar__10__cO__91282,Vvar__11__cI__91283,Vvar__12__cplus__91284,Vvar__13__ctimes__91289,Vvar__14__cminus__91294,Vvar__15__copp__91299,Vvar__16__ceqb__91302,Vvar__17__cleb__91307,Vvar__18__phi__91312,Vvar__19__E__91315,Vvar__20__pow__phi__91316,Vvar__21__rpow__91319,Vvar__6__ropp__91268)
                 => ( c_24__type__93144___24t(Vvar__0__R__91250,Vvar__1__rO__91251,Vvar__2__rI__91252,Vvar__3__rplus__91253,Vvar__4__rtimes__91258,Vvar__5__rminus__91263,Vvar__6__ropp__91268,Vvar__7__req__91271,Vvar__8__rle__91276,Vvar__9__C__91281,Vvar__10__cO__91282,Vvar__11__cI__91283,Vvar__12__cplus__91284,Vvar__13__ctimes__91289,Vvar__14__cminus__91294,Vvar__15__copp__91299,Vvar__16__ceqb__91302,Vvar__17__cleb__91307,Vvar__18__phi__91312,Vvar__19__E__91315,Vvar__20__pow__phi__91316,Vvar__21__rpow__91319,Vvar__7__req__91271)
                   => ( c_24__type__93490___24t(Vvar__0__R__91250,Vvar__1__rO__91251,Vvar__2__rI__91252,Vvar__3__rplus__91253,Vvar__4__rtimes__91258,Vvar__5__rminus__91263,Vvar__6__ropp__91268,Vvar__7__req__91271,Vvar__8__rle__91276,Vvar__9__C__91281,Vvar__10__cO__91282,Vvar__11__cI__91283,Vvar__12__cplus__91284,Vvar__13__ctimes__91289,Vvar__14__cminus__91294,Vvar__15__copp__91299,Vvar__16__ceqb__91302,Vvar__17__cleb__91307,Vvar__18__phi__91312,Vvar__19__E__91315,Vvar__20__pow__phi__91316,Vvar__21__rpow__91319,Vvar__8__rle__91276)
                     => ( cType___24t(Vvar__9__C__91281)
                       => ( t(Vvar__10__cO__91282,Vvar__9__C__91281)
                         => ( t(Vvar__11__cI__91283,Vvar__9__C__91281)
                           => ( c_24__type__93836___24t(Vvar__0__R__91250,Vvar__1__rO__91251,Vvar__2__rI__91252,Vvar__3__rplus__91253,Vvar__4__rtimes__91258,Vvar__5__rminus__91263,Vvar__6__ropp__91268,Vvar__7__req__91271,Vvar__8__rle__91276,Vvar__9__C__91281,Vvar__10__cO__91282,Vvar__11__cI__91283,Vvar__12__cplus__91284,Vvar__13__ctimes__91289,Vvar__14__cminus__91294,Vvar__15__copp__91299,Vvar__16__ceqb__91302,Vvar__17__cleb__91307,Vvar__18__phi__91312,Vvar__19__E__91315,Vvar__20__pow__phi__91316,Vvar__21__rpow__91319,Vvar__12__cplus__91284)
                             => ( c_24__type__94182___24t(Vvar__0__R__91250,Vvar__1__rO__91251,Vvar__2__rI__91252,Vvar__3__rplus__91253,Vvar__4__rtimes__91258,Vvar__5__rminus__91263,Vvar__6__ropp__91268,Vvar__7__req__91271,Vvar__8__rle__91276,Vvar__9__C__91281,Vvar__10__cO__91282,Vvar__11__cI__91283,Vvar__12__cplus__91284,Vvar__13__ctimes__91289,Vvar__14__cminus__91294,Vvar__15__copp__91299,Vvar__16__ceqb__91302,Vvar__17__cleb__91307,Vvar__18__phi__91312,Vvar__19__E__91315,Vvar__20__pow__phi__91316,Vvar__21__rpow__91319,Vvar__13__ctimes__91289)
                               => ( c_24__type__94528___24t(Vvar__0__R__91250,Vvar__1__rO__91251,Vvar__2__rI__91252,Vvar__3__rplus__91253,Vvar__4__rtimes__91258,Vvar__5__rminus__91263,Vvar__6__ropp__91268,Vvar__7__req__91271,Vvar__8__rle__91276,Vvar__9__C__91281,Vvar__10__cO__91282,Vvar__11__cI__91283,Vvar__12__cplus__91284,Vvar__13__ctimes__91289,Vvar__14__cminus__91294,Vvar__15__copp__91299,Vvar__16__ceqb__91302,Vvar__17__cleb__91307,Vvar__18__phi__91312,Vvar__19__E__91315,Vvar__20__pow__phi__91316,Vvar__21__rpow__91319,Vvar__14__cminus__91294)
                                 => ( c_24__type__94851___24t(Vvar__0__R__91250,Vvar__1__rO__91251,Vvar__2__rI__91252,Vvar__3__rplus__91253,Vvar__4__rtimes__91258,Vvar__5__rminus__91263,Vvar__6__ropp__91268,Vvar__7__req__91271,Vvar__8__rle__91276,Vvar__9__C__91281,Vvar__10__cO__91282,Vvar__11__cI__91283,Vvar__12__cplus__91284,Vvar__13__ctimes__91289,Vvar__14__cminus__91294,Vvar__15__copp__91299,Vvar__16__ceqb__91302,Vvar__17__cleb__91307,Vvar__18__phi__91312,Vvar__19__E__91315,Vvar__20__pow__phi__91316,Vvar__21__rpow__91319,Vvar__15__copp__91299)
                                   => ( c_24__type__95197___24t(Vvar__0__R__91250,Vvar__1__rO__91251,Vvar__2__rI__91252,Vvar__3__rplus__91253,Vvar__4__rtimes__91258,Vvar__5__rminus__91263,Vvar__6__ropp__91268,Vvar__7__req__91271,Vvar__8__rle__91276,Vvar__9__C__91281,Vvar__10__cO__91282,Vvar__11__cI__91283,Vvar__12__cplus__91284,Vvar__13__ctimes__91289,Vvar__14__cminus__91294,Vvar__15__copp__91299,Vvar__16__ceqb__91302,Vvar__17__cleb__91307,Vvar__18__phi__91312,Vvar__19__E__91315,Vvar__20__pow__phi__91316,Vvar__21__rpow__91319,Vvar__16__ceqb__91302)
                                     => ( c_24__type__95543___24t(Vvar__0__R__91250,Vvar__1__rO__91251,Vvar__2__rI__91252,Vvar__3__rplus__91253,Vvar__4__rtimes__91258,Vvar__5__rminus__91263,Vvar__6__ropp__91268,Vvar__7__req__91271,Vvar__8__rle__91276,Vvar__9__C__91281,Vvar__10__cO__91282,Vvar__11__cI__91283,Vvar__12__cplus__91284,Vvar__13__ctimes__91289,Vvar__14__cminus__91294,Vvar__15__copp__91299,Vvar__16__ceqb__91302,Vvar__17__cleb__91307,Vvar__18__phi__91312,Vvar__19__E__91315,Vvar__20__pow__phi__91316,Vvar__21__rpow__91319,Vvar__17__cleb__91307)
                                       => ( c_24__type__95866___24t(Vvar__0__R__91250,Vvar__1__rO__91251,Vvar__2__rI__91252,Vvar__3__rplus__91253,Vvar__4__rtimes__91258,Vvar__5__rminus__91263,Vvar__6__ropp__91268,Vvar__7__req__91271,Vvar__8__rle__91276,Vvar__9__C__91281,Vvar__10__cO__91282,Vvar__11__cI__91283,Vvar__12__cplus__91284,Vvar__13__ctimes__91289,Vvar__14__cminus__91294,Vvar__15__copp__91299,Vvar__16__ceqb__91302,Vvar__17__cleb__91307,Vvar__18__phi__91312,Vvar__19__E__91315,Vvar__20__pow__phi__91316,Vvar__21__rpow__91319,Vvar__18__phi__91312)
                                         => ( cType___24t(Vvar__19__E__91315)
                                           => ( c_24__type__96189___24t(Vvar__0__R__91250,Vvar__1__rO__91251,Vvar__2__rI__91252,Vvar__3__rplus__91253,Vvar__4__rtimes__91258,Vvar__5__rminus__91263,Vvar__6__ropp__91268,Vvar__7__req__91271,Vvar__8__rle__91276,Vvar__9__C__91281,Vvar__10__cO__91282,Vvar__11__cI__91283,Vvar__12__cplus__91284,Vvar__13__ctimes__91289,Vvar__14__cminus__91294,Vvar__15__copp__91299,Vvar__16__ceqb__91302,Vvar__17__cleb__91307,Vvar__18__phi__91312,Vvar__19__E__91315,Vvar__20__pow__phi__91316,Vvar__21__rpow__91319,Vvar__20__pow__phi__91316)
                                             => ( c_24__type__96535___24t(Vvar__0__R__91250,Vvar__1__rO__91251,Vvar__2__rI__91252,Vvar__3__rplus__91253,Vvar__4__rtimes__91258,Vvar__5__rminus__91263,Vvar__6__ropp__91268,Vvar__7__req__91271,Vvar__8__rle__91276,Vvar__9__C__91281,Vvar__10__cO__91282,Vvar__11__cI__91283,Vvar__12__cplus__91284,Vvar__13__ctimes__91289,Vvar__14__cminus__91294,Vvar__15__copp__91299,Vvar__16__ceqb__91302,Vvar__17__cleb__91307,Vvar__18__phi__91312,Vvar__19__E__91315,Vvar__20__pow__phi__91316,Vvar__21__rpow__91319,Vvar__21__rpow__91319)
                                               => ( cCoq_2emicromega_2eRingMicromega_2eSORaddon___24a22(Vvar__0__R__91250,Vvar__1__rO__91251,Vvar__2__rI__91252,Vvar__3__rplus__91253,Vvar__4__rtimes__91258,Vvar__5__rminus__91263,Vvar__6__ropp__91268,Vvar__7__req__91271,Vvar__8__rle__91276,Vvar__9__C__91281,Vvar__10__cO__91282,Vvar__11__cI__91283,Vvar__12__cplus__91284,Vvar__13__ctimes__91289,Vvar__14__cminus__91294,Vvar__15__copp__91299,Vvar__16__ceqb__91302,Vvar__17__cleb__91307,Vvar__18__phi__91312,Vvar__19__E__91315,Vvar__20__pow__phi__91316,Vvar__21__rpow__91319)
                                                 => ( cCoq_2esetoid__ring_2eRing__theory_2ering__morph___24a17(Vvar__0__R__91250,Vvar__1__rO__91251,Vvar__2__rI__91252,Vvar__3__rplus__91253,Vvar__4__rtimes__91258,Vvar__5__rminus__91263,Vvar__6__ropp__91268,Vvar__7__req__91271,Vvar__9__C__91281,Vvar__10__cO__91282,Vvar__11__cI__91283,Vvar__12__cplus__91284,Vvar__13__ctimes__91289,Vvar__14__cminus__91294,Vvar__15__copp__91299,Vvar__16__ceqb__91302,Vvar__18__phi__91312)
                                                    & cCoq_2esetoid__ring_2eRing__theory_2epower__theory___24a7(Vvar__0__R__91250,Vvar__2__rI__91252,Vvar__4__rtimes__91258,Vvar__7__req__91271,Vvar__19__E__91315,Vvar__20__pow__phi__91316,Vvar__21__rpow__91319)
                                                    & ! [Vvar__var__var__var__var__var__24__x__91402__91405__91415__91418__91421__91424] :
                                                        ( t(Vvar__var__var__var__var__var__24__x__91402__91405__91415__91418__91421__91424,Vvar__9__C__91281)
                                                       => ! [Vvar__var__var__var__var__var__25__y__91403__91406__91416__91419__91422__91425] :
                                                            ( t(Vvar__var__var__var__var__var__25__y__91403__91406__91416__91419__91422__91425,Vvar__9__C__91281)
                                                           => ( happ(happ(Vvar__16__ceqb__91302,Vvar__var__var__var__var__var__24__x__91402__91405__91415__91418__91421__91424),Vvar__var__var__var__var__var__25__y__91403__91406__91416__91419__91422__91425) = cCoq_2eInit_2eDatatypes_2efalse
                                                             => ~ p(happ(happ(Vvar__7__req__91271,happ(Vvar__18__phi__91312,Vvar__var__var__var__var__var__24__x__91402__91405__91415__91418__91421__91424)),happ(Vvar__18__phi__91312,Vvar__var__var__var__var__var__25__y__91403__91406__91416__91419__91422__91425))) ) ) )
                                                    & ! [Vvar__var__var__var__var__var__25__x__91409__91412__91427__91430__91433__91436] :
                                                        ( t(Vvar__var__var__var__var__var__25__x__91409__91412__91427__91430__91433__91436,Vvar__9__C__91281)
                                                       => ! [Vvar__var__var__var__var__var__26__y__91410__91413__91428__91431__91434__91437] :
                                                            ( t(Vvar__var__var__var__var__var__26__y__91410__91413__91428__91431__91434__91437,Vvar__9__C__91281)
                                                           => ( happ(happ(Vvar__17__cleb__91307,Vvar__var__var__var__var__var__25__x__91409__91412__91427__91430__91433__91436),Vvar__var__var__var__var__var__26__y__91410__91413__91428__91431__91434__91437) = cCoq_2eInit_2eDatatypes_2etrue
                                                             => p(happ(happ(Vvar__8__rle__91276,happ(Vvar__18__phi__91312,Vvar__var__var__var__var__var__25__x__91409__91412__91427__91430__91433__91436)),happ(Vvar__18__phi__91312,Vvar__var__var__var__var__var__26__y__91410__91413__91428__91431__91434__91437))) ) ) )
                                                    & p(c_24True) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.micromega.Tauto.GFormula',axiom,
    ! [Vvar__0__TA__2054,Vvar__1__TX__2055,Vvar__2__AA__2056,Vvar__3__AF__2057,VX2058] :
      ( cType___24t(Vvar__0__TA__2054)
     => ( cType___24t(Vvar__1__TX__2055)
       => ( cType___24t(Vvar__2__AA__2056)
         => ( cType___24t(Vvar__3__AF__2057)
           => ( cCoq_2emicromega_2eTauto_2eGFormula___24t(Vvar__0__TA__2054,Vvar__1__TX__2055,Vvar__2__AA__2056,Vvar__3__AF__2057,VX2058)
             => ( VX2058 = cCoq_2emicromega_2eTauto_2eTT___24a4(Vvar__0__TA__2054,Vvar__1__TX__2055,Vvar__2__AA__2056,Vvar__3__AF__2057)
                | VX2058 = cCoq_2emicromega_2eTauto_2eFF___24a4(Vvar__0__TA__2054,Vvar__1__TX__2055,Vvar__2__AA__2056,Vvar__3__AF__2057)
                | ? [Vvar__4___24Anonymous__2071] :
                    ( t(Vvar__4___24Anonymous__2071,Vvar__1__TX__2055)
                    & VX2058 = cCoq_2emicromega_2eTauto_2eX___24a5(Vvar__0__TA__2054,Vvar__1__TX__2055,Vvar__2__AA__2056,Vvar__3__AF__2057,Vvar__4___24Anonymous__2071) )
                | ? [Vvar__4___24Anonymous__2076] :
                    ( t(Vvar__4___24Anonymous__2076,Vvar__0__TA__2054)
                    & ? [Vvar__5___24Anonymous__2077] :
                        ( t(Vvar__5___24Anonymous__2077,Vvar__2__AA__2056)
                        & VX2058 = cCoq_2emicromega_2eTauto_2eA___24a6(Vvar__0__TA__2054,Vvar__1__TX__2055,Vvar__2__AA__2056,Vvar__3__AF__2057,Vvar__4___24Anonymous__2076,Vvar__5___24Anonymous__2077) ) )
                | ? [Vvar__4___24Anonymous__2082] :
                    ( cCoq_2emicromega_2eTauto_2eGFormula___24t(Vvar__0__TA__2054,Vvar__1__TX__2055,Vvar__2__AA__2056,Vvar__3__AF__2057,Vvar__4___24Anonymous__2082)
                    & ? [Vvar__5___24Anonymous__2083] :
                        ( cCoq_2emicromega_2eTauto_2eGFormula___24t(Vvar__0__TA__2054,Vvar__1__TX__2055,Vvar__2__AA__2056,Vvar__3__AF__2057,Vvar__5___24Anonymous__2083)
                        & VX2058 = cCoq_2emicromega_2eTauto_2eCj___24a6(Vvar__0__TA__2054,Vvar__1__TX__2055,Vvar__2__AA__2056,Vvar__3__AF__2057,Vvar__4___24Anonymous__2082,Vvar__5___24Anonymous__2083) ) )
                | ? [Vvar__4___24Anonymous__2088] :
                    ( cCoq_2emicromega_2eTauto_2eGFormula___24t(Vvar__0__TA__2054,Vvar__1__TX__2055,Vvar__2__AA__2056,Vvar__3__AF__2057,Vvar__4___24Anonymous__2088)
                    & ? [Vvar__5___24Anonymous__2089] :
                        ( cCoq_2emicromega_2eTauto_2eGFormula___24t(Vvar__0__TA__2054,Vvar__1__TX__2055,Vvar__2__AA__2056,Vvar__3__AF__2057,Vvar__5___24Anonymous__2089)
                        & VX2058 = cCoq_2emicromega_2eTauto_2eD___24a6(Vvar__0__TA__2054,Vvar__1__TX__2055,Vvar__2__AA__2056,Vvar__3__AF__2057,Vvar__4___24Anonymous__2088,Vvar__5___24Anonymous__2089) ) )
                | ? [Vvar__4___24Anonymous__2094] :
                    ( cCoq_2emicromega_2eTauto_2eGFormula___24t(Vvar__0__TA__2054,Vvar__1__TX__2055,Vvar__2__AA__2056,Vvar__3__AF__2057,Vvar__4___24Anonymous__2094)
                    & VX2058 = cCoq_2emicromega_2eTauto_2eN___24a5(Vvar__0__TA__2054,Vvar__1__TX__2055,Vvar__2__AA__2056,Vvar__3__AF__2057,Vvar__4___24Anonymous__2094) )
                | ? [Vvar__4___24Anonymous__2099] :
                    ( cCoq_2emicromega_2eTauto_2eGFormula___24t(Vvar__0__TA__2054,Vvar__1__TX__2055,Vvar__2__AA__2056,Vvar__3__AF__2057,Vvar__4___24Anonymous__2099)
                    & ? [Vvar__5___24Anonymous__2100] :
                        ( cCoq_2eInit_2eDatatypes_2eoption___24t(Vvar__3__AF__2057,Vvar__5___24Anonymous__2100)
                        & ? [Vvar__6___24Anonymous__2101] :
                            ( cCoq_2emicromega_2eTauto_2eGFormula___24t(Vvar__0__TA__2054,Vvar__1__TX__2055,Vvar__2__AA__2056,Vvar__3__AF__2057,Vvar__6___24Anonymous__2101)
                            & VX2058 = cCoq_2emicromega_2eTauto_2eI___24a7(Vvar__0__TA__2054,Vvar__1__TX__2055,Vvar__2__AA__2056,Vvar__3__AF__2057,Vvar__4___24Anonymous__2099,Vvar__5___24Anonymous__2100,Vvar__6___24Anonymous__2101) ) ) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.micromega.VarMap.t',axiom,
    ! [Vvar__0__A__113186,VX113187] :
      ( cType___24t(Vvar__0__A__113186)
     => ( cCoq_2emicromega_2eVarMap_2et___24t(Vvar__0__A__113186,VX113187)
       => ( VX113187 = cCoq_2emicromega_2eVarMap_2eEmpty___24a1(Vvar__0__A__113186)
          | ? [Vvar__1___24Anonymous__113190] :
              ( t(Vvar__1___24Anonymous__113190,Vvar__0__A__113186)
              & VX113187 = cCoq_2emicromega_2eVarMap_2eElt___24a2(Vvar__0__A__113186,Vvar__1___24Anonymous__113190) )
          | ? [Vvar__1___24Anonymous__113192] :
              ( cCoq_2emicromega_2eVarMap_2et___24t(Vvar__0__A__113186,Vvar__1___24Anonymous__113192)
              & ? [Vvar__2___24Anonymous__113193] :
                  ( t(Vvar__2___24Anonymous__113193,Vvar__0__A__113186)
                  & ? [Vvar__3___24Anonymous__113194] :
                      ( cCoq_2emicromega_2eVarMap_2et___24t(Vvar__0__A__113186,Vvar__3___24Anonymous__113194)
                      & VX113187 = cCoq_2emicromega_2eVarMap_2eBranch___24a4(Vvar__0__A__113186,Vvar__1___24Anonymous__113192,Vvar__2___24Anonymous__113193,Vvar__3___24Anonymous__113194) ) ) ) ) ) ) ).

fof('$_inversion_Coq.micromega.ZMicromega.Vars.Facts.MP.Dec.FSetDecideAuxiliary.FSet_Prop',axiom,
    ! [Vvar__0___24Anonymous__113533] :
      ( cProp___24t(Vvar__0___24Anonymous__113533)
     => ( cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__Prop___24a1(Vvar__0___24Anonymous__113533)
       => ( ? [Vvar__0__P__113535] :
              ( cProp___24t(Vvar__0__P__113535)
              & cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__elt__Prop___24a1(Vvar__0__P__113535)
              & Vvar__0___24Anonymous__113533 = Vvar__0__P__113535 )
          | ? [Vvar__0__s__113537] :
              ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(Vvar__0__s__113537)
              & Vvar__0___24Anonymous__113533 = c_24__prop__113546___24a2(Vvar__0___24Anonymous__113533,Vvar__0__s__113537) )
          | ? [Vvar__0__s1__113539] :
              ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(Vvar__0__s1__113539)
              & ? [Vvar__1__s2__113540] :
                  ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(Vvar__1__s2__113540)
                  & Vvar__0___24Anonymous__113533 = c_24__prop__113547___24a3(Vvar__0___24Anonymous__113533,Vvar__0__s1__113539,Vvar__1__s2__113540) ) )
          | ? [Vvar__0__s1__113543] :
              ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(Vvar__0__s1__113543)
              & ? [Vvar__1__s2__113544] :
                  ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(Vvar__1__s2__113544)
                  & Vvar__0___24Anonymous__113533 = c_24__prop__113548___24a3(Vvar__0___24Anonymous__113533,Vvar__0__s1__113543,Vvar__1__s2__113544) ) ) ) ) ) ).

fof('$_inversion_Coq.micromega.ZMicromega.Vars.Facts.MP.Dec.FSetDecideAuxiliary.FSet_elt_Prop',axiom,
    ! [Vvar__0___24Anonymous__113502] :
      ( cProp___24t(Vvar__0___24Anonymous__113502)
     => ( cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__elt__Prop___24a1(Vvar__0___24Anonymous__113502)
       => ( ? [Vvar__0__S__113504] :
              ( cType___24t(Vvar__0__S__113504)
              & ? [Vvar__1__x__113505] :
                  ( t(Vvar__1__x__113505,Vvar__0__S__113504)
                  & ? [Vvar__2__y__113506] :
                      ( t(Vvar__2__y__113506,Vvar__0__S__113504)
                      & Vvar__0___24Anonymous__113502 = c_24__prop__113526___24a4(Vvar__0___24Anonymous__113502,Vvar__0__S__113504,Vvar__1__x__113505,Vvar__2__y__113506) ) ) )
          | ? [Vvar__0__x__113507] :
              ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0__x__113507)
              & ? [Vvar__1__y__113508] :
                  ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1__y__113508)
                  & Vvar__0___24Anonymous__113502 = c_24__prop__113527___24a3(Vvar__0___24Anonymous__113502,Vvar__0__x__113507,Vvar__1__y__113508) ) )
          | ? [Vvar__0__x__113509] :
              ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(Vvar__0__x__113509)
              & ? [Vvar__1__s__113510] :
                  ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(Vvar__1__s__113510)
                  & Vvar__0___24Anonymous__113502 = c_24__prop__113528___24a3(Vvar__0___24Anonymous__113502,Vvar__0__x__113509,Vvar__1__s__113510) ) )
          | Vvar__0___24Anonymous__113502 = c_24True
          | Vvar__0___24Anonymous__113502 = c_24False
          | ? [Vvar__0__P__113511] :
              ( cProp___24t(Vvar__0__P__113511)
              & ? [Vvar__1__Q__113512] :
                  ( cProp___24t(Vvar__1__Q__113512)
                  & cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__elt__Prop___24a1(Vvar__0__P__113511)
                  & cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__elt__Prop___24a1(Vvar__1__Q__113512)
                  & Vvar__0___24Anonymous__113502 = c_24__prop__113529___24a3(Vvar__0___24Anonymous__113502,Vvar__0__P__113511,Vvar__1__Q__113512) ) )
          | ? [Vvar__0__P__113515] :
              ( cProp___24t(Vvar__0__P__113515)
              & ? [Vvar__1__Q__113516] :
                  ( cProp___24t(Vvar__1__Q__113516)
                  & cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__elt__Prop___24a1(Vvar__0__P__113515)
                  & cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__elt__Prop___24a1(Vvar__1__Q__113516)
                  & Vvar__0___24Anonymous__113502 = c_24__prop__113530___24a3(Vvar__0___24Anonymous__113502,Vvar__0__P__113515,Vvar__1__Q__113516) ) )
          | ? [Vvar__0__P__113519] :
              ( cProp___24t(Vvar__0__P__113519)
              & ? [Vvar__1__Q__113520] :
                  ( cProp___24t(Vvar__1__Q__113520)
                  & cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__elt__Prop___24a1(Vvar__0__P__113519)
                  & cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__elt__Prop___24a1(Vvar__1__Q__113520)
                  & Vvar__0___24Anonymous__113502 = c_24__prop__113531___24a3(Vvar__0___24Anonymous__113502,Vvar__0__P__113519,Vvar__1__Q__113520) ) )
          | ? [Vvar__0__P__113524] :
              ( cProp___24t(Vvar__0__P__113524)
              & cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__elt__Prop___24a1(Vvar__0__P__113524)
              & Vvar__0___24Anonymous__113502 = c_24__prop__113532___24a2(Vvar__0___24Anonymous__113502,Vvar__0__P__113524) ) ) ) ) ).

fof('$_inversion_Coq.micromega.ZMicromega.ZArithProof',axiom,
    ! [VX113288] :
      ( cCoq_2emicromega_2eZMicromega_2eZArithProof___24t(VX113288)
     => ( VX113288 = cCoq_2emicromega_2eZMicromega_2eDoneProof
        | ? [Vvar__0___24Anonymous__113289] :
            ( cCoq_2emicromega_2eZMicromega_2eZWitness___24t(Vvar__0___24Anonymous__113289)
            & ? [Vvar__1___24Anonymous__113290] :
                ( cCoq_2emicromega_2eZMicromega_2eZArithProof___24t(Vvar__1___24Anonymous__113290)
                & VX113288 = cCoq_2emicromega_2eZMicromega_2eRatProof___24a2(Vvar__0___24Anonymous__113289,Vvar__1___24Anonymous__113290) ) )
        | ? [Vvar__0___24Anonymous__113291] :
            ( cCoq_2emicromega_2eZMicromega_2eZWitness___24t(Vvar__0___24Anonymous__113291)
            & ? [Vvar__1___24Anonymous__113292] :
                ( cCoq_2emicromega_2eZMicromega_2eZArithProof___24t(Vvar__1___24Anonymous__113292)
                & VX113288 = cCoq_2emicromega_2eZMicromega_2eCutProof___24a2(Vvar__0___24Anonymous__113291,Vvar__1___24Anonymous__113292) ) )
        | ? [Vvar__0___24Anonymous__113293] :
            ( cCoq_2emicromega_2eZMicromega_2eZWitness___24t(Vvar__0___24Anonymous__113293)
            & ? [Vvar__1___24Anonymous__113294] :
                ( cCoq_2emicromega_2eZMicromega_2eZWitness___24t(Vvar__1___24Anonymous__113294)
                & ? [Vvar__2___24Anonymous__113295] :
                    ( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2emicromega_2eZMicromega_2eZArithProof,Vvar__2___24Anonymous__113295)
                    & VX113288 = cCoq_2emicromega_2eZMicromega_2eEnumProof___24a3(Vvar__0___24Anonymous__113293,Vvar__1___24Anonymous__113294,Vvar__2___24Anonymous__113295) ) ) ) ) ) ).

fof('$_inversion_Coq.micromega.ZMicromega.is_diff_env_elt',axiom,
    ! [Vvar__0__fr__113333,Vvar__1__env__113334,Vvar__2__env_27__113337,Vvar__3__x__113340] :
      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0__fr__113333)
     => ( c_24__type__113361___24t(Vvar__0__fr__113333,Vvar__1__env__113334,Vvar__2__env_27__113337,Vvar__3__x__113340,Vvar__1__env__113334)
       => ( c_24__type__113370___24t(Vvar__0__fr__113333,Vvar__1__env__113334,Vvar__2__env_27__113337,Vvar__3__x__113340,Vvar__2__env_27__113337)
         => ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__3__x__113340)
           => ( cCoq_2emicromega_2eZMicromega_2eis__diff__env__elt___24a4(Vvar__0__fr__113333,Vvar__1__env__113334,Vvar__2__env_27__113337,Vvar__3__x__113340)
             => ( happ(Vvar__1__env__113334,Vvar__3__x__113340) = happ(Vvar__2__env_27__113337,Vvar__3__x__113340)
                & happ(Vvar__1__env__113334,Vvar__3__x__113340) = cCoq_2eZArith_2eBinIntDef_2eZ_2esub___24a2(happ(Vvar__2__env_27__113337,cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(Vvar__0__fr__113333,Vvar__3__x__113340))),happ(Vvar__2__env_27__113337,cCoq_2eNumbers_2eBinNums_2exI___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(Vvar__0__fr__113333,Vvar__3__x__113340))))
                & cCoq_2eZArith_2eBinInt_2eZ_2ege___24a2(happ(Vvar__2__env_27__113337,cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(Vvar__0__fr__113333,Vvar__3__x__113340))),cCoq_2eNumbers_2eBinNums_2eZ0)
                & cCoq_2eZArith_2eBinInt_2eZ_2ege___24a2(happ(Vvar__2__env_27__113337,cCoq_2eNumbers_2eBinNums_2exI___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(Vvar__0__fr__113333,Vvar__3__x__113340))),cCoq_2eNumbers_2eBinNums_2eZ0)
                & p(c_24True) ) ) ) ) ) ) ).

fof('$_inversion_Coq.setoid_ring.Field_theory.FExpr',axiom,
    ! [Vvar__0__C__3469,VX3470] :
      ( cType___24t(Vvar__0__C__3469)
     => ( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__3469,VX3470)
       => ( VX3470 = cCoq_2esetoid__ring_2eField__theory_2eFEO___24a1(Vvar__0__C__3469)
          | VX3470 = cCoq_2esetoid__ring_2eField__theory_2eFEI___24a1(Vvar__0__C__3469)
          | ? [Vvar__1___24Anonymous__3474] :
              ( t(Vvar__1___24Anonymous__3474,Vvar__0__C__3469)
              & VX3470 = cCoq_2esetoid__ring_2eField__theory_2eFEc___24a2(Vvar__0__C__3469,Vvar__1___24Anonymous__3474) )
          | ? [Vvar__1___24Anonymous__3476] :
              ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__3476)
              & VX3470 = cCoq_2esetoid__ring_2eField__theory_2eFEX___24a2(Vvar__0__C__3469,Vvar__1___24Anonymous__3476) )
          | ? [Vvar__1___24Anonymous__3478] :
              ( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__3469,Vvar__1___24Anonymous__3478)
              & ? [Vvar__2___24Anonymous__3479] :
                  ( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__3469,Vvar__2___24Anonymous__3479)
                  & VX3470 = cCoq_2esetoid__ring_2eField__theory_2eFEadd___24a3(Vvar__0__C__3469,Vvar__1___24Anonymous__3478,Vvar__2___24Anonymous__3479) ) )
          | ? [Vvar__1___24Anonymous__3481] :
              ( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__3469,Vvar__1___24Anonymous__3481)
              & ? [Vvar__2___24Anonymous__3482] :
                  ( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__3469,Vvar__2___24Anonymous__3482)
                  & VX3470 = cCoq_2esetoid__ring_2eField__theory_2eFEsub___24a3(Vvar__0__C__3469,Vvar__1___24Anonymous__3481,Vvar__2___24Anonymous__3482) ) )
          | ? [Vvar__1___24Anonymous__3484] :
              ( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__3469,Vvar__1___24Anonymous__3484)
              & ? [Vvar__2___24Anonymous__3485] :
                  ( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__3469,Vvar__2___24Anonymous__3485)
                  & VX3470 = cCoq_2esetoid__ring_2eField__theory_2eFEmul___24a3(Vvar__0__C__3469,Vvar__1___24Anonymous__3484,Vvar__2___24Anonymous__3485) ) )
          | ? [Vvar__1___24Anonymous__3487] :
              ( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__3469,Vvar__1___24Anonymous__3487)
              & VX3470 = cCoq_2esetoid__ring_2eField__theory_2eFEopp___24a2(Vvar__0__C__3469,Vvar__1___24Anonymous__3487) )
          | ? [Vvar__1___24Anonymous__3489] :
              ( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__3469,Vvar__1___24Anonymous__3489)
              & VX3470 = cCoq_2esetoid__ring_2eField__theory_2eFEinv___24a2(Vvar__0__C__3469,Vvar__1___24Anonymous__3489) )
          | ? [Vvar__1___24Anonymous__3491] :
              ( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__3469,Vvar__1___24Anonymous__3491)
              & ? [Vvar__2___24Anonymous__3492] :
                  ( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__3469,Vvar__2___24Anonymous__3492)
                  & VX3470 = cCoq_2esetoid__ring_2eField__theory_2eFEdiv___24a3(Vvar__0__C__3469,Vvar__1___24Anonymous__3491,Vvar__2___24Anonymous__3492) ) )
          | ? [Vvar__1___24Anonymous__3494] :
              ( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__3469,Vvar__1___24Anonymous__3494)
              & ? [Vvar__2___24Anonymous__3495] :
                  ( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__2___24Anonymous__3495)
                  & VX3470 = cCoq_2esetoid__ring_2eField__theory_2eFEpow___24a3(Vvar__0__C__3469,Vvar__1___24Anonymous__3494,Vvar__2___24Anonymous__3495) ) ) ) ) ) ).

fof('$_inversion_Coq.setoid_ring.Field_theory.almost_field_theory',axiom,
    ! [Vvar__0__R__2665,Vvar__1__rO__2666,Vvar__2__rI__2667,Vvar__3__radd__2668,Vvar__4__rmul__2673,Vvar__5__rsub__2678,Vvar__6__ropp__2683,Vvar__7__rdiv__2686,Vvar__8__rinv__2691,Vvar__9__req__2694] :
      ( cType___24t(Vvar__0__R__2665)
     => ( t(Vvar__1__rO__2666,Vvar__0__R__2665)
       => ( t(Vvar__2__rI__2667,Vvar__0__R__2665)
         => ( c_24__type__2859___24t(Vvar__0__R__2665,Vvar__1__rO__2666,Vvar__2__rI__2667,Vvar__3__radd__2668,Vvar__4__rmul__2673,Vvar__5__rsub__2678,Vvar__6__ropp__2683,Vvar__7__rdiv__2686,Vvar__8__rinv__2691,Vvar__9__req__2694,Vvar__3__radd__2668)
           => ( c_24__type__2952___24t(Vvar__0__R__2665,Vvar__1__rO__2666,Vvar__2__rI__2667,Vvar__3__radd__2668,Vvar__4__rmul__2673,Vvar__5__rsub__2678,Vvar__6__ropp__2683,Vvar__7__rdiv__2686,Vvar__8__rinv__2691,Vvar__9__req__2694,Vvar__4__rmul__2673)
             => ( c_24__type__3045___24t(Vvar__0__R__2665,Vvar__1__rO__2666,Vvar__2__rI__2667,Vvar__3__radd__2668,Vvar__4__rmul__2673,Vvar__5__rsub__2678,Vvar__6__ropp__2683,Vvar__7__rdiv__2686,Vvar__8__rinv__2691,Vvar__9__req__2694,Vvar__5__rsub__2678)
               => ( c_24__type__3127___24t(Vvar__0__R__2665,Vvar__1__rO__2666,Vvar__2__rI__2667,Vvar__3__radd__2668,Vvar__4__rmul__2673,Vvar__5__rsub__2678,Vvar__6__ropp__2683,Vvar__7__rdiv__2686,Vvar__8__rinv__2691,Vvar__9__req__2694,Vvar__6__ropp__2683)
                 => ( c_24__type__3220___24t(Vvar__0__R__2665,Vvar__1__rO__2666,Vvar__2__rI__2667,Vvar__3__radd__2668,Vvar__4__rmul__2673,Vvar__5__rsub__2678,Vvar__6__ropp__2683,Vvar__7__rdiv__2686,Vvar__8__rinv__2691,Vvar__9__req__2694,Vvar__7__rdiv__2686)
                   => ( c_24__type__3302___24t(Vvar__0__R__2665,Vvar__1__rO__2666,Vvar__2__rI__2667,Vvar__3__radd__2668,Vvar__4__rmul__2673,Vvar__5__rsub__2678,Vvar__6__ropp__2683,Vvar__7__rdiv__2686,Vvar__8__rinv__2691,Vvar__9__req__2694,Vvar__8__rinv__2691)
                     => ( c_24__type__3395___24t(Vvar__0__R__2665,Vvar__1__rO__2666,Vvar__2__rI__2667,Vvar__3__radd__2668,Vvar__4__rmul__2673,Vvar__5__rsub__2678,Vvar__6__ropp__2683,Vvar__7__rdiv__2686,Vvar__8__rinv__2691,Vvar__9__req__2694,Vvar__9__req__2694)
                       => ( cCoq_2esetoid__ring_2eField__theory_2ealmost__field__theory___24a10(Vvar__0__R__2665,Vvar__1__rO__2666,Vvar__2__rI__2667,Vvar__3__radd__2668,Vvar__4__rmul__2673,Vvar__5__rsub__2678,Vvar__6__ropp__2683,Vvar__7__rdiv__2686,Vvar__8__rinv__2691,Vvar__9__req__2694)
                         => ( cCoq_2esetoid__ring_2eRing__theory_2ealmost__ring__theory___24a8(Vvar__0__R__2665,Vvar__1__rO__2666,Vvar__2__rI__2667,Vvar__3__radd__2668,Vvar__4__rmul__2673,Vvar__5__rsub__2678,Vvar__6__ropp__2683,Vvar__9__req__2694)
                            & ~ p(happ(happ(Vvar__9__req__2694,Vvar__2__rI__2667),Vvar__1__rO__2666))
                            & ! [Vvar__var__var__var__var__var__var__12__p__2737__2739__2746__2748__2750__2752__2754] :
                                ( t(Vvar__var__var__var__var__var__var__12__p__2737__2739__2746__2748__2750__2752__2754,Vvar__0__R__2665)
                               => ! [Vvar__var__var__var__var__var__var__13__q__2738__2740__2747__2749__2751__2753__2755] :
                                    ( t(Vvar__var__var__var__var__var__var__13__q__2738__2740__2747__2749__2751__2753__2755,Vvar__0__R__2665)
                                   => p(happ(happ(Vvar__9__req__2694,happ(happ(Vvar__7__rdiv__2686,Vvar__var__var__var__var__var__var__12__p__2737__2739__2746__2748__2750__2752__2754),Vvar__var__var__var__var__var__var__13__q__2738__2740__2747__2749__2751__2753__2755)),happ(happ(Vvar__4__rmul__2673,Vvar__var__var__var__var__var__var__12__p__2737__2739__2746__2748__2750__2752__2754),happ(Vvar__8__rinv__2691,Vvar__var__var__var__var__var__var__13__q__2738__2740__2747__2749__2751__2753__2755)))) ) )
                            & ! [Vvar__var__var__var__var__var__var__var__13__p__2742__2744__2756__2758__2760__2762__2764__2766] :
                                ( t(Vvar__var__var__var__var__var__var__var__13__p__2742__2744__2756__2758__2760__2762__2764__2766,Vvar__0__R__2665)
                               => ( ~ p(happ(happ(Vvar__9__req__2694,Vvar__var__var__var__var__var__var__var__13__p__2742__2744__2756__2758__2760__2762__2764__2766),Vvar__1__rO__2666))
                                 => p(happ(happ(Vvar__9__req__2694,happ(happ(Vvar__4__rmul__2673,happ(Vvar__8__rinv__2691,Vvar__var__var__var__var__var__var__var__13__p__2742__2744__2756__2758__2760__2762__2764__2766)),Vvar__var__var__var__var__var__var__var__13__p__2742__2744__2756__2758__2760__2762__2764__2766)),Vvar__2__rI__2667)) ) )
                            & p(c_24True) ) ) ) ) ) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.setoid_ring.Field_theory.field_theory',axiom,
    ! [Vvar__0__R__108018,Vvar__1__rO__108019,Vvar__2__rI__108020,Vvar__3__radd__108021,Vvar__4__rmul__108026,Vvar__5__rsub__108031,Vvar__6__ropp__108036,Vvar__7__rdiv__108039,Vvar__8__rinv__108044,Vvar__9__req__108047] :
      ( cType___24t(Vvar__0__R__108018)
     => ( t(Vvar__1__rO__108019,Vvar__0__R__108018)
       => ( t(Vvar__2__rI__108020,Vvar__0__R__108018)
         => ( c_24__type__108212___24t(Vvar__0__R__108018,Vvar__1__rO__108019,Vvar__2__rI__108020,Vvar__3__radd__108021,Vvar__4__rmul__108026,Vvar__5__rsub__108031,Vvar__6__ropp__108036,Vvar__7__rdiv__108039,Vvar__8__rinv__108044,Vvar__9__req__108047,Vvar__3__radd__108021)
           => ( c_24__type__108305___24t(Vvar__0__R__108018,Vvar__1__rO__108019,Vvar__2__rI__108020,Vvar__3__radd__108021,Vvar__4__rmul__108026,Vvar__5__rsub__108031,Vvar__6__ropp__108036,Vvar__7__rdiv__108039,Vvar__8__rinv__108044,Vvar__9__req__108047,Vvar__4__rmul__108026)
             => ( c_24__type__108398___24t(Vvar__0__R__108018,Vvar__1__rO__108019,Vvar__2__rI__108020,Vvar__3__radd__108021,Vvar__4__rmul__108026,Vvar__5__rsub__108031,Vvar__6__ropp__108036,Vvar__7__rdiv__108039,Vvar__8__rinv__108044,Vvar__9__req__108047,Vvar__5__rsub__108031)
               => ( c_24__type__108480___24t(Vvar__0__R__108018,Vvar__1__rO__108019,Vvar__2__rI__108020,Vvar__3__radd__108021,Vvar__4__rmul__108026,Vvar__5__rsub__108031,Vvar__6__ropp__108036,Vvar__7__rdiv__108039,Vvar__8__rinv__108044,Vvar__9__req__108047,Vvar__6__ropp__108036)
                 => ( c_24__type__108573___24t(Vvar__0__R__108018,Vvar__1__rO__108019,Vvar__2__rI__108020,Vvar__3__radd__108021,Vvar__4__rmul__108026,Vvar__5__rsub__108031,Vvar__6__ropp__108036,Vvar__7__rdiv__108039,Vvar__8__rinv__108044,Vvar__9__req__108047,Vvar__7__rdiv__108039)
                   => ( c_24__type__108655___24t(Vvar__0__R__108018,Vvar__1__rO__108019,Vvar__2__rI__108020,Vvar__3__radd__108021,Vvar__4__rmul__108026,Vvar__5__rsub__108031,Vvar__6__ropp__108036,Vvar__7__rdiv__108039,Vvar__8__rinv__108044,Vvar__9__req__108047,Vvar__8__rinv__108044)
                     => ( c_24__type__108748___24t(Vvar__0__R__108018,Vvar__1__rO__108019,Vvar__2__rI__108020,Vvar__3__radd__108021,Vvar__4__rmul__108026,Vvar__5__rsub__108031,Vvar__6__ropp__108036,Vvar__7__rdiv__108039,Vvar__8__rinv__108044,Vvar__9__req__108047,Vvar__9__req__108047)
                       => ( cCoq_2esetoid__ring_2eField__theory_2efield__theory___24a10(Vvar__0__R__108018,Vvar__1__rO__108019,Vvar__2__rI__108020,Vvar__3__radd__108021,Vvar__4__rmul__108026,Vvar__5__rsub__108031,Vvar__6__ropp__108036,Vvar__7__rdiv__108039,Vvar__8__rinv__108044,Vvar__9__req__108047)
                         => ( cCoq_2esetoid__ring_2eRing__theory_2ering__theory___24a8(Vvar__0__R__108018,Vvar__1__rO__108019,Vvar__2__rI__108020,Vvar__3__radd__108021,Vvar__4__rmul__108026,Vvar__5__rsub__108031,Vvar__6__ropp__108036,Vvar__9__req__108047)
                            & ~ p(happ(happ(Vvar__9__req__108047,Vvar__2__rI__108020),Vvar__1__rO__108019))
                            & ! [Vvar__var__var__var__var__var__var__12__p__108090__108092__108099__108101__108103__108105__108107] :
                                ( t(Vvar__var__var__var__var__var__var__12__p__108090__108092__108099__108101__108103__108105__108107,Vvar__0__R__108018)
                               => ! [Vvar__var__var__var__var__var__var__13__q__108091__108093__108100__108102__108104__108106__108108] :
                                    ( t(Vvar__var__var__var__var__var__var__13__q__108091__108093__108100__108102__108104__108106__108108,Vvar__0__R__108018)
                                   => p(happ(happ(Vvar__9__req__108047,happ(happ(Vvar__7__rdiv__108039,Vvar__var__var__var__var__var__var__12__p__108090__108092__108099__108101__108103__108105__108107),Vvar__var__var__var__var__var__var__13__q__108091__108093__108100__108102__108104__108106__108108)),happ(happ(Vvar__4__rmul__108026,Vvar__var__var__var__var__var__var__12__p__108090__108092__108099__108101__108103__108105__108107),happ(Vvar__8__rinv__108044,Vvar__var__var__var__var__var__var__13__q__108091__108093__108100__108102__108104__108106__108108)))) ) )
                            & ! [Vvar__var__var__var__var__var__var__var__13__p__108095__108097__108109__108111__108113__108115__108117__108119] :
                                ( t(Vvar__var__var__var__var__var__var__var__13__p__108095__108097__108109__108111__108113__108115__108117__108119,Vvar__0__R__108018)
                               => ( ~ p(happ(happ(Vvar__9__req__108047,Vvar__var__var__var__var__var__var__var__13__p__108095__108097__108109__108111__108113__108115__108117__108119),Vvar__1__rO__108019))
                                 => p(happ(happ(Vvar__9__req__108047,happ(happ(Vvar__4__rmul__108026,happ(Vvar__8__rinv__108044,Vvar__var__var__var__var__var__var__var__13__p__108095__108097__108109__108111__108113__108115__108117__108119)),Vvar__var__var__var__var__var__var__var__13__p__108095__108097__108109__108111__108113__108115__108117__108119)),Vvar__2__rI__108020)) ) )
                            & p(c_24True) ) ) ) ) ) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.setoid_ring.Field_theory.linear',axiom,
    ! [Vvar__0__C__4081,VX4082] :
      ( cType___24t(Vvar__0__C__4081)
     => ( cCoq_2esetoid__ring_2eField__theory_2elinear___24t(Vvar__0__C__4081,VX4082)
       => ? [Vvar__1__num__4084] :
            ( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__4081,Vvar__1__num__4084)
            & ? [Vvar__2__denum__4085] :
                ( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__4081,Vvar__2__denum__4085)
                & ? [Vvar__3__condition__4086] :
                    ( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(Vvar__0__C__4081),Vvar__3__condition__4086)
                    & VX4082 = cCoq_2esetoid__ring_2eField__theory_2emk__linear___24a4(Vvar__0__C__4081,Vvar__1__num__4084,Vvar__2__denum__4085,Vvar__3__condition__4086) ) ) ) ) ) ).

fof('$_inversion_Coq.setoid_ring.Field_theory.rsplit',axiom,
    ! [Vvar__0__C__1002,VX1003] :
      ( cType___24t(Vvar__0__C__1002)
     => ( cCoq_2esetoid__ring_2eField__theory_2ersplit___24t(Vvar__0__C__1002,VX1003)
       => ? [Vvar__1__rsplit__left__1005] :
            ( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__1002,Vvar__1__rsplit__left__1005)
            & ? [Vvar__2__rsplit__common__1006] :
                ( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__1002,Vvar__2__rsplit__common__1006)
                & ? [Vvar__3__rsplit__right__1007] :
                    ( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__1002,Vvar__3__rsplit__right__1007)
                    & VX1003 = cCoq_2esetoid__ring_2eField__theory_2emk__rsplit___24a4(Vvar__0__C__1002,Vvar__1__rsplit__left__1005,Vvar__2__rsplit__common__1006,Vvar__3__rsplit__right__1007) ) ) ) ) ) ).

fof('$_inversion_Coq.setoid_ring.Field_theory.semi_field_theory',axiom,
    ! [Vvar__0__R__108754,Vvar__1__rO__108755,Vvar__2__rI__108756,Vvar__3__radd__108757,Vvar__4__rmul__108762,Vvar__5__rdiv__108767,Vvar__6__rinv__108772,Vvar__7__req__108775] :
      ( cType___24t(Vvar__0__R__108754)
     => ( t(Vvar__1__rO__108755,Vvar__0__R__108754)
       => ( t(Vvar__2__rI__108756,Vvar__0__R__108754)
         => ( c_24__type__108902___24t(Vvar__0__R__108754,Vvar__1__rO__108755,Vvar__2__rI__108756,Vvar__3__radd__108757,Vvar__4__rmul__108762,Vvar__5__rdiv__108767,Vvar__6__rinv__108772,Vvar__7__req__108775,Vvar__3__radd__108757)
           => ( c_24__type__108965___24t(Vvar__0__R__108754,Vvar__1__rO__108755,Vvar__2__rI__108756,Vvar__3__radd__108757,Vvar__4__rmul__108762,Vvar__5__rdiv__108767,Vvar__6__rinv__108772,Vvar__7__req__108775,Vvar__4__rmul__108762)
             => ( c_24__type__109028___24t(Vvar__0__R__108754,Vvar__1__rO__108755,Vvar__2__rI__108756,Vvar__3__radd__108757,Vvar__4__rmul__108762,Vvar__5__rdiv__108767,Vvar__6__rinv__108772,Vvar__7__req__108775,Vvar__5__rdiv__108767)
               => ( c_24__type__109082___24t(Vvar__0__R__108754,Vvar__1__rO__108755,Vvar__2__rI__108756,Vvar__3__radd__108757,Vvar__4__rmul__108762,Vvar__5__rdiv__108767,Vvar__6__rinv__108772,Vvar__7__req__108775,Vvar__6__rinv__108772)
                 => ( c_24__type__109145___24t(Vvar__0__R__108754,Vvar__1__rO__108755,Vvar__2__rI__108756,Vvar__3__radd__108757,Vvar__4__rmul__108762,Vvar__5__rdiv__108767,Vvar__6__rinv__108772,Vvar__7__req__108775,Vvar__7__req__108775)
                   => ( cCoq_2esetoid__ring_2eField__theory_2esemi__field__theory___24a8(Vvar__0__R__108754,Vvar__1__rO__108755,Vvar__2__rI__108756,Vvar__3__radd__108757,Vvar__4__rmul__108762,Vvar__5__rdiv__108767,Vvar__6__rinv__108772,Vvar__7__req__108775)
                     => ( cCoq_2esetoid__ring_2eRing__theory_2esemi__ring__theory___24a6(Vvar__0__R__108754,Vvar__1__rO__108755,Vvar__2__rI__108756,Vvar__3__radd__108757,Vvar__4__rmul__108762,Vvar__7__req__108775)
                        & ~ p(happ(happ(Vvar__7__req__108775,Vvar__2__rI__108756),Vvar__1__rO__108755))
                        & ! [Vvar__var__var__var__var__var__var__10__p__108810__108812__108819__108821__108823__108825__108827] :
                            ( t(Vvar__var__var__var__var__var__var__10__p__108810__108812__108819__108821__108823__108825__108827,Vvar__0__R__108754)
                           => ! [Vvar__var__var__var__var__var__var__11__q__108811__108813__108820__108822__108824__108826__108828] :
                                ( t(Vvar__var__var__var__var__var__var__11__q__108811__108813__108820__108822__108824__108826__108828,Vvar__0__R__108754)
                               => p(happ(happ(Vvar__7__req__108775,happ(happ(Vvar__5__rdiv__108767,Vvar__var__var__var__var__var__var__10__p__108810__108812__108819__108821__108823__108825__108827),Vvar__var__var__var__var__var__var__11__q__108811__108813__108820__108822__108824__108826__108828)),happ(happ(Vvar__4__rmul__108762,Vvar__var__var__var__var__var__var__10__p__108810__108812__108819__108821__108823__108825__108827),happ(Vvar__6__rinv__108772,Vvar__var__var__var__var__var__var__11__q__108811__108813__108820__108822__108824__108826__108828)))) ) )
                        & ! [Vvar__var__var__var__var__var__var__var__11__p__108815__108817__108829__108831__108833__108835__108837__108839] :
                            ( t(Vvar__var__var__var__var__var__var__var__11__p__108815__108817__108829__108831__108833__108835__108837__108839,Vvar__0__R__108754)
                           => ( ~ p(happ(happ(Vvar__7__req__108775,Vvar__var__var__var__var__var__var__var__11__p__108815__108817__108829__108831__108833__108835__108837__108839),Vvar__1__rO__108755))
                             => p(happ(happ(Vvar__7__req__108775,happ(happ(Vvar__4__rmul__108762,happ(Vvar__6__rinv__108772,Vvar__var__var__var__var__var__var__var__11__p__108815__108817__108829__108831__108833__108835__108837__108839)),Vvar__var__var__var__var__var__var__var__11__p__108815__108817__108829__108831__108833__108835__108837__108839)),Vvar__2__rI__108756)) ) )
                        & p(c_24True) ) ) ) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.setoid_ring.InitialRing.hypo',axiom,
    ! [VX109236] :
      ( cCoq_2esetoid__ring_2eInitialRing_2ehypo___24t(VX109236)
     => ? [Vvar__0__hypo__type__109237] :
          ( cType___24t(Vvar__0__hypo__type__109237)
          & ? [Vvar__1__hypo__proof__109238] :
              ( t(Vvar__1__hypo__proof__109238,Vvar__0__hypo__type__109237)
              & VX109236 = cCoq_2esetoid__ring_2eInitialRing_2emkhypo___24a2(Vvar__0__hypo__type__109237,Vvar__1__hypo__proof__109238) ) ) ) ).

fof('$_inversion_Coq.setoid_ring.Ring_polynom.Mon',axiom,
    ! [VX5207] :
      ( cCoq_2esetoid__ring_2eRing__polynom_2eMon___24t(VX5207)
     => ( VX5207 = cCoq_2esetoid__ring_2eRing__polynom_2emon0
        | ? [Vvar__0___24Anonymous__5208] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__5208)
            & ? [Vvar__1___24Anonymous__5209] :
                ( cCoq_2esetoid__ring_2eRing__polynom_2eMon___24t(Vvar__1___24Anonymous__5209)
                & VX5207 = cCoq_2esetoid__ring_2eRing__polynom_2ezmon___24a2(Vvar__0___24Anonymous__5208,Vvar__1___24Anonymous__5209) ) )
        | ? [Vvar__0___24Anonymous__5210] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__5210)
            & ? [Vvar__1___24Anonymous__5211] :
                ( cCoq_2esetoid__ring_2eRing__polynom_2eMon___24t(Vvar__1___24Anonymous__5211)
                & VX5207 = cCoq_2esetoid__ring_2eRing__polynom_2evmon___24a2(Vvar__0___24Anonymous__5210,Vvar__1___24Anonymous__5211) ) ) ) ) ).

fof('$_inversion_Coq.setoid_ring.Ring_polynom.PExpr',axiom,
    ! [Vvar__0__C__5298,VX5299] :
      ( cType___24t(Vvar__0__C__5298)
     => ( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__5298,VX5299)
       => ( VX5299 = cCoq_2esetoid__ring_2eRing__polynom_2ePEO___24a1(Vvar__0__C__5298)
          | VX5299 = cCoq_2esetoid__ring_2eRing__polynom_2ePEI___24a1(Vvar__0__C__5298)
          | ? [Vvar__1___24Anonymous__5303] :
              ( t(Vvar__1___24Anonymous__5303,Vvar__0__C__5298)
              & VX5299 = cCoq_2esetoid__ring_2eRing__polynom_2ePEc___24a2(Vvar__0__C__5298,Vvar__1___24Anonymous__5303) )
          | ? [Vvar__1___24Anonymous__5305] :
              ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__5305)
              & VX5299 = cCoq_2esetoid__ring_2eRing__polynom_2ePEX___24a2(Vvar__0__C__5298,Vvar__1___24Anonymous__5305) )
          | ? [Vvar__1___24Anonymous__5307] :
              ( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__5298,Vvar__1___24Anonymous__5307)
              & ? [Vvar__2___24Anonymous__5308] :
                  ( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__5298,Vvar__2___24Anonymous__5308)
                  & VX5299 = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(Vvar__0__C__5298,Vvar__1___24Anonymous__5307,Vvar__2___24Anonymous__5308) ) )
          | ? [Vvar__1___24Anonymous__5310] :
              ( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__5298,Vvar__1___24Anonymous__5310)
              & ? [Vvar__2___24Anonymous__5311] :
                  ( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__5298,Vvar__2___24Anonymous__5311)
                  & VX5299 = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(Vvar__0__C__5298,Vvar__1___24Anonymous__5310,Vvar__2___24Anonymous__5311) ) )
          | ? [Vvar__1___24Anonymous__5313] :
              ( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__5298,Vvar__1___24Anonymous__5313)
              & ? [Vvar__2___24Anonymous__5314] :
                  ( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__5298,Vvar__2___24Anonymous__5314)
                  & VX5299 = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(Vvar__0__C__5298,Vvar__1___24Anonymous__5313,Vvar__2___24Anonymous__5314) ) )
          | ? [Vvar__1___24Anonymous__5316] :
              ( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__5298,Vvar__1___24Anonymous__5316)
              & VX5299 = cCoq_2esetoid__ring_2eRing__polynom_2ePEopp___24a2(Vvar__0__C__5298,Vvar__1___24Anonymous__5316) )
          | ? [Vvar__1___24Anonymous__5318] :
              ( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__5298,Vvar__1___24Anonymous__5318)
              & ? [Vvar__2___24Anonymous__5319] :
                  ( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__2___24Anonymous__5319)
                  & VX5299 = cCoq_2esetoid__ring_2eRing__polynom_2ePEpow___24a3(Vvar__0__C__5298,Vvar__1___24Anonymous__5318,Vvar__2___24Anonymous__5319) ) ) ) ) ) ).

fof('$_inversion_Coq.setoid_ring.Ring_polynom.Pol',axiom,
    ! [Vvar__0__C__5160,VX5161] :
      ( cType___24t(Vvar__0__C__5160)
     => ( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vvar__0__C__5160,VX5161)
       => ( ? [Vvar__1___24Anonymous__5163] :
              ( t(Vvar__1___24Anonymous__5163,Vvar__0__C__5160)
              & VX5161 = cCoq_2esetoid__ring_2eRing__polynom_2ePc___24a2(Vvar__0__C__5160,Vvar__1___24Anonymous__5163) )
          | ? [Vvar__1___24Anonymous__5165] :
              ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__5165)
              & ? [Vvar__2___24Anonymous__5166] :
                  ( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vvar__0__C__5160,Vvar__2___24Anonymous__5166)
                  & VX5161 = cCoq_2esetoid__ring_2eRing__polynom_2ePinj___24a3(Vvar__0__C__5160,Vvar__1___24Anonymous__5165,Vvar__2___24Anonymous__5166) ) )
          | ? [Vvar__1___24Anonymous__5168] :
              ( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vvar__0__C__5160,Vvar__1___24Anonymous__5168)
              & ? [Vvar__2___24Anonymous__5169] :
                  ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2___24Anonymous__5169)
                  & ? [Vvar__3___24Anonymous__5170] :
                      ( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vvar__0__C__5160,Vvar__3___24Anonymous__5170)
                      & VX5161 = cCoq_2esetoid__ring_2eRing__polynom_2ePX___24a4(Vvar__0__C__5160,Vvar__1___24Anonymous__5168,Vvar__2___24Anonymous__5169,Vvar__3___24Anonymous__5170) ) ) ) ) ) ) ).

fof('$_inversion_Coq.setoid_ring.Ring_theory.almost_ring_theory',axiom,
    ! [Vvar__0__R__7666,Vvar__1__rO__7667,Vvar__2__rI__7668,Vvar__3__radd__7669,Vvar__4__rmul__7674,Vvar__5__rsub__7679,Vvar__6__ropp__7684,Vvar__7__req__7687] :
      ( cType___24t(Vvar__0__R__7666)
     => ( t(Vvar__1__rO__7667,Vvar__0__R__7666)
       => ( t(Vvar__2__rI__7668,Vvar__0__R__7666)
         => ( c_24__type__7915___24t(Vvar__0__R__7666,Vvar__1__rO__7667,Vvar__2__rI__7668,Vvar__3__radd__7669,Vvar__4__rmul__7674,Vvar__5__rsub__7679,Vvar__6__ropp__7684,Vvar__7__req__7687,Vvar__3__radd__7669)
           => ( c_24__type__7978___24t(Vvar__0__R__7666,Vvar__1__rO__7667,Vvar__2__rI__7668,Vvar__3__radd__7669,Vvar__4__rmul__7674,Vvar__5__rsub__7679,Vvar__6__ropp__7684,Vvar__7__req__7687,Vvar__4__rmul__7674)
             => ( c_24__type__8041___24t(Vvar__0__R__7666,Vvar__1__rO__7667,Vvar__2__rI__7668,Vvar__3__radd__7669,Vvar__4__rmul__7674,Vvar__5__rsub__7679,Vvar__6__ropp__7684,Vvar__7__req__7687,Vvar__5__rsub__7679)
               => ( c_24__type__8095___24t(Vvar__0__R__7666,Vvar__1__rO__7667,Vvar__2__rI__7668,Vvar__3__radd__7669,Vvar__4__rmul__7674,Vvar__5__rsub__7679,Vvar__6__ropp__7684,Vvar__7__req__7687,Vvar__6__ropp__7684)
                 => ( c_24__type__8158___24t(Vvar__0__R__7666,Vvar__1__rO__7667,Vvar__2__rI__7668,Vvar__3__radd__7669,Vvar__4__rmul__7674,Vvar__5__rsub__7679,Vvar__6__ropp__7684,Vvar__7__req__7687,Vvar__7__req__7687)
                   => ( cCoq_2esetoid__ring_2eRing__theory_2ealmost__ring__theory___24a8(Vvar__0__R__7666,Vvar__1__rO__7667,Vvar__2__rI__7668,Vvar__3__radd__7669,Vvar__4__rmul__7674,Vvar__5__rsub__7679,Vvar__6__ropp__7684,Vvar__7__req__7687)
                     => ( ! [Vvar__var__var__var__var__var__8__x__7720__7721__7774__7775__7776__7777] :
                            ( t(Vvar__var__var__var__var__var__8__x__7720__7721__7774__7775__7776__7777,Vvar__0__R__7666)
                           => p(happ(happ(Vvar__7__req__7687,happ(happ(Vvar__3__radd__7669,Vvar__1__rO__7667),Vvar__var__var__var__var__var__8__x__7720__7721__7774__7775__7776__7777)),Vvar__var__var__var__var__var__8__x__7720__7721__7774__7775__7776__7777)) )
                        & ! [Vvar__var__var__var__var__9__x__7723__7725__7778__7780__7782] :
                            ( t(Vvar__var__var__var__var__9__x__7723__7725__7778__7780__7782,Vvar__0__R__7666)
                           => ! [Vvar__var__var__var__var__10__y__7724__7726__7779__7781__7783] :
                                ( t(Vvar__var__var__var__var__10__y__7724__7726__7779__7781__7783,Vvar__0__R__7666)
                               => p(happ(happ(Vvar__7__req__7687,happ(happ(Vvar__3__radd__7669,Vvar__var__var__var__var__9__x__7723__7725__7778__7780__7782),Vvar__var__var__var__var__10__y__7724__7726__7779__7781__7783)),happ(happ(Vvar__3__radd__7669,Vvar__var__var__var__var__10__y__7724__7726__7779__7781__7783),Vvar__var__var__var__var__9__x__7723__7725__7778__7780__7782))) ) )
                        & ! [Vvar__var__var__var__var__10__x__7728__7731__7784__7787__7790] :
                            ( t(Vvar__var__var__var__var__10__x__7728__7731__7784__7787__7790,Vvar__0__R__7666)
                           => ! [Vvar__var__var__var__var__11__y__7729__7732__7785__7788__7791] :
                                ( t(Vvar__var__var__var__var__11__y__7729__7732__7785__7788__7791,Vvar__0__R__7666)
                               => ! [Vvar__var__var__var__var__12__z__7730__7733__7786__7789__7792] :
                                    ( t(Vvar__var__var__var__var__12__z__7730__7733__7786__7789__7792,Vvar__0__R__7666)
                                   => p(happ(happ(Vvar__7__req__7687,happ(happ(Vvar__3__radd__7669,Vvar__var__var__var__var__10__x__7728__7731__7784__7787__7790),happ(happ(Vvar__3__radd__7669,Vvar__var__var__var__var__11__y__7729__7732__7785__7788__7791),Vvar__var__var__var__var__12__z__7730__7733__7786__7789__7792))),happ(happ(Vvar__3__radd__7669,happ(happ(Vvar__3__radd__7669,Vvar__var__var__var__var__10__x__7728__7731__7784__7787__7790),Vvar__var__var__var__var__11__y__7729__7732__7785__7788__7791)),Vvar__var__var__var__var__12__z__7730__7733__7786__7789__7792))) ) ) )
                        & ! [Vvar__var__var__var__var__var__11__x__7735__7736__7793__7794__7795__7796] :
                            ( t(Vvar__var__var__var__var__var__11__x__7735__7736__7793__7794__7795__7796,Vvar__0__R__7666)
                           => p(happ(happ(Vvar__7__req__7687,happ(happ(Vvar__4__rmul__7674,Vvar__2__rI__7668),Vvar__var__var__var__var__var__11__x__7735__7736__7793__7794__7795__7796)),Vvar__var__var__var__var__var__11__x__7735__7736__7793__7794__7795__7796)) )
                        & ! [Vvar__var__var__var__var__var__12__x__7738__7739__7797__7798__7799__7800] :
                            ( t(Vvar__var__var__var__var__var__12__x__7738__7739__7797__7798__7799__7800,Vvar__0__R__7666)
                           => p(happ(happ(Vvar__7__req__7687,happ(happ(Vvar__4__rmul__7674,Vvar__1__rO__7667),Vvar__var__var__var__var__var__12__x__7738__7739__7797__7798__7799__7800)),Vvar__1__rO__7667)) )
                        & ! [Vvar__var__var__var__var__13__x__7741__7743__7801__7803__7805] :
                            ( t(Vvar__var__var__var__var__13__x__7741__7743__7801__7803__7805,Vvar__0__R__7666)
                           => ! [Vvar__var__var__var__var__14__y__7742__7744__7802__7804__7806] :
                                ( t(Vvar__var__var__var__var__14__y__7742__7744__7802__7804__7806,Vvar__0__R__7666)
                               => p(happ(happ(Vvar__7__req__7687,happ(happ(Vvar__4__rmul__7674,Vvar__var__var__var__var__13__x__7741__7743__7801__7803__7805),Vvar__var__var__var__var__14__y__7742__7744__7802__7804__7806)),happ(happ(Vvar__4__rmul__7674,Vvar__var__var__var__var__14__y__7742__7744__7802__7804__7806),Vvar__var__var__var__var__13__x__7741__7743__7801__7803__7805))) ) )
                        & ! [Vvar__var__var__var__var__14__x__7746__7749__7807__7810__7813] :
                            ( t(Vvar__var__var__var__var__14__x__7746__7749__7807__7810__7813,Vvar__0__R__7666)
                           => ! [Vvar__var__var__var__var__15__y__7747__7750__7808__7811__7814] :
                                ( t(Vvar__var__var__var__var__15__y__7747__7750__7808__7811__7814,Vvar__0__R__7666)
                               => ! [Vvar__var__var__var__var__16__z__7748__7751__7809__7812__7815] :
                                    ( t(Vvar__var__var__var__var__16__z__7748__7751__7809__7812__7815,Vvar__0__R__7666)
                                   => p(happ(happ(Vvar__7__req__7687,happ(happ(Vvar__4__rmul__7674,Vvar__var__var__var__var__14__x__7746__7749__7807__7810__7813),happ(happ(Vvar__4__rmul__7674,Vvar__var__var__var__var__15__y__7747__7750__7808__7811__7814),Vvar__var__var__var__var__16__z__7748__7751__7809__7812__7815))),happ(happ(Vvar__4__rmul__7674,happ(happ(Vvar__4__rmul__7674,Vvar__var__var__var__var__14__x__7746__7749__7807__7810__7813),Vvar__var__var__var__var__15__y__7747__7750__7808__7811__7814)),Vvar__var__var__var__var__16__z__7748__7751__7809__7812__7815))) ) ) )
                        & ! [Vvar__var__var__var__var__var__15__x__7753__7756__7816__7819__7822__7825] :
                            ( t(Vvar__var__var__var__var__var__15__x__7753__7756__7816__7819__7822__7825,Vvar__0__R__7666)
                           => ! [Vvar__var__var__var__var__var__16__y__7754__7757__7817__7820__7823__7826] :
                                ( t(Vvar__var__var__var__var__var__16__y__7754__7757__7817__7820__7823__7826,Vvar__0__R__7666)
                               => ! [Vvar__var__var__var__var__var__17__z__7755__7758__7818__7821__7824__7827] :
                                    ( t(Vvar__var__var__var__var__var__17__z__7755__7758__7818__7821__7824__7827,Vvar__0__R__7666)
                                   => p(happ(happ(Vvar__7__req__7687,happ(happ(Vvar__4__rmul__7674,happ(happ(Vvar__3__radd__7669,Vvar__var__var__var__var__var__15__x__7753__7756__7816__7819__7822__7825),Vvar__var__var__var__var__var__16__y__7754__7757__7817__7820__7823__7826)),Vvar__var__var__var__var__var__17__z__7755__7758__7818__7821__7824__7827)),happ(happ(Vvar__3__radd__7669,happ(happ(Vvar__4__rmul__7674,Vvar__var__var__var__var__var__15__x__7753__7756__7816__7819__7822__7825),Vvar__var__var__var__var__var__17__z__7755__7758__7818__7821__7824__7827)),happ(happ(Vvar__4__rmul__7674,Vvar__var__var__var__var__var__16__y__7754__7757__7817__7820__7823__7826),Vvar__var__var__var__var__var__17__z__7755__7758__7818__7821__7824__7827)))) ) ) )
                        & ! [Vvar__var__var__var__var__var__16__x__7760__7762__7828__7830__7832__7834] :
                            ( t(Vvar__var__var__var__var__var__16__x__7760__7762__7828__7830__7832__7834,Vvar__0__R__7666)
                           => ! [Vvar__var__var__var__var__var__17__y__7761__7763__7829__7831__7833__7835] :
                                ( t(Vvar__var__var__var__var__var__17__y__7761__7763__7829__7831__7833__7835,Vvar__0__R__7666)
                               => p(happ(happ(Vvar__7__req__7687,happ(Vvar__6__ropp__7684,happ(happ(Vvar__4__rmul__7674,Vvar__var__var__var__var__var__16__x__7760__7762__7828__7830__7832__7834),Vvar__var__var__var__var__var__17__y__7761__7763__7829__7831__7833__7835))),happ(happ(Vvar__4__rmul__7674,happ(Vvar__6__ropp__7684,Vvar__var__var__var__var__var__16__x__7760__7762__7828__7830__7832__7834)),Vvar__var__var__var__var__var__17__y__7761__7763__7829__7831__7833__7835))) ) )
                        & ! [Vvar__var__var__var__var__var__17__x__7765__7767__7836__7838__7840__7842] :
                            ( t(Vvar__var__var__var__var__var__17__x__7765__7767__7836__7838__7840__7842,Vvar__0__R__7666)
                           => ! [Vvar__var__var__var__var__var__18__y__7766__7768__7837__7839__7841__7843] :
                                ( t(Vvar__var__var__var__var__var__18__y__7766__7768__7837__7839__7841__7843,Vvar__0__R__7666)
                               => p(happ(happ(Vvar__7__req__7687,happ(Vvar__6__ropp__7684,happ(happ(Vvar__3__radd__7669,Vvar__var__var__var__var__var__17__x__7765__7767__7836__7838__7840__7842),Vvar__var__var__var__var__var__18__y__7766__7768__7837__7839__7841__7843))),happ(happ(Vvar__3__radd__7669,happ(Vvar__6__ropp__7684,Vvar__var__var__var__var__var__17__x__7765__7767__7836__7838__7840__7842)),happ(Vvar__6__ropp__7684,Vvar__var__var__var__var__var__18__y__7766__7768__7837__7839__7841__7843)))) ) )
                        & ! [Vvar__var__var__var__var__var__var__18__x__7770__7772__7844__7846__7848__7850__7852] :
                            ( t(Vvar__var__var__var__var__var__var__18__x__7770__7772__7844__7846__7848__7850__7852,Vvar__0__R__7666)
                           => ! [Vvar__var__var__var__var__var__var__19__y__7771__7773__7845__7847__7849__7851__7853] :
                                ( t(Vvar__var__var__var__var__var__var__19__y__7771__7773__7845__7847__7849__7851__7853,Vvar__0__R__7666)
                               => p(happ(happ(Vvar__7__req__7687,happ(happ(Vvar__5__rsub__7679,Vvar__var__var__var__var__var__var__18__x__7770__7772__7844__7846__7848__7850__7852),Vvar__var__var__var__var__var__var__19__y__7771__7773__7845__7847__7849__7851__7853)),happ(happ(Vvar__3__radd__7669,Vvar__var__var__var__var__var__var__18__x__7770__7772__7844__7846__7848__7850__7852),happ(Vvar__6__ropp__7684,Vvar__var__var__var__var__var__var__19__y__7771__7773__7845__7847__7849__7851__7853)))) ) )
                        & p(c_24True) ) ) ) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.setoid_ring.Ring_theory.div_theory',axiom,
    ! [Vvar__0__R__11323,Vvar__1__req__11324,Vvar__2__C__11329,Vvar__3__cadd__11330,Vvar__4__cmul__11335,Vvar__5__phi__11340,Vvar__6__cdiv__11343] :
      ( cType___24t(Vvar__0__R__11323)
     => ( c_24__type__11463___24t(Vvar__0__R__11323,Vvar__1__req__11324,Vvar__2__C__11329,Vvar__3__cadd__11330,Vvar__4__cmul__11335,Vvar__5__phi__11340,Vvar__6__cdiv__11343,Vvar__1__req__11324)
       => ( cType___24t(Vvar__2__C__11329)
         => ( c_24__type__11513___24t(Vvar__0__R__11323,Vvar__1__req__11324,Vvar__2__C__11329,Vvar__3__cadd__11330,Vvar__4__cmul__11335,Vvar__5__phi__11340,Vvar__6__cdiv__11343,Vvar__3__cadd__11330)
           => ( c_24__type__11563___24t(Vvar__0__R__11323,Vvar__1__req__11324,Vvar__2__C__11329,Vvar__3__cadd__11330,Vvar__4__cmul__11335,Vvar__5__phi__11340,Vvar__6__cdiv__11343,Vvar__4__cmul__11335)
             => ( c_24__type__11605___24t(Vvar__0__R__11323,Vvar__1__req__11324,Vvar__2__C__11329,Vvar__3__cadd__11330,Vvar__4__cmul__11335,Vvar__5__phi__11340,Vvar__6__cdiv__11343,Vvar__5__phi__11340)
               => ( c_24__type__11655___24t(Vvar__0__R__11323,Vvar__1__req__11324,Vvar__2__C__11329,Vvar__3__cadd__11330,Vvar__4__cmul__11335,Vvar__5__phi__11340,Vvar__6__cdiv__11343,Vvar__6__cdiv__11343)
                 => ( cCoq_2esetoid__ring_2eRing__theory_2ediv__theory___24a7(Vvar__0__R__11323,Vvar__1__req__11324,Vvar__2__C__11329,Vvar__3__cadd__11330,Vvar__4__cmul__11335,Vvar__5__phi__11340,Vvar__6__cdiv__11343)
                   => ( ! [Vvar__var__var__var__var__var__var__var__7__a__11375__11380__11385__11390__11395__11400__11405__11410] :
                          ( t(Vvar__var__var__var__var__var__var__var__7__a__11375__11380__11385__11390__11395__11400__11405__11410,Vvar__2__C__11329)
                         => ! [Vvar__var__var__var__var__var__var__var__8__b__11376__11381__11386__11391__11396__11401__11406__11411] :
                              ( t(Vvar__var__var__var__var__var__var__var__8__b__11376__11381__11386__11391__11396__11401__11406__11411,Vvar__2__C__11329)
                             => c_24__case__Coq_2eInit_2eDatatypes_2eprod_2411718___24a9(Vvar__0__R__11323,Vvar__1__req__11324,Vvar__2__C__11329,Vvar__3__cadd__11330,Vvar__4__cmul__11335,Vvar__5__phi__11340,Vvar__6__cdiv__11343,Vvar__var__var__var__var__var__var__var__7__a__11375__11380__11385__11390__11395__11400__11405__11410,Vvar__var__var__var__var__var__var__var__8__b__11376__11381__11386__11391__11396__11401__11406__11411) ) )
                      & p(c_24True) ) ) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.setoid_ring.Ring_theory.power_theory',axiom,
    ! [Vvar__0__R__11738,Vvar__1__rI__11739,Vvar__2__rmul__11740,Vvar__3__req__11745,Vvar__4__Cpow__11750,Vvar__5__Cp__phi__11751,Vvar__6__rpow__11754] :
      ( cType___24t(Vvar__0__R__11738)
     => ( t(Vvar__1__rI__11739,Vvar__0__R__11738)
       => ( c_24__type__11840___24t(Vvar__0__R__11738,Vvar__1__rI__11739,Vvar__2__rmul__11740,Vvar__3__req__11745,Vvar__4__Cpow__11750,Vvar__5__Cp__phi__11751,Vvar__6__rpow__11754,Vvar__2__rmul__11740)
         => ( c_24__type__11884___24t(Vvar__0__R__11738,Vvar__1__rI__11739,Vvar__2__rmul__11740,Vvar__3__req__11745,Vvar__4__Cpow__11750,Vvar__5__Cp__phi__11751,Vvar__6__rpow__11754,Vvar__3__req__11745)
           => ( cType___24t(Vvar__4__Cpow__11750)
             => ( c_24__type__11920___24t(Vvar__0__R__11738,Vvar__1__rI__11739,Vvar__2__rmul__11740,Vvar__3__req__11745,Vvar__4__Cpow__11750,Vvar__5__Cp__phi__11751,Vvar__6__rpow__11754,Vvar__5__Cp__phi__11751)
               => ( c_24__type__11964___24t(Vvar__0__R__11738,Vvar__1__rI__11739,Vvar__2__rmul__11740,Vvar__3__req__11745,Vvar__4__Cpow__11750,Vvar__5__Cp__phi__11751,Vvar__6__rpow__11754,Vvar__6__rpow__11754)
                 => ( cCoq_2esetoid__ring_2eRing__theory_2epower__theory___24a7(Vvar__0__R__11738,Vvar__1__rI__11739,Vvar__2__rmul__11740,Vvar__3__req__11745,Vvar__4__Cpow__11750,Vvar__5__Cp__phi__11751,Vvar__6__rpow__11754)
                   => ( ! [Vvar__var__var__var__var__var__var__var__7__r__11782__11784__11786__11788__11790__11792__11794__11796] :
                          ( t(Vvar__var__var__var__var__var__var__var__7__r__11782__11784__11786__11788__11790__11792__11794__11796,Vvar__0__R__11738)
                         => ! [Vvar__var__var__var__var__var__var__var__8__n__11783__11785__11787__11789__11791__11793__11795__11797] :
                              ( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__var__var__var__var__var__var__var__8__n__11783__11785__11787__11789__11791__11793__11795__11797)
                             => p(happ(happ(Vvar__3__req__11745,happ(happ(Vvar__6__rpow__11754,Vvar__var__var__var__var__var__var__var__7__r__11782__11784__11786__11788__11790__11792__11794__11796),happ(Vvar__5__Cp__phi__11751,Vvar__var__var__var__var__var__var__var__8__n__11783__11785__11787__11789__11791__11793__11795__11797))),cCoq_2esetoid__ring_2eRing__theory_2epow__N___24a5(Vvar__0__R__11738,Vvar__1__rI__11739,Vvar__2__rmul__11740,Vvar__var__var__var__var__var__var__var__7__r__11782__11784__11786__11788__11790__11792__11794__11796,Vvar__var__var__var__var__var__var__var__8__n__11783__11785__11787__11789__11791__11793__11795__11797))) ) )
                      & p(c_24True) ) ) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.setoid_ring.Ring_theory.ring_eq_ext',axiom,
    ! [Vvar__0__R__8260,Vvar__1__radd__8261,Vvar__2__rmul__8266,Vvar__3__ropp__8271,Vvar__4__req__8274] :
      ( cType___24t(Vvar__0__R__8260)
     => ( c_24__type__8365___24t(Vvar__0__R__8260,Vvar__1__radd__8261,Vvar__2__rmul__8266,Vvar__3__ropp__8271,Vvar__4__req__8274,Vvar__1__radd__8261)
       => ( c_24__type__8395___24t(Vvar__0__R__8260,Vvar__1__radd__8261,Vvar__2__rmul__8266,Vvar__3__ropp__8271,Vvar__4__req__8274,Vvar__2__rmul__8266)
         => ( c_24__type__8419___24t(Vvar__0__R__8260,Vvar__1__radd__8261,Vvar__2__rmul__8266,Vvar__3__ropp__8271,Vvar__4__req__8274,Vvar__3__ropp__8271)
           => ( c_24__type__8449___24t(Vvar__0__R__8260,Vvar__1__radd__8261,Vvar__2__rmul__8266,Vvar__3__ropp__8271,Vvar__4__req__8274,Vvar__4__req__8274)
             => ( cCoq_2esetoid__ring_2eRing__theory_2ering__eq__ext___24a5(Vvar__0__R__8260,Vvar__1__radd__8261,Vvar__2__rmul__8266,Vvar__3__ropp__8271,Vvar__4__req__8274)
               => ( cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__8479___24a5(Vvar__0__R__8260,Vvar__1__radd__8261,Vvar__2__rmul__8266,Vvar__3__ropp__8271,Vvar__4__req__8274),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(Vvar__0__R__8260,c_24__type__8503___24a5(Vvar__0__R__8260,Vvar__1__radd__8261,Vvar__2__rmul__8266,Vvar__3__ropp__8271,Vvar__4__req__8274),Vvar__4__req__8274,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(Vvar__0__R__8260,Vvar__0__R__8260,Vvar__4__req__8274,Vvar__4__req__8274)),Vvar__1__radd__8261)
                  & cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__8536___24a5(Vvar__0__R__8260,Vvar__1__radd__8261,Vvar__2__rmul__8266,Vvar__3__ropp__8271,Vvar__4__req__8274),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(Vvar__0__R__8260,c_24__type__8560___24a5(Vvar__0__R__8260,Vvar__1__radd__8261,Vvar__2__rmul__8266,Vvar__3__ropp__8271,Vvar__4__req__8274),Vvar__4__req__8274,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(Vvar__0__R__8260,Vvar__0__R__8260,Vvar__4__req__8274,Vvar__4__req__8274)),Vvar__2__rmul__8266)
                  & cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__8587___24a5(Vvar__0__R__8260,Vvar__1__radd__8261,Vvar__2__rmul__8266,Vvar__3__ropp__8271,Vvar__4__req__8274),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(Vvar__0__R__8260,Vvar__0__R__8260,Vvar__4__req__8274,Vvar__4__req__8274),Vvar__3__ropp__8271)
                  & p(c_24True) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.setoid_ring.Ring_theory.ring_kind',axiom,
    ! [VX112501] :
      ( cCoq_2esetoid__ring_2eRing__theory_2ering__kind___24t(VX112501)
     => ( VX112501 = cCoq_2esetoid__ring_2eRing__theory_2eAbstract
        | ? [Vvar__0__R__112502] :
            ( cType___24t(Vvar__0__R__112502)
            & ? [Vvar__1__req__112503] :
                ( c_24__type__1300___24t(Vvar__0__R__112502,Vvar__1__req__112503)
                & ? [Vvar__2__reqb__112508] :
                    ( c_24__type__1063___24t(Vvar__0__R__112502,Vvar__2__reqb__112508)
                    & ! [Vvar__var__3__x__112514__112517] :
                        ( t(Vvar__var__3__x__112514__112517,Vvar__0__R__112502)
                       => ! [Vvar__var__4__y__112515__112518] :
                            ( t(Vvar__var__4__y__112515__112518,Vvar__0__R__112502)
                           => ( happ(happ(Vvar__2__reqb__112508,Vvar__var__3__x__112514__112517),Vvar__var__4__y__112515__112518) = cCoq_2eInit_2eDatatypes_2etrue
                             => p(happ(happ(Vvar__1__req__112503,Vvar__var__3__x__112514__112517),Vvar__var__4__y__112515__112518)) ) ) )
                    & VX112501 = cCoq_2esetoid__ring_2eRing__theory_2eComputational___24a3(Vvar__0__R__112502,Vvar__1__req__112503,Vvar__2__reqb__112508) ) ) )
        | ? [Vvar__0__R__112520] :
            ( cType___24t(Vvar__0__R__112520)
            & ? [Vvar__1__rO__112521] :
                ( t(Vvar__1__rO__112521,Vvar__0__R__112520)
                & ? [Vvar__2__rI__112522] :
                    ( t(Vvar__2__rI__112522,Vvar__0__R__112520)
                    & ? [Vvar__3__radd__112523] :
                        ( c_24__type__1058___24t(Vvar__0__R__112520,Vvar__3__radd__112523)
                        & ? [Vvar__4__rmul__112528] :
                            ( c_24__type__1058___24t(Vvar__0__R__112520,Vvar__4__rmul__112528)
                            & ? [Vvar__5__rsub__112533] :
                                ( c_24__type__1058___24t(Vvar__0__R__112520,Vvar__5__rsub__112533)
                                & ? [Vvar__6__ropp__112538] :
                                    ( c_24__type__1278___24t(Vvar__0__R__112520,Vvar__6__ropp__112538)
                                    & ? [Vvar__7__req__112541] :
                                        ( c_24__type__1300___24t(Vvar__0__R__112520,Vvar__7__req__112541)
                                        & ? [Vvar__8__C__112546] :
                                            ( cType___24t(Vvar__8__C__112546)
                                            & ? [Vvar__9__cO__112547] :
                                                ( t(Vvar__9__cO__112547,Vvar__8__C__112546)
                                                & ? [Vvar__10__cI__112548] :
                                                    ( t(Vvar__10__cI__112548,Vvar__8__C__112546)
                                                    & ? [Vvar__11__cadd__112549] :
                                                        ( c_24__type__1310___24t(Vvar__0__R__112520,Vvar__8__C__112546,Vvar__11__cadd__112549)
                                                        & ? [Vvar__12__cmul__112554] :
                                                            ( c_24__type__1310___24t(Vvar__0__R__112520,Vvar__8__C__112546,Vvar__12__cmul__112554)
                                                            & ? [Vvar__13__csub__112559] :
                                                                ( c_24__type__1310___24t(Vvar__0__R__112520,Vvar__8__C__112546,Vvar__13__csub__112559)
                                                                & ? [Vvar__14__copp__112564] :
                                                                    ( c_24__type__1324___24t(Vvar__0__R__112520,Vvar__8__C__112546,Vvar__14__copp__112564)
                                                                    & ? [Vvar__15__ceqb__112567] :
                                                                        ( c_24__type__1331___24t(Vvar__0__R__112520,Vvar__8__C__112546,Vvar__15__ceqb__112567)
                                                                        & ? [Vvar__16__phi__112572] :
                                                                            ( c_24__type__1335___24t(Vvar__0__R__112520,Vvar__8__C__112546,Vvar__16__phi__112572)
                                                                            & cCoq_2esetoid__ring_2eRing__theory_2ering__morph___24a17(Vvar__0__R__112520,Vvar__1__rO__112521,Vvar__2__rI__112522,Vvar__3__radd__112523,Vvar__4__rmul__112528,Vvar__5__rsub__112533,Vvar__6__ropp__112538,Vvar__7__req__112541,Vvar__8__C__112546,Vvar__9__cO__112547,Vvar__10__cI__112548,Vvar__11__cadd__112549,Vvar__12__cmul__112554,Vvar__13__csub__112559,Vvar__14__copp__112564,Vvar__15__ceqb__112567,Vvar__16__phi__112572)
                                                                            & VX112501 = cCoq_2esetoid__ring_2eRing__theory_2eMorphism___24a17(Vvar__0__R__112520,Vvar__1__rO__112521,Vvar__2__rI__112522,Vvar__3__radd__112523,Vvar__4__rmul__112528,Vvar__5__rsub__112533,Vvar__6__ropp__112538,Vvar__7__req__112541,Vvar__8__C__112546,Vvar__9__cO__112547,Vvar__10__cI__112548,Vvar__11__cadd__112549,Vvar__12__cmul__112554,Vvar__13__csub__112559,Vvar__14__copp__112564,Vvar__15__ceqb__112567,Vvar__16__phi__112572) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.setoid_ring.Ring_theory.ring_morph',axiom,
    ! [Vvar__0__R__8590,Vvar__1__rO__8591,Vvar__2__rI__8592,Vvar__3__radd__8593,Vvar__4__rmul__8598,Vvar__5__rsub__8603,Vvar__6__ropp__8608,Vvar__7__req__8611,Vvar__8__C__8616,Vvar__9__cO__8617,Vvar__10__cI__8618,Vvar__11__cadd__8619,Vvar__12__cmul__8624,Vvar__13__csub__8629,Vvar__14__copp__8634,Vvar__15__ceqb__8637,Vvar__16__phi__8642] :
      ( cType___24t(Vvar__0__R__8590)
     => ( t(Vvar__1__rO__8591,Vvar__0__R__8590)
       => ( t(Vvar__2__rI__8592,Vvar__0__R__8590)
         => ( c_24__type__8986___24t(Vvar__0__R__8590,Vvar__1__rO__8591,Vvar__2__rI__8592,Vvar__3__radd__8593,Vvar__4__rmul__8598,Vvar__5__rsub__8603,Vvar__6__ropp__8608,Vvar__7__req__8611,Vvar__8__C__8616,Vvar__9__cO__8617,Vvar__10__cI__8618,Vvar__11__cadd__8619,Vvar__12__cmul__8624,Vvar__13__csub__8629,Vvar__14__copp__8634,Vvar__15__ceqb__8637,Vvar__16__phi__8642,Vvar__3__radd__8593)
           => ( c_24__type__9199___24t(Vvar__0__R__8590,Vvar__1__rO__8591,Vvar__2__rI__8592,Vvar__3__radd__8593,Vvar__4__rmul__8598,Vvar__5__rsub__8603,Vvar__6__ropp__8608,Vvar__7__req__8611,Vvar__8__C__8616,Vvar__9__cO__8617,Vvar__10__cI__8618,Vvar__11__cadd__8619,Vvar__12__cmul__8624,Vvar__13__csub__8629,Vvar__14__copp__8634,Vvar__15__ceqb__8637,Vvar__16__phi__8642,Vvar__4__rmul__8598)
             => ( c_24__type__9412___24t(Vvar__0__R__8590,Vvar__1__rO__8591,Vvar__2__rI__8592,Vvar__3__radd__8593,Vvar__4__rmul__8598,Vvar__5__rsub__8603,Vvar__6__ropp__8608,Vvar__7__req__8611,Vvar__8__C__8616,Vvar__9__cO__8617,Vvar__10__cI__8618,Vvar__11__cadd__8619,Vvar__12__cmul__8624,Vvar__13__csub__8629,Vvar__14__copp__8634,Vvar__15__ceqb__8637,Vvar__16__phi__8642,Vvar__5__rsub__8603)
               => ( c_24__type__9607___24t(Vvar__0__R__8590,Vvar__1__rO__8591,Vvar__2__rI__8592,Vvar__3__radd__8593,Vvar__4__rmul__8598,Vvar__5__rsub__8603,Vvar__6__ropp__8608,Vvar__7__req__8611,Vvar__8__C__8616,Vvar__9__cO__8617,Vvar__10__cI__8618,Vvar__11__cadd__8619,Vvar__12__cmul__8624,Vvar__13__csub__8629,Vvar__14__copp__8634,Vvar__15__ceqb__8637,Vvar__16__phi__8642,Vvar__6__ropp__8608)
                 => ( c_24__type__9820___24t(Vvar__0__R__8590,Vvar__1__rO__8591,Vvar__2__rI__8592,Vvar__3__radd__8593,Vvar__4__rmul__8598,Vvar__5__rsub__8603,Vvar__6__ropp__8608,Vvar__7__req__8611,Vvar__8__C__8616,Vvar__9__cO__8617,Vvar__10__cI__8618,Vvar__11__cadd__8619,Vvar__12__cmul__8624,Vvar__13__csub__8629,Vvar__14__copp__8634,Vvar__15__ceqb__8637,Vvar__16__phi__8642,Vvar__7__req__8611)
                   => ( cType___24t(Vvar__8__C__8616)
                     => ( t(Vvar__9__cO__8617,Vvar__8__C__8616)
                       => ( t(Vvar__10__cI__8618,Vvar__8__C__8616)
                         => ( c_24__type__10033___24t(Vvar__0__R__8590,Vvar__1__rO__8591,Vvar__2__rI__8592,Vvar__3__radd__8593,Vvar__4__rmul__8598,Vvar__5__rsub__8603,Vvar__6__ropp__8608,Vvar__7__req__8611,Vvar__8__C__8616,Vvar__9__cO__8617,Vvar__10__cI__8618,Vvar__11__cadd__8619,Vvar__12__cmul__8624,Vvar__13__csub__8629,Vvar__14__copp__8634,Vvar__15__ceqb__8637,Vvar__16__phi__8642,Vvar__11__cadd__8619)
                           => ( c_24__type__10246___24t(Vvar__0__R__8590,Vvar__1__rO__8591,Vvar__2__rI__8592,Vvar__3__radd__8593,Vvar__4__rmul__8598,Vvar__5__rsub__8603,Vvar__6__ropp__8608,Vvar__7__req__8611,Vvar__8__C__8616,Vvar__9__cO__8617,Vvar__10__cI__8618,Vvar__11__cadd__8619,Vvar__12__cmul__8624,Vvar__13__csub__8629,Vvar__14__copp__8634,Vvar__15__ceqb__8637,Vvar__16__phi__8642,Vvar__12__cmul__8624)
                             => ( c_24__type__10459___24t(Vvar__0__R__8590,Vvar__1__rO__8591,Vvar__2__rI__8592,Vvar__3__radd__8593,Vvar__4__rmul__8598,Vvar__5__rsub__8603,Vvar__6__ropp__8608,Vvar__7__req__8611,Vvar__8__C__8616,Vvar__9__cO__8617,Vvar__10__cI__8618,Vvar__11__cadd__8619,Vvar__12__cmul__8624,Vvar__13__csub__8629,Vvar__14__copp__8634,Vvar__15__ceqb__8637,Vvar__16__phi__8642,Vvar__13__csub__8629)
                               => ( c_24__type__10654___24t(Vvar__0__R__8590,Vvar__1__rO__8591,Vvar__2__rI__8592,Vvar__3__radd__8593,Vvar__4__rmul__8598,Vvar__5__rsub__8603,Vvar__6__ropp__8608,Vvar__7__req__8611,Vvar__8__C__8616,Vvar__9__cO__8617,Vvar__10__cI__8618,Vvar__11__cadd__8619,Vvar__12__cmul__8624,Vvar__13__csub__8629,Vvar__14__copp__8634,Vvar__15__ceqb__8637,Vvar__16__phi__8642,Vvar__14__copp__8634)
                                 => ( c_24__type__10867___24t(Vvar__0__R__8590,Vvar__1__rO__8591,Vvar__2__rI__8592,Vvar__3__radd__8593,Vvar__4__rmul__8598,Vvar__5__rsub__8603,Vvar__6__ropp__8608,Vvar__7__req__8611,Vvar__8__C__8616,Vvar__9__cO__8617,Vvar__10__cI__8618,Vvar__11__cadd__8619,Vvar__12__cmul__8624,Vvar__13__csub__8629,Vvar__14__copp__8634,Vvar__15__ceqb__8637,Vvar__16__phi__8642,Vvar__15__ceqb__8637)
                                   => ( c_24__type__11062___24t(Vvar__0__R__8590,Vvar__1__rO__8591,Vvar__2__rI__8592,Vvar__3__radd__8593,Vvar__4__rmul__8598,Vvar__5__rsub__8603,Vvar__6__ropp__8608,Vvar__7__req__8611,Vvar__8__C__8616,Vvar__9__cO__8617,Vvar__10__cI__8618,Vvar__11__cadd__8619,Vvar__12__cmul__8624,Vvar__13__csub__8629,Vvar__14__copp__8634,Vvar__15__ceqb__8637,Vvar__16__phi__8642,Vvar__16__phi__8642)
                                     => ( cCoq_2esetoid__ring_2eRing__theory_2ering__morph___24a17(Vvar__0__R__8590,Vvar__1__rO__8591,Vvar__2__rI__8592,Vvar__3__radd__8593,Vvar__4__rmul__8598,Vvar__5__rsub__8603,Vvar__6__ropp__8608,Vvar__7__req__8611,Vvar__8__C__8616,Vvar__9__cO__8617,Vvar__10__cI__8618,Vvar__11__cadd__8619,Vvar__12__cmul__8624,Vvar__13__csub__8629,Vvar__14__copp__8634,Vvar__15__ceqb__8637,Vvar__16__phi__8642)
                                       => ( p(happ(happ(Vvar__7__req__8611,happ(Vvar__16__phi__8642,Vvar__9__cO__8617)),Vvar__1__rO__8591))
                                          & p(happ(happ(Vvar__7__req__8611,happ(Vvar__16__phi__8642,Vvar__10__cI__8618)),Vvar__2__rI__8592))
                                          & ! [Vvar__var__var__var__var__var__var__19__x__8704__8706__8728__8730__8732__8734__8736] :
                                              ( t(Vvar__var__var__var__var__var__var__19__x__8704__8706__8728__8730__8732__8734__8736,Vvar__8__C__8616)
                                             => ! [Vvar__var__var__var__var__var__var__20__y__8705__8707__8729__8731__8733__8735__8737] :
                                                  ( t(Vvar__var__var__var__var__var__var__20__y__8705__8707__8729__8731__8733__8735__8737,Vvar__8__C__8616)
                                                 => p(happ(happ(Vvar__7__req__8611,happ(Vvar__16__phi__8642,happ(happ(Vvar__11__cadd__8619,Vvar__var__var__var__var__var__var__19__x__8704__8706__8728__8730__8732__8734__8736),Vvar__var__var__var__var__var__var__20__y__8705__8707__8729__8731__8733__8735__8737))),happ(happ(Vvar__3__radd__8593,happ(Vvar__16__phi__8642,Vvar__var__var__var__var__var__var__19__x__8704__8706__8728__8730__8732__8734__8736)),happ(Vvar__16__phi__8642,Vvar__var__var__var__var__var__var__20__y__8705__8707__8729__8731__8733__8735__8737)))) ) )
                                          & ! [Vvar__var__var__var__var__var__var__20__x__8709__8711__8738__8740__8742__8744__8746] :
                                              ( t(Vvar__var__var__var__var__var__var__20__x__8709__8711__8738__8740__8742__8744__8746,Vvar__8__C__8616)
                                             => ! [Vvar__var__var__var__var__var__var__21__y__8710__8712__8739__8741__8743__8745__8747] :
                                                  ( t(Vvar__var__var__var__var__var__var__21__y__8710__8712__8739__8741__8743__8745__8747,Vvar__8__C__8616)
                                                 => p(happ(happ(Vvar__7__req__8611,happ(Vvar__16__phi__8642,happ(happ(Vvar__13__csub__8629,Vvar__var__var__var__var__var__var__20__x__8709__8711__8738__8740__8742__8744__8746),Vvar__var__var__var__var__var__var__21__y__8710__8712__8739__8741__8743__8745__8747))),happ(happ(Vvar__5__rsub__8603,happ(Vvar__16__phi__8642,Vvar__var__var__var__var__var__var__20__x__8709__8711__8738__8740__8742__8744__8746)),happ(Vvar__16__phi__8642,Vvar__var__var__var__var__var__var__21__y__8710__8712__8739__8741__8743__8745__8747)))) ) )
                                          & ! [Vvar__var__var__var__var__var__var__21__x__8714__8716__8748__8750__8752__8754__8756] :
                                              ( t(Vvar__var__var__var__var__var__var__21__x__8714__8716__8748__8750__8752__8754__8756,Vvar__8__C__8616)
                                             => ! [Vvar__var__var__var__var__var__var__22__y__8715__8717__8749__8751__8753__8755__8757] :
                                                  ( t(Vvar__var__var__var__var__var__var__22__y__8715__8717__8749__8751__8753__8755__8757,Vvar__8__C__8616)
                                                 => p(happ(happ(Vvar__7__req__8611,happ(Vvar__16__phi__8642,happ(happ(Vvar__12__cmul__8624,Vvar__var__var__var__var__var__var__21__x__8714__8716__8748__8750__8752__8754__8756),Vvar__var__var__var__var__var__var__22__y__8715__8717__8749__8751__8753__8755__8757))),happ(happ(Vvar__4__rmul__8598,happ(Vvar__16__phi__8642,Vvar__var__var__var__var__var__var__21__x__8714__8716__8748__8750__8752__8754__8756)),happ(Vvar__16__phi__8642,Vvar__var__var__var__var__var__var__22__y__8715__8717__8749__8751__8753__8755__8757)))) ) )
                                          & ! [Vvar__var__var__var__var__var__var__22__x__8719__8720__8758__8759__8760__8761__8762] :
                                              ( t(Vvar__var__var__var__var__var__var__22__x__8719__8720__8758__8759__8760__8761__8762,Vvar__8__C__8616)
                                             => p(happ(happ(Vvar__7__req__8611,happ(Vvar__16__phi__8642,happ(Vvar__14__copp__8634,Vvar__var__var__var__var__var__var__22__x__8719__8720__8758__8759__8760__8761__8762))),happ(Vvar__6__ropp__8608,happ(Vvar__16__phi__8642,Vvar__var__var__var__var__var__var__22__x__8719__8720__8758__8759__8760__8761__8762)))) )
                                          & ! [Vvar__var__var__var__var__var__23__x__8722__8725__8763__8766__8769__8772] :
                                              ( t(Vvar__var__var__var__var__var__23__x__8722__8725__8763__8766__8769__8772,Vvar__8__C__8616)
                                             => ! [Vvar__var__var__var__var__var__24__y__8723__8726__8764__8767__8770__8773] :
                                                  ( t(Vvar__var__var__var__var__var__24__y__8723__8726__8764__8767__8770__8773,Vvar__8__C__8616)
                                                 => ( happ(happ(Vvar__15__ceqb__8637,Vvar__var__var__var__var__var__23__x__8722__8725__8763__8766__8769__8772),Vvar__var__var__var__var__var__24__y__8723__8726__8764__8767__8770__8773) = cCoq_2eInit_2eDatatypes_2etrue
                                                   => p(happ(happ(Vvar__7__req__8611,happ(Vvar__16__phi__8642,Vvar__var__var__var__var__var__23__x__8722__8725__8763__8766__8769__8772)),happ(Vvar__16__phi__8642,Vvar__var__var__var__var__var__24__y__8723__8726__8764__8767__8770__8773))) ) ) )
                                          & p(c_24True) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.setoid_ring.Ring_theory.ring_theory',axiom,
    ! [Vvar__0__R__110790,Vvar__1__rO__110791,Vvar__2__rI__110792,Vvar__3__radd__110793,Vvar__4__rmul__110798,Vvar__5__rsub__110803,Vvar__6__ropp__110808,Vvar__7__req__110811] :
      ( cType___24t(Vvar__0__R__110790)
     => ( t(Vvar__1__rO__110791,Vvar__0__R__110790)
       => ( t(Vvar__2__rI__110792,Vvar__0__R__110790)
         => ( c_24__type__111014___24t(Vvar__0__R__110790,Vvar__1__rO__110791,Vvar__2__rI__110792,Vvar__3__radd__110793,Vvar__4__rmul__110798,Vvar__5__rsub__110803,Vvar__6__ropp__110808,Vvar__7__req__110811,Vvar__3__radd__110793)
           => ( c_24__type__111077___24t(Vvar__0__R__110790,Vvar__1__rO__110791,Vvar__2__rI__110792,Vvar__3__radd__110793,Vvar__4__rmul__110798,Vvar__5__rsub__110803,Vvar__6__ropp__110808,Vvar__7__req__110811,Vvar__4__rmul__110798)
             => ( c_24__type__111140___24t(Vvar__0__R__110790,Vvar__1__rO__110791,Vvar__2__rI__110792,Vvar__3__radd__110793,Vvar__4__rmul__110798,Vvar__5__rsub__110803,Vvar__6__ropp__110808,Vvar__7__req__110811,Vvar__5__rsub__110803)
               => ( c_24__type__111194___24t(Vvar__0__R__110790,Vvar__1__rO__110791,Vvar__2__rI__110792,Vvar__3__radd__110793,Vvar__4__rmul__110798,Vvar__5__rsub__110803,Vvar__6__ropp__110808,Vvar__7__req__110811,Vvar__6__ropp__110808)
                 => ( c_24__type__111257___24t(Vvar__0__R__110790,Vvar__1__rO__110791,Vvar__2__rI__110792,Vvar__3__radd__110793,Vvar__4__rmul__110798,Vvar__5__rsub__110803,Vvar__6__ropp__110808,Vvar__7__req__110811,Vvar__7__req__110811)
                   => ( cCoq_2esetoid__ring_2eRing__theory_2ering__theory___24a8(Vvar__0__R__110790,Vvar__1__rO__110791,Vvar__2__rI__110792,Vvar__3__radd__110793,Vvar__4__rmul__110798,Vvar__5__rsub__110803,Vvar__6__ropp__110808,Vvar__7__req__110811)
                     => ( ! [Vvar__var__var__var__var__var__8__x__110844__110845__110888__110889__110890__110891] :
                            ( t(Vvar__var__var__var__var__var__8__x__110844__110845__110888__110889__110890__110891,Vvar__0__R__110790)
                           => p(happ(happ(Vvar__7__req__110811,happ(happ(Vvar__3__radd__110793,Vvar__1__rO__110791),Vvar__var__var__var__var__var__8__x__110844__110845__110888__110889__110890__110891)),Vvar__var__var__var__var__var__8__x__110844__110845__110888__110889__110890__110891)) )
                        & ! [Vvar__var__var__var__var__9__x__110847__110849__110892__110894__110896] :
                            ( t(Vvar__var__var__var__var__9__x__110847__110849__110892__110894__110896,Vvar__0__R__110790)
                           => ! [Vvar__var__var__var__var__10__y__110848__110850__110893__110895__110897] :
                                ( t(Vvar__var__var__var__var__10__y__110848__110850__110893__110895__110897,Vvar__0__R__110790)
                               => p(happ(happ(Vvar__7__req__110811,happ(happ(Vvar__3__radd__110793,Vvar__var__var__var__var__9__x__110847__110849__110892__110894__110896),Vvar__var__var__var__var__10__y__110848__110850__110893__110895__110897)),happ(happ(Vvar__3__radd__110793,Vvar__var__var__var__var__10__y__110848__110850__110893__110895__110897),Vvar__var__var__var__var__9__x__110847__110849__110892__110894__110896))) ) )
                        & ! [Vvar__var__var__var__var__10__x__110852__110855__110898__110901__110904] :
                            ( t(Vvar__var__var__var__var__10__x__110852__110855__110898__110901__110904,Vvar__0__R__110790)
                           => ! [Vvar__var__var__var__var__11__y__110853__110856__110899__110902__110905] :
                                ( t(Vvar__var__var__var__var__11__y__110853__110856__110899__110902__110905,Vvar__0__R__110790)
                               => ! [Vvar__var__var__var__var__12__z__110854__110857__110900__110903__110906] :
                                    ( t(Vvar__var__var__var__var__12__z__110854__110857__110900__110903__110906,Vvar__0__R__110790)
                                   => p(happ(happ(Vvar__7__req__110811,happ(happ(Vvar__3__radd__110793,Vvar__var__var__var__var__10__x__110852__110855__110898__110901__110904),happ(happ(Vvar__3__radd__110793,Vvar__var__var__var__var__11__y__110853__110856__110899__110902__110905),Vvar__var__var__var__var__12__z__110854__110857__110900__110903__110906))),happ(happ(Vvar__3__radd__110793,happ(happ(Vvar__3__radd__110793,Vvar__var__var__var__var__10__x__110852__110855__110898__110901__110904),Vvar__var__var__var__var__11__y__110853__110856__110899__110902__110905)),Vvar__var__var__var__var__12__z__110854__110857__110900__110903__110906))) ) ) )
                        & ! [Vvar__var__var__var__var__var__11__x__110859__110860__110907__110908__110909__110910] :
                            ( t(Vvar__var__var__var__var__var__11__x__110859__110860__110907__110908__110909__110910,Vvar__0__R__110790)
                           => p(happ(happ(Vvar__7__req__110811,happ(happ(Vvar__4__rmul__110798,Vvar__2__rI__110792),Vvar__var__var__var__var__var__11__x__110859__110860__110907__110908__110909__110910)),Vvar__var__var__var__var__var__11__x__110859__110860__110907__110908__110909__110910)) )
                        & ! [Vvar__var__var__var__var__12__x__110862__110864__110911__110913__110915] :
                            ( t(Vvar__var__var__var__var__12__x__110862__110864__110911__110913__110915,Vvar__0__R__110790)
                           => ! [Vvar__var__var__var__var__13__y__110863__110865__110912__110914__110916] :
                                ( t(Vvar__var__var__var__var__13__y__110863__110865__110912__110914__110916,Vvar__0__R__110790)
                               => p(happ(happ(Vvar__7__req__110811,happ(happ(Vvar__4__rmul__110798,Vvar__var__var__var__var__12__x__110862__110864__110911__110913__110915),Vvar__var__var__var__var__13__y__110863__110865__110912__110914__110916)),happ(happ(Vvar__4__rmul__110798,Vvar__var__var__var__var__13__y__110863__110865__110912__110914__110916),Vvar__var__var__var__var__12__x__110862__110864__110911__110913__110915))) ) )
                        & ! [Vvar__var__var__var__var__13__x__110867__110870__110917__110920__110923] :
                            ( t(Vvar__var__var__var__var__13__x__110867__110870__110917__110920__110923,Vvar__0__R__110790)
                           => ! [Vvar__var__var__var__var__14__y__110868__110871__110918__110921__110924] :
                                ( t(Vvar__var__var__var__var__14__y__110868__110871__110918__110921__110924,Vvar__0__R__110790)
                               => ! [Vvar__var__var__var__var__15__z__110869__110872__110919__110922__110925] :
                                    ( t(Vvar__var__var__var__var__15__z__110869__110872__110919__110922__110925,Vvar__0__R__110790)
                                   => p(happ(happ(Vvar__7__req__110811,happ(happ(Vvar__4__rmul__110798,Vvar__var__var__var__var__13__x__110867__110870__110917__110920__110923),happ(happ(Vvar__4__rmul__110798,Vvar__var__var__var__var__14__y__110868__110871__110918__110921__110924),Vvar__var__var__var__var__15__z__110869__110872__110919__110922__110925))),happ(happ(Vvar__4__rmul__110798,happ(happ(Vvar__4__rmul__110798,Vvar__var__var__var__var__13__x__110867__110870__110917__110920__110923),Vvar__var__var__var__var__14__y__110868__110871__110918__110921__110924)),Vvar__var__var__var__var__15__z__110869__110872__110919__110922__110925))) ) ) )
                        & ! [Vvar__var__var__var__var__var__14__x__110874__110877__110926__110929__110932__110935] :
                            ( t(Vvar__var__var__var__var__var__14__x__110874__110877__110926__110929__110932__110935,Vvar__0__R__110790)
                           => ! [Vvar__var__var__var__var__var__15__y__110875__110878__110927__110930__110933__110936] :
                                ( t(Vvar__var__var__var__var__var__15__y__110875__110878__110927__110930__110933__110936,Vvar__0__R__110790)
                               => ! [Vvar__var__var__var__var__var__16__z__110876__110879__110928__110931__110934__110937] :
                                    ( t(Vvar__var__var__var__var__var__16__z__110876__110879__110928__110931__110934__110937,Vvar__0__R__110790)
                                   => p(happ(happ(Vvar__7__req__110811,happ(happ(Vvar__4__rmul__110798,happ(happ(Vvar__3__radd__110793,Vvar__var__var__var__var__var__14__x__110874__110877__110926__110929__110932__110935),Vvar__var__var__var__var__var__15__y__110875__110878__110927__110930__110933__110936)),Vvar__var__var__var__var__var__16__z__110876__110879__110928__110931__110934__110937)),happ(happ(Vvar__3__radd__110793,happ(happ(Vvar__4__rmul__110798,Vvar__var__var__var__var__var__14__x__110874__110877__110926__110929__110932__110935),Vvar__var__var__var__var__var__16__z__110876__110879__110928__110931__110934__110937)),happ(happ(Vvar__4__rmul__110798,Vvar__var__var__var__var__var__15__y__110875__110878__110927__110930__110933__110936),Vvar__var__var__var__var__var__16__z__110876__110879__110928__110931__110934__110937)))) ) ) )
                        & ! [Vvar__var__var__var__var__var__var__15__x__110881__110883__110938__110940__110942__110944__110946] :
                            ( t(Vvar__var__var__var__var__var__var__15__x__110881__110883__110938__110940__110942__110944__110946,Vvar__0__R__110790)
                           => ! [Vvar__var__var__var__var__var__var__16__y__110882__110884__110939__110941__110943__110945__110947] :
                                ( t(Vvar__var__var__var__var__var__var__16__y__110882__110884__110939__110941__110943__110945__110947,Vvar__0__R__110790)
                               => p(happ(happ(Vvar__7__req__110811,happ(happ(Vvar__5__rsub__110803,Vvar__var__var__var__var__var__var__15__x__110881__110883__110938__110940__110942__110944__110946),Vvar__var__var__var__var__var__var__16__y__110882__110884__110939__110941__110943__110945__110947)),happ(happ(Vvar__3__radd__110793,Vvar__var__var__var__var__var__var__15__x__110881__110883__110938__110940__110942__110944__110946),happ(Vvar__6__ropp__110808,Vvar__var__var__var__var__var__var__16__y__110882__110884__110939__110941__110943__110945__110947)))) ) )
                        & ! [Vvar__var__var__var__var__var__var__16__x__110886__110887__110948__110949__110950__110951__110952] :
                            ( t(Vvar__var__var__var__var__var__var__16__x__110886__110887__110948__110949__110950__110951__110952,Vvar__0__R__110790)
                           => p(happ(happ(Vvar__7__req__110811,happ(happ(Vvar__3__radd__110793,Vvar__var__var__var__var__var__var__16__x__110886__110887__110948__110949__110950__110951__110952),happ(Vvar__6__ropp__110808,Vvar__var__var__var__var__var__var__16__x__110886__110887__110948__110949__110950__110951__110952))),Vvar__1__rO__110791)) )
                        & p(c_24True) ) ) ) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.setoid_ring.Ring_theory.semi_morph',axiom,
    ! [Vvar__0__R__111499,Vvar__1__rO__111500,Vvar__2__rI__111501,Vvar__3__radd__111502,Vvar__4__rmul__111507,Vvar__5__req__111512,Vvar__6__C__111517,Vvar__7__cO__111518,Vvar__8__cI__111519,Vvar__9__cadd__111520,Vvar__10__cmul__111525,Vvar__11__ceqb__111530,Vvar__12__phi__111535] :
      ( cType___24t(Vvar__0__R__111499)
     => ( t(Vvar__1__rO__111500,Vvar__0__R__111499)
       => ( t(Vvar__2__rI__111501,Vvar__0__R__111499)
         => ( c_24__type__111752___24t(Vvar__0__R__111499,Vvar__1__rO__111500,Vvar__2__rI__111501,Vvar__3__radd__111502,Vvar__4__rmul__111507,Vvar__5__req__111512,Vvar__6__C__111517,Vvar__7__cO__111518,Vvar__8__cI__111519,Vvar__9__cadd__111520,Vvar__10__cmul__111525,Vvar__11__ceqb__111530,Vvar__12__phi__111535,Vvar__3__radd__111502)
           => ( c_24__type__111877___24t(Vvar__0__R__111499,Vvar__1__rO__111500,Vvar__2__rI__111501,Vvar__3__radd__111502,Vvar__4__rmul__111507,Vvar__5__req__111512,Vvar__6__C__111517,Vvar__7__cO__111518,Vvar__8__cI__111519,Vvar__9__cadd__111520,Vvar__10__cmul__111525,Vvar__11__ceqb__111530,Vvar__12__phi__111535,Vvar__4__rmul__111507)
             => ( c_24__type__112002___24t(Vvar__0__R__111499,Vvar__1__rO__111500,Vvar__2__rI__111501,Vvar__3__radd__111502,Vvar__4__rmul__111507,Vvar__5__req__111512,Vvar__6__C__111517,Vvar__7__cO__111518,Vvar__8__cI__111519,Vvar__9__cadd__111520,Vvar__10__cmul__111525,Vvar__11__ceqb__111530,Vvar__12__phi__111535,Vvar__5__req__111512)
               => ( cType___24t(Vvar__6__C__111517)
                 => ( t(Vvar__7__cO__111518,Vvar__6__C__111517)
                   => ( t(Vvar__8__cI__111519,Vvar__6__C__111517)
                     => ( c_24__type__112127___24t(Vvar__0__R__111499,Vvar__1__rO__111500,Vvar__2__rI__111501,Vvar__3__radd__111502,Vvar__4__rmul__111507,Vvar__5__req__111512,Vvar__6__C__111517,Vvar__7__cO__111518,Vvar__8__cI__111519,Vvar__9__cadd__111520,Vvar__10__cmul__111525,Vvar__11__ceqb__111530,Vvar__12__phi__111535,Vvar__9__cadd__111520)
                       => ( c_24__type__112252___24t(Vvar__0__R__111499,Vvar__1__rO__111500,Vvar__2__rI__111501,Vvar__3__radd__111502,Vvar__4__rmul__111507,Vvar__5__req__111512,Vvar__6__C__111517,Vvar__7__cO__111518,Vvar__8__cI__111519,Vvar__9__cadd__111520,Vvar__10__cmul__111525,Vvar__11__ceqb__111530,Vvar__12__phi__111535,Vvar__10__cmul__111525)
                         => ( c_24__type__112377___24t(Vvar__0__R__111499,Vvar__1__rO__111500,Vvar__2__rI__111501,Vvar__3__radd__111502,Vvar__4__rmul__111507,Vvar__5__req__111512,Vvar__6__C__111517,Vvar__7__cO__111518,Vvar__8__cI__111519,Vvar__9__cadd__111520,Vvar__10__cmul__111525,Vvar__11__ceqb__111530,Vvar__12__phi__111535,Vvar__11__ceqb__111530)
                           => ( c_24__type__112488___24t(Vvar__0__R__111499,Vvar__1__rO__111500,Vvar__2__rI__111501,Vvar__3__radd__111502,Vvar__4__rmul__111507,Vvar__5__req__111512,Vvar__6__C__111517,Vvar__7__cO__111518,Vvar__8__cI__111519,Vvar__9__cadd__111520,Vvar__10__cmul__111525,Vvar__11__ceqb__111530,Vvar__12__phi__111535,Vvar__12__phi__111535)
                             => ( cCoq_2esetoid__ring_2eRing__theory_2esemi__morph___24a13(Vvar__0__R__111499,Vvar__1__rO__111500,Vvar__2__rI__111501,Vvar__3__radd__111502,Vvar__4__rmul__111507,Vvar__5__req__111512,Vvar__6__C__111517,Vvar__7__cO__111518,Vvar__8__cI__111519,Vvar__9__cadd__111520,Vvar__10__cmul__111525,Vvar__11__ceqb__111530,Vvar__12__phi__111535)
                               => ( p(happ(happ(Vvar__5__req__111512,happ(Vvar__12__phi__111535,Vvar__7__cO__111518)),Vvar__1__rO__111500))
                                  & p(happ(happ(Vvar__5__req__111512,happ(Vvar__12__phi__111535,Vvar__8__cI__111519)),Vvar__2__rI__111501))
                                  & ! [Vvar__var__var__var__var__var__var__15__x__111581__111583__111597__111599__111601__111603__111605] :
                                      ( t(Vvar__var__var__var__var__var__var__15__x__111581__111583__111597__111599__111601__111603__111605,Vvar__6__C__111517)
                                     => ! [Vvar__var__var__var__var__var__var__16__y__111582__111584__111598__111600__111602__111604__111606] :
                                          ( t(Vvar__var__var__var__var__var__var__16__y__111582__111584__111598__111600__111602__111604__111606,Vvar__6__C__111517)
                                         => p(happ(happ(Vvar__5__req__111512,happ(Vvar__12__phi__111535,happ(happ(Vvar__9__cadd__111520,Vvar__var__var__var__var__var__var__15__x__111581__111583__111597__111599__111601__111603__111605),Vvar__var__var__var__var__var__var__16__y__111582__111584__111598__111600__111602__111604__111606))),happ(happ(Vvar__3__radd__111502,happ(Vvar__12__phi__111535,Vvar__var__var__var__var__var__var__15__x__111581__111583__111597__111599__111601__111603__111605)),happ(Vvar__12__phi__111535,Vvar__var__var__var__var__var__var__16__y__111582__111584__111598__111600__111602__111604__111606)))) ) )
                                  & ! [Vvar__var__var__var__var__var__var__16__x__111586__111588__111607__111609__111611__111613__111615] :
                                      ( t(Vvar__var__var__var__var__var__var__16__x__111586__111588__111607__111609__111611__111613__111615,Vvar__6__C__111517)
                                     => ! [Vvar__var__var__var__var__var__var__17__y__111587__111589__111608__111610__111612__111614__111616] :
                                          ( t(Vvar__var__var__var__var__var__var__17__y__111587__111589__111608__111610__111612__111614__111616,Vvar__6__C__111517)
                                         => p(happ(happ(Vvar__5__req__111512,happ(Vvar__12__phi__111535,happ(happ(Vvar__10__cmul__111525,Vvar__var__var__var__var__var__var__16__x__111586__111588__111607__111609__111611__111613__111615),Vvar__var__var__var__var__var__var__17__y__111587__111589__111608__111610__111612__111614__111616))),happ(happ(Vvar__4__rmul__111507,happ(Vvar__12__phi__111535,Vvar__var__var__var__var__var__var__16__x__111586__111588__111607__111609__111611__111613__111615)),happ(Vvar__12__phi__111535,Vvar__var__var__var__var__var__var__17__y__111587__111589__111608__111610__111612__111614__111616)))) ) )
                                  & ! [Vvar__var__var__var__var__var__17__x__111591__111594__111617__111620__111623__111626] :
                                      ( t(Vvar__var__var__var__var__var__17__x__111591__111594__111617__111620__111623__111626,Vvar__6__C__111517)
                                     => ! [Vvar__var__var__var__var__var__18__y__111592__111595__111618__111621__111624__111627] :
                                          ( t(Vvar__var__var__var__var__var__18__y__111592__111595__111618__111621__111624__111627,Vvar__6__C__111517)
                                         => ( happ(happ(Vvar__11__ceqb__111530,Vvar__var__var__var__var__var__17__x__111591__111594__111617__111620__111623__111626),Vvar__var__var__var__var__var__18__y__111592__111595__111618__111621__111624__111627) = cCoq_2eInit_2eDatatypes_2etrue
                                           => p(happ(happ(Vvar__5__req__111512,happ(Vvar__12__phi__111535,Vvar__var__var__var__var__var__17__x__111591__111594__111617__111620__111623__111626)),happ(Vvar__12__phi__111535,Vvar__var__var__var__var__var__18__y__111592__111595__111618__111621__111624__111627))) ) ) )
                                  & p(c_24True) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.setoid_ring.Ring_theory.semi_ring_theory',axiom,
    ! [Vvar__0__R__110526,Vvar__1__rO__110527,Vvar__2__rI__110528,Vvar__3__radd__110529,Vvar__4__rmul__110534,Vvar__5__req__110539] :
      ( cType___24t(Vvar__0__R__110526)
     => ( t(Vvar__1__rO__110527,Vvar__0__R__110526)
       => ( t(Vvar__2__rI__110528,Vvar__0__R__110526)
         => ( c_24__type__110694___24t(Vvar__0__R__110526,Vvar__1__rO__110527,Vvar__2__rI__110528,Vvar__3__radd__110529,Vvar__4__rmul__110534,Vvar__5__req__110539,Vvar__3__radd__110529)
           => ( c_24__type__110733___24t(Vvar__0__R__110526,Vvar__1__rO__110527,Vvar__2__rI__110528,Vvar__3__radd__110529,Vvar__4__rmul__110534,Vvar__5__req__110539,Vvar__4__rmul__110534)
             => ( c_24__type__110772___24t(Vvar__0__R__110526,Vvar__1__rO__110527,Vvar__2__rI__110528,Vvar__3__radd__110529,Vvar__4__rmul__110534,Vvar__5__req__110539,Vvar__5__req__110539)
               => ( cCoq_2esetoid__ring_2eRing__theory_2esemi__ring__theory___24a6(Vvar__0__R__110526,Vvar__1__rO__110527,Vvar__2__rI__110528,Vvar__3__radd__110529,Vvar__4__rmul__110534,Vvar__5__req__110539)
                 => ( ! [Vvar__var__var__var__var__var__6__n__110564__110565__110603__110604__110605__110606] :
                        ( t(Vvar__var__var__var__var__var__6__n__110564__110565__110603__110604__110605__110606,Vvar__0__R__110526)
                       => p(happ(happ(Vvar__5__req__110539,happ(happ(Vvar__3__radd__110529,Vvar__1__rO__110527),Vvar__var__var__var__var__var__6__n__110564__110565__110603__110604__110605__110606)),Vvar__var__var__var__var__var__6__n__110564__110565__110603__110604__110605__110606)) )
                    & ! [Vvar__var__var__var__var__7__n__110567__110569__110607__110609__110611] :
                        ( t(Vvar__var__var__var__var__7__n__110567__110569__110607__110609__110611,Vvar__0__R__110526)
                       => ! [Vvar__var__var__var__var__8__m__110568__110570__110608__110610__110612] :
                            ( t(Vvar__var__var__var__var__8__m__110568__110570__110608__110610__110612,Vvar__0__R__110526)
                           => p(happ(happ(Vvar__5__req__110539,happ(happ(Vvar__3__radd__110529,Vvar__var__var__var__var__7__n__110567__110569__110607__110609__110611),Vvar__var__var__var__var__8__m__110568__110570__110608__110610__110612)),happ(happ(Vvar__3__radd__110529,Vvar__var__var__var__var__8__m__110568__110570__110608__110610__110612),Vvar__var__var__var__var__7__n__110567__110569__110607__110609__110611))) ) )
                    & ! [Vvar__var__var__var__var__8__n__110572__110575__110613__110616__110619] :
                        ( t(Vvar__var__var__var__var__8__n__110572__110575__110613__110616__110619,Vvar__0__R__110526)
                       => ! [Vvar__var__var__var__var__9__m__110573__110576__110614__110617__110620] :
                            ( t(Vvar__var__var__var__var__9__m__110573__110576__110614__110617__110620,Vvar__0__R__110526)
                           => ! [Vvar__var__var__var__var__10__p__110574__110577__110615__110618__110621] :
                                ( t(Vvar__var__var__var__var__10__p__110574__110577__110615__110618__110621,Vvar__0__R__110526)
                               => p(happ(happ(Vvar__5__req__110539,happ(happ(Vvar__3__radd__110529,Vvar__var__var__var__var__8__n__110572__110575__110613__110616__110619),happ(happ(Vvar__3__radd__110529,Vvar__var__var__var__var__9__m__110573__110576__110614__110617__110620),Vvar__var__var__var__var__10__p__110574__110577__110615__110618__110621))),happ(happ(Vvar__3__radd__110529,happ(happ(Vvar__3__radd__110529,Vvar__var__var__var__var__8__n__110572__110575__110613__110616__110619),Vvar__var__var__var__var__9__m__110573__110576__110614__110617__110620)),Vvar__var__var__var__var__10__p__110574__110577__110615__110618__110621))) ) ) )
                    & ! [Vvar__var__var__var__var__var__9__n__110579__110580__110622__110623__110624__110625] :
                        ( t(Vvar__var__var__var__var__var__9__n__110579__110580__110622__110623__110624__110625,Vvar__0__R__110526)
                       => p(happ(happ(Vvar__5__req__110539,happ(happ(Vvar__4__rmul__110534,Vvar__2__rI__110528),Vvar__var__var__var__var__var__9__n__110579__110580__110622__110623__110624__110625)),Vvar__var__var__var__var__var__9__n__110579__110580__110622__110623__110624__110625)) )
                    & ! [Vvar__var__var__var__var__var__10__n__110582__110583__110626__110627__110628__110629] :
                        ( t(Vvar__var__var__var__var__var__10__n__110582__110583__110626__110627__110628__110629,Vvar__0__R__110526)
                       => p(happ(happ(Vvar__5__req__110539,happ(happ(Vvar__4__rmul__110534,Vvar__1__rO__110527),Vvar__var__var__var__var__var__10__n__110582__110583__110626__110627__110628__110629)),Vvar__1__rO__110527)) )
                    & ! [Vvar__var__var__var__var__11__n__110585__110587__110630__110632__110634] :
                        ( t(Vvar__var__var__var__var__11__n__110585__110587__110630__110632__110634,Vvar__0__R__110526)
                       => ! [Vvar__var__var__var__var__12__m__110586__110588__110631__110633__110635] :
                            ( t(Vvar__var__var__var__var__12__m__110586__110588__110631__110633__110635,Vvar__0__R__110526)
                           => p(happ(happ(Vvar__5__req__110539,happ(happ(Vvar__4__rmul__110534,Vvar__var__var__var__var__11__n__110585__110587__110630__110632__110634),Vvar__var__var__var__var__12__m__110586__110588__110631__110633__110635)),happ(happ(Vvar__4__rmul__110534,Vvar__var__var__var__var__12__m__110586__110588__110631__110633__110635),Vvar__var__var__var__var__11__n__110585__110587__110630__110632__110634))) ) )
                    & ! [Vvar__var__var__var__var__12__n__110590__110593__110636__110639__110642] :
                        ( t(Vvar__var__var__var__var__12__n__110590__110593__110636__110639__110642,Vvar__0__R__110526)
                       => ! [Vvar__var__var__var__var__13__m__110591__110594__110637__110640__110643] :
                            ( t(Vvar__var__var__var__var__13__m__110591__110594__110637__110640__110643,Vvar__0__R__110526)
                           => ! [Vvar__var__var__var__var__14__p__110592__110595__110638__110641__110644] :
                                ( t(Vvar__var__var__var__var__14__p__110592__110595__110638__110641__110644,Vvar__0__R__110526)
                               => p(happ(happ(Vvar__5__req__110539,happ(happ(Vvar__4__rmul__110534,Vvar__var__var__var__var__12__n__110590__110593__110636__110639__110642),happ(happ(Vvar__4__rmul__110534,Vvar__var__var__var__var__13__m__110591__110594__110637__110640__110643),Vvar__var__var__var__var__14__p__110592__110595__110638__110641__110644))),happ(happ(Vvar__4__rmul__110534,happ(happ(Vvar__4__rmul__110534,Vvar__var__var__var__var__12__n__110590__110593__110636__110639__110642),Vvar__var__var__var__var__13__m__110591__110594__110637__110640__110643)),Vvar__var__var__var__var__14__p__110592__110595__110638__110641__110644))) ) ) )
                    & ! [Vvar__var__var__var__var__var__13__n__110597__110600__110645__110648__110651__110654] :
                        ( t(Vvar__var__var__var__var__var__13__n__110597__110600__110645__110648__110651__110654,Vvar__0__R__110526)
                       => ! [Vvar__var__var__var__var__var__14__m__110598__110601__110646__110649__110652__110655] :
                            ( t(Vvar__var__var__var__var__var__14__m__110598__110601__110646__110649__110652__110655,Vvar__0__R__110526)
                           => ! [Vvar__var__var__var__var__var__15__p__110599__110602__110647__110650__110653__110656] :
                                ( t(Vvar__var__var__var__var__var__15__p__110599__110602__110647__110650__110653__110656,Vvar__0__R__110526)
                               => p(happ(happ(Vvar__5__req__110539,happ(happ(Vvar__4__rmul__110534,happ(happ(Vvar__3__radd__110529,Vvar__var__var__var__var__var__13__n__110597__110600__110645__110648__110651__110654),Vvar__var__var__var__var__var__14__m__110598__110601__110646__110649__110652__110655)),Vvar__var__var__var__var__var__15__p__110599__110602__110647__110650__110653__110656)),happ(happ(Vvar__3__radd__110529,happ(happ(Vvar__4__rmul__110534,Vvar__var__var__var__var__var__13__n__110597__110600__110645__110648__110651__110654),Vvar__var__var__var__var__var__15__p__110599__110602__110647__110650__110653__110656)),happ(happ(Vvar__4__rmul__110534,Vvar__var__var__var__var__var__14__m__110598__110601__110646__110649__110652__110655),Vvar__var__var__var__var__var__15__p__110599__110602__110647__110650__110653__110656)))) ) ) )
                    & p(c_24True) ) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.setoid_ring.Ring_theory.sign_theory',axiom,
    ! [Vvar__0__C__11222,Vvar__1__copp__11223,Vvar__2__ceqb__11226,Vvar__3__get__sign__11231] :
      ( cType___24t(Vvar__0__C__11222)
     => ( c_24__type__11278___24t(Vvar__0__C__11222,Vvar__1__copp__11223,Vvar__2__ceqb__11226,Vvar__3__get__sign__11231,Vvar__1__copp__11223)
       => ( c_24__type__11297___24t(Vvar__0__C__11222,Vvar__1__copp__11223,Vvar__2__ceqb__11226,Vvar__3__get__sign__11231,Vvar__2__ceqb__11226)
         => ( c_24__type__11311___24t(Vvar__0__C__11222,Vvar__1__copp__11223,Vvar__2__ceqb__11226,Vvar__3__get__sign__11231,Vvar__3__get__sign__11231)
           => ( cCoq_2esetoid__ring_2eRing__theory_2esign__theory___24a4(Vvar__0__C__11222,Vvar__1__copp__11223,Vvar__2__ceqb__11226,Vvar__3__get__sign__11231)
             => ( ! [Vvar__var__var__var__var__var__4__c__11248__11251__11254__11257__11260__11263] :
                    ( t(Vvar__var__var__var__var__var__4__c__11248__11251__11254__11257__11260__11263,Vvar__0__C__11222)
                   => ! [Vvar__var__var__var__var__var__5__c_27__11249__11252__11255__11258__11261__11264] :
                        ( t(Vvar__var__var__var__var__var__5__c_27__11249__11252__11255__11258__11261__11264,Vvar__0__C__11222)
                       => ( happ(Vvar__3__get__sign__11231,Vvar__var__var__var__var__var__4__c__11248__11251__11254__11257__11260__11263) = cCoq_2eInit_2eDatatypes_2eSome___24a2(Vvar__0__C__11222,Vvar__var__var__var__var__var__5__c_27__11249__11252__11255__11258__11261__11264)
                         => happ(happ(Vvar__2__ceqb__11226,Vvar__var__var__var__var__var__4__c__11248__11251__11254__11257__11260__11263),happ(Vvar__1__copp__11223,Vvar__var__var__var__var__var__5__c_27__11249__11252__11255__11258__11261__11264)) = cCoq_2eInit_2eDatatypes_2etrue ) ) )
                & p(c_24True) ) ) ) ) ) ) ).

fof('$_inversion_Coq.setoid_ring.Ring_theory.sring_eq_ext',axiom,
    ! [Vvar__0__R__111277,Vvar__1__radd__111278,Vvar__2__rmul__111283,Vvar__3__req__111288] :
      ( cType___24t(Vvar__0__R__111277)
     => ( c_24__type__111363___24t(Vvar__0__R__111277,Vvar__1__radd__111278,Vvar__2__rmul__111283,Vvar__3__req__111288,Vvar__1__radd__111278)
       => ( c_24__type__111386___24t(Vvar__0__R__111277,Vvar__1__radd__111278,Vvar__2__rmul__111283,Vvar__3__req__111288,Vvar__2__rmul__111283)
         => ( c_24__type__111409___24t(Vvar__0__R__111277,Vvar__1__radd__111278,Vvar__2__rmul__111283,Vvar__3__req__111288,Vvar__3__req__111288)
           => ( cCoq_2esetoid__ring_2eRing__theory_2esring__eq__ext___24a4(Vvar__0__R__111277,Vvar__1__radd__111278,Vvar__2__rmul__111283,Vvar__3__req__111288)
             => ( cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__111432___24a4(Vvar__0__R__111277,Vvar__1__radd__111278,Vvar__2__rmul__111283,Vvar__3__req__111288),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(Vvar__0__R__111277,c_24__type__111450___24a4(Vvar__0__R__111277,Vvar__1__radd__111278,Vvar__2__rmul__111283,Vvar__3__req__111288),Vvar__3__req__111288,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(Vvar__0__R__111277,Vvar__0__R__111277,Vvar__3__req__111288,Vvar__3__req__111288)),Vvar__1__radd__111278)
                & cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__111476___24a4(Vvar__0__R__111277,Vvar__1__radd__111278,Vvar__2__rmul__111283,Vvar__3__req__111288),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(Vvar__0__R__111277,c_24__type__111494___24a4(Vvar__0__R__111277,Vvar__1__radd__111278,Vvar__2__rmul__111283,Vvar__3__req__111288),Vvar__3__req__111288,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(Vvar__0__R__111277,Vvar__0__R__111277,Vvar__3__req__111288,Vvar__3__req__111288)),Vvar__2__rmul__111283)
                & p(c_24True) ) ) ) ) ) ) ).

fof('$_inversion_Hammer.Tactics.Reconstr.ReconstrT',axiom,
    ! [VX109834] :
      ( cHammer_2eTactics_2eReconstr_2eReconstrT___24t(VX109834)
     => ( VX109834 = cHammer_2eTactics_2eReconstr_2eEmpty
        | VX109834 = cHammer_2eTactics_2eReconstr_2eAllHyps ) ) ).

fof('$_inversion_IntMap.Map.Map',axiom,
    ! [Vvar__0__A__31,VX32] :
      ( cType___24t(Vvar__0__A__31)
     => ( cIntMap_2eMap_2eMap___24t(Vvar__0__A__31,VX32)
       => ( VX32 = cIntMap_2eMap_2eM0___24a1(Vvar__0__A__31)
          | ? [Vvar__1___24Anonymous__35] :
              ( cIntMap_2eMap_2ead___24t(Vvar__1___24Anonymous__35)
              & ? [Vvar__2___24Anonymous__36] :
                  ( t(Vvar__2___24Anonymous__36,Vvar__0__A__31)
                  & VX32 = cIntMap_2eMap_2eM1___24a3(Vvar__0__A__31,Vvar__1___24Anonymous__35,Vvar__2___24Anonymous__36) ) )
          | ? [Vvar__1___24Anonymous__38] :
              ( cIntMap_2eMap_2eMap___24t(Vvar__0__A__31,Vvar__1___24Anonymous__38)
              & ? [Vvar__2___24Anonymous__39] :
                  ( cIntMap_2eMap_2eMap___24t(Vvar__0__A__31,Vvar__2___24Anonymous__39)
                  & VX32 = cIntMap_2eMap_2eM2___24a3(Vvar__0__A__31,Vvar__1___24Anonymous__38,Vvar__2___24Anonymous__39) ) ) ) ) ) ).

fof('$_lam_101',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1] : c_24__lam__101___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = cCoq_2eInit_2eDatatypes_2eNone___24a1(Vv__CANONICAL__0) ).

fof('$_lam_109',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__109___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__109___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = cCoq_2eInit_2eDatatypes_2eNone___24a1(Vv__CANONICAL__0) ) ) ) ) ) ).

fof('$_lam_113894',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1] :
      ( c_24__lam__113894___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1)
    <=> p(Vv__CANONICAL__1) ) ).

fof('$_lam_120322',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1] : c_24__lam__120322___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = Vv__CANONICAL__0 ).

fof('$_lam_122197',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1] : c_24__lam__122197___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = Vv__CANONICAL__0 ).

fof('$_lam_122260',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
     => ( ( Vv__CANONICAL__1 = cCoq_2eInit_2eDatatypes_2eO
          & c_24__lam__122260___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = cCoq_2eInit_2eDatatypes_2etrue )
        | ? [Vvar__0___24Anonymous__122261] :
            ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__122261)
            & Vv__CANONICAL__1 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__122261)
            & c_24__lam__122260___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = cCoq_2ePArith_2eBinPosDef_2ePos_2etestbit__nat___24a2(Vv__CANONICAL__0,Vvar__0___24Anonymous__122261) ) ) ) ).

fof('$_lam_122267',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
     => ( ( Vv__CANONICAL__1 = cCoq_2eInit_2eDatatypes_2eO
          & c_24__lam__122267___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = cCoq_2eInit_2eDatatypes_2efalse )
        | ? [Vvar__0___24Anonymous__122268] :
            ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__122268)
            & Vv__CANONICAL__1 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__122268)
            & c_24__lam__122267___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = cCoq_2ePArith_2eBinPosDef_2ePos_2etestbit__nat___24a2(Vv__CANONICAL__0,Vvar__0___24Anonymous__122268) ) ) ) ).

fof('$_lam_122271',axiom,
    ! [Vv__CANONICAL__0] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
     => ( ( Vv__CANONICAL__0 = cCoq_2eInit_2eDatatypes_2eO
          & c_24__lam__122271___24a1(Vv__CANONICAL__0) = cCoq_2eInit_2eDatatypes_2etrue )
        | ? [Vvar__0___24Anonymous__122272] :
            ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__122272)
            & Vv__CANONICAL__0 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__122272)
            & c_24__lam__122271___24a1(Vv__CANONICAL__0) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ).

fof('$_lam_136',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] :
      ( cType___24t(Vv__CANONICAL__0)
     => ( cIntMap_2eMap_2ead___24t(Vv__CANONICAL__3)
       => ( ( Vv__CANONICAL__3 = cCoq_2eNumbers_2eBinNums_2eN0
            & c_24__lam__136___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__137] :
              ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__137)
              & ( cType___24t(Vv__CANONICAL__0)
               => ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__137)
                 => ( Vv__CANONICAL__3 = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__137)
                    & ( ? [Vvar__0___24Anonymous__141] :
                          ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__141)
                          & Vvar__0___24Anonymous__137 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__141)
                          & c_24__lam__136___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__141)) )
                      | ? [Vvar__0___24Anonymous__142] :
                          ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__142)
                          & Vvar__0___24Anonymous__137 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__142)
                          & c_24__lam__136___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__142)) )
                      | ( Vvar__0___24Anonymous__137 = cCoq_2eNumbers_2eBinNums_2exH
                        & c_24__lam__136___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_1461',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] :
      ( c_24__lam__1461___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_173527',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] :
      ( c_24__lam__173527___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
    <=> ( cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1)
        & cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(Vv__CANONICAL__1,Vv__CANONICAL__2) ) ) ).

fof('$_lam_173531',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] :
      ( c_24__lam__173531___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
    <=> ( cCoq_2eInit_2ePeano_2ele___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1)
        & cCoq_2eInit_2ePeano_2elt___24a2(Vv__CANONICAL__1,Vv__CANONICAL__2) ) ) ).

fof('$_lam_173555',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4] :
      ( c_24__lam__173555___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4)
    <=> p(happ(Vv__CANONICAL__3,happ(Vv__CANONICAL__2,Vv__CANONICAL__4))) ) ).

fof('$_lam_173584',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1] :
      ( c_24__lam__173584___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1)
    <=> Vv__CANONICAL__0 != Vv__CANONICAL__1 ) ).

fof('$_lam_1802',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__1805] :
                ( t(Vvar__1___24Anonymous__1805,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__1805)
                & c_24__lam__1802___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__1802___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_1852',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__1852___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4) = Vv__CANONICAL__1 )
          | ? [Vvar__1___24Anonymous__1856] :
              ( cIntMap_2eMap_2ead___24t(Vvar__1___24Anonymous__1856)
              & ? [Vvar__2___24Anonymous__1857] :
                  ( t(Vvar__2___24Anonymous__1857,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__1856)
                       => ( Vv__CANONICAL__4 = cIntMap_2eMap_2eM1___24a3(Vv__CANONICAL__0,Vvar__1___24Anonymous__1856,Vvar__2___24Anonymous__1857)
                          & ( ? [Vvar__1___24Anonymous__1865] :
                                ( t(Vvar__1___24Anonymous__1865,Vv__CANONICAL__0)
                                & cIntMap_2eMap_2eMapGet___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__1___24Anonymous__1856) = cCoq_2eInit_2eDatatypes_2eSome___24a2(Vv__CANONICAL__0,Vvar__1___24Anonymous__1865)
                                & c_24__lam__1852___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__1856) )
                            | ( cIntMap_2eMap_2eMapGet___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__1___24Anonymous__1856) = cCoq_2eInit_2eDatatypes_2eNone___24a1(Vv__CANONICAL__0)
                              & c_24__lam__1852___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__1856,Vvar__2___24Anonymous__1857) ) ) ) ) ) ) ) )
          | ? [Vvar__1___24Anonymous__1868] :
              ( cIntMap_2eMap_2eMap___24t(Vv__CANONICAL__0,Vvar__1___24Anonymous__1868)
              & ? [Vvar__2___24Anonymous__1869] :
                  ( cIntMap_2eMap_2eMap___24t(Vv__CANONICAL__0,Vvar__2___24Anonymous__1869)
                  & Vv__CANONICAL__4 = cIntMap_2eMap_2eM2___24a3(Vv__CANONICAL__0,Vvar__1___24Anonymous__1868,Vvar__2___24Anonymous__1869)
                  & c_24__lam__1852___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__1868),cIntMap_2eMap_2eMapDelta___24a3(Vv__CANONICAL__0,Vv__CANONICAL__3,Vvar__2___24Anonymous__1869)) ) ) ) ) ) ).

fof('$_lam_1903',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__1906] :
                ( t(Vvar__1___24Anonymous__1906,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__1906)
                        & ( ? [Vvar__1___24Anonymous__1911] :
                              ( t(Vvar__1___24Anonymous__1911,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__1911)
                              & c_24__lam__1903___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__1903___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = cCoq_2eInit_2eDatatypes_2eSome___24a2(Vv__CANONICAL__0,Vvar__1___24Anonymous__1906) ) ) ) ) ) ) )
            | ( 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__1916] :
                          ( t(Vvar__1___24Anonymous__1916,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__1916)
                          & c_24__lam__1903___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = cCoq_2eInit_2eDatatypes_2eSome___24a2(Vv__CANONICAL__0,Vvar__1___24Anonymous__1916) )
                      | ( cIntMap_2eMap_2eMapGet___24a3(Vv__CANONICAL__0,Vv__CANONICAL__2,Vv__CANONICAL__3) = cCoq_2eInit_2eDatatypes_2eNone___24a1(Vv__CANONICAL__0)
                        & c_24__lam__1903___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = cCoq_2eInit_2eDatatypes_2eNone___24a1(Vv__CANONICAL__0) ) ) ) ) ) ) ) ) ) ) ).

fof('$_lam_363',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] : c_24__lam__363___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = cIntMap_2eMap_2eM0___24a1(Vv__CANONICAL__0) ).

fof('$_lam_378',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__381] :
                  ( t(Vvar__1___24Anonymous__381,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__381)
                  & c_24__lam__378___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__378___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_436',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__436___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__440] :
                ( cIntMap_2eMap_2ead___24t(Vvar__1___24Anonymous__440)
                & ? [Vvar__2___24Anonymous__441] :
                    ( t(Vvar__2___24Anonymous__441,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__440)
                           => ( Vv__CANONICAL__5 = cIntMap_2eMap_2eM1___24a3(Vv__CANONICAL__1,Vvar__1___24Anonymous__440,Vvar__2___24Anonymous__441)
                              & ( ? [Vvar__1___24Anonymous__449] :
                                    ( t(Vvar__1___24Anonymous__449,Vv__CANONICAL__0)
                                    & cIntMap_2eMap_2eMapGet___24a3(Vv__CANONICAL__0,Vv__CANONICAL__2,Vvar__1___24Anonymous__440) = cCoq_2eInit_2eDatatypes_2eSome___24a2(Vv__CANONICAL__0,Vvar__1___24Anonymous__449)
                                    & c_24__lam__436___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__440,Vvar__1___24Anonymous__449) )
                                | ( cIntMap_2eMap_2eMapGet___24a3(Vv__CANONICAL__0,Vv__CANONICAL__2,Vvar__1___24Anonymous__440) = cCoq_2eInit_2eDatatypes_2eNone___24a1(Vv__CANONICAL__0)
                                  & c_24__lam__436___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__452] :
                ( cIntMap_2eMap_2eMap___24t(Vv__CANONICAL__1,Vvar__1___24Anonymous__452)
                & ? [Vvar__2___24Anonymous__453] :
                    ( cIntMap_2eMap_2eMap___24t(Vv__CANONICAL__1,Vvar__2___24Anonymous__453)
                    & Vv__CANONICAL__5 = cIntMap_2eMap_2eM2___24a3(Vv__CANONICAL__1,Vvar__1___24Anonymous__452,Vvar__2___24Anonymous__453)
                    & c_24__lam__436___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__452),cIntMap_2eFset_2eMapDomRestrTo___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__4,Vvar__2___24Anonymous__453)) ) ) ) ) ) ) ).

fof('$_lam_477',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__480] :
                  ( t(Vvar__1___24Anonymous__480,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__480)
                  & c_24__lam__477___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__477___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_527',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__530] :
                  ( t(Vvar__1___24Anonymous__530,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__530)
                  & c_24__lam__527___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__527___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4) = Vv__CANONICAL__2 ) ) ) ) ) ) ).

fof('$_lam_569',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__569___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__573] :
                ( cIntMap_2eMap_2ead___24t(Vvar__1___24Anonymous__573)
                & ? [Vvar__2___24Anonymous__574] :
                    ( t(Vvar__2___24Anonymous__574,Vv__CANONICAL__1)
                    & Vv__CANONICAL__5 = cIntMap_2eMap_2eM1___24a3(Vv__CANONICAL__1,Vvar__1___24Anonymous__573,Vvar__2___24Anonymous__574)
                    & c_24__lam__569___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__573) ) )
            | ? [Vvar__1___24Anonymous__577] :
                ( cIntMap_2eMap_2eMap___24t(Vv__CANONICAL__1,Vvar__1___24Anonymous__577)
                & ? [Vvar__2___24Anonymous__578] :
                    ( cIntMap_2eMap_2eMap___24t(Vv__CANONICAL__1,Vvar__2___24Anonymous__578)
                    & Vv__CANONICAL__5 = cIntMap_2eMap_2eM2___24a3(Vv__CANONICAL__1,Vvar__1___24Anonymous__577,Vvar__2___24Anonymous__578)
                    & c_24__lam__569___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__577),cIntMap_2eFset_2eMapDomRestrBy___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__4,Vvar__2___24Anonymous__578)) ) ) ) ) ) ) ).

fof('$_lam_600',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__603] :
                  ( t(Vvar__1___24Anonymous__603,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__603)
                  & c_24__lam__600___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__600___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_686',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4] :
      ( cType___24t(Vv__CANONICAL__0)
     => ( cIntMap_2eMap_2ead___24t(Vv__CANONICAL__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__686___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__687] :
                ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__687)
                & cCoq_2eNArith_2eBinNatDef_2eN_2elxor___24a2(Vv__CANONICAL__1,Vv__CANONICAL__3) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__687)
                & c_24__lam__686___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__687) ) ) ) ) ) ).

fof('$_lam_723',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__723___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__724] :
              ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__724)
              & ( cType___24t(Vv__CANONICAL__0)
               => ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__724)
                 => ( Vv__CANONICAL__3 = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__724)
                    & ( ? [Vvar__0___24Anonymous__728] :
                          ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__728)
                          & Vvar__0___24Anonymous__724 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__728)
                          & c_24__lam__723___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__728),Vv__CANONICAL__4)) )
                      | ? [Vvar__0___24Anonymous__729] :
                          ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__729)
                          & Vvar__0___24Anonymous__724 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__729)
                          & c_24__lam__723___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__729),Vv__CANONICAL__4),Vv__CANONICAL__2) )
                      | ( Vvar__0___24Anonymous__724 = cCoq_2eNumbers_2eBinNums_2exH
                        & c_24__lam__723___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_854',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1] : c_24__lam__854___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = cIntMap_2eMap_2eM0___24a1(Vv__CANONICAL__0) ).

fof('$_lam_862',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__862___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__862___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = Vv__CANONICAL__1 ) ) ) ) ) ).

fof('$_lam_870',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__870___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__870___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_910',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1] : c_24__lam__910___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = Vv__CANONICAL__1 ).

fof('$_lam_914',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] : c_24__lam__914___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_946',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__946___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4) = Vv__CANONICAL__1 )
          | ? [Vvar__1___24Anonymous__950] :
              ( cIntMap_2eMap_2ead___24t(Vvar__1___24Anonymous__950)
              & ? [Vvar__2___24Anonymous__951] :
                  ( t(Vvar__2___24Anonymous__951,Vv__CANONICAL__0)
                  & Vv__CANONICAL__4 = cIntMap_2eMap_2eM1___24a3(Vv__CANONICAL__0,Vvar__1___24Anonymous__950,Vvar__2___24Anonymous__951)
                  & c_24__lam__946___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__950,Vvar__2___24Anonymous__951) ) )
          | ? [Vvar__1___24Anonymous__954] :
              ( cIntMap_2eMap_2eMap___24t(Vv__CANONICAL__0,Vvar__1___24Anonymous__954)
              & ? [Vvar__2___24Anonymous__955] :
                  ( cIntMap_2eMap_2eMap___24t(Vv__CANONICAL__0,Vvar__2___24Anonymous__955)
                  & Vv__CANONICAL__4 = cIntMap_2eMap_2eM2___24a3(Vv__CANONICAL__0,Vvar__1___24Anonymous__954,Vvar__2___24Anonymous__955)
                  & c_24__lam__946___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__954),cIntMap_2eMap_2eMapMerge___24a3(Vv__CANONICAL__0,Vv__CANONICAL__3,Vvar__2___24Anonymous__955)) ) ) ) ) ) ).

fof('$_lam_96901',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] :
      ( c_24__lam__96901___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3)
    <=> p(happ(happ(Vv__CANONICAL__2,Vv__CANONICAL__3),Vv__CANONICAL__1)) ) ).

fof('$_lam_96909',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] :
      ( c_24__lam__96909___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3)
    <=> ~ p(happ(happ(Vv__CANONICAL__2,Vv__CANONICAL__3),Vv__CANONICAL__1)) ) ).

fof('$_lam_96917',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] :
      ( c_24__lam__96917___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3)
    <=> p(happ(happ(Vv__CANONICAL__2,Vv__CANONICAL__1),Vv__CANONICAL__3)) ) ).

fof('$_lam_96925',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] :
      ( c_24__lam__96925___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3)
    <=> p(happ(happ(Vv__CANONICAL__2,Vv__CANONICAL__1),Vv__CANONICAL__3)) ) ).

fof('$_lam_971',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__974] :
                ( t(Vvar__1___24Anonymous__974,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__974)
                & c_24__lam__971___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = cCoq_2eInit_2eDatatypes_2eSome___24a2(Vv__CANONICAL__0,Vvar__1___24Anonymous__974) )
            | ( cIntMap_2eMap_2eMapGet___24a3(Vv__CANONICAL__0,Vv__CANONICAL__2,Vv__CANONICAL__3) = cCoq_2eInit_2eDatatypes_2eNone___24a1(Vv__CANONICAL__0)
              & c_24__lam__971___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('$_prop_107393',axiom,
    ! [V0__n,V1__m] :
      ( p(c_24__prop__107393___24a2(V0__n,V1__m))
    <=> V0__n = V1__m ) ).

fof('$_prop_113526',axiom,
    ! [Vvar__0___24Anonymous__113502,Vvar__0__S__113504,Vvar__1__x__113505,Vvar__2__y__113506] :
      ( p(c_24__prop__113526___24a4(Vvar__0___24Anonymous__113502,Vvar__0__S__113504,Vvar__1__x__113505,Vvar__2__y__113506))
    <=> Vvar__1__x__113505 = Vvar__2__y__113506 ) ).

fof('$_prop_113527',axiom,
    ! [Vvar__0___24Anonymous__113502,Vvar__0__x__113507,Vvar__1__y__113508] :
      ( p(c_24__prop__113527___24a3(Vvar__0___24Anonymous__113502,Vvar__0__x__113507,Vvar__1__y__113508))
    <=> Vvar__0__x__113507 = Vvar__1__y__113508 ) ).

fof('$_prop_113528',axiom,
    ! [Vvar__0___24Anonymous__113502,Vvar__0__x__113509,Vvar__1__s__113510] :
      ( p(c_24__prop__113528___24a3(Vvar__0___24Anonymous__113502,Vvar__0__x__113509,Vvar__1__s__113510))
    <=> cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2emem___24a2(Vvar__0__x__113509,Vvar__1__s__113510) = cCoq_2eInit_2eDatatypes_2etrue ) ).

fof('$_prop_113529',axiom,
    ! [Vvar__0___24Anonymous__113502,Vvar__0__P__113511,Vvar__1__Q__113512] :
      ( p(c_24__prop__113529___24a3(Vvar__0___24Anonymous__113502,Vvar__0__P__113511,Vvar__1__Q__113512))
    <=> ( p(Vvar__0__P__113511)
        & p(Vvar__1__Q__113512) ) ) ).

fof('$_prop_113530',axiom,
    ! [Vvar__0___24Anonymous__113502,Vvar__0__P__113515,Vvar__1__Q__113516] :
      ( p(c_24__prop__113530___24a3(Vvar__0___24Anonymous__113502,Vvar__0__P__113515,Vvar__1__Q__113516))
    <=> ( p(Vvar__0__P__113515)
        | p(Vvar__1__Q__113516) ) ) ).

fof('$_prop_113531',axiom,
    ! [Vvar__0___24Anonymous__113502,Vvar__0__P__113519,Vvar__1__Q__113520] :
      ( p(c_24__prop__113531___24a3(Vvar__0___24Anonymous__113502,Vvar__0__P__113519,Vvar__1__Q__113520))
    <=> ( p(Vvar__0__P__113519)
       => p(Vvar__1__Q__113520) ) ) ).

fof('$_prop_113532',axiom,
    ! [Vvar__0___24Anonymous__113502,Vvar__0__P__113524] :
      ( p(c_24__prop__113532___24a2(Vvar__0___24Anonymous__113502,Vvar__0__P__113524))
    <=> ~ p(Vvar__0__P__113524) ) ).

fof('$_prop_113546',axiom,
    ! [Vvar__0___24Anonymous__113533,Vvar__0__s__113537] :
      ( p(c_24__prop__113546___24a2(Vvar__0___24Anonymous__113533,Vvar__0__s__113537))
    <=> ! [Vvar__1__a__113538] :
          ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(Vvar__1__a__113538)
         => ~ cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eIn___24a2(Vvar__1__a__113538,Vvar__0__s__113537) ) ) ).

fof('$_prop_113547',axiom,
    ! [Vvar__0___24Anonymous__113533,Vvar__0__s1__113539,Vvar__1__s2__113540] :
      ( p(c_24__prop__113547___24a3(Vvar__0___24Anonymous__113533,Vvar__0__s1__113539,Vvar__1__s2__113540))
    <=> ! [Vvar__2__a__113541] :
          ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(Vvar__2__a__113541)
         => ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eIn___24a2(Vvar__2__a__113541,Vvar__0__s1__113539)
           => cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eIn___24a2(Vvar__2__a__113541,Vvar__1__s2__113540) ) ) ) ).

fof('$_prop_113548',axiom,
    ! [Vvar__0___24Anonymous__113533,Vvar__0__s1__113543,Vvar__1__s2__113544] :
      ( p(c_24__prop__113548___24a3(Vvar__0___24Anonymous__113533,Vvar__0__s1__113543,Vvar__1__s2__113544))
    <=> ! [Vvar__2__a__113545] :
          ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(Vvar__2__a__113545)
         => ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eIn___24a2(Vvar__2__a__113545,Vvar__0__s1__113543)
          <=> cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eIn___24a2(Vvar__2__a__113545,Vvar__1__s2__113544) ) ) ) ).

fof('$_prop_286',axiom,
    ( p(c_24__prop__286)
  <=> cCoq_2eInit_2eDatatypes_2etrue = cCoq_2eInit_2eDatatypes_2etrue ) ).

fof('$_prop_287',axiom,
    ( p(c_24__prop__287)
  <=> cCoq_2eInit_2eDatatypes_2etrue = cCoq_2eInit_2eDatatypes_2efalse ) ).

fof('$_prop_288',axiom,
    ( p(c_24__prop__288)
  <=> cCoq_2eInit_2eDatatypes_2efalse = cCoq_2eInit_2eDatatypes_2etrue ) ).

fof('$_prop_289',axiom,
    ( p(c_24__prop__289)
  <=> cCoq_2eInit_2eDatatypes_2efalse = cCoq_2eInit_2eDatatypes_2efalse ) ).

fof('$_prop_292',axiom,
    ! [Vv__CANONICAL__0] :
      ( p(c_24__prop__292___24a1(Vv__CANONICAL__0))
    <=> Vv__CANONICAL__0 = cCoq_2eInit_2eDatatypes_2etrue ) ).

fof('$_prop_293',axiom,
    ! [Vv__CANONICAL__0] :
      ( p(c_24__prop__293___24a1(Vv__CANONICAL__0))
    <=> Vv__CANONICAL__0 = cCoq_2eInit_2eDatatypes_2efalse ) ).

fof('$_type_1000',axiom,
    ! [Vvar__1001] :
      ( c_24__type__1000___24t(Vvar__1001)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
         => cCoq_2eInit_2eDatatypes_2enat___24t(happ(Vvar__1001,Vv__CANONICAL__0)) ) ) ).

fof('$_type_10033',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__10034] :
      ( c_24__type__10033___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__10034)
    <=> ! [Vv__CANONICAL__17] :
          ( t(Vv__CANONICAL__17,Vv__CANONICAL__8)
         => ! [Vv__CANONICAL__18] :
              ( t(Vv__CANONICAL__18,Vv__CANONICAL__8)
             => t(happ(happ(Vvar__10034,Vv__CANONICAL__17),Vv__CANONICAL__18),Vv__CANONICAL__8) ) ) ) ).

fof('$_type_10246',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__10247] :
      ( c_24__type__10246___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__10247)
    <=> ! [Vv__CANONICAL__17] :
          ( t(Vv__CANONICAL__17,Vv__CANONICAL__8)
         => ! [Vv__CANONICAL__18] :
              ( t(Vv__CANONICAL__18,Vv__CANONICAL__8)
             => t(happ(happ(Vvar__10247,Vv__CANONICAL__17),Vv__CANONICAL__18),Vv__CANONICAL__8) ) ) ) ).

fof('$_type_103711',axiom,
    ! [Vvar__103712] :
      ( c_24__type__103711___24t(Vvar__103712)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( c_24__type__1058___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__103712,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__0) ) ) ) ) ) ) ).

fof('$_type_104040',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__104041] :
      ( c_24__type__104040___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__104041)
    <=> ! [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__104041,Vv__CANONICAL__4),Vv__CANONICAL__5)) ) ) ) ).

fof('$_type_104081',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__104082] :
      ( c_24__type__104081___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__104082)
    <=> ! [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__104082,Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ).

fof('$_type_104292',axiom,
    ! [Vvar__104293] :
      ( c_24__type__104292___24t(Vvar__104293)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eStrings_2eAscii_2eascii___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cCoq_2eStrings_2eString_2estring___24t(Vv__CANONICAL__1)
             => cCoq_2eStrings_2eString_2estring___24t(happ(happ(Vvar__104293,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_10459',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__10460] :
      ( c_24__type__10459___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__10460)
    <=> ! [Vv__CANONICAL__17] :
          ( t(Vv__CANONICAL__17,Vv__CANONICAL__8)
         => ! [Vv__CANONICAL__18] :
              ( t(Vv__CANONICAL__18,Vv__CANONICAL__8)
             => t(happ(happ(Vvar__10460,Vv__CANONICAL__17),Vv__CANONICAL__18),Vv__CANONICAL__8) ) ) ) ).

fof('$_type_105131',axiom,
    ! [Vvar__105132] :
      ( c_24__type__105131___24t(Vvar__105132)
    <=> ! [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)
                     => ! [Vv__CANONICAL__4] :
                          ( c_24__type__2000___24t(Vv__CANONICAL__1,Vv__CANONICAL__4)
                         => ! [Vv__CANONICAL__5] :
                              ( c_24__type__105136___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__5)
                             => ! [Vv__CANONICAL__6] :
                                  ( cCoq_2emicromega_2eTauto_2eGFormula___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__6)
                                 => cProp___24t(happ(happ(happ(happ(happ(happ(happ(Vvar__105132,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__6)) ) ) ) ) ) ) ) ) ).

fof('$_type_105136',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__105137] :
      ( c_24__type__105136___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__105137)
    <=> ! [Vv__CANONICAL__2] :
          ( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
         => cProp___24t(happ(Vvar__105137,Vv__CANONICAL__2)) ) ) ).

fof('$_type_1058',axiom,
    ! [Vv__CANONICAL__0,Vvar__1059] :
      ( c_24__type__1058___24t(Vv__CANONICAL__0,Vvar__1059)
    <=> ! [Vv__CANONICAL__1] :
          ( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__2] :
              ( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
             => t(happ(happ(Vvar__1059,Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_106212',axiom,
    ! [Vvar__106213] :
      ( c_24__type__106212___24t(Vvar__106213)
    <=> ! [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] :
                      ( c_24__type__13403___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__3)
                     => ! [Vv__CANONICAL__4] :
                          ( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
                         => ! [Vv__CANONICAL__5] :
                              ( cCoq_2eInit_2eDatatypes_2eprod___24t(Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__5)
                             => cProp___24t(happ(happ(happ(happ(happ(happ(Vvar__106213,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5)) ) ) ) ) ) ) ) ).

fof('$_type_1063',axiom,
    ! [Vv__CANONICAL__0,Vvar__1064] :
      ( c_24__type__1063___24t(Vv__CANONICAL__0,Vvar__1064)
    <=> ! [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__1064,Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ).

fof('$_type_10654',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__10655] :
      ( c_24__type__10654___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__10655)
    <=> ! [Vv__CANONICAL__17] :
          ( t(Vv__CANONICAL__17,Vv__CANONICAL__8)
         => t(happ(Vvar__10655,Vv__CANONICAL__17),Vv__CANONICAL__8) ) ) ).

fof('$_type_106545',axiom,
    ! [Vvar__106546] :
      ( c_24__type__106545___24t(Vvar__106546)
    <=> ! [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__106546,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_106985',axiom,
    ! [Vvar__106986] :
      ( c_24__type__106985___24t(Vvar__106986)
    <=> ! [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__106986,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_107019',axiom,
    ! [Vvar__107020] :
      ( c_24__type__107019___24t(Vvar__107020)
    <=> ! [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__107020,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_107075',axiom,
    ! [Vvar__107076] :
      ( c_24__type__107075___24t(Vvar__107076)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__1)
             => cCoq_2eNumbers_2eBinNums_2epositive___24t(happ(happ(Vvar__107076,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_107117',axiom,
    ! [Vvar__107118] :
      ( c_24__type__107117___24t(Vvar__107118)
    <=> ! [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__107118,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).

fof('$_type_107166',axiom,
    ! [Vvar__107167] :
      ( c_24__type__107166___24t(Vvar__107167)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(Vv__CANONICAL__1)
             => cCoq_2eInit_2eDatatypes_2ebool___24t(happ(happ(Vvar__107167,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_107194',axiom,
    ! [Vvar__107195] :
      ( c_24__type__107194___24t(Vvar__107195)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(Vv__CANONICAL__1)
             => cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(happ(happ(Vvar__107195,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_107205',axiom,
    ! [Vvar__107206] :
      ( c_24__type__107205___24t(Vvar__107206)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( c_24__type__107210___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
             => ! [Vv__CANONICAL__2] :
                  ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(Vv__CANONICAL__2)
                 => ! [Vv__CANONICAL__3] :
                      ( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
                     => t(happ(happ(happ(happ(Vvar__107206,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__0) ) ) ) ) ) ).

fof('$_type_107210',axiom,
    ! [Vv__CANONICAL__0,Vvar__107211] :
      ( c_24__type__107210___24t(Vv__CANONICAL__0,Vvar__107211)
    <=> ! [Vv__CANONICAL__1] :
          ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(Vv__CANONICAL__1)
         => ! [Vv__CANONICAL__2] :
              ( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
             => t(happ(happ(Vvar__107211,Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_107284',axiom,
    ! [Vvar__107285] :
      ( c_24__type__107284___24t(Vvar__107285)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(Vv__CANONICAL__1)
             => cProp___24t(happ(happ(Vvar__107285,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_107287',axiom,
    ! [Vvar__107288] :
      ( c_24__type__107287___24t(Vvar__107288)
    <=> ! [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__107288,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_107291',axiom,
    ! [Vvar__107292] :
      ( c_24__type__107291___24t(Vvar__107292)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(Vv__CANONICAL__0)
         => cCoq_2eNumbers_2eBinNums_2epositive___24t(happ(Vvar__107292,Vv__CANONICAL__0)) ) ) ).

fof('$_type_107326',axiom,
    ! [Vvar__107327] :
      ( c_24__type__107326___24t(Vvar__107327)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
         => cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(Vvar__107327,Vv__CANONICAL__0)) ) ) ).

fof('$_type_107360',axiom,
    ! [Vvar__107361] :
      ( c_24__type__107360___24t(Vvar__107361)
    <=> ! [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_2ecomparison___24t(happ(happ(Vvar__107361,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_107365',axiom,
    ! [Vvar__107366] :
      ( c_24__type__107365___24t(Vvar__107366)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__0)
         => cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(Vvar__107366,Vv__CANONICAL__0)) ) ) ).

fof('$_type_107422',axiom,
    ! [Vvar__107423] :
      ( c_24__type__107422___24t(Vvar__107423)
    <=> ! [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__107423,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_107441',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__107442] :
      ( c_24__type__107441___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__107442)
    <=> ! [Vv__CANONICAL__3] :
          ( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__3)
         => cProp___24t(happ(Vvar__107442,Vv__CANONICAL__3)) ) ) ).

fof('$_type_107462',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__107463] :
      ( c_24__type__107462___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__107463)
    <=> ! [Vv__CANONICAL__3] :
          ( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__3)
         => cProp___24t(happ(Vvar__107463,Vv__CANONICAL__3)) ) ) ).

fof('$_type_107497',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__107498] :
      ( c_24__type__107497___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__107498)
    <=> ! [Vv__CANONICAL__5] :
          ( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__5)
         => cProp___24t(happ(Vvar__107498,Vv__CANONICAL__5)) ) ) ).

fof('$_type_107505',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__107506] :
      ( c_24__type__107505___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__107506)
    <=> ! [Vv__CANONICAL__5] :
          ( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__5)
         => cProp___24t(happ(Vvar__107506,Vv__CANONICAL__5)) ) ) ).

fof('$_type_107511',axiom,
    ! [Vvar__107512] :
      ( c_24__type__107511___24t(Vvar__107512)
    <=> ! [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__107512,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).

fof('$_type_107524',axiom,
    ! [Vvar__107525] :
      ( c_24__type__107524___24t(Vvar__107525)
    <=> ! [Vv__CANONICAL__0] :
          ( cProp___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__1)
             => cType___24t(happ(happ(Vvar__107525,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_107581',axiom,
    ! [Vvar__107582] :
      ( c_24__type__107581___24t(Vvar__107582)
    <=> ! [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__107582,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).

fof('$_type_107638',axiom,
    ! [Vvar__107639] :
      ( c_24__type__107638___24t(Vvar__107639)
    <=> ! [Vv__CANONICAL__0] :
          ( cProp___24t(Vv__CANONICAL__0)
         => cProp___24t(happ(Vvar__107639,Vv__CANONICAL__0)) ) ) ).

fof('$_type_107689',axiom,
    ! [Vvar__107690] :
      ( c_24__type__107689___24t(Vvar__107690)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
             => cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vv__CANONICAL__0,happ(happ(Vvar__107690,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_107692',axiom,
    ! [Vvar__107693] :
      ( c_24__type__107692___24t(Vvar__107693)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__1)
             => cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vv__CANONICAL__0,happ(happ(Vvar__107693,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_107742',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__107743] :
      ( c_24__type__107742___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__107743)
    <=> ! [Vv__CANONICAL__6] :
          ( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
         => cType___24t(happ(Vvar__107743,Vv__CANONICAL__6)) ) ) ).

fof('$_type_107770',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__107771] :
      ( c_24__type__107770___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__107771)
    <=> ! [Vv__CANONICAL__6] :
          ( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
         => cType___24t(happ(Vvar__107771,Vv__CANONICAL__6)) ) ) ).

fof('$_type_108007',axiom,
    ! [Vvar__108008] :
      ( c_24__type__108007___24t(Vvar__108008)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
         => cCoq_2eNumbers_2eBinNums_2eN___24t(happ(Vvar__108008,Vv__CANONICAL__0)) ) ) ).

fof('$_type_108212',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__108213] :
      ( c_24__type__108212___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__108213)
    <=> ! [Vv__CANONICAL__10] :
          ( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__11] :
              ( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
             => t(happ(happ(Vvar__108213,Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_108305',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__108306] :
      ( c_24__type__108305___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__108306)
    <=> ! [Vv__CANONICAL__10] :
          ( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__11] :
              ( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
             => t(happ(happ(Vvar__108306,Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_108398',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__108399] :
      ( c_24__type__108398___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__108399)
    <=> ! [Vv__CANONICAL__10] :
          ( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__11] :
              ( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
             => t(happ(happ(Vvar__108399,Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_108480',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__108481] :
      ( c_24__type__108480___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__108481)
    <=> ! [Vv__CANONICAL__10] :
          ( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
         => t(happ(Vvar__108481,Vv__CANONICAL__10),Vv__CANONICAL__0) ) ) ).

fof('$_type_108573',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__108574] :
      ( c_24__type__108573___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__108574)
    <=> ! [Vv__CANONICAL__10] :
          ( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__11] :
              ( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
             => t(happ(happ(Vvar__108574,Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_108655',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__108656] :
      ( c_24__type__108655___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__108656)
    <=> ! [Vv__CANONICAL__10] :
          ( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
         => t(happ(Vvar__108656,Vv__CANONICAL__10),Vv__CANONICAL__0) ) ) ).

fof('$_type_10867',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__10868] :
      ( c_24__type__10867___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__10868)
    <=> ! [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__10868,Vv__CANONICAL__17),Vv__CANONICAL__18)) ) ) ) ).

fof('$_type_108748',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__108749] :
      ( c_24__type__108748___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__108749)
    <=> ! [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__108749,Vv__CANONICAL__10),Vv__CANONICAL__11)) ) ) ) ).

fof('$_type_108902',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__108903] :
      ( c_24__type__108902___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__108903)
    <=> ! [Vv__CANONICAL__8] :
          ( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__9] :
              ( t(Vv__CANONICAL__9,Vv__CANONICAL__0)
             => t(happ(happ(Vvar__108903,Vv__CANONICAL__8),Vv__CANONICAL__9),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_108965',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__108966] :
      ( c_24__type__108965___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__108966)
    <=> ! [Vv__CANONICAL__8] :
          ( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__9] :
              ( t(Vv__CANONICAL__9,Vv__CANONICAL__0)
             => t(happ(happ(Vvar__108966,Vv__CANONICAL__8),Vv__CANONICAL__9),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_109028',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__109029] :
      ( c_24__type__109028___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__109029)
    <=> ! [Vv__CANONICAL__8] :
          ( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__9] :
              ( t(Vv__CANONICAL__9,Vv__CANONICAL__0)
             => t(happ(happ(Vvar__109029,Vv__CANONICAL__8),Vv__CANONICAL__9),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_109082',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__109083] :
      ( c_24__type__109082___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__109083)
    <=> ! [Vv__CANONICAL__8] :
          ( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
         => t(happ(Vvar__109083,Vv__CANONICAL__8),Vv__CANONICAL__0) ) ) ).

fof('$_type_109145',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__109146] :
      ( c_24__type__109145___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__109146)
    <=> ! [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__109146,Vv__CANONICAL__8),Vv__CANONICAL__9)) ) ) ) ).

fof('$_type_109156',axiom,
    ! [Vvar__109157] :
      ( c_24__type__109156___24t(Vvar__109157)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
         => cType___24t(happ(Vvar__109157,Vv__CANONICAL__0)) ) ) ).

fof('$_type_109192',axiom,
    ! [Vvar__109193] :
      ( c_24__type__109192___24t(Vvar__109193)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
             => ! [Vv__CANONICAL__2] :
                  ( c_24__type__1058___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
                 => ! [Vv__CANONICAL__3] :
                      ( c_24__type__1058___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__109193,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__0) ) ) ) ) ) ) ).

fof('$_type_109265',axiom,
    ! [Vvar__109266] :
      ( c_24__type__109265___24t(Vvar__109266)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cType___24t(Vv__CANONICAL__1)
             => ! [Vv__CANONICAL__2] :
                  ( c_24__type__11983___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__109266,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__0) ) ) ) ) ) ) ).

fof('$_type_109296',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__109297] :
      ( c_24__type__109296___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__109297)
    <=> ! [Vv__CANONICAL__3] :
          ( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
         => cProp___24t(happ(Vvar__109297,Vv__CANONICAL__3)) ) ) ).

fof('$_type_109320',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__109321] :
      ( c_24__type__109320___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__109321)
    <=> ! [Vv__CANONICAL__3] :
          ( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
         => cProp___24t(happ(Vvar__109321,Vv__CANONICAL__3)) ) ) ).

fof('$_type_109367',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__109368] :
      ( c_24__type__109367___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__109368)
    <=> ! [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__109368,Vv__CANONICAL__5),Vv__CANONICAL__6)) ) ) ) ).

fof('$_type_109402',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__109403] :
      ( c_24__type__109402___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__109403)
    <=> ! [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__109403,Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ).

fof('$_type_109404',axiom,
    ! [Vvar__109405] :
      ( c_24__type__109404___24t(Vvar__109405)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => cProp___24t(happ(Vvar__109405,Vv__CANONICAL__0)) ) ) ).

fof('$_type_109418',axiom,
    ! [Vvar__109419] :
      ( c_24__type__109418___24t(Vvar__109419)
    <=> ! [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_2ecomparison___24t(happ(happ(Vvar__109419,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_109437',axiom,
    ! [Vvar__109438] :
      ( c_24__type__109437___24t(Vvar__109438)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
         => cCoq_2eInit_2eDatatypes_2ebool___24t(happ(Vvar__109438,Vv__CANONICAL__0)) ) ) ).

fof('$_type_109512',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__109513] :
      ( c_24__type__109512___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__109513)
    <=> ! [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__109513,Vv__CANONICAL__5),Vv__CANONICAL__6)) ) ) ) ).

fof('$_type_109531',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__109532] :
      ( c_24__type__109531___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__109532)
    <=> ! [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__109532,Vv__CANONICAL__5),Vv__CANONICAL__6)) ) ) ) ).

fof('$_type_109551',axiom,
    ! [Vvar__109552] :
      ( c_24__type__109551___24t(Vvar__109552)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( c_24__type__1300___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
             => ! [Vv__CANONICAL__2] :
                  ( c_24__type__1300___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__109552,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ) ) ) ).

fof('$_type_109636',axiom,
    ! [Vvar__109637] :
      ( c_24__type__109636___24t(Vvar__109637)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eQArith_2eQArith__base_2eQ___24t(Vv__CANONICAL__0)
         => cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(Vvar__109637,Vv__CANONICAL__0)) ) ) ).

fof('$_type_109641',axiom,
    ! [Vvar__109642] :
      ( c_24__type__109641___24t(Vvar__109642)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eQArith_2eQArith__base_2eQ___24t(Vv__CANONICAL__0)
         => cCoq_2eNumbers_2eBinNums_2epositive___24t(happ(Vvar__109642,Vv__CANONICAL__0)) ) ) ).

fof('$_type_109824',axiom,
    ! [Vvar__109825] :
      ( c_24__type__109824___24t(Vvar__109825)
    <=> ! [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__109825,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_109827',axiom,
    ! [Vvar__109828] :
      ( c_24__type__109827___24t(Vvar__109828)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__0)
         => cCoq_2eReals_2eRdefinitions_2eR___24t(happ(Vvar__109828,Vv__CANONICAL__0)) ) ) ).

fof('$_type_109830',axiom,
    ! [Vvar__109831] :
      ( c_24__type__109830___24t(Vvar__109831)
    <=> ! [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__109831,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_109832',axiom,
    ! [Vvar__109833] :
      ( c_24__type__109832___24t(Vvar__109833)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__0)
         => cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(Vvar__109833,Vv__CANONICAL__0)) ) ) ).

fof('$_type_109836',axiom,
    ! [Vvar__109837] :
      ( c_24__type__109836___24t(Vvar__109837)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
             => cProp___24t(happ(happ(Vvar__109837,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_109890',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__109891] :
      ( c_24__type__109890___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__109891)
    <=> ! [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__109891,Vv__CANONICAL__4),Vv__CANONICAL__5)) ) ) ) ).

fof('$_type_109988',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__109989] :
      ( c_24__type__109988___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__109989)
    <=> ! [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__109989,Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ).

fof('$_type_110469',axiom,
    ! [Vvar__110470] :
      ( c_24__type__110469___24t(Vvar__110470)
    <=> ! [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__110470,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_110504',axiom,
    ! [Vvar__110505] :
      ( c_24__type__110504___24t(Vvar__110505)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vv__CANONICAL__0,happ(Vvar__110505,Vv__CANONICAL__0)) ) ) ).

fof('$_type_110507',axiom,
    ! [Vvar__110508] :
      ( c_24__type__110507___24t(Vvar__110508)
    <=> ! [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__110508,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_110510',axiom,
    ! [Vvar__110511] :
      ( c_24__type__110510___24t(Vvar__110511)
    <=> ! [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__110511,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_110519',axiom,
    ! [Vvar__110520] :
      ( c_24__type__110519___24t(Vvar__110520)
    <=> ! [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__110520,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_11062',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__11063] :
      ( c_24__type__11062___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__11063)
    <=> ! [Vv__CANONICAL__17] :
          ( t(Vv__CANONICAL__17,Vv__CANONICAL__8)
         => t(happ(Vvar__11063,Vv__CANONICAL__17),Vv__CANONICAL__0) ) ) ).

fof('$_type_110694',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__110695] :
      ( c_24__type__110694___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__110695)
    <=> ! [Vv__CANONICAL__6] :
          ( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__7] :
              ( t(Vv__CANONICAL__7,Vv__CANONICAL__0)
             => t(happ(happ(Vvar__110695,Vv__CANONICAL__6),Vv__CANONICAL__7),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_110733',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__110734] :
      ( c_24__type__110733___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__110734)
    <=> ! [Vv__CANONICAL__6] :
          ( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__7] :
              ( t(Vv__CANONICAL__7,Vv__CANONICAL__0)
             => t(happ(happ(Vvar__110734,Vv__CANONICAL__6),Vv__CANONICAL__7),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_110772',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__110773] :
      ( c_24__type__110772___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__110773)
    <=> ! [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__110773,Vv__CANONICAL__6),Vv__CANONICAL__7)) ) ) ) ).

fof('$_type_111014',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__111015] :
      ( c_24__type__111014___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__111015)
    <=> ! [Vv__CANONICAL__8] :
          ( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__9] :
              ( t(Vv__CANONICAL__9,Vv__CANONICAL__0)
             => t(happ(happ(Vvar__111015,Vv__CANONICAL__8),Vv__CANONICAL__9),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_111077',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__111078] :
      ( c_24__type__111077___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__111078)
    <=> ! [Vv__CANONICAL__8] :
          ( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__9] :
              ( t(Vv__CANONICAL__9,Vv__CANONICAL__0)
             => t(happ(happ(Vvar__111078,Vv__CANONICAL__8),Vv__CANONICAL__9),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_111140',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__111141] :
      ( c_24__type__111140___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__111141)
    <=> ! [Vv__CANONICAL__8] :
          ( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__9] :
              ( t(Vv__CANONICAL__9,Vv__CANONICAL__0)
             => t(happ(happ(Vvar__111141,Vv__CANONICAL__8),Vv__CANONICAL__9),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_111194',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__111195] :
      ( c_24__type__111194___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__111195)
    <=> ! [Vv__CANONICAL__8] :
          ( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
         => t(happ(Vvar__111195,Vv__CANONICAL__8),Vv__CANONICAL__0) ) ) ).

fof('$_type_111257',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__111258] :
      ( c_24__type__111257___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__111258)
    <=> ! [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__111258,Vv__CANONICAL__8),Vv__CANONICAL__9)) ) ) ) ).

fof('$_type_111363',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__111364] :
      ( c_24__type__111363___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__111364)
    <=> ! [Vv__CANONICAL__4] :
          ( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__5] :
              ( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
             => t(happ(happ(Vvar__111364,Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_111386',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__111387] :
      ( c_24__type__111386___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__111387)
    <=> ! [Vv__CANONICAL__4] :
          ( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__5] :
              ( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
             => t(happ(happ(Vvar__111387,Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_111409',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__111410] :
      ( c_24__type__111409___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__111410)
    <=> ! [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__111410,Vv__CANONICAL__4),Vv__CANONICAL__5)) ) ) ) ).

fof('$_type_111432',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__111433] :
      ( c_24__type__111432___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__111433)
    <=> ! [Vv__CANONICAL__4] :
          ( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__5] :
              ( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
             => t(happ(happ(Vvar__111433,Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_111450',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__111451] :
      ( c_24__type__111450___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__111451)
    <=> ! [Vv__CANONICAL__4] :
          ( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
         => t(happ(Vvar__111451,Vv__CANONICAL__4),Vv__CANONICAL__0) ) ) ).

fof('$_type_111476',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__111477] :
      ( c_24__type__111476___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__111477)
    <=> ! [Vv__CANONICAL__4] :
          ( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__5] :
              ( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
             => t(happ(happ(Vvar__111477,Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_111494',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__111495] :
      ( c_24__type__111494___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__111495)
    <=> ! [Vv__CANONICAL__4] :
          ( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
         => t(happ(Vvar__111495,Vv__CANONICAL__4),Vv__CANONICAL__0) ) ) ).

fof('$_type_111752',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__111753] :
      ( c_24__type__111752___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__111753)
    <=> ! [Vv__CANONICAL__13] :
          ( t(Vv__CANONICAL__13,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__14] :
              ( t(Vv__CANONICAL__14,Vv__CANONICAL__0)
             => t(happ(happ(Vvar__111753,Vv__CANONICAL__13),Vv__CANONICAL__14),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_111877',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__111878] :
      ( c_24__type__111877___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__111878)
    <=> ! [Vv__CANONICAL__13] :
          ( t(Vv__CANONICAL__13,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__14] :
              ( t(Vv__CANONICAL__14,Vv__CANONICAL__0)
             => t(happ(happ(Vvar__111878,Vv__CANONICAL__13),Vv__CANONICAL__14),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_112002',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__112003] :
      ( c_24__type__112002___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__112003)
    <=> ! [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__112003,Vv__CANONICAL__13),Vv__CANONICAL__14)) ) ) ) ).

fof('$_type_112127',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__112128] :
      ( c_24__type__112127___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__112128)
    <=> ! [Vv__CANONICAL__13] :
          ( t(Vv__CANONICAL__13,Vv__CANONICAL__6)
         => ! [Vv__CANONICAL__14] :
              ( t(Vv__CANONICAL__14,Vv__CANONICAL__6)
             => t(happ(happ(Vvar__112128,Vv__CANONICAL__13),Vv__CANONICAL__14),Vv__CANONICAL__6) ) ) ) ).

fof('$_type_112252',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__112253] :
      ( c_24__type__112252___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__112253)
    <=> ! [Vv__CANONICAL__13] :
          ( t(Vv__CANONICAL__13,Vv__CANONICAL__6)
         => ! [Vv__CANONICAL__14] :
              ( t(Vv__CANONICAL__14,Vv__CANONICAL__6)
             => t(happ(happ(Vvar__112253,Vv__CANONICAL__13),Vv__CANONICAL__14),Vv__CANONICAL__6) ) ) ) ).

fof('$_type_112377',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__112378] :
      ( c_24__type__112377___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__112378)
    <=> ! [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__112378,Vv__CANONICAL__13),Vv__CANONICAL__14)) ) ) ) ).

fof('$_type_112488',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__112489] :
      ( c_24__type__112488___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__112489)
    <=> ! [Vv__CANONICAL__13] :
          ( t(Vv__CANONICAL__13,Vv__CANONICAL__6)
         => t(happ(Vvar__112489,Vv__CANONICAL__13),Vv__CANONICAL__0) ) ) ).

fof('$_type_112498',axiom,
    ! [Vvar__112499] :
      ( c_24__type__112498___24t(Vvar__112499)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
             => t(happ(happ(Vvar__112499,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_112711',axiom,
    ! [Vvar__112712] :
      ( c_24__type__112711___24t(Vvar__112712)
    <=> ! [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__112712,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_112751',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__112752] :
      ( c_24__type__112751___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__112752)
    <=> ! [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__112752,Vv__CANONICAL__4),Vv__CANONICAL__5)) ) ) ) ).

fof('$_type_112771',axiom,
    ! [Vvar__112772] :
      ( c_24__type__112771___24t(Vvar__112772)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cType___24t(Vv__CANONICAL__1)
             => ! [Vv__CANONICAL__2] :
                  ( c_24__type__1300___24t(Vv__CANONICAL__1,Vv__CANONICAL__2)
                 => ! [Vv__CANONICAL__3] :
                      ( c_24__type__112781___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__3)
                     => cProp___24t(happ(happ(happ(happ(Vvar__112772,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).

fof('$_type_11278',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__11279] :
      ( c_24__type__11278___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__11279)
    <=> ! [Vv__CANONICAL__4] :
          ( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
         => t(happ(Vvar__11279,Vv__CANONICAL__4),Vv__CANONICAL__0) ) ) ).

fof('$_type_112781',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__112782] :
      ( c_24__type__112781___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__112782)
    <=> ! [Vv__CANONICAL__2] :
          ( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__3] :
              ( t(Vv__CANONICAL__3,Vv__CANONICAL__1)
             => t(happ(happ(Vvar__112782,Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__1) ) ) ) ).

fof('$_type_112814',axiom,
    ! [Vvar__112815] :
      ( c_24__type__112814___24t(Vvar__112815)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cType___24t(Vv__CANONICAL__1)
             => ! [Vv__CANONICAL__2] :
                  ( c_24__type__1300___24t(Vv__CANONICAL__1,Vv__CANONICAL__2)
                 => ! [Vv__CANONICAL__3] :
                      ( c_24__type__112824___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__3)
                     => ! [Vv__CANONICAL__4] :
                          ( c_24__type__112781___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__4)
                         => cProp___24t(happ(happ(happ(happ(happ(Vvar__112815,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ) ) ) ).

fof('$_type_112824',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__112825] :
      ( c_24__type__112824___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__112825)
    <=> ! [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__112825,Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ).

fof('$_type_112921',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__112922] :
      ( c_24__type__112921___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__112922)
    <=> ! [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__112922,Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ).

fof('$_type_112960',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__112961] :
      ( c_24__type__112960___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__112961)
    <=> ! [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__112961,Vv__CANONICAL__4),Vv__CANONICAL__5)) ) ) ) ).

fof('$_type_11297',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__11298] :
      ( c_24__type__11297___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__11298)
    <=> ! [Vv__CANONICAL__4] :
          ( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__5] :
              ( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
             => cCoq_2eInit_2eDatatypes_2ebool___24t(happ(happ(Vvar__11298,Vv__CANONICAL__4),Vv__CANONICAL__5)) ) ) ) ).

fof('$_type_112995',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__112996] :
      ( c_24__type__112995___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__112996)
    <=> ! [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__112996,Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ).

fof('$_type_113030',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__113031] :
      ( c_24__type__113030___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__113031)
    <=> ! [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__113031,Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ).

fof('$_type_113056',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__113057] :
      ( c_24__type__113056___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__113057)
    <=> ! [Vv__CANONICAL__3] :
          ( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
         => cProp___24t(happ(Vvar__113057,Vv__CANONICAL__3)) ) ) ).

fof('$_type_113064',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__113065] :
      ( c_24__type__113064___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__113065)
    <=> ! [Vv__CANONICAL__3] :
          ( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
         => cProp___24t(happ(Vvar__113065,Vv__CANONICAL__3)) ) ) ).

fof('$_type_113072',axiom,
    ! [Vvar__113073] :
      ( c_24__type__113072___24t(Vvar__113073)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( c_24__type__2000___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
             => ! [Vv__CANONICAL__2] :
                  ( c_24__type__2000___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
                 => cType___24t(happ(happ(happ(Vvar__113073,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).

fof('$_type_113102',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__113103] :
      ( c_24__type__113102___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__113103)
    <=> ! [Vv__CANONICAL__2] :
          ( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
         => cType___24t(happ(Vvar__113103,Vv__CANONICAL__2)) ) ) ).

fof('$_type_113106',axiom,
    ! [Vvar__113107] :
      ( c_24__type__113106___24t(Vvar__113107)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( c_24__type__113109___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
             => cType___24t(happ(happ(Vvar__113107,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_113109',axiom,
    ! [Vv__CANONICAL__0,Vvar__113110] :
      ( c_24__type__113109___24t(Vv__CANONICAL__0,Vvar__113110)
    <=> ! [Vv__CANONICAL__1] :
          ( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
         => cType___24t(happ(Vvar__113110,Vv__CANONICAL__1)) ) ) ).

fof('$_type_11311',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__11312] :
      ( c_24__type__11311___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__11312)
    <=> ! [Vv__CANONICAL__4] :
          ( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
         => cCoq_2eInit_2eDatatypes_2eoption___24t(Vv__CANONICAL__0,happ(Vvar__11312,Vv__CANONICAL__4)) ) ) ).

fof('$_type_113143',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__113144] :
      ( c_24__type__113143___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__113144)
    <=> ! [Vv__CANONICAL__3] :
          ( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
         => cType___24t(happ(Vvar__113144,Vv__CANONICAL__3)) ) ) ).

fof('$_type_113151',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__113152] :
      ( c_24__type__113151___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__113152)
    <=> ! [Vv__CANONICAL__3] :
          ( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
         => cType___24t(happ(Vvar__113152,Vv__CANONICAL__3)) ) ) ).

fof('$_type_113159',axiom,
    ! [Vvar__113160] :
      ( c_24__type__113159___24t(Vvar__113160)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( c_24__type__113109___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
             => ! [Vv__CANONICAL__2] :
                  ( c_24__type__113109___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
                 => cType___24t(happ(happ(happ(Vvar__113160,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).

fof('$_type_113176',axiom,
    ! [Vvar__113177] :
      ( c_24__type__113176___24t(Vvar__113177)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ( p(c_24False)
           => t(happ(Vvar__113177,Vv__CANONICAL__0),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_113232',axiom,
    ! [Vvar__113233] :
      ( c_24__type__113232___24t(Vvar__113233)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
             => cType___24t(happ(happ(Vvar__113233,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_113284',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__113285] :
      ( c_24__type__113284___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__113285)
    <=> ! [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__113285,Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ).

fof('$_type_113361',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__113362] :
      ( c_24__type__113361___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__113362)
    <=> ! [Vv__CANONICAL__4] :
          ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__4)
         => cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(Vvar__113362,Vv__CANONICAL__4)) ) ) ).

fof('$_type_113370',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__113371] :
      ( c_24__type__113370___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__113371)
    <=> ! [Vv__CANONICAL__4] :
          ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__4)
         => cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(Vvar__113371,Vv__CANONICAL__4)) ) ) ).

fof('$_type_113469',axiom,
    ! [Vvar__113470] :
      ( c_24__type__113469___24t(Vvar__113470)
    <=> ! [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__113470,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_113565',axiom,
    ! [Vvar__113566] :
      ( c_24__type__113565___24t(Vvar__113566)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__0)
         => cCoq_2eInit_2eDatatypes_2enat___24t(happ(Vvar__113566,Vv__CANONICAL__0)) ) ) ).

fof('$_type_113571',axiom,
    ! [Vvar__113572] :
      ( c_24__type__113571___24t(Vvar__113572)
    <=> ! [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__113572,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_113589',axiom,
    ! [Vvar__113590] :
      ( c_24__type__113589___24t(Vvar__113590)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__0)
         => cCoq_2ePArith_2eBinPosDef_2ePos_2emask___24t(happ(Vvar__113590,Vv__CANONICAL__0)) ) ) ).

fof('$_type_113607',axiom,
    ! [Vvar__113608] :
      ( c_24__type__113607___24t(Vvar__113608)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( c_24__type__1278___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__113608,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__0) ) ) ) ) ) ).

fof('$_type_113613',axiom,
    ! [Vvar__113614] :
      ( c_24__type__113613___24t(Vvar__113614)
    <=> ! [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__113614,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_113627',axiom,
    ! [Vvar__113628] :
      ( c_24__type__113627___24t(Vvar__113628)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( c_24__type__1058___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__113628,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__0) ) ) ) ) ) ).

fof('$_type_113691',axiom,
    ! [Vvar__113692] :
      ( c_24__type__113691___24t(Vvar__113692)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__0)
         => cType___24t(happ(Vvar__113692,Vv__CANONICAL__0)) ) ) ).

fof('$_type_113778',axiom,
    ! [Vvar__113779] :
      ( c_24__type__113778___24t(Vvar__113779)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
         => cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(Vvar__113779,Vv__CANONICAL__0)) ) ) ).

fof('$_type_113782',axiom,
    ! [Vvar__113783] :
      ( c_24__type__113782___24t(Vvar__113783)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
         => cCoq_2eNumbers_2eBinNums_2epositive___24t(happ(Vvar__113783,Vv__CANONICAL__0)) ) ) ).

fof('$_type_113899',axiom,
    ! [Vvar__113900] :
      ( c_24__type__113899___24t(Vvar__113900)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( c_24__type__2000___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
             => ! [Vv__CANONICAL__2] :
                  ( cCoq_2emicromega_2eTauto_2eBFormula___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
                 => cProp___24t(happ(happ(happ(Vvar__113900,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).

fof('$_type_113922',axiom,
    ! [Vvar__113923] :
      ( c_24__type__113922___24t(Vvar__113923)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( c_24__type__14035___24t(Vv__CANONICAL__1)
             => ! [Vv__CANONICAL__2] :
                  ( c_24__type__14035___24t(Vv__CANONICAL__2)
                 => cProp___24t(happ(happ(happ(Vvar__113923,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).

fof('$_type_11463',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__11464] :
      ( c_24__type__11463___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__11464)
    <=> ! [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__11464,Vv__CANONICAL__7),Vv__CANONICAL__8)) ) ) ) ).

fof('$_type_11513',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__11514] :
      ( c_24__type__11513___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__11514)
    <=> ! [Vv__CANONICAL__7] :
          ( t(Vv__CANONICAL__7,Vv__CANONICAL__2)
         => ! [Vv__CANONICAL__8] :
              ( t(Vv__CANONICAL__8,Vv__CANONICAL__2)
             => t(happ(happ(Vvar__11514,Vv__CANONICAL__7),Vv__CANONICAL__8),Vv__CANONICAL__2) ) ) ) ).

fof('$_type_11563',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__11564] :
      ( c_24__type__11563___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__11564)
    <=> ! [Vv__CANONICAL__7] :
          ( t(Vv__CANONICAL__7,Vv__CANONICAL__2)
         => ! [Vv__CANONICAL__8] :
              ( t(Vv__CANONICAL__8,Vv__CANONICAL__2)
             => t(happ(happ(Vvar__11564,Vv__CANONICAL__7),Vv__CANONICAL__8),Vv__CANONICAL__2) ) ) ) ).

fof('$_type_115933',axiom,
    ! [Vvar__115934] :
      ( c_24__type__115933___24t(Vvar__115934)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
         => cCoq_2eInit_2eDatatypes_2ebool___24t(happ(Vvar__115934,Vv__CANONICAL__0)) ) ) ).

fof('$_type_11605',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__11606] :
      ( c_24__type__11605___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__11606)
    <=> ! [Vv__CANONICAL__7] :
          ( t(Vv__CANONICAL__7,Vv__CANONICAL__2)
         => t(happ(Vvar__11606,Vv__CANONICAL__7),Vv__CANONICAL__0) ) ) ).

fof('$_type_11655',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__11656] :
      ( c_24__type__11655___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__11656)
    <=> ! [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__11656,Vv__CANONICAL__7),Vv__CANONICAL__8)) ) ) ) ).

fof('$_type_116798',axiom,
    ! [Vv__CANONICAL__0,Vvar__116799] :
      ( c_24__type__116798___24t(Vv__CANONICAL__0,Vvar__116799)
    <=> ! [Vv__CANONICAL__1] :
          ( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
         => cType___24t(happ(Vvar__116799,Vv__CANONICAL__1)) ) ) ).

fof('$_type_116811',axiom,
    ! [Vvar__116812] :
      ( c_24__type__116811___24t(Vvar__116812)
    <=> ! [Vv__CANONICAL__0] :
          ( c_24__type__109156___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( t(Vv__CANONICAL__1,happ(Vv__CANONICAL__0,cCoq_2eInit_2eDatatypes_2eO))
             => ! [Vv__CANONICAL__2] :
                  ( c_24__type__116816___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
                 => ! [Vv__CANONICAL__3] :
                      ( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__3)
                     => t(happ(happ(happ(happ(Vvar__116812,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),happ(Vv__CANONICAL__0,Vv__CANONICAL__3)) ) ) ) ) ) ).

fof('$_type_116816',axiom,
    ! [Vv__CANONICAL__0,Vvar__116817] :
      ( c_24__type__116816___24t(Vv__CANONICAL__0,Vvar__116817)
    <=> ! [Vv__CANONICAL__1] :
          ( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
         => ! [Vv__CANONICAL__2] :
              ( t(Vv__CANONICAL__2,happ(Vv__CANONICAL__0,Vv__CANONICAL__1))
             => t(happ(happ(Vvar__116817,Vv__CANONICAL__1),Vv__CANONICAL__2),happ(Vv__CANONICAL__0,cCoq_2eInit_2eDatatypes_2eS___24a1(Vv__CANONICAL__1))) ) ) ) ).

fof('$_type_116818',axiom,
    ! [Vvar__116819] :
      ( c_24__type__116818___24t(Vvar__116819)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eInit_2eDatatypes_2ecomparison___24t(Vv__CANONICAL__0)
         => cCoq_2eInit_2eDatatypes_2ecomparison___24t(happ(Vvar__116819,Vv__CANONICAL__0)) ) ) ).

fof('$_type_116820',axiom,
    ! [Vvar__116821] :
      ( c_24__type__116820___24t(Vvar__116821)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eInit_2eDecimal_2euint___24t(Vv__CANONICAL__0)
         => cCoq_2eInit_2eDecimal_2euint___24t(happ(Vvar__116821,Vv__CANONICAL__0)) ) ) ).

fof('$_type_11731',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__11732] :
      ( c_24__type__11731___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__11732)
    <=> ! [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__11732,Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ).

fof('$_type_117554',axiom,
    ! [Vvar__117555] :
      ( c_24__type__117554___24t(Vvar__117555)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__1)
             => cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vv__CANONICAL__0,happ(happ(Vvar__117555,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_117559',axiom,
    ! [Vvar__117560] :
      ( c_24__type__117559___24t(Vvar__117560)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
             => ! [Vv__CANONICAL__2] :
                  ( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
                 => cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vv__CANONICAL__0,happ(happ(happ(Vvar__117560,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).

fof('$_type_117562',axiom,
    ! [Vvar__117563] :
      ( c_24__type__117562___24t(Vvar__117563)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
             => cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vv__CANONICAL__0,happ(happ(Vvar__117563,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_117906',axiom,
    ! [Vvar__117907] :
      ( c_24__type__117906___24t(Vvar__117907)
    <=> ! [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] :
                  ( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
                 => t(happ(happ(happ(Vvar__117907,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__0) ) ) ) ) ).

fof('$_type_117936',axiom,
    ! [Vvar__117937] :
      ( c_24__type__117936___24t(Vvar__117937)
    <=> ! [Vv__CANONICAL__0] :
          ( c_24__type__109437___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( c_24__type__109437___24t(Vv__CANONICAL__1)
             => cProp___24t(happ(happ(Vvar__117937,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_117969',axiom,
    ! [Vvar__117970] :
      ( c_24__type__117969___24t(Vvar__117970)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eQArith_2eQArith__base_2eQ___24t(Vv__CANONICAL__0)
         => cCoq_2emicromega_2eRMicromega_2eRcst___24t(happ(Vvar__117970,Vv__CANONICAL__0)) ) ) ).

fof('$_type_118013',axiom,
    ! [Vvar__118014] :
      ( c_24__type__118013___24t(Vvar__118014)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
         => cCoq_2eReals_2eRdefinitions_2eR___24t(happ(Vvar__118014,Vv__CANONICAL__0)) ) ) ).

fof('$_type_118269',axiom,
    ! [Vvar__118270] :
      ( c_24__type__118269___24t(Vvar__118270)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( c_24__type__1058___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__118270,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__0) ) ) ) ) ) ).

fof('$_type_118300',axiom,
    ! [Vvar__118301] :
      ( c_24__type__118300___24t(Vvar__118301)
    <=> ! [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__118301,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ) ).

fof('$_type_118305',axiom,
    ! [Vvar__118306] :
      ( c_24__type__118305___24t(Vvar__118306)
    <=> ! [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__118306,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ) ).

fof('$_type_118375',axiom,
    ! [Vvar__118376] :
      ( c_24__type__118375___24t(Vvar__118376)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( c_24__type__1300___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
             => cProp___24t(happ(happ(Vvar__118376,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_118387',axiom,
    ! [Vvar__118388] :
      ( c_24__type__118387___24t(Vvar__118388)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( c_24__type__118390___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__118388,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).

fof('$_type_118390',axiom,
    ! [Vv__CANONICAL__0,Vvar__118391] :
      ( c_24__type__118390___24t(Vv__CANONICAL__0,Vvar__118391)
    <=> ! [Vv__CANONICAL__1] :
          ( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
         => cCoq_2eInit_2eDatatypes_2enat___24t(happ(Vvar__118391,Vv__CANONICAL__1)) ) ) ).

fof('$_type_11840',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__11841] :
      ( c_24__type__11840___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__11841)
    <=> ! [Vv__CANONICAL__7] :
          ( t(Vv__CANONICAL__7,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__8] :
              ( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
             => t(happ(happ(Vvar__11841,Vv__CANONICAL__7),Vv__CANONICAL__8),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_11884',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__11885] :
      ( c_24__type__11884___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__11885)
    <=> ! [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__11885,Vv__CANONICAL__7),Vv__CANONICAL__8)) ) ) ) ).

fof('$_type_11920',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__11921] :
      ( c_24__type__11920___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__11921)
    <=> ! [Vv__CANONICAL__7] :
          ( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__7)
         => t(happ(Vvar__11921,Vv__CANONICAL__7),Vv__CANONICAL__4) ) ) ).

fof('$_type_11964',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__11965] :
      ( c_24__type__11964___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__11965)
    <=> ! [Vv__CANONICAL__7] :
          ( t(Vv__CANONICAL__7,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__8] :
              ( t(Vv__CANONICAL__8,Vv__CANONICAL__4)
             => t(happ(happ(Vvar__11965,Vv__CANONICAL__7),Vv__CANONICAL__8),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_11983',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__11984] :
      ( c_24__type__11983___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__11984)
    <=> ! [Vv__CANONICAL__2] :
          ( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__3] :
              ( t(Vv__CANONICAL__3,Vv__CANONICAL__1)
             => t(happ(happ(Vvar__11984,Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_119946',axiom,
    ! [Vvar__119947] :
      ( c_24__type__119946___24t(Vvar__119947)
    <=> ! [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_2ebool___24t(happ(happ(Vvar__119947,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_120317',axiom,
    ! [Vvar__120318] :
      ( c_24__type__120317___24t(Vvar__120318)
    <=> ! [Vv__CANONICAL__0] :
          ( c_24__type__313___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( c_24__type__313___24t(Vv__CANONICAL__1)
             => cProp___24t(happ(happ(Vvar__120318,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_120334',axiom,
    ! [Vvar__120335] :
      ( c_24__type__120334___24t(Vvar__120335)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
             => ! [Vv__CANONICAL__2] :
                  ( c_24__type__120339___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
                 => ! [Vv__CANONICAL__3] :
                      ( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__3)
                     => t(happ(happ(happ(happ(Vvar__120335,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__0) ) ) ) ) ) ).

fof('$_type_120339',axiom,
    ! [Vv__CANONICAL__0,Vvar__120340] :
      ( c_24__type__120339___24t(Vv__CANONICAL__0,Vvar__120340)
    <=> ! [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__120340,Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_120432',axiom,
    ! [Vvar__120433] :
      ( c_24__type__120432___24t(Vvar__120433)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__0)
         => cCoq_2eInit_2eDatatypes_2enat___24t(happ(Vvar__120433,Vv__CANONICAL__0)) ) ) ).

fof('$_type_12044',axiom,
    ! [Vvar__12045] :
      ( c_24__type__12044___24t(Vvar__12045)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( c_24__type__2000___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__12045,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ) ).

fof('$_type_120473',axiom,
    ! [Vvar__120474] :
      ( c_24__type__120473___24t(Vvar__120474)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(Vv__CANONICAL__0)
         => cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt,happ(Vvar__120474,Vv__CANONICAL__0)) ) ) ).

fof('$_type_12063',axiom,
    ! [Vvar__12064] :
      ( c_24__type__12063___24t(Vvar__12064)
    <=> ! [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)
                     => cCoq_2emicromega_2eTauto_2eGFormula___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,happ(happ(happ(happ(Vvar__12064,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).

fof('$_type_12081',axiom,
    ! [Vvar__12082] :
      ( c_24__type__12081___24t(Vvar__12082)
    <=> ! [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)
                     => ! [Vv__CANONICAL__4] :
                          ( t(Vv__CANONICAL__4,Vv__CANONICAL__1)
                         => cCoq_2emicromega_2eTauto_2eGFormula___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,happ(happ(happ(happ(happ(Vvar__12082,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ) ) ) ).

fof('$_type_120879',axiom,
    ! [Vvar__120880] :
      ( c_24__type__120879___24t(Vvar__120880)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eInit_2eByte_2ebyte___24t(Vv__CANONICAL__0)
         => cCoq_2eInit_2eByte_2ebyte___24t(happ(Vvar__120880,Vv__CANONICAL__0)) ) ) ).

fof('$_type_120882',axiom,
    ! [Vvar__120883] :
      ( c_24__type__120882___24t(Vvar__120883)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eInit_2eDecimal_2euint___24t(Vv__CANONICAL__0)
         => cCoq_2eInit_2eDecimal_2eint___24t(happ(Vvar__120883,Vv__CANONICAL__0)) ) ) ).

fof('$_type_120895',axiom,
    ! [Vvar__120896] :
      ( c_24__type__120895___24t(Vvar__120896)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eInit_2eDecimal_2eint___24t(Vv__CANONICAL__0)
         => cCoq_2eInit_2eDecimal_2eint___24t(happ(Vvar__120896,Vv__CANONICAL__0)) ) ) ).

fof('$_type_120898',axiom,
    ! [Vvar__120899] :
      ( c_24__type__120898___24t(Vvar__120899)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cCoq_2emicromega_2eEnvRing_2eMon___24t(Vv__CANONICAL__1)
             => cCoq_2emicromega_2eEnvRing_2eMon___24t(happ(happ(Vvar__120899,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_120908',axiom,
    ! [Vvar__120909] :
      ( c_24__type__120908___24t(Vvar__120909)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
             => ! [Vv__CANONICAL__2] :
                  ( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
                 => ( Vv__CANONICAL__1 = Vv__CANONICAL__2
                   => cProp___24t(happ(happ(happ(Vvar__120909,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ) ).

fof('$_type_120913',axiom,
    ! [Vvar__120914] :
      ( c_24__type__120913___24t(Vvar__120914)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
             => cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vv__CANONICAL__0,happ(happ(Vvar__120914,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_120918',axiom,
    ! [Vv__CANONICAL__0,Vvar__120919] :
      ( c_24__type__120918___24t(Vv__CANONICAL__0,Vvar__120919)
    <=> ! [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__120919,Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ).

fof('$_type_120929',axiom,
    ! [Vvar__120930] :
      ( c_24__type__120929___24t(Vvar__120930)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( c_24__type__120918___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__120930,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__0) ) ) ) ) ) ).

fof('$_type_120948',axiom,
    ! [Vvar__120949] :
      ( c_24__type__120948___24t(Vvar__120949)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
             => cCoq_2esetoid__ring_2eInitialRing_2ehypo___24t(happ(happ(Vvar__120949,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_12098',axiom,
    ! [Vvar__12099] :
      ( c_24__type__12098___24t(Vvar__12099)
    <=> ! [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)
                     => ! [Vv__CANONICAL__4] :
                          ( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
                         => ! [Vv__CANONICAL__5] :
                              ( t(Vv__CANONICAL__5,Vv__CANONICAL__2)
                             => cCoq_2emicromega_2eTauto_2eGFormula___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,happ(happ(happ(happ(happ(happ(Vvar__12099,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5)) ) ) ) ) ) ) ) ).

fof('$_type_120985',axiom,
    ! [Vvar__120986] :
      ( c_24__type__120985___24t(Vvar__120986)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
             => ! [Vv__CANONICAL__2] :
                  ( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__2)
                 => ! [Vv__CANONICAL__3] :
                      ( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__3)
                     => cCoq_2eInit_2eDatatypes_2enat___24t(happ(happ(happ(happ(Vvar__120986,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).

fof('$_type_12115',axiom,
    ! [Vvar__12116] :
      ( c_24__type__12115___24t(Vvar__12116)
    <=> ! [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)
                     => ! [Vv__CANONICAL__4] :
                          ( cCoq_2emicromega_2eTauto_2eGFormula___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4)
                         => ! [Vv__CANONICAL__5] :
                              ( cCoq_2emicromega_2eTauto_2eGFormula___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__5)
                             => cCoq_2emicromega_2eTauto_2eGFormula___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,happ(happ(happ(happ(happ(happ(Vvar__12116,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5)) ) ) ) ) ) ) ) ).

fof('$_type_121347',axiom,
    ! [Vvar__121348] :
      ( c_24__type__121347___24t(Vvar__121348)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
         => cCoq_2emicromega_2eRMicromega_2eRcst___24t(happ(Vvar__121348,Vv__CANONICAL__0)) ) ) ).

fof('$_type_121350',axiom,
    ! [Vvar__121351] :
      ( c_24__type__121350___24t(Vvar__121351)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2emicromega_2eRMicromega_2eRcst___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cCoq_2emicromega_2eRMicromega_2eRcst___24t(Vv__CANONICAL__1)
             => cCoq_2emicromega_2eRMicromega_2eRcst___24t(happ(happ(Vvar__121351,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_121354',axiom,
    ! [Vvar__121355] :
      ( c_24__type__121354___24t(Vvar__121355)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2emicromega_2eRMicromega_2eRcst___24t(Vv__CANONICAL__0)
         => cCoq_2emicromega_2eRMicromega_2eRcst___24t(happ(Vvar__121355,Vv__CANONICAL__0)) ) ) ).

fof('$_type_12142',axiom,
    ! [Vvar__12143] :
      ( c_24__type__12142___24t(Vvar__12143)
    <=> ! [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)
                     => ! [Vv__CANONICAL__4] :
                          ( cCoq_2emicromega_2eTauto_2eGFormula___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4)
                         => cCoq_2emicromega_2eTauto_2eGFormula___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,happ(happ(happ(happ(happ(Vvar__12143,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ) ) ) ).

fof('$_type_121554',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__121555] :
      ( c_24__type__121554___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__121555)
    <=> ! [Vv__CANONICAL__6] :
          ( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
         => cType___24t(happ(Vvar__121555,Vv__CANONICAL__6)) ) ) ).

fof('$_type_121583',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__121584] :
      ( c_24__type__121583___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__121584)
    <=> ! [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__121584,Vv__CANONICAL__6),Vv__CANONICAL__7)) ) ) ) ).

fof('$_type_121620',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__121621] :
      ( c_24__type__121620___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__121621)
    <=> ! [Vv__CANONICAL__6] :
          ( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__7] :
              ( t(Vv__CANONICAL__7,happ(Vv__CANONICAL__1,Vv__CANONICAL__6))
             => ! [Vv__CANONICAL__8] :
                  ( t(Vv__CANONICAL__8,happ(Vv__CANONICAL__1,Vv__CANONICAL__6))
                 => cProp___24t(happ(happ(happ(Vvar__121621,Vv__CANONICAL__6),Vv__CANONICAL__7),Vv__CANONICAL__8)) ) ) ) ) ).

fof('$_type_121692',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__121693] :
      ( c_24__type__121692___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__121693)
    <=> ! [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__121693,Vv__CANONICAL__6),Vv__CANONICAL__7)) ) ) ) ).

fof('$_type_121717',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__121718] :
      ( c_24__type__121717___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__121718)
    <=> ! [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__121718,Vv__CANONICAL__6),Vv__CANONICAL__7)) ) ) ) ).

fof('$_type_121759',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__121760] :
      ( c_24__type__121759___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__121760)
    <=> ! [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__121760,Vv__CANONICAL__4),Vv__CANONICAL__5)) ) ) ) ).

fof('$_type_121869',axiom,
    ! [Vvar__121870] :
      ( c_24__type__121869___24t(Vvar__121870)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( c_24__type__113109___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__121870,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).

fof('$_type_121886',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__121887] :
      ( c_24__type__121886___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__121887)
    <=> ! [Vv__CANONICAL__2] :
          ( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
         => cProp___24t(happ(Vvar__121887,Vv__CANONICAL__2)) ) ) ).

fof('$_type_121892',axiom,
    ! [Vvar__121893] :
      ( c_24__type__121892___24t(Vvar__121893)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( c_24__type__2000___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
             => ! [Vv__CANONICAL__2] :
                  ( cCoq_2eInit_2eSpecif_2esig___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
                 => t(happ(happ(happ(Vvar__121893,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__0) ) ) ) ) ).

fof('$_type_121909',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__121910] :
      ( c_24__type__121909___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__121910)
    <=> ! [Vv__CANONICAL__2] :
          ( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
         => cType___24t(happ(Vvar__121910,Vv__CANONICAL__2)) ) ) ).

fof('$_type_121915',axiom,
    ! [Vvar__121916] :
      ( c_24__type__121915___24t(Vvar__121916)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( c_24__type__113109___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
             => ! [Vv__CANONICAL__2] :
                  ( cCoq_2eInit_2eSpecif_2esigT___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
                 => t(happ(happ(happ(Vvar__121916,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__0) ) ) ) ) ).

fof('$_type_121945',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__121946] :
      ( c_24__type__121945___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__121946)
    <=> ! [Vv__CANONICAL__4] :
          ( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
         => cProp___24t(happ(Vvar__121946,Vv__CANONICAL__4)) ) ) ).

fof('$_type_122041',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__122042] :
      ( c_24__type__122041___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__122042)
    <=> ! [Vv__CANONICAL__6] :
          ( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__7] :
              ( t(Vv__CANONICAL__7,Vv__CANONICAL__1)
             => cProp___24t(happ(happ(Vvar__122042,Vv__CANONICAL__6),Vv__CANONICAL__7)) ) ) ) ).

fof('$_type_122191',axiom,
    ! [Vvar__122192] :
      ( c_24__type__122191___24t(Vvar__122192)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(Vv__CANONICAL__1)
             => ! [Vv__CANONICAL__2] :
                  ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(Vv__CANONICAL__2)
                 => cProp___24t(happ(happ(happ(Vvar__122192,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).

fof('$_type_122209',axiom,
    ! [Vvar__122210] :
      ( c_24__type__122209___24t(Vvar__122210)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
             => ! [Vv__CANONICAL__2] :
                  ( c_24__type__122214___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
                 => ! [Vv__CANONICAL__3] :
                      ( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__3)
                     => t(happ(happ(happ(happ(Vvar__122210,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__0) ) ) ) ) ) ).

fof('$_type_122214',axiom,
    ! [Vv__CANONICAL__0,Vvar__122215] :
      ( c_24__type__122214___24t(Vv__CANONICAL__0,Vvar__122215)
    <=> ! [Vv__CANONICAL__1] :
          ( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__1)
         => ! [Vv__CANONICAL__2] :
              ( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
             => t(happ(happ(Vvar__122215,Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_122218',axiom,
    ! [Vvar__122219] :
      ( c_24__type__122218___24t(Vvar__122219)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__0)
         => cCoq_2eInit_2eDatatypes_2enat___24t(happ(Vvar__122219,Vv__CANONICAL__0)) ) ) ).

fof('$_type_122274',axiom,
    ! [Vvar__122275] :
      ( c_24__type__122274___24t(Vvar__122275)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
             => cCoq_2eInit_2eDatatypes_2ebool___24t(happ(happ(Vvar__122275,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_122281',axiom,
    ! [Vvar__122282] :
      ( c_24__type__122281___24t(Vvar__122282)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
         => cCoq_2eNumbers_2eBinNums_2epositive___24t(happ(Vvar__122282,Vv__CANONICAL__0)) ) ) ).

fof('$_type_122302',axiom,
    ! [Vvar__122303] :
      ( c_24__type__122302___24t(Vvar__122303)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eInit_2eDatatypes_2ecomparison___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cCoq_2eInit_2eDatatypes_2ecomparison___24t(Vv__CANONICAL__1)
             => cCoq_2eInit_2eDatatypes_2ecomparison___24t(happ(happ(Vvar__122303,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_122309',axiom,
    ! [Vvar__122310] :
      ( c_24__type__122309___24t(Vvar__122310)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eStrings_2eString_2estring___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cCoq_2eStrings_2eString_2estring___24t(Vv__CANONICAL__1)
             => cProp___24t(happ(happ(Vvar__122310,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_122313',axiom,
    ! [Vvar__122314] :
      ( c_24__type__122313___24t(Vvar__122314)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
         => cCoq_2eInit_2eDatatypes_2enat___24t(happ(Vvar__122314,Vv__CANONICAL__0)) ) ) ).

fof('$_type_122328',axiom,
    ! [Vvar__122329] :
      ( c_24__type__122328___24t(Vvar__122329)
    <=> ! [Vv__CANONICAL__0] :
          ( c_24__type__115933___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( c_24__type__115933___24t(Vv__CANONICAL__1)
             => cProp___24t(happ(happ(Vvar__122329,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_122816',axiom,
    ! [Vvar__122817] :
      ( c_24__type__122816___24t(Vvar__122817)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eInit_2eDatatypes_2eunit___24t(Vv__CANONICAL__0)
         => cProp___24t(happ(Vvar__122817,Vv__CANONICAL__0)) ) ) ).

fof('$_type_12694',axiom,
    ! [Vvar__12695] :
      ( c_24__type__12694___24t(Vvar__12695)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cType___24t(Vv__CANONICAL__1)
             => cCoq_2emicromega_2eTauto_2ecnf___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,happ(happ(Vvar__12695,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_1278',axiom,
    ! [Vv__CANONICAL__0,Vvar__1279] :
      ( c_24__type__1278___24t(Vv__CANONICAL__0,Vvar__1279)
    <=> ! [Vv__CANONICAL__1] :
          ( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
         => t(happ(Vvar__1279,Vv__CANONICAL__1),Vv__CANONICAL__0) ) ) ).

fof('$_type_12873',axiom,
    ! [Vvar__12874] :
      ( c_24__type__12873___24t(Vvar__12874)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cType___24t(Vv__CANONICAL__1)
             => ! [Vv__CANONICAL__2] :
                  ( cCoq_2emicromega_2eTauto_2ecnf___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
                 => ! [Vv__CANONICAL__3] :
                      ( cCoq_2emicromega_2eTauto_2ecnf___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__3)
                     => cCoq_2emicromega_2eTauto_2ecnf___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,happ(happ(happ(happ(Vvar__12874,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).

fof('$_type_1300',axiom,
    ! [Vv__CANONICAL__0,Vvar__1301] :
      ( c_24__type__1300___24t(Vv__CANONICAL__0,Vvar__1301)
    <=> ! [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__1301,Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ).

fof('$_type_1310',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__1311] :
      ( c_24__type__1310___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__1311)
    <=> ! [Vv__CANONICAL__2] :
          ( t(Vv__CANONICAL__2,Vv__CANONICAL__1)
         => ! [Vv__CANONICAL__3] :
              ( t(Vv__CANONICAL__3,Vv__CANONICAL__1)
             => t(happ(happ(Vvar__1311,Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__1) ) ) ) ).

fof('$_type_1324',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__1325] :
      ( c_24__type__1324___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__1325)
    <=> ! [Vv__CANONICAL__2] :
          ( t(Vv__CANONICAL__2,Vv__CANONICAL__1)
         => t(happ(Vvar__1325,Vv__CANONICAL__2),Vv__CANONICAL__1) ) ) ).

fof('$_type_1331',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__1332] :
      ( c_24__type__1331___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__1332)
    <=> ! [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__1332,Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ).

fof('$_type_1335',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__1336] :
      ( c_24__type__1335___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__1336)
    <=> ! [Vv__CANONICAL__2] :
          ( t(Vv__CANONICAL__2,Vv__CANONICAL__1)
         => t(happ(Vvar__1336,Vv__CANONICAL__2),Vv__CANONICAL__0) ) ) ).

fof('$_type_13396',axiom,
    ! [Vvar__13397] :
      ( c_24__type__13396___24t(Vvar__13397)
    <=> ! [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] :
                      ( c_24__type__13403___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__3)
                     => ! [Vv__CANONICAL__4] :
                          ( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
                         => ! [Vv__CANONICAL__5] :
                              ( cCoq_2emicromega_2eTauto_2eclause___24t(Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__5)
                             => cProp___24t(happ(happ(happ(happ(happ(happ(Vvar__13397,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5)) ) ) ) ) ) ) ) ).

fof('$_type_13403',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__13404] :
      ( c_24__type__13403___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__13404)
    <=> ! [Vv__CANONICAL__2] :
          ( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__3] :
              ( t(Vv__CANONICAL__3,Vv__CANONICAL__1)
             => cProp___24t(happ(happ(Vvar__13404,Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ).

fof('$_type_13427',axiom,
    ! [Vvar__13428] :
      ( c_24__type__13427___24t(Vvar__13428)
    <=> ! [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] :
                      ( c_24__type__13403___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__3)
                     => ! [Vv__CANONICAL__4] :
                          ( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
                         => ! [Vv__CANONICAL__5] :
                              ( cCoq_2emicromega_2eTauto_2ecnf___24t(Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__5)
                             => cProp___24t(happ(happ(happ(happ(happ(happ(Vvar__13428,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5)) ) ) ) ) ) ) ) ).

fof('$_type_14',axiom,
    ! [Vvar__15] :
      ( c_24__type__14___24t(Vvar__15)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => cType___24t(happ(Vvar__15,Vv__CANONICAL__0)) ) ) ).

fof('$_type_14014',axiom,
    ! [Vvar__14015] :
      ( c_24__type__14014___24t(Vvar__14015)
    <=> ! [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__14015,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_14035',axiom,
    ! [Vvar__14036] :
      ( c_24__type__14035___24t(Vvar__14036)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__0)
         => cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(Vvar__14036,Vv__CANONICAL__0)) ) ) ).

fof('$_type_1426',axiom,
    ! [Vvar__1427] :
      ( c_24__type__1426___24t(Vvar__1427)
    <=> ! [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__1427,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).

fof('$_type_1430',axiom,
    ! [Vvar__1431] :
      ( c_24__type__1430___24t(Vvar__1431)
    <=> ! [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__1431,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_1444',axiom,
    ! [Vvar__1445] :
      ( c_24__type__1444___24t(Vvar__1445)
    <=> ! [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__1445,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_1456',axiom,
    ! [Vvar__1457] :
      ( c_24__type__1456___24t(Vvar__1457)
    <=> ! [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__1461___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2),happ(happ(happ(Vvar__1457,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ) ).

fof('$_type_146',axiom,
    ! [Vvar__147] :
      ( c_24__type__146___24t(Vvar__147)
    <=> ! [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__147,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).

fof('$_type_157',axiom,
    ! [Vv__CANONICAL__0,Vvar__158] :
      ( c_24__type__157___24t(Vv__CANONICAL__0,Vvar__158)
    <=> ! [Vv__CANONICAL__1] :
          ( cIntMap_2eMap_2ead___24t(Vv__CANONICAL__1)
         => cCoq_2eInit_2eDatatypes_2eoption___24t(Vv__CANONICAL__0,happ(Vvar__158,Vv__CANONICAL__1)) ) ) ).

fof('$_type_164738',axiom,
    ! [Vvar__164739] :
      ( c_24__type__164738___24t(Vvar__164739)
    <=> ! [Vv__CANONICAL__0] :
          ( cProp___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cProp___24t(Vv__CANONICAL__1)
             => ! [Vv__CANONICAL__2] :
                  ( c_24__type__164742___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
                 => ! [Vv__CANONICAL__3] :
                      ( c_24__type__164749___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3)
                     => ! [Vv__CANONICAL__4] :
                          ( c_24__type__164756___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__164739,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_164742',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__164743] :
      ( c_24__type__164742___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__164743)
    <=> ! [Vv__CANONICAL__2] :
          ( cCoq_2eInit_2eSpecif_2esumbool___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
         => cType___24t(happ(Vvar__164743,Vv__CANONICAL__2)) ) ) ).

fof('$_type_164749',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__164750] :
      ( c_24__type__164749___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__164750)
    <=> ( p(Vv__CANONICAL__0)
       => t(Vvar__164750,happ(Vv__CANONICAL__2,cCoq_2eInit_2eSpecif_2eleft___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1))) ) ) ).

fof('$_type_164756',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__164757] :
      ( c_24__type__164756___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__164757)
    <=> ( p(Vv__CANONICAL__1)
       => t(Vvar__164757,happ(Vv__CANONICAL__2,cCoq_2eInit_2eSpecif_2eright___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1))) ) ) ).

fof('$_type_172555',axiom,
    ! [Vv__CANONICAL__0,Vvar__172556] :
      ( c_24__type__172555___24t(Vv__CANONICAL__0,Vvar__172556)
    <=> ! [Vv__CANONICAL__1] :
          ( cCoq_2eInit_2eDatatypes_2eunit___24t(Vv__CANONICAL__1)
         => cType___24t(happ(Vvar__172556,Vv__CANONICAL__1)) ) ) ).

fof('$_type_172560',axiom,
    ! [Vvar__172561] :
      ( c_24__type__172560___24t(Vvar__172561)
    <=> ! [Vv__CANONICAL__0] :
          ( c_24__type__172562___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( t(Vv__CANONICAL__1,happ(Vv__CANONICAL__0,cCoq_2eInit_2eDatatypes_2ett))
             => ! [Vv__CANONICAL__2] :
                  ( cCoq_2eInit_2eDatatypes_2eunit___24t(Vv__CANONICAL__2)
                 => t(happ(happ(happ(Vvar__172561,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),happ(Vv__CANONICAL__0,Vv__CANONICAL__2)) ) ) ) ) ).

fof('$_type_172562',axiom,
    ! [Vvar__172563] :
      ( c_24__type__172562___24t(Vvar__172563)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eInit_2eDatatypes_2eunit___24t(Vv__CANONICAL__0)
         => cType___24t(happ(Vvar__172563,Vv__CANONICAL__0)) ) ) ).

fof('$_type_172691',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__172692] :
      ( c_24__type__172691___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__172692)
    <=> ! [Vv__CANONICAL__2] :
          ( cCoq_2eInit_2eDatatypes_2eprod___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
         => cProp___24t(happ(Vvar__172692,Vv__CANONICAL__2)) ) ) ).

fof('$_type_172843',axiom,
    ! [Vvar__172844] :
      ( c_24__type__172843___24t(Vvar__172844)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2emicromega_2eRingMicromega_2eNFormula___24t(cCoq_2eNumbers_2eBinNums_2eZ,Vv__CANONICAL__0)
         => cCoq_2eInit_2eDatatypes_2ebool___24t(happ(Vvar__172844,Vv__CANONICAL__0)) ) ) ).

fof('$_type_173538',axiom,
    ! [Vvar__173539] :
      ( c_24__type__173538___24t(Vvar__173539)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
             => ! [Vv__CANONICAL__2] :
                  ( cCoq_2emicromega_2eRingMicromega_2eOp2___24t(Vv__CANONICAL__2)
                 => ! [Vv__CANONICAL__3] :
                      ( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
                     => cCoq_2emicromega_2eRingMicromega_2eFormula___24t(Vv__CANONICAL__0,happ(happ(happ(happ(Vvar__173539,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).

fof('$_type_173544',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__173545] :
      ( c_24__type__173544___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__173545)
    <=> ! [Vv__CANONICAL__2] :
          ( t(Vv__CANONICAL__2,Vv__CANONICAL__1)
         => cProp___24t(happ(Vvar__173545,Vv__CANONICAL__2)) ) ) ).

fof('$_type_173588',axiom,
    ! [Vvar__173589] :
      ( c_24__type__173588___24t(Vvar__173589)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2emicromega_2eRingMicromega_2eOp2___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__1)
             => ! [Vv__CANONICAL__2] :
                  ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__2)
                 => cProp___24t(happ(happ(happ(Vvar__173589,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).

fof('$_type_183418',axiom,
    ! [Vvar__183419] :
      ( c_24__type__183418___24t(Vvar__183419)
    <=> ! [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__183419,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).

fof('$_type_1934',axiom,
    ! [Vvar__1935] :
      ( c_24__type__1934___24t(Vvar__1935)
    <=> ! [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__1935,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_1993',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__1994] :
      ( c_24__type__1993___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__1994)
    <=> ! [Vv__CANONICAL__2] :
          ( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
         => cProp___24t(happ(Vvar__1994,Vv__CANONICAL__2)) ) ) ).

fof('$_type_1997',axiom,
    ! [Vvar__1998] :
      ( c_24__type__1997___24t(Vvar__1998)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( c_24__type__2000___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
             => cType___24t(happ(happ(Vvar__1998,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_2000',axiom,
    ! [Vv__CANONICAL__0,Vvar__2001] :
      ( c_24__type__2000___24t(Vv__CANONICAL__0,Vvar__2001)
    <=> ! [Vv__CANONICAL__1] :
          ( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
         => cProp___24t(happ(Vvar__2001,Vv__CANONICAL__1)) ) ) ).

fof('$_type_2014',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__2015] :
      ( c_24__type__2014___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__2015)
    <=> ! [Vv__CANONICAL__2] :
          ( cCoq_2eInit_2eSpecif_2esig___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
         => cProp___24t(happ(Vvar__2015,Vv__CANONICAL__2)) ) ) ).

fof('$_type_2028',axiom,
    ! [Vvar__2029] :
      ( c_24__type__2028___24t(Vvar__2029)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cProp___24t(Vv__CANONICAL__1)
             => cType___24t(happ(happ(Vvar__2029,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_2108',axiom,
    ! [Vvar__2109] :
      ( c_24__type__2108___24t(Vvar__2109)
    <=> ! [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__2109,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).

fof('$_type_2518',axiom,
    ! [Vvar__2519] :
      ( c_24__type__2518___24t(Vvar__2519)
    <=> ! [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)
                     => ! [Vv__CANONICAL__4] :
                          ( cCoq_2emicromega_2eTauto_2eGFormula___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4)
                         => ! [Vv__CANONICAL__5] :
                              ( cCoq_2eInit_2eDatatypes_2eoption___24t(Vv__CANONICAL__3,Vv__CANONICAL__5)
                             => ! [Vv__CANONICAL__6] :
                                  ( cCoq_2emicromega_2eTauto_2eGFormula___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__6)
                                 => cCoq_2emicromega_2eTauto_2eGFormula___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,happ(happ(happ(happ(happ(happ(happ(Vvar__2519,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__6)) ) ) ) ) ) ) ) ) ).

fof('$_type_2520',axiom,
    ! [Vvar__2521] :
      ( c_24__type__2520___24t(Vvar__2521)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__0)
         => cCoq_2eInit_2eDatatypes_2ebool___24t(happ(Vvar__2521,Vv__CANONICAL__0)) ) ) ).

fof('$_type_2522',axiom,
    ! [Vvar__2523] :
      ( c_24__type__2522___24t(Vvar__2523)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
         => cProp___24t(happ(Vvar__2523,Vv__CANONICAL__0)) ) ) ).

fof('$_type_2568',axiom,
    ! [Vvar__2569] :
      ( c_24__type__2568___24t(Vvar__2569)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cType___24t(Vv__CANONICAL__1)
             => cType___24t(happ(happ(Vvar__2569,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_26',axiom,
    ! [Vvar__27] :
      ( c_24__type__26___24t(Vvar__27)
    <=> ! [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__27,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_260',axiom,
    ! [Vvar__261] :
      ( c_24__type__260___24t(Vvar__261)
    <=> ! [Vv__CANONICAL__0] :
          ( cProp___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cProp___24t(Vv__CANONICAL__1)
             => cType___24t(happ(happ(Vvar__261,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_2610',axiom,
    ! [Vvar__2611] :
      ( c_24__type__2610___24t(Vvar__2611)
    <=> ! [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__2611,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).

fof('$_type_2630',axiom,
    ! [Vvar__2631] :
      ( c_24__type__2630___24t(Vvar__2631)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,happ(Vvar__2631,Vv__CANONICAL__0)) ) ) ).

fof('$_type_2635',axiom,
    ! [Vvar__2636] :
      ( c_24__type__2635___24t(Vvar__2636)
    <=> ! [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__2636,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).

fof('$_type_2638',axiom,
    ! [Vv__CANONICAL__0,Vvar__2639] :
      ( c_24__type__2638___24t(Vv__CANONICAL__0,Vvar__2639)
    <=> ! [Vv__CANONICAL__1] :
          ( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
         => cProp___24t(happ(Vvar__2639,Vv__CANONICAL__1)) ) ) ).

fof('$_type_2651',axiom,
    ! [Vvar__2652] :
      ( c_24__type__2651___24t(Vvar__2652)
    <=> ! [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__2652,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_2663',axiom,
    ! [Vvar__2664] :
      ( c_24__type__2663___24t(Vvar__2664)
    <=> ! [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__2664,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).

fof('$_type_28',axiom,
    ! [Vvar__29] :
      ( c_24__type__28___24t(Vvar__29)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => cCoq_2eInit_2eDatatypes_2eoption___24t(Vv__CANONICAL__0,happ(Vvar__29,Vv__CANONICAL__0)) ) ) ).

fof('$_type_282',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__283] :
      ( c_24__type__282___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__283)
    <=> ! [Vv__CANONICAL__2] :
          ( cCoq_2eInit_2eSpecif_2esumbool___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
         => cProp___24t(happ(Vvar__283,Vv__CANONICAL__2)) ) ) ).

fof('$_type_2859',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__2860] :
      ( c_24__type__2859___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__2860)
    <=> ! [Vv__CANONICAL__10] :
          ( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__11] :
              ( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
             => t(happ(happ(Vvar__2860,Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_290',axiom,
    ! [Vvar__291] :
      ( c_24__type__290___24t(Vvar__291)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__0)
         => cCoq_2eInit_2eSpecif_2esumbool___24t(c_24__prop__292___24a1(Vv__CANONICAL__0),c_24__prop__293___24a1(Vv__CANONICAL__0),happ(Vvar__291,Vv__CANONICAL__0)) ) ) ).

fof('$_type_295',axiom,
    ! [Vvar__296] :
      ( c_24__type__295___24t(Vvar__296)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__0)
         => cCoq_2eNumbers_2eBinNums_2eN___24t(happ(Vvar__296,Vv__CANONICAL__0)) ) ) ).

fof('$_type_2952',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__2953] :
      ( c_24__type__2952___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__2953)
    <=> ! [Vv__CANONICAL__10] :
          ( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__11] :
              ( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
             => t(happ(happ(Vvar__2953,Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_3045',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__3046] :
      ( c_24__type__3045___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__3046)
    <=> ! [Vv__CANONICAL__10] :
          ( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__11] :
              ( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
             => t(happ(happ(Vvar__3046,Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_305',axiom,
    ! [Vvar__306] :
      ( c_24__type__305___24t(Vvar__306)
    <=> ! [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__306,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_3127',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__3128] :
      ( c_24__type__3127___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__3128)
    <=> ! [Vv__CANONICAL__10] :
          ( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
         => t(happ(Vvar__3128,Vv__CANONICAL__10),Vv__CANONICAL__0) ) ) ).

fof('$_type_313',axiom,
    ! [Vvar__314] :
      ( c_24__type__313___24t(Vvar__314)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__0)
         => cCoq_2eInit_2eDatatypes_2ebool___24t(happ(Vvar__314,Vv__CANONICAL__0)) ) ) ).

fof('$_type_3220',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__3221] :
      ( c_24__type__3220___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__3221)
    <=> ! [Vv__CANONICAL__10] :
          ( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__11] :
              ( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
             => t(happ(happ(Vvar__3221,Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_326',axiom,
    ! [Vvar__327] :
      ( c_24__type__326___24t(Vvar__327)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__0)
         => cCoq_2eNumbers_2eBinNums_2eN___24t(happ(Vvar__327,Vv__CANONICAL__0)) ) ) ).

fof('$_type_3302',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__3303] :
      ( c_24__type__3302___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__3303)
    <=> ! [Vv__CANONICAL__10] :
          ( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
         => t(happ(Vvar__3303,Vv__CANONICAL__10),Vv__CANONICAL__0) ) ) ).

fof('$_type_3395',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__3396] :
      ( c_24__type__3395___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__3396)
    <=> ! [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__3396,Vv__CANONICAL__10),Vv__CANONICAL__11)) ) ) ) ).

fof('$_type_461',axiom,
    ! [Vvar__462] :
      ( c_24__type__461___24t(Vvar__462)
    <=> ! [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__462,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).

fof('$_type_4992',axiom,
    ! [Vvar__4993] :
      ( c_24__type__4992___24t(Vvar__4993)
    <=> ! [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__4993,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).

fof('$_type_5038',axiom,
    ! [Vvar__5039] :
      ( c_24__type__5038___24t(Vvar__5039)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cType___24t(Vv__CANONICAL__1)
             => ! [Vv__CANONICAL__2] :
                  ( c_24__type__5045___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__5039,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__0) ) ) ) ) ) ) ).

fof('$_type_5045',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__5046] :
      ( c_24__type__5045___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__5046)
    <=> ! [Vv__CANONICAL__2] :
          ( t(Vv__CANONICAL__2,Vv__CANONICAL__1)
         => ! [Vv__CANONICAL__3] :
              ( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
             => t(happ(happ(Vvar__5046,Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_5091',axiom,
    ! [Vvar__5092] :
      ( c_24__type__5091___24t(Vvar__5092)
    <=> ! [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__5092,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_5117',axiom,
    ! [Vvar__5118] :
      ( c_24__type__5117___24t(Vvar__5118)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( c_24__type__2000___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__5118,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).

fof('$_type_5523',axiom,
    ! [Vvar__5524] :
      ( c_24__type__5523___24t(Vvar__5524)
    <=> ! [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__5524,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).

fof('$_type_605',axiom,
    ! [Vvar__606] :
      ( c_24__type__605___24t(Vvar__606)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => cIntMap_2eMap_2eMap___24t(Vv__CANONICAL__0,happ(Vvar__606,Vv__CANONICAL__0)) ) ) ).

fof('$_type_610',axiom,
    ! [Vvar__611] :
      ( c_24__type__610___24t(Vvar__611)
    <=> ! [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__611,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).

fof('$_type_613',axiom,
    ! [Vv__CANONICAL__0,Vvar__614] :
      ( c_24__type__613___24t(Vv__CANONICAL__0,Vvar__614)
    <=> ! [Vv__CANONICAL__1] :
          ( cIntMap_2eMap_2eMap___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
         => cProp___24t(happ(Vvar__614,Vv__CANONICAL__1)) ) ) ).

fof('$_type_71',axiom,
    ! [Vvar__72] :
      ( c_24__type__71___24t(Vvar__72)
    <=> ! [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__72,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).

fof('$_type_736',axiom,
    ! [Vvar__737] :
      ( c_24__type__736___24t(Vvar__737)
    <=> ! [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__737,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).

fof('$_type_7640',axiom,
    ! [Vvar__7641] :
      ( c_24__type__7640___24t(Vvar__7641)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( c_24__type__1058___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__7641,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__0) ) ) ) ) ) ).

fof('$_type_7661',axiom,
    ! [Vvar__7662] :
      ( c_24__type__7661___24t(Vvar__7662)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
             => ! [Vv__CANONICAL__2] :
                  ( c_24__type__1058___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__7662,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__0) ) ) ) ) ) ) ).

fof('$_type_7915',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__7916] :
      ( c_24__type__7915___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__7916)
    <=> ! [Vv__CANONICAL__8] :
          ( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__9] :
              ( t(Vv__CANONICAL__9,Vv__CANONICAL__0)
             => t(happ(happ(Vvar__7916,Vv__CANONICAL__8),Vv__CANONICAL__9),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_7978',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__7979] :
      ( c_24__type__7978___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__7979)
    <=> ! [Vv__CANONICAL__8] :
          ( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__9] :
              ( t(Vv__CANONICAL__9,Vv__CANONICAL__0)
             => t(happ(happ(Vvar__7979,Vv__CANONICAL__8),Vv__CANONICAL__9),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_8041',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__8042] :
      ( c_24__type__8041___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__8042)
    <=> ! [Vv__CANONICAL__8] :
          ( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__9] :
              ( t(Vv__CANONICAL__9,Vv__CANONICAL__0)
             => t(happ(happ(Vvar__8042,Vv__CANONICAL__8),Vv__CANONICAL__9),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_8095',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__8096] :
      ( c_24__type__8095___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__8096)
    <=> ! [Vv__CANONICAL__8] :
          ( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
         => t(happ(Vvar__8096,Vv__CANONICAL__8),Vv__CANONICAL__0) ) ) ).

fof('$_type_8158',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__8159] :
      ( c_24__type__8158___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__8159)
    <=> ! [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__8159,Vv__CANONICAL__8),Vv__CANONICAL__9)) ) ) ) ).

fof('$_type_8365',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__8366] :
      ( c_24__type__8365___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__8366)
    <=> ! [Vv__CANONICAL__5] :
          ( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__6] :
              ( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
             => t(happ(happ(Vvar__8366,Vv__CANONICAL__5),Vv__CANONICAL__6),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_8395',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__8396] :
      ( c_24__type__8395___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__8396)
    <=> ! [Vv__CANONICAL__5] :
          ( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__6] :
              ( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
             => t(happ(happ(Vvar__8396,Vv__CANONICAL__5),Vv__CANONICAL__6),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_8419',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__8420] :
      ( c_24__type__8419___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__8420)
    <=> ! [Vv__CANONICAL__5] :
          ( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
         => t(happ(Vvar__8420,Vv__CANONICAL__5),Vv__CANONICAL__0) ) ) ).

fof('$_type_8449',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__8450] :
      ( c_24__type__8449___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__8450)
    <=> ! [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__8450,Vv__CANONICAL__5),Vv__CANONICAL__6)) ) ) ) ).

fof('$_type_8479',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__8480] :
      ( c_24__type__8479___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__8480)
    <=> ! [Vv__CANONICAL__5] :
          ( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__6] :
              ( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
             => t(happ(happ(Vvar__8480,Vv__CANONICAL__5),Vv__CANONICAL__6),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_8503',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__8504] :
      ( c_24__type__8503___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__8504)
    <=> ! [Vv__CANONICAL__5] :
          ( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
         => t(happ(Vvar__8504,Vv__CANONICAL__5),Vv__CANONICAL__0) ) ) ).

fof('$_type_8536',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__8537] :
      ( c_24__type__8536___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__8537)
    <=> ! [Vv__CANONICAL__5] :
          ( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__6] :
              ( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
             => t(happ(happ(Vvar__8537,Vv__CANONICAL__5),Vv__CANONICAL__6),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_85484',axiom,
    ! [Vvar__85485] :
      ( c_24__type__85484___24t(Vvar__85485)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__0)
         => cProp___24t(happ(Vvar__85485,Vv__CANONICAL__0)) ) ) ).

fof('$_type_85487',axiom,
    ! [Vvar__85488] :
      ( c_24__type__85487___24t(Vvar__85488)
    <=> ! [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__85488,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_85536',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__85537] :
      ( c_24__type__85536___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__85537)
    <=> ! [Vv__CANONICAL__2] :
          ( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
         => t(happ(Vvar__85537,Vv__CANONICAL__2),Vv__CANONICAL__1) ) ) ).

fof('$_type_85541',axiom,
    ! [Vvar__85542] :
      ( c_24__type__85541___24t(Vvar__85542)
    <=> ! [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)
                 => cCoq_2eInit_2eDatatypes_2esum___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,happ(happ(happ(Vvar__85542,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).

fof('$_type_85546',axiom,
    ! [Vvar__85547] :
      ( c_24__type__85546___24t(Vvar__85547)
    <=> ! [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)
                 => cCoq_2eInit_2eDatatypes_2esum___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,happ(happ(happ(Vvar__85547,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).

fof('$_type_85558',axiom,
    ! [Vvar__85559] :
      ( c_24__type__85558___24t(Vvar__85559)
    <=> ! [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__85559,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__0) ) ) ) ) ).

fof('$_type_85570',axiom,
    ! [Vvar__85571] :
      ( c_24__type__85570___24t(Vvar__85571)
    <=> ! [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__85571,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__1) ) ) ) ) ).

fof('$_type_8560',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__8561] :
      ( c_24__type__8560___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__8561)
    <=> ! [Vv__CANONICAL__5] :
          ( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
         => t(happ(Vvar__8561,Vv__CANONICAL__5),Vv__CANONICAL__0) ) ) ).

fof('$_type_85706',axiom,
    ! [Vv__CANONICAL__0,Vvar__85707] :
      ( c_24__type__85706___24t(Vv__CANONICAL__0,Vvar__85707)
    <=> ! [Vv__CANONICAL__1] :
          ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__1)
         => t(happ(Vvar__85707,Vv__CANONICAL__1),Vv__CANONICAL__0) ) ) ).

fof('$_type_8587',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__8588] :
      ( c_24__type__8587___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__8588)
    <=> ! [Vv__CANONICAL__5] :
          ( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
         => t(happ(Vvar__8588,Vv__CANONICAL__5),Vv__CANONICAL__0) ) ) ).

fof('$_type_85920',axiom,
    ! [Vvar__85921] :
      ( c_24__type__85920___24t(Vvar__85921)
    <=> ! [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__85921,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_85925',axiom,
    ! [Vvar__85926] :
      ( c_24__type__85925___24t(Vvar__85926)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__1)
             => ! [Vv__CANONICAL__2] :
                  ( cCoq_2emicromega_2eEnvRing_2ePol___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
                 => cCoq_2emicromega_2eEnvRing_2ePol___24t(Vv__CANONICAL__0,happ(happ(happ(Vvar__85926,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).

fof('$_type_85933',axiom,
    ! [Vvar__85934] :
      ( c_24__type__85933___24t(Vvar__85934)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cCoq_2emicromega_2eEnvRing_2ePol___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
             => ! [Vv__CANONICAL__2] :
                  ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__2)
                 => ! [Vv__CANONICAL__3] :
                      ( cCoq_2emicromega_2eEnvRing_2ePol___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
                     => cCoq_2emicromega_2eEnvRing_2ePol___24t(Vv__CANONICAL__0,happ(happ(happ(happ(Vvar__85934,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).

fof('$_type_874',axiom,
    ! [Vvar__875] :
      ( c_24__type__874___24t(Vvar__875)
    <=> ! [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__875,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).

fof('$_type_89670',axiom,
    ! [Vvar__89671] :
      ( c_24__type__89670___24t(Vvar__89671)
    <=> ! [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__1461___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2),happ(happ(happ(Vvar__89671,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ) ).

fof('$_type_89676',axiom,
    ! [Vvar__89677] :
      ( c_24__type__89676___24t(Vvar__89677)
    <=> ! [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__89677,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_89690',axiom,
    ! [Vvar__89691] :
      ( c_24__type__89690___24t(Vvar__89691)
    <=> ! [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__89691,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__0) ) ) ) ) ).

fof('$_type_89733',axiom,
    ! [Vvar__89734] :
      ( c_24__type__89733___24t(Vvar__89734)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
             => ! [Vv__CANONICAL__2] :
                  ( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
                 => ! [Vv__CANONICAL__3] :
                      ( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
                     => t(happ(happ(happ(happ(Vvar__89734,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__0) ) ) ) ) ) ).

fof('$_type_89772',axiom,
    ! [Vvar__89773] :
      ( c_24__type__89772___24t(Vvar__89773)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cType___24t(Vv__CANONICAL__1)
             => ! [Vv__CANONICAL__2] :
                  ( c_24__type__85536___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
                 => ! [Vv__CANONICAL__3] :
                      ( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
                     => cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__1,happ(happ(happ(happ(Vvar__89773,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).

fof('$_type_89840',axiom,
    ! [Vvar__89841] :
      ( c_24__type__89840___24t(Vvar__89841)
    <=> ! [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__89841,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_89842',axiom,
    ! [Vvar__89843] :
      ( c_24__type__89842___24t(Vvar__89843)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
         => cProp___24t(happ(Vvar__89843,Vv__CANONICAL__0)) ) ) ).

fof('$_type_8986',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__8987] :
      ( c_24__type__8986___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__8987)
    <=> ! [Vv__CANONICAL__17] :
          ( t(Vv__CANONICAL__17,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__18] :
              ( t(Vv__CANONICAL__18,Vv__CANONICAL__0)
             => t(happ(happ(Vvar__8987,Vv__CANONICAL__17),Vv__CANONICAL__18),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_90276',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__90277] :
      ( c_24__type__90276___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__90277)
    <=> ! [Vv__CANONICAL__10] :
          ( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__11] :
              ( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
             => t(happ(happ(Vvar__90277,Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_90377',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__90378] :
      ( c_24__type__90377___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__90378)
    <=> ! [Vv__CANONICAL__10] :
          ( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__11] :
              ( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
             => t(happ(happ(Vvar__90378,Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_90478',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__90479] :
      ( c_24__type__90478___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__90479)
    <=> ! [Vv__CANONICAL__10] :
          ( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__11] :
              ( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
             => t(happ(happ(Vvar__90479,Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_90568',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__90569] :
      ( c_24__type__90568___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__90569)
    <=> ! [Vv__CANONICAL__10] :
          ( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
         => t(happ(Vvar__90569,Vv__CANONICAL__10),Vv__CANONICAL__0) ) ) ).

fof('$_type_90669',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__90670] :
      ( c_24__type__90669___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__90670)
    <=> ! [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__90670,Vv__CANONICAL__10),Vv__CANONICAL__11)) ) ) ) ).

fof('$_type_90770',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__90771] :
      ( c_24__type__90770___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__90771)
    <=> ! [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__90771,Vv__CANONICAL__10),Vv__CANONICAL__11)) ) ) ) ).

fof('$_type_90871',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__90872] :
      ( c_24__type__90871___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__90872)
    <=> ! [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__90872,Vv__CANONICAL__10),Vv__CANONICAL__11)) ) ) ) ).

fof('$_type_91218',axiom,
    ! [Vvar__91219] :
      ( c_24__type__91218___24t(Vvar__91219)
    <=> ! [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__91219,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_91245',axiom,
    ! [Vvar__91246] :
      ( c_24__type__91245___24t(Vvar__91246)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( c_24__type__2000___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__91246,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).

fof('$_type_91783',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__91784] :
      ( c_24__type__91783___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__91784)
    <=> ! [Vv__CANONICAL__22] :
          ( t(Vv__CANONICAL__22,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__23] :
              ( t(Vv__CANONICAL__23,Vv__CANONICAL__0)
             => t(happ(happ(Vvar__91784,Vv__CANONICAL__22),Vv__CANONICAL__23),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_9199',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__9200] :
      ( c_24__type__9199___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__9200)
    <=> ! [Vv__CANONICAL__17] :
          ( t(Vv__CANONICAL__17,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__18] :
              ( t(Vv__CANONICAL__18,Vv__CANONICAL__0)
             => t(happ(happ(Vvar__9200,Vv__CANONICAL__17),Vv__CANONICAL__18),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_92129',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__92130] :
      ( c_24__type__92129___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__92130)
    <=> ! [Vv__CANONICAL__22] :
          ( t(Vv__CANONICAL__22,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__23] :
              ( t(Vv__CANONICAL__23,Vv__CANONICAL__0)
             => t(happ(happ(Vvar__92130,Vv__CANONICAL__22),Vv__CANONICAL__23),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_92475',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__92476] :
      ( c_24__type__92475___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__92476)
    <=> ! [Vv__CANONICAL__22] :
          ( t(Vv__CANONICAL__22,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__23] :
              ( t(Vv__CANONICAL__23,Vv__CANONICAL__0)
             => t(happ(happ(Vvar__92476,Vv__CANONICAL__22),Vv__CANONICAL__23),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_92798',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__92799] :
      ( c_24__type__92798___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__92799)
    <=> ! [Vv__CANONICAL__22] :
          ( t(Vv__CANONICAL__22,Vv__CANONICAL__0)
         => t(happ(Vvar__92799,Vv__CANONICAL__22),Vv__CANONICAL__0) ) ) ).

fof('$_type_93144',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__93145] :
      ( c_24__type__93144___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__93145)
    <=> ! [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__93145,Vv__CANONICAL__22),Vv__CANONICAL__23)) ) ) ) ).

fof('$_type_93490',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__93491] :
      ( c_24__type__93490___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__93491)
    <=> ! [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__93491,Vv__CANONICAL__22),Vv__CANONICAL__23)) ) ) ) ).

fof('$_type_93836',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__93837] :
      ( c_24__type__93836___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__93837)
    <=> ! [Vv__CANONICAL__22] :
          ( t(Vv__CANONICAL__22,Vv__CANONICAL__9)
         => ! [Vv__CANONICAL__23] :
              ( t(Vv__CANONICAL__23,Vv__CANONICAL__9)
             => t(happ(happ(Vvar__93837,Vv__CANONICAL__22),Vv__CANONICAL__23),Vv__CANONICAL__9) ) ) ) ).

fof('$_type_9412',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__9413] :
      ( c_24__type__9412___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__9413)
    <=> ! [Vv__CANONICAL__17] :
          ( t(Vv__CANONICAL__17,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__18] :
              ( t(Vv__CANONICAL__18,Vv__CANONICAL__0)
             => t(happ(happ(Vvar__9413,Vv__CANONICAL__17),Vv__CANONICAL__18),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_94182',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__94183] :
      ( c_24__type__94182___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__94183)
    <=> ! [Vv__CANONICAL__22] :
          ( t(Vv__CANONICAL__22,Vv__CANONICAL__9)
         => ! [Vv__CANONICAL__23] :
              ( t(Vv__CANONICAL__23,Vv__CANONICAL__9)
             => t(happ(happ(Vvar__94183,Vv__CANONICAL__22),Vv__CANONICAL__23),Vv__CANONICAL__9) ) ) ) ).

fof('$_type_94528',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__94529] :
      ( c_24__type__94528___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__94529)
    <=> ! [Vv__CANONICAL__22] :
          ( t(Vv__CANONICAL__22,Vv__CANONICAL__9)
         => ! [Vv__CANONICAL__23] :
              ( t(Vv__CANONICAL__23,Vv__CANONICAL__9)
             => t(happ(happ(Vvar__94529,Vv__CANONICAL__22),Vv__CANONICAL__23),Vv__CANONICAL__9) ) ) ) ).

fof('$_type_94851',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__94852] :
      ( c_24__type__94851___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__94852)
    <=> ! [Vv__CANONICAL__22] :
          ( t(Vv__CANONICAL__22,Vv__CANONICAL__9)
         => t(happ(Vvar__94852,Vv__CANONICAL__22),Vv__CANONICAL__9) ) ) ).

fof('$_type_95197',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__95198] :
      ( c_24__type__95197___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__95198)
    <=> ! [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__95198,Vv__CANONICAL__22),Vv__CANONICAL__23)) ) ) ) ).

fof('$_type_95543',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__95544] :
      ( c_24__type__95543___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__95544)
    <=> ! [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__95544,Vv__CANONICAL__22),Vv__CANONICAL__23)) ) ) ) ).

fof('$_type_95866',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__95867] :
      ( c_24__type__95866___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__95867)
    <=> ! [Vv__CANONICAL__22] :
          ( t(Vv__CANONICAL__22,Vv__CANONICAL__9)
         => t(happ(Vvar__95867,Vv__CANONICAL__22),Vv__CANONICAL__0) ) ) ).

fof('$_type_9607',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__9608] :
      ( c_24__type__9607___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__9608)
    <=> ! [Vv__CANONICAL__17] :
          ( t(Vv__CANONICAL__17,Vv__CANONICAL__0)
         => t(happ(Vvar__9608,Vv__CANONICAL__17),Vv__CANONICAL__0) ) ) ).

fof('$_type_96189',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__96190] :
      ( c_24__type__96189___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__96190)
    <=> ! [Vv__CANONICAL__22] :
          ( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__22)
         => t(happ(Vvar__96190,Vv__CANONICAL__22),Vv__CANONICAL__19) ) ) ).

fof('$_type_96535',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__96536] :
      ( c_24__type__96535___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__96536)
    <=> ! [Vv__CANONICAL__22] :
          ( t(Vv__CANONICAL__22,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__23] :
              ( t(Vv__CANONICAL__23,Vv__CANONICAL__19)
             => t(happ(happ(Vvar__96536,Vv__CANONICAL__22),Vv__CANONICAL__23),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_96883',axiom,
    ! [Vvar__96884] :
      ( c_24__type__96883___24t(Vvar__96884)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( c_24__type__1058___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
             => ! [Vv__CANONICAL__2] :
                  ( c_24__type__1058___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
                 => ! [Vv__CANONICAL__3] :
                      ( cType___24t(Vv__CANONICAL__3)
                     => ! [Vv__CANONICAL__4] :
                          ( c_24__type__1335___24t(Vv__CANONICAL__0,Vv__CANONICAL__3,Vv__CANONICAL__4)
                         => ! [Vv__CANONICAL__5] :
                              ( cCoq_2emicromega_2eRingMicromega_2ePolEnv___24t(Vv__CANONICAL__0,Vv__CANONICAL__5)
                             => ! [Vv__CANONICAL__6] :
                                  ( cCoq_2emicromega_2eRingMicromega_2ePolC___24t(Vv__CANONICAL__3,Vv__CANONICAL__6)
                                 => t(happ(happ(happ(happ(happ(happ(happ(Vvar__96884,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__6),Vv__CANONICAL__0) ) ) ) ) ) ) ) ) ).

fof('$_type_96968',axiom,
    ! [Vvar__96969] :
      ( c_24__type__96968___24t(Vvar__96969)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
             => ! [Vv__CANONICAL__2] :
                  ( c_24__type__1300___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
                 => ! [Vv__CANONICAL__3] :
                      ( c_24__type__1300___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
                     => ! [Vv__CANONICAL__4] :
                          ( c_24__type__1300___24t(Vv__CANONICAL__0,Vv__CANONICAL__4)
                         => ! [Vv__CANONICAL__5] :
                              ( cCoq_2emicromega_2eRingMicromega_2eOp1___24t(Vv__CANONICAL__5)
                             => ! [Vv__CANONICAL__6] :
                                  ( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
                                 => cProp___24t(happ(happ(happ(happ(happ(happ(happ(Vvar__96969,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__6)) ) ) ) ) ) ) ) ) ).

fof('$_type_981',axiom,
    ! [Vvar__982] :
      ( c_24__type__981___24t(Vvar__982)
    <=> ! [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__982,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_9820',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__9821] :
      ( c_24__type__9820___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__9821)
    <=> ! [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__9821,Vv__CANONICAL__17),Vv__CANONICAL__18)) ) ) ) ).

fof('$_type_98271',axiom,
    ! [Vvar__98272] :
      ( c_24__type__98271___24t(Vvar__98272)
    <=> ! [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__98272,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_98276',axiom,
    ! [Vvar__98277] :
      ( c_24__type__98276___24t(Vvar__98277)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__1)
             => ! [Vv__CANONICAL__2] :
                  ( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
                 => cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vv__CANONICAL__0,happ(happ(happ(Vvar__98277,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).

fof('$_type_98284',axiom,
    ! [Vvar__98285] :
      ( c_24__type__98284___24t(Vvar__98285)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
             => ! [Vv__CANONICAL__2] :
                  ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__2)
                 => ! [Vv__CANONICAL__3] :
                      ( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
                     => cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vv__CANONICAL__0,happ(happ(happ(happ(Vvar__98285,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).

fof('$_type_983',axiom,
    ! [Vvar__984] :
      ( c_24__type__983___24t(Vvar__984)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__0)
         => cCoq_2eNumbers_2eBinNums_2epositive___24t(happ(Vvar__984,Vv__CANONICAL__0)) ) ) ).

fof('$_type_98426',axiom,
    ! [Vvar__98427] :
      ( c_24__type__98426___24t(Vvar__98427)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( c_24__type__1063___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
             => ! [Vv__CANONICAL__2] :
                  ( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
                 => ! [Vv__CANONICAL__3] :
                      ( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
                     => cCoq_2eInit_2eDatatypes_2ebool___24t(happ(happ(happ(happ(Vvar__98427,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).

fof('$_type_985',axiom,
    ! [Vvar__986] :
      ( c_24__type__985___24t(Vvar__986)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__0)
         => cProp___24t(happ(Vvar__986,Vv__CANONICAL__0)) ) ) ).

fof('$_type_99179',axiom,
    ! [Vvar__99180] :
      ( c_24__type__99179___24t(Vvar__99180)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cCoq_2esetoid__ring_2eRing__polynom_2eMon___24t(Vv__CANONICAL__1)
             => cCoq_2esetoid__ring_2eRing__polynom_2eMon___24t(happ(happ(Vvar__99180,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_typeof_Coq.Arith.EqNat.eq_nat',axiom,
    c_24__type__5091___24t(cCoq_2eArith_2eEqNat_2eeq__nat) ).

fof('$_typeof_Coq.Arith.PeanoNat.Nat.b2n',axiom,
    c_24__type__122218___24t(cCoq_2eArith_2ePeanoNat_2eNat_2eb2n) ).

fof('$_typeof_Coq.Arith.PeanoNat.Nat.divide',axiom,
    c_24__type__5091___24t(cCoq_2eArith_2ePeanoNat_2eNat_2edivide) ).

fof('$_typeof_Coq.Arith.PeanoNat.Nat.eq',axiom,
    c_24__type__5091___24t(cCoq_2eArith_2ePeanoNat_2eNat_2eeq) ).

fof('$_typeof_Coq.Arith.PeanoNat.Nat.eqf',axiom,
    c_24__type__117936___24t(cCoq_2eArith_2ePeanoNat_2eNat_2eeqf) ).

fof('$_typeof_Coq.Arith.PeanoNat.Nat.le',axiom,
    c_24__type__5091___24t(cCoq_2eArith_2ePeanoNat_2eNat_2ele) ).

fof('$_typeof_Coq.Arith.PeanoNat.Nat.lt',axiom,
    c_24__type__5091___24t(cCoq_2eArith_2ePeanoNat_2eNat_2elt) ).

fof('$_typeof_Coq.Arith.PeanoNat.Nat.recursion',axiom,
    c_24__type__120334___24t(cCoq_2eArith_2ePeanoNat_2eNat_2erecursion) ).

fof('$_typeof_Coq.Arith.Plus.tail_plus',axiom,
    c_24__type__1934___24t(cCoq_2eArith_2ePlus_2etail__plus) ).

fof('$_typeof_Coq.Arith.Wf_nat.ltof',axiom,
    c_24__type__118387___24t(cCoq_2eArith_2eWf__nat_2eltof) ).

fof('$_typeof_Coq.Bool.Bool.Is_true',axiom,
    c_24__type__85484___24t(cCoq_2eBool_2eBool_2eIs__true) ).

fof('$_typeof_Coq.Bool.Bool.eqb',axiom,
    c_24__type__85487___24t(cCoq_2eBool_2eBool_2eeqb) ).

fof('$_typeof_Coq.Bool.Bool.ifb',axiom,
    c_24__type__107511___24t(cCoq_2eBool_2eBool_2eifb) ).

fof('$_typeof_Coq.Bool.Bool.reflect',axiom,
    c_24__type__107524___24t(cCoq_2eBool_2eBool_2ereflect) ).

fof('$_typeof_Coq.Bool.Bvector.Bvector',axiom,
    c_24__type__109156___24t(cCoq_2eBool_2eBvector_2eBvector) ).

fof('$_typeof_Coq.Bool.Sumbool.sumbool_of_bool',axiom,
    c_24__type__290___24t(cCoq_2eBool_2eSumbool_2esumbool__of__bool) ).

fof('$_typeof_Coq.Bool.Zerob.zerob',axiom,
    c_24__type__109437___24t(cCoq_2eBool_2eZerob_2ezerob) ).

fof('$_typeof_Coq.FSets.FSetPositive.PositiveSet.Equal',axiom,
    c_24__type__107287___24t(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eEqual) ).

fof('$_typeof_Coq.FSets.FSetPositive.PositiveSet.In',axiom,
    c_24__type__107284___24t(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eIn) ).

fof('$_typeof_Coq.FSets.FSetPositive.PositiveSet.Leaf',axiom,
    cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree___24t(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eLeaf) ).

fof('$_typeof_Coq.FSets.FSetPositive.PositiveSet.Node',axiom,
    c_24__type__107117___24t(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eNode) ).

fof('$_typeof_Coq.FSets.FSetPositive.PositiveSet.elements',axiom,
    c_24__type__120473___24t(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelements) ).

fof('$_typeof_Coq.FSets.FSetPositive.PositiveSet.elt',axiom,
    cType___24t(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt) ).

fof('$_typeof_Coq.FSets.FSetPositive.PositiveSet.empty',axiom,
    cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eempty) ).

fof('$_typeof_Coq.FSets.FSetPositive.PositiveSet.eq',axiom,
    c_24__type__107287___24t(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eeq) ).

fof('$_typeof_Coq.FSets.FSetPositive.PositiveSet.fold',axiom,
    c_24__type__107205___24t(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2efold) ).

fof('$_typeof_Coq.FSets.FSetPositive.PositiveSet.mem',axiom,
    c_24__type__107166___24t(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2emem) ).

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.FSets.FSetPositive.PositiveSet.union',axiom,
    c_24__type__107194___24t(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eunion) ).

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__120879___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.CompOpp',axiom,
    c_24__type__116818___24t(cCoq_2eInit_2eDatatypes_2eCompOpp) ).

fof('$_typeof_Coq.Init.Datatypes.CompareSpecT',axiom,
    c_24__type__107581___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__28___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__1000___24t(cCoq_2eInit_2eDatatypes_2eS) ).

fof('$_typeof_Coq.Init.Datatypes.Some',axiom,
    c_24__type__26___24t(cCoq_2eInit_2eDatatypes_2eSome) ).

fof('$_typeof_Coq.Init.Datatypes.andb',axiom,
    c_24__type__85487___24t(cCoq_2eInit_2eDatatypes_2eandb) ).

fof('$_typeof_Coq.Init.Datatypes.app',axiom,
    c_24__type__2663___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__2635___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__85558___24t(cCoq_2eInit_2eDatatypes_2efst) ).

fof('$_typeof_Coq.Init.Datatypes.id',axiom,
    cCoq_2eInit_2eDatatypes_2eID___24t(cCoq_2eInit_2eDatatypes_2eid) ).

fof('$_typeof_Coq.Init.Datatypes.implb',axiom,
    c_24__type__85487___24t(cCoq_2eInit_2eDatatypes_2eimplb) ).

fof('$_typeof_Coq.Init.Datatypes.inl',axiom,
    c_24__type__85541___24t(cCoq_2eInit_2eDatatypes_2einl) ).

fof('$_typeof_Coq.Init.Datatypes.inr',axiom,
    c_24__type__85546___24t(cCoq_2eInit_2eDatatypes_2einr) ).

fof('$_typeof_Coq.Init.Datatypes.length',axiom,
    c_24__type__2651___24t(cCoq_2eInit_2eDatatypes_2elength) ).

fof('$_typeof_Coq.Init.Datatypes.list',axiom,
    c_24__type__14___24t(cCoq_2eInit_2eDatatypes_2elist) ).

fof('$_typeof_Coq.Init.Datatypes.nat',axiom,
    cType___24t(cCoq_2eInit_2eDatatypes_2enat) ).

fof('$_typeof_Coq.Init.Datatypes.nat_rect',axiom,
    c_24__type__116811___24t(cCoq_2eInit_2eDatatypes_2enat__rect) ).

fof('$_typeof_Coq.Init.Datatypes.negb',axiom,
    c_24__type__2520___24t(cCoq_2eInit_2eDatatypes_2enegb) ).

fof('$_typeof_Coq.Init.Datatypes.nil',axiom,
    c_24__type__2630___24t(cCoq_2eInit_2eDatatypes_2enil) ).

fof('$_typeof_Coq.Init.Datatypes.option',axiom,
    c_24__type__14___24t(cCoq_2eInit_2eDatatypes_2eoption) ).

fof('$_typeof_Coq.Init.Datatypes.orb',axiom,
    c_24__type__85487___24t(cCoq_2eInit_2eDatatypes_2eorb) ).

fof('$_typeof_Coq.Init.Datatypes.pair',axiom,
    c_24__type__2610___24t(cCoq_2eInit_2eDatatypes_2epair) ).

fof('$_typeof_Coq.Init.Datatypes.prod',axiom,
    c_24__type__2568___24t(cCoq_2eInit_2eDatatypes_2eprod) ).

fof('$_typeof_Coq.Init.Datatypes.snd',axiom,
    c_24__type__85570___24t(cCoq_2eInit_2eDatatypes_2esnd) ).

fof('$_typeof_Coq.Init.Datatypes.sum',axiom,
    c_24__type__2568___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.unit_rec',axiom,
    c_24__type__172560___24t(cCoq_2eInit_2eDatatypes_2eunit__rec) ).

fof('$_typeof_Coq.Init.Datatypes.unit_rect',axiom,
    c_24__type__172560___24t(cCoq_2eInit_2eDatatypes_2eunit__rect) ).

fof('$_typeof_Coq.Init.Datatypes.xorb',axiom,
    c_24__type__85487___24t(cCoq_2eInit_2eDatatypes_2exorb) ).

fof('$_typeof_Coq.Init.Decimal.D0',axiom,
    c_24__type__116820___24t(cCoq_2eInit_2eDecimal_2eD0) ).

fof('$_typeof_Coq.Init.Decimal.D1',axiom,
    c_24__type__116820___24t(cCoq_2eInit_2eDecimal_2eD1) ).

fof('$_typeof_Coq.Init.Decimal.D2',axiom,
    c_24__type__116820___24t(cCoq_2eInit_2eDecimal_2eD2) ).

fof('$_typeof_Coq.Init.Decimal.D3',axiom,
    c_24__type__116820___24t(cCoq_2eInit_2eDecimal_2eD3) ).

fof('$_typeof_Coq.Init.Decimal.D4',axiom,
    c_24__type__116820___24t(cCoq_2eInit_2eDecimal_2eD4) ).

fof('$_typeof_Coq.Init.Decimal.D5',axiom,
    c_24__type__116820___24t(cCoq_2eInit_2eDecimal_2eD5) ).

fof('$_typeof_Coq.Init.Decimal.D6',axiom,
    c_24__type__116820___24t(cCoq_2eInit_2eDecimal_2eD6) ).

fof('$_typeof_Coq.Init.Decimal.D7',axiom,
    c_24__type__116820___24t(cCoq_2eInit_2eDecimal_2eD7) ).

fof('$_typeof_Coq.Init.Decimal.D8',axiom,
    c_24__type__116820___24t(cCoq_2eInit_2eDecimal_2eD8) ).

fof('$_typeof_Coq.Init.Decimal.D9',axiom,
    c_24__type__116820___24t(cCoq_2eInit_2eDecimal_2eD9) ).

fof('$_typeof_Coq.Init.Decimal.Nil',axiom,
    cCoq_2eInit_2eDecimal_2euint___24t(cCoq_2eInit_2eDecimal_2eNil) ).

fof('$_typeof_Coq.Init.Decimal.Pos',axiom,
    c_24__type__120882___24t(cCoq_2eInit_2eDecimal_2ePos) ).

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.int_of_int',axiom,
    c_24__type__120895___24t(cCoq_2eInit_2eDecimal_2eint__of__int) ).

fof('$_typeof_Coq.Init.Decimal.nzhead',axiom,
    c_24__type__116820___24t(cCoq_2eInit_2eDecimal_2enzhead) ).

fof('$_typeof_Coq.Init.Decimal.uint',axiom,
    cType___24t(cCoq_2eInit_2eDecimal_2euint) ).

fof('$_typeof_Coq.Init.Decimal.uint_of_uint',axiom,
    c_24__type__116820___24t(cCoq_2eInit_2eDecimal_2euint__of__uint) ).

fof('$_typeof_Coq.Init.Logic_Type.notT',axiom,
    c_24__type__109404___24t(cCoq_2eInit_2eLogic__Type_2enotT) ).

fof('$_typeof_Coq.Init.Nat.add',axiom,
    c_24__type__1934___24t(cCoq_2eInit_2eNat_2eadd) ).

fof('$_typeof_Coq.Init.Nat.compare',axiom,
    c_24__type__109418___24t(cCoq_2eInit_2eNat_2ecompare) ).

fof('$_typeof_Coq.Init.Nat.div2',axiom,
    c_24__type__1000___24t(cCoq_2eInit_2eNat_2ediv2) ).

fof('$_typeof_Coq.Init.Nat.double',axiom,
    c_24__type__1000___24t(cCoq_2eInit_2eNat_2edouble) ).

fof('$_typeof_Coq.Init.Nat.eqb',axiom,
    c_24__type__89840___24t(cCoq_2eInit_2eNat_2eeqb) ).

fof('$_typeof_Coq.Init.Nat.even',axiom,
    c_24__type__109437___24t(cCoq_2eInit_2eNat_2eeven) ).

fof('$_typeof_Coq.Init.Nat.leb',axiom,
    c_24__type__89840___24t(cCoq_2eInit_2eNat_2eleb) ).

fof('$_typeof_Coq.Init.Nat.log2_iter',axiom,
    c_24__type__120985___24t(cCoq_2eInit_2eNat_2elog2__iter) ).

fof('$_typeof_Coq.Init.Nat.max',axiom,
    c_24__type__1934___24t(cCoq_2eInit_2eNat_2emax) ).

fof('$_typeof_Coq.Init.Nat.min',axiom,
    c_24__type__1934___24t(cCoq_2eInit_2eNat_2emin) ).

fof('$_typeof_Coq.Init.Nat.mul',axiom,
    c_24__type__1934___24t(cCoq_2eInit_2eNat_2emul) ).

fof('$_typeof_Coq.Init.Nat.pow',axiom,
    c_24__type__1934___24t(cCoq_2eInit_2eNat_2epow) ).

fof('$_typeof_Coq.Init.Nat.pred',axiom,
    c_24__type__1000___24t(cCoq_2eInit_2eNat_2epred) ).

fof('$_typeof_Coq.Init.Nat.square',axiom,
    c_24__type__1000___24t(cCoq_2eInit_2eNat_2esquare) ).

fof('$_typeof_Coq.Init.Nat.sub',axiom,
    c_24__type__1934___24t(cCoq_2eInit_2eNat_2esub) ).

fof('$_typeof_Coq.Init.Nat.succ',axiom,
    c_24__type__1000___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__1934___24t(cCoq_2eInit_2eNat_2etail__add) ).

fof('$_typeof_Coq.Init.Nat.testbit',axiom,
    c_24__type__89840___24t(cCoq_2eInit_2eNat_2etestbit) ).

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__2522___24t(cCoq_2eInit_2ePeano_2eIsSucc) ).

fof('$_typeof_Coq.Init.Peano.ge',axiom,
    c_24__type__5091___24t(cCoq_2eInit_2ePeano_2ege) ).

fof('$_typeof_Coq.Init.Peano.gt',axiom,
    c_24__type__5091___24t(cCoq_2eInit_2ePeano_2egt) ).

fof('$_typeof_Coq.Init.Peano.lt',axiom,
    c_24__type__5091___24t(cCoq_2eInit_2ePeano_2elt) ).

fof('$_typeof_Coq.Init.Specif.Exc',axiom,
    c_24__type__14___24t(cCoq_2eInit_2eSpecif_2eExc) ).

fof('$_typeof_Coq.Init.Specif.except',axiom,
    c_24__type__113176___24t(cCoq_2eInit_2eSpecif_2eexcept) ).

fof('$_typeof_Coq.Init.Specif.exist',axiom,
    c_24__type__12044___24t(cCoq_2eInit_2eSpecif_2eexist) ).

fof('$_typeof_Coq.Init.Specif.existT',axiom,
    c_24__type__121869___24t(cCoq_2eInit_2eSpecif_2eexistT) ).

fof('$_typeof_Coq.Init.Specif.left',axiom,
    c_24__type__118300___24t(cCoq_2eInit_2eSpecif_2eleft) ).

fof('$_typeof_Coq.Init.Specif.proj1_sig',axiom,
    c_24__type__121892___24t(cCoq_2eInit_2eSpecif_2eproj1__sig) ).

fof('$_typeof_Coq.Init.Specif.projT1',axiom,
    c_24__type__121915___24t(cCoq_2eInit_2eSpecif_2eprojT1) ).

fof('$_typeof_Coq.Init.Specif.right',axiom,
    c_24__type__118305___24t(cCoq_2eInit_2eSpecif_2eright) ).

fof('$_typeof_Coq.Init.Specif.sig',axiom,
    c_24__type__1997___24t(cCoq_2eInit_2eSpecif_2esig) ).

fof('$_typeof_Coq.Init.Specif.sig2',axiom,
    c_24__type__113072___24t(cCoq_2eInit_2eSpecif_2esig2) ).

fof('$_typeof_Coq.Init.Specif.sigT',axiom,
    c_24__type__113106___24t(cCoq_2eInit_2eSpecif_2esigT) ).

fof('$_typeof_Coq.Init.Specif.sigT2',axiom,
    c_24__type__113159___24t(cCoq_2eInit_2eSpecif_2esigT2) ).

fof('$_typeof_Coq.Init.Specif.sumbool',axiom,
    c_24__type__260___24t(cCoq_2eInit_2eSpecif_2esumbool) ).

fof('$_typeof_Coq.Init.Specif.sumbool_rec',axiom,
    c_24__type__164738___24t(cCoq_2eInit_2eSpecif_2esumbool__rec) ).

fof('$_typeof_Coq.Init.Specif.sumor',axiom,
    c_24__type__2028___24t(cCoq_2eInit_2eSpecif_2esumor) ).

fof('$_typeof_Coq.Init.Wf.well_founded',axiom,
    c_24__type__118375___24t(cCoq_2eInit_2eWf_2ewell__founded) ).

fof('$_typeof_Coq.Lists.List.In',axiom,
    c_24__type__4992___24t(cCoq_2eLists_2eList_2eIn) ).

fof('$_typeof_Coq.Lists.List.fold_left',axiom,
    c_24__type__109265___24t(cCoq_2eLists_2eList_2efold__left) ).

fof('$_typeof_Coq.Lists.List.fold_right',axiom,
    c_24__type__5038___24t(cCoq_2eLists_2eList_2efold__right) ).

fof('$_typeof_Coq.Lists.List.hd',axiom,
    c_24__type__89690___24t(cCoq_2eLists_2eList_2ehd) ).

fof('$_typeof_Coq.Lists.List.last',axiom,
    c_24__type__117906___24t(cCoq_2eLists_2eList_2elast) ).

fof('$_typeof_Coq.Lists.List.map',axiom,
    c_24__type__89772___24t(cCoq_2eLists_2eList_2emap) ).

fof('$_typeof_Coq.Lists.List.nth',axiom,
    c_24__type__89733___24t(cCoq_2eLists_2eList_2enth) ).

fof('$_typeof_Coq.Lists.SetoidList.transpose',axiom,
    c_24__type__112771___24t(cCoq_2eLists_2eSetoidList_2etranspose) ).

fof('$_typeof_Coq.Lists.SetoidList.transpose2',axiom,
    c_24__type__112771___24t(cCoq_2eLists_2eSetoidList_2etranspose2) ).

fof('$_typeof_Coq.Lists.SetoidList.transpose_restr',axiom,
    c_24__type__112814___24t(cCoq_2eLists_2eSetoidList_2etranspose__restr) ).

fof('$_typeof_Coq.Lists.SetoidList.transpose_restr2',axiom,
    c_24__type__112814___24t(cCoq_2eLists_2eSetoidList_2etranspose__restr2) ).

fof('$_typeof_Coq.Logic.Decidable.decidable',axiom,
    c_24__type__107638___24t(cCoq_2eLogic_2eDecidable_2edecidable) ).

fof('$_typeof_Coq.Logic.EqdepFacts.UIP_on_',axiom,
    c_24__type__120908___24t(cCoq_2eLogic_2eEqdepFacts_2eUIP__on__) ).

fof('$_typeof_Coq.NArith.BinNat.N.divide',axiom,
    c_24__type__113571___24t(cCoq_2eNArith_2eBinNat_2eN_2edivide) ).

fof('$_typeof_Coq.NArith.BinNat.N.eq',axiom,
    c_24__type__113571___24t(cCoq_2eNArith_2eBinNat_2eN_2eeq) ).

fof('$_typeof_Coq.NArith.BinNat.N.eqf',axiom,
    c_24__type__120317___24t(cCoq_2eNArith_2eBinNat_2eN_2eeqf) ).

fof('$_typeof_Coq.NArith.BinNat.N.le',axiom,
    c_24__type__113571___24t(cCoq_2eNArith_2eBinNat_2eN_2ele) ).

fof('$_typeof_Coq.NArith.BinNat.N.lt',axiom,
    c_24__type__113571___24t(cCoq_2eNArith_2eBinNat_2eN_2elt) ).

fof('$_typeof_Coq.NArith.BinNat.N.recursion',axiom,
    c_24__type__122209___24t(cCoq_2eNArith_2eBinNat_2eN_2erecursion) ).

fof('$_typeof_Coq.NArith.BinNatDef.N.add',axiom,
    c_24__type__981___24t(cCoq_2eNArith_2eBinNatDef_2eN_2eadd) ).

fof('$_typeof_Coq.NArith.BinNatDef.N.div2',axiom,
    c_24__type__295___24t(cCoq_2eNArith_2eBinNatDef_2eN_2ediv2) ).

fof('$_typeof_Coq.NArith.BinNatDef.N.double',axiom,
    c_24__type__295___24t(cCoq_2eNArith_2eBinNatDef_2eN_2edouble) ).

fof('$_typeof_Coq.NArith.BinNatDef.N.eqb',axiom,
    c_24__type__305___24t(cCoq_2eNArith_2eBinNatDef_2eN_2eeqb) ).

fof('$_typeof_Coq.NArith.BinNatDef.N.even',axiom,
    c_24__type__313___24t(cCoq_2eNArith_2eBinNatDef_2eN_2eeven) ).

fof('$_typeof_Coq.NArith.BinNatDef.N.lxor',axiom,
    c_24__type__981___24t(cCoq_2eNArith_2eBinNatDef_2eN_2elxor) ).

fof('$_typeof_Coq.NArith.BinNatDef.N.max',axiom,
    c_24__type__981___24t(cCoq_2eNArith_2eBinNatDef_2eN_2emax) ).

fof('$_typeof_Coq.NArith.BinNatDef.N.min',axiom,
    c_24__type__981___24t(cCoq_2eNArith_2eBinNatDef_2eN_2emin) ).

fof('$_typeof_Coq.NArith.BinNatDef.N.mul',axiom,
    c_24__type__981___24t(cCoq_2eNArith_2eBinNatDef_2eN_2emul) ).

fof('$_typeof_Coq.NArith.BinNatDef.N.pred',axiom,
    c_24__type__295___24t(cCoq_2eNArith_2eBinNatDef_2eN_2epred) ).

fof('$_typeof_Coq.NArith.BinNatDef.N.succ',axiom,
    c_24__type__295___24t(cCoq_2eNArith_2eBinNatDef_2eN_2esucc) ).

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__305___24t(cCoq_2eNArith_2eBinNatDef_2eN_2etestbit) ).

fof('$_typeof_Coq.NArith.BinNatDef.N.to_nat',axiom,
    c_24__type__113565___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.Ndigits.eqf',axiom,
    c_24__type__117936___24t(cCoq_2eNArith_2eNdigits_2eeqf) ).

fof('$_typeof_Coq.Numbers.BinNums.N',axiom,
    cType___24t(cCoq_2eNumbers_2eBinNums_2eN) ).

fof('$_typeof_Coq.Numbers.BinNums.N0',axiom,
    cCoq_2eNumbers_2eBinNums_2eN___24t(cCoq_2eNumbers_2eBinNums_2eN0) ).

fof('$_typeof_Coq.Numbers.BinNums.Npos',axiom,
    c_24__type__326___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__14035___24t(cCoq_2eNumbers_2eBinNums_2eZneg) ).

fof('$_typeof_Coq.Numbers.BinNums.Zpos',axiom,
    c_24__type__14035___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__983___24t(cCoq_2eNumbers_2eBinNums_2exI) ).

fof('$_typeof_Coq.Numbers.BinNums.xO',axiom,
    c_24__type__983___24t(cCoq_2eNumbers_2eBinNums_2exO) ).

fof('$_typeof_Coq.PArith.BinPos.Pos.PeanoView',axiom,
    c_24__type__113691___24t(cCoq_2ePArith_2eBinPos_2ePos_2ePeanoView) ).

fof('$_typeof_Coq.PArith.BinPos.Pos.eq',axiom,
    c_24__type__107019___24t(cCoq_2ePArith_2eBinPos_2ePos_2eeq) ).

fof('$_typeof_Coq.PArith.BinPos.Pos.le',axiom,
    c_24__type__107019___24t(cCoq_2ePArith_2eBinPos_2ePos_2ele) ).

fof('$_typeof_Coq.PArith.BinPos.Pos.lt',axiom,
    c_24__type__107019___24t(cCoq_2ePArith_2eBinPos_2ePos_2elt) ).

fof('$_typeof_Coq.PArith.BinPos.Pos.switch_Eq',axiom,
    c_24__type__122302___24t(cCoq_2ePArith_2eBinPos_2ePos_2eswitch__Eq) ).

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__113589___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2eIsPos) ).

fof('$_typeof_Coq.PArith.BinPosDef.Pos.add',axiom,
    c_24__type__107075___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2eadd) ).

fof('$_typeof_Coq.PArith.BinPosDef.Pos.compare',axiom,
    c_24__type__113613___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare) ).

fof('$_typeof_Coq.PArith.BinPosDef.Pos.div2',axiom,
    c_24__type__983___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2ediv2) ).

fof('$_typeof_Coq.PArith.BinPosDef.Pos.eqb',axiom,
    c_24__type__119946___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2eeqb) ).

fof('$_typeof_Coq.PArith.BinPosDef.Pos.iter',axiom,
    c_24__type__113607___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2eiter) ).

fof('$_typeof_Coq.PArith.BinPosDef.Pos.iter_op',axiom,
    c_24__type__113627___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2eiter__op) ).

fof('$_typeof_Coq.PArith.BinPosDef.Pos.mask',axiom,
    cType___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2emask) ).

fof('$_typeof_Coq.PArith.BinPosDef.Pos.max',axiom,
    c_24__type__107075___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2emax) ).

fof('$_typeof_Coq.PArith.BinPosDef.Pos.min',axiom,
    c_24__type__107075___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2emin) ).

fof('$_typeof_Coq.PArith.BinPosDef.Pos.mul',axiom,
    c_24__type__107075___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2emul) ).

fof('$_typeof_Coq.PArith.BinPosDef.Pos.of_nat',axiom,
    c_24__type__122281___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2eof__nat) ).

fof('$_typeof_Coq.PArith.BinPosDef.Pos.of_succ_nat',axiom,
    c_24__type__122281___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2eof__succ__nat) ).

fof('$_typeof_Coq.PArith.BinPosDef.Pos.size_nat',axiom,
    c_24__type__120432___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2esize__nat) ).

fof('$_typeof_Coq.PArith.BinPosDef.Pos.sub',axiom,
    c_24__type__107075___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2esub) ).

fof('$_typeof_Coq.PArith.BinPosDef.Pos.succ',axiom,
    c_24__type__983___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2esucc) ).

fof('$_typeof_Coq.PArith.BinPosDef.Pos.t',axiom,
    cType___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2et) ).

fof('$_typeof_Coq.PArith.BinPosDef.Pos.testbit_nat',axiom,
    c_24__type__122274___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2etestbit__nat) ).

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__109641___24t(cCoq_2eQArith_2eQArith__base_2eQden) ).

fof('$_typeof_Coq.QArith.QArith_base.Qmake',axiom,
    c_24__type__91218___24t(cCoq_2eQArith_2eQArith__base_2eQmake) ).

fof('$_typeof_Coq.QArith.QArith_base.Qnum',axiom,
    c_24__type__109636___24t(cCoq_2eQArith_2eQArith__base_2eQnum) ).

fof('$_typeof_Coq.Reals.RIneq.Rsqr',axiom,
    c_24__type__109827___24t(cCoq_2eReals_2eRIneq_2eRsqr) ).

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.IZR',axiom,
    c_24__type__118013___24t(cCoq_2eReals_2eRdefinitions_2eIZR) ).

fof('$_typeof_Coq.Reals.Rdefinitions.R',axiom,
    cType___24t(cCoq_2eReals_2eRdefinitions_2eR) ).

fof('$_typeof_Coq.Reals.Rdefinitions.R0',axiom,
    cCoq_2eReals_2eRdefinitions_2eR___24t(cCoq_2eReals_2eRdefinitions_2eR0) ).

fof('$_typeof_Coq.Reals.Rdefinitions.R1',axiom,
    cCoq_2eReals_2eRdefinitions_2eR___24t(cCoq_2eReals_2eRdefinitions_2eR1) ).

fof('$_typeof_Coq.Reals.Rdefinitions.Rge',axiom,
    c_24__type__109830___24t(cCoq_2eReals_2eRdefinitions_2eRge) ).

fof('$_typeof_Coq.Reals.Rdefinitions.Rgt',axiom,
    c_24__type__109830___24t(cCoq_2eReals_2eRdefinitions_2eRgt) ).

fof('$_typeof_Coq.Reals.Rdefinitions.Rinv',axiom,
    c_24__type__109827___24t(cCoq_2eReals_2eRdefinitions_2eRinv) ).

fof('$_typeof_Coq.Reals.Rdefinitions.Rle',axiom,
    c_24__type__109830___24t(cCoq_2eReals_2eRdefinitions_2eRle) ).

fof('$_typeof_Coq.Reals.Rdefinitions.Rlt',axiom,
    c_24__type__109830___24t(cCoq_2eReals_2eRdefinitions_2eRlt) ).

fof('$_typeof_Coq.Reals.Rdefinitions.Rmult',axiom,
    c_24__type__109824___24t(cCoq_2eReals_2eRdefinitions_2eRmult) ).

fof('$_typeof_Coq.Reals.Rdefinitions.Ropp',axiom,
    c_24__type__109827___24t(cCoq_2eReals_2eRdefinitions_2eRopp) ).

fof('$_typeof_Coq.Reals.Rdefinitions.Rplus',axiom,
    c_24__type__109824___24t(cCoq_2eReals_2eRdefinitions_2eRplus) ).

fof('$_typeof_Coq.Reals.Rdefinitions.up',axiom,
    c_24__type__109832___24t(cCoq_2eReals_2eRdefinitions_2eup) ).

fof('$_typeof_Coq.Reals.Rfunctions.Z_spec',axiom,
    c_24__type__110469___24t(cCoq_2eReals_2eRfunctions_2eZ__spec) ).

fof('$_typeof_Coq.Relations.Relation_Definitions.relation',axiom,
    c_24__type__14___24t(cCoq_2eRelations_2eRelation__Definitions_2erelation) ).

fof('$_typeof_Coq.Setoids.Setoid.Setoid_Theory',axiom,
    c_24__type__112711___24t(cCoq_2eSetoids_2eSetoid_2eSetoid__Theory) ).

fof('$_typeof_Coq.Sets.Relations_1.Relation',axiom,
    c_24__type__14___24t(cCoq_2eSets_2eRelations__1_2eRelation) ).

fof('$_typeof_Coq.Strings.Ascii.Ascii',axiom,
    c_24__type__107422___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,
    c_24__type__104292___24t(cCoq_2eStrings_2eString_2eString) ).

fof('$_typeof_Coq.Strings.String.string',axiom,
    cType___24t(cCoq_2eStrings_2eString_2estring) ).

fof('$_typeof_Coq.Structures.GenericMinMax.gmax',axiom,
    c_24__type__120929___24t(cCoq_2eStructures_2eGenericMinMax_2egmax) ).

fof('$_typeof_Coq.Structures.GenericMinMax.gmin',axiom,
    c_24__type__120929___24t(cCoq_2eStructures_2eGenericMinMax_2egmin) ).

fof('$_typeof_Coq.Structures.OrderedType.Compare',axiom,
    c_24__type__109551___24t(cCoq_2eStructures_2eOrderedType_2eCompare) ).

fof('$_typeof_Coq.Structures.OrderedTypeEx.N_as_OT.eq',axiom,
    c_24__type__113571___24t(cCoq_2eStructures_2eOrderedTypeEx_2eN__as__OT_2eeq) ).

fof('$_typeof_Coq.Structures.OrderedTypeEx.N_as_OT.lt',axiom,
    c_24__type__113571___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__5091___24t(cCoq_2eStructures_2eOrderedTypeEx_2eNat__as__OT_2eeq) ).

fof('$_typeof_Coq.Structures.OrderedTypeEx.Nat_as_OT.lt',axiom,
    c_24__type__5091___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__107019___24t(cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2ebits__lt) ).

fof('$_typeof_Coq.Structures.OrderedTypeEx.PositiveOrderedTypeBits.eq',axiom,
    c_24__type__107019___24t(cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2eeq) ).

fof('$_typeof_Coq.Structures.OrderedTypeEx.PositiveOrderedTypeBits.lt',axiom,
    c_24__type__107019___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__107019___24t(cCoq_2eStructures_2eOrderedTypeEx_2ePositive__as__OT_2eeq) ).

fof('$_typeof_Coq.Structures.OrderedTypeEx.Positive_as_OT.lt',axiom,
    c_24__type__107019___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.lt',axiom,
    c_24__type__122309___24t(cCoq_2eStructures_2eOrderedTypeEx_2eString__as__OT_2elt) ).

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__14014___24t(cCoq_2eStructures_2eOrderedTypeEx_2eZ__as__OT_2eeq) ).

fof('$_typeof_Coq.Structures.OrderedTypeEx.Z_as_OT.lt',axiom,
    c_24__type__14014___24t(cCoq_2eStructures_2eOrderedTypeEx_2eZ__as__OT_2elt) ).

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__109156___24t(cCoq_2eVectors_2eFin_2et) ).

fof('$_typeof_Coq.Vectors.VectorDef.t',axiom,
    c_24__type__113232___24t(cCoq_2eVectors_2eVectorDef_2et) ).

fof('$_typeof_Coq.ZArith.BinInt.Z.Private_Div.Quot2Div.div',axiom,
    c_24__type__106545___24t(cCoq_2eZArith_2eBinInt_2eZ_2ePrivate__Div_2eQuot2Div_2ediv) ).

fof('$_typeof_Coq.ZArith.BinInt.Z.Private_Div.Quot2Div.modulo',axiom,
    c_24__type__106545___24t(cCoq_2eZArith_2eBinInt_2eZ_2ePrivate__Div_2eQuot2Div_2emodulo) ).

fof('$_typeof_Coq.ZArith.BinInt.Z.divide',axiom,
    c_24__type__14014___24t(cCoq_2eZArith_2eBinInt_2eZ_2edivide) ).

fof('$_typeof_Coq.ZArith.BinInt.Z.eq',axiom,
    c_24__type__14014___24t(cCoq_2eZArith_2eBinInt_2eZ_2eeq) ).

fof('$_typeof_Coq.ZArith.BinInt.Z.eqf',axiom,
    c_24__type__122328___24t(cCoq_2eZArith_2eBinInt_2eZ_2eeqf) ).

fof('$_typeof_Coq.ZArith.BinInt.Z.ge',axiom,
    c_24__type__14014___24t(cCoq_2eZArith_2eBinInt_2eZ_2ege) ).

fof('$_typeof_Coq.ZArith.BinInt.Z.gt',axiom,
    c_24__type__14014___24t(cCoq_2eZArith_2eBinInt_2eZ_2egt) ).

fof('$_typeof_Coq.ZArith.BinInt.Z.le',axiom,
    c_24__type__14014___24t(cCoq_2eZArith_2eBinInt_2eZ_2ele) ).

fof('$_typeof_Coq.ZArith.BinInt.Z.lt',axiom,
    c_24__type__14014___24t(cCoq_2eZArith_2eBinInt_2eZ_2elt) ).

fof('$_typeof_Coq.ZArith.BinInt.Zne',axiom,
    c_24__type__14014___24t(cCoq_2eZArith_2eBinInt_2eZne) ).

fof('$_typeof_Coq.ZArith.BinIntDef.Z.abs',axiom,
    c_24__type__107326___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2eabs) ).

fof('$_typeof_Coq.ZArith.BinIntDef.Z.abs_N',axiom,
    c_24__type__108007___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2eabs__N) ).

fof('$_typeof_Coq.ZArith.BinIntDef.Z.abs_nat',axiom,
    c_24__type__122313___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2eabs__nat) ).

fof('$_typeof_Coq.ZArith.BinIntDef.Z.add',axiom,
    c_24__type__106545___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2eadd) ).

fof('$_typeof_Coq.ZArith.BinIntDef.Z.compare',axiom,
    c_24__type__107360___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare) ).

fof('$_typeof_Coq.ZArith.BinIntDef.Z.div',axiom,
    c_24__type__106545___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2ediv) ).

fof('$_typeof_Coq.ZArith.BinIntDef.Z.even',axiom,
    c_24__type__115933___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2eeven) ).

fof('$_typeof_Coq.ZArith.BinIntDef.Z.leb',axiom,
    c_24__type__106985___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2eleb) ).

fof('$_typeof_Coq.ZArith.BinIntDef.Z.max',axiom,
    c_24__type__106545___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2emax) ).

fof('$_typeof_Coq.ZArith.BinIntDef.Z.min',axiom,
    c_24__type__106545___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2emin) ).

fof('$_typeof_Coq.ZArith.BinIntDef.Z.modulo',axiom,
    c_24__type__106545___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2emodulo) ).

fof('$_typeof_Coq.ZArith.BinIntDef.Z.mul',axiom,
    c_24__type__106545___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2emul) ).

fof('$_typeof_Coq.ZArith.BinIntDef.Z.odd',axiom,
    c_24__type__115933___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2eodd) ).

fof('$_typeof_Coq.ZArith.BinIntDef.Z.of_N',axiom,
    c_24__type__107365___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2eof__N) ).

fof('$_typeof_Coq.ZArith.BinIntDef.Z.opp',axiom,
    c_24__type__107326___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2eopp) ).

fof('$_typeof_Coq.ZArith.BinIntDef.Z.pow',axiom,
    c_24__type__106545___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2epow) ).

fof('$_typeof_Coq.ZArith.BinIntDef.Z.pred',axiom,
    c_24__type__107326___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2epred) ).

fof('$_typeof_Coq.ZArith.BinIntDef.Z.sub',axiom,
    c_24__type__106545___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2esub) ).

fof('$_typeof_Coq.ZArith.BinIntDef.Z.succ',axiom,
    c_24__type__107326___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_N',axiom,
    c_24__type__108007___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2eto__N) ).

fof('$_typeof_Coq.ZArith.BinIntDef.Z.to_nat',axiom,
    c_24__type__122313___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2eto__nat) ).

fof('$_typeof_Coq.ZArith.BinIntDef.Z.to_pos',axiom,
    c_24__type__113782___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__106985___24t(cCoq_2eZArith_2eZbool_2eZeq__bool) ).

fof('$_typeof_Coq.ZArith.Zeven.Zeven',axiom,
    c_24__type__89842___24t(cCoq_2eZArith_2eZeven_2eZeven) ).

fof('$_typeof_Coq.ZArith.Zeven.Zodd',axiom,
    c_24__type__89842___24t(cCoq_2eZArith_2eZeven_2eZodd) ).

fof('$_typeof_Coq.ZArith.Zlogarithm.Is_power',axiom,
    c_24__type__985___24t(cCoq_2eZArith_2eZlogarithm_2eIs__power) ).

fof('$_typeof_Coq.ZArith.Zlogarithm.log_inf',axiom,
    c_24__type__14035___24t(cCoq_2eZArith_2eZlogarithm_2elog__inf) ).

fof('$_typeof_Coq.ZArith.Znumtheory.Euclid',axiom,
    c_24__type__110469___24t(cCoq_2eZArith_2eZnumtheory_2eEuclid) ).

fof('$_typeof_Coq.ZArith.Zpower.Zdiv_rest_proofs',axiom,
    c_24__type__113469___24t(cCoq_2eZArith_2eZpower_2eZdiv__rest__proofs) ).

fof('$_typeof_Coq.micromega.Env.Env',axiom,
    c_24__type__14___24t(cCoq_2emicromega_2eEnv_2eEnv) ).

fof('$_typeof_Coq.micromega.EnvRing.Mon',axiom,
    cType___24t(cCoq_2emicromega_2eEnvRing_2eMon) ).

fof('$_typeof_Coq.micromega.EnvRing.PEX',axiom,
    c_24__type__107692___24t(cCoq_2emicromega_2eEnvRing_2ePEX) ).

fof('$_typeof_Coq.micromega.EnvRing.PEc',axiom,
    c_24__type__107689___24t(cCoq_2emicromega_2eEnvRing_2ePEc) ).

fof('$_typeof_Coq.micromega.EnvRing.PExpr',axiom,
    c_24__type__14___24t(cCoq_2emicromega_2eEnvRing_2ePExpr) ).

fof('$_typeof_Coq.micromega.EnvRing.PX',axiom,
    c_24__type__85933___24t(cCoq_2emicromega_2eEnvRing_2ePX) ).

fof('$_typeof_Coq.micromega.EnvRing.Pc',axiom,
    c_24__type__85920___24t(cCoq_2emicromega_2eEnvRing_2ePc) ).

fof('$_typeof_Coq.micromega.EnvRing.Pinj',axiom,
    c_24__type__85925___24t(cCoq_2emicromega_2eEnvRing_2ePinj) ).

fof('$_typeof_Coq.micromega.EnvRing.Pol',axiom,
    c_24__type__14___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.EnvRing.vmon',axiom,
    c_24__type__120898___24t(cCoq_2emicromega_2eEnvRing_2evmon) ).

fof('$_typeof_Coq.micromega.EnvRing.zmon',axiom,
    c_24__type__120898___24t(cCoq_2emicromega_2eEnvRing_2ezmon) ).

fof('$_typeof_Coq.micromega.QMicromega.QWitness',axiom,
    cType___24t(cCoq_2emicromega_2eQMicromega_2eQWitness) ).

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.CInv',axiom,
    c_24__type__121354___24t(cCoq_2emicromega_2eRMicromega_2eCInv) ).

fof('$_typeof_Coq.micromega.RMicromega.CMinus',axiom,
    c_24__type__121350___24t(cCoq_2emicromega_2eRMicromega_2eCMinus) ).

fof('$_typeof_Coq.micromega.RMicromega.CMult',axiom,
    c_24__type__121350___24t(cCoq_2emicromega_2eRMicromega_2eCMult) ).

fof('$_typeof_Coq.micromega.RMicromega.COpp',axiom,
    c_24__type__121354___24t(cCoq_2emicromega_2eRMicromega_2eCOpp) ).

fof('$_typeof_Coq.micromega.RMicromega.CPlus',axiom,
    c_24__type__121350___24t(cCoq_2emicromega_2eRMicromega_2eCPlus) ).

fof('$_typeof_Coq.micromega.RMicromega.CQ',axiom,
    c_24__type__117969___24t(cCoq_2emicromega_2eRMicromega_2eCQ) ).

fof('$_typeof_Coq.micromega.RMicromega.CZ',axiom,
    c_24__type__121347___24t(cCoq_2emicromega_2eRMicromega_2eCZ) ).

fof('$_typeof_Coq.micromega.RMicromega.RWitness',axiom,
    cType___24t(cCoq_2emicromega_2eRMicromega_2eRWitness) ).

fof('$_typeof_Coq.micromega.RMicromega.Rcst',axiom,
    cType___24t(cCoq_2emicromega_2eRMicromega_2eRcst) ).

fof('$_typeof_Coq.micromega.Refl.make_conj',axiom,
    c_24__type__5117___24t(cCoq_2emicromega_2eRefl_2emake__conj) ).

fof('$_typeof_Coq.micromega.Refl.make_impl',axiom,
    c_24__type__91245___24t(cCoq_2emicromega_2eRefl_2emake__impl) ).

fof('$_typeof_Coq.micromega.RingMicromega.Build_Formula',axiom,
    c_24__type__173538___24t(cCoq_2emicromega_2eRingMicromega_2eBuild__Formula) ).

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__14___24t(cCoq_2emicromega_2eRingMicromega_2eFormula) ).

fof('$_typeof_Coq.micromega.RingMicromega.NFormula',axiom,
    c_24__type__14___24t(cCoq_2emicromega_2eRingMicromega_2eNFormula) ).

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__14___24t(cCoq_2emicromega_2eRingMicromega_2ePolC) ).

fof('$_typeof_Coq.micromega.RingMicromega.PolEnv',axiom,
    c_24__type__14___24t(cCoq_2emicromega_2eRingMicromega_2ePolEnv) ).

fof('$_typeof_Coq.micromega.RingMicromega.Psatz',axiom,
    c_24__type__14___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.RingMicromega.eval_op1',axiom,
    c_24__type__96968___24t(cCoq_2emicromega_2eRingMicromega_2eeval__op1) ).

fof('$_typeof_Coq.micromega.RingMicromega.eval_pol',axiom,
    c_24__type__96883___24t(cCoq_2emicromega_2eRingMicromega_2eeval__pol) ).

fof('$_typeof_Coq.micromega.RingMicromega.ge_bool',axiom,
    c_24__type__89840___24t(cCoq_2emicromega_2eRingMicromega_2ege__bool) ).

fof('$_typeof_Coq.micromega.Tauto.A',axiom,
    c_24__type__12098___24t(cCoq_2emicromega_2eTauto_2eA) ).

fof('$_typeof_Coq.micromega.Tauto.BFormula',axiom,
    c_24__type__14___24t(cCoq_2emicromega_2eTauto_2eBFormula) ).

fof('$_typeof_Coq.micromega.Tauto.Cj',axiom,
    c_24__type__12115___24t(cCoq_2emicromega_2eTauto_2eCj) ).

fof('$_typeof_Coq.micromega.Tauto.D',axiom,
    c_24__type__12115___24t(cCoq_2emicromega_2eTauto_2eD) ).

fof('$_typeof_Coq.micromega.Tauto.FF',axiom,
    c_24__type__12063___24t(cCoq_2emicromega_2eTauto_2eFF) ).

fof('$_typeof_Coq.micromega.Tauto.GFormula',axiom,
    c_24__type__2108___24t(cCoq_2emicromega_2eTauto_2eGFormula) ).

fof('$_typeof_Coq.micromega.Tauto.I',axiom,
    c_24__type__2518___24t(cCoq_2emicromega_2eTauto_2eI) ).

fof('$_typeof_Coq.micromega.Tauto.N',axiom,
    c_24__type__12142___24t(cCoq_2emicromega_2eTauto_2eN) ).

fof('$_typeof_Coq.micromega.Tauto.TFormula',axiom,
    c_24__type__2108___24t(cCoq_2emicromega_2eTauto_2eTFormula) ).

fof('$_typeof_Coq.micromega.Tauto.TT',axiom,
    c_24__type__12063___24t(cCoq_2emicromega_2eTauto_2eTT) ).

fof('$_typeof_Coq.micromega.Tauto.X',axiom,
    c_24__type__12081___24t(cCoq_2emicromega_2eTauto_2eX) ).

fof('$_typeof_Coq.micromega.Tauto.and_cnf',axiom,
    c_24__type__12873___24t(cCoq_2emicromega_2eTauto_2eand__cnf) ).

fof('$_typeof_Coq.micromega.Tauto.clause',axiom,
    c_24__type__2568___24t(cCoq_2emicromega_2eTauto_2eclause) ).

fof('$_typeof_Coq.micromega.Tauto.cnf',axiom,
    c_24__type__2568___24t(cCoq_2emicromega_2eTauto_2ecnf) ).

fof('$_typeof_Coq.micromega.Tauto.cnf_ff',axiom,
    c_24__type__12694___24t(cCoq_2emicromega_2eTauto_2ecnf__ff) ).

fof('$_typeof_Coq.micromega.Tauto.cnf_tt',axiom,
    c_24__type__12694___24t(cCoq_2emicromega_2eTauto_2ecnf__tt) ).

fof('$_typeof_Coq.micromega.Tauto.eval_bf',axiom,
    c_24__type__113899___24t(cCoq_2emicromega_2eTauto_2eeval__bf) ).

fof('$_typeof_Coq.micromega.Tauto.eval_clause',axiom,
    c_24__type__13396___24t(cCoq_2emicromega_2eTauto_2eeval__clause) ).

fof('$_typeof_Coq.micromega.Tauto.eval_cnf',axiom,
    c_24__type__13427___24t(cCoq_2emicromega_2eTauto_2eeval__cnf) ).

fof('$_typeof_Coq.micromega.Tauto.eval_f',axiom,
    c_24__type__105131___24t(cCoq_2emicromega_2eTauto_2eeval__f) ).

fof('$_typeof_Coq.micromega.Tauto.eval_tt',axiom,
    c_24__type__106212___24t(cCoq_2emicromega_2eTauto_2eeval__tt) ).

fof('$_typeof_Coq.micromega.VarMap.t',axiom,
    c_24__type__14___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.Vars.Facts.Add',axiom,
    c_24__type__122191___24t(cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eAdd) ).

fof('$_typeof_Coq.micromega.ZMicromega.Vars.max_element',axiom,
    c_24__type__107291___24t(cCoq_2emicromega_2eZMicromega_2eVars_2emax__element) ).

fof('$_typeof_Coq.micromega.ZMicromega.ZArithProof',axiom,
    cType___24t(cCoq_2emicromega_2eZMicromega_2eZArithProof) ).

fof('$_typeof_Coq.micromega.ZMicromega.ZWitness',axiom,
    cType___24t(cCoq_2emicromega_2eZMicromega_2eZWitness) ).

fof('$_typeof_Coq.micromega.ZMicromega.Zeval_op2',axiom,
    c_24__type__173588___24t(cCoq_2emicromega_2eZMicromega_2eZeval__op2) ).

fof('$_typeof_Coq.micromega.ZMicromega.Zunsat',axiom,
    c_24__type__172843___24t(cCoq_2emicromega_2eZMicromega_2eZunsat) ).

fof('$_typeof_Coq.micromega.ZMicromega.agree_env',axiom,
    c_24__type__113922___24t(cCoq_2emicromega_2eZMicromega_2eagree__env) ).

fof('$_typeof_Coq.micromega.ZMicromega.coneMember',axiom,
    cType___24t(cCoq_2emicromega_2eZMicromega_2econeMember) ).

fof('$_typeof_Coq.omega.PreOmega.Z_of_N\'',axiom,
    c_24__type__107365___24t(cCoq_2eomega_2ePreOmega_2eZ__of__N_27) ).

fof('$_typeof_Coq.omega.PreOmega.Z_of_nat\'',axiom,
    c_24__type__113778___24t(cCoq_2eomega_2ePreOmega_2eZ__of__nat_27) ).

fof('$_typeof_Coq.omega.PreOmega.Zneg\'',axiom,
    c_24__type__14035___24t(cCoq_2eomega_2ePreOmega_2eZneg_27) ).

fof('$_typeof_Coq.omega.PreOmega.Zpos\'',axiom,
    c_24__type__14035___24t(cCoq_2eomega_2ePreOmega_2eZpos_27) ).

fof('$_typeof_Coq.setoid_ring.ArithRing.protected_to_nat',axiom,
    c_24__type__113565___24t(cCoq_2esetoid__ring_2eArithRing_2eprotected__to__nat) ).

fof('$_typeof_Coq.setoid_ring.Field_theory.FEX',axiom,
    c_24__type__117554___24t(cCoq_2esetoid__ring_2eField__theory_2eFEX) ).

fof('$_typeof_Coq.setoid_ring.Field_theory.FEc',axiom,
    c_24__type__120913___24t(cCoq_2esetoid__ring_2eField__theory_2eFEc) ).

fof('$_typeof_Coq.setoid_ring.Field_theory.FEinv',axiom,
    c_24__type__117562___24t(cCoq_2esetoid__ring_2eField__theory_2eFEinv) ).

fof('$_typeof_Coq.setoid_ring.Field_theory.FEmul',axiom,
    c_24__type__117559___24t(cCoq_2esetoid__ring_2eField__theory_2eFEmul) ).

fof('$_typeof_Coq.setoid_ring.Field_theory.FExpr',axiom,
    c_24__type__14___24t(cCoq_2esetoid__ring_2eField__theory_2eFExpr) ).

fof('$_typeof_Coq.setoid_ring.Field_theory.linear',axiom,
    c_24__type__14___24t(cCoq_2esetoid__ring_2eField__theory_2elinear) ).

fof('$_typeof_Coq.setoid_ring.Field_theory.rsplit',axiom,
    c_24__type__14___24t(cCoq_2esetoid__ring_2eField__theory_2ersplit) ).

fof('$_typeof_Coq.setoid_ring.InitialRing.Nopp',axiom,
    c_24__type__295___24t(cCoq_2esetoid__ring_2eInitialRing_2eNopp) ).

fof('$_typeof_Coq.setoid_ring.InitialRing.NotConstant',axiom,
    cCoq_2eInit_2eDatatypes_2ebool___24t(cCoq_2esetoid__ring_2eInitialRing_2eNotConstant) ).

fof('$_typeof_Coq.setoid_ring.InitialRing.Nword',axiom,
    cType___24t(cCoq_2esetoid__ring_2eInitialRing_2eNword) ).

fof('$_typeof_Coq.setoid_ring.InitialRing.gen_phiPOS',axiom,
    c_24__type__109192___24t(cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS) ).

fof('$_typeof_Coq.setoid_ring.InitialRing.gen_phiPOS1',axiom,
    c_24__type__109192___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.InitialRing.mkhypo',axiom,
    c_24__type__120948___24t(cCoq_2esetoid__ring_2eInitialRing_2emkhypo) ).

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__110504___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePEI) ).

fof('$_typeof_Coq.setoid_ring.Ring_polynom.PEO',axiom,
    c_24__type__110504___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePEO) ).

fof('$_typeof_Coq.setoid_ring.Ring_polynom.PEX',axiom,
    c_24__type__110510___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePEX) ).

fof('$_typeof_Coq.setoid_ring.Ring_polynom.PEadd',axiom,
    c_24__type__5523___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePEadd) ).

fof('$_typeof_Coq.setoid_ring.Ring_polynom.PEc',axiom,
    c_24__type__110507___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePEc) ).

fof('$_typeof_Coq.setoid_ring.Ring_polynom.PEmul',axiom,
    c_24__type__5523___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePEmul) ).

fof('$_typeof_Coq.setoid_ring.Ring_polynom.PEopp',axiom,
    c_24__type__110519___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePEopp) ).

fof('$_typeof_Coq.setoid_ring.Ring_polynom.PEsub',axiom,
    c_24__type__5523___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePEsub) ).

fof('$_typeof_Coq.setoid_ring.Ring_polynom.PExpr',axiom,
    c_24__type__14___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr) ).

fof('$_typeof_Coq.setoid_ring.Ring_polynom.PX',axiom,
    c_24__type__98284___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePX) ).

fof('$_typeof_Coq.setoid_ring.Ring_polynom.Pc',axiom,
    c_24__type__98271___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePc) ).

fof('$_typeof_Coq.setoid_ring.Ring_polynom.Peq',axiom,
    c_24__type__98426___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePeq) ).

fof('$_typeof_Coq.setoid_ring.Ring_polynom.Pinj',axiom,
    c_24__type__98276___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePinj) ).

fof('$_typeof_Coq.setoid_ring.Ring_polynom.Pol',axiom,
    c_24__type__14___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePol) ).

fof('$_typeof_Coq.setoid_ring.Ring_polynom.mkmult_pow',axiom,
    c_24__type__103711___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_polynom.vmon',axiom,
    c_24__type__99179___24t(cCoq_2esetoid__ring_2eRing__polynom_2evmon) ).

fof('$_typeof_Coq.setoid_ring.Ring_polynom.zmon',axiom,
    c_24__type__99179___24t(cCoq_2esetoid__ring_2eRing__polynom_2ezmon) ).

fof('$_typeof_Coq.setoid_ring.Ring_tac.ring_subst_niter',axiom,
    cCoq_2eInit_2eDatatypes_2enat___24t(cCoq_2esetoid__ring_2eRing__tac_2ering__subst__niter) ).

fof('$_typeof_Coq.setoid_ring.Ring_theory.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__112498___24t(cCoq_2esetoid__ring_2eRing__theory_2eIDphi) ).

fof('$_typeof_Coq.setoid_ring.Ring_theory.SRopp',axiom,
    c_24__type__112498___24t(cCoq_2esetoid__ring_2eRing__theory_2eSRopp) ).

fof('$_typeof_Coq.setoid_ring.Ring_theory.SRsub',axiom,
    c_24__type__118269___24t(cCoq_2esetoid__ring_2eRing__theory_2eSRsub) ).

fof('$_typeof_Coq.setoid_ring.Ring_theory.id_phi_N',axiom,
    c_24__type__295___24t(cCoq_2esetoid__ring_2eRing__theory_2eid__phi__N) ).

fof('$_typeof_Coq.setoid_ring.Ring_theory.pow_N',axiom,
    c_24__type__7661___24t(cCoq_2esetoid__ring_2eRing__theory_2epow__N) ).

fof('$_typeof_Coq.setoid_ring.Ring_theory.pow_pos',axiom,
    c_24__type__7640___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.AllHyps',axiom,
    cHammer_2eTactics_2eReconstr_2eReconstrT___24t(cHammer_2eTactics_2eReconstr_2eAllHyps) ).

fof('$_typeof_Hammer.Tactics.Reconstr.Empty',axiom,
    cHammer_2eTactics_2eReconstr_2eReconstrT___24t(cHammer_2eTactics_2eReconstr_2eEmpty) ).

fof('$_typeof_Hammer.Tactics.Reconstr.ReconstrT',axiom,
    cType___24t(cHammer_2eTactics_2eReconstr_2eReconstrT) ).

fof('$_typeof_Hammer.Tactics.Reconstr.rdone',axiom,
    c_24__type__109836___24t(cHammer_2eTactics_2eReconstr_2erdone) ).

fof('$_typeof_Hammer.Tactics.Tactics.default',axiom,
    cCoq_2eInit_2eDatatypes_2eunit___24t(cHammer_2eTactics_2eTactics_2edefault) ).

fof('$_typeof_Hammer.Tactics.Tactics.hints',axiom,
    cCoq_2eInit_2eDatatypes_2eunit___24t(cHammer_2eTactics_2eTactics_2ehints) ).

fof('$_typeof_Hammer.Tactics.Tactics.logic',axiom,
    cCoq_2eInit_2eDatatypes_2eunit___24t(cHammer_2eTactics_2eTactics_2elogic) ).

fof('$_typeof_Hammer.Tactics.Tactics.nohints',axiom,
    cCoq_2eInit_2eDatatypes_2eunit___24t(cHammer_2eTactics_2eTactics_2enohints) ).

fof('$_typeof_Hammer.Tactics.Tactics.none',axiom,
    cCoq_2eInit_2eDatatypes_2eunit___24t(cHammer_2eTactics_2eTactics_2enone) ).

fof('$_typeof_Hammer.Tactics.Tactics.rdone',axiom,
    c_24__type__109836___24t(cHammer_2eTactics_2eTactics_2erdone) ).

fof('$_typeof_IntMap.Fset.FSet',axiom,
    cType___24t(cIntMap_2eFset_2eFSet) ).

fof('$_typeof_IntMap.Fset.FSetDelta',axiom,
    c_24__type__89676___24t(cIntMap_2eFset_2eFSetDelta) ).

fof('$_typeof_IntMap.Fset.FSetDiff',axiom,
    c_24__type__89676___24t(cIntMap_2eFset_2eFSetDiff) ).

fof('$_typeof_IntMap.Fset.FSetInter',axiom,
    c_24__type__89676___24t(cIntMap_2eFset_2eFSetInter) ).

fof('$_typeof_IntMap.Fset.FSetUnion',axiom,
    c_24__type__89676___24t(cIntMap_2eFset_2eFSetUnion) ).

fof('$_typeof_IntMap.Fset.MapDom',axiom,
    c_24__type__1444___24t(cIntMap_2eFset_2eMapDom) ).

fof('$_typeof_IntMap.Fset.MapDomRestrBy',axiom,
    c_24__type__461___24t(cIntMap_2eFset_2eMapDomRestrBy) ).

fof('$_typeof_IntMap.Fset.MapDomRestrTo',axiom,
    c_24__type__461___24t(cIntMap_2eFset_2eMapDomRestrTo) ).

fof('$_typeof_IntMap.Fset.MapDom_semantics_2',axiom,
    c_24__type__1456___24t(cIntMap_2eFset_2eMapDom__semantics__2) ).

fof('$_typeof_IntMap.Fset.in_FSet',axiom,
    c_24__type__1430___24t(cIntMap_2eFset_2ein__FSet) ).

fof('$_typeof_IntMap.Fset.in_dom',axiom,
    c_24__type__1426___24t(cIntMap_2eFset_2ein__dom) ).

fof('$_typeof_IntMap.Fset.in_dom_some',axiom,
    c_24__type__89670___24t(cIntMap_2eFset_2ein__dom__some) ).

fof('$_typeof_IntMap.Map.M0',axiom,
    c_24__type__605___24t(cIntMap_2eMap_2eM0) ).

fof('$_typeof_IntMap.Map.M1',axiom,
    c_24__type__610___24t(cIntMap_2eMap_2eM1) ).

fof('$_typeof_IntMap.Map.M2',axiom,
    c_24__type__71___24t(cIntMap_2eMap_2eM2) ).

fof('$_typeof_IntMap.Map.Map',axiom,
    c_24__type__14___24t(cIntMap_2eMap_2eMap) ).

fof('$_typeof_IntMap.Map.MapDelta',axiom,
    c_24__type__71___24t(cIntMap_2eMap_2eMapDelta) ).

fof('$_typeof_IntMap.Map.MapGet',axiom,
    c_24__type__146___24t(cIntMap_2eMap_2eMapGet) ).

fof('$_typeof_IntMap.Map.MapMerge',axiom,
    c_24__type__71___24t(cIntMap_2eMap_2eMapMerge) ).

fof('$_typeof_IntMap.Map.MapPut',axiom,
    c_24__type__736___24t(cIntMap_2eMap_2eMapPut) ).

fof('$_typeof_IntMap.Map.MapRemove',axiom,
    c_24__type__874___24t(cIntMap_2eMap_2eMapRemove) ).

fof('$_typeof_IntMap.Map.ad',axiom,
    cType___24t(cIntMap_2eMap_2ead) ).

fof('$_typeof_Mapaxioms.eqmap',axiom,
    c_24__type__183418___24t(cMapaxioms_2eeqmap) ).

fof('Coq.Arith.PeanoNat.Nat.Private_OrderTac.Tac.eq_refl',axiom,
    ! [V0__x] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)
     => V0__x = V0__x ) ).

fof('Coq.Arith.PeanoNat.Nat.Private_OrderTac.Tac.eq_sym',axiom,
    ! [V0__x] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)
     => ! [V1__y] :
          ( cCoq_2eInit_2eDatatypes_2enat___24t(V1__y)
         => ( V0__x = V1__y
           => V1__y = V0__x ) ) ) ).

fof('Coq.Arith.PeanoNat.Nat.Private_OrderTac.Tac.le_antisym',axiom,
    ! [V0__x] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)
     => ! [V1__y] :
          ( cCoq_2eInit_2eDatatypes_2enat___24t(V1__y)
         => ( cCoq_2eInit_2ePeano_2ele___24a2(V0__x,V1__y)
           => ( cCoq_2eInit_2ePeano_2ele___24a2(V1__y,V0__x)
             => V0__x = V1__y ) ) ) ) ).

fof('Coq.Arith.PeanoNat.Nat.Private_OrderTac.Tac.le_refl',axiom,
    ! [V0__x] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)
     => cCoq_2eInit_2ePeano_2ele___24a2(V0__x,V0__x) ) ).

fof('Coq.Arith.PeanoNat.Nat.Private_OrderTac.Tac.lt_irrefl',axiom,
    ! [V0__x] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)
     => ~ cCoq_2eInit_2ePeano_2elt___24a2(V0__x,V0__x) ) ).

fof('Coq.Arith.PeanoNat.Nat.Private_OrderTac.Tac.not_ge_lt',axiom,
    ! [V0__x] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)
     => ! [V1__y] :
          ( cCoq_2eInit_2eDatatypes_2enat___24t(V1__y)
         => ( ~ cCoq_2eInit_2ePeano_2ele___24a2(V1__y,V0__x)
           => cCoq_2eInit_2ePeano_2elt___24a2(V0__x,V1__y) ) ) ) ).

fof('Coq.Arith.PeanoNat.Nat.Private_OrderTac.Tac.not_gt_le',axiom,
    ! [V0__x] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)
     => ! [V1__y] :
          ( cCoq_2eInit_2eDatatypes_2enat___24t(V1__y)
         => ( ~ cCoq_2eInit_2ePeano_2elt___24a2(V1__y,V0__x)
           => cCoq_2eInit_2ePeano_2ele___24a2(V0__x,V1__y) ) ) ) ).

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.Private_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.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.divide_refl',axiom,
    ! [V0__n] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
     => cCoq_2eArith_2ePeanoNat_2eNat_2edivide___24a2(V0__n,V0__n) ) ).

fof('Coq.Arith.PeanoNat.Nat.eq_equiv',axiom,
    cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(cCoq_2eInit_2eDatatypes_2enat,c_3d___24a1(cCoq_2eInit_2eDatatypes_2enat)) ).

fof('Coq.Arith.PeanoNat.Nat.eq_le_incl',axiom,
    ! [V0__n] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
     => ! [V1__m] :
          ( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
         => ( V0__n = V1__m
           => cCoq_2eInit_2ePeano_2ele___24a2(V0__n,V1__m) ) ) ) ).

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_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_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_0_1',axiom,
    cCoq_2eInit_2ePeano_2elt___24a2(cCoq_2eInit_2eDatatypes_2eO,cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO)) ).

fof('Coq.Arith.PeanoNat.Nat.lt_1_2',axiom,
    cCoq_2eInit_2ePeano_2elt___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO),cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO))) ).

fof('Coq.Arith.PeanoNat.Nat.lt_ge_cases',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(V1__m,V0__n) ) ) ) ).

fof('Coq.Arith.PeanoNat.Nat.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.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.lt_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_2elt___24a2(V0__n,V1__m)
               => ( cCoq_2eInit_2ePeano_2elt___24a2(V1__m,V2__p)
                 => cCoq_2eInit_2ePeano_2elt___24a2(V0__n,V2__p) ) ) ) ) ) ).

fof('Coq.Arith.PeanoNat.Nat.lt_trichotomy',axiom,
    ! [V0__n] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
     => ! [V1__m] :
          ( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
         => ( cCoq_2eInit_2ePeano_2elt___24a2(V0__n,V1__m)
            | V0__n = V1__m
            | cCoq_2eInit_2ePeano_2elt___24a2(V1__m,V0__n) ) ) ) ).

fof('Coq.Arith.PeanoNat.Nat.lt_wf',axiom,
    ! [V0__z] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(V0__z)
     => cCoq_2eInit_2eWf_2ewell__founded___24a2(cCoq_2eInit_2eDatatypes_2enat,c_24__lam__173531___24a1(V0__z)) ) ).

fof('Coq.Arith.PeanoNat.Nat.mul_comm',axiom,
    ! [V0__n] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
     => ! [V1__m] :
          ( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
         => cCoq_2eInit_2eNat_2emul___24a2(V0__n,V1__m) = cCoq_2eInit_2eNat_2emul___24a2(V1__m,V0__n) ) ) ).

fof('Coq.Arith.PeanoNat.Nat.one_succ',axiom,
    cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO) = cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO) ).

fof('Coq.Arith.Wf_nat.lt_wf_double_ind',axiom,
    ! [V0__P] :
      ( c_24__type__5091___24t(V0__P)
     => ( ! [V1__n] :
            ( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
           => ! [V2__m] :
                ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__m)
               => ( ! [V3__p] :
                      ( cCoq_2eInit_2eDatatypes_2enat___24t(V3__p)
                     => ! [V4__q] :
                          ( cCoq_2eInit_2eDatatypes_2enat___24t(V4__q)
                         => ( cCoq_2eInit_2ePeano_2elt___24a2(V3__p,V1__n)
                           => p(happ(happ(V0__P,V3__p),V4__q)) ) ) )
                 => ( ! [V4__p] :
                        ( cCoq_2eInit_2eDatatypes_2enat___24t(V4__p)
                       => ( cCoq_2eInit_2ePeano_2elt___24a2(V4__p,V2__m)
                         => p(happ(happ(V0__P,V1__n),V4__p)) ) )
                   => p(happ(happ(V0__P,V1__n),V2__m)) ) ) ) )
       => ! [V2__n] :
            ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__n)
           => ! [V3__m] :
                ( cCoq_2eInit_2eDatatypes_2enat___24t(V3__m)
               => p(happ(happ(V0__P,V2__n),V3__m)) ) ) ) ) ).

fof('Coq.Arith.Wf_nat.lt_wf_ind',axiom,
    ! [V0__n] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
     => ! [V1__P] :
          ( c_24__type__2522___24t(V1__P)
         => ( ! [V2__n] :
                ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__n)
               => ( ! [V3__m] :
                      ( cCoq_2eInit_2eDatatypes_2enat___24t(V3__m)
                     => ( cCoq_2eInit_2ePeano_2elt___24a2(V3__m,V2__n)
                       => p(happ(V1__P,V3__m)) ) )
                 => p(happ(V1__P,V2__n)) ) )
           => p(happ(V1__P,V0__n)) ) ) ) ).

fof('Coq.Bool.Bool.absurd_eq_bool',axiom,
    ! [V0__b] :
      ( cCoq_2eInit_2eDatatypes_2ebool___24t(V0__b)
     => ! [V1__b_27] :
          ( cCoq_2eInit_2eDatatypes_2ebool___24t(V1__b_27)
         => ( p(c_24False)
           => V0__b = V1__b_27 ) ) ) ).

fof('Coq.Bool.Bool.orb_comm',axiom,
    ! [V0__b1] :
      ( cCoq_2eInit_2eDatatypes_2ebool___24t(V0__b1)
     => ! [V1__b2] :
          ( cCoq_2eInit_2eDatatypes_2ebool___24t(V1__b2)
         => cCoq_2eInit_2eDatatypes_2eorb___24a2(V0__b1,V1__b2) = cCoq_2eInit_2eDatatypes_2eorb___24a2(V1__b2,V0__b1) ) ) ).

fof('Coq.Init.Datatypes.idProp',axiom,
    p(cCoq_2eInit_2eDatatypes_2eIDProp) ).

fof('Coq.Init.Datatypes.list_ind',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__P] :
          ( c_24__type__2638___24t(V0__A,V1__P)
         => ( p(happ(V1__P,cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)))
           => ( ! [V3__a] :
                  ( t(V3__a,V0__A)
                 => ! [V4__l] :
                      ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V4__l)
                     => ( p(happ(V1__P,V4__l))
                       => p(happ(V1__P,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V3__a,V4__l))) ) ) )
             => ! [V4__l] :
                  ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V4__l)
                 => p(happ(V1__P,V4__l)) ) ) ) ) ) ).

fof('Coq.Init.Datatypes.nat_ind',axiom,
    ! [V0__P] :
      ( c_24__type__2522___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__172691___24t(V0__A,V1__B,V2__P)
             => ( ! [V3__a] :
                    ( t(V3__a,V0__A)
                   => ! [V4__b] :
                        ( t(V4__b,V1__B)
                       => p(happ(V2__P,cCoq_2eInit_2eDatatypes_2epair___24a4(V0__A,V1__B,V3__a,V4__b))) ) )
               => ! [V4__p] :
                    ( cCoq_2eInit_2eDatatypes_2eprod___24t(V0__A,V1__B,V4__p)
                   => p(happ(V2__P,V4__p)) ) ) ) ) ) ).

fof('Coq.Init.Datatypes.unit_ind',axiom,
    ! [V0__P] :
      ( c_24__type__122816___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.Datatypes.unit_sind',axiom,
    ! [V0__P] :
      ( c_24__type__122816___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.Specif.sig_ind',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__P] :
          ( c_24__type__2000___24t(V0__A,V1__P)
         => ! [V2__P] :
              ( c_24__type__2014___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__282___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.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_false_iff',axiom,
    ( ( p(c_24False)
     => p(c_24False) )
  <=> p(c_24True) ) ).

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.Logic.Decidable.not_true_iff',axiom,
    ( ( p(c_24True)
     => p(c_24False) )
  <=> 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_antisym',axiom,
    ! [V0__x] :
      ( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__x)
     => ! [V1__y] :
          ( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__y)
         => ( cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(V0__x,V1__y)
           => ( cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(V1__y,V0__x)
             => V0__x = V1__y ) ) ) ) ).

fof('Coq.NArith.BinNat.N.Private_OrderTac.Tac.le_refl',axiom,
    ! [V0__x] :
      ( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__x)
     => cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(V0__x,V0__x) ) ).

fof('Coq.NArith.BinNat.N.Private_OrderTac.Tac.lt_irrefl',axiom,
    ! [V0__x] :
      ( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__x)
     => ~ cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V0__x,V0__x) ) ).

fof('Coq.NArith.BinNat.N.Private_OrderTac.Tac.not_gt_le',axiom,
    ! [V0__x] :
      ( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__x)
     => ! [V1__y] :
          ( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__y)
         => ( ~ cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V1__y,V0__x)
           => cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(V0__x,V1__y) ) ) ) ).

fof('Coq.NArith.BinNat.N.Private_Tac.eq_refl',axiom,
    ! [V0__x] :
      ( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__x)
     => V0__x = V0__x ) ).

fof('Coq.NArith.BinNat.N.Private_Tac.eq_sym',axiom,
    ! [V0__x] :
      ( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__x)
     => ! [V1__y] :
          ( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__y)
         => ( V0__x = V1__y
           => V1__y = V0__x ) ) ) ).

fof('Coq.NArith.BinNat.N.Private_Tac.le_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_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.divide_refl',axiom,
    ! [V0__n] :
      ( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
     => cCoq_2eNArith_2eBinNat_2eN_2edivide___24a2(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.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_gt_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_2elt___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.le_trans',axiom,
    ! [V0__n] :
      ( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
     => ! [V1__m] :
          ( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
         => ! [V2__p] :
              ( cCoq_2eNumbers_2eBinNums_2eN___24t(V2__p)
             => ( cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(V0__n,V1__m)
               => ( cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(V1__m,V2__p)
                 => cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(V0__n,V2__p) ) ) ) ) ) ).

fof('Coq.NArith.BinNat.N.lt_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_2elt___24a2(V0__n,V1__m)
            | cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(V1__m,V0__n) ) ) ) ).

fof('Coq.NArith.BinNat.N.lt_le_incl',axiom,
    ! [V0__n] :
      ( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
     => ! [V1__m] :
          ( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
         => ( cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V0__n,V1__m)
           => cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(V0__n,V1__m) ) ) ) ).

fof('Coq.NArith.BinNat.N.lt_trichotomy',axiom,
    ! [V0__n] :
      ( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
     => ! [V1__m] :
          ( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
         => ( cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V0__n,V1__m)
            | V0__n = V1__m
            | cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V1__m,V0__n) ) ) ) ).

fof('Coq.NArith.BinNat.N.lt_wf',axiom,
    ! [V0__z] :
      ( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__z)
     => cCoq_2eInit_2eWf_2ewell__founded___24a2(cCoq_2eNumbers_2eBinNums_2eN,c_24__lam__173527___24a1(V0__z)) ) ).

fof('Coq.NArith.BinNat.N.mul_comm',axiom,
    ! [V0__n] :
      ( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
     => ! [V1__m] :
          ( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
         => cCoq_2eNArith_2eBinNatDef_2eN_2emul___24a2(V0__n,V1__m) = cCoq_2eNArith_2eBinNatDef_2eN_2emul___24a2(V1__m,V0__n) ) ) ).

fof('Coq.NArith.Ndec.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.PArith.BinPos.Pos.Private_Tac.eq_refl',axiom,
    ! [V0__x] :
      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V0__x)
     => V0__x = V0__x ) ).

fof('Coq.PArith.BinPos.Pos.Private_Tac.eq_sym',axiom,
    ! [V0__x] :
      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V0__x)
     => ! [V1__y] :
          ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__y)
         => ( V0__x = V1__y
           => V1__y = V0__x ) ) ) ).

fof('Coq.PArith.BinPos.Pos.Private_Tac.le_refl',axiom,
    ! [V0__x] :
      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V0__x)
     => cCoq_2ePArith_2eBinPos_2ePos_2ele___24a2(V0__x,V0__x) ) ).

fof('Coq.PArith.BinPos.Pos.Private_Tac.lt_irrefl',axiom,
    ! [V0__x] :
      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V0__x)
     => ~ cCoq_2ePArith_2eBinPos_2ePos_2elt___24a2(V0__x,V0__x) ) ).

fof('Coq.PArith.BinPos.Pos.le_lt_trans',axiom,
    ! [V0__n] :
      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V0__n)
     => ! [V1__m] :
          ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__m)
         => ! [V2__p] :
              ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V2__p)
             => ( cCoq_2ePArith_2eBinPos_2ePos_2ele___24a2(V0__n,V1__m)
               => ( cCoq_2ePArith_2eBinPos_2ePos_2elt___24a2(V1__m,V2__p)
                 => cCoq_2ePArith_2eBinPos_2ePos_2elt___24a2(V0__n,V2__p) ) ) ) ) ) ).

fof('Coq.PArith.BinPos.Pos.le_refl',axiom,
    ! [V0__p] :
      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V0__p)
     => cCoq_2ePArith_2eBinPos_2ePos_2ele___24a2(V0__p,V0__p) ) ).

fof('Coq.PArith.BinPos.Pos.lt_succ_diag_r',axiom,
    ! [V0__p] :
      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V0__p)
     => cCoq_2ePArith_2eBinPos_2ePos_2elt___24a2(V0__p,cCoq_2ePArith_2eBinPosDef_2ePos_2esucc___24a1(V0__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_antisym',axiom,
    ! [V0__x] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
     => ! [V1__y] :
          ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
         => ( cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__x,V1__y)
           => ( cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V1__y,V0__x)
             => V0__x = V1__y ) ) ) ) ).

fof('Coq.ZArith.BinInt.Z.Private_OrderTac.Tac.le_refl',axiom,
    ! [V0__x] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
     => cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__x,V0__x) ) ).

fof('Coq.ZArith.BinInt.Z.Private_OrderTac.Tac.lt_irrefl',axiom,
    ! [V0__x] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
     => ~ p(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)
           => p(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)
         => ( ~ p(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.Private_Tac.lt_irrefl',axiom,
    ! [V0__x] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
     => ~ p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__x,V0__x)) ) ).

fof('Coq.ZArith.BinInt.Z.add_comm',axiom,
    ! [V0__n] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
     => ! [V1__m] :
          ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
         => cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__n,V1__m) = cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V1__m,V0__n) ) ) ).

fof('Coq.ZArith.BinInt.Z.divide_0_l',axiom,
    ! [V0__n] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
     => ( cCoq_2eZArith_2eBinInt_2eZ_2edivide___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V0__n)
       => V0__n = cCoq_2eNumbers_2eBinNums_2eZ0 ) ) ).

fof('Coq.ZArith.BinInt.Z.divide_0_r',axiom,
    ! [V0__n] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
     => cCoq_2eZArith_2eBinInt_2eZ_2edivide___24a2(V0__n,cCoq_2eNumbers_2eBinNums_2eZ0) ) ).

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_decidable',axiom,
    ! [V0__n] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
     => ! [V1__m] :
          ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
         => cCoq_2eLogic_2eDecidable_2edecidable___24a1(c_24__prop__107393___24a2(V0__n,V1__m)) ) ) ).

fof('Coq.ZArith.BinInt.Z.eq_equiv',axiom,
    cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(cCoq_2eNumbers_2eBinNums_2eZ,c_3d___24a1(cCoq_2eNumbers_2eBinNums_2eZ)) ).

fof('Coq.ZArith.BinInt.Z.eq_stepl',axiom,
    ! [V0__x] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
     => ! [V1__y] :
          ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
         => ! [V2__z] :
              ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__z)
             => ( V0__x = V1__y
               => ( V0__x = V2__z
                 => V2__z = V1__y ) ) ) ) ) ).

fof('Coq.ZArith.BinInt.Z.ge_le_iff',axiom,
    ! [V0__n] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
     => ! [V1__m] :
          ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
         => ( cCoq_2eZArith_2eBinInt_2eZ_2ege___24a2(V0__n,V1__m)
          <=> cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V1__m,V0__n) ) ) ) ).

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)
            | p(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_0_1',axiom,
    p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH))) ).

fof('Coq.ZArith.BinInt.Z.lt_decidable',axiom,
    ! [V0__n] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
     => ! [V1__m] :
          ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
         => cCoq_2eLogic_2eDecidable_2edecidable___24a1(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__n,V1__m)) ) ) ).

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)
         => ( p(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)
         => ( p(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_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)
             => ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__n,V1__m))
               => ( cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V1__m,V2__p)
                 => p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__n,V2__p)) ) ) ) ) ) ).

fof('Coq.ZArith.BinInt.Z.lt_nge',axiom,
    ! [V0__n] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
     => ! [V1__m] :
          ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
         => ( p(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_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)
             => ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__n,V1__m))
               => ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V1__m,V2__p))
                 => p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__n,V2__p)) ) ) ) ) ) ).

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)
         => ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__n,V1__m))
            | V0__n = V1__m
            | p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V1__m,V0__n)) ) ) ) ).

fof('Coq.ZArith.BinInt.Z.mod_divide',axiom,
    ! [V0__a] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
     => ! [V1__b] :
          ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__b)
         => ( V1__b != cCoq_2eNumbers_2eBinNums_2eZ0
           => ( cCoq_2eZArith_2eBinIntDef_2eZ_2emodulo___24a2(V0__a,V1__b) = cCoq_2eNumbers_2eBinNums_2eZ0
            <=> cCoq_2eZArith_2eBinInt_2eZ_2edivide___24a2(V1__b,V0__a) ) ) ) ) ).

fof('Coq.ZArith.BinInt.Z.mul_comm',axiom,
    ! [V0__n] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
     => ! [V1__m] :
          ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
         => cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n,V1__m) = cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__m,V0__n) ) ) ).

fof('Coq.micromega.OrderedRing.Rle_antisymm',axiom,
    ! [V0__R] :
      ( cType___24t(V0__R)
     => ! [V1__rO] :
          ( t(V1__rO,V0__R)
         => ! [V2__rI] :
              ( t(V2__rI,V0__R)
             => ! [V3__rplus] :
                  ( c_24__type__1058___24t(V0__R,V3__rplus)
                 => ! [V4__rtimes] :
                      ( c_24__type__1058___24t(V0__R,V4__rtimes)
                     => ! [V5__rminus] :
                          ( c_24__type__1058___24t(V0__R,V5__rminus)
                         => ! [V6__ropp] :
                              ( c_24__type__1278___24t(V0__R,V6__ropp)
                             => ! [V7__req] :
                                  ( c_24__type__1300___24t(V0__R,V7__req)
                                 => ! [V8__rle] :
                                      ( c_24__type__1300___24t(V0__R,V8__rle)
                                     => ! [V9__rlt] :
                                          ( c_24__type__1300___24t(V0__R,V9__rlt)
                                         => ( cCoq_2emicromega_2eOrderedRing_2eSOR___24a10(V0__R,V1__rO,V2__rI,V3__rplus,V4__rtimes,V5__rminus,V6__ropp,V7__req,V8__rle,V9__rlt)
                                           => ! [V11__n] :
                                                ( t(V11__n,V0__R)
                                               => ! [V12__m] :
                                                    ( t(V12__m,V0__R)
                                                   => ( p(happ(happ(V8__rle,V11__n),V12__m))
                                                     => ( p(happ(happ(V8__rle,V12__m),V11__n))
                                                       => p(happ(happ(V7__req,V11__n),V12__m)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).

fof('Coq.micromega.OrderedRing.Rle_gt_cases',axiom,
    ! [V0__R] :
      ( cType___24t(V0__R)
     => ! [V1__rO] :
          ( t(V1__rO,V0__R)
         => ! [V2__rI] :
              ( t(V2__rI,V0__R)
             => ! [V3__rplus] :
                  ( c_24__type__1058___24t(V0__R,V3__rplus)
                 => ! [V4__rtimes] :
                      ( c_24__type__1058___24t(V0__R,V4__rtimes)
                     => ! [V5__rminus] :
                          ( c_24__type__1058___24t(V0__R,V5__rminus)
                         => ! [V6__ropp] :
                              ( c_24__type__1278___24t(V0__R,V6__ropp)
                             => ! [V7__req] :
                                  ( c_24__type__1300___24t(V0__R,V7__req)
                                 => ! [V8__rle] :
                                      ( c_24__type__1300___24t(V0__R,V8__rle)
                                     => ! [V9__rlt] :
                                          ( c_24__type__1300___24t(V0__R,V9__rlt)
                                         => ( cCoq_2emicromega_2eOrderedRing_2eSOR___24a10(V0__R,V1__rO,V2__rI,V3__rplus,V4__rtimes,V5__rminus,V6__ropp,V7__req,V8__rle,V9__rlt)
                                           => ! [V11__n] :
                                                ( t(V11__n,V0__R)
                                               => ! [V12__m] :
                                                    ( t(V12__m,V0__R)
                                                   => ( p(happ(happ(V8__rle,V11__n),V12__m))
                                                      | p(happ(happ(V9__rlt,V12__m),V11__n)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).

fof('Coq.micromega.OrderedRing.Rle_lt_trans',axiom,
    ! [V0__R] :
      ( cType___24t(V0__R)
     => ! [V1__rO] :
          ( t(V1__rO,V0__R)
         => ! [V2__rI] :
              ( t(V2__rI,V0__R)
             => ! [V3__rplus] :
                  ( c_24__type__1058___24t(V0__R,V3__rplus)
                 => ! [V4__rtimes] :
                      ( c_24__type__1058___24t(V0__R,V4__rtimes)
                     => ! [V5__rminus] :
                          ( c_24__type__1058___24t(V0__R,V5__rminus)
                         => ! [V6__ropp] :
                              ( c_24__type__1278___24t(V0__R,V6__ropp)
                             => ! [V7__req] :
                                  ( c_24__type__1300___24t(V0__R,V7__req)
                                 => ! [V8__rle] :
                                      ( c_24__type__1300___24t(V0__R,V8__rle)
                                     => ! [V9__rlt] :
                                          ( c_24__type__1300___24t(V0__R,V9__rlt)
                                         => ( cCoq_2emicromega_2eOrderedRing_2eSOR___24a10(V0__R,V1__rO,V2__rI,V3__rplus,V4__rtimes,V5__rminus,V6__ropp,V7__req,V8__rle,V9__rlt)
                                           => ! [V11__n] :
                                                ( t(V11__n,V0__R)
                                               => ! [V12__m] :
                                                    ( t(V12__m,V0__R)
                                                   => ! [V13__p] :
                                                        ( t(V13__p,V0__R)
                                                       => ( p(happ(happ(V8__rle,V11__n),V12__m))
                                                         => ( p(happ(happ(V9__rlt,V12__m),V13__p))
                                                           => p(happ(happ(V9__rlt,V11__n),V13__p)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).

fof('Coq.micromega.OrderedRing.Rle_refl',axiom,
    ! [V0__R] :
      ( cType___24t(V0__R)
     => ! [V1__rO] :
          ( t(V1__rO,V0__R)
         => ! [V2__rI] :
              ( t(V2__rI,V0__R)
             => ! [V3__rplus] :
                  ( c_24__type__1058___24t(V0__R,V3__rplus)
                 => ! [V4__rtimes] :
                      ( c_24__type__1058___24t(V0__R,V4__rtimes)
                     => ! [V5__rminus] :
                          ( c_24__type__1058___24t(V0__R,V5__rminus)
                         => ! [V6__ropp] :
                              ( c_24__type__1278___24t(V0__R,V6__ropp)
                             => ! [V7__req] :
                                  ( c_24__type__1300___24t(V0__R,V7__req)
                                 => ! [V8__rle] :
                                      ( c_24__type__1300___24t(V0__R,V8__rle)
                                     => ! [V9__rlt] :
                                          ( c_24__type__1300___24t(V0__R,V9__rlt)
                                         => ( cCoq_2emicromega_2eOrderedRing_2eSOR___24a10(V0__R,V1__rO,V2__rI,V3__rplus,V4__rtimes,V5__rminus,V6__ropp,V7__req,V8__rle,V9__rlt)
                                           => ! [V11__n] :
                                                ( t(V11__n,V0__R)
                                               => p(happ(happ(V8__rle,V11__n),V11__n)) ) ) ) ) ) ) ) ) ) ) ) ) ).

fof('Coq.micromega.OrderedRing.Rle_trans',axiom,
    ! [V0__R] :
      ( cType___24t(V0__R)
     => ! [V1__rO] :
          ( t(V1__rO,V0__R)
         => ! [V2__rI] :
              ( t(V2__rI,V0__R)
             => ! [V3__rplus] :
                  ( c_24__type__1058___24t(V0__R,V3__rplus)
                 => ! [V4__rtimes] :
                      ( c_24__type__1058___24t(V0__R,V4__rtimes)
                     => ! [V5__rminus] :
                          ( c_24__type__1058___24t(V0__R,V5__rminus)
                         => ! [V6__ropp] :
                              ( c_24__type__1278___24t(V0__R,V6__ropp)
                             => ! [V7__req] :
                                  ( c_24__type__1300___24t(V0__R,V7__req)
                                 => ! [V8__rle] :
                                      ( c_24__type__1300___24t(V0__R,V8__rle)
                                     => ! [V9__rlt] :
                                          ( c_24__type__1300___24t(V0__R,V9__rlt)
                                         => ( cCoq_2emicromega_2eOrderedRing_2eSOR___24a10(V0__R,V1__rO,V2__rI,V3__rplus,V4__rtimes,V5__rminus,V6__ropp,V7__req,V8__rle,V9__rlt)
                                           => ! [V11__n] :
                                                ( t(V11__n,V0__R)
                                               => ! [V12__m] :
                                                    ( t(V12__m,V0__R)
                                                   => ! [V13__p] :
                                                        ( t(V13__p,V0__R)
                                                       => ( p(happ(happ(V8__rle,V11__n),V12__m))
                                                         => ( p(happ(happ(V8__rle,V12__m),V13__p))
                                                           => p(happ(happ(V8__rle,V11__n),V13__p)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).

fof('Coq.micromega.OrderedRing.Rlt_0_1',axiom,
    ! [V0__R] :
      ( cType___24t(V0__R)
     => ! [V1__rO] :
          ( t(V1__rO,V0__R)
         => ! [V2__rI] :
              ( t(V2__rI,V0__R)
             => ! [V3__rplus] :
                  ( c_24__type__1058___24t(V0__R,V3__rplus)
                 => ! [V4__rtimes] :
                      ( c_24__type__1058___24t(V0__R,V4__rtimes)
                     => ! [V5__rminus] :
                          ( c_24__type__1058___24t(V0__R,V5__rminus)
                         => ! [V6__ropp] :
                              ( c_24__type__1278___24t(V0__R,V6__ropp)
                             => ! [V7__req] :
                                  ( c_24__type__1300___24t(V0__R,V7__req)
                                 => ! [V8__rle] :
                                      ( c_24__type__1300___24t(V0__R,V8__rle)
                                     => ! [V9__rlt] :
                                          ( c_24__type__1300___24t(V0__R,V9__rlt)
                                         => ( cCoq_2emicromega_2eOrderedRing_2eSOR___24a10(V0__R,V1__rO,V2__rI,V3__rplus,V4__rtimes,V5__rminus,V6__ropp,V7__req,V8__rle,V9__rlt)
                                           => p(happ(happ(V9__rlt,V1__rO),V2__rI)) ) ) ) ) ) ) ) ) ) ) ) ).

fof('Coq.micromega.OrderedRing.Rlt_le_trans',axiom,
    ! [V0__R] :
      ( cType___24t(V0__R)
     => ! [V1__rO] :
          ( t(V1__rO,V0__R)
         => ! [V2__rI] :
              ( t(V2__rI,V0__R)
             => ! [V3__rplus] :
                  ( c_24__type__1058___24t(V0__R,V3__rplus)
                 => ! [V4__rtimes] :
                      ( c_24__type__1058___24t(V0__R,V4__rtimes)
                     => ! [V5__rminus] :
                          ( c_24__type__1058___24t(V0__R,V5__rminus)
                         => ! [V6__ropp] :
                              ( c_24__type__1278___24t(V0__R,V6__ropp)
                             => ! [V7__req] :
                                  ( c_24__type__1300___24t(V0__R,V7__req)
                                 => ! [V8__rle] :
                                      ( c_24__type__1300___24t(V0__R,V8__rle)
                                     => ! [V9__rlt] :
                                          ( c_24__type__1300___24t(V0__R,V9__rlt)
                                         => ( cCoq_2emicromega_2eOrderedRing_2eSOR___24a10(V0__R,V1__rO,V2__rI,V3__rplus,V4__rtimes,V5__rminus,V6__ropp,V7__req,V8__rle,V9__rlt)
                                           => ! [V11__n] :
                                                ( t(V11__n,V0__R)
                                               => ! [V12__m] :
                                                    ( t(V12__m,V0__R)
                                                   => ! [V13__p] :
                                                        ( t(V13__p,V0__R)
                                                       => ( p(happ(happ(V9__rlt,V11__n),V12__m))
                                                         => ( p(happ(happ(V8__rle,V12__m),V13__p))
                                                           => p(happ(happ(V9__rlt,V11__n),V13__p)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).

fof('Coq.micromega.OrderedRing.Rlt_lt_succ',axiom,
    ! [V0__R] :
      ( cType___24t(V0__R)
     => ! [V1__rO] :
          ( t(V1__rO,V0__R)
         => ! [V2__rI] :
              ( t(V2__rI,V0__R)
             => ! [V3__rplus] :
                  ( c_24__type__1058___24t(V0__R,V3__rplus)
                 => ! [V4__rtimes] :
                      ( c_24__type__1058___24t(V0__R,V4__rtimes)
                     => ! [V5__rminus] :
                          ( c_24__type__1058___24t(V0__R,V5__rminus)
                         => ! [V6__ropp] :
                              ( c_24__type__1278___24t(V0__R,V6__ropp)
                             => ! [V7__req] :
                                  ( c_24__type__1300___24t(V0__R,V7__req)
                                 => ! [V8__rle] :
                                      ( c_24__type__1300___24t(V0__R,V8__rle)
                                     => ! [V9__rlt] :
                                          ( c_24__type__1300___24t(V0__R,V9__rlt)
                                         => ( cCoq_2emicromega_2eOrderedRing_2eSOR___24a10(V0__R,V1__rO,V2__rI,V3__rplus,V4__rtimes,V5__rminus,V6__ropp,V7__req,V8__rle,V9__rlt)
                                           => ! [V11__n] :
                                                ( t(V11__n,V0__R)
                                               => ! [V12__m] :
                                                    ( t(V12__m,V0__R)
                                                   => ( p(happ(happ(V9__rlt,V11__n),V12__m))
                                                     => p(happ(happ(V9__rlt,V11__n),happ(happ(V3__rplus,V2__rI),V12__m))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).

fof('Coq.micromega.OrderedRing.Rlt_succ_r',axiom,
    ! [V0__R] :
      ( cType___24t(V0__R)
     => ! [V1__rO] :
          ( t(V1__rO,V0__R)
         => ! [V2__rI] :
              ( t(V2__rI,V0__R)
             => ! [V3__rplus] :
                  ( c_24__type__1058___24t(V0__R,V3__rplus)
                 => ! [V4__rtimes] :
                      ( c_24__type__1058___24t(V0__R,V4__rtimes)
                     => ! [V5__rminus] :
                          ( c_24__type__1058___24t(V0__R,V5__rminus)
                         => ! [V6__ropp] :
                              ( c_24__type__1278___24t(V0__R,V6__ropp)
                             => ! [V7__req] :
                                  ( c_24__type__1300___24t(V0__R,V7__req)
                                 => ! [V8__rle] :
                                      ( c_24__type__1300___24t(V0__R,V8__rle)
                                     => ! [V9__rlt] :
                                          ( c_24__type__1300___24t(V0__R,V9__rlt)
                                         => ( cCoq_2emicromega_2eOrderedRing_2eSOR___24a10(V0__R,V1__rO,V2__rI,V3__rplus,V4__rtimes,V5__rminus,V6__ropp,V7__req,V8__rle,V9__rlt)
                                           => ! [V11__n] :
                                                ( t(V11__n,V0__R)
                                               => p(happ(happ(V9__rlt,V11__n),happ(happ(V3__rplus,V2__rI),V11__n))) ) ) ) ) ) ) ) ) ) ) ) ) ).

fof('Coq.micromega.OrderedRing.Rlt_trans',axiom,
    ! [V0__R] :
      ( cType___24t(V0__R)
     => ! [V1__rO] :
          ( t(V1__rO,V0__R)
         => ! [V2__rI] :
              ( t(V2__rI,V0__R)
             => ! [V3__rplus] :
                  ( c_24__type__1058___24t(V0__R,V3__rplus)
                 => ! [V4__rtimes] :
                      ( c_24__type__1058___24t(V0__R,V4__rtimes)
                     => ! [V5__rminus] :
                          ( c_24__type__1058___24t(V0__R,V5__rminus)
                         => ! [V6__ropp] :
                              ( c_24__type__1278___24t(V0__R,V6__ropp)
                             => ! [V7__req] :
                                  ( c_24__type__1300___24t(V0__R,V7__req)
                                 => ! [V8__rle] :
                                      ( c_24__type__1300___24t(V0__R,V8__rle)
                                     => ! [V9__rlt] :
                                          ( c_24__type__1300___24t(V0__R,V9__rlt)
                                         => ( cCoq_2emicromega_2eOrderedRing_2eSOR___24a10(V0__R,V1__rO,V2__rI,V3__rplus,V4__rtimes,V5__rminus,V6__ropp,V7__req,V8__rle,V9__rlt)
                                           => ! [V11__n] :
                                                ( t(V11__n,V0__R)
                                               => ! [V12__m] :
                                                    ( t(V12__m,V0__R)
                                                   => ! [V13__p] :
                                                        ( t(V13__p,V0__R)
                                                       => ( p(happ(happ(V9__rlt,V11__n),V12__m))
                                                         => ( p(happ(happ(V9__rlt,V12__m),V13__p))
                                                           => p(happ(happ(V9__rlt,V11__n),V13__p)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).

fof('Coq.micromega.OrderedRing.Rlt_trichotomy',axiom,
    ! [V0__R] :
      ( cType___24t(V0__R)
     => ! [V1__rO] :
          ( t(V1__rO,V0__R)
         => ! [V2__rI] :
              ( t(V2__rI,V0__R)
             => ! [V3__rplus] :
                  ( c_24__type__1058___24t(V0__R,V3__rplus)
                 => ! [V4__rtimes] :
                      ( c_24__type__1058___24t(V0__R,V4__rtimes)
                     => ! [V5__rminus] :
                          ( c_24__type__1058___24t(V0__R,V5__rminus)
                         => ! [V6__ropp] :
                              ( c_24__type__1278___24t(V0__R,V6__ropp)
                             => ! [V7__req] :
                                  ( c_24__type__1300___24t(V0__R,V7__req)
                                 => ! [V8__rle] :
                                      ( c_24__type__1300___24t(V0__R,V8__rle)
                                     => ! [V9__rlt] :
                                          ( c_24__type__1300___24t(V0__R,V9__rlt)
                                         => ( cCoq_2emicromega_2eOrderedRing_2eSOR___24a10(V0__R,V1__rO,V2__rI,V3__rplus,V4__rtimes,V5__rminus,V6__ropp,V7__req,V8__rle,V9__rlt)
                                           => ! [V11__n] :
                                                ( t(V11__n,V0__R)
                                               => ! [V12__m] :
                                                    ( t(V12__m,V0__R)
                                                   => ( p(happ(happ(V9__rlt,V11__n),V12__m))
                                                      | p(happ(happ(V7__req,V11__n),V12__m))
                                                      | p(happ(happ(V9__rlt,V12__m),V11__n)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).

fof('Coq.micromega.OrderedRing.Rplus_0_l',axiom,
    ! [V0__R] :
      ( cType___24t(V0__R)
     => ! [V1__rO] :
          ( t(V1__rO,V0__R)
         => ! [V2__rI] :
              ( t(V2__rI,V0__R)
             => ! [V3__rplus] :
                  ( c_24__type__1058___24t(V0__R,V3__rplus)
                 => ! [V4__rtimes] :
                      ( c_24__type__1058___24t(V0__R,V4__rtimes)
                     => ! [V5__rminus] :
                          ( c_24__type__1058___24t(V0__R,V5__rminus)
                         => ! [V6__ropp] :
                              ( c_24__type__1278___24t(V0__R,V6__ropp)
                             => ! [V7__req] :
                                  ( c_24__type__1300___24t(V0__R,V7__req)
                                 => ! [V8__rle] :
                                      ( c_24__type__1300___24t(V0__R,V8__rle)
                                     => ! [V9__rlt] :
                                          ( c_24__type__1300___24t(V0__R,V9__rlt)
                                         => ( cCoq_2emicromega_2eOrderedRing_2eSOR___24a10(V0__R,V1__rO,V2__rI,V3__rplus,V4__rtimes,V5__rminus,V6__ropp,V7__req,V8__rle,V9__rlt)
                                           => ! [V11__n] :
                                                ( t(V11__n,V0__R)
                                               => p(happ(happ(V7__req,happ(happ(V3__rplus,V1__rO),V11__n)),V11__n)) ) ) ) ) ) ) ) ) ) ) ) ) ).

fof('Coq.micromega.OrderedRing.Rplus_0_r',axiom,
    ! [V0__R] :
      ( cType___24t(V0__R)
     => ! [V1__rO] :
          ( t(V1__rO,V0__R)
         => ! [V2__rI] :
              ( t(V2__rI,V0__R)
             => ! [V3__rplus] :
                  ( c_24__type__1058___24t(V0__R,V3__rplus)
                 => ! [V4__rtimes] :
                      ( c_24__type__1058___24t(V0__R,V4__rtimes)
                     => ! [V5__rminus] :
                          ( c_24__type__1058___24t(V0__R,V5__rminus)
                         => ! [V6__ropp] :
                              ( c_24__type__1278___24t(V0__R,V6__ropp)
                             => ! [V7__req] :
                                  ( c_24__type__1300___24t(V0__R,V7__req)
                                 => ! [V8__rle] :
                                      ( c_24__type__1300___24t(V0__R,V8__rle)
                                     => ! [V9__rlt] :
                                          ( c_24__type__1300___24t(V0__R,V9__rlt)
                                         => ( cCoq_2emicromega_2eOrderedRing_2eSOR___24a10(V0__R,V1__rO,V2__rI,V3__rplus,V4__rtimes,V5__rminus,V6__ropp,V7__req,V8__rle,V9__rlt)
                                           => ! [V11__n] :
                                                ( t(V11__n,V0__R)
                                               => p(happ(happ(V7__req,happ(happ(V3__rplus,V11__n),V1__rO)),V11__n)) ) ) ) ) ) ) ) ) ) ) ) ) ).

fof('Coq.micromega.OrderedRing.Rplus_comm',axiom,
    ! [V0__R] :
      ( cType___24t(V0__R)
     => ! [V1__rO] :
          ( t(V1__rO,V0__R)
         => ! [V2__rI] :
              ( t(V2__rI,V0__R)
             => ! [V3__rplus] :
                  ( c_24__type__1058___24t(V0__R,V3__rplus)
                 => ! [V4__rtimes] :
                      ( c_24__type__1058___24t(V0__R,V4__rtimes)
                     => ! [V5__rminus] :
                          ( c_24__type__1058___24t(V0__R,V5__rminus)
                         => ! [V6__ropp] :
                              ( c_24__type__1278___24t(V0__R,V6__ropp)
                             => ! [V7__req] :
                                  ( c_24__type__1300___24t(V0__R,V7__req)
                                 => ! [V8__rle] :
                                      ( c_24__type__1300___24t(V0__R,V8__rle)
                                     => ! [V9__rlt] :
                                          ( c_24__type__1300___24t(V0__R,V9__rlt)
                                         => ( cCoq_2emicromega_2eOrderedRing_2eSOR___24a10(V0__R,V1__rO,V2__rI,V3__rplus,V4__rtimes,V5__rminus,V6__ropp,V7__req,V8__rle,V9__rlt)
                                           => ! [V11__n] :
                                                ( t(V11__n,V0__R)
                                               => ! [V12__m] :
                                                    ( t(V12__m,V0__R)
                                                   => p(happ(happ(V7__req,happ(happ(V3__rplus,V11__n),V12__m)),happ(happ(V3__rplus,V12__m),V11__n))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).

fof('Coq.micromega.OrderedRing.Rplus_le_lt_mono',axiom,
    ! [V0__R] :
      ( cType___24t(V0__R)
     => ! [V1__rO] :
          ( t(V1__rO,V0__R)
         => ! [V2__rI] :
              ( t(V2__rI,V0__R)
             => ! [V3__rplus] :
                  ( c_24__type__1058___24t(V0__R,V3__rplus)
                 => ! [V4__rtimes] :
                      ( c_24__type__1058___24t(V0__R,V4__rtimes)
                     => ! [V5__rminus] :
                          ( c_24__type__1058___24t(V0__R,V5__rminus)
                         => ! [V6__ropp] :
                              ( c_24__type__1278___24t(V0__R,V6__ropp)
                             => ! [V7__req] :
                                  ( c_24__type__1300___24t(V0__R,V7__req)
                                 => ! [V8__rle] :
                                      ( c_24__type__1300___24t(V0__R,V8__rle)
                                     => ! [V9__rlt] :
                                          ( c_24__type__1300___24t(V0__R,V9__rlt)
                                         => ( cCoq_2emicromega_2eOrderedRing_2eSOR___24a10(V0__R,V1__rO,V2__rI,V3__rplus,V4__rtimes,V5__rminus,V6__ropp,V7__req,V8__rle,V9__rlt)
                                           => ! [V11__n] :
                                                ( t(V11__n,V0__R)
                                               => ! [V12__m] :
                                                    ( t(V12__m,V0__R)
                                                   => ! [V13__p] :
                                                        ( t(V13__p,V0__R)
                                                       => ! [V14__q] :
                                                            ( t(V14__q,V0__R)
                                                           => ( p(happ(happ(V8__rle,V11__n),V12__m))
                                                             => ( p(happ(happ(V9__rlt,V13__p),V14__q))
                                                               => p(happ(happ(V9__rlt,happ(happ(V3__rplus,V11__n),V13__p)),happ(happ(V3__rplus,V12__m),V14__q))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).

fof('Coq.micromega.OrderedRing.Rplus_le_mono',axiom,
    ! [V0__R] :
      ( cType___24t(V0__R)
     => ! [V1__rO] :
          ( t(V1__rO,V0__R)
         => ! [V2__rI] :
              ( t(V2__rI,V0__R)
             => ! [V3__rplus] :
                  ( c_24__type__1058___24t(V0__R,V3__rplus)
                 => ! [V4__rtimes] :
                      ( c_24__type__1058___24t(V0__R,V4__rtimes)
                     => ! [V5__rminus] :
                          ( c_24__type__1058___24t(V0__R,V5__rminus)
                         => ! [V6__ropp] :
                              ( c_24__type__1278___24t(V0__R,V6__ropp)
                             => ! [V7__req] :
                                  ( c_24__type__1300___24t(V0__R,V7__req)
                                 => ! [V8__rle] :
                                      ( c_24__type__1300___24t(V0__R,V8__rle)
                                     => ! [V9__rlt] :
                                          ( c_24__type__1300___24t(V0__R,V9__rlt)
                                         => ( cCoq_2emicromega_2eOrderedRing_2eSOR___24a10(V0__R,V1__rO,V2__rI,V3__rplus,V4__rtimes,V5__rminus,V6__ropp,V7__req,V8__rle,V9__rlt)
                                           => ! [V11__n] :
                                                ( t(V11__n,V0__R)
                                               => ! [V12__m] :
                                                    ( t(V12__m,V0__R)
                                                   => ! [V13__p] :
                                                        ( t(V13__p,V0__R)
                                                       => ! [V14__q] :
                                                            ( t(V14__q,V0__R)
                                                           => ( p(happ(happ(V8__rle,V11__n),V12__m))
                                                             => ( p(happ(happ(V8__rle,V13__p),V14__q))
                                                               => p(happ(happ(V8__rle,happ(happ(V3__rplus,V11__n),V13__p)),happ(happ(V3__rplus,V12__m),V14__q))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).

fof('Coq.micromega.OrderedRing.Rplus_lt_le_mono',axiom,
    ! [V0__R] :
      ( cType___24t(V0__R)
     => ! [V1__rO] :
          ( t(V1__rO,V0__R)
         => ! [V2__rI] :
              ( t(V2__rI,V0__R)
             => ! [V3__rplus] :
                  ( c_24__type__1058___24t(V0__R,V3__rplus)
                 => ! [V4__rtimes] :
                      ( c_24__type__1058___24t(V0__R,V4__rtimes)
                     => ! [V5__rminus] :
                          ( c_24__type__1058___24t(V0__R,V5__rminus)
                         => ! [V6__ropp] :
                              ( c_24__type__1278___24t(V0__R,V6__ropp)
                             => ! [V7__req] :
                                  ( c_24__type__1300___24t(V0__R,V7__req)
                                 => ! [V8__rle] :
                                      ( c_24__type__1300___24t(V0__R,V8__rle)
                                     => ! [V9__rlt] :
                                          ( c_24__type__1300___24t(V0__R,V9__rlt)
                                         => ( cCoq_2emicromega_2eOrderedRing_2eSOR___24a10(V0__R,V1__rO,V2__rI,V3__rplus,V4__rtimes,V5__rminus,V6__ropp,V7__req,V8__rle,V9__rlt)
                                           => ! [V11__n] :
                                                ( t(V11__n,V0__R)
                                               => ! [V12__m] :
                                                    ( t(V12__m,V0__R)
                                                   => ! [V13__p] :
                                                        ( t(V13__p,V0__R)
                                                       => ! [V14__q] :
                                                            ( t(V14__q,V0__R)
                                                           => ( p(happ(happ(V9__rlt,V11__n),V12__m))
                                                             => ( p(happ(happ(V8__rle,V13__p),V14__q))
                                                               => p(happ(happ(V9__rlt,happ(happ(V3__rplus,V11__n),V13__p)),happ(happ(V3__rplus,V12__m),V14__q))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).

fof('Coq.micromega.OrderedRing.Rplus_lt_mono',axiom,
    ! [V0__R] :
      ( cType___24t(V0__R)
     => ! [V1__rO] :
          ( t(V1__rO,V0__R)
         => ! [V2__rI] :
              ( t(V2__rI,V0__R)
             => ! [V3__rplus] :
                  ( c_24__type__1058___24t(V0__R,V3__rplus)
                 => ! [V4__rtimes] :
                      ( c_24__type__1058___24t(V0__R,V4__rtimes)
                     => ! [V5__rminus] :
                          ( c_24__type__1058___24t(V0__R,V5__rminus)
                         => ! [V6__ropp] :
                              ( c_24__type__1278___24t(V0__R,V6__ropp)
                             => ! [V7__req] :
                                  ( c_24__type__1300___24t(V0__R,V7__req)
                                 => ! [V8__rle] :
                                      ( c_24__type__1300___24t(V0__R,V8__rle)
                                     => ! [V9__rlt] :
                                          ( c_24__type__1300___24t(V0__R,V9__rlt)
                                         => ( cCoq_2emicromega_2eOrderedRing_2eSOR___24a10(V0__R,V1__rO,V2__rI,V3__rplus,V4__rtimes,V5__rminus,V6__ropp,V7__req,V8__rle,V9__rlt)
                                           => ! [V11__n] :
                                                ( t(V11__n,V0__R)
                                               => ! [V12__m] :
                                                    ( t(V12__m,V0__R)
                                                   => ! [V13__p] :
                                                        ( t(V13__p,V0__R)
                                                       => ! [V14__q] :
                                                            ( t(V14__q,V0__R)
                                                           => ( p(happ(happ(V9__rlt,V11__n),V12__m))
                                                             => ( p(happ(happ(V9__rlt,V13__p),V14__q))
                                                               => p(happ(happ(V9__rlt,happ(happ(V3__rplus,V11__n),V13__p)),happ(happ(V3__rplus,V12__m),V14__q))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).

fof('Coq.micromega.OrderedRing.Rplus_nonneg_nonneg',axiom,
    ! [V0__R] :
      ( cType___24t(V0__R)
     => ! [V1__rO] :
          ( t(V1__rO,V0__R)
         => ! [V2__rI] :
              ( t(V2__rI,V0__R)
             => ! [V3__rplus] :
                  ( c_24__type__1058___24t(V0__R,V3__rplus)
                 => ! [V4__rtimes] :
                      ( c_24__type__1058___24t(V0__R,V4__rtimes)
                     => ! [V5__rminus] :
                          ( c_24__type__1058___24t(V0__R,V5__rminus)
                         => ! [V6__ropp] :
                              ( c_24__type__1278___24t(V0__R,V6__ropp)
                             => ! [V7__req] :
                                  ( c_24__type__1300___24t(V0__R,V7__req)
                                 => ! [V8__rle] :
                                      ( c_24__type__1300___24t(V0__R,V8__rle)
                                     => ! [V9__rlt] :
                                          ( c_24__type__1300___24t(V0__R,V9__rlt)
                                         => ( cCoq_2emicromega_2eOrderedRing_2eSOR___24a10(V0__R,V1__rO,V2__rI,V3__rplus,V4__rtimes,V5__rminus,V6__ropp,V7__req,V8__rle,V9__rlt)
                                           => ! [V11__n] :
                                                ( t(V11__n,V0__R)
                                               => ! [V12__m] :
                                                    ( t(V12__m,V0__R)
                                                   => ( p(happ(happ(V8__rle,V1__rO),V11__n))
                                                     => ( p(happ(happ(V8__rle,V1__rO),V12__m))
                                                       => p(happ(happ(V8__rle,V1__rO),happ(happ(V3__rplus,V11__n),V12__m))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).

fof('Coq.micromega.OrderedRing.Rplus_nonneg_pos',axiom,
    ! [V0__R] :
      ( cType___24t(V0__R)
     => ! [V1__rO] :
          ( t(V1__rO,V0__R)
         => ! [V2__rI] :
              ( t(V2__rI,V0__R)
             => ! [V3__rplus] :
                  ( c_24__type__1058___24t(V0__R,V3__rplus)
                 => ! [V4__rtimes] :
                      ( c_24__type__1058___24t(V0__R,V4__rtimes)
                     => ! [V5__rminus] :
                          ( c_24__type__1058___24t(V0__R,V5__rminus)
                         => ! [V6__ropp] :
                              ( c_24__type__1278___24t(V0__R,V6__ropp)
                             => ! [V7__req] :
                                  ( c_24__type__1300___24t(V0__R,V7__req)
                                 => ! [V8__rle] :
                                      ( c_24__type__1300___24t(V0__R,V8__rle)
                                     => ! [V9__rlt] :
                                          ( c_24__type__1300___24t(V0__R,V9__rlt)
                                         => ( cCoq_2emicromega_2eOrderedRing_2eSOR___24a10(V0__R,V1__rO,V2__rI,V3__rplus,V4__rtimes,V5__rminus,V6__ropp,V7__req,V8__rle,V9__rlt)
                                           => ! [V11__n] :
                                                ( t(V11__n,V0__R)
                                               => ! [V12__m] :
                                                    ( t(V12__m,V0__R)
                                                   => ( p(happ(happ(V8__rle,V1__rO),V11__n))
                                                     => ( p(happ(happ(V9__rlt,V1__rO),V12__m))
                                                       => p(happ(happ(V9__rlt,V1__rO),happ(happ(V3__rplus,V11__n),V12__m))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).

fof('Coq.micromega.OrderedRing.Rplus_pos_nonneg',axiom,
    ! [V0__R] :
      ( cType___24t(V0__R)
     => ! [V1__rO] :
          ( t(V1__rO,V0__R)
         => ! [V2__rI] :
              ( t(V2__rI,V0__R)
             => ! [V3__rplus] :
                  ( c_24__type__1058___24t(V0__R,V3__rplus)
                 => ! [V4__rtimes] :
                      ( c_24__type__1058___24t(V0__R,V4__rtimes)
                     => ! [V5__rminus] :
                          ( c_24__type__1058___24t(V0__R,V5__rminus)
                         => ! [V6__ropp] :
                              ( c_24__type__1278___24t(V0__R,V6__ropp)
                             => ! [V7__req] :
                                  ( c_24__type__1300___24t(V0__R,V7__req)
                                 => ! [V8__rle] :
                                      ( c_24__type__1300___24t(V0__R,V8__rle)
                                     => ! [V9__rlt] :
                                          ( c_24__type__1300___24t(V0__R,V9__rlt)
                                         => ( cCoq_2emicromega_2eOrderedRing_2eSOR___24a10(V0__R,V1__rO,V2__rI,V3__rplus,V4__rtimes,V5__rminus,V6__ropp,V7__req,V8__rle,V9__rlt)
                                           => ! [V11__n] :
                                                ( t(V11__n,V0__R)
                                               => ! [V12__m] :
                                                    ( t(V12__m,V0__R)
                                                   => ( p(happ(happ(V9__rlt,V1__rO),V11__n))
                                                     => ( p(happ(happ(V8__rle,V1__rO),V12__m))
                                                       => p(happ(happ(V9__rlt,V1__rO),happ(happ(V3__rplus,V11__n),V12__m))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).

fof('Coq.micromega.OrderedRing.Rplus_pos_pos',axiom,
    ! [V0__R] :
      ( cType___24t(V0__R)
     => ! [V1__rO] :
          ( t(V1__rO,V0__R)
         => ! [V2__rI] :
              ( t(V2__rI,V0__R)
             => ! [V3__rplus] :
                  ( c_24__type__1058___24t(V0__R,V3__rplus)
                 => ! [V4__rtimes] :
                      ( c_24__type__1058___24t(V0__R,V4__rtimes)
                     => ! [V5__rminus] :
                          ( c_24__type__1058___24t(V0__R,V5__rminus)
                         => ! [V6__ropp] :
                              ( c_24__type__1278___24t(V0__R,V6__ropp)
                             => ! [V7__req] :
                                  ( c_24__type__1300___24t(V0__R,V7__req)
                                 => ! [V8__rle] :
                                      ( c_24__type__1300___24t(V0__R,V8__rle)
                                     => ! [V9__rlt] :
                                          ( c_24__type__1300___24t(V0__R,V9__rlt)
                                         => ( cCoq_2emicromega_2eOrderedRing_2eSOR___24a10(V0__R,V1__rO,V2__rI,V3__rplus,V4__rtimes,V5__rminus,V6__ropp,V7__req,V8__rle,V9__rlt)
                                           => ! [V11__n] :
                                                ( t(V11__n,V0__R)
                                               => ! [V12__m] :
                                                    ( t(V12__m,V0__R)
                                                   => ( p(happ(happ(V9__rlt,V1__rO),V11__n))
                                                     => ( p(happ(happ(V9__rlt,V1__rO),V12__m))
                                                       => p(happ(happ(V9__rlt,V1__rO),happ(happ(V3__rplus,V11__n),V12__m))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).

fof('Coq.micromega.OrderedRing.Rtimes_0_l',axiom,
    ! [V0__R] :
      ( cType___24t(V0__R)
     => ! [V1__rO] :
          ( t(V1__rO,V0__R)
         => ! [V2__rI] :
              ( t(V2__rI,V0__R)
             => ! [V3__rplus] :
                  ( c_24__type__1058___24t(V0__R,V3__rplus)
                 => ! [V4__rtimes] :
                      ( c_24__type__1058___24t(V0__R,V4__rtimes)
                     => ! [V5__rminus] :
                          ( c_24__type__1058___24t(V0__R,V5__rminus)
                         => ! [V6__ropp] :
                              ( c_24__type__1278___24t(V0__R,V6__ropp)
                             => ! [V7__req] :
                                  ( c_24__type__1300___24t(V0__R,V7__req)
                                 => ! [V8__rle] :
                                      ( c_24__type__1300___24t(V0__R,V8__rle)
                                     => ! [V9__rlt] :
                                          ( c_24__type__1300___24t(V0__R,V9__rlt)
                                         => ( cCoq_2emicromega_2eOrderedRing_2eSOR___24a10(V0__R,V1__rO,V2__rI,V3__rplus,V4__rtimes,V5__rminus,V6__ropp,V7__req,V8__rle,V9__rlt)
                                           => ! [V11__n] :
                                                ( t(V11__n,V0__R)
                                               => p(happ(happ(V7__req,happ(happ(V4__rtimes,V1__rO),V11__n)),V1__rO)) ) ) ) ) ) ) ) ) ) ) ) ) ).

fof('Coq.micromega.OrderedRing.Rtimes_0_r',axiom,
    ! [V0__R] :
      ( cType___24t(V0__R)
     => ! [V1__rO] :
          ( t(V1__rO,V0__R)
         => ! [V2__rI] :
              ( t(V2__rI,V0__R)
             => ! [V3__rplus] :
                  ( c_24__type__1058___24t(V0__R,V3__rplus)
                 => ! [V4__rtimes] :
                      ( c_24__type__1058___24t(V0__R,V4__rtimes)
                     => ! [V5__rminus] :
                          ( c_24__type__1058___24t(V0__R,V5__rminus)
                         => ! [V6__ropp] :
                              ( c_24__type__1278___24t(V0__R,V6__ropp)
                             => ! [V7__req] :
                                  ( c_24__type__1300___24t(V0__R,V7__req)
                                 => ! [V8__rle] :
                                      ( c_24__type__1300___24t(V0__R,V8__rle)
                                     => ! [V9__rlt] :
                                          ( c_24__type__1300___24t(V0__R,V9__rlt)
                                         => ( cCoq_2emicromega_2eOrderedRing_2eSOR___24a10(V0__R,V1__rO,V2__rI,V3__rplus,V4__rtimes,V5__rminus,V6__ropp,V7__req,V8__rle,V9__rlt)
                                           => ! [V11__n] :
                                                ( t(V11__n,V0__R)
                                               => p(happ(happ(V7__req,happ(happ(V4__rtimes,V11__n),V1__rO)),V1__rO)) ) ) ) ) ) ) ) ) ) ) ) ) ).

fof('Coq.micromega.OrderedRing.Rtimes_comm',axiom,
    ! [V0__R] :
      ( cType___24t(V0__R)
     => ! [V1__rO] :
          ( t(V1__rO,V0__R)
         => ! [V2__rI] :
              ( t(V2__rI,V0__R)
             => ! [V3__rplus] :
                  ( c_24__type__1058___24t(V0__R,V3__rplus)
                 => ! [V4__rtimes] :
                      ( c_24__type__1058___24t(V0__R,V4__rtimes)
                     => ! [V5__rminus] :
                          ( c_24__type__1058___24t(V0__R,V5__rminus)
                         => ! [V6__ropp] :
                              ( c_24__type__1278___24t(V0__R,V6__ropp)
                             => ! [V7__req] :
                                  ( c_24__type__1300___24t(V0__R,V7__req)
                                 => ! [V8__rle] :
                                      ( c_24__type__1300___24t(V0__R,V8__rle)
                                     => ! [V9__rlt] :
                                          ( c_24__type__1300___24t(V0__R,V9__rlt)
                                         => ( cCoq_2emicromega_2eOrderedRing_2eSOR___24a10(V0__R,V1__rO,V2__rI,V3__rplus,V4__rtimes,V5__rminus,V6__ropp,V7__req,V8__rle,V9__rlt)
                                           => ! [V11__n] :
                                                ( t(V11__n,V0__R)
                                               => ! [V12__m] :
                                                    ( t(V12__m,V0__R)
                                                   => p(happ(happ(V7__req,happ(happ(V4__rtimes,V11__n),V12__m)),happ(happ(V4__rtimes,V12__m),V11__n))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).

fof('Coq.micromega.OrderedRing.Rtimes_neg_neg',axiom,
    ! [V0__R] :
      ( cType___24t(V0__R)
     => ! [V1__rO] :
          ( t(V1__rO,V0__R)
         => ! [V2__rI] :
              ( t(V2__rI,V0__R)
             => ! [V3__rplus] :
                  ( c_24__type__1058___24t(V0__R,V3__rplus)
                 => ! [V4__rtimes] :
                      ( c_24__type__1058___24t(V0__R,V4__rtimes)
                     => ! [V5__rminus] :
                          ( c_24__type__1058___24t(V0__R,V5__rminus)
                         => ! [V6__ropp] :
                              ( c_24__type__1278___24t(V0__R,V6__ropp)
                             => ! [V7__req] :
                                  ( c_24__type__1300___24t(V0__R,V7__req)
                                 => ! [V8__rle] :
                                      ( c_24__type__1300___24t(V0__R,V8__rle)
                                     => ! [V9__rlt] :
                                          ( c_24__type__1300___24t(V0__R,V9__rlt)
                                         => ( cCoq_2emicromega_2eOrderedRing_2eSOR___24a10(V0__R,V1__rO,V2__rI,V3__rplus,V4__rtimes,V5__rminus,V6__ropp,V7__req,V8__rle,V9__rlt)
                                           => ! [V11__n] :
                                                ( t(V11__n,V0__R)
                                               => ! [V12__m] :
                                                    ( t(V12__m,V0__R)
                                                   => ( p(happ(happ(V9__rlt,V11__n),V1__rO))
                                                     => ( p(happ(happ(V9__rlt,V12__m),V1__rO))
                                                       => p(happ(happ(V9__rlt,V1__rO),happ(happ(V4__rtimes,V11__n),V12__m))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).

fof('Coq.micromega.OrderedRing.Rtimes_nonneg_nonneg',axiom,
    ! [V0__R] :
      ( cType___24t(V0__R)
     => ! [V1__rO] :
          ( t(V1__rO,V0__R)
         => ! [V2__rI] :
              ( t(V2__rI,V0__R)
             => ! [V3__rplus] :
                  ( c_24__type__1058___24t(V0__R,V3__rplus)
                 => ! [V4__rtimes] :
                      ( c_24__type__1058___24t(V0__R,V4__rtimes)
                     => ! [V5__rminus] :
                          ( c_24__type__1058___24t(V0__R,V5__rminus)
                         => ! [V6__ropp] :
                              ( c_24__type__1278___24t(V0__R,V6__ropp)
                             => ! [V7__req] :
                                  ( c_24__type__1300___24t(V0__R,V7__req)
                                 => ! [V8__rle] :
                                      ( c_24__type__1300___24t(V0__R,V8__rle)
                                     => ! [V9__rlt] :
                                          ( c_24__type__1300___24t(V0__R,V9__rlt)
                                         => ( cCoq_2emicromega_2eOrderedRing_2eSOR___24a10(V0__R,V1__rO,V2__rI,V3__rplus,V4__rtimes,V5__rminus,V6__ropp,V7__req,V8__rle,V9__rlt)
                                           => ! [V11__n] :
                                                ( t(V11__n,V0__R)
                                               => ! [V12__m] :
                                                    ( t(V12__m,V0__R)
                                                   => ( p(happ(happ(V8__rle,V1__rO),V11__n))
                                                     => ( p(happ(happ(V8__rle,V1__rO),V12__m))
                                                       => p(happ(happ(V8__rle,V1__rO),happ(happ(V4__rtimes,V11__n),V12__m))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).

fof('Coq.micromega.OrderedRing.Rtimes_pos_neg',axiom,
    ! [V0__R] :
      ( cType___24t(V0__R)
     => ! [V1__rO] :
          ( t(V1__rO,V0__R)
         => ! [V2__rI] :
              ( t(V2__rI,V0__R)
             => ! [V3__rplus] :
                  ( c_24__type__1058___24t(V0__R,V3__rplus)
                 => ! [V4__rtimes] :
                      ( c_24__type__1058___24t(V0__R,V4__rtimes)
                     => ! [V5__rminus] :
                          ( c_24__type__1058___24t(V0__R,V5__rminus)
                         => ! [V6__ropp] :
                              ( c_24__type__1278___24t(V0__R,V6__ropp)
                             => ! [V7__req] :
                                  ( c_24__type__1300___24t(V0__R,V7__req)
                                 => ! [V8__rle] :
                                      ( c_24__type__1300___24t(V0__R,V8__rle)
                                     => ! [V9__rlt] :
                                          ( c_24__type__1300___24t(V0__R,V9__rlt)
                                         => ( cCoq_2emicromega_2eOrderedRing_2eSOR___24a10(V0__R,V1__rO,V2__rI,V3__rplus,V4__rtimes,V5__rminus,V6__ropp,V7__req,V8__rle,V9__rlt)
                                           => ! [V11__n] :
                                                ( t(V11__n,V0__R)
                                               => ! [V12__m] :
                                                    ( t(V12__m,V0__R)
                                                   => ( p(happ(happ(V9__rlt,V1__rO),V11__n))
                                                     => ( p(happ(happ(V9__rlt,V12__m),V1__rO))
                                                       => p(happ(happ(V9__rlt,happ(happ(V4__rtimes,V11__n),V12__m)),V1__rO)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).

fof('Coq.micromega.OrderedRing.Rtimes_pos_pos',axiom,
    ! [V0__R] :
      ( cType___24t(V0__R)
     => ! [V1__rO] :
          ( t(V1__rO,V0__R)
         => ! [V2__rI] :
              ( t(V2__rI,V0__R)
             => ! [V3__rplus] :
                  ( c_24__type__1058___24t(V0__R,V3__rplus)
                 => ! [V4__rtimes] :
                      ( c_24__type__1058___24t(V0__R,V4__rtimes)
                     => ! [V5__rminus] :
                          ( c_24__type__1058___24t(V0__R,V5__rminus)
                         => ! [V6__ropp] :
                              ( c_24__type__1278___24t(V0__R,V6__ropp)
                             => ! [V7__req] :
                                  ( c_24__type__1300___24t(V0__R,V7__req)
                                 => ! [V8__rle] :
                                      ( c_24__type__1300___24t(V0__R,V8__rle)
                                     => ! [V9__rlt] :
                                          ( c_24__type__1300___24t(V0__R,V9__rlt)
                                         => ( cCoq_2emicromega_2eOrderedRing_2eSOR___24a10(V0__R,V1__rO,V2__rI,V3__rplus,V4__rtimes,V5__rminus,V6__ropp,V7__req,V8__rle,V9__rlt)
                                           => ! [V11__n] :
                                                ( t(V11__n,V0__R)
                                               => ! [V12__m] :
                                                    ( t(V12__m,V0__R)
                                                   => ( p(happ(happ(V9__rlt,V1__rO),V11__n))
                                                     => ( p(happ(happ(V9__rlt,V1__rO),V12__m))
                                                       => p(happ(happ(V9__rlt,V1__rO),happ(happ(V4__rtimes,V11__n),V12__m))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).

fof('Coq.micromega.OrderedRing.Rtimes_square_nonneg',axiom,
    ! [V0__R] :
      ( cType___24t(V0__R)
     => ! [V1__rO] :
          ( t(V1__rO,V0__R)
         => ! [V2__rI] :
              ( t(V2__rI,V0__R)
             => ! [V3__rplus] :
                  ( c_24__type__1058___24t(V0__R,V3__rplus)
                 => ! [V4__rtimes] :
                      ( c_24__type__1058___24t(V0__R,V4__rtimes)
                     => ! [V5__rminus] :
                          ( c_24__type__1058___24t(V0__R,V5__rminus)
                         => ! [V6__ropp] :
                              ( c_24__type__1278___24t(V0__R,V6__ropp)
                             => ! [V7__req] :
                                  ( c_24__type__1300___24t(V0__R,V7__req)
                                 => ! [V8__rle] :
                                      ( c_24__type__1300___24t(V0__R,V8__rle)
                                     => ! [V9__rlt] :
                                          ( c_24__type__1300___24t(V0__R,V9__rlt)
                                         => ( cCoq_2emicromega_2eOrderedRing_2eSOR___24a10(V0__R,V1__rO,V2__rI,V3__rplus,V4__rtimes,V5__rminus,V6__ropp,V7__req,V8__rle,V9__rlt)
                                           => ! [V11__n] :
                                                ( t(V11__n,V0__R)
                                               => p(happ(happ(V8__rle,V1__rO),happ(happ(V4__rtimes,V11__n),V11__n))) ) ) ) ) ) ) ) ) ) ) ) ) ).

fof('Coq.micromega.Tauto.eval_bf_map',axiom,
    ! [V0__T] :
      ( cType___24t(V0__T)
     => ! [V1__U] :
          ( cType___24t(V1__U)
         => ! [V2__fct] :
              ( c_24__type__85536___24t(V0__T,V1__U,V2__fct)
             => ! [V3__env] :
                  ( c_24__type__173544___24t(V0__T,V1__U,V3__env)
                 => ! [V4__f] :
                      ( cCoq_2emicromega_2eTauto_2eGFormula___24t(V0__T,cProp,cCoq_2eInit_2eDatatypes_2eunit,cCoq_2eInit_2eDatatypes_2eunit,V4__f)
                     => cCoq_2emicromega_2eTauto_2eeval__bf___24a3(V1__U,V3__env,cCoq_2emicromega_2eTauto_2emap__bformula___24a7(V0__T,V1__U,cProp,cCoq_2eInit_2eDatatypes_2eunit,cCoq_2eInit_2eDatatypes_2eunit,V2__fct,V4__f)) = cCoq_2emicromega_2eTauto_2eeval__bf___24a3(V0__T,c_24__lam__173555___24a4(V0__T,V1__U,V2__fct,V3__env),V4__f) ) ) ) ) ) ).

fof('Coq.micromega.ZCoeff.req_refl',axiom,
    ! [V0__R] :
      ( cType___24t(V0__R)
     => ! [V1__rO] :
          ( t(V1__rO,V0__R)
         => ! [V2__rI] :
              ( t(V2__rI,V0__R)
             => ! [V3__rplus] :
                  ( c_24__type__1058___24t(V0__R,V3__rplus)
                 => ! [V4__rtimes] :
                      ( c_24__type__1058___24t(V0__R,V4__rtimes)
                     => ! [V5__rminus] :
                          ( c_24__type__1058___24t(V0__R,V5__rminus)
                         => ! [V6__ropp] :
                              ( c_24__type__1278___24t(V0__R,V6__ropp)
                             => ! [V7__req] :
                                  ( c_24__type__1300___24t(V0__R,V7__req)
                                 => ! [V8__rle] :
                                      ( c_24__type__1300___24t(V0__R,V8__rle)
                                     => ! [V9__rlt] :
                                          ( c_24__type__1300___24t(V0__R,V9__rlt)
                                         => ( cCoq_2emicromega_2eOrderedRing_2eSOR___24a10(V0__R,V1__rO,V2__rI,V3__rplus,V4__rtimes,V5__rminus,V6__ropp,V7__req,V8__rle,V9__rlt)
                                           => ! [V11__x] :
                                                ( t(V11__x,V0__R)
                                               => p(happ(happ(V7__req,V11__x),V11__x)) ) ) ) ) ) ) ) ) ) ) ) ) ).

fof('Coq.micromega.ZCoeff.req_sym',axiom,
    ! [V0__R] :
      ( cType___24t(V0__R)
     => ! [V1__rO] :
          ( t(V1__rO,V0__R)
         => ! [V2__rI] :
              ( t(V2__rI,V0__R)
             => ! [V3__rplus] :
                  ( c_24__type__1058___24t(V0__R,V3__rplus)
                 => ! [V4__rtimes] :
                      ( c_24__type__1058___24t(V0__R,V4__rtimes)
                     => ! [V5__rminus] :
                          ( c_24__type__1058___24t(V0__R,V5__rminus)
                         => ! [V6__ropp] :
                              ( c_24__type__1278___24t(V0__R,V6__ropp)
                             => ! [V7__req] :
                                  ( c_24__type__1300___24t(V0__R,V7__req)
                                 => ! [V8__rle] :
                                      ( c_24__type__1300___24t(V0__R,V8__rle)
                                     => ! [V9__rlt] :
                                          ( c_24__type__1300___24t(V0__R,V9__rlt)
                                         => ( cCoq_2emicromega_2eOrderedRing_2eSOR___24a10(V0__R,V1__rO,V2__rI,V3__rplus,V4__rtimes,V5__rminus,V6__ropp,V7__req,V8__rle,V9__rlt)
                                           => ! [V11__x] :
                                                ( t(V11__x,V0__R)
                                               => ! [V12__y] :
                                                    ( t(V12__y,V0__R)
                                                   => ( p(happ(happ(V7__req,V11__x),V12__y))
                                                     => p(happ(happ(V7__req,V12__y),V11__x)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).

fof('Coq.micromega.ZCoeff.req_trans',axiom,
    ! [V0__R] :
      ( cType___24t(V0__R)
     => ! [V1__rO] :
          ( t(V1__rO,V0__R)
         => ! [V2__rI] :
              ( t(V2__rI,V0__R)
             => ! [V3__rplus] :
                  ( c_24__type__1058___24t(V0__R,V3__rplus)
                 => ! [V4__rtimes] :
                      ( c_24__type__1058___24t(V0__R,V4__rtimes)
                     => ! [V5__rminus] :
                          ( c_24__type__1058___24t(V0__R,V5__rminus)
                         => ! [V6__ropp] :
                              ( c_24__type__1278___24t(V0__R,V6__ropp)
                             => ! [V7__req] :
                                  ( c_24__type__1300___24t(V0__R,V7__req)
                                 => ! [V8__rle] :
                                      ( c_24__type__1300___24t(V0__R,V8__rle)
                                     => ! [V9__rlt] :
                                          ( c_24__type__1300___24t(V0__R,V9__rlt)
                                         => ( cCoq_2emicromega_2eOrderedRing_2eSOR___24a10(V0__R,V1__rO,V2__rI,V3__rplus,V4__rtimes,V5__rminus,V6__ropp,V7__req,V8__rle,V9__rlt)
                                           => ! [V11__x] :
                                                ( t(V11__x,V0__R)
                                               => ! [V12__y] :
                                                    ( t(V12__y,V0__R)
                                                   => ! [V13__z] :
                                                        ( t(V13__z,V0__R)
                                                       => ( p(happ(happ(V7__req,V11__x),V12__y))
                                                         => ( p(happ(happ(V7__req,V12__y),V13__z))
                                                           => p(happ(happ(V7__req,V11__x),V13__z)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).

fof('Coq.micromega.ZMicromega.Vars.max_element_max',axiom,
    ! [V0__x] :
      ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(V0__x)
     => ! [V1__vars] :
          ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(V1__vars)
         => ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2emem___24a2(V0__x,V1__vars) = cCoq_2eInit_2eDatatypes_2etrue
           => cCoq_2ePArith_2eBinPos_2ePos_2ele___24a2(V0__x,cCoq_2emicromega_2eZMicromega_2eVars_2emax__element___24a1(V1__vars)) ) ) ) ).

fof('Coq.micromega.ZMicromega.Zeval_nformula_dec',axiom,
    ! [V0__env] :
      ( cCoq_2emicromega_2eRingMicromega_2ePolEnv___24t(cCoq_2eNumbers_2eBinNums_2eZ,V0__env)
     => ! [V1__d] :
          ( cCoq_2emicromega_2eRingMicromega_2eNFormula___24t(cCoq_2eNumbers_2eBinNums_2eZ,V1__d)
         => ( cCoq_2emicromega_2eZMicromega_2eeval__nformula___24a2(V0__env,V1__d)
            | ~ cCoq_2emicromega_2eZMicromega_2eeval__nformula___24a2(V0__env,V1__d) ) ) ) ).

fof('Coq.micromega.ZMicromega.is_diff_env_ex',axiom,
    ! [V0__s] :
      ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(V0__s)
     => ! [V1__env] :
          ( c_24__type__14035___24t(V1__env)
         => cCoq_2emicromega_2eZMicromega_2eis__diff__env___24a3(V0__s,V1__env,cCoq_2emicromega_2eZMicromega_2emk__diff__env___24a2(V0__s,V1__env)) ) ) ).

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.ARadd_0_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__1058___24t(V0__R,V3__radd)
                 => ! [V4__rmul] :
                      ( c_24__type__1058___24t(V0__R,V4__rmul)
                     => ! [V5__rsub] :
                          ( c_24__type__1058___24t(V0__R,V5__rsub)
                         => ! [V6__ropp] :
                              ( c_24__type__1278___24t(V0__R,V6__ropp)
                             => ! [V7__req] :
                                  ( c_24__type__1300___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(V3__radd,V1__rO),V9__x)),V9__x)) ) ) ) ) ) ) ) ) ) ) ).

fof('Coq.setoid_ring.Ring_theory.ARadd_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__1058___24t(V0__R,V3__radd)
                 => ! [V4__rmul] :
                      ( c_24__type__1058___24t(V0__R,V4__rmul)
                     => ! [V5__rsub] :
                          ( c_24__type__1058___24t(V0__R,V5__rsub)
                         => ! [V6__ropp] :
                              ( c_24__type__1278___24t(V0__R,V6__ropp)
                             => ! [V7__req] :
                                  ( c_24__type__1300___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(V3__radd,V9__x),happ(happ(V3__radd,V10__y),V11__z))),happ(happ(V3__radd,happ(happ(V3__radd,V9__x),V10__y)),V11__z))) ) ) ) ) ) ) ) ) ) ) ) ) ).

fof('Coq.setoid_ring.Ring_theory.ARmul_0_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__1058___24t(V0__R,V3__radd)
                 => ! [V4__rmul] :
                      ( c_24__type__1058___24t(V0__R,V4__rmul)
                     => ! [V5__rsub] :
                          ( c_24__type__1058___24t(V0__R,V5__rsub)
                         => ! [V6__ropp] :
                              ( c_24__type__1278___24t(V0__R,V6__ropp)
                             => ! [V7__req] :
                                  ( c_24__type__1300___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,V1__rO),V9__x)),V1__rO)) ) ) ) ) ) ) ) ) ) ) ).

fof('Coq.setoid_ring.Ring_theory.ARmul_0_r',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__1058___24t(V0__R,V3__radd)
                 => ! [V4__rmul] :
                      ( c_24__type__1058___24t(V0__R,V4__rmul)
                     => ! [V5__rsub] :
                          ( c_24__type__1058___24t(V0__R,V5__rsub)
                         => ! [V6__ropp] :
                              ( c_24__type__1278___24t(V0__R,V6__ropp)
                             => ! [V7__req] :
                                  ( c_24__type__1300___24t(V0__R,V7__req)
                                 => ( cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(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)
                                     => ! [V10__x] :
                                          ( t(V10__x,V0__R)
                                         => p(happ(happ(V7__req,happ(happ(V4__rmul,V10__x),V1__rO)),V1__rO)) ) ) ) ) ) ) ) ) ) ) ) ).

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__1058___24t(V0__R,V3__radd)
                 => ! [V4__rmul] :
                      ( c_24__type__1058___24t(V0__R,V4__rmul)
                     => ! [V5__rsub] :
                          ( c_24__type__1058___24t(V0__R,V5__rsub)
                         => ! [V6__ropp] :
                              ( c_24__type__1278___24t(V0__R,V6__ropp)
                             => ! [V7__req] :
                                  ( c_24__type__1300___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__1058___24t(V0__R,V3__radd)
                 => ! [V4__rmul] :
                      ( c_24__type__1058___24t(V0__R,V4__rmul)
                     => ! [V5__rsub] :
                          ( c_24__type__1058___24t(V0__R,V5__rsub)
                         => ! [V6__ropp] :
                              ( c_24__type__1278___24t(V0__R,V6__ropp)
                             => ! [V7__req] :
                                  ( c_24__type__1300___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('Coq.setoid_ring.Ring_theory.ARmul_comm',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__1058___24t(V0__R,V3__radd)
                 => ! [V4__rmul] :
                      ( c_24__type__1058___24t(V0__R,V4__rmul)
                     => ! [V5__rsub] :
                          ( c_24__type__1058___24t(V0__R,V5__rsub)
                         => ! [V6__ropp] :
                              ( c_24__type__1278___24t(V0__R,V6__ropp)
                             => ! [V7__req] :
                                  ( c_24__type__1300___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)
                                           => p(happ(happ(V7__req,happ(happ(V4__rmul,V9__x),V10__y)),happ(happ(V4__rmul,V10__y),V9__x))) ) ) ) ) ) ) ) ) ) ) ) ).

fof('Coq.setoid_ring.Ring_theory.ARopp_mul_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__1058___24t(V0__R,V3__radd)
                 => ! [V4__rmul] :
                      ( c_24__type__1058___24t(V0__R,V4__rmul)
                     => ! [V5__rsub] :
                          ( c_24__type__1058___24t(V0__R,V5__rsub)
                         => ! [V6__ropp] :
                              ( c_24__type__1278___24t(V0__R,V6__ropp)
                             => ! [V7__req] :
                                  ( c_24__type__1300___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)
                                           => p(happ(happ(V7__req,happ(V6__ropp,happ(happ(V4__rmul,V9__x),V10__y))),happ(happ(V4__rmul,happ(V6__ropp,V9__x)),V10__y))) ) ) ) ) ) ) ) ) ) ) ) ).

fof('Coq.setoid_ring.Ring_theory.ARsub_def',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__1058___24t(V0__R,V3__radd)
                 => ! [V4__rmul] :
                      ( c_24__type__1058___24t(V0__R,V4__rmul)
                     => ! [V5__rsub] :
                          ( c_24__type__1058___24t(V0__R,V5__rsub)
                         => ! [V6__ropp] :
                              ( c_24__type__1278___24t(V0__R,V6__ropp)
                             => ! [V7__req] :
                                  ( c_24__type__1300___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)
                                           => p(happ(happ(V7__req,happ(happ(V5__rsub,V9__x),V10__y)),happ(happ(V3__radd,V9__x),happ(V6__ropp,V10__y)))) ) ) ) ) ) ) ) ) ) ) ) ).

fof('Coq.setoid_ring.Ring_theory.mk_art',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__1058___24t(V0__R,V3__radd)
                 => ! [V4__rmul] :
                      ( c_24__type__1058___24t(V0__R,V4__rmul)
                     => ! [V5__rsub] :
                          ( c_24__type__1058___24t(V0__R,V5__rsub)
                         => ! [V6__ropp] :
                              ( c_24__type__1278___24t(V0__R,V6__ropp)
                             => ! [V7__req] :
                                  ( c_24__type__1300___24t(V0__R,V7__req)
                                 => ( ! [V8__x] :
                                        ( t(V8__x,V0__R)
                                       => p(happ(happ(V7__req,happ(happ(V3__radd,V1__rO),V8__x)),V8__x)) )
                                   => ( ! [V9__x] :
                                          ( t(V9__x,V0__R)
                                         => ! [V10__y] :
                                              ( t(V10__y,V0__R)
                                             => p(happ(happ(V7__req,happ(happ(V3__radd,V9__x),V10__y)),happ(happ(V3__radd,V10__y),V9__x))) ) )
                                     => ( ! [V10__x] :
                                            ( t(V10__x,V0__R)
                                           => ! [V11__y] :
                                                ( t(V11__y,V0__R)
                                               => ! [V12__z] :
                                                    ( t(V12__z,V0__R)
                                                   => p(happ(happ(V7__req,happ(happ(V3__radd,V10__x),happ(happ(V3__radd,V11__y),V12__z))),happ(happ(V3__radd,happ(happ(V3__radd,V10__x),V11__y)),V12__z))) ) ) )
                                       => ( ! [V11__x] :
                                              ( t(V11__x,V0__R)
                                             => p(happ(happ(V7__req,happ(happ(V4__rmul,V2__rI),V11__x)),V11__x)) )
                                         => ( ! [V12__x] :
                                                ( t(V12__x,V0__R)
                                               => p(happ(happ(V7__req,happ(happ(V4__rmul,V1__rO),V12__x)),V1__rO)) )
                                           => ( ! [V13__x] :
                                                  ( t(V13__x,V0__R)
                                                 => ! [V14__y] :
                                                      ( t(V14__y,V0__R)
                                                     => p(happ(happ(V7__req,happ(happ(V4__rmul,V13__x),V14__y)),happ(happ(V4__rmul,V14__y),V13__x))) ) )
                                             => ( ! [V14__x] :
                                                    ( t(V14__x,V0__R)
                                                   => ! [V15__y] :
                                                        ( t(V15__y,V0__R)
                                                       => ! [V16__z] :
                                                            ( t(V16__z,V0__R)
                                                           => p(happ(happ(V7__req,happ(happ(V4__rmul,V14__x),happ(happ(V4__rmul,V15__y),V16__z))),happ(happ(V4__rmul,happ(happ(V4__rmul,V14__x),V15__y)),V16__z))) ) ) )
                                               => ( ! [V15__x] :
                                                      ( t(V15__x,V0__R)
                                                     => ! [V16__y] :
                                                          ( t(V16__y,V0__R)
                                                         => ! [V17__z] :
                                                              ( t(V17__z,V0__R)
                                                             => p(happ(happ(V7__req,happ(happ(V4__rmul,happ(happ(V3__radd,V15__x),V16__y)),V17__z)),happ(happ(V3__radd,happ(happ(V4__rmul,V15__x),V17__z)),happ(happ(V4__rmul,V16__y),V17__z)))) ) ) )
                                                 => ( ! [V16__x] :
                                                        ( t(V16__x,V0__R)
                                                       => ! [V17__y] :
                                                            ( t(V17__y,V0__R)
                                                           => p(happ(happ(V7__req,happ(V6__ropp,happ(happ(V4__rmul,V16__x),V17__y))),happ(happ(V4__rmul,happ(V6__ropp,V16__x)),V17__y))) ) )
                                                   => ( ! [V17__x] :
                                                          ( t(V17__x,V0__R)
                                                         => ! [V18__y] :
                                                              ( t(V18__y,V0__R)
                                                             => p(happ(happ(V7__req,happ(V6__ropp,happ(happ(V3__radd,V17__x),V18__y))),happ(happ(V3__radd,happ(V6__ropp,V17__x)),happ(V6__ropp,V18__y)))) ) )
                                                     => ( ! [V18__x] :
                                                            ( t(V18__x,V0__R)
                                                           => ! [V19__y] :
                                                                ( t(V19__y,V0__R)
                                                               => p(happ(happ(V7__req,happ(happ(V5__rsub,V18__x),V19__y)),happ(happ(V3__radd,V18__x),happ(V6__ropp,V19__y)))) ) )
                                                       => 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) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).

fof('Coq.setoid_ring.Ring_theory.mk_rt',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__1058___24t(V0__R,V3__radd)
                 => ! [V4__rmul] :
                      ( c_24__type__1058___24t(V0__R,V4__rmul)
                     => ! [V5__rsub] :
                          ( c_24__type__1058___24t(V0__R,V5__rsub)
                         => ! [V6__ropp] :
                              ( c_24__type__1278___24t(V0__R,V6__ropp)
                             => ! [V7__req] :
                                  ( c_24__type__1300___24t(V0__R,V7__req)
                                 => ( ! [V8__x] :
                                        ( t(V8__x,V0__R)
                                       => p(happ(happ(V7__req,happ(happ(V3__radd,V1__rO),V8__x)),V8__x)) )
                                   => ( ! [V9__x] :
                                          ( t(V9__x,V0__R)
                                         => ! [V10__y] :
                                              ( t(V10__y,V0__R)
                                             => p(happ(happ(V7__req,happ(happ(V3__radd,V9__x),V10__y)),happ(happ(V3__radd,V10__y),V9__x))) ) )
                                     => ( ! [V10__x] :
                                            ( t(V10__x,V0__R)
                                           => ! [V11__y] :
                                                ( t(V11__y,V0__R)
                                               => ! [V12__z] :
                                                    ( t(V12__z,V0__R)
                                                   => p(happ(happ(V7__req,happ(happ(V3__radd,V10__x),happ(happ(V3__radd,V11__y),V12__z))),happ(happ(V3__radd,happ(happ(V3__radd,V10__x),V11__y)),V12__z))) ) ) )
                                       => ( ! [V11__x] :
                                              ( t(V11__x,V0__R)
                                             => p(happ(happ(V7__req,happ(happ(V4__rmul,V2__rI),V11__x)),V11__x)) )
                                         => ( ! [V12__x] :
                                                ( t(V12__x,V0__R)
                                               => ! [V13__y] :
                                                    ( t(V13__y,V0__R)
                                                   => p(happ(happ(V7__req,happ(happ(V4__rmul,V12__x),V13__y)),happ(happ(V4__rmul,V13__y),V12__x))) ) )
                                           => ( ! [V13__x] :
                                                  ( t(V13__x,V0__R)
                                                 => ! [V14__y] :
                                                      ( t(V14__y,V0__R)
                                                     => ! [V15__z] :
                                                          ( t(V15__z,V0__R)
                                                         => p(happ(happ(V7__req,happ(happ(V4__rmul,V13__x),happ(happ(V4__rmul,V14__y),V15__z))),happ(happ(V4__rmul,happ(happ(V4__rmul,V13__x),V14__y)),V15__z))) ) ) )
                                             => ( ! [V14__x] :
                                                    ( t(V14__x,V0__R)
                                                   => ! [V15__y] :
                                                        ( t(V15__y,V0__R)
                                                       => ! [V16__z] :
                                                            ( t(V16__z,V0__R)
                                                           => p(happ(happ(V7__req,happ(happ(V4__rmul,happ(happ(V3__radd,V14__x),V15__y)),V16__z)),happ(happ(V3__radd,happ(happ(V4__rmul,V14__x),V16__z)),happ(happ(V4__rmul,V15__y),V16__z)))) ) ) )
                                               => ( ! [V15__x] :
                                                      ( t(V15__x,V0__R)
                                                     => ! [V16__y] :
                                                          ( t(V16__y,V0__R)
                                                         => p(happ(happ(V7__req,happ(happ(V5__rsub,V15__x),V16__y)),happ(happ(V3__radd,V15__x),happ(V6__ropp,V16__y)))) ) )
                                                 => ( ! [V16__x] :
                                                        ( t(V16__x,V0__R)
                                                       => p(happ(happ(V7__req,happ(happ(V3__radd,V16__x),happ(V6__ropp,V16__x))),V1__rO)) )
                                                   => cCoq_2esetoid__ring_2eRing__theory_2ering__theory___24a8(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__req) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).

fof('IntMap.Fset.FSet_Dom',axiom,
    ! [V0__s] :
      ( cIntMap_2eFset_2eFSet___24t(V0__s)
     => cIntMap_2eFset_2eMapDom___24a2(cCoq_2eInit_2eDatatypes_2eunit,V0__s) = V0__s ) ).

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__600___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__477___24a4(V0__A,V1__B,V2__m,V3__m_27)) ) ) ) ) ).

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_FSet_delta',axiom,
    ! [V0__s] :
      ( cIntMap_2eFset_2eFSet___24t(V0__s)
     => ! [V1__s_27] :
          ( cIntMap_2eFset_2eFSet___24t(V1__s_27)
         => ! [V2__a] :
              ( cIntMap_2eMap_2ead___24t(V2__a)
             => cIntMap_2eFset_2ein__FSet___24a2(V2__a,cIntMap_2eFset_2eFSetDelta___24a2(V0__s,V1__s_27)) = cCoq_2eInit_2eDatatypes_2exorb___24a2(cIntMap_2eFset_2ein__FSet___24a2(V2__a,V0__s),cIntMap_2eFset_2ein__FSet___24a2(V2__a,V1__s_27)) ) ) ) ).

fof('IntMap.Fset.in_FSet_diff',axiom,
    ! [V0__s] :
      ( cIntMap_2eFset_2eFSet___24t(V0__s)
     => ! [V1__s_27] :
          ( cIntMap_2eFset_2eFSet___24t(V1__s_27)
         => ! [V2__a] :
              ( cIntMap_2eMap_2ead___24t(V2__a)
             => cIntMap_2eFset_2ein__FSet___24a2(V2__a,cIntMap_2eFset_2eFSetDiff___24a2(V0__s,V1__s_27)) = cCoq_2eInit_2eDatatypes_2eandb___24a2(cIntMap_2eFset_2ein__FSet___24a2(V2__a,V0__s),cCoq_2eInit_2eDatatypes_2enegb___24a1(cIntMap_2eFset_2ein__FSet___24a2(V2__a,V1__s_27))) ) ) ) ).

fof('IntMap.Fset.in_FSet_inter',axiom,
    ! [V0__s] :
      ( cIntMap_2eFset_2eFSet___24t(V0__s)
     => ! [V1__s_27] :
          ( cIntMap_2eFset_2eFSet___24t(V1__s_27)
         => ! [V2__a] :
              ( cIntMap_2eMap_2ead___24t(V2__a)
             => cIntMap_2eFset_2ein__FSet___24a2(V2__a,cIntMap_2eFset_2eFSetInter___24a2(V0__s,V1__s_27)) = cCoq_2eInit_2eDatatypes_2eandb___24a2(cIntMap_2eFset_2ein__FSet___24a2(V2__a,V0__s),cIntMap_2eFset_2ein__FSet___24a2(V2__a,V1__s_27)) ) ) ) ).

fof('IntMap.Fset.in_FSet_union',axiom,
    ! [V0__s] :
      ( cIntMap_2eFset_2eFSet___24t(V0__s)
     => ! [V1__s_27] :
          ( cIntMap_2eFset_2eFSet___24t(V1__s_27)
         => ! [V2__a] :
              ( cIntMap_2eMap_2ead___24t(V2__a)
             => cIntMap_2eFset_2ein__FSet___24a2(V2__a,cIntMap_2eFset_2eFSetUnion___24a2(V0__s,V1__s_27)) = cCoq_2eInit_2eDatatypes_2eorb___24a2(cIntMap_2eFset_2ein__FSet___24a2(V2__a,V0__s),cIntMap_2eFset_2ein__FSet___24a2(V2__a,V1__s_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.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.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__1903___24a3(V0__A,V1__m,V2__m_27)) ) ) ) ).

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__971___24a3(V0__A,V1__m,V2__m_27)) ) ) ) ).

fof('IntMap.Map.Map_ind',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__P] :
          ( c_24__type__613___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('Mapaxioms.FSetDelta_assoc',axiom,
    ! [V0__s] :
      ( cIntMap_2eFset_2eFSet___24t(V0__s)
     => ! [V1__s_27] :
          ( cIntMap_2eFset_2eFSet___24t(V1__s_27)
         => ! [V2__s_27_27] :
              ( cIntMap_2eFset_2eFSet___24t(V2__s_27_27)
             => cMapaxioms_2eeqmap___24a3(cCoq_2eInit_2eDatatypes_2eunit,cIntMap_2eMap_2eMapDelta___24a3(cCoq_2eInit_2eDatatypes_2eunit,cIntMap_2eMap_2eMapDelta___24a3(cCoq_2eInit_2eDatatypes_2eunit,V0__s,V1__s_27),V2__s_27_27),cIntMap_2eMap_2eMapDelta___24a3(cCoq_2eInit_2eDatatypes_2eunit,V0__s,cIntMap_2eMap_2eMapDelta___24a3(cCoq_2eInit_2eDatatypes_2eunit,V1__s_27,V2__s_27_27))) ) ) ) ).

fof('Mapaxioms.FSetUnion_comm',axiom,
    ! [V0__s] :
      ( cIntMap_2eFset_2eFSet___24t(V0__s)
     => ! [V1__s_27] :
          ( cIntMap_2eFset_2eFSet___24t(V1__s_27)
         => cMapaxioms_2eeqmap___24a3(cCoq_2eInit_2eDatatypes_2eunit,cIntMap_2eFset_2eFSetUnion___24a2(V0__s,V1__s_27),cIntMap_2eFset_2eFSetUnion___24a2(V1__s_27,V0__s)) ) ) ).

fof('Mapaxioms.FSet_ext',axiom,
    ! [V0__s] :
      ( cIntMap_2eFset_2eFSet___24t(V0__s)
     => ! [V1__s_27] :
          ( cIntMap_2eFset_2eFSet___24t(V1__s_27)
         => ( ! [V2__a] :
                ( cIntMap_2eMap_2ead___24t(V2__a)
               => cIntMap_2eFset_2ein__FSet___24a2(V2__a,V0__s) = cIntMap_2eFset_2ein__FSet___24a2(V2__a,V1__s_27) )
           => cMapaxioms_2eeqmap___24a3(cCoq_2eInit_2eDatatypes_2eunit,V0__s,V1__s_27) ) ) ) ).

fof('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)
             => cMapaxioms_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('Mapaxioms.MapDelta_empty_m',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__m] :
          ( cIntMap_2eMap_2eMap___24t(V0__A,V1__m)
         => cMapaxioms_2eeqmap___24a3(V0__A,cIntMap_2eMap_2eMapDelta___24a3(V0__A,cIntMap_2eMap_2eM0___24a1(V0__A),V1__m),V1__m) ) ) ).

fof('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)
                     => ( cMapaxioms_2eeqmap___24a3(V0__A,V1__m1,V3__m_271)
                       => ( cMapaxioms_2eeqmap___24a3(V0__A,V2__m2,V4__m_272)
                         => cMapaxioms_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('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)
                 => ( cMapaxioms_2eeqmap___24a3(V0__A,V1__m1,V2__m_271)
                   => cMapaxioms_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('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)
                 => ( cMapaxioms_2eeqmap___24a3(V0__A,V2__m2,V3__m_272)
                   => cMapaxioms_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('Mapaxioms.MapDelta_m_empty',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__m] :
          ( cIntMap_2eMap_2eMap___24t(V0__A,V1__m)
         => cMapaxioms_2eeqmap___24a3(V0__A,cIntMap_2eMap_2eMapDelta___24a3(V0__A,V1__m,cIntMap_2eMap_2eM0___24a1(V0__A)),V1__m) ) ) ).

fof('Mapaxioms.MapDelta_nilpotent',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__m] :
          ( cIntMap_2eMap_2eMap___24t(V0__A,V1__m)
         => cMapaxioms_2eeqmap___24a3(V0__A,cIntMap_2eMap_2eMapDelta___24a3(V0__A,V1__m,V1__m),cIntMap_2eMap_2eM0___24a1(V0__A)) ) ) ).

fof('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)
             => cMapaxioms_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('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)
                     => cMapaxioms_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('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)
                         => cMapaxioms_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('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)
                 => cMapaxioms_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('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)
                         => cMapaxioms_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('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)
                         => cMapaxioms_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('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)
             => cMapaxioms_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('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)
                         => ( cMapaxioms_2eeqmap___24a3(V0__A,V2__m1,V4__m_271)
                           => ( cMapaxioms_2eeqmap___24a3(V1__B,V3__m2,V5__m_272)
                             => cMapaxioms_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('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)
                     => ( cMapaxioms_2eeqmap___24a3(V0__A,V2__m1,V4__m_271)
                       => cMapaxioms_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('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)
                     => ( cMapaxioms_2eeqmap___24a3(V1__B,V3__m2,V4__m_272)
                       => cMapaxioms_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('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)
             => cMapaxioms_2eeqmap___24a3(V0__A,cIntMap_2eFset_2eMapDomRestrBy___24a4(V0__A,V1__B,V2__m,cIntMap_2eMap_2eM0___24a1(V1__B)),V2__m) ) ) ) ).

fof('Mapaxioms.MapDomRestrBy_m_m',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__m] :
          ( cIntMap_2eMap_2eMap___24t(V0__A,V1__m)
         => cMapaxioms_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('Mapaxioms.MapDomRestrBy_m_m_1',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__m] :
          ( cIntMap_2eMap_2eMap___24t(V0__A,V1__m)
         => cMapaxioms_2eeqmap___24a3(V0__A,cIntMap_2eFset_2eMapDomRestrBy___24a4(V0__A,V0__A,V1__m,V1__m),cIntMap_2eMap_2eM0___24a1(V0__A)) ) ) ).

fof('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)
                         => cMapaxioms_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('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)
                         => cMapaxioms_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('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)
                 => cMapaxioms_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('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)
                         => cMapaxioms_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('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)
                         => cMapaxioms_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('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)
             => cMapaxioms_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('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)
                         => ( cMapaxioms_2eeqmap___24a3(V0__A,V2__m1,V4__m_271)
                           => ( cMapaxioms_2eeqmap___24a3(V1__B,V3__m2,V5__m_272)
                             => cMapaxioms_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('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)
                     => ( cMapaxioms_2eeqmap___24a3(V0__A,V2__m1,V4__m_271)
                       => cMapaxioms_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('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)
                     => ( cMapaxioms_2eeqmap___24a3(V1__B,V3__m2,V4__m_272)
                       => cMapaxioms_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('Mapaxioms.MapDomRestrTo_idempotent',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__m] :
          ( cIntMap_2eMap_2eMap___24t(V0__A,V1__m)
         => cMapaxioms_2eeqmap___24a3(V0__A,cIntMap_2eFset_2eMapDomRestrTo___24a4(V0__A,V0__A,V1__m,V1__m),V1__m) ) ) ).

fof('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)
             => cMapaxioms_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('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)
                 => cMapaxioms_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('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)
                 => cMapaxioms_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('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)
                 => cMapaxioms_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('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)
                     => cMapaxioms_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('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)
                     => cMapaxioms_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('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)
                 => cMapaxioms_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('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)
                 => cMapaxioms_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('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)
             => ( cMapaxioms_2eeqmap___24a3(V0__A,cIntMap_2eMap_2eMapMerge___24a3(V0__A,V1__m,V2__m_27),cIntMap_2eMap_2eM0___24a1(V0__A))
               => cMapaxioms_2eeqmap___24a3(V0__A,V1__m,cIntMap_2eMap_2eM0___24a1(V0__A)) ) ) ) ) ).

fof('Mapaxioms.MapMerge_empty_m',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__m] :
          ( cIntMap_2eMap_2eMap___24t(V0__A,V1__m)
         => cMapaxioms_2eeqmap___24a3(V0__A,cIntMap_2eMap_2eMapMerge___24a3(V0__A,cIntMap_2eMap_2eM0___24a1(V0__A),V1__m),V1__m) ) ) ).

fof('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)
             => ( cMapaxioms_2eeqmap___24a3(V0__A,cIntMap_2eMap_2eMapMerge___24a3(V0__A,V1__m,V2__m_27),cIntMap_2eMap_2eM0___24a1(V0__A))
               => cMapaxioms_2eeqmap___24a3(V0__A,V2__m_27,cIntMap_2eMap_2eM0___24a1(V0__A)) ) ) ) ) ).

fof('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)
                     => ( cMapaxioms_2eeqmap___24a3(V0__A,V1__m1,V3__m_271)
                       => ( cMapaxioms_2eeqmap___24a3(V0__A,V2__m2,V4__m_272)
                         => cMapaxioms_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('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)
                 => ( cMapaxioms_2eeqmap___24a3(V0__A,V1__m1,V2__m_271)
                   => cMapaxioms_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('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)
                 => ( cMapaxioms_2eeqmap___24a3(V0__A,V2__m2,V3__m_272)
                   => cMapaxioms_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('Mapaxioms.MapMerge_idempotent',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__m] :
          ( cIntMap_2eMap_2eMap___24t(V0__A,V1__m)
         => cMapaxioms_2eeqmap___24a3(V0__A,cIntMap_2eMap_2eMapMerge___24a3(V0__A,V1__m,V1__m),V1__m) ) ) ).

fof('Mapaxioms.MapMerge_m_empty',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__m] :
          ( cIntMap_2eMap_2eMap___24t(V0__A,V1__m)
         => cMapaxioms_2eeqmap___24a3(V0__A,cIntMap_2eMap_2eMapMerge___24a3(V0__A,V1__m,cIntMap_2eMap_2eM0___24a1(V0__A)),V1__m) ) ) ).

fof('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)
                 => cMapaxioms_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('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)
                 => cMapaxioms_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('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)
             => ( cMapaxioms_2eeqmap___24a3(V0__A,V1__m,V2__m_27)
               => ! [V4__a] :
                    ( cIntMap_2eMap_2ead___24t(V4__a)
                   => ! [V5__y] :
                        ( t(V5__y,V0__A)
                       => cMapaxioms_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('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)
             => ( cMapaxioms_2eeqmap___24a3(V0__A,V1__m,V2__m_27)
               => ! [V4__a] :
                    ( cIntMap_2eMap_2ead___24t(V4__a)
                   => ! [V5__y] :
                        ( t(V5__y,V0__A)
                       => cMapaxioms_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('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)
                     => cMapaxioms_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('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)
             => ( cMapaxioms_2eeqmap___24a3(V0__A,V1__m,V2__m_27)
               => ! [V4__a] :
                    ( cIntMap_2eMap_2ead___24t(V4__a)
                   => cMapaxioms_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('Mapaxioms.eqm_refl',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__f] :
          ( c_24__type__157___24t(V0__A,V1__f)
         => cIntMap_2eMap_2eeqm___24a3(V0__A,V1__f,V1__f) ) ) ).

fof('Mapaxioms.eqm_sym',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__f] :
          ( c_24__type__157___24t(V0__A,V1__f)
         => ! [V2__f_27] :
              ( c_24__type__157___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('Mapaxioms.eqm_trans',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__f] :
          ( c_24__type__157___24t(V0__A,V1__f)
         => ! [V2__f_27] :
              ( c_24__type__157___24t(V0__A,V2__f_27)
             => ! [V3__f_27_27] :
                  ( c_24__type__157___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('Mapaxioms.eqmap_refl',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__m] :
          ( cIntMap_2eMap_2eMap___24t(V0__A,V1__m)
         => cMapaxioms_2eeqmap___24a3(V0__A,V1__m,V1__m) ) ) ).

fof('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)
             => ( cMapaxioms_2eeqmap___24a3(V0__A,V1__m,V2__m_27)
               => cMapaxioms_2eeqmap___24a3(V0__A,V2__m_27,V1__m) ) ) ) ) ).

fof('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)
                 => ( cMapaxioms_2eeqmap___24a3(V0__A,V1__m,V2__m_27)
                   => ( cMapaxioms_2eeqmap___24a3(V0__A,V2__m_27,V3__m_27_27)
                     => cMapaxioms_2eeqmap___24a3(V0__A,V1__m,V3__m_27_27) ) ) ) ) ) ) ).

fof('$adef_IntMap.Map.M0_$a1',axiom,
    ! [V_24X1] : happ(cIntMap_2eMap_2eM0,V_24X1) = cIntMap_2eMap_2eM0___24a1(V_24X1) ).

fof('$adef_Coq.FSets.FSetPositive.PositiveSet.xfold_$a5',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2exfold,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2exfold___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).

fof('$adef_Coq.Arith.PeanoNat.Nat.eqf_$a2',axiom,
    ! [V_24X1,V_24X2] :
      ( p(happ(happ(cCoq_2eArith_2ePeanoNat_2eNat_2eeqf,V_24X1),V_24X2))
    <=> cCoq_2eArith_2ePeanoNat_2eNat_2eeqf___24a2(V_24X1,V_24X2) ) ).

fof('$adef_Coq.micromega.ZMicromega.Vars.max_element_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2emicromega_2eZMicromega_2eVars_2emax__element,V_24X1) = cCoq_2emicromega_2eZMicromega_2eVars_2emax__element___24a1(V_24X1) ).

fof('$adef_Coq.NArith.Ndigits.eqf_$a2',axiom,
    ! [V_24X1,V_24X2] :
      ( p(happ(happ(cCoq_2eNArith_2eNdigits_2eeqf,V_24X1),V_24X2))
    <=> cCoq_2eNArith_2eNdigits_2eeqf___24a2(V_24X1,V_24X2) ) ).

fof('$adef_Coq.PArith.BinPos.Pos.PeanoSucc_$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('$adef_Coq.setoid_ring.Ring_theory.SRopp_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2esetoid__ring_2eRing__theory_2eSRopp,V_24X1) = cCoq_2esetoid__ring_2eRing__theory_2eSRopp___24a1(V_24X1) ).

fof('$adef_$_lam_96901_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__96901,V_24X1),V_24X2),V_24X3) = c_24__lam__96901___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_Coq.Reals.Rdefinitions.IZR_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eReals_2eRdefinitions_2eIZR,V_24X1) = cCoq_2eReals_2eRdefinitions_2eIZR___24a1(V_24X1) ).

fof('$adef_Coq.Relations.Relation_Definitions.preorder_$a2',axiom,
    ! [V_24X1,V_24X2] :
      ( p(happ(happ(cCoq_2eRelations_2eRelation__Definitions_2epreorder,V_24X1),V_24X2))
    <=> cCoq_2eRelations_2eRelation__Definitions_2epreorder___24a2(V_24X1,V_24X2) ) ).

fof('$adef_Coq.Init.Datatypes.None_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eInit_2eDatatypes_2eNone,V_24X1) = cCoq_2eInit_2eDatatypes_2eNone___24a1(V_24X1) ).

fof('$adef_Coq.ZArith.BinIntDef.Z.to_nat_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eZArith_2eBinIntDef_2eZ_2eto__nat,V_24X1) = cCoq_2eZArith_2eBinIntDef_2eZ_2eto__nat___24a1(V_24X1) ).

fof('$adef_Coq.NArith.BinNat.N.lt_$a2',axiom,
    ! [V_24X1,V_24X2] :
      ( p(happ(happ(cCoq_2eNArith_2eBinNat_2eN_2elt,V_24X1),V_24X2))
    <=> cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V_24X1,V_24X2) ) ).

fof('$adef_Coq.Vectors.VectorDef.cons_$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('$adef_Coq.micromega.ZMicromega.eval_nformula_$a2',axiom,
    ! [V_24X1,V_24X2] :
      ( p(happ(happ(cCoq_2emicromega_2eZMicromega_2eeval__nformula,V_24X1),V_24X2))
    <=> cCoq_2emicromega_2eZMicromega_2eeval__nformula___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('$adef_$_lam_854_$a1',axiom,
    ! [V_24X1] : happ(c_24__lam__854,V_24X1) = c_24__lam__854___24a1(V_24X1) ).

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('$adef_$_lam_862_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__lam__862,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__lam__862___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).

fof('$adef_Coq.PArith.BinPosDef.Pos.of_nat_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2ePArith_2eBinPosDef_2ePos_2eof__nat,V_24X1) = cCoq_2ePArith_2eBinPosDef_2ePos_2eof__nat___24a1(V_24X1) ).

fof('$adef_Coq.Init.Decimal.nzhead_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eInit_2eDecimal_2enzhead,V_24X1) = cCoq_2eInit_2eDecimal_2enzhead___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('$adef_$_lam_363_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(c_24__lam__363,V_24X1),V_24X2) = c_24__lam__363___24a2(V_24X1,V_24X2) ).

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('$adef_Coq.micromega.RingMicromega.PsatzMulC_$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_173527_$a1',axiom,
    ! [V_24X1] : happ(c_24__lam__173527,V_24X1) = c_24__lam__173527___24a1(V_24X1) ).

fof('$adef_Coq.micromega.RingMicromega.eval_pol_$a5',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2emicromega_2eRingMicromega_2eeval__pol,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2emicromega_2eRingMicromega_2eeval__pol___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('$adef_Coq.Vectors.VectorDef.Forall_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] :
      ( p(happ(happ(happ(happ(cCoq_2eVectors_2eVectorDef_2eForall,V_24X1),V_24X2),V_24X3),V_24X4))
    <=> cCoq_2eVectors_2eVectorDef_2eForall___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).

fof('$adef_$_lam_686_$a5',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(c_24__lam__686,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = c_24__lam__686___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).

fof('$adef_Coq.Init.Datatypes.implb_$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('$adef_$_lam_862_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__862,V_24X1),V_24X2),V_24X3) = c_24__lam__862___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_Coq.micromega.Tauto.eval_tt_$a5',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2emicromega_2eTauto_2eeval__tt,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2emicromega_2eTauto_2eeval__tt___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).

fof('$adef_Coq.micromega.ZMicromega.is_diff_env_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] :
      ( p(happ(happ(happ(cCoq_2emicromega_2eZMicromega_2eis__diff__env,V_24X1),V_24X2),V_24X3))
    <=> cCoq_2emicromega_2eZMicromega_2eis__diff__env___24a3(V_24X1,V_24X2,V_24X3) ) ).

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('$adef_Coq.setoid_ring.Ring_polynom.PEmul_$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('$adef_Coq.micromega.DeclConstant.GT_$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('$adef_Coq.Init.Nat.log2_iter_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2eInit_2eNat_2elog2__iter,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2eInit_2eNat_2elog2__iter___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).

fof('$adef_Coq.Relations.Relation_Definitions.symmetric_$a2',axiom,
    ! [V_24X1,V_24X2] :
      ( p(happ(happ(cCoq_2eRelations_2eRelation__Definitions_2esymmetric,V_24X1),V_24X2))
    <=> cCoq_2eRelations_2eRelation__Definitions_2esymmetric___24a2(V_24X1,V_24X2) ) ).

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_96925_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__96925,V_24X1),V_24X2),V_24X3) = c_24__lam__96925___24a3(V_24X1,V_24X2,V_24X3) ).

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('$adef_Coq.setoid_ring.Ring_polynom.Pol_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2esetoid__ring_2eRing__polynom_2ePol,V_24X1) = cCoq_2esetoid__ring_2eRing__polynom_2ePol___24a1(V_24X1) ).

fof('$adef_Coq.FSets.FSetPositive.PositiveSet.mem_$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('$adef_Coq.Arith.Between.P_nth_$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('$adef_Coq.Relations.Relation_Operators.clos_refl_sym_trans_n1_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] :
      ( p(happ(happ(happ(happ(cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans__n1,V_24X1),V_24X2),V_24X3),V_24X4))
    <=> cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans__n1___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).

fof('$adef_$_prop_113529_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__prop__113529,V_24X1),V_24X2),V_24X3) = c_24__prop__113529___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_Coq.Reals.Rdefinitions.IPR_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eReals_2eRdefinitions_2eIPR,V_24X1) = cCoq_2eReals_2eRdefinitions_2eIPR___24a1(V_24X1) ).

fof('$adef_Coq.micromega.Env.Env_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2emicromega_2eEnv_2eEnv,V_24X1) = cCoq_2emicromega_2eEnv_2eEnv___24a1(V_24X1) ).

fof('$adef_Coq.Init.Datatypes.CompareSpecT_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2eInit_2eDatatypes_2eCompareSpecT,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2eInit_2eDatatypes_2eCompareSpecT___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).

fof('$adef_Coq.ZArith.BinIntDef.Z.pred_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eZArith_2eBinIntDef_2eZ_2epred,V_24X1) = cCoq_2eZArith_2eBinIntDef_2eZ_2epred___24a1(V_24X1) ).

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('$adef_Coq.setoid_ring.Field_theory.FEdiv_$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('$adef_IntMap.Map.MapDelta_$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('$adef_Coq.Init.Nat.compare_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eNat_2ecompare,V_24X1),V_24X2) = cCoq_2eInit_2eNat_2ecompare___24a2(V_24X1,V_24X2) ).

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('$adef_Coq.micromega.Tauto.eval_f_$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_2emicromega_2eTauto_2eeval__f,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7))
    <=> cCoq_2emicromega_2eTauto_2eeval__f___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7) ) ).

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('$adef_Coq.Init.Specif.existT_$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('$adef_Coq.Init.Decimal.D6_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eInit_2eDecimal_2eD6,V_24X1) = cCoq_2eInit_2eDecimal_2eD6___24a1(V_24X1) ).

fof('$adef_Coq.Init.Specif.sig_$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('$adef_Coq.ZArith.BinIntDef.Z.leb_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eBinIntDef_2eZ_2eleb,V_24X1),V_24X2) = cCoq_2eZArith_2eBinIntDef_2eZ_2eleb___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.Relations.Relation_Operators.lexprod_$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_2elexprod,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6))
    <=> cCoq_2eRelations_2eRelation__Operators_2elexprod___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ) ).

fof('$adef_Coq.setoid_ring.Field_theory.FEmul_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2esetoid__ring_2eField__theory_2eFEmul,V_24X1),V_24X2),V_24X3) = cCoq_2esetoid__ring_2eField__theory_2eFEmul___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_Coq.ZArith.BinIntDef.Z.mul_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eBinIntDef_2eZ_2emul,V_24X1),V_24X2) = cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V_24X1,V_24X2) ).

fof('$adef_$_lam_173531_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] :
      ( p(happ(happ(happ(c_24__lam__173531,V_24X1),V_24X2),V_24X3))
    <=> c_24__lam__173531___24a3(V_24X1,V_24X2,V_24X3) ) ).

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('$adef_Coq.FSets.FSetPositive.PositiveSet.Equal_$a2',axiom,
    ! [V_24X1,V_24X2] :
      ( p(happ(happ(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eEqual,V_24X1),V_24X2))
    <=> cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eEqual___24a2(V_24X1,V_24X2) ) ).

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('$adef_Coq.setoid_ring.Ring_polynom.mkmult_pow_$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('$adef_Coq.Init.Specif.sumbool_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eSpecif_2esumbool,V_24X1),V_24X2) = cCoq_2eInit_2eSpecif_2esumbool___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.setoid_ring.Field_theory.mk_rsplit_$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('$adef_Coq.Lists.List.last_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eLists_2eList_2elast,V_24X1),V_24X2),V_24X3) = cCoq_2eLists_2eList_2elast___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_$_prop_113546_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(c_24__prop__113546,V_24X1),V_24X2) = c_24__prop__113546___24a2(V_24X1,V_24X2) ).

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('$adef_Coq.setoid_ring.Ring_theory.semi_ring_theory_$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('$adef_Coq.micromega.RingMicromega.check_inconsistent_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2emicromega_2eRingMicromega_2echeck__inconsistent,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2emicromega_2eRingMicromega_2echeck__inconsistent___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).

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('$adef_IntMap.Map.makeM2_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cIntMap_2eMap_2emakeM2,V_24X1),V_24X2),V_24X3) = cIntMap_2eMap_2emakeM2___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_Coq.Init.Specif.proj1_sig_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eInit_2eSpecif_2eproj1__sig,V_24X1),V_24X2),V_24X3) = cCoq_2eInit_2eSpecif_2eproj1__sig___24a3(V_24X1,V_24X2,V_24X3) ).

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('$adef_Coq.FSets.FSetPositive.PositiveSet.ct_$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('$adef_Coq.Init.Nat.max_$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('$adef_$_case_Coq.Init.Datatypes.nat$110440_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__case__Coq_2eInit_2eDatatypes_2enat_24110440,V_24X1),V_24X2),V_24X3) = c_24__case__Coq_2eInit_2eDatatypes_2enat_24110440___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_Coq.PArith.BinPosDef.Pos.pred_N_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2ePArith_2eBinPosDef_2ePos_2epred__N,V_24X1) = cCoq_2ePArith_2eBinPosDef_2ePos_2epred__N___24a1(V_24X1) ).

fof('$adef_$_lam_436_$a5',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(c_24__lam__436,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = c_24__lam__436___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).

fof('$adef_Coq.Structures.OrderedTypeEx.Z_as_OT.lt_$a2',axiom,
    ! [V_24X1,V_24X2] :
      ( p(happ(happ(cCoq_2eStructures_2eOrderedTypeEx_2eZ__as__OT_2elt,V_24X1),V_24X2))
    <=> cCoq_2eStructures_2eOrderedTypeEx_2eZ__as__OT_2elt___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('$adef_Coq.setoid_ring.Ring_polynom.Peq_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2ePeq,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).

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('$adef_$_lam_1852_$a5',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(c_24__lam__1852,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = c_24__lam__1852___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('$adef_Coq.Arith.Plus.tail_plus_$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('$adef_Coq.Init.Datatypes.CompOpp_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eInit_2eDatatypes_2eCompOpp,V_24X1) = cCoq_2eInit_2eDatatypes_2eCompOpp___24a1(V_24X1) ).

fof('$adef_$_lam_910_$a1',axiom,
    ! [V_24X1] : happ(c_24__lam__910,V_24X1) = c_24__lam__910___24a1(V_24X1) ).

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('$adef_Coq.Init.Datatypes.unit_rec_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eInit_2eDatatypes_2eunit__rec,V_24X1) = cCoq_2eInit_2eDatatypes_2eunit__rec___24a1(V_24X1) ).

fof('$adef_$_lam_723_$a5',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(c_24__lam__723,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = c_24__lam__723___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).

fof('$adef_Coq.Init.Nat.square_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eInit_2eNat_2esquare,V_24X1) = cCoq_2eInit_2eNat_2esquare___24a1(V_24X1) ).

fof('$adef_Coq.setoid_ring.Field_theory.FExpr_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2esetoid__ring_2eField__theory_2eFExpr,V_24X1) = cCoq_2esetoid__ring_2eField__theory_2eFExpr___24a1(V_24X1) ).

fof('$adef_$_lam_173527_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] :
      ( p(happ(happ(happ(c_24__lam__173527,V_24X1),V_24X2),V_24X3))
    <=> c_24__lam__173527___24a3(V_24X1,V_24X2,V_24X3) ) ).

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('$adef_$_lam_96909_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__96909,V_24X1),V_24X2),V_24X3) = c_24__lam__96909___24a3(V_24X1,V_24X2,V_24X3) ).

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('$adef_Coq.micromega.Tauto.BFormula_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2emicromega_2eTauto_2eBFormula,V_24X1) = cCoq_2emicromega_2eTauto_2eBFormula___24a1(V_24X1) ).

fof('$adef_Coq.Init.Datatypes.id_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eDatatypes_2eid,V_24X1),V_24X2) = cCoq_2eInit_2eDatatypes_2eid___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.micromega.ZMicromega.agree_env_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] :
      ( p(happ(happ(happ(cCoq_2emicromega_2eZMicromega_2eagree__env,V_24X1),V_24X2),V_24X3))
    <=> cCoq_2emicromega_2eZMicromega_2eagree__env___24a3(V_24X1,V_24X2,V_24X3) ) ).

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('$adef_Coq.micromega.Tauto.and_cnf_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2emicromega_2eTauto_2eand__cnf,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2emicromega_2eTauto_2eand__cnf___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).

fof('$adef_Coq.Relations.Relation_Definitions.order_$a2',axiom,
    ! [V_24X1,V_24X2] :
      ( p(happ(happ(cCoq_2eRelations_2eRelation__Definitions_2eorder,V_24X1),V_24X2))
    <=> cCoq_2eRelations_2eRelation__Definitions_2eorder___24a2(V_24X1,V_24X2) ) ).

fof('$adef_Coq.micromega.Tauto.eval_cnf_$a6',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] :
      ( p(happ(happ(happ(happ(happ(happ(cCoq_2emicromega_2eTauto_2eeval__cnf,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6))
    <=> cCoq_2emicromega_2eTauto_2eeval__cnf___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ) ).

fof('$adef_Coq.micromega.Tauto.cnf_ff_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2emicromega_2eTauto_2ecnf__ff,V_24X1),V_24X2) = cCoq_2emicromega_2eTauto_2ecnf__ff___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.micromega.Tauto.TFormula_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2emicromega_2eTauto_2eTFormula,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2emicromega_2eTauto_2eTFormula___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).

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('$adef_Coq.FSets.FSetPositive.PositiveSet.elements_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelements,V_24X1) = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelements___24a1(V_24X1) ).

fof('$adef_$_lam_870_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__lam__870,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__lam__870___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).

fof('$adef_Coq.Bool.Zerob.zerob_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eBool_2eZerob_2ezerob,V_24X1) = cCoq_2eBool_2eZerob_2ezerob___24a1(V_24X1) ).

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('$adef_IntMap.Map.M1_$a1',axiom,
    ! [V_24X1] : happ(cIntMap_2eMap_2eM1,V_24X1) = cIntMap_2eMap_2eM1___24a1(V_24X1) ).

fof('$adef_Coq.Init.Nat.eqb_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eNat_2eeqb,V_24X1),V_24X2) = cCoq_2eInit_2eNat_2eeqb___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.setoid_ring.Ring_theory.div_theory_$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('$adef_Coq.NArith.BinNat.N.divide_$a2',axiom,
    ! [V_24X1,V_24X2] :
      ( p(happ(happ(cCoq_2eNArith_2eBinNat_2eN_2edivide,V_24X1),V_24X2))
    <=> cCoq_2eNArith_2eBinNat_2eN_2edivide___24a2(V_24X1,V_24X2) ) ).

fof('$adef_Coq.Lists.SetoidList.transpose2_$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('$adef_Coq.PArith.BinPosDef.Pos.testbit_nat_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2ePArith_2eBinPosDef_2ePos_2etestbit__nat,V_24X1) = cCoq_2ePArith_2eBinPosDef_2ePos_2etestbit__nat___24a1(V_24X1) ).

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('$adef_$_lam_109_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__lam__109,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__lam__109___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).

fof('$adef_Coq.ZArith.BinIntDef.Z.to_N_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eZArith_2eBinIntDef_2eZ_2eto__N,V_24X1) = cCoq_2eZArith_2eBinIntDef_2eZ_2eto__N___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('$adef_Coq.Relations.Relation_Definitions.reflexive_$a2',axiom,
    ! [V_24X1,V_24X2] :
      ( p(happ(happ(cCoq_2eRelations_2eRelation__Definitions_2ereflexive,V_24X1),V_24X2))
    <=> cCoq_2eRelations_2eRelation__Definitions_2ereflexive___24a2(V_24X1,V_24X2) ) ).

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('$adef_Coq.NArith.BinNatDef.N.max_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2eNArith_2eBinNatDef_2eN_2emax,V_24X1),V_24X2) = cCoq_2eNArith_2eBinNatDef_2eN_2emax___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.Reals.Rdefinitions.Rge_$a2',axiom,
    ! [V_24X1,V_24X2] :
      ( p(happ(happ(cCoq_2eReals_2eRdefinitions_2eRge,V_24X1),V_24X2))
    <=> cCoq_2eReals_2eRdefinitions_2eRge___24a2(V_24X1,V_24X2) ) ).

fof('$adef_Coq.Init.Datatypes.CompGtT_$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('$adef_$_prop_113528_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__prop__113528,V_24X1),V_24X2),V_24X3) = c_24__prop__113528___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_Coq.Reals.Rdefinitions.Rmult_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2eReals_2eRdefinitions_2eRmult,V_24X1),V_24X2) = cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.Reals.Rfunctions.ZintNeg_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2eReals_2eRfunctions_2eZintNeg,V_24X1),V_24X2) = cCoq_2eReals_2eRfunctions_2eZintNeg___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.ZArith.Znumtheory.Bezout_$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('$adef_Coq.micromega.Tauto.cnf_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2emicromega_2eTauto_2ecnf,V_24X1),V_24X2) = cCoq_2emicromega_2eTauto_2ecnf___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('$adef_Coq.Numbers.BinNums.Npos_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eNumbers_2eBinNums_2eNpos,V_24X1) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(V_24X1) ).

fof('$adef_Coq.micromega.ZMicromega.mk_diff_env_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2emicromega_2eZMicromega_2emk__diff__env,V_24X1),V_24X2) = cCoq_2emicromega_2eZMicromega_2emk__diff__env___24a2(V_24X1,V_24X2) ).

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_910_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(c_24__lam__910,V_24X1),V_24X2) = c_24__lam__910___24a2(V_24X1,V_24X2) ).

fof('$adef_$_lam_113894_$a2',axiom,
    ! [V_24X1,V_24X2] :
      ( p(happ(happ(c_24__lam__113894,V_24X1),V_24X2))
    <=> c_24__lam__113894___24a2(V_24X1,V_24X2) ) ).

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_122267_$a1',axiom,
    ! [V_24X1] : happ(c_24__lam__122267,V_24X1) = c_24__lam__122267___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('$adef_$_lam_600_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__lam__600,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__lam__600___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).

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('$adef_$_lam_971_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__971,V_24X1),V_24X2),V_24X3) = c_24__lam__971___24a3(V_24X1,V_24X2,V_24X3) ).

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('$adef_Coq.ZArith.BinIntDef.Z.abs_nat_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eZArith_2eBinIntDef_2eZ_2eabs__nat,V_24X1) = cCoq_2eZArith_2eBinIntDef_2eZ_2eabs__nat___24a1(V_24X1) ).

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('$adef_$_prop_113532_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(c_24__prop__113532,V_24X1),V_24X2) = c_24__prop__113532___24a2(V_24X1,V_24X2) ).

fof('$adef_$_lam_1802_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__1802,V_24X1),V_24X2),V_24X3) = c_24__lam__1802___24a3(V_24X1,V_24X2,V_24X3) ).

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('$adef_Coq.NArith.BinNat.N.recursion_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eNArith_2eBinNat_2eN_2erecursion,V_24X1) = cCoq_2eNArith_2eBinNat_2eN_2erecursion___24a1(V_24X1) ).

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('$adef_$_lam_477_$a5',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(c_24__lam__477,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = c_24__lam__477___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).

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('$adef_Coq.Init.Nat.testbit_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eNat_2etestbit,V_24X1),V_24X2) = cCoq_2eInit_2eNat_2etestbit___24a2(V_24X1,V_24X2) ).

fof('$adef_$_prop_107393_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(c_24__prop__107393,V_24X1),V_24X2) = c_24__prop__107393___24a2(V_24X1,V_24X2) ).

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('$adef_Coq.Reals.Rdefinitions.Ropp_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eReals_2eRdefinitions_2eRopp,V_24X1) = cCoq_2eReals_2eRdefinitions_2eRopp___24a1(V_24X1) ).

fof('$adef_$_lam_173531_$a1',axiom,
    ! [V_24X1] : happ(c_24__lam__173531,V_24X1) = c_24__lam__173531___24a1(V_24X1) ).

fof('$adef_Coq.Arith.Even.odd_$a1',axiom,
    ! [V_24X1] :
      ( p(happ(cCoq_2eArith_2eEven_2eodd,V_24X1))
    <=> cCoq_2eArith_2eEven_2eodd___24a1(V_24X1) ) ).

fof('$adef_Coq.Lists.List.ForallOrdPairs_$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('$adef_Coq.Relations.Relation_Operators.clos_trans_1n_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] :
      ( p(happ(happ(happ(happ(cCoq_2eRelations_2eRelation__Operators_2eclos__trans__1n,V_24X1),V_24X2),V_24X3),V_24X4))
    <=> cCoq_2eRelations_2eRelation__Operators_2eclos__trans__1n___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('$adef_IntMap.Fset.MapDomRestrBy_$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('$adef_Coq.Init.Nat.add_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eNat_2eadd,V_24X1),V_24X2) = cCoq_2eInit_2eNat_2eadd___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.Init.Specif.sigT2_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eInit_2eSpecif_2esigT2,V_24X1),V_24X2),V_24X3) = cCoq_2eInit_2eSpecif_2esigT2___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_Coq.Structures.OrderedType.Compare_$a5',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2eStructures_2eOrderedType_2eCompare,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2eStructures_2eOrderedType_2eCompare___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).

fof('$adef_Coq.setoid_ring.Field_theory.FEc_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2esetoid__ring_2eField__theory_2eFEc,V_24X1),V_24X2) = cCoq_2esetoid__ring_2eField__theory_2eFEc___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.Classes.Morphisms.Proper_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] :
      ( p(happ(happ(happ(cCoq_2eClasses_2eMorphisms_2eProper,V_24X1),V_24X2),V_24X3))
    <=> cCoq_2eClasses_2eMorphisms_2eProper___24a3(V_24X1,V_24X2,V_24X3) ) ).

fof('$adef_Coq.ZArith.BinIntDef.Z.pos_sub_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eBinIntDef_2eZ_2epos__sub,V_24X1),V_24X2) = cCoq_2eZArith_2eBinIntDef_2eZ_2epos__sub___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.Init.Specif.right_$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('$adef_$_lam_122197_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(c_24__lam__122197,V_24X1),V_24X2) = c_24__lam__122197___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('$adef_$_fix_113688_v_CANONICAL_0_$a1',axiom,
    ! [V_24X1] : happ(c_24__fix__113688__v__CANONICAL__0,V_24X1) = c_24__fix__113688__v__CANONICAL__0___24a1(V_24X1) ).

fof('$adef_$_lam_854_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(c_24__lam__854,V_24X1),V_24X2) = c_24__lam__854___24a2(V_24X1,V_24X2) ).

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('$adef_Coq.ZArith.BinIntDef.Z.div_eucl_$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('$adef_Coq.micromega.RMicromega.CMinus_$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('$adef_Coq.setoid_ring.Field_theory.FEadd_$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('$adef_Coq.ZArith.BinIntDef.Z.odd_$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('$adef_$_lam_173555_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__lam__173555,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__lam__173555___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).

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_1461_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] :
      ( p(happ(happ(happ(happ(c_24__lam__1461,V_24X1),V_24X2),V_24X3),V_24X4))
    <=> c_24__lam__1461___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).

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('$adef_Coq.setoid_ring.Ring_theory.SRsub_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__theory_2eSRsub,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2esetoid__ring_2eRing__theory_2eSRsub___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).

fof('$adef_Coq.micromega.Tauto.map_bformula_$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_2emap__bformula,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7) = cCoq_2emicromega_2eTauto_2emap__bformula___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7) ).

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('$adef_Coq.micromega.RingMicromega.PolC_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2emicromega_2eRingMicromega_2ePolC,V_24X1) = cCoq_2emicromega_2eRingMicromega_2ePolC___24a1(V_24X1) ).

fof('$adef_IntMap.Map.M2_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cIntMap_2eMap_2eM2,V_24X1),V_24X2),V_24X3) = cIntMap_2eMap_2eM2___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_Coq.Lists.SetoidList.InA_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] :
      ( p(happ(happ(happ(happ(cCoq_2eLists_2eSetoidList_2eInA,V_24X1),V_24X2),V_24X3),V_24X4))
    <=> cCoq_2eLists_2eSetoidList_2eInA___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).

fof('$adef_Coq.Reals.Rdefinitions.Rlt_$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('$adef_Coq.setoid_ring.Field_theory.mk_linear_$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('$adef_Coq.Relations.Relation_Operators.Ltl_$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('$adef_Coq.Init.Nat.pow_$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('$adef_Coq.PArith.BinPos.Pos.switch_Eq_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2ePArith_2eBinPos_2ePos_2eswitch__Eq,V_24X1),V_24X2) = cCoq_2ePArith_2eBinPos_2ePos_2eswitch__Eq___24a2(V_24X1,V_24X2) ).

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('$adef_Coq.ZArith.BinInt.Z.gt_$a2',axiom,
    ! [V_24X1,V_24X2] :
      ( p(happ(happ(cCoq_2eZArith_2eBinInt_2eZ_2egt,V_24X1),V_24X2))
    <=> cCoq_2eZArith_2eBinInt_2eZ_2egt___24a2(V_24X1,V_24X2) ) ).

fof('$adef_Coq.Init.Logic.eq_rect_$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('$adef_Coq.Numbers.BinNums.xO_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eNumbers_2eBinNums_2exO,V_24X1) = cCoq_2eNumbers_2eBinNums_2exO___24a1(V_24X1) ).

fof('$adef_Coq.micromega.EnvRing.Pphi_$a5',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2emicromega_2eEnvRing_2ePphi,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2emicromega_2eEnvRing_2ePphi___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).

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('$adef_$_lam_1852_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__lam__1852,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__lam__1852___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).

fof('$adef_Coq.setoid_ring.Field_theory.FEinv_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2esetoid__ring_2eField__theory_2eFEinv,V_24X1),V_24X2) = cCoq_2esetoid__ring_2eField__theory_2eFEinv___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.ZArith.Zpower.Zdiv_rest_proof_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2eZArith_2eZpower_2eZdiv__rest__proof,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2eZArith_2eZpower_2eZdiv__rest__proof___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).

fof('$adef_Coq.Init.Wf.Acc_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] :
      ( p(happ(happ(happ(cCoq_2eInit_2eWf_2eAcc,V_24X1),V_24X2),V_24X3))
    <=> cCoq_2eInit_2eWf_2eAcc___24a3(V_24X1,V_24X2,V_24X3) ) ).

fof('$adef_Coq.setoid_ring.Ring_theory.pow_N_$a5',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__theory_2epow__N,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2esetoid__ring_2eRing__theory_2epow__N___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).

fof('$adef_Coq.setoid_ring.Field_theory.semi_field_theory_$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('$adef_Coq.Init.Decimal.D8_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eInit_2eDecimal_2eD8,V_24X1) = cCoq_2eInit_2eDecimal_2eD8___24a1(V_24X1) ).

fof('$adef_Coq.Relations.Relation_Operators.swapprod_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] :
      ( p(happ(happ(happ(happ(cCoq_2eRelations_2eRelation__Operators_2eswapprod,V_24X1),V_24X2),V_24X3),V_24X4))
    <=> cCoq_2eRelations_2eRelation__Operators_2eswapprod___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).

fof('$adef_$_lam_914_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__914,V_24X1),V_24X2),V_24X3) = c_24__lam__914___24a3(V_24X1,V_24X2,V_24X3) ).

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('$adef_Coq.NArith.BinNatDef.N.pred_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eNArith_2eBinNatDef_2eN_2epred,V_24X1) = cCoq_2eNArith_2eBinNatDef_2eN_2epred___24a1(V_24X1) ).

fof('$adef_Coq.micromega.OrderedRing.SOR_$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('$adef_Coq.Relations.Relation_Operators.clos_refl_trans_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] :
      ( p(happ(happ(happ(happ(cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans,V_24X1),V_24X2),V_24X3),V_24X4))
    <=> cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).

fof('$adef_Coq.Init.Datatypes.sum_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eDatatypes_2esum,V_24X1),V_24X2) = cCoq_2eInit_2eDatatypes_2esum___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.NArith.BinNatDef.N.min_$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('$adef_Coq.ZArith.Znumtheory.Zis_gcd_$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('$adef_Coq.Relations.Relation_Operators.clos_trans_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] :
      ( p(happ(happ(happ(happ(cCoq_2eRelations_2eRelation__Operators_2eclos__trans,V_24X1),V_24X2),V_24X3),V_24X4))
    <=> cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).

fof('$adef_Coq.Relations.Relation_Operators.clos_refl_sym_trans_1n_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] :
      ( p(happ(happ(happ(happ(cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans__1n,V_24X1),V_24X2),V_24X3),V_24X4))
    <=> cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans__1n___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('$adef_$_lam_946_$a5',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(c_24__lam__946,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = c_24__lam__946___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).

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('$adef_$_case_Coq.Init.Datatypes.prod$11718_$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_2411718,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_2411718___24a9(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9) ) ).

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_477_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__lam__477,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__lam__477___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).

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_569_$a6',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(c_24__lam__569,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = c_24__lam__569___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).

fof('$adef_$_lam_96901_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] :
      ( p(happ(happ(happ(happ(c_24__lam__96901,V_24X1),V_24X2),V_24X3),V_24X4))
    <=> c_24__lam__96901___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).

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('$adef_Coq.PArith.BinPos.Pos.le_$a2',axiom,
    ! [V_24X1,V_24X2] :
      ( p(happ(happ(cCoq_2ePArith_2eBinPos_2ePos_2ele,V_24X1),V_24X2))
    <=> cCoq_2ePArith_2eBinPos_2ePos_2ele___24a2(V_24X1,V_24X2) ) ).

fof('$adef_Coq.Init.Nat.mul_$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('$adef_Coq.micromega.Tauto.eval_clause_$a5',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2emicromega_2eTauto_2eeval__clause,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2emicromega_2eTauto_2eeval__clause___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).

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('$adef_Coq.Init.Decimal.D7_$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('$adef_Coq.Arith.PeanoNat.Nat.divide_$a2',axiom,
    ! [V_24X1,V_24X2] :
      ( p(happ(happ(cCoq_2eArith_2ePeanoNat_2eNat_2edivide,V_24X1),V_24X2))
    <=> cCoq_2eArith_2ePeanoNat_2eNat_2edivide___24a2(V_24X1,V_24X2) ) ).

fof('$adef_Coq.setoid_ring.Field_theory.rsplit_$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('$adef_Coq.Classes.RelationClasses.Equivalence_$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('$adef_$_lam_122197_$a1',axiom,
    ! [V_24X1] : happ(c_24__lam__122197,V_24X1) = c_24__lam__122197___24a1(V_24X1) ).

fof('$adef_Coq.Logic.Decidable.decidable_$a1',axiom,
    ! [V_24X1] :
      ( p(happ(cCoq_2eLogic_2eDecidable_2edecidable,V_24X1))
    <=> cCoq_2eLogic_2eDecidable_2edecidable___24a1(V_24X1) ) ).

fof('$adef_Coq.Relations.Relation_Operators.clos_trans_n1_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] :
      ( p(happ(happ(happ(happ(cCoq_2eRelations_2eRelation__Operators_2eclos__trans__n1,V_24X1),V_24X2),V_24X3),V_24X4))
    <=> cCoq_2eRelations_2eRelation__Operators_2eclos__trans__n1___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).

fof('$adef_Coq.Relations.Relation_Definitions.PER_$a2',axiom,
    ! [V_24X1,V_24X2] :
      ( p(happ(happ(cCoq_2eRelations_2eRelation__Definitions_2ePER,V_24X1),V_24X2))
    <=> cCoq_2eRelations_2eRelation__Definitions_2ePER___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('$adef_$_case_Coq.Init.Datatypes.list$110186_$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_24110186,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = c_24__case__Coq_2eInit_2eDatatypes_2elist_24110186___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).

fof('$adef_IntMap.Fset.in_dom_$a1',axiom,
    ! [V_24X1] : happ(cIntMap_2eFset_2ein__dom,V_24X1) = cIntMap_2eFset_2ein__dom___24a1(V_24X1) ).

fof('$adef_Coq.ZArith.BinInt.Z.eqf_$a2',axiom,
    ! [V_24X1,V_24X2] :
      ( p(happ(happ(cCoq_2eZArith_2eBinInt_2eZ_2eeqf,V_24X1),V_24X2))
    <=> cCoq_2eZArith_2eBinInt_2eZ_2eeqf___24a2(V_24X1,V_24X2) ) ).

fof('$adef_Coq.PArith.BinPos.Pos.lt_$a2',axiom,
    ! [V_24X1,V_24X2] :
      ( p(happ(happ(cCoq_2ePArith_2eBinPos_2ePos_2elt,V_24X1),V_24X2))
    <=> cCoq_2ePArith_2eBinPos_2ePos_2elt___24a2(V_24X1,V_24X2) ) ).

fof('$adef_$_lam_569_$a5',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(c_24__lam__569,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = c_24__lam__569___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).

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('$adef_Coq.PArith.BinPosDef.Pos.to_nat_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2ePArith_2eBinPosDef_2ePos_2eto__nat,V_24X1) = cCoq_2ePArith_2eBinPosDef_2ePos_2eto__nat___24a1(V_24X1) ).

fof('$adef_Coq.Init.Decimal.D0_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eInit_2eDecimal_2eD0,V_24X1) = cCoq_2eInit_2eDecimal_2eD0___24a1(V_24X1) ).

fof('$adef_Coq.Relations.Relation_Definitions.antisymmetric_$a2',axiom,
    ! [V_24X1,V_24X2] :
      ( p(happ(happ(cCoq_2eRelations_2eRelation__Definitions_2eantisymmetric,V_24X1),V_24X2))
    <=> cCoq_2eRelations_2eRelation__Definitions_2eantisymmetric___24a2(V_24X1,V_24X2) ) ).

fof('$adef_$_case_Coq.Numbers.BinNums.Z$110457_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__case__Coq_2eNumbers_2eBinNums_2eZ_24110457,V_24X1),V_24X2),V_24X3) = c_24__case__Coq_2eNumbers_2eBinNums_2eZ_24110457___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_Coq.ZArith.BinIntDef.Z.abs_N_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eZArith_2eBinIntDef_2eZ_2eabs__N,V_24X1) = cCoq_2eZArith_2eBinIntDef_2eZ_2eabs__N___24a1(V_24X1) ).

fof('$adef_$_prop_113526_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__prop__113526,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__prop__113526___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).

fof('$adef_Coq.PArith.BinPosDef.Pos.size_nat_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2ePArith_2eBinPosDef_2ePos_2esize__nat,V_24X1) = cCoq_2ePArith_2eBinPosDef_2ePos_2esize__nat___24a1(V_24X1) ).

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('$adef_$_fix_107045_1_add_carry_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(c_24__fix__107045__1__add__carry,V_24X1),V_24X2) = c_24__fix__107045__1__add__carry___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.Lists.List.nth_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2eLists_2eList_2enth,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2eLists_2eList_2enth___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).

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('$adef_$_lam_173584_$a2',axiom,
    ! [V_24X1,V_24X2] :
      ( p(happ(happ(c_24__lam__173584,V_24X1),V_24X2))
    <=> c_24__lam__173584___24a2(V_24X1,V_24X2) ) ).

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('$adef_Coq.micromega.VarMap.Branch_$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('$adef_Coq.micromega.ZMicromega.Zeval_op2_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2emicromega_2eZMicromega_2eZeval__op2,V_24X1) = cCoq_2emicromega_2eZMicromega_2eZeval__op2___24a1(V_24X1) ).

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_136_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__lam__136,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__lam__136___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).

fof('$adef_Coq.Structures.OrderedTypeEx.PositiveOrderedTypeBits.bits_lt_$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('$adef_Mapaxioms.eqmap_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] :
      ( p(happ(happ(happ(cMapaxioms_2eeqmap,V_24X1),V_24X2),V_24X3))
    <=> cMapaxioms_2eeqmap___24a3(V_24X1,V_24X2,V_24X3) ) ).

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('$adef_Coq.Relations.Relation_Operators.Desc_$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('$adef_Coq.FSets.FSetPositive.PositiveSet.xelements_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2exelements,V_24X1),V_24X2),V_24X3) = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2exelements___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_$_lam_96917_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] :
      ( p(happ(happ(happ(happ(c_24__lam__96917,V_24X1),V_24X2),V_24X3),V_24X4))
    <=> c_24__lam__96917___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).

fof('$adef_$_prop_113530_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__prop__113530,V_24X1),V_24X2),V_24X3) = c_24__prop__113530___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_$_lam_96909_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] :
      ( p(happ(happ(happ(happ(c_24__lam__96909,V_24X1),V_24X2),V_24X3),V_24X4))
    <=> c_24__lam__96909___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('$adef_Coq.Init.Datatypes.prod_$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('$adef_Coq.Init.Specif.Exc_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eInit_2eSpecif_2eExc,V_24X1) = cCoq_2eInit_2eSpecif_2eExc___24a1(V_24X1) ).

fof('$adef_Coq.Vectors.VectorDef.Forall2_$a6',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] :
      ( p(happ(happ(happ(happ(happ(happ(cCoq_2eVectors_2eVectorDef_2eForall2,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6))
    <=> cCoq_2eVectors_2eVectorDef_2eForall2___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ) ).

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('$adef_Coq.QArith.QArith_base.Qden_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eQArith_2eQArith__base_2eQden,V_24X1) = cCoq_2eQArith_2eQArith__base_2eQden___24a1(V_24X1) ).

fof('$adef_Coq.setoid_ring.InitialRing.gen_phiPOS_$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('$adef_Coq.NArith.BinNatDef.N.div2_$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('$adef_$_lam_101_$a1',axiom,
    ! [V_24X1] : happ(c_24__lam__101,V_24X1) = c_24__lam__101___24a1(V_24X1) ).

fof('$adef_Coq.micromega.Tauto.eval_tt_$a6',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] :
      ( p(happ(happ(happ(happ(happ(happ(cCoq_2emicromega_2eTauto_2eeval__tt,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6))
    <=> cCoq_2emicromega_2eTauto_2eeval__tt___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ) ).

fof('$adef_$_lam_1903_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__lam__1903,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__lam__1903___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).

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('$adef_Coq.Strings.Ascii.nat_of_ascii_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eStrings_2eAscii_2enat__of__ascii,V_24X1) = cCoq_2eStrings_2eAscii_2enat__of__ascii___24a1(V_24X1) ).

fof('$adef_Coq.NArith.BinNat.N.peano_rect_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eNArith_2eBinNat_2eN_2epeano__rect,V_24X1) = cCoq_2eNArith_2eBinNat_2eN_2epeano__rect___24a1(V_24X1) ).

fof('$adef_Coq.Vectors.VectorDef.t_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eVectors_2eVectorDef_2et,V_24X1) = cCoq_2eVectors_2eVectorDef_2et___24a1(V_24X1) ).

fof('$adef_$_lam_122271_$a1',axiom,
    ! [V_24X1] : happ(c_24__lam__122271,V_24X1) = c_24__lam__122271___24a1(V_24X1) ).

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('$adef_$_let_var_6_p_7628_7630_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__let__var__6__p__7628__7630,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__let__var__6__p__7628__7630___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).

fof('$adef_Coq.ZArith.BinInt.Z.lt_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eBinInt_2eZ_2elt,V_24X1),V_24X2) = cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V_24X1,V_24X2) ).

fof('$adef_$_let_var_6_p_7626_7629_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__let__var__6__p__7626__7629,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__let__var__6__p__7626__7629___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).

fof('$adef_Coq.setoid_ring.Field_theory.linear_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2esetoid__ring_2eField__theory_2elinear,V_24X1) = cCoq_2esetoid__ring_2eField__theory_2elinear___24a1(V_24X1) ).

fof('$adef_$_case_Coq.Init.Datatypes.list$110273_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__case__Coq_2eInit_2eDatatypes_2elist_24110273,V_24X1),V_24X2),V_24X3) = c_24__case__Coq_2eInit_2eDatatypes_2elist_24110273___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_Coq.Arith.PeanoNat.Nat.b2n_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eArith_2ePeanoNat_2eNat_2eb2n,V_24X1) = cCoq_2eArith_2ePeanoNat_2eNat_2eb2n___24a1(V_24X1) ).

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('$adef_$_lam_120322_$a1',axiom,
    ! [V_24X1] : happ(c_24__lam__120322,V_24X1) = c_24__lam__120322___24a1(V_24X1) ).

fof('$adef_$_lam_378_$a5',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(c_24__lam__378,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = c_24__lam__378___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('$adef_Coq.micromega.RingMicromega.ge_bool_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2emicromega_2eRingMicromega_2ege__bool,V_24X1),V_24X2) = cCoq_2emicromega_2eRingMicromega_2ege__bool___24a2(V_24X1,V_24X2) ).

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('$adef_Coq.setoid_ring.Ring_polynom.PEpow_$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('$adef_Coq.NArith.BinNatDef.N.to_nat_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eNArith_2eBinNatDef_2eN_2eto__nat,V_24X1) = cCoq_2eNArith_2eBinNatDef_2eN_2eto__nat___24a1(V_24X1) ).

fof('$adef_Coq.ZArith.Zeven.Zeven_$a1',axiom,
    ! [V_24X1] :
      ( p(happ(cCoq_2eZArith_2eZeven_2eZeven,V_24X1))
    <=> cCoq_2eZArith_2eZeven_2eZeven___24a1(V_24X1) ) ).

fof('$adef_$_lam_600_$a5',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(c_24__lam__600,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = c_24__lam__600___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('$adef_Coq.setoid_ring.Ring_polynom.PX_$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('$adef_$_lam_527_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__lam__527,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__lam__527___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).

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('$adef_Coq.PArith.BinPosDef.Pos.sub_mask_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2ePArith_2eBinPosDef_2ePos_2esub__mask,V_24X1),V_24X2) = cCoq_2ePArith_2eBinPosDef_2ePos_2esub__mask___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('$adef_Coq.Init.Specif.inright_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eSpecif_2einright,V_24X1),V_24X2) = cCoq_2eInit_2eSpecif_2einright___24a2(V_24X1,V_24X2) ).

fof('$adef_$_lam_914_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__lam__914,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__lam__914___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).

fof('$adef_$_lam_971_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__lam__971,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__lam__971___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).

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('$adef_$_lam_122260_$a1',axiom,
    ! [V_24X1] : happ(c_24__lam__122260,V_24X1) = c_24__lam__122260___24a1(V_24X1) ).

fof('$adef_Coq.Init.Datatypes.unit_rect_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eInit_2eDatatypes_2eunit__rect,V_24X1) = cCoq_2eInit_2eDatatypes_2eunit__rect___24a1(V_24X1) ).

fof('$adef_IntMap.Map.MapGet_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cIntMap_2eMap_2eMapGet,V_24X1),V_24X2) = cIntMap_2eMap_2eMapGet___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.Strings.String.String_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2eStrings_2eString_2eString,V_24X1),V_24X2) = cCoq_2eStrings_2eString_2eString___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.Relations.Relation_Definitions.equivalence_$a2',axiom,
    ! [V_24X1,V_24X2] :
      ( p(happ(happ(cCoq_2eRelations_2eRelation__Definitions_2eequivalence,V_24X1),V_24X2))
    <=> cCoq_2eRelations_2eRelation__Definitions_2eequivalence___24a2(V_24X1,V_24X2) ) ).

fof('$adef_Coq.ZArith.Znumtheory.Euclid_intro_$a5',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2eZArith_2eZnumtheory_2eEuclid__intro,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2eZArith_2eZnumtheory_2eEuclid__intro___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).

fof('$adef_Coq.Init.Datatypes.CompEqT_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eInit_2eDatatypes_2eCompEqT,V_24X1),V_24X2),V_24X3) = cCoq_2eInit_2eDatatypes_2eCompEqT___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_Coq.micromega.RingMicromega.PsatzMulE_$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('$adef_$_prop_113547_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__prop__113547,V_24X1),V_24X2),V_24X3) = c_24__prop__113547___24a3(V_24X1,V_24X2,V_24X3) ).

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('$adef_$_lam_122260_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(c_24__lam__122260,V_24X1),V_24X2) = c_24__lam__122260___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.micromega.Tauto.FF_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2emicromega_2eTauto_2eFF,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2emicromega_2eTauto_2eFF___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).

fof('$adef_Coq.ZArith.BinIntDef.Z.abs_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eZArith_2eBinIntDef_2eZ_2eabs,V_24X1) = cCoq_2eZArith_2eBinIntDef_2eZ_2eabs___24a1(V_24X1) ).

fof('$adef_Coq.PArith.BinPosDef.Pos.min_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2ePArith_2eBinPosDef_2ePos_2emin,V_24X1),V_24X2) = cCoq_2ePArith_2eBinPosDef_2ePos_2emin___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.NArith.BinNatDef.N.odd_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eNArith_2eBinNatDef_2eN_2eodd,V_24X1) = cCoq_2eNArith_2eBinNatDef_2eN_2eodd___24a1(V_24X1) ).

fof('$adef_Coq.FSets.FSetPositive.PositiveSet.In_$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('$adef_Coq.Init.Nat.leb_$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('$adef_IntMap.Map.MapPut_$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('$adef_Coq.Relations.Relation_Definitions.transitive_$a2',axiom,
    ! [V_24X1,V_24X2] :
      ( p(happ(happ(cCoq_2eRelations_2eRelation__Definitions_2etransitive,V_24X1),V_24X2))
    <=> cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2(V_24X1,V_24X2) ) ).

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('$adef_$_case_Coq.Init.Datatypes.nat$110462_$a1',axiom,
    ! [V_24X1] : happ(c_24__case__Coq_2eInit_2eDatatypes_2enat_24110462,V_24X1) = c_24__case__Coq_2eInit_2eDatatypes_2enat_24110462___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('$adef_Coq.Vectors.Fin.FS_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2eVectors_2eFin_2eFS,V_24X1),V_24X2) = cCoq_2eVectors_2eFin_2eFS___24a2(V_24X1,V_24X2) ).

fof('$adef_$_lam_946_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__lam__946,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__lam__946___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).

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('$adef_Coq.micromega.EnvRing.PExpr_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2emicromega_2eEnvRing_2ePExpr,V_24X1) = cCoq_2emicromega_2eEnvRing_2ePExpr___24a1(V_24X1) ).

fof('$adef_$_lam_436_$a6',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(c_24__lam__436,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = c_24__lam__436___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).

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('$adef_Coq.Init.Peano.ge_$a2',axiom,
    ! [V_24X1,V_24X2] :
      ( p(happ(happ(cCoq_2eInit_2ePeano_2ege,V_24X1),V_24X2))
    <=> cCoq_2eInit_2ePeano_2ege___24a2(V_24X1,V_24X2) ) ).

fof('$adef_$_lam_723_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__723,V_24X1),V_24X2),V_24X3) = c_24__lam__723___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_$_lam_96917_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__96917,V_24X1),V_24X2),V_24X3) = c_24__lam__96917___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_Coq.Relations.Relation_Operators.clos_refl_trans_1n_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] :
      ( p(happ(happ(happ(happ(cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans__1n,V_24X1),V_24X2),V_24X3),V_24X4))
    <=> cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans__1n___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).

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('$adef_Coq.Init.Datatypes.unit_rect_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eInit_2eDatatypes_2eunit__rect,V_24X1),V_24X2),V_24X3) = cCoq_2eInit_2eDatatypes_2eunit__rect___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_Coq.Lists.SetoidList.NoDupA_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] :
      ( p(happ(happ(happ(cCoq_2eLists_2eSetoidList_2eNoDupA,V_24X1),V_24X2),V_24X3))
    <=> cCoq_2eLists_2eSetoidList_2eNoDupA___24a3(V_24X1,V_24X2,V_24X3) ) ).

fof('$adef_Coq.micromega.RingMicromega.eval_op1_$a6',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(cCoq_2emicromega_2eRingMicromega_2eeval__op1,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = cCoq_2emicromega_2eRingMicromega_2eeval__op1___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).

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('$adef_Coq.Logic.EqdepFacts.UIP_on__$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] :
      ( p(happ(happ(happ(cCoq_2eLogic_2eEqdepFacts_2eUIP__on__,V_24X1),V_24X2),V_24X3))
    <=> cCoq_2eLogic_2eEqdepFacts_2eUIP__on_____24a3(V_24X1,V_24X2,V_24X3) ) ).

fof('$adef_Coq.Init.Byte.byte_of_byte_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eInit_2eByte_2ebyte__of__byte,V_24X1) = cCoq_2eInit_2eByte_2ebyte__of__byte___24a1(V_24X1) ).

fof('$adef_$_lam_686_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__686,V_24X1),V_24X2),V_24X3) = c_24__lam__686___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_Coq.Arith.EqNat.eq_nat_$a2',axiom,
    ! [V_24X1,V_24X2] :
      ( p(happ(happ(cCoq_2eArith_2eEqNat_2eeq__nat,V_24X1),V_24X2))
    <=> cCoq_2eArith_2eEqNat_2eeq__nat___24a2(V_24X1,V_24X2) ) ).

fof('$adef_IntMap.Fset.FSetUnion_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cIntMap_2eFset_2eFSetUnion,V_24X1),V_24X2) = cIntMap_2eFset_2eFSetUnion___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.Init.Datatypes.nat_rect_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2eInit_2eDatatypes_2enat__rect,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2eInit_2eDatatypes_2enat__rect___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).

fof('$adef_$_case_Coq.Numbers.BinNums.positive$113672_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(c_24__case__Coq_2eNumbers_2eBinNums_2epositive_24113672,V_24X1),V_24X2) = c_24__case__Coq_2eNumbers_2eBinNums_2epositive_24113672___24a2(V_24X1,V_24X2) ).

fof('$adef_$_lam_870_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__870,V_24X1),V_24X2),V_24X3) = c_24__lam__870___24a3(V_24X1,V_24X2,V_24X3) ).

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('$adef_Coq.micromega.EnvRing.vmon_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2emicromega_2eEnvRing_2evmon,V_24X1),V_24X2) = cCoq_2emicromega_2eEnvRing_2evmon___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.micromega.Tauto.X_$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('$adef_Coq.Init.Specif.sumor_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eSpecif_2esumor,V_24X1),V_24X2) = cCoq_2eInit_2eSpecif_2esumor___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.micromega.RMicromega.CInv_$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('$adef_Coq.ZArith.Znumtheory.rel_prime_$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('$adef_Coq.Init.Specif.exist_$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_1461_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__1461,V_24X1),V_24X2),V_24X3) = c_24__lam__1461___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_Coq.Init.Specif.projT1_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eInit_2eSpecif_2eprojT1,V_24X1),V_24X2),V_24X3) = cCoq_2eInit_2eSpecif_2eprojT1___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_Coq.Lists.List.map_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2eLists_2eList_2emap,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2eLists_2eList_2emap___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('$adef_Coq.Init.Specif.inleft_$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('$adef_$_lam_1903_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__1903,V_24X1),V_24X2),V_24X3) = c_24__lam__1903___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_$_lam_120322_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(c_24__lam__120322,V_24X1),V_24X2) = c_24__lam__120322___24a2(V_24X1,V_24X2) ).

fof('$adef_$_prop_113548_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__prop__113548,V_24X1),V_24X2),V_24X3) = c_24__prop__113548___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('$adef_Coq.setoid_ring.Field_theory.field_theory_$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('$adef_$_prop_113531_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__prop__113531,V_24X1),V_24X2),V_24X3) = c_24__prop__113531___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('$adef_Coq.Init.Decimal.int_of_int_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eInit_2eDecimal_2eint__of__int,V_24X1) = cCoq_2eInit_2eDecimal_2eint__of__int___24a1(V_24X1) ).

fof('$adef_$_lam_527_$a5',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(c_24__lam__527,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = c_24__lam__527___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).

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('$adef_Coq.micromega.Tauto.cnf_tt_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2emicromega_2eTauto_2ecnf__tt,V_24X1),V_24X2) = cCoq_2emicromega_2eTauto_2ecnf__tt___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.FSets.FSetPositive.PositiveSet.union_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eunion,V_24X1),V_24X2) = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eunion___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.PArith.BinPosDef.Pos.max_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2ePArith_2eBinPosDef_2ePos_2emax,V_24X1),V_24X2) = cCoq_2ePArith_2eBinPosDef_2ePos_2emax___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.ZArith.BinIntDef.Z.pow_pos_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eBinIntDef_2eZ_2epow__pos,V_24X1),V_24X2) = cCoq_2eZArith_2eBinIntDef_2eZ_2epow__pos___24a2(V_24X1,V_24X2) ).

fof('$adef_$_lam_109_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__109,V_24X1),V_24X2),V_24X3) = c_24__lam__109___24a3(V_24X1,V_24X2,V_24X3) ).

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('$adef_Coq.micromega.RingMicromega.Psatz_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2emicromega_2eRingMicromega_2ePsatz,V_24X1) = cCoq_2emicromega_2eRingMicromega_2ePsatz___24a1(V_24X1) ).

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('$adef_$_prop_293_$a1',axiom,
    ! [V_24X1] : happ(c_24__prop__293,V_24X1) = c_24__prop__293___24a1(V_24X1) ).

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('$adef_$_prop_292_$a1',axiom,
    ! [V_24X1] : happ(c_24__prop__292,V_24X1) = c_24__prop__292___24a1(V_24X1) ).

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('$adef_Coq.micromega.Tauto.clause_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2emicromega_2eTauto_2eclause,V_24X1),V_24X2) = cCoq_2emicromega_2eTauto_2eclause___24a2(V_24X1,V_24X2) ).

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('$adef_$_lam_363_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__363,V_24X1),V_24X2),V_24X3) = c_24__lam__363___24a3(V_24X1,V_24X2,V_24X3) ).

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('$adef_$_prop_113527_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__prop__113527,V_24X1),V_24X2),V_24X3) = c_24__prop__113527___24a3(V_24X1,V_24X2,V_24X3) ).

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('$adef_$_fix_110318_v_CANONICAL_1_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__fix__110318__v__CANONICAL__1,V_24X1),V_24X2),V_24X3) = c_24__fix__110318__v__CANONICAL__1___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_Coq.NArith.BinNatDef.N.lxor_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2eNArith_2eBinNatDef_2eN_2elxor,V_24X1),V_24X2) = cCoq_2eNArith_2eBinNatDef_2eN_2elxor___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.ZArith.Zlogarithm.log_inf_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eZArith_2eZlogarithm_2elog__inf,V_24X1) = cCoq_2eZArith_2eZlogarithm_2elog__inf___24a1(V_24X1) ).

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('$adef_Coq.PArith.BinPosDef.Pos.sub_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2ePArith_2eBinPosDef_2ePos_2esub,V_24X1),V_24X2) = cCoq_2ePArith_2eBinPosDef_2ePos_2esub___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.NArith.BinNatDef.N.compare_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2eNArith_2eBinNatDef_2eN_2ecompare,V_24X1),V_24X2) = cCoq_2eNArith_2eBinNatDef_2eN_2ecompare___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.Init.Decimal.uint_of_uint_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eInit_2eDecimal_2euint__of__uint,V_24X1) = cCoq_2eInit_2eDecimal_2euint__of__uint___24a1(V_24X1) ).

fof('$adef_Coq.PArith.BinPosDef.Pos.lxor_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2ePArith_2eBinPosDef_2ePos_2elxor,V_24X1),V_24X2) = cCoq_2ePArith_2eBinPosDef_2ePos_2elxor___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.Init.Datatypes.fst_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eInit_2eDatatypes_2efst,V_24X1),V_24X2),V_24X3) = cCoq_2eInit_2eDatatypes_2efst___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_Coq.micromega.VarMap.Empty_$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('$adef_Coq.PArith.BinPos.Pos.PeanoView_$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('$adef_IntMap.Fset.FSetDiff_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cIntMap_2eFset_2eFSetDiff,V_24X1),V_24X2) = cIntMap_2eFset_2eFSetDiff___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.Init.Nat.min_$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('$adef_Coq.Reals.RIneq.Rsqr_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eReals_2eRIneq_2eRsqr,V_24X1) = cCoq_2eReals_2eRIneq_2eRsqr___24a1(V_24X1) ).

fof('$adef_Coq.PArith.BinPosDef.Pos.compare_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare,V_24X1),V_24X2) = cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.setoid_ring.InitialRing.mkhypo_$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('$adef_$_lam_378_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__lam__378,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__lam__378___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).

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('$adef_Coq.micromega.Tauto.eval_bf_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2emicromega_2eTauto_2eeval__bf,V_24X1),V_24X2),V_24X3) = cCoq_2emicromega_2eTauto_2eeval__bf___24a3(V_24X1,V_24X2,V_24X3) ).

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('$adef_Coq.micromega.Tauto.eval_clause_$a6',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] :
      ( p(happ(happ(happ(happ(happ(happ(cCoq_2emicromega_2eTauto_2eeval__clause,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6))
    <=> cCoq_2emicromega_2eTauto_2eeval__clause___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ) ).

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('$adef_$_lam_173555_$a5',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] :
      ( p(happ(happ(happ(happ(happ(c_24__lam__173555,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5))
    <=> c_24__lam__173555___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ) ).

fof('$adef_Coq.Init.Nat.odd_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eInit_2eNat_2eodd,V_24X1) = cCoq_2eInit_2eNat_2eodd___24a1(V_24X1) ).

fof('$adef_Coq.setoid_ring.Ring_theory.sign_theory_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] :
      ( p(happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__theory_2esign__theory,V_24X1),V_24X2),V_24X3),V_24X4))
    <=> cCoq_2esetoid__ring_2eRing__theory_2esign__theory___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).

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('$adef_Coq.setoid_ring.Field_theory.FEX_$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('$adef_$_lam_1802_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__lam__1802,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__lam__1802___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('$adef_Coq.Vectors.VectorDef.nil_$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('$adef_Coq.Init.Decimal.D3_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eInit_2eDecimal_2eD3,V_24X1) = cCoq_2eInit_2eDecimal_2eD3___24a1(V_24X1) ).

fof('$adef_IntMap.Map.eqm_$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('$adef_Coq.micromega.RingMicromega.NFormula_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2emicromega_2eRingMicromega_2eNFormula,V_24X1) = cCoq_2emicromega_2eRingMicromega_2eNFormula___24a1(V_24X1) ).

fof('$adef_Coq.FSets.FSetPositive.PositiveSet.fold_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2efold,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2efold___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).

fof('$adef_Coq.ZArith.BinIntDef.Z.pow_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eBinIntDef_2eZ_2epow,V_24X1),V_24X2) = cCoq_2eZArith_2eBinIntDef_2eZ_2epow___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.Relations.Relation_Operators.clos_refl_trans_n1_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] :
      ( p(happ(happ(happ(happ(cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans__n1,V_24X1),V_24X2),V_24X3),V_24X4))
    <=> cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans__n1___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).

fof('$adef_IntMap.Map.Map_$a1',axiom,
    ! [V_24X1] : happ(cIntMap_2eMap_2eMap,V_24X1) = cIntMap_2eMap_2eMap___24a1(V_24X1) ).

fof('$adef_$_lam_113894_$a1',axiom,
    ! [V_24X1] : happ(c_24__lam__113894,V_24X1) = c_24__lam__113894___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('$adef_Coq.Init.Specif.sig2_$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('$adef_$_lam_101_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(c_24__lam__101,V_24X1),V_24X2) = c_24__lam__101___24a2(V_24X1,V_24X2) ).

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('$adef_Coq.PArith.BinPosDef.Pos.testbit_nat_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2ePArith_2eBinPosDef_2ePos_2etestbit__nat,V_24X1),V_24X2) = cCoq_2ePArith_2eBinPosDef_2ePos_2etestbit__nat___24a2(V_24X1,V_24X2) ).

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('$adef_$_lam_136_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__136,V_24X1),V_24X2),V_24X3) = c_24__lam__136___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_Coq.ZArith.Zpower.Zdiv_rest_proofs_$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('$adef_IntMap.Fset.FSetDelta_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cIntMap_2eFset_2eFSetDelta,V_24X1),V_24X2) = cIntMap_2eFset_2eFSetDelta___24a2(V_24X1,V_24X2) ).

fof('$adef_$_lam_122267_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(c_24__lam__122267,V_24X1),V_24X2) = c_24__lam__122267___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.Init.Peano.gt_$a2',axiom,
    ! [V_24X1,V_24X2] :
      ( p(happ(happ(cCoq_2eInit_2ePeano_2egt,V_24X1),V_24X2))
    <=> cCoq_2eInit_2ePeano_2egt___24a2(V_24X1,V_24X2) ) ).

fof('$adef_$_lam_96925_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] :
      ( p(happ(happ(happ(happ(c_24__lam__96925,V_24X1),V_24X2),V_24X3),V_24X4))
    <=> c_24__lam__96925___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).

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_117562',axiom,
    ! [V_24Y] :
      ( c_24__type__117562___24t(V_24Y)
    <=> t(V_24Y,c_24__type__117562) ) ).

fof('$tdef_$_type_113778',axiom,
    ! [V_24Y] :
      ( c_24__type__113778___24t(V_24Y)
    <=> t(V_24Y,c_24__type__113778) ) ).

fof('$tdef_$_type_117936',axiom,
    ! [V_24Y] :
      ( c_24__type__117936___24t(V_24Y)
    <=> t(V_24Y,c_24__type__117936) ) ).

fof('$tdef_$_type_8449',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
      ( c_24__type__8449___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
    <=> t(V_24Y,c_24__type__8449___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).

fof('$tdef_$_type_98284',axiom,
    ! [V_24Y] :
      ( c_24__type__98284___24t(V_24Y)
    <=> t(V_24Y,c_24__type__98284) ) ).

fof('$tdef_$_type_119946',axiom,
    ! [V_24Y] :
      ( c_24__type__119946___24t(V_24Y)
    <=> t(V_24Y,c_24__type__119946) ) ).

fof('$tdef_$_type_122309',axiom,
    ! [V_24Y] :
      ( c_24__type__122309___24t(V_24Y)
    <=> t(V_24Y,c_24__type__122309) ) ).

fof('$tdef_$_type_1456',axiom,
    ! [V_24Y] :
      ( c_24__type__1456___24t(V_24Y)
    <=> t(V_24Y,c_24__type__1456) ) ).

fof('$tdef_$_type_96968',axiom,
    ! [V_24Y] :
      ( c_24__type__96968___24t(V_24Y)
    <=> t(V_24Y,c_24__type__96968) ) ).

fof('$tdef_$_type_111363',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
      ( c_24__type__111363___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
    <=> t(V_24Y,c_24__type__111363___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).

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('$tdef_$_type_116820',axiom,
    ! [V_24Y] :
      ( c_24__type__116820___24t(V_24Y)
    <=> t(V_24Y,c_24__type__116820) ) ).

fof('$tdef_$_type_14035',axiom,
    ! [V_24Y] :
      ( c_24__type__14035___24t(V_24Y)
    <=> t(V_24Y,c_24__type__14035) ) ).

fof('$tdef_$_type_11655',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y] :
      ( c_24__type__11655___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y)
    <=> t(V_24Y,c_24__type__11655___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7)) ) ).

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_109836',axiom,
    ! [V_24Y] :
      ( c_24__type__109836___24t(V_24Y)
    <=> t(V_24Y,c_24__type__109836) ) ).

fof('$tdef_$_type_93144',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__93144___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__93144___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_90377',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__90377___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__90377___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).

fof('$tdef_$_type_5045',axiom,
    ! [V_24X1,V_24X2,V_24Y] :
      ( c_24__type__5045___24t(V_24X1,V_24X2,V_24Y)
    <=> t(V_24Y,c_24__type__5045___24a2(V_24X1,V_24X2)) ) ).

fof('$tdef_$_type_326',axiom,
    ! [V_24Y] :
      ( c_24__type__326___24t(V_24Y)
    <=> t(V_24Y,c_24__type__326) ) ).

fof('$tdef_$_type_109988',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24Y] :
      ( c_24__type__109988___24t(V_24X1,V_24X2,V_24X3,V_24Y)
    <=> t(V_24Y,c_24__type__109988___24a3(V_24X1,V_24X2,V_24X3)) ) ).

fof('$tdef_$_type_109320',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24Y] :
      ( c_24__type__109320___24t(V_24X1,V_24X2,V_24X3,V_24Y)
    <=> t(V_24Y,c_24__type__109320___24a3(V_24X1,V_24X2,V_24X3)) ) ).

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_1063',axiom,
    ! [V_24X1,V_24Y] :
      ( c_24__type__1063___24t(V_24X1,V_24Y)
    <=> t(V_24Y,c_24__type__1063___24a1(V_24X1)) ) ).

fof('$tdef_$_type_2000',axiom,
    ! [V_24X1,V_24Y] :
      ( c_24__type__2000___24t(V_24X1,V_24Y)
    <=> t(V_24Y,c_24__type__2000___24a1(V_24X1)) ) ).

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_109404',axiom,
    ! [V_24Y] :
      ( c_24__type__109404___24t(V_24Y)
    <=> t(V_24Y,c_24__type__109404) ) ).

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('$tdef_$_type_2630',axiom,
    ! [V_24Y] :
      ( c_24__type__2630___24t(V_24Y)
    <=> t(V_24Y,c_24__type__2630) ) ).

fof('$tdef_$_type_107742',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y] :
      ( c_24__type__107742___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y)
    <=> t(V_24Y,c_24__type__107742___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6)) ) ).

fof('$tdef_$_type_85706',axiom,
    ! [V_24X1,V_24Y] :
      ( c_24__type__85706___24t(V_24X1,V_24Y)
    <=> t(V_24Y,c_24__type__85706___24a1(V_24X1)) ) ).

fof('$tdef_$_type_85925',axiom,
    ! [V_24Y] :
      ( c_24__type__85925___24t(V_24Y)
    <=> t(V_24Y,c_24__type__85925) ) ).

fof('$tdef_$_type_98276',axiom,
    ! [V_24Y] :
      ( c_24__type__98276___24t(V_24Y)
    <=> t(V_24Y,c_24__type__98276) ) ).

fof('$tdef_$_type_89670',axiom,
    ! [V_24Y] :
      ( c_24__type__89670___24t(V_24Y)
    <=> t(V_24Y,c_24__type__89670) ) ).

fof('$tdef_$_type_10459',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__10459___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__10459___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_2859',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__2859___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__2859___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).

fof('$tdef_$_type_8503',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
      ( c_24__type__8503___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
    <=> t(V_24Y,c_24__type__8503___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).

fof('$tdef_$_type_121909',axiom,
    ! [V_24X1,V_24X2,V_24Y] :
      ( c_24__type__121909___24t(V_24X1,V_24X2,V_24Y)
    <=> t(V_24Y,c_24__type__121909___24a2(V_24X1,V_24X2)) ) ).

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_113064',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24Y] :
      ( c_24__type__113064___24t(V_24X1,V_24X2,V_24X3,V_24Y)
    <=> t(V_24Y,c_24__type__113064___24a3(V_24X1,V_24X2,V_24X3)) ) ).

fof('$tdef_$_type_115933',axiom,
    ! [V_24Y] :
      ( c_24__type__115933___24t(V_24Y)
    <=> t(V_24Y,c_24__type__115933) ) ).

fof('$tdef_$_type_113607',axiom,
    ! [V_24Y] :
      ( c_24__type__113607___24t(V_24Y)
    <=> t(V_24Y,c_24__type__113607) ) ).

fof('$tdef_$_type_1997',axiom,
    ! [V_24Y] :
      ( c_24__type__1997___24t(V_24Y)
    <=> t(V_24Y,c_24__type__1997) ) ).

fof('$tdef_$_type_111257',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
      ( c_24__type__111257___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__111257___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).

fof('$tdef_$_type_108480',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__108480___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__108480___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).

fof('$tdef_$_type_92129',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__92129___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__92129___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.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_107422',axiom,
    ! [V_24Y] :
      ( c_24__type__107422___24t(V_24Y)
    <=> t(V_24Y,c_24__type__107422) ) ).

fof('$tdef_$_type_985',axiom,
    ! [V_24Y] :
      ( c_24__type__985___24t(V_24Y)
    <=> t(V_24Y,c_24__type__985) ) ).

fof('$tdef_$_type_109402',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24Y] :
      ( c_24__type__109402___24t(V_24X1,V_24X2,V_24X3,V_24Y)
    <=> t(V_24Y,c_24__type__109402___24a3(V_24X1,V_24X2,V_24X3)) ) ).

fof('$tdef_$_type_26',axiom,
    ! [V_24Y] :
      ( c_24__type__26___24t(V_24Y)
    <=> t(V_24Y,c_24__type__26) ) ).

fof('$tdef_$_type_89690',axiom,
    ! [V_24Y] :
      ( c_24__type__89690___24t(V_24Y)
    <=> t(V_24Y,c_24__type__89690) ) ).

fof('$tdef_$_type_2522',axiom,
    ! [V_24Y] :
      ( c_24__type__2522___24t(V_24Y)
    <=> t(V_24Y,c_24__type__2522) ) ).

fof('$tdef_$_type_121759',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
      ( c_24__type__121759___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
    <=> t(V_24Y,c_24__type__121759___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).

fof('$tdef_$_type_113361',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
      ( c_24__type__113361___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
    <=> t(V_24Y,c_24__type__113361___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).

fof('$tdef_$_type_121350',axiom,
    ! [V_24Y] :
      ( c_24__type__121350___24t(V_24Y)
    <=> t(V_24Y,c_24__type__121350) ) ).

fof('$tdef_$_type_108902',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
      ( c_24__type__108902___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__108902___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('$tdef_$_type_113565',axiom,
    ! [V_24Y] :
      ( c_24__type__113565___24t(V_24Y)
    <=> t(V_24Y,c_24__type__113565) ) ).

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_12694',axiom,
    ! [V_24Y] :
      ( c_24__type__12694___24t(V_24Y)
    <=> t(V_24Y,c_24__type__12694) ) ).

fof('$tdef_$_type_111014',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
      ( c_24__type__111014___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__111014___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).

fof('$tdef_$_type_109145',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
      ( c_24__type__109145___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__109145___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).

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_172555',axiom,
    ! [V_24X1,V_24Y] :
      ( c_24__type__172555___24t(V_24X1,V_24Y)
    <=> t(V_24Y,c_24__type__172555___24a1(V_24X1)) ) ).

fof('$tdef_$_type_98271',axiom,
    ! [V_24Y] :
      ( c_24__type__98271___24t(V_24Y)
    <=> t(V_24Y,c_24__type__98271) ) ).

fof('$tdef_$_type_8479',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
      ( c_24__type__8479___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
    <=> t(V_24Y,c_24__type__8479___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).

fof('$tdef_$_type_109890',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
      ( c_24__type__109890___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
    <=> t(V_24Y,c_24__type__109890___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).

fof('$tdef_$_type_113589',axiom,
    ! [V_24Y] :
      ( c_24__type__113589___24t(V_24Y)
    <=> t(V_24Y,c_24__type__113589) ) ).

fof('$tdef_$_type_89676',axiom,
    ! [V_24Y] :
      ( c_24__type__89676___24t(V_24Y)
    <=> t(V_24Y,c_24__type__89676) ) ).

fof('$tdef_$_type_118387',axiom,
    ! [V_24Y] :
      ( c_24__type__118387___24t(V_24Y)
    <=> t(V_24Y,c_24__type__118387) ) ).

fof('$tdef_$_type_11062',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__11062___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__11062___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_113176',axiom,
    ! [V_24Y] :
      ( c_24__type__113176___24t(V_24Y)
    <=> t(V_24Y,c_24__type__113176) ) ).

fof('$tdef_$_type_9199',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__9199___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__9199___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_14',axiom,
    ! [V_24Y] :
      ( c_24__type__14___24t(V_24Y)
    <=> t(V_24Y,c_24__type__14) ) ).

fof('$tdef_$_type_121692',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y] :
      ( c_24__type__121692___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y)
    <=> t(V_24Y,c_24__type__121692___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6)) ) ).

fof('$tdef_$_type_290',axiom,
    ! [V_24Y] :
      ( c_24__type__290___24t(V_24Y)
    <=> t(V_24Y,c_24__type__290) ) ).

fof('$tdef_$_type_8587',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
      ( c_24__type__8587___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
    <=> t(V_24Y,c_24__type__8587___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).

fof('$tdef_$_type_461',axiom,
    ! [V_24Y] :
      ( c_24__type__461___24t(V_24Y)
    <=> t(V_24Y,c_24__type__461) ) ).

fof('$tdef_$_type_105131',axiom,
    ! [V_24Y] :
      ( c_24__type__105131___24t(V_24Y)
    <=> t(V_24Y,c_24__type__105131) ) ).

fof('$tdef_$_type_96535',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__96535___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__96535___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_5523',axiom,
    ! [V_24Y] :
      ( c_24__type__5523___24t(V_24Y)
    <=> t(V_24Y,c_24__type__5523) ) ).

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_94182',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__94182___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__94182___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.micromega.RMicromega.Rcst',axiom,
    ! [V_24Y] :
      ( cCoq_2emicromega_2eRMicromega_2eRcst___24t(V_24Y)
    <=> t(V_24Y,cCoq_2emicromega_2eRMicromega_2eRcst) ) ).

fof('$tdef_Coq.micromega.RingMicromega.PolEnv',axiom,
    ! [V_24X1,V_24Y] :
      ( cCoq_2emicromega_2eRingMicromega_2ePolEnv___24t(V_24X1,V_24Y)
    <=> t(V_24Y,cCoq_2emicromega_2eRingMicromega_2ePolEnv___24a1(V_24X1)) ) ).

fof('$tdef_$_type_8560',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
      ( c_24__type__8560___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
    <=> t(V_24Y,c_24__type__8560___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).

fof('$tdef_$_type_11563',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y] :
      ( c_24__type__11563___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y)
    <=> t(V_24Y,c_24__type__11563___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7)) ) ).

fof('$tdef_$_type_121717',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y] :
      ( c_24__type__121717___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y)
    <=> t(V_24Y,c_24__type__121717___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6)) ) ).

fof('$tdef_$_type_313',axiom,
    ! [V_24Y] :
      ( c_24__type__313___24t(V_24Y)
    <=> t(V_24Y,c_24__type__313) ) ).

fof('$tdef_$_type_107291',axiom,
    ! [V_24Y] :
      ( c_24__type__107291___24t(V_24Y)
    <=> t(V_24Y,c_24__type__107291) ) ).

fof('$tdef_$_type_104040',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
      ( c_24__type__104040___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
    <=> t(V_24Y,c_24__type__104040___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).

fof('$tdef_$_type_116818',axiom,
    ! [V_24Y] :
      ( c_24__type__116818___24t(V_24Y)
    <=> t(V_24Y,c_24__type__116818) ) ).

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_113469',axiom,
    ! [V_24Y] :
      ( c_24__type__113469___24t(V_24Y)
    <=> t(V_24Y,c_24__type__113469) ) ).

fof('$tdef_$_type_110733',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y] :
      ( c_24__type__110733___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y)
    <=> t(V_24Y,c_24__type__110733___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6)) ) ).

fof('$tdef_$_type_113571',axiom,
    ! [V_24Y] :
      ( c_24__type__113571___24t(V_24Y)
    <=> t(V_24Y,c_24__type__113571) ) ).

fof('$tdef_$_type_613',axiom,
    ! [V_24X1,V_24Y] :
      ( c_24__type__613___24t(V_24X1,V_24Y)
    <=> t(V_24Y,c_24__type__613___24a1(V_24X1)) ) ).

fof('$tdef_$_type_2014',axiom,
    ! [V_24X1,V_24X2,V_24Y] :
      ( c_24__type__2014___24t(V_24X1,V_24X2,V_24Y)
    <=> t(V_24Y,c_24__type__2014___24a2(V_24X1,V_24X2)) ) ).

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_90478',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__90478___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__90478___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).

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_85558',axiom,
    ! [V_24Y] :
      ( c_24__type__85558___24t(V_24Y)
    <=> t(V_24Y,c_24__type__85558) ) ).

fof('$tdef_$_type_113030',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24Y] :
      ( c_24__type__113030___24t(V_24X1,V_24X2,V_24X3,V_24Y)
    <=> t(V_24Y,c_24__type__113030___24a3(V_24X1,V_24X2,V_24X3)) ) ).

fof('$tdef_$_type_173538',axiom,
    ! [V_24Y] :
      ( c_24__type__173538___24t(V_24Y)
    <=> t(V_24Y,c_24__type__173538) ) ).

fof('$tdef_$_type_108398',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__108398___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__108398___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).

fof('$tdef_$_type_120432',axiom,
    ! [V_24Y] :
      ( c_24__type__120432___24t(V_24Y)
    <=> t(V_24Y,c_24__type__120432) ) ).

fof('$tdef_$_type_10033',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__10033___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__10033___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_3395',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__3395___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__3395___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).

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_Coq.micromega.RingMicromega.Op2',axiom,
    ! [V_24Y] :
      ( cCoq_2emicromega_2eRingMicromega_2eOp2___24t(V_24Y)
    <=> t(V_24Y,cCoq_2emicromega_2eRingMicromega_2eOp2) ) ).

fof('$tdef_$_type_112781',axiom,
    ! [V_24X1,V_24X2,V_24Y] :
      ( c_24__type__112781___24t(V_24X1,V_24X2,V_24Y)
    <=> t(V_24Y,c_24__type__112781___24a2(V_24X1,V_24X2)) ) ).

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_7640',axiom,
    ! [V_24Y] :
      ( c_24__type__7640___24t(V_24Y)
    <=> t(V_24Y,c_24__type__7640) ) ).

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_12115',axiom,
    ! [V_24Y] :
      ( c_24__type__12115___24t(V_24Y)
    <=> t(V_24Y,c_24__type__12115) ) ).

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_5038',axiom,
    ! [V_24Y] :
      ( c_24__type__5038___24t(V_24Y)
    <=> t(V_24Y,c_24__type__5038) ) ).

fof('$tdef_$_type_109551',axiom,
    ! [V_24Y] :
      ( c_24__type__109551___24t(V_24Y)
    <=> t(V_24Y,c_24__type__109551) ) ).

fof('$tdef_$_type_96189',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__96189___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__96189___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_113151',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24Y] :
      ( c_24__type__113151___24t(V_24X1,V_24X2,V_24X3,V_24Y)
    <=> t(V_24Y,c_24__type__113151___24a3(V_24X1,V_24X2,V_24X3)) ) ).

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_118300',axiom,
    ! [V_24Y] :
      ( c_24__type__118300___24t(V_24Y)
    <=> t(V_24Y,c_24__type__118300) ) ).

fof('$tdef_$_type_10867',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__10867___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__10867___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_85546',axiom,
    ! [V_24Y] :
      ( c_24__type__85546___24t(V_24Y)
    <=> t(V_24Y,c_24__type__85546) ) ).

fof('$tdef_$_type_117559',axiom,
    ! [V_24Y] :
      ( c_24__type__117559___24t(V_24Y)
    <=> t(V_24Y,c_24__type__117559) ) ).

fof('$tdef_$_type_107326',axiom,
    ! [V_24Y] :
      ( c_24__type__107326___24t(V_24Y)
    <=> t(V_24Y,c_24__type__107326) ) ).

fof('$tdef_IntMap.Map.ad',axiom,
    ! [V_24Y] :
      ( cIntMap_2eMap_2ead___24t(V_24Y)
    <=> t(V_24Y,cIntMap_2eMap_2ead) ) ).

fof('$tdef_$_type_112824',axiom,
    ! [V_24X1,V_24X2,V_24Y] :
      ( c_24__type__112824___24t(V_24X1,V_24X2,V_24Y)
    <=> t(V_24Y,c_24__type__112824___24a2(V_24X1,V_24X2)) ) ).

fof('$tdef_$_type_120882',axiom,
    ! [V_24Y] :
      ( c_24__type__120882___24t(V_24Y)
    <=> t(V_24Y,c_24__type__120882) ) ).

fof('$tdef_$_type_112127',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__112127___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__112127___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_12081',axiom,
    ! [V_24Y] :
      ( c_24__type__12081___24t(V_24Y)
    <=> t(V_24Y,c_24__type__12081) ) ).

fof('$tdef_$_type_14014',axiom,
    ! [V_24Y] :
      ( c_24__type__14014___24t(V_24Y)
    <=> t(V_24Y,c_24__type__14014) ) ).

fof('$tdef_$_type_89733',axiom,
    ! [V_24Y] :
      ( c_24__type__89733___24t(V_24Y)
    <=> t(V_24Y,c_24__type__89733) ) ).

fof('$tdef_$_type_173544',axiom,
    ! [V_24X1,V_24X2,V_24Y] :
      ( c_24__type__173544___24t(V_24X1,V_24X2,V_24Y)
    <=> t(V_24Y,c_24__type__173544___24a2(V_24X1,V_24X2)) ) ).

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_107360',axiom,
    ! [V_24Y] :
      ( c_24__type__107360___24t(V_24Y)
    <=> t(V_24Y,c_24__type__107360) ) ).

fof('$tdef_$_type_94851',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__94851___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__94851___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_113102',axiom,
    ! [V_24X1,V_24X2,V_24Y] :
      ( c_24__type__113102___24t(V_24X1,V_24X2,V_24Y)
    <=> t(V_24Y,c_24__type__113102___24a2(V_24X1,V_24X2)) ) ).

fof('$tdef_$_type_983',axiom,
    ! [V_24Y] :
      ( c_24__type__983___24t(V_24Y)
    <=> t(V_24Y,c_24__type__983) ) ).

fof('$tdef_$_type_107462',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24Y] :
      ( c_24__type__107462___24t(V_24X1,V_24X2,V_24X3,V_24Y)
    <=> t(V_24Y,c_24__type__107462___24a3(V_24X1,V_24X2,V_24X3)) ) ).

fof('$tdef_$_type_110694',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y] :
      ( c_24__type__110694___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y)
    <=> t(V_24Y,c_24__type__110694___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6)) ) ).

fof('$tdef_$_type_1331',axiom,
    ! [V_24X1,V_24X2,V_24Y] :
      ( c_24__type__1331___24t(V_24X1,V_24X2,V_24Y)
    <=> t(V_24Y,c_24__type__1331___24a2(V_24X1,V_24X2)) ) ).

fof('$tdef_$_type_117554',axiom,
    ! [V_24Y] :
      ( c_24__type__117554___24t(V_24Y)
    <=> t(V_24Y,c_24__type__117554) ) ).

fof('$tdef_$_type_107284',axiom,
    ! [V_24Y] :
      ( c_24__type__107284___24t(V_24Y)
    <=> t(V_24Y,c_24__type__107284) ) ).

fof('$tdef_$_type_106545',axiom,
    ! [V_24Y] :
      ( c_24__type__106545___24t(V_24Y)
    <=> t(V_24Y,c_24__type__106545) ) ).

fof('$tdef_$_type_107689',axiom,
    ! [V_24Y] :
      ( c_24__type__107689___24t(V_24Y)
    <=> t(V_24Y,c_24__type__107689) ) ).

fof('$tdef_$_type_109418',axiom,
    ! [V_24Y] :
      ( c_24__type__109418___24t(V_24Y)
    <=> t(V_24Y,c_24__type__109418) ) ).

fof('$tdef_$_type_95866',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__95866___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__95866___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_113370',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
      ( c_24__type__113370___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
    <=> t(V_24Y,c_24__type__113370___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).

fof('$tdef_$_type_117969',axiom,
    ! [V_24Y] :
      ( c_24__type__117969___24t(V_24Y)
    <=> t(V_24Y,c_24__type__117969) ) ).

fof('$tdef_$_type_92475',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__92475___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__92475___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_107365',axiom,
    ! [V_24Y] :
      ( c_24__type__107365___24t(V_24Y)
    <=> t(V_24Y,c_24__type__107365) ) ).

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_736',axiom,
    ! [V_24Y] :
      ( c_24__type__736___24t(V_24Y)
    <=> t(V_24Y,c_24__type__736) ) ).

fof('$tdef_$_type_109265',axiom,
    ! [V_24Y] :
      ( c_24__type__109265___24t(V_24Y)
    <=> t(V_24Y,c_24__type__109265) ) ).

fof('$tdef_$_type_122209',axiom,
    ! [V_24Y] :
      ( c_24__type__122209___24t(V_24Y)
    <=> t(V_24Y,c_24__type__122209) ) ).

fof('$tdef_$_type_121869',axiom,
    ! [V_24Y] :
      ( c_24__type__121869___24t(V_24Y)
    <=> t(V_24Y,c_24__type__121869) ) ).

fof('$tdef_$_type_112252',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__112252___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__112252___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_109824',axiom,
    ! [V_24Y] :
      ( c_24__type__109824___24t(V_24Y)
    <=> t(V_24Y,c_24__type__109824) ) ).

fof('$tdef_$_type_11964',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y] :
      ( c_24__type__11964___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y)
    <=> t(V_24Y,c_24__type__11964___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7)) ) ).

fof('$tdef_$_type_107770',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y] :
      ( c_24__type__107770___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y)
    <=> t(V_24Y,c_24__type__107770___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6)) ) ).

fof('$tdef_$_type_113922',axiom,
    ! [V_24Y] :
      ( c_24__type__113922___24t(V_24Y)
    <=> t(V_24Y,c_24__type__113922) ) ).

fof('$tdef_$_type_103711',axiom,
    ! [V_24Y] :
      ( c_24__type__103711___24t(V_24Y)
    <=> t(V_24Y,c_24__type__103711) ) ).

fof('$tdef_$_type_111194',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
      ( c_24__type__111194___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__111194___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).

fof('$tdef_$_type_874',axiom,
    ! [V_24Y] :
      ( c_24__type__874___24t(V_24Y)
    <=> t(V_24Y,c_24__type__874) ) ).

fof('$tdef_$_type_157',axiom,
    ! [V_24X1,V_24Y] :
      ( c_24__type__157___24t(V_24X1,V_24Y)
    <=> t(V_24Y,c_24__type__157___24a1(V_24X1)) ) ).

fof('$tdef_$_type_106212',axiom,
    ! [V_24Y] :
      ( c_24__type__106212___24t(V_24Y)
    <=> t(V_24Y,c_24__type__106212) ) ).

fof('$tdef_$_type_112960',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
      ( c_24__type__112960___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
    <=> t(V_24Y,c_24__type__112960___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).

fof('$tdef_$_type_90871',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__90871___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__90871___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).

fof('$tdef_$_type_605',axiom,
    ! [V_24Y] :
      ( c_24__type__605___24t(V_24Y)
    <=> t(V_24Y,c_24__type__605) ) ).

fof('$tdef_$_type_92798',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__92798___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__92798___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_121892',axiom,
    ! [V_24Y] :
      ( c_24__type__121892___24t(V_24Y)
    <=> t(V_24Y,c_24__type__121892) ) ).

fof('$tdef_Coq.micromega.Tauto.cnf',axiom,
    ! [V_24X1,V_24X2,V_24Y] :
      ( cCoq_2emicromega_2eTauto_2ecnf___24t(V_24X1,V_24X2,V_24Y)
    <=> t(V_24Y,cCoq_2emicromega_2eTauto_2ecnf___24a2(V_24X1,V_24X2)) ) ).

fof('$tdef_$_type_164749',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24Y] :
      ( c_24__type__164749___24t(V_24X1,V_24X2,V_24X3,V_24Y)
    <=> t(V_24Y,c_24__type__164749___24a3(V_24X1,V_24X2,V_24X3)) ) ).

fof('$tdef_$_type_110469',axiom,
    ! [V_24Y] :
      ( c_24__type__110469___24t(V_24Y)
    <=> t(V_24Y,c_24__type__110469) ) ).

fof('$tdef_$_type_122302',axiom,
    ! [V_24Y] :
      ( c_24__type__122302___24t(V_24Y)
    <=> t(V_24Y,c_24__type__122302) ) ).

fof('$tdef_$_type_113691',axiom,
    ! [V_24Y] :
      ( c_24__type__113691___24t(V_24Y)
    <=> t(V_24Y,c_24__type__113691) ) ).

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_112771',axiom,
    ! [V_24Y] :
      ( c_24__type__112771___24t(V_24Y)
    <=> t(V_24Y,c_24__type__112771) ) ).

fof('$tdef_$_type_1324',axiom,
    ! [V_24X1,V_24X2,V_24Y] :
      ( c_24__type__1324___24t(V_24X1,V_24X2,V_24Y)
    <=> t(V_24Y,c_24__type__1324___24a2(V_24X1,V_24X2)) ) ).

fof('$tdef_Coq.QArith.QArith_base.Q',axiom,
    ! [V_24Y] :
      ( cCoq_2eQArith_2eQArith__base_2eQ___24t(V_24Y)
    <=> t(V_24Y,cCoq_2eQArith_2eQArith__base_2eQ) ) ).

fof('$tdef_$_type_2518',axiom,
    ! [V_24Y] :
      ( c_24__type__2518___24t(V_24Y)
    <=> t(V_24Y,c_24__type__2518) ) ).

fof('$tdef_$_type_108212',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__108212___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__108212___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).

fof('$tdef_Coq.PArith.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_295',axiom,
    ! [V_24Y] :
      ( c_24__type__295___24t(V_24Y)
    <=> t(V_24Y,c_24__type__295) ) ).

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_111432',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
      ( c_24__type__111432___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
    <=> t(V_24Y,c_24__type__111432___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).

fof('$tdef_$_type_108305',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__108305___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__108305___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).

fof('$tdef_$_type_122218',axiom,
    ! [V_24Y] :
      ( c_24__type__122218___24t(V_24Y)
    <=> t(V_24Y,c_24__type__122218) ) ).

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_122274',axiom,
    ! [V_24Y] :
      ( c_24__type__122274___24t(V_24Y)
    <=> t(V_24Y,c_24__type__122274) ) ).

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_107075',axiom,
    ! [V_24Y] :
      ( c_24__type__107075___24t(V_24Y)
    <=> t(V_24Y,c_24__type__107075) ) ).

fof('$tdef_$_type_11297',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
      ( c_24__type__11297___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
    <=> t(V_24Y,c_24__type__11297___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).

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_2651',axiom,
    ! [V_24Y] :
      ( c_24__type__2651___24t(V_24Y)
    <=> t(V_24Y,c_24__type__2651) ) ).

fof('$tdef_$_type_109830',axiom,
    ! [V_24Y] :
      ( c_24__type__109830___24t(V_24Y)
    <=> t(V_24Y,c_24__type__109830) ) ).

fof('$tdef_$_type_121583',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y] :
      ( c_24__type__121583___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y)
    <=> t(V_24Y,c_24__type__121583___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6)) ) ).

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_90568',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__90568___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__90568___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).

fof('$tdef_$_type_109082',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
      ( c_24__type__109082___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__109082___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).

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_Coq.micromega.Tauto.clause',axiom,
    ! [V_24X1,V_24X2,V_24Y] :
      ( cCoq_2emicromega_2eTauto_2eclause___24t(V_24X1,V_24X2,V_24Y)
    <=> t(V_24Y,cCoq_2emicromega_2eTauto_2eclause___24a2(V_24X1,V_24X2)) ) ).

fof('$tdef_$_type_107287',axiom,
    ! [V_24Y] :
      ( c_24__type__107287___24t(V_24Y)
    <=> t(V_24Y,c_24__type__107287) ) ).

fof('$tdef_$_type_120317',axiom,
    ! [V_24Y] :
      ( c_24__type__120317___24t(V_24Y)
    <=> t(V_24Y,c_24__type__120317) ) ).

fof('$tdef_$_type_981',axiom,
    ! [V_24Y] :
      ( c_24__type__981___24t(V_24Y)
    <=> t(V_24Y,c_24__type__981) ) ).

fof('$tdef_$_type_120879',axiom,
    ! [V_24Y] :
      ( c_24__type__120879___24t(V_24Y)
    <=> t(V_24Y,c_24__type__120879) ) ).

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_98426',axiom,
    ! [V_24Y] :
      ( c_24__type__98426___24t(V_24Y)
    <=> t(V_24Y,c_24__type__98426) ) ).

fof('$tdef_$_type_11463',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y] :
      ( c_24__type__11463___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y)
    <=> t(V_24Y,c_24__type__11463___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7)) ) ).

fof('$tdef_$_type_1993',axiom,
    ! [V_24X1,V_24X2,V_24Y] :
      ( c_24__type__1993___24t(V_24X1,V_24X2,V_24Y)
    <=> t(V_24Y,c_24__type__1993___24a2(V_24X1,V_24X2)) ) ).

fof('$tdef_$_type_28',axiom,
    ! [V_24Y] :
      ( c_24__type__28___24t(V_24Y)
    <=> t(V_24Y,c_24__type__28) ) ).

fof('$tdef_$_type_104081',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24Y] :
      ( c_24__type__104081___24t(V_24X1,V_24X2,V_24X3,V_24Y)
    <=> t(V_24Y,c_24__type__104081___24a3(V_24X1,V_24X2,V_24X3)) ) ).

fof('$tdef_$_type_1430',axiom,
    ! [V_24Y] :
      ( c_24__type__1430___24t(V_24Y)
    <=> t(V_24Y,c_24__type__1430) ) ).

fof('$tdef_$_type_120334',axiom,
    ! [V_24Y] :
      ( c_24__type__120334___24t(V_24Y)
    <=> t(V_24Y,c_24__type__120334) ) ).

fof('$tdef_$_type_118013',axiom,
    ! [V_24Y] :
      ( c_24__type__118013___24t(V_24Y)
    <=> t(V_24Y,c_24__type__118013) ) ).

fof('$tdef_$_type_120913',axiom,
    ! [V_24Y] :
      ( c_24__type__120913___24t(V_24Y)
    <=> t(V_24Y,c_24__type__120913) ) ).

fof('$tdef_$_type_122041',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y] :
      ( c_24__type__122041___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y)
    <=> t(V_24Y,c_24__type__122041___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6)) ) ).

fof('$tdef_$_type_107205',axiom,
    ! [V_24Y] :
      ( c_24__type__107205___24t(V_24Y)
    <=> t(V_24Y,c_24__type__107205) ) ).

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('$tdef_$_type_8041',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
      ( c_24__type__8041___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__8041___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).

fof('$tdef_$_type_107166',axiom,
    ! [V_24Y] :
      ( c_24__type__107166___24t(V_24Y)
    <=> t(V_24Y,c_24__type__107166) ) ).

fof('$tdef_$_type_113899',axiom,
    ! [V_24Y] :
      ( c_24__type__113899___24t(V_24Y)
    <=> t(V_24Y,c_24__type__113899) ) ).

fof('$tdef_$_type_11278',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
      ( c_24__type__11278___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
    <=> t(V_24Y,c_24__type__11278___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).

fof('$tdef_$_type_112488',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__112488___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__112488___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_111386',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
      ( c_24__type__111386___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
    <=> t(V_24Y,c_24__type__111386___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).

fof('$tdef_$_type_2610',axiom,
    ! [V_24Y] :
      ( c_24__type__2610___24t(V_24Y)
    <=> t(V_24Y,c_24__type__2610) ) ).

fof('$tdef_$_type_172843',axiom,
    ! [V_24Y] :
      ( c_24__type__172843___24t(V_24Y)
    <=> t(V_24Y,c_24__type__172843) ) ).

fof('$tdef_$_type_96883',axiom,
    ! [V_24Y] :
      ( c_24__type__96883___24t(V_24Y)
    <=> t(V_24Y,c_24__type__96883) ) ).

fof('$tdef_$_type_118269',axiom,
    ! [V_24Y] :
      ( c_24__type__118269___24t(V_24Y)
    <=> t(V_24Y,c_24__type__118269) ) ).

fof('$tdef_$_type_107581',axiom,
    ! [V_24Y] :
      ( c_24__type__107581___24t(V_24Y)
    <=> t(V_24Y,c_24__type__107581) ) ).

fof('$tdef_$_type_95197',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__95197___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__95197___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_120898',axiom,
    ! [V_24Y] :
      ( c_24__type__120898___24t(V_24Y)
    <=> t(V_24Y,c_24__type__120898) ) ).

fof('$tdef_Coq.ZArith.Znumtheory.Euclid',axiom,
    ! [V_24X1,V_24X2,V_24Y] :
      ( cCoq_2eZArith_2eZnumtheory_2eEuclid___24t(V_24X1,V_24X2,V_24Y)
    <=> t(V_24Y,cCoq_2eZArith_2eZnumtheory_2eEuclid___24a2(V_24X1,V_24X2)) ) ).

fof('$tdef_Coq.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('$tdef_$_type_107511',axiom,
    ! [V_24Y] :
      ( c_24__type__107511___24t(V_24Y)
    <=> t(V_24Y,c_24__type__107511) ) ).

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_2635',axiom,
    ! [V_24Y] :
      ( c_24__type__2635___24t(V_24Y)
    <=> t(V_24Y,c_24__type__2635) ) ).

fof('$tdef_$_type_183418',axiom,
    ! [V_24Y] :
      ( c_24__type__183418___24t(V_24Y)
    <=> t(V_24Y,c_24__type__183418) ) ).

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_3127',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__3127___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__3127___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).

fof('$tdef_$_type_11840',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y] :
      ( c_24__type__11840___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y)
    <=> t(V_24Y,c_24__type__11840___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7)) ) ).

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_111752',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__111752___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__111752___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_172562',axiom,
    ! [V_24Y] :
      ( c_24__type__172562___24t(V_24Y)
    <=> t(V_24Y,c_24__type__172562) ) ).

fof('$tdef_$_type_120895',axiom,
    ! [V_24Y] :
      ( c_24__type__120895___24t(V_24Y)
    <=> t(V_24Y,c_24__type__120895) ) ).

fof('$tdef_$_type_93836',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__93836___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__93836___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_112711',axiom,
    ! [V_24Y] :
      ( c_24__type__112711___24t(V_24Y)
    <=> t(V_24Y,c_24__type__112711) ) ).

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_1934',axiom,
    ! [V_24Y] :
      ( c_24__type__1934___24t(V_24Y)
    <=> t(V_24Y,c_24__type__1934) ) ).

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_94528',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__94528___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__94528___24a22(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22)) ) ).

fof('$tdef_Coq.Init.Datatypes.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_108573',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__108573___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__108573___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).

fof('$tdef_$_type_122328',axiom,
    ! [V_24Y] :
      ( c_24__type__122328___24t(V_24Y)
    <=> t(V_24Y,c_24__type__122328) ) ).

fof('$tdef_$_type_121354',axiom,
    ! [V_24Y] :
      ( c_24__type__121354___24t(V_24Y)
    <=> t(V_24Y,c_24__type__121354) ) ).

fof('$tdef_$_type_1278',axiom,
    ! [V_24X1,V_24Y] :
      ( c_24__type__1278___24t(V_24X1,V_24Y)
    <=> t(V_24Y,c_24__type__1278___24a1(V_24X1)) ) ).

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_12142',axiom,
    ! [V_24Y] :
      ( c_24__type__12142___24t(V_24Y)
    <=> t(V_24Y,c_24__type__12142) ) ).

fof('$tdef_$_type_109028',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
      ( c_24__type__109028___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__109028___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).

fof('$tdef_Coq.micromega.QMicromega.QWitness',axiom,
    ! [V_24Y] :
      ( cCoq_2emicromega_2eQMicromega_2eQWitness___24t(V_24Y)
    <=> t(V_24Y,cCoq_2emicromega_2eQMicromega_2eQWitness) ) ).

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_107194',axiom,
    ! [V_24Y] :
      ( c_24__type__107194___24t(V_24Y)
    <=> t(V_24Y,c_24__type__107194) ) ).

fof('$tdef_$_type_8419',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
      ( c_24__type__8419___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
    <=> t(V_24Y,c_24__type__8419___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).

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_164738',axiom,
    ! [V_24Y] :
      ( c_24__type__164738___24t(V_24Y)
    <=> t(V_24Y,c_24__type__164738) ) ).

fof('$tdef_$_type_109832',axiom,
    ! [V_24Y] :
      ( c_24__type__109832___24t(V_24Y)
    <=> t(V_24Y,c_24__type__109832) ) ).

fof('$tdef_$_type_1444',axiom,
    ! [V_24Y] :
      ( c_24__type__1444___24t(V_24Y)
    <=> t(V_24Y,c_24__type__1444) ) ).

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_113109',axiom,
    ! [V_24X1,V_24Y] :
      ( c_24__type__113109___24t(V_24X1,V_24Y)
    <=> t(V_24Y,c_24__type__113109___24a1(V_24X1)) ) ).

fof('$tdef_$_type_7661',axiom,
    ! [V_24Y] :
      ( c_24__type__7661___24t(V_24Y)
    <=> t(V_24Y,c_24__type__7661) ) ).

fof('$tdef_$_type_107497',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
      ( c_24__type__107497___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
    <=> t(V_24Y,c_24__type__107497___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).

fof('$tdef_$_type_89772',axiom,
    ! [V_24Y] :
      ( c_24__type__89772___24t(V_24Y)
    <=> t(V_24Y,c_24__type__89772) ) ).

fof('$tdef_$_type_107441',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24Y] :
      ( c_24__type__107441___24t(V_24X1,V_24X2,V_24X3,V_24Y)
    <=> t(V_24Y,c_24__type__107441___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_110772',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y] :
      ( c_24__type__110772___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y)
    <=> t(V_24Y,c_24__type__110772___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6)) ) ).

fof('$tdef_$_type_10246',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__10246___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__10246___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_108748',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__108748___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__108748___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).

fof('$tdef_$_type_90669',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__90669___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__90669___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).

fof('$tdef_$_type_12873',axiom,
    ! [V_24Y] :
      ( c_24__type__12873___24t(V_24Y)
    <=> t(V_24Y,c_24__type__12873) ) ).

fof('$tdef_$_type_8395',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
      ( c_24__type__8395___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
    <=> t(V_24Y,c_24__type__8395___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).

fof('$tdef_$_type_111077',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
      ( c_24__type__111077___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__111077___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).

fof('$tdef_$_type_260',axiom,
    ! [V_24Y] :
      ( c_24__type__260___24t(V_24Y)
    <=> t(V_24Y,c_24__type__260) ) ).

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_91218',axiom,
    ! [V_24Y] :
      ( c_24__type__91218___24t(V_24Y)
    <=> t(V_24Y,c_24__type__91218) ) ).

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_111450',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
      ( c_24__type__111450___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
    <=> t(V_24Y,c_24__type__111450___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).

fof('$tdef_$_type_2638',axiom,
    ! [V_24X1,V_24Y] :
      ( c_24__type__2638___24t(V_24X1,V_24Y)
    <=> t(V_24Y,c_24__type__2638___24a1(V_24X1)) ) ).

fof('$tdef_$_type_2520',axiom,
    ! [V_24Y] :
      ( c_24__type__2520___24t(V_24Y)
    <=> t(V_24Y,c_24__type__2520) ) ).

fof('$tdef_$_type_122816',axiom,
    ! [V_24Y] :
      ( c_24__type__122816___24t(V_24Y)
    <=> t(V_24Y,c_24__type__122816) ) ).

fof('$tdef_$_type_107638',axiom,
    ! [V_24Y] :
      ( c_24__type__107638___24t(V_24Y)
    <=> t(V_24Y,c_24__type__107638) ) ).

fof('$tdef_$_type_108965',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
      ( c_24__type__108965___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__108965___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).

fof('$tdef_$_type_118375',axiom,
    ! [V_24Y] :
      ( c_24__type__118375___24t(V_24Y)
    <=> t(V_24Y,c_24__type__118375) ) ).

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_Coq.micromega.Tauto.BFormula',axiom,
    ! [V_24X1,V_24Y] :
      ( cCoq_2emicromega_2eTauto_2eBFormula___24t(V_24X1,V_24Y)
    <=> t(V_24Y,cCoq_2emicromega_2eTauto_2eBFormula___24a1(V_24X1)) ) ).

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_120918',axiom,
    ! [V_24X1,V_24Y] :
      ( c_24__type__120918___24t(V_24X1,V_24Y)
    <=> t(V_24Y,c_24__type__120918___24a1(V_24X1)) ) ).

fof('$tdef_$_type_122191',axiom,
    ! [V_24Y] :
      ( c_24__type__122191___24t(V_24Y)
    <=> t(V_24Y,c_24__type__122191) ) ).

fof('$tdef_$_type_111409',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
      ( c_24__type__111409___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
    <=> t(V_24Y,c_24__type__111409___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).

fof('$tdef_$_type_13403',axiom,
    ! [V_24X1,V_24X2,V_24Y] :
      ( c_24__type__13403___24t(V_24X1,V_24X2,V_24Y)
    <=> t(V_24Y,c_24__type__13403___24a2(V_24X1,V_24X2)) ) ).

fof('$tdef_$_type_113284',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24Y] :
      ( c_24__type__113284___24t(V_24X1,V_24X2,V_24X3,V_24Y)
    <=> t(V_24Y,c_24__type__113284___24a3(V_24X1,V_24X2,V_24X3)) ) ).

fof('$tdef_$_type_305',axiom,
    ! [V_24Y] :
      ( c_24__type__305___24t(V_24Y)
    <=> t(V_24Y,c_24__type__305) ) ).

fof('$tdef_$_type_109367',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
      ( c_24__type__109367___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
    <=> t(V_24Y,c_24__type__109367___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).

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_2952',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__2952___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__2952___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.nonnegreal',axiom,
    ! [V_24Y] :
      ( cCoq_2eReals_2eRIneq_2enonnegreal___24t(V_24Y)
    <=> t(V_24Y,cCoq_2eReals_2eRIneq_2enonnegreal) ) ).

fof('$tdef_$_type_12044',axiom,
    ! [V_24Y] :
      ( c_24__type__12044___24t(V_24Y)
    <=> t(V_24Y,c_24__type__12044) ) ).

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_89840',axiom,
    ! [V_24Y] :
      ( c_24__type__89840___24t(V_24Y)
    <=> t(V_24Y,c_24__type__89840) ) ).

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_91245',axiom,
    ! [V_24Y] :
      ( c_24__type__91245___24t(V_24Y)
    <=> t(V_24Y,c_24__type__91245) ) ).

fof('$tdef_$_type_116798',axiom,
    ! [V_24X1,V_24Y] :
      ( c_24__type__116798___24t(V_24X1,V_24Y)
    <=> t(V_24Y,c_24__type__116798___24a1(V_24X1)) ) ).

fof('$tdef_$_type_13427',axiom,
    ! [V_24Y] :
      ( c_24__type__13427___24t(V_24Y)
    <=> t(V_24Y,c_24__type__13427) ) ).

fof('$tdef_IntMap.Fset.FSet',axiom,
    ! [V_24Y] :
      ( cIntMap_2eFset_2eFSet___24t(V_24Y)
    <=> t(V_24Y,cIntMap_2eFset_2eFSet) ) ).

fof('$tdef_$_type_9412',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__9412___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__9412___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.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_111476',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
      ( c_24__type__111476___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
    <=> t(V_24Y,c_24__type__111476___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).

fof('$tdef_$_type_7978',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
      ( c_24__type__7978___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__7978___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).

fof('$tdef_$_type_110507',axiom,
    ! [V_24Y] :
      ( c_24__type__110507___24t(V_24Y)
    <=> t(V_24Y,c_24__type__110507) ) ).

fof('$tdef_$_type_282',axiom,
    ! [V_24X1,V_24X2,V_24Y] :
      ( c_24__type__282___24t(V_24X1,V_24X2,V_24Y)
    <=> t(V_24Y,c_24__type__282___24a2(V_24X1,V_24X2)) ) ).

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_113627',axiom,
    ! [V_24Y] :
      ( c_24__type__113627___24t(V_24Y)
    <=> t(V_24Y,c_24__type__113627) ) ).

fof('$tdef_$_type_107692',axiom,
    ! [V_24Y] :
      ( c_24__type__107692___24t(V_24Y)
    <=> t(V_24Y,c_24__type__107692) ) ).

fof('$tdef_$_type_118390',axiom,
    ! [V_24X1,V_24Y] :
      ( c_24__type__118390___24t(V_24X1,V_24Y)
    <=> t(V_24Y,c_24__type__118390___24a1(V_24X1)) ) ).

fof('$tdef_$_type_107505',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
      ( c_24__type__107505___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
    <=> t(V_24Y,c_24__type__107505___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).

fof('$tdef_$_type_121620',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y] :
      ( c_24__type__121620___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y)
    <=> t(V_24Y,c_24__type__121620___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6)) ) ).

fof('$tdef_$_type_120948',axiom,
    ! [V_24Y] :
      ( c_24__type__120948___24t(V_24Y)
    <=> t(V_24Y,c_24__type__120948) ) ).

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_112814',axiom,
    ! [V_24Y] :
      ( c_24__type__112814___24t(V_24Y)
    <=> t(V_24Y,c_24__type__112814) ) ).

fof('$tdef_$_type_3045',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__3045___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__3045___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).

fof('$tdef_$_type_112751',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
      ( c_24__type__112751___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
    <=> t(V_24Y,c_24__type__112751___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).

fof('$tdef_$_type_610',axiom,
    ! [V_24Y] :
      ( c_24__type__610___24t(V_24Y)
    <=> t(V_24Y,c_24__type__610) ) ).

fof('$tdef_$_type_12098',axiom,
    ! [V_24Y] :
      ( c_24__type__12098___24t(V_24Y)
    <=> t(V_24Y,c_24__type__12098) ) ).

fof('$tdef_$_type_122313',axiom,
    ! [V_24Y] :
      ( c_24__type__122313___24t(V_24Y)
    <=> t(V_24Y,c_24__type__122313) ) ).

fof('$tdef_$_type_9607',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__9607___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__9607___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.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_110519',axiom,
    ! [V_24Y] :
      ( c_24__type__110519___24t(V_24Y)
    <=> t(V_24Y,c_24__type__110519) ) ).

fof('$tdef_$_type_113232',axiom,
    ! [V_24Y] :
      ( c_24__type__113232___24t(V_24Y)
    <=> t(V_24Y,c_24__type__113232) ) ).

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_11983',axiom,
    ! [V_24X1,V_24X2,V_24Y] :
      ( c_24__type__11983___24t(V_24X1,V_24X2,V_24Y)
    <=> t(V_24Y,c_24__type__11983___24a2(V_24X1,V_24X2)) ) ).

fof('$tdef_$_type_11311',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
      ( c_24__type__11311___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
    <=> t(V_24Y,c_24__type__11311___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).

fof('$tdef_$_type_113143',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24Y] :
      ( c_24__type__113143___24t(V_24X1,V_24X2,V_24X3,V_24Y)
    <=> t(V_24Y,c_24__type__113143___24a3(V_24X1,V_24X2,V_24X3)) ) ).

fof('$tdef_$_type_93490',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__93490___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__93490___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_113072',axiom,
    ! [V_24Y] :
      ( c_24__type__113072___24t(V_24Y)
    <=> t(V_24Y,c_24__type__113072) ) ).

fof('$tdef_$_type_4992',axiom,
    ! [V_24Y] :
      ( c_24__type__4992___24t(V_24Y)
    <=> t(V_24Y,c_24__type__4992) ) ).

fof('$tdef_$_type_2028',axiom,
    ! [V_24Y] :
      ( c_24__type__2028___24t(V_24Y)
    <=> t(V_24Y,c_24__type__2028) ) ).

fof('$tdef_$_type_11920',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y] :
      ( c_24__type__11920___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y)
    <=> t(V_24Y,c_24__type__11920___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7)) ) ).

fof('$tdef_$_type_2663',axiom,
    ! [V_24Y] :
      ( c_24__type__2663___24t(V_24Y)
    <=> t(V_24Y,c_24__type__2663) ) ).

fof('$tdef_$_type_1310',axiom,
    ! [V_24X1,V_24X2,V_24Y] :
      ( c_24__type__1310___24t(V_24X1,V_24X2,V_24Y)
    <=> t(V_24Y,c_24__type__1310___24a2(V_24X1,V_24X2)) ) ).

fof('$tdef_$_type_11731',axiom,
    ! [V_24X1,V_24X2,V_24Y] :
      ( c_24__type__11731___24t(V_24X1,V_24X2,V_24Y)
    <=> t(V_24Y,c_24__type__11731___24a2(V_24X1,V_24X2)) ) ).

fof('$tdef_$_type_109531',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
      ( c_24__type__109531___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
    <=> t(V_24Y,c_24__type__109531___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).

fof('$tdef_$_type_8536',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
      ( c_24__type__8536___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
    <=> t(V_24Y,c_24__type__8536___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).

fof('$tdef_$_type_118305',axiom,
    ! [V_24Y] :
      ( c_24__type__118305___24t(V_24Y)
    <=> t(V_24Y,c_24__type__118305) ) ).

fof('$tdef_$_type_113782',axiom,
    ! [V_24Y] :
      ( c_24__type__113782___24t(V_24Y)
    <=> t(V_24Y,c_24__type__113782) ) ).

fof('$tdef_$_type_5117',axiom,
    ! [V_24Y] :
      ( c_24__type__5117___24t(V_24Y)
    <=> t(V_24Y,c_24__type__5117) ) ).

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_Coq.micromega.RingMicromega.Op1',axiom,
    ! [V_24Y] :
      ( cCoq_2emicromega_2eRingMicromega_2eOp1___24t(V_24Y)
    <=> t(V_24Y,cCoq_2emicromega_2eRingMicromega_2eOp1) ) ).

fof('$tdef_$_type_85487',axiom,
    ! [V_24Y] :
      ( c_24__type__85487___24t(V_24Y)
    <=> t(V_24Y,c_24__type__85487) ) ).

fof('$tdef_$_type_113613',axiom,
    ! [V_24Y] :
      ( c_24__type__113613___24t(V_24Y)
    <=> t(V_24Y,c_24__type__113613) ) ).

fof('$tdef_$_type_109827',axiom,
    ! [V_24Y] :
      ( c_24__type__109827___24t(V_24Y)
    <=> t(V_24Y,c_24__type__109827) ) ).

fof('$tdef_$_type_91783',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__91783___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__91783___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_116811',axiom,
    ! [V_24Y] :
      ( c_24__type__116811___24t(V_24Y)
    <=> t(V_24Y,c_24__type__116811) ) ).

fof('$tdef_$_type_112498',axiom,
    ! [V_24Y] :
      ( c_24__type__112498___24t(V_24Y)
    <=> t(V_24Y,c_24__type__112498) ) ).

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_13396',axiom,
    ! [V_24Y] :
      ( c_24__type__13396___24t(V_24Y)
    <=> t(V_24Y,c_24__type__13396) ) ).

fof('$tdef_$_type_164742',axiom,
    ! [V_24X1,V_24X2,V_24Y] :
      ( c_24__type__164742___24t(V_24X1,V_24X2,V_24Y)
    <=> t(V_24Y,c_24__type__164742___24a2(V_24X1,V_24X2)) ) ).

fof('$tdef_$_type_1000',axiom,
    ! [V_24Y] :
      ( c_24__type__1000___24t(V_24Y)
    <=> t(V_24Y,c_24__type__1000) ) ).

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_109512',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
      ( c_24__type__109512___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
    <=> t(V_24Y,c_24__type__109512___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).

fof('$tdef_$_type_120908',axiom,
    ! [V_24Y] :
      ( c_24__type__120908___24t(V_24Y)
    <=> t(V_24Y,c_24__type__120908) ) ).

fof('$tdef_$_type_8095',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
      ( c_24__type__8095___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__8095___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).

fof('$tdef_$_type_113106',axiom,
    ! [V_24Y] :
      ( c_24__type__113106___24t(V_24Y)
    <=> t(V_24Y,c_24__type__113106) ) ).

fof('$tdef_$_type_10654',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__10654___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__10654___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_110510',axiom,
    ! [V_24Y] :
      ( c_24__type__110510___24t(V_24Y)
    <=> t(V_24Y,c_24__type__110510) ) ).

fof('$tdef_$_type_3220',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__3220___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__3220___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).

fof('$tdef_$_type_113056',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24Y] :
      ( c_24__type__113056___24t(V_24X1,V_24X2,V_24X3,V_24Y)
    <=> t(V_24Y,c_24__type__113056___24a3(V_24X1,V_24X2,V_24X3)) ) ).

fof('$tdef_$_type_85484',axiom,
    ! [V_24Y] :
      ( c_24__type__85484___24t(V_24Y)
    <=> t(V_24Y,c_24__type__85484) ) ).

fof('$tdef_$_type_122281',axiom,
    ! [V_24Y] :
      ( c_24__type__122281___24t(V_24Y)
    <=> t(V_24Y,c_24__type__122281) ) ).

fof('$tdef_$_type_111494',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
      ( c_24__type__111494___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
    <=> t(V_24Y,c_24__type__111494___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).

fof('$tdef_$_type_121347',axiom,
    ! [V_24Y] :
      ( c_24__type__121347___24t(V_24Y)
    <=> t(V_24Y,c_24__type__121347) ) ).

fof('$tdef_$_type_12063',axiom,
    ! [V_24Y] :
      ( c_24__type__12063___24t(V_24Y)
    <=> t(V_24Y,c_24__type__12063) ) ).

fof('$tdef_$_type_116816',axiom,
    ! [V_24X1,V_24Y] :
      ( c_24__type__116816___24t(V_24X1,V_24Y)
    <=> t(V_24Y,c_24__type__116816___24a1(V_24X1)) ) ).

fof('$tdef_$_type_173588',axiom,
    ! [V_24Y] :
      ( c_24__type__173588___24t(V_24Y)
    <=> t(V_24Y,c_24__type__173588) ) ).

fof('$tdef_$_type_104292',axiom,
    ! [V_24Y] :
      ( c_24__type__104292___24t(V_24Y)
    <=> t(V_24Y,c_24__type__104292) ) ).

fof('$tdef_$_type_109296',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24Y] :
      ( c_24__type__109296___24t(V_24X1,V_24X2,V_24X3,V_24Y)
    <=> t(V_24Y,c_24__type__109296___24a3(V_24X1,V_24X2,V_24X3)) ) ).

fof('$tdef_$_type_105136',axiom,
    ! [V_24X1,V_24X2,V_24Y] :
      ( c_24__type__105136___24t(V_24X1,V_24X2,V_24Y)
    <=> t(V_24Y,c_24__type__105136___24a2(V_24X1,V_24X2)) ) ).

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_1426',axiom,
    ! [V_24Y] :
      ( c_24__type__1426___24t(V_24Y)
    <=> t(V_24Y,c_24__type__1426) ) ).

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_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_89842',axiom,
    ! [V_24Y] :
      ( c_24__type__89842___24t(V_24Y)
    <=> t(V_24Y,c_24__type__89842) ) ).

fof('$tdef_$_type_71',axiom,
    ! [V_24Y] :
      ( c_24__type__71___24t(V_24Y)
    <=> t(V_24Y,c_24__type__71) ) ).

fof('$tdef_$_type_7915',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
      ( c_24__type__7915___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__7915___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).

fof('$tdef_$_type_112921',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24Y] :
      ( c_24__type__112921___24t(V_24X1,V_24X2,V_24X3,V_24Y)
    <=> t(V_24Y,c_24__type__112921___24a3(V_24X1,V_24X2,V_24X3)) ) ).

fof('$tdef_$_type_109641',axiom,
    ! [V_24Y] :
      ( c_24__type__109641___24t(V_24Y)
    <=> t(V_24Y,c_24__type__109641) ) ).

fof('$tdef_$_type_8365',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
      ( c_24__type__8365___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
    <=> t(V_24Y,c_24__type__8365___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).

fof('$tdef_$_type_8158',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
      ( c_24__type__8158___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__8158___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).

fof('$tdef_$_type_90276',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__90276___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__90276___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).

fof('$tdef_$_type_85570',axiom,
    ! [V_24Y] :
      ( c_24__type__85570___24t(V_24Y)
    <=> t(V_24Y,c_24__type__85570) ) ).

fof('$tdef_$_type_2108',axiom,
    ! [V_24Y] :
      ( c_24__type__2108___24t(V_24Y)
    <=> t(V_24Y,c_24__type__2108) ) ).

fof('$tdef_$_type_109192',axiom,
    ! [V_24Y] :
      ( c_24__type__109192___24t(V_24Y)
    <=> t(V_24Y,c_24__type__109192) ) ).

fof('$tdef_$_type_107210',axiom,
    ! [V_24X1,V_24Y] :
      ( c_24__type__107210___24t(V_24X1,V_24Y)
    <=> t(V_24Y,c_24__type__107210___24a1(V_24X1)) ) ).

fof('$tdef_$_type_9820',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__9820___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__9820___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_1335',axiom,
    ! [V_24X1,V_24X2,V_24Y] :
      ( c_24__type__1335___24t(V_24X1,V_24X2,V_24Y)
    <=> t(V_24Y,c_24__type__1335___24a2(V_24X1,V_24X2)) ) ).

fof('$tdef_$_type_110504',axiom,
    ! [V_24Y] :
      ( c_24__type__110504___24t(V_24Y)
    <=> t(V_24Y,c_24__type__110504) ) ).

fof('$tdef_$_type_108007',axiom,
    ! [V_24Y] :
      ( c_24__type__108007___24t(V_24Y)
    <=> t(V_24Y,c_24__type__108007) ) ).

fof('$tdef_$_type_85933',axiom,
    ! [V_24Y] :
      ( c_24__type__85933___24t(V_24Y)
    <=> t(V_24Y,c_24__type__85933) ) ).

fof('$tdef_$_type_121554',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y] :
      ( c_24__type__121554___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y)
    <=> t(V_24Y,c_24__type__121554___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6)) ) ).

fof('$tdef_$_type_120985',axiom,
    ! [V_24Y] :
      ( c_24__type__120985___24t(V_24Y)
    <=> t(V_24Y,c_24__type__120985) ) ).

fof('$tdef_$_type_8986',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__8986___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__8986___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_117906',axiom,
    ! [V_24Y] :
      ( c_24__type__117906___24t(V_24Y)
    <=> t(V_24Y,c_24__type__117906) ) ).

fof('$tdef_$_type_120473',axiom,
    ! [V_24Y] :
      ( c_24__type__120473___24t(V_24Y)
    <=> t(V_24Y,c_24__type__120473) ) ).

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_107524',axiom,
    ! [V_24Y] :
      ( c_24__type__107524___24t(V_24Y)
    <=> t(V_24Y,c_24__type__107524) ) ).

fof('$tdef_$_type_109636',axiom,
    ! [V_24Y] :
      ( c_24__type__109636___24t(V_24Y)
    <=> t(V_24Y,c_24__type__109636) ) ).

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_112995',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24Y] :
      ( c_24__type__112995___24t(V_24X1,V_24X2,V_24X3,V_24Y)
    <=> t(V_24Y,c_24__type__112995___24a3(V_24X1,V_24X2,V_24X3)) ) ).

fof('$tdef_$_type_172560',axiom,
    ! [V_24Y] :
      ( c_24__type__172560___24t(V_24Y)
    <=> t(V_24Y,c_24__type__172560) ) ).

fof('$tdef_$_type_121945',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
      ( c_24__type__121945___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
    <=> t(V_24Y,c_24__type__121945___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).

fof('$tdef_$_type_85541',axiom,
    ! [V_24Y] :
      ( c_24__type__85541___24t(V_24Y)
    <=> t(V_24Y,c_24__type__85541) ) ).

fof('$tdef_$_type_111140',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
      ( c_24__type__111140___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__111140___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).

fof('$tdef_Coq.micromega.RMicromega.RWitness',axiom,
    ! [V_24Y] :
      ( cCoq_2emicromega_2eRMicromega_2eRWitness___24t(V_24Y)
    <=> t(V_24Y,cCoq_2emicromega_2eRMicromega_2eRWitness) ) ).

fof('$tdef_$_type_1058',axiom,
    ! [V_24X1,V_24Y] :
      ( c_24__type__1058___24t(V_24X1,V_24Y)
    <=> t(V_24Y,c_24__type__1058___24a1(V_24X1)) ) ).

fof('$tdef_$_type_99179',axiom,
    ! [V_24Y] :
      ( c_24__type__99179___24t(V_24Y)
    <=> t(V_24Y,c_24__type__99179) ) ).

fof('$tdef_$_type_5091',axiom,
    ! [V_24Y] :
      ( c_24__type__5091___24t(V_24Y)
    <=> t(V_24Y,c_24__type__5091) ) ).

fof('$tdef_$_type_146',axiom,
    ! [V_24Y] :
      ( c_24__type__146___24t(V_24Y)
    <=> t(V_24Y,c_24__type__146) ) ).

fof('$tdef_$_type_108655',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__108655___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__108655___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).

fof('$tdef_$_type_3302',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__3302___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__3302___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).

fof('$tdef_$_type_85920',axiom,
    ! [V_24Y] :
      ( c_24__type__85920___24t(V_24Y)
    <=> t(V_24Y,c_24__type__85920) ) ).

fof('$tdef_$_type_2568',axiom,
    ! [V_24Y] :
      ( c_24__type__2568___24t(V_24Y)
    <=> t(V_24Y,c_24__type__2568) ) ).

fof('$tdef_$_type_11884',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y] :
      ( c_24__type__11884___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y)
    <=> t(V_24Y,c_24__type__11884___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7)) ) ).

fof('$tdef_$_type_111877',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__111877___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__111877___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_106985',axiom,
    ! [V_24Y] :
      ( c_24__type__106985___24t(V_24Y)
    <=> t(V_24Y,c_24__type__106985) ) ).

fof('$tdef_$_type_85536',axiom,
    ! [V_24X1,V_24X2,V_24Y] :
      ( c_24__type__85536___24t(V_24X1,V_24X2,V_24Y)
    <=> t(V_24Y,c_24__type__85536___24a2(V_24X1,V_24X2)) ) ).

fof('$tdef_$_type_121915',axiom,
    ! [V_24Y] :
      ( c_24__type__121915___24t(V_24Y)
    <=> t(V_24Y,c_24__type__121915) ) ).

fof('$tdef_$_type_172691',axiom,
    ! [V_24X1,V_24X2,V_24Y] :
      ( c_24__type__172691___24t(V_24X1,V_24X2,V_24Y)
    <=> t(V_24Y,c_24__type__172691___24a2(V_24X1,V_24X2)) ) ).

fof('$tdef_$_type_112377',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__112377___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__112377___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_121886',axiom,
    ! [V_24X1,V_24X2,V_24Y] :
      ( c_24__type__121886___24t(V_24X1,V_24X2,V_24Y)
    <=> t(V_24Y,c_24__type__121886___24a2(V_24X1,V_24X2)) ) ).

fof('$tdef_Type',axiom,
    ! [V_24Y] :
      ( cType___24t(V_24Y)
    <=> t(V_24Y,cType) ) ).

fof('$tdef_$_type_164756',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24Y] :
      ( c_24__type__164756___24t(V_24X1,V_24X2,V_24X3,V_24Y)
    <=> t(V_24Y,c_24__type__164756___24a3(V_24X1,V_24X2,V_24X3)) ) ).

fof('$tdef_$_type_107117',axiom,
    ! [V_24Y] :
      ( c_24__type__107117___24t(V_24Y)
    <=> t(V_24Y,c_24__type__107117) ) ).

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_90770',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__90770___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__90770___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).

fof('$tdef_Coq.micromega.RingMicromega.NFormula',axiom,
    ! [V_24X1,V_24Y] :
      ( cCoq_2emicromega_2eRingMicromega_2eNFormula___24t(V_24X1,V_24Y)
    <=> t(V_24Y,cCoq_2emicromega_2eRingMicromega_2eNFormula___24a1(V_24X1)) ) ).

fof('$tdef_$_type_109156',axiom,
    ! [V_24Y] :
      ( c_24__type__109156___24t(V_24Y)
    <=> t(V_24Y,c_24__type__109156) ) ).

fof('$tdef_$_type_107019',axiom,
    ! [V_24Y] :
      ( c_24__type__107019___24t(V_24Y)
    <=> t(V_24Y,c_24__type__107019) ) ).

fof('$tdef_$_type_120339',axiom,
    ! [V_24X1,V_24Y] :
      ( c_24__type__120339___24t(V_24X1,V_24Y)
    <=> t(V_24Y,c_24__type__120339___24a1(V_24X1)) ) ).

fof('$tdef_$_type_122214',axiom,
    ! [V_24X1,V_24Y] :
      ( c_24__type__122214___24t(V_24X1,V_24Y)
    <=> t(V_24Y,c_24__type__122214___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_109437',axiom,
    ! [V_24Y] :
      ( c_24__type__109437___24t(V_24Y)
    <=> t(V_24Y,c_24__type__109437) ) ).

fof('$tdef_$_type_113159',axiom,
    ! [V_24Y] :
      ( c_24__type__113159___24t(V_24Y)
    <=> t(V_24Y,c_24__type__113159) ) ).

fof('$tdef_$_type_95543',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__95543___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__95543___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_11605',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y] :
      ( c_24__type__11605___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y)
    <=> t(V_24Y,c_24__type__11605___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7)) ) ).

fof('$tdef_Coq.setoid_ring.InitialRing.Nword',axiom,
    ! [V_24Y] :
      ( cCoq_2esetoid__ring_2eInitialRing_2eNword___24t(V_24Y)
    <=> t(V_24Y,cCoq_2esetoid__ring_2eInitialRing_2eNword) ) ).

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_1300',axiom,
    ! [V_24X1,V_24Y] :
      ( c_24__type__1300___24t(V_24X1,V_24Y)
    <=> t(V_24Y,c_24__type__1300___24a1(V_24X1)) ) ).

fof('$tdef_$_type_120929',axiom,
    ! [V_24Y] :
      ( c_24__type__120929___24t(V_24Y)
    <=> t(V_24Y,c_24__type__120929) ) ).

fof('$tdef_$_type_112002',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__112002___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__112002___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_11513',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y] :
      ( c_24__type__11513___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y)
    <=> t(V_24Y,c_24__type__11513___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7)) ) ).

fof('_HAMMER_GOAL',conjecture,
    ! [V0__s] :
      ( cIntMap_2eFset_2eFSet___24t(V0__s)
     => ! [V1__s_27] :
          ( cIntMap_2eFset_2eFSet___24t(V1__s_27)
         => ! [V2__s_27_27] :
              ( cIntMap_2eFset_2eFSet___24t(V2__s_27_27)
             => cMapaxioms_2eeqmap___24a3(cCoq_2eInit_2eDatatypes_2eunit,cIntMap_2eFset_2eFSetUnion___24a2(cIntMap_2eFset_2eFSetUnion___24a2(V0__s,V1__s_27),V2__s_27_27),cIntMap_2eFset_2eFSetUnion___24a2(V0__s,cIntMap_2eFset_2eFSetUnion___24a2(V1__s_27,V2__s_27_27))) ) ) ) ).

%------------------------------------------------------------------------------