TPTP Problem File: SEV614+1.p

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%------------------------------------------------------------------------------
% File     : SEV614+1 : TPTP v9.3.1. Released v9.3.0.
% Domain   : Set theory
% Problem  : CoqHammer - GenRec Fix equiv
% 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    : GenRec.Fix.equiv.p [Kal26]

% Status   : Unknown
% Rating   : 1.00 v9.3.0
% Syntax   : Number of formulae    : 3019 (1270 unt;   0 def)
%            Number of atoms       : 9988 (2678 equ)
%            Maximal formula atoms :  257 (   3 avg)
%            Number of connectives : 7062 (  93   ~; 760   |;1754   &)
%                                         (1174 <=>;3281  =>;   0  <=;   0 <~>)
%            Maximal formula depth :  258 (   6 avg)
%            Maximal term depth    :   23 (   1 avg)
%            Number of predicates  :  643 ( 642 usr;   0 prp; 1-23 aty)
%            Number of functors    : 1746 (1746 usr;1140 con; 0-22 aty)
%            Number of variables   : 9952 (9261   !; 691   ?)
% SPC      : FOF_UNK_RFO_SEQ

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

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

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

fof('$_case_Coq.Init.Datatypes.list$31552',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_2431639___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_2431552___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__31556] :
                ( t(Vvar__1___24Anonymous__31556,Vv__CANONICAL__0)
                & ? [Vvar__2___24Anonymous__31557] :
                    ( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vvar__2___24Anonymous__31557)
                    & c_24__case__Coq_2eInit_2eDatatypes_2elist_2431639___24a3(Vv__CANONICAL__0,Vv__CANONICAL__4,Vv__CANONICAL__5) = cCoq_2eInit_2eDatatypes_2econs___24a3(Vv__CANONICAL__0,Vvar__1___24Anonymous__31556,Vvar__2___24Anonymous__31557)
                    & c_24__case__Coq_2eInit_2eDatatypes_2elist_2431552___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__31556,c_24__fix__31684__v__CANONICAL__1___24a3(Vv__CANONICAL__0,Vvar__2___24Anonymous__31557,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$31639',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_2431639___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__31643] :
              ( t(Vvar__1___24Anonymous__31643,Vv__CANONICAL__0)
              & ? [Vvar__2___24Anonymous__31644] :
                  ( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vvar__2___24Anonymous__31644)
                  & Vv__CANONICAL__2 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vv__CANONICAL__0,Vvar__1___24Anonymous__31643,Vvar__2___24Anonymous__31644)
                  & c_24__case__Coq_2eInit_2eDatatypes_2elist_2431639___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = cCoq_2eInit_2eDatatypes_2econs___24a3(Vv__CANONICAL__0,Vvar__1___24Anonymous__31643,c_24__fix__31684__v__CANONICAL__1___24a3(Vv__CANONICAL__0,Vvar__2___24Anonymous__31644,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$17068',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_2417068___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = cCoq_2eNumbers_2eBinNums_2eZ0 )
        | ? [Vvar__0___24Anonymous__17069] :
            ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__17069)
            & Vv__CANONICAL__2 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__17069)
            & c_24__case__Coq_2eInit_2eDatatypes_2enat_2417068___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__17069)) ) ) ) ).

fof('$_case_Coq.Init.Datatypes.nat$17090',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_2417090___24a1(Vv__CANONICAL__0) = cCoq_2eNumbers_2eBinNums_2eZ0 )
        | ? [Vvar__0___24Anonymous__17091] :
            ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__17091)
            & Vv__CANONICAL__0 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__17091)
            & c_24__case__Coq_2eInit_2eDatatypes_2enat_2417090___24a1(Vv__CANONICAL__0) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eof__succ__nat___24a1(Vvar__0___24Anonymous__17091)) ) ) ) ).

fof('$_case_Coq.Init.Datatypes.prod$10432',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__10445___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__10437] :
                  ( t(Vvar__2___24Anonymous__10437,Vv__CANONICAL__2)
                  & ? [Vvar__3___24Anonymous__10438] :
                      ( t(Vvar__3___24Anonymous__10438,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__10437,Vvar__3___24Anonymous__10438)
                      & ( c_24__case__Coq_2eInit_2eDatatypes_2eprod_2410432___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__10437)),Vvar__3___24Anonymous__10438)))) ) ) ) ) ) ) ) ) ).

fof('$_case_Coq.Numbers.BinNums.Z$17085',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_2417090___24a1(Vv__CANONICAL__2) = cCoq_2eNumbers_2eBinNums_2eZ0
          & c_24__case__Coq_2eNumbers_2eBinNums_2eZ_2417085___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = cCoq_2eNumbers_2eBinNums_2eZ0 )
        | ? [Vvar__0___24Anonymous__17086] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__17086)
            & c_24__case__Coq_2eInit_2eDatatypes_2enat_2417090___24a1(Vv__CANONICAL__2) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__17086)
            & c_24__case__Coq_2eNumbers_2eBinNums_2eZ_2417085___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__17086) )
        | ? [Vvar__0___24Anonymous__17087] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__17087)
            & c_24__case__Coq_2eInit_2eDatatypes_2enat_2417090___24a1(Vv__CANONICAL__2) = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__17087)
            & c_24__case__Coq_2eNumbers_2eBinNums_2eZ_2417085___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__17087) ) ) ) ).

fof('$_case_Coq.Numbers.BinNums.positive$29653',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1] :
      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__1)
     => ( ? [Vvar__0___24Anonymous__29654] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__29654)
            & Vv__CANONICAL__1 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__29654)
            & c_24__case__Coq_2eNumbers_2eBinNums_2epositive_2429653___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = cCoq_2eNumbers_2eBinNums_2exO___24a1(c_24__fix__29669__v__CANONICAL__0___24a1(Vvar__0___24Anonymous__29654)) )
        | ? [Vvar__0___24Anonymous__29661] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__29661)
            & Vv__CANONICAL__1 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__29661)
            & c_24__case__Coq_2eNumbers_2eBinNums_2epositive_2429653___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__29661) )
        | ( Vv__CANONICAL__1 = cCoq_2eNumbers_2eBinNums_2exH
          & c_24__case__Coq_2eNumbers_2eBinNums_2epositive_2429653___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2eNumbers_2eBinNums_2exH) ) ) ) ).

fof('$_def_$_let_var_6_p_27099_27102',axiom,
    ! [V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__27098] : c_24__let__var__6__p__27099__27102___24a4(V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__27098) = cCoq_2esetoid__ring_2eRing__theory_2epow__pos___24a4(V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__27098) ).

fof('$_def_$_let_var_6_p_27101_27103',axiom,
    ! [V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__27100] : c_24__let__var__6__p__27101__27103___24a4(V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__27100) = cCoq_2esetoid__ring_2eRing__theory_2epow__pos___24a4(V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__27100) ).

fof('$_def_Coq.Arith.Between.in_int',axiom,
    ! [V0__p,V1__q,V2__r] :
      ( cCoq_2eArith_2eBetween_2ein__int___24a3(V0__p,V1__q,V2__r)
    <=> ( cCoq_2eInit_2ePeano_2ele___24a2(V0__p,V2__r)
        & cCoq_2eInit_2ePeano_2elt___24a2(V2__r,V1__q) ) ) ).

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__26169] :
                  ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__26169)
                  & V2__m = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__26169)
                  & ( cCoq_2eArith_2eEqNat_2eeq__nat___24a2(V1__n,V2__m)
                  <=> p(c_24False) ) ) ) ) )
        | ? [Vvar__0___24Anonymous__26170] :
            ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__26170)
            & ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__m)
             => ( V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__26170)
                & ( ( V2__m = cCoq_2eInit_2eDatatypes_2eO
                    & ( cCoq_2eArith_2eEqNat_2eeq__nat___24a2(V1__n,V2__m)
                    <=> p(c_24False) ) )
                  | ? [Vvar__0___24Anonymous__26173] :
                      ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__26173)
                      & V2__m = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__26173)
                      & ( cCoq_2eArith_2eEqNat_2eeq__nat___24a2(V1__n,V2__m)
                      <=> cCoq_2eArith_2eEqNat_2eeq__nat___24a2(Vvar__0___24Anonymous__26170,Vvar__0___24Anonymous__26173) ) ) ) ) ) ) ) ) ).

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__32940___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__30782] :
            ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__30782)
            & V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__30782)
            & cCoq_2eArith_2ePlus_2etail__plus___24a2(V1__n,V2__m) = cCoq_2eArith_2ePlus_2etail__plus___24a2(Vvar__0___24Anonymous__30782,cCoq_2eInit_2eDatatypes_2eS___24a1(V2__m)) ) ) ) ).

fof('$_def_Coq.Arith.Wf_nat.gtof',axiom,
    ! [V0__A,V1__f,V2__a,V3__b] :
      ( cCoq_2eArith_2eWf__nat_2egtof___24a4(V0__A,V1__f,V2__a,V3__b)
    <=> cCoq_2eInit_2ePeano_2egt___24a2(happ(V1__f,V3__b),happ(V1__f,V2__a)) ) ).

fof('$_def_Coq.Arith.Wf_nat.inv_lt_rel',axiom,
    ! [V0__A,V1__F,V2__x,V3__y] :
      ( cCoq_2eArith_2eWf__nat_2einv__lt__rel___24a4(V0__A,V1__F,V2__x,V3__y)
    <=> cCoq_2eInit_2eLogic_2eex2___24a3(cCoq_2eInit_2eDatatypes_2enat,c_24__lam__2486___24a3(V0__A,V1__F,V2__x),c_24__lam__2501___24a3(V0__A,V1__F,V3__y)) ) ).

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.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__32902] :
            ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__32902)
            & V0__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__32902)
            & 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.Subset',axiom,
    ! [V0__s,V1__s_27] :
      ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eSubset___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.elt',axiom,
    ! [Vvar__24734] :
      ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(Vvar__24734)
    <=> cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__24734) ) ).

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.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__24737] :
            ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree___24t(Vvar__0___24Anonymous__24737)
            & ? [Vvar__1___24Anonymous__24738] :
                ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__1___24Anonymous__24738)
                & ? [Vvar__2___24Anonymous__24739] :
                    ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree___24t(Vvar__2___24Anonymous__24739)
                    & ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(V1__i)
                     => ( V2__m = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eNode___24a3(Vvar__0___24Anonymous__24737,Vvar__1___24Anonymous__24738,Vvar__2___24Anonymous__24739)
                        & ( ? [Vvar__0___24Anonymous__24752] :
                              ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__24752)
                              & V1__i = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__24752)
                              & cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2emem___24a2(V1__i,V2__m) = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2emem___24a2(Vvar__0___24Anonymous__24752,Vvar__2___24Anonymous__24739) )
                          | ? [Vvar__0___24Anonymous__24753] :
                              ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__24753)
                              & V1__i = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__24753)
                              & cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2emem___24a2(V1__i,V2__m) = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2emem___24a2(Vvar__0___24Anonymous__24753,Vvar__0___24Anonymous__24737) )
                          | ( V1__i = cCoq_2eNumbers_2eBinNums_2exH
                            & cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2emem___24a2(V1__i,V2__m) = Vvar__1___24Anonymous__24738 ) ) ) ) ) ) ) ) ) ).

fof('$_def_Coq.FSets.FSetPositive.PositiveSet.t',axiom,
    ! [Vvar__24735] :
      ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(Vvar__24735)
    <=> cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree___24t(Vvar__24735) ) ).

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__26117] :
      ( cCoq_2eInit_2eDatatypes_2eID___24t(Vvar__26117)
    <=> ! [V0__A] :
          ( cType___24t(V0__A)
         => ! [V1___24Anonymous] :
              ( t(V1___24Anonymous,V0__A)
             => t(happ(happ(Vvar__26117,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__11937] :
              ( t(Vvar__1___24Anonymous__11937,V0__A)
              & ? [Vvar__2___24Anonymous__11938] :
                  ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__11938)
                  & V2__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__11937,Vvar__2___24Anonymous__11938)
                  & cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V2__l,V3__m) = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__11937,cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,Vvar__2___24Anonymous__11938,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__11857] :
              ( t(Vvar__2___24Anonymous__11857,V0__A)
              & ? [Vvar__3___24Anonymous__11858] :
                  ( t(Vvar__3___24Anonymous__11858,V1__B)
                  & V2__p = cCoq_2eInit_2eDatatypes_2epair___24a4(V0__A,V1__B,Vvar__2___24Anonymous__11857,Vvar__3___24Anonymous__11858)
                  & cCoq_2eInit_2eDatatypes_2efst___24a3(V0__A,V1__B,V2__p) = Vvar__2___24Anonymous__11857 ) ) ) ) ) ).

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__11927] :
              ( t(Vvar__1___24Anonymous__11927,V0__A)
              & ? [Vvar__2___24Anonymous__11928] :
                  ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__11928)
                  & V2__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__11927,Vvar__2___24Anonymous__11928)
                  & cCoq_2eInit_2eDatatypes_2elength___24a2(V0__A,V2__l) = cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2elength___24a2(V0__A,Vvar__2___24Anonymous__11928)) ) ) ) ) ) ).

fof('$_def_Coq.Init.Datatypes.nat_rect',axiom,
    ! [V0__P,V1__f,V2__f,V4__n] :
      ( c_24__type__11784___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__11782] :
              ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__11782)
              & V4__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__11782)
              & cCoq_2eInit_2eDatatypes_2enat__rect___24a4(V0__P,V1__f,V2__f,V4__n) = happ(happ(V2__f,Vvar__0___24Anonymous__11782),cCoq_2eInit_2eDatatypes_2enat__rect___24a4(V0__P,V1__f,V2__f,Vvar__0___24Anonymous__11782)) ) ) ) ) ).

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__29772] :
              ( t(Vvar__2___24Anonymous__29772,V0__A)
              & ? [Vvar__3___24Anonymous__29773] :
                  ( t(Vvar__3___24Anonymous__29773,V1__B)
                  & V2__p = cCoq_2eInit_2eDatatypes_2epair___24a4(V0__A,V1__B,Vvar__2___24Anonymous__29772,Vvar__3___24Anonymous__29773)
                  & cCoq_2eInit_2eDatatypes_2esnd___24a3(V0__A,V1__B,V2__p) = Vvar__3___24Anonymous__29773 ) ) ) ) ) ).

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__29781] :
            ( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0___24Anonymous__29781)
            & V1__d = cCoq_2eInit_2eDecimal_2eD0___24a1(Vvar__0___24Anonymous__29781)
            & cCoq_2eInit_2eDecimal_2enzhead___24a1(V1__d) = cCoq_2eInit_2eDecimal_2enzhead___24a1(Vvar__0___24Anonymous__29781) )
        | ? [Vvar__0___24Anonymous__29782] :
            ( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0___24Anonymous__29782)
            & V1__d = cCoq_2eInit_2eDecimal_2eD1___24a1(Vvar__0___24Anonymous__29782)
            & cCoq_2eInit_2eDecimal_2enzhead___24a1(V1__d) = V1__d )
        | ? [Vvar__0___24Anonymous__29783] :
            ( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0___24Anonymous__29783)
            & V1__d = cCoq_2eInit_2eDecimal_2eD2___24a1(Vvar__0___24Anonymous__29783)
            & cCoq_2eInit_2eDecimal_2enzhead___24a1(V1__d) = V1__d )
        | ? [Vvar__0___24Anonymous__29784] :
            ( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0___24Anonymous__29784)
            & V1__d = cCoq_2eInit_2eDecimal_2eD3___24a1(Vvar__0___24Anonymous__29784)
            & cCoq_2eInit_2eDecimal_2enzhead___24a1(V1__d) = V1__d )
        | ? [Vvar__0___24Anonymous__29785] :
            ( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0___24Anonymous__29785)
            & V1__d = cCoq_2eInit_2eDecimal_2eD4___24a1(Vvar__0___24Anonymous__29785)
            & cCoq_2eInit_2eDecimal_2enzhead___24a1(V1__d) = V1__d )
        | ? [Vvar__0___24Anonymous__29786] :
            ( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0___24Anonymous__29786)
            & V1__d = cCoq_2eInit_2eDecimal_2eD5___24a1(Vvar__0___24Anonymous__29786)
            & cCoq_2eInit_2eDecimal_2enzhead___24a1(V1__d) = V1__d )
        | ? [Vvar__0___24Anonymous__29787] :
            ( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0___24Anonymous__29787)
            & V1__d = cCoq_2eInit_2eDecimal_2eD6___24a1(Vvar__0___24Anonymous__29787)
            & cCoq_2eInit_2eDecimal_2enzhead___24a1(V1__d) = V1__d )
        | ? [Vvar__0___24Anonymous__29788] :
            ( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0___24Anonymous__29788)
            & V1__d = cCoq_2eInit_2eDecimal_2eD7___24a1(Vvar__0___24Anonymous__29788)
            & cCoq_2eInit_2eDecimal_2enzhead___24a1(V1__d) = V1__d )
        | ? [Vvar__0___24Anonymous__29789] :
            ( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0___24Anonymous__29789)
            & V1__d = cCoq_2eInit_2eDecimal_2eD8___24a1(Vvar__0___24Anonymous__29789)
            & cCoq_2eInit_2eDecimal_2enzhead___24a1(V1__d) = V1__d )
        | ? [Vvar__0___24Anonymous__29790] :
            ( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0___24Anonymous__29790)
            & V1__d = cCoq_2eInit_2eDecimal_2eD9___24a1(Vvar__0___24Anonymous__29790)
            & 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__4765] :
            ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__4765)
            & V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__4765)
            & cCoq_2eInit_2eNat_2eadd___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eNat_2eadd___24a2(Vvar__0___24Anonymous__4765,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__30137] :
                  ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__30137)
                  & V2__m = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__30137)
                  & cCoq_2eInit_2eNat_2ecompare___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2eLt ) ) ) )
        | ? [Vvar__0___24Anonymous__30138] :
            ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__30138)
            & ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__m)
             => ( V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__30138)
                & ( ( V2__m = cCoq_2eInit_2eDatatypes_2eO
                    & cCoq_2eInit_2eNat_2ecompare___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2eGt )
                  | ? [Vvar__0___24Anonymous__30141] :
                      ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__30141)
                      & V2__m = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__30141)
                      & cCoq_2eInit_2eNat_2ecompare___24a2(V1__n,V2__m) = cCoq_2eInit_2eNat_2ecompare___24a2(Vvar__0___24Anonymous__30138,Vvar__0___24Anonymous__30141) ) ) ) ) ) ) ) ).

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__15034] :
            ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__15034)
            & ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__15034)
             => ( V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__15034)
                & ( ( Vvar__0___24Anonymous__15034 = cCoq_2eInit_2eDatatypes_2eO
                    & cCoq_2eInit_2eNat_2ediv2___24a1(V1__n) = cCoq_2eInit_2eDatatypes_2eO )
                  | ? [Vvar__0___24Anonymous__15037] :
                      ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__15037)
                      & Vvar__0___24Anonymous__15034 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__15037)
                      & cCoq_2eInit_2eNat_2ediv2___24a1(V1__n) = cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eNat_2ediv2___24a1(Vvar__0___24Anonymous__15037)) ) ) ) ) ) ) ) ).

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__30130] :
                  ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__30130)
                  & V2__m = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__30130)
                  & cCoq_2eInit_2eNat_2eeqb___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) )
        | ? [Vvar__0___24Anonymous__30131] :
            ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__30131)
            & ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__m)
             => ( V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__30131)
                & ( ( V2__m = cCoq_2eInit_2eDatatypes_2eO
                    & cCoq_2eInit_2eNat_2eeqb___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2efalse )
                  | ? [Vvar__0___24Anonymous__30134] :
                      ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__30134)
                      & V2__m = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__30134)
                      & cCoq_2eInit_2eNat_2eeqb___24a2(V1__n,V2__m) = cCoq_2eInit_2eNat_2eeqb___24a2(Vvar__0___24Anonymous__30131,Vvar__0___24Anonymous__30134) ) ) ) ) ) ) ) ).

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__30158] :
            ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__30158)
            & ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__30158)
             => ( V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__30158)
                & ( ( Vvar__0___24Anonymous__30158 = cCoq_2eInit_2eDatatypes_2eO
                    & cCoq_2eInit_2eNat_2eeven___24a1(V1__n) = cCoq_2eInit_2eDatatypes_2efalse )
                  | ? [Vvar__0___24Anonymous__30161] :
                      ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__30161)
                      & Vvar__0___24Anonymous__30158 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__30161)
                      & cCoq_2eInit_2eNat_2eeven___24a1(V1__n) = cCoq_2eInit_2eNat_2eeven___24a1(Vvar__0___24Anonymous__30161) ) ) ) ) ) ) ) ).

fof('$_def_Coq.Init.Nat.gcd',axiom,
    ! [V1__a,V2__b] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(V1__a)
     => ( ( V1__a = cCoq_2eInit_2eDatatypes_2eO
          & cCoq_2eInit_2eNat_2egcd___24a2(V1__a,V2__b) = V2__b )
        | ? [Vvar__0___24Anonymous__30171] :
            ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__30171)
            & V1__a = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__30171)
            & cCoq_2eInit_2eNat_2egcd___24a2(V1__a,V2__b) = cCoq_2eInit_2eNat_2egcd___24a2(cCoq_2eInit_2eNat_2emodulo___24a2(V2__b,cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__30171)),cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__30171)) ) ) ) ).

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__15026] :
            ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__15026)
            & ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__m)
             => ( V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__15026)
                & ( ( V2__m = cCoq_2eInit_2eDatatypes_2eO
                    & cCoq_2eInit_2eNat_2eleb___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2efalse )
                  | ? [Vvar__0___24Anonymous__15029] :
                      ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__15029)
                      & V2__m = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__15029)
                      & cCoq_2eInit_2eNat_2eleb___24a2(V1__n,V2__m) = cCoq_2eInit_2eNat_2eleb___24a2(Vvar__0___24Anonymous__15026,Vvar__0___24Anonymous__15029) ) ) ) ) ) ) ) ).

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__30187] :
            ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__30187)
            & ( cCoq_2eInit_2eDatatypes_2enat___24t(V4__r)
             => ( V1__k = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__30187)
                & ( ( 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__30187,cCoq_2eInit_2eDatatypes_2eS___24a1(V2__p),cCoq_2eInit_2eDatatypes_2eS___24a1(V3__q),V3__q) )
                  | ? [Vvar__0___24Anonymous__30190] :
                      ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__30190)
                      & V4__r = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__30190)
                      & cCoq_2eInit_2eNat_2elog2__iter___24a4(V1__k,V2__p,V3__q,V4__r) = cCoq_2eInit_2eNat_2elog2__iter___24a4(Vvar__0___24Anonymous__30187,V2__p,cCoq_2eInit_2eDatatypes_2eS___24a1(V3__q),Vvar__0___24Anonymous__30190) ) ) ) ) ) ) ) ).

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__30146] :
            ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__30146)
            & ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__m)
             => ( V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__30146)
                & ( ( V2__m = cCoq_2eInit_2eDatatypes_2eO
                    & cCoq_2eInit_2eNat_2emax___24a2(V1__n,V2__m) = V1__n )
                  | ? [Vvar__0___24Anonymous__30149] :
                      ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__30149)
                      & V2__m = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__30149)
                      & cCoq_2eInit_2eNat_2emax___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eNat_2emax___24a2(Vvar__0___24Anonymous__30146,Vvar__0___24Anonymous__30149)) ) ) ) ) ) ) ) ).

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__30152] :
            ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__30152)
            & ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__m)
             => ( V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__30152)
                & ( ( V2__m = cCoq_2eInit_2eDatatypes_2eO
                    & cCoq_2eInit_2eNat_2emin___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2eO )
                  | ? [Vvar__0___24Anonymous__30155] :
                      ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__30155)
                      & V2__m = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__30155)
                      & cCoq_2eInit_2eNat_2emin___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eNat_2emin___24a2(Vvar__0___24Anonymous__30152,Vvar__0___24Anonymous__30155)) ) ) ) ) ) ) ) ).

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__15017] :
            ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__15017)
            & V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__15017)
            & cCoq_2eInit_2eNat_2emul___24a2(V1__n,V2__m) = cCoq_2eInit_2eNat_2eadd___24a2(V2__m,cCoq_2eInit_2eNat_2emul___24a2(Vvar__0___24Anonymous__15017,V2__m)) ) ) ) ).

fof('$_def_Coq.Init.Nat.one',axiom,
    cCoq_2eInit_2eNat_2eone = cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO) ).

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__30165] :
            ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__30165)
            & V2__m = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__30165)
            & 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__30165)) ) ) ) ).

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__15015] :
            ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__15015)
            & V0__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__15015)
            & cCoq_2eInit_2eNat_2epred___24a1(V0__n) = Vvar__0___24Anonymous__15015 ) ) ) ).

fof('$_def_Coq.Init.Nat.sqrt_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_2esqrt__iter___24a4(V1__k,V2__p,V3__q,V4__r) = V2__p )
        | ? [Vvar__0___24Anonymous__30174] :
            ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__30174)
            & ( cCoq_2eInit_2eDatatypes_2enat___24t(V4__r)
             => ( V1__k = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__30174)
                & ( ( V4__r = cCoq_2eInit_2eDatatypes_2eO
                    & cCoq_2eInit_2eNat_2esqrt__iter___24a4(V1__k,V2__p,V3__q,V4__r) = cCoq_2eInit_2eNat_2esqrt__iter___24a4(Vvar__0___24Anonymous__30174,cCoq_2eInit_2eDatatypes_2eS___24a1(V2__p),cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(V3__q)),cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(V3__q))) )
                  | ? [Vvar__0___24Anonymous__30177] :
                      ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__30177)
                      & V4__r = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__30177)
                      & cCoq_2eInit_2eNat_2esqrt__iter___24a4(V1__k,V2__p,V3__q,V4__r) = cCoq_2eInit_2eNat_2esqrt__iter___24a4(Vvar__0___24Anonymous__30174,V2__p,V3__q,Vvar__0___24Anonymous__30177) ) ) ) ) ) ) ) ).

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__15020] :
            ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__15020)
            & ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__m)
             => ( V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__15020)
                & ( ( V2__m = cCoq_2eInit_2eDatatypes_2eO
                    & cCoq_2eInit_2eNat_2esub___24a2(V1__n,V2__m) = V1__n )
                  | ? [Vvar__0___24Anonymous__15023] :
                      ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__15023)
                      & V2__m = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__15023)
                      & cCoq_2eInit_2eNat_2esub___24a2(V1__n,V2__m) = cCoq_2eInit_2eNat_2esub___24a2(Vvar__0___24Anonymous__15020,Vvar__0___24Anonymous__15023) ) ) ) ) ) ) ) ).

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

fof('$_def_Coq.Init.Nat.t',axiom,
    ! [Vvar__27040] :
      ( cCoq_2eInit_2eNat_2et___24t(Vvar__27040)
    <=> cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__27040) ) ).

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__30168] :
            ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__30168)
            & V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__30168)
            & cCoq_2eInit_2eNat_2etail__add___24a2(V1__n,V2__m) = cCoq_2eInit_2eNat_2etail__add___24a2(Vvar__0___24Anonymous__30168,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__30198] :
            ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__30198)
            & V2__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__30198)
            & cCoq_2eInit_2eNat_2etestbit___24a2(V1__a,V2__n) = cCoq_2eInit_2eNat_2etestbit___24a2(cCoq_2eInit_2eNat_2ediv2___24a1(V1__a),Vvar__0___24Anonymous__30198) ) ) ) ).

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__27041] :
            ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__27041)
            & V0__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__27041)
            & ( 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__32519___24t(V0__A,V1__P,V1__P)
       => ( cCoq_2eInit_2eSpecif_2esig___24t(V0__A,V1__P,V2__e)
         => ? [Vvar__2__x__32513] :
              ( t(Vvar__2__x__32513,V0__A)
              & p(happ(V1__P,Vvar__2__x__32513))
              & V2__e = cCoq_2eInit_2eSpecif_2eexist___24a3(V0__A,V1__P,Vvar__2__x__32513)
              & cCoq_2eInit_2eSpecif_2eproj1__sig___24a3(V0__A,V1__P,V2__e) = Vvar__2__x__32513 ) ) ) ) ).

fof('$_def_Coq.Init.Specif.projT1',axiom,
    ! [V0__A,V1__P,V2__x] :
      ( cType___24t(V0__A)
     => ( c_24__type__32542___24t(V0__A,V1__P,V1__P)
       => ( cCoq_2eInit_2eSpecif_2esigT___24t(V0__A,V1__P,V2__x)
         => ? [Vvar__2__x__32536] :
              ( t(Vvar__2__x__32536,V0__A)
              & ? [Vvar__3___24Anonymous__32537] :
                  ( t(Vvar__3___24Anonymous__32537,happ(V1__P,Vvar__2__x__32536))
                  & V2__x = cCoq_2eInit_2eSpecif_2eexistT___24a4(V0__A,V1__P,Vvar__2__x__32536,Vvar__3___24Anonymous__32537)
                  & cCoq_2eInit_2eSpecif_2eprojT1___24a3(V0__A,V1__P,V2__x) = Vvar__2__x__32536 ) ) ) ) ) ).

fof('$_def_Coq.Init.Wf.Fix',axiom,
    ! [V0__A,V1__R,V3__P,V4__F,V5__x] : cCoq_2eInit_2eWf_2eFix___24a5(V0__A,V1__R,V3__P,V4__F,V5__x) = cCoq_2eInit_2eWf_2eFix__F___24a5(V0__A,V1__R,V3__P,V4__F,V5__x) ).

fof('$_def_Coq.Init.Wf.Fix_F',axiom,
    ! [V0__A,V1__R,V2__P,V3__F,V5__x] : cCoq_2eInit_2eWf_2eFix__F___24a5(V0__A,V1__R,V2__P,V3__F,V5__x) = happ(happ(V3__F,V5__x),c_24__lam__555___24a5(V0__A,V1__R,V2__P,V3__F,V5__x)) ).

fof('$_def_Coq.Init.Wf.Fix_F_2',axiom,
    ! [V0__A,V1__B,V2__R,V3__P,V4__F,V6__x,V7__x_27] : cCoq_2eInit_2eWf_2eFix__F__2___24a7(V0__A,V1__B,V2__R,V3__P,V4__F,V6__x,V7__x_27) = happ(happ(happ(V4__F,V6__x),V7__x_27),c_24__lam__1023___24a7(V0__A,V1__B,V2__R,V3__P,V4__F,V6__x,V7__x_27)) ).

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.Init.Wf.well_founded_induction',axiom,
    ! [V0__A,V1__R,V3__P] : cCoq_2eInit_2eWf_2ewell__founded__induction___24a3(V0__A,V1__R,V3__P) = cCoq_2eInit_2eWf_2ewell__founded__induction__type___24a3(V0__A,V1__R,V3__P) ).

fof('$_def_Coq.Init.Wf.well_founded_induction_type',axiom,
    ! [V0__A,V1__R,V3__P,V4__X,V5__a] : cCoq_2eInit_2eWf_2ewell__founded__induction__type___24a5(V0__A,V1__R,V3__P,V4__X,V5__a) = cCoq_2eInit_2eWf_2eAcc__rect___24a5(V0__A,V1__R,V3__P,c_24__lam__389___24a4(V0__A,V1__R,V3__P,V4__X),V5__a) ).

fof('$_def_Coq.Init.Wf.well_founded_induction_type_2',axiom,
    ! [V0__A,V1__B,V2__R,V3__P,V5__X,V6__a,V7__b] : cCoq_2eInit_2eWf_2ewell__founded__induction__type__2___24a7(V0__A,V1__B,V2__R,V3__P,V5__X,V6__a,V7__b) = cCoq_2eInit_2eWf_2eFix__F__2___24a7(V0__A,V1__B,V2__R,V3__P,V5__X,V6__a,V7__b) ).

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__14833] :
              ( t(Vvar__1___24Anonymous__14833,V0__A)
              & ? [Vvar__2___24Anonymous__14834] :
                  ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__14834)
                  & V3__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__14833,Vvar__2___24Anonymous__14834)
                  & ( cCoq_2eLists_2eList_2eIn___24a3(V0__A,V2__a,V3__l)
                  <=> ( Vvar__1___24Anonymous__14833 = V2__a
                      | cCoq_2eLists_2eList_2eIn___24a3(V0__A,V2__a,Vvar__2___24Anonymous__14834) ) ) ) ) ) ) ) ).

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__29927] :
                ( t(Vvar__1___24Anonymous__29927,V1__B)
                & ? [Vvar__2___24Anonymous__29928] :
                    ( cCoq_2eInit_2eDatatypes_2elist___24t(V1__B,Vvar__2___24Anonymous__29928)
                    & V4__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V1__B,Vvar__1___24Anonymous__29927,Vvar__2___24Anonymous__29928)
                    & 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__29928,happ(happ(V2__f,V5__a0),Vvar__1___24Anonymous__29927)) ) ) ) ) ) ) ).

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__29956] :
                ( t(Vvar__1___24Anonymous__29956,V1__B)
                & ? [Vvar__2___24Anonymous__29957] :
                    ( cCoq_2eInit_2eDatatypes_2elist___24t(V1__B,Vvar__2___24Anonymous__29957)
                    & V5__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V1__B,Vvar__1___24Anonymous__29956,Vvar__2___24Anonymous__29957)
                    & cCoq_2eLists_2eList_2efold__right___24a5(V0__A,V1__B,V2__f,V3__a0,V5__l) = happ(happ(V2__f,Vvar__1___24Anonymous__29956),cCoq_2eLists_2eList_2efold__right___24a5(V0__A,V1__B,V2__f,V3__a0,Vvar__2___24Anonymous__29957)) ) ) ) ) ) ) ).

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__29882] :
              ( t(Vvar__1___24Anonymous__29882,V0__A)
              & ? [Vvar__2___24Anonymous__29883] :
                  ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__29883)
                  & V2__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__29882,Vvar__2___24Anonymous__29883)
                  & cCoq_2eLists_2eList_2ehd___24a3(V0__A,V1__default,V2__l) = Vvar__1___24Anonymous__29882 ) ) ) ) ) ).

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__29903] :
              ( t(Vvar__1___24Anonymous__29903,V0__A)
              & ? [Vvar__2___24Anonymous__29904] :
                  ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__29904)
                  & ( cType___24t(V0__A)
                   => ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__29904)
                     => ( V2__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__29903,Vvar__2___24Anonymous__29904)
                        & ( ( Vvar__2___24Anonymous__29904 = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)
                            & cCoq_2eLists_2eList_2elast___24a3(V0__A,V2__l,V3__d) = Vvar__1___24Anonymous__29903 )
                          | ? [Vvar__1___24Anonymous__29915] :
                              ( t(Vvar__1___24Anonymous__29915,V0__A)
                              & ? [Vvar__2___24Anonymous__29916] :
                                  ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__29916)
                                  & Vvar__2___24Anonymous__29904 = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__29915,Vvar__2___24Anonymous__29916)
                                  & cCoq_2eLists_2eList_2elast___24a3(V0__A,V2__l,V3__d) = cCoq_2eLists_2eList_2elast___24a3(V0__A,Vvar__2___24Anonymous__29904,V3__d) ) ) ) ) ) ) ) ) ) ) ) ).

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__14845] :
                      ( t(Vvar__1___24Anonymous__14845,V0__A)
                      & ? [Vvar__2___24Anonymous__14846] :
                          ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__14846)
                          & V3__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__14845,Vvar__2___24Anonymous__14846)
                          & cCoq_2eLists_2eList_2enth___24a4(V0__A,V2__n,V3__l,V4__default) = Vvar__1___24Anonymous__14845 ) ) ) ) ) )
          | ? [Vvar__0___24Anonymous__14848] :
              ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__14848)
              & ( cType___24t(V0__A)
               => ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l)
                 => ( V2__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__14848)
                    & ( ( 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__14855] :
                          ( t(Vvar__1___24Anonymous__14855,V0__A)
                          & ? [Vvar__2___24Anonymous__14856] :
                              ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__14856)
                              & V3__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__14855,Vvar__2___24Anonymous__14856)
                              & cCoq_2eLists_2eList_2enth___24a4(V0__A,V2__n,V3__l,V4__default) = cCoq_2eLists_2eList_2enth___24a4(V0__A,Vvar__0___24Anonymous__14848,Vvar__2___24Anonymous__14856,V4__default) ) ) ) ) ) ) ) ) ) ) ).

fof('$_def_Coq.Lists.List.tl',axiom,
    ! [V0__A,V1__l] :
      ( cType___24t(V0__A)
     => ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V1__l)
       => ( ( V1__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)
            & cCoq_2eLists_2eList_2etl___24a2(V0__A,V1__l) = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A) )
          | ? [Vvar__1___24Anonymous__29893] :
              ( t(Vvar__1___24Anonymous__29893,V0__A)
              & ? [Vvar__2___24Anonymous__29894] :
                  ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__29894)
                  & V1__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__29893,Vvar__2___24Anonymous__29894)
                  & cCoq_2eLists_2eList_2etl___24a2(V0__A,V1__l) = Vvar__2___24Anonymous__29894 ) ) ) ) ) ).

fof('$_def_Coq.Lists.SetoidList.compat_op',axiom,
    ! [V0__A,V1__B,V2__eqA,V3__eqB,V4__f] :
      ( cCoq_2eLists_2eSetoidList_2ecompat__op___24a5(V0__A,V1__B,V2__eqA,V3__eqB,V4__f)
    <=> cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__28659___24a2(V0__A,V1__B),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V0__A,c_24__type__4348___24a2(V0__A,V1__B),V2__eqA,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V1__B,V1__B,V3__eqB,V3__eqB)),V4__f) ) ).

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

fof('$_def_Coq.Logic.EqdepFacts.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__32918___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__24452] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__24452)
            & ( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
             => ( V0__n = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__24452)
                & ( ( V1__m = cCoq_2eNumbers_2eBinNums_2eN0
                    & cCoq_2eNArith_2eBinNatDef_2eN_2eadd___24a2(V0__n,V1__m) = V0__n )
                  | ? [Vvar__0___24Anonymous__24455] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__24455)
                      & V1__m = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__24455)
                      & cCoq_2eNArith_2eBinNatDef_2eN_2eadd___24a2(V0__n,V1__m) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(Vvar__0___24Anonymous__24452,Vvar__0___24Anonymous__24455)) ) ) ) ) ) ) ) ).

fof('$_def_Coq.NArith.BinNatDef.N.compare',axiom,
    ! [V0__n,V1__m] :
      ( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
     => ( ( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
         => ( V0__n = cCoq_2eNumbers_2eBinNums_2eN0
            & ( ( V1__m = cCoq_2eNumbers_2eBinNums_2eN0
                & cCoq_2eNArith_2eBinNatDef_2eN_2ecompare___24a2(V0__n,V1__m) = cCoq_2eInit_2eDatatypes_2eEq )
              | ? [Vvar__0___24Anonymous__24467] :
                  ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__24467)
                  & V1__m = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__24467)
                  & cCoq_2eNArith_2eBinNatDef_2eN_2ecompare___24a2(V0__n,V1__m) = cCoq_2eInit_2eDatatypes_2eLt ) ) ) )
        | ? [Vvar__0___24Anonymous__24468] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__24468)
            & ( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
             => ( V0__n = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__24468)
                & ( ( V1__m = cCoq_2eNumbers_2eBinNums_2eN0
                    & cCoq_2eNArith_2eBinNatDef_2eN_2ecompare___24a2(V0__n,V1__m) = cCoq_2eInit_2eDatatypes_2eGt )
                  | ? [Vvar__0___24Anonymous__24471] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__24471)
                      & V1__m = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__24471)
                      & cCoq_2eNArith_2eBinNatDef_2eN_2ecompare___24a2(V0__n,V1__m) = cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare___24a2(Vvar__0___24Anonymous__24468,Vvar__0___24Anonymous__24471) ) ) ) ) ) ) ) ).

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__24486] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__24486)
            & ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__24486)
             => ( V0__n = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__24486)
                & ( ? [Vvar__0___24Anonymous__24490] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__24490)
                      & Vvar__0___24Anonymous__24486 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__24490)
                      & cCoq_2eNArith_2eBinNatDef_2eN_2ediv2___24a1(V0__n) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__24490) )
                  | ? [Vvar__0___24Anonymous__24491] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__24491)
                      & Vvar__0___24Anonymous__24486 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__24491)
                      & cCoq_2eNArith_2eBinNatDef_2eN_2ediv2___24a1(V0__n) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__24491) )
                  | ( Vvar__0___24Anonymous__24486 = 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__24450] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__24450)
            & V0__n = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__24450)
            & cCoq_2eNArith_2eBinNatDef_2eN_2edouble___24a1(V0__n) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__24450)) ) ) ) ).

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__24476] :
                  ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__24476)
                  & V2__m = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__24476)
                  & cCoq_2eNArith_2eBinNatDef_2eN_2eeqb___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) )
        | ? [Vvar__0___24Anonymous__24477] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__24477)
            & ( cCoq_2eNumbers_2eBinNums_2eN___24t(V2__m)
             => ( V1__n = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__24477)
                & ( ( V2__m = cCoq_2eNumbers_2eBinNums_2eN0
                    & cCoq_2eNArith_2eBinNatDef_2eN_2eeqb___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2efalse )
                  | ? [Vvar__0___24Anonymous__24480] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__24480)
                      & V2__m = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__24480)
                      & cCoq_2eNArith_2eBinNatDef_2eN_2eeqb___24a2(V1__n,V2__m) = cCoq_2ePArith_2eBinPosDef_2ePos_2eeqb___24a2(Vvar__0___24Anonymous__24477,Vvar__0___24Anonymous__24480) ) ) ) ) ) ) ) ).

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__24492] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__24492)
            & ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__24492)
             => ( V0__n = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__24492)
                & ( ? [Vvar__0___24Anonymous__24496] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__24496)
                      & Vvar__0___24Anonymous__24492 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__24496)
                      & cCoq_2eNArith_2eBinNatDef_2eN_2eeven___24a1(V0__n) = cCoq_2eInit_2eDatatypes_2efalse )
                  | ? [Vvar__0___24Anonymous__24497] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__24497)
                      & Vvar__0___24Anonymous__24492 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__24497)
                      & cCoq_2eNArith_2eBinNatDef_2eN_2eeven___24a1(V0__n) = cCoq_2eInit_2eDatatypes_2etrue )
                  | ( Vvar__0___24Anonymous__24492 = cCoq_2eNumbers_2eBinNums_2exH
                    & cCoq_2eNArith_2eBinNatDef_2eN_2eeven___24a1(V0__n) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ) ) ) ).

fof('$_def_Coq.NArith.BinNatDef.N.land',axiom,
    ! [V0__n,V1__m] :
      ( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
     => ( ( V0__n = cCoq_2eNumbers_2eBinNums_2eN0
          & cCoq_2eNArith_2eBinNatDef_2eN_2eland___24a2(V0__n,V1__m) = cCoq_2eNumbers_2eBinNums_2eN0 )
        | ? [Vvar__0___24Anonymous__24518] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__24518)
            & ( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
             => ( V0__n = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__24518)
                & ( ( V1__m = cCoq_2eNumbers_2eBinNums_2eN0
                    & cCoq_2eNArith_2eBinNatDef_2eN_2eland___24a2(V0__n,V1__m) = cCoq_2eNumbers_2eBinNums_2eN0 )
                  | ? [Vvar__0___24Anonymous__24521] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__24521)
                      & V1__m = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__24521)
                      & cCoq_2eNArith_2eBinNatDef_2eN_2eland___24a2(V0__n,V1__m) = cCoq_2ePArith_2eBinPosDef_2ePos_2eland___24a2(Vvar__0___24Anonymous__24518,Vvar__0___24Anonymous__24521) ) ) ) ) ) ) ) ).

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__24529] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__24529)
            & ( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
             => ( V0__n = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__24529)
                & ( ( V1__m = cCoq_2eNumbers_2eBinNums_2eN0
                    & cCoq_2eNArith_2eBinNatDef_2eN_2elxor___24a2(V0__n,V1__m) = V0__n )
                  | ? [Vvar__0___24Anonymous__24532] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__24532)
                      & V1__m = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__24532)
                      & cCoq_2eNArith_2eBinNatDef_2eN_2elxor___24a2(V0__n,V1__m) = cCoq_2ePArith_2eBinPosDef_2ePos_2elxor___24a2(Vvar__0___24Anonymous__24529,Vvar__0___24Anonymous__24532) ) ) ) ) ) ) ) ).

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__2638] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__2638)
            & ( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
             => ( V0__n = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__2638)
                & ( ( V1__m = cCoq_2eNumbers_2eBinNums_2eN0
                    & cCoq_2eNArith_2eBinNatDef_2eN_2emul___24a2(V0__n,V1__m) = cCoq_2eNumbers_2eBinNums_2eN0 )
                  | ? [Vvar__0___24Anonymous__2641] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__2641)
                      & V1__m = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__2641)
                      & cCoq_2eNArith_2eBinNatDef_2eN_2emul___24a2(V0__n,V1__m) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2emul___24a2(Vvar__0___24Anonymous__2638,Vvar__0___24Anonymous__2641)) ) ) ) ) ) ) ) ).

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__24451] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__24451)
            & V0__n = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__24451)
            & cCoq_2eNArith_2eBinNatDef_2eN_2epred___24a1(V0__n) = cCoq_2ePArith_2eBinPosDef_2ePos_2epred__N___24a1(Vvar__0___24Anonymous__24451) ) ) ) ).

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__2635] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__2635)
            & V0__n = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__2635)
            & cCoq_2eNArith_2eBinNatDef_2eN_2esucc___24a1(V0__n) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2esucc___24a1(Vvar__0___24Anonymous__2635)) ) ) ) ).

fof('$_def_Coq.NArith.BinNatDef.N.succ_pos',axiom,
    ! [V0__n] :
      ( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
     => ( ( V0__n = cCoq_2eNumbers_2eBinNums_2eN0
          & cCoq_2eNArith_2eBinNatDef_2eN_2esucc__pos___24a1(V0__n) = cCoq_2eNumbers_2eBinNums_2exH )
        | ? [Vvar__0___24Anonymous__32913] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__32913)
            & V0__n = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__32913)
            & cCoq_2eNArith_2eBinNatDef_2eN_2esucc__pos___24a1(V0__n) = cCoq_2ePArith_2eBinPosDef_2ePos_2esucc___24a1(Vvar__0___24Anonymous__32913) ) ) ) ).

fof('$_def_Coq.NArith.BinNatDef.N.t',axiom,
    ! [Vvar__29581] :
      ( cCoq_2eNArith_2eBinNatDef_2eN_2et___24t(Vvar__29581)
    <=> cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__29581) ) ).

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__24534] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__24534)
            & V0__a = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__24534)
            & cCoq_2eNArith_2eBinNatDef_2eN_2etestbit___24a2(V0__a,V1__n) = cCoq_2ePArith_2eBinPosDef_2ePos_2etestbit___24a2(Vvar__0___24Anonymous__24534,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__24536] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__24536)
            & V0__a = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__24536)
            & cCoq_2eNArith_2eBinNatDef_2eN_2eto__nat___24a1(V0__a) = cCoq_2ePArith_2eBinPosDef_2ePos_2eto__nat___24a1(Vvar__0___24Anonymous__24536) ) ) ) ).

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.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.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__32983] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__32983)
            & V0__p = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__32983)
            & cCoq_2ePArith_2eBinPosDef_2ePos_2ediv2___24a1(V0__p) = Vvar__0___24Anonymous__32983 )
        | ? [Vvar__0___24Anonymous__32984] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__32984)
            & V0__p = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__32984)
            & cCoq_2ePArith_2eBinPosDef_2ePos_2ediv2___24a1(V0__p) = Vvar__0___24Anonymous__32984 )
        | ( V0__p = cCoq_2eNumbers_2eBinNums_2exH
          & cCoq_2ePArith_2eBinPosDef_2ePos_2ediv2___24a1(V0__p) = cCoq_2eNumbers_2eBinNums_2exH ) ) ) ).

fof('$_def_Coq.PArith.BinPosDef.Pos.div2_up',axiom,
    ! [V0__p] :
      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V0__p)
     => ( ? [Vvar__0___24Anonymous__32985] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__32985)
            & V0__p = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__32985)
            & cCoq_2ePArith_2eBinPosDef_2ePos_2ediv2__up___24a1(V0__p) = cCoq_2ePArith_2eBinPosDef_2ePos_2esucc___24a1(Vvar__0___24Anonymous__32985) )
        | ? [Vvar__0___24Anonymous__32986] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__32986)
            & V0__p = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__32986)
            & cCoq_2ePArith_2eBinPosDef_2ePos_2ediv2__up___24a1(V0__p) = Vvar__0___24Anonymous__32986 )
        | ( V0__p = cCoq_2eNumbers_2eBinNums_2exH
          & cCoq_2ePArith_2eBinPosDef_2ePos_2ediv2__up___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__32996] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__32996)
            & ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V2__q)
             => ( V1__p = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__32996)
                & ( ? [Vvar__0___24Anonymous__33000] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__33000)
                      & V2__q = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__33000)
                      & cCoq_2ePArith_2eBinPosDef_2ePos_2eeqb___24a2(V1__p,V2__q) = cCoq_2ePArith_2eBinPosDef_2ePos_2eeqb___24a2(Vvar__0___24Anonymous__32996,Vvar__0___24Anonymous__33000) )
                  | ? [Vvar__0___24Anonymous__33001] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__33001)
                      & V2__q = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__33001)
                      & 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__33002] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__33002)
            & ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V2__q)
             => ( V1__p = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__33002)
                & ( ? [Vvar__0___24Anonymous__33006] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__33006)
                      & V2__q = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__33006)
                      & cCoq_2ePArith_2eBinPosDef_2ePos_2eeqb___24a2(V1__p,V2__q) = cCoq_2eInit_2eDatatypes_2efalse )
                  | ? [Vvar__0___24Anonymous__33007] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__33007)
                      & V2__q = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__33007)
                      & cCoq_2ePArith_2eBinPosDef_2ePos_2eeqb___24a2(V1__p,V2__q) = cCoq_2ePArith_2eBinPosDef_2ePos_2eeqb___24a2(Vvar__0___24Anonymous__33002,Vvar__0___24Anonymous__33007) )
                  | ( 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__33008] :
                  ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__33008)
                  & V2__q = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__33008)
                  & cCoq_2ePArith_2eBinPosDef_2ePos_2eeqb___24a2(V1__p,V2__q) = cCoq_2eInit_2eDatatypes_2efalse )
              | ? [Vvar__0___24Anonymous__33009] :
                  ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__33009)
                  & V2__q = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__33009)
                  & 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__29586] :
              ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__29586)
              & V4__n = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__29586)
              & 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__29586),Vvar__0___24Anonymous__29586)) )
          | ? [Vvar__0___24Anonymous__29587] :
              ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__29587)
              & V4__n = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__29587)
              & 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__29587),Vvar__0___24Anonymous__29587) )
          | ( 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__29599] :
              ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__29599)
              & V3__p = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__29599)
              & 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__29599,happ(happ(V1__op,V4__a),V4__a))) )
          | ? [Vvar__0___24Anonymous__29600] :
              ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__29600)
              & V3__p = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__29600)
              & 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__29600,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__24726] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__24726)
            & V1__x = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__24726)
            & 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__24726,V2__y))) )
        | ? [Vvar__0___24Anonymous__24727] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__24727)
            & V1__x = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__24727)
            & cCoq_2ePArith_2eBinPosDef_2ePos_2emul___24a2(V1__x,V2__y) = cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2emul___24a2(Vvar__0___24Anonymous__24727,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__33044] :
            ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__33044)
            & ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__33044)
             => ( V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__33044)
                & ( ( Vvar__0___24Anonymous__33044 = cCoq_2eInit_2eDatatypes_2eO
                    & cCoq_2ePArith_2eBinPosDef_2ePos_2eof__nat___24a1(V1__n) = cCoq_2eNumbers_2eBinNums_2exH )
                  | ? [Vvar__0___24Anonymous__33047] :
                      ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__33047)
                      & Vvar__0___24Anonymous__33044 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__33047)
                      & 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__33044)) ) ) ) ) ) ) ) ).

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__33051] :
            ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__33051)
            & V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__33051)
            & 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__33051)) ) ) ) ).

fof('$_def_Coq.PArith.BinPosDef.Pos.size',axiom,
    ! [V1__p] :
      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__p)
     => ( ? [Vvar__0___24Anonymous__32991] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__32991)
            & V1__p = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__32991)
            & cCoq_2ePArith_2eBinPosDef_2ePos_2esize___24a1(V1__p) = cCoq_2ePArith_2eBinPosDef_2ePos_2esucc___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2esize___24a1(Vvar__0___24Anonymous__32991)) )
        | ? [Vvar__0___24Anonymous__32992] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__32992)
            & V1__p = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__32992)
            & cCoq_2ePArith_2eBinPosDef_2ePos_2esize___24a1(V1__p) = cCoq_2ePArith_2eBinPosDef_2ePos_2esucc___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2esize___24a1(Vvar__0___24Anonymous__32992)) )
        | ( V1__p = cCoq_2eNumbers_2eBinNums_2exH
          & cCoq_2ePArith_2eBinPosDef_2ePos_2esize___24a1(V1__p) = cCoq_2eNumbers_2eBinNums_2exH ) ) ) ).

fof('$_def_Coq.PArith.BinPosDef.Pos.size_nat',axiom,
    ! [V1__p] :
      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__p)
     => ( ? [Vvar__0___24Anonymous__32988] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__32988)
            & V1__p = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__32988)
            & cCoq_2ePArith_2eBinPosDef_2ePos_2esize__nat___24a1(V1__p) = cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2esize__nat___24a1(Vvar__0___24Anonymous__32988)) )
        | ? [Vvar__0___24Anonymous__32989] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__32989)
            & V1__p = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__32989)
            & cCoq_2ePArith_2eBinPosDef_2ePos_2esize__nat___24a1(V1__p) = cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2esize__nat___24a1(Vvar__0___24Anonymous__32989)) )
        | ( 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__32981] :
              ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__32981)
              & cCoq_2ePArith_2eBinPosDef_2ePos_2esub__mask___24a2(V0__x,V1__y) = cCoq_2ePArith_2eBinPosDef_2ePos_2eIsPos___24a1(Vvar__0___24Anonymous__32981)
              & cCoq_2ePArith_2eBinPosDef_2ePos_2esub___24a2(V0__x,V1__y) = Vvar__0___24Anonymous__32981 )
          | ( 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__32977] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__32977)
            & V1__x = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__32977)
            & cCoq_2ePArith_2eBinPosDef_2ePos_2esucc___24a1(V1__x) = cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2esucc___24a1(Vvar__0___24Anonymous__32977)) )
        | ? [Vvar__0___24Anonymous__32978] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__32978)
            & V1__x = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__32978)
            & cCoq_2ePArith_2eBinPosDef_2ePos_2esucc___24a1(V1__x) = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__32978) )
        | ( 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__29584] :
      ( cCoq_2ePArith_2eBinPosDef_2ePos_2et___24t(Vvar__29584)
    <=> cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__29584) ) ).

fof('$_def_Coq.PArith.BinPosDef.Pos.testbit_nat',axiom,
    ! [V1__p] :
      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__p)
     => ( ? [Vvar__0___24Anonymous__33014] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__33014)
            & V1__p = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__33014)
            & cCoq_2ePArith_2eBinPosDef_2ePos_2etestbit__nat___24a1(V1__p) = c_24__lam__33027___24a1(Vvar__0___24Anonymous__33014) )
        | ? [Vvar__0___24Anonymous__33018] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__33018)
            & V1__p = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__33018)
            & cCoq_2ePArith_2eBinPosDef_2ePos_2etestbit__nat___24a1(V1__p) = c_24__lam__33034___24a1(Vvar__0___24Anonymous__33018) )
        | ( V1__p = cCoq_2eNumbers_2eBinNums_2exH
          & cCoq_2ePArith_2eBinPosDef_2ePos_2etestbit__nat___24a1(V1__p) = c_24__lam__33038 ) ) ) ).

fof('$_def_Coq.QArith.QArith_base.Qden',axiom,
    ! [V0__q] :
      ( cCoq_2eQArith_2eQArith__base_2eQ___24t(V0__q)
     => ? [Vvar__0__Qnum__16477] :
          ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__0__Qnum__16477)
          & ? [Vvar__1__Qden__16478] :
              ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1__Qden__16478)
              & V0__q = cCoq_2eQArith_2eQArith__base_2eQmake___24a2(Vvar__0__Qnum__16477,Vvar__1__Qden__16478)
              & cCoq_2eQArith_2eQArith__base_2eQden___24a1(V0__q) = Vvar__1__Qden__16478 ) ) ) ).

fof('$_def_Coq.QArith.QArith_base.Qnum',axiom,
    ! [V0__q] :
      ( cCoq_2eQArith_2eQArith__base_2eQ___24t(V0__q)
     => ? [Vvar__0__Qnum__16472] :
          ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__0__Qnum__16472)
          & ? [Vvar__1__Qden__16473] :
              ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1__Qden__16473)
              & V0__q = cCoq_2eQArith_2eQArith__base_2eQmake___24a2(Vvar__0__Qnum__16472,Vvar__1__Qden__16473)
              & cCoq_2eQArith_2eQArith__base_2eQnum___24a1(V0__q) = Vvar__0__Qnum__16472 ) ) ) ).

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__16765] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__16765)
            & V0__z = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__16765)
            & cCoq_2eReals_2eRdefinitions_2eIZR___24a1(V0__z) = cCoq_2eReals_2eRdefinitions_2eIPR___24a1(Vvar__0___24Anonymous__16765) )
        | ? [Vvar__0___24Anonymous__16766] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__16766)
            & V0__z = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__16766)
            & cCoq_2eReals_2eRdefinitions_2eIZR___24a1(V0__z) = cCoq_2eReals_2eRdefinitions_2eRopp___24a1(cCoq_2eReals_2eRdefinitions_2eIPR___24a1(Vvar__0___24Anonymous__16766)) ) ) ) ).

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.reflexive',axiom,
    ! [V0__A,V1__R] :
      ( cCoq_2eRelations_2eRelation__Definitions_2ereflexive___24a2(V0__A,V1__R)
    <=> ! [V2__x] :
          ( t(V2__x,V0__A)
         => p(happ(happ(V1__R,V2__x),V2__x)) ) ) ).

fof('$_def_Coq.Relations.Relation_Definitions.relation',axiom,
    ! [V0__A] : cCoq_2eRelations_2eRelation__Definitions_2erelation___24a1(V0__A) = c_24__type__117___24a1(V0__A) ).

fof('$_def_Coq.Relations.Relation_Definitions.symmetric',axiom,
    ! [V0__A,V1__R] :
      ( cCoq_2eRelations_2eRelation__Definitions_2esymmetric___24a2(V0__A,V1__R)
    <=> ! [V2__x] :
          ( t(V2__x,V0__A)
         => ! [V3__y] :
              ( t(V3__y,V0__A)
             => ( p(happ(happ(V1__R,V2__x),V3__y))
               => p(happ(happ(V1__R,V3__y),V2__x)) ) ) ) ) ).

fof('$_def_Coq.Relations.Relation_Definitions.transitive',axiom,
    ! [V0__A,V1__R] :
      ( cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2(V0__A,V1__R)
    <=> ! [V2__x] :
          ( t(V2__x,V0__A)
         => ! [V3__y] :
              ( t(V3__y,V0__A)
             => ! [V4__z] :
                  ( t(V4__z,V0__A)
                 => ( p(happ(happ(V1__R,V2__x),V3__y))
                   => ( p(happ(happ(V1__R,V3__y),V4__z))
                     => p(happ(happ(V1__R,V2__x),V4__z)) ) ) ) ) ) ) ).

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__117___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__29843___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__29843___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__29582] :
      ( cCoq_2eStructures_2eOrderedTypeEx_2eN__as__OT_2et___24t(Vvar__29582)
    <=> cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__29582) ) ).

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__29583] :
      ( cCoq_2eStructures_2eOrderedTypeEx_2eNat__as__OT_2et___24t(Vvar__29583)
    <=> cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__29583) ) ).

fof('$_def_Coq.Structures.OrderedTypeEx.PositiveOrderedTypeBits.bits_lt',axiom,
    ! [V1__p,V2__q] :
      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__p)
     => ( ? [Vvar__0___24Anonymous__29519] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__29519)
            & ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V2__q)
             => ( V1__p = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__29519)
                & ( ? [Vvar__0___24Anonymous__29523] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__29523)
                      & V2__q = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__29523)
                      & ( cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2ebits__lt___24a2(V1__p,V2__q)
                      <=> cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2ebits__lt___24a2(Vvar__0___24Anonymous__29519,Vvar__0___24Anonymous__29523) ) )
                  | ? [Vvar__0___24Anonymous__29524] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__29524)
                      & V2__q = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__29524)
                      & ( 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__29525] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__29525)
            & ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V2__q)
             => ( V1__p = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__29525)
                & ( ? [Vvar__0___24Anonymous__29529] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__29529)
                      & V2__q = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__29529)
                      & ( cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2ebits__lt___24a2(V1__p,V2__q)
                      <=> p(c_24True) ) )
                  | ? [Vvar__0___24Anonymous__29530] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__29530)
                      & V2__q = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__29530)
                      & ( cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2ebits__lt___24a2(V1__p,V2__q)
                      <=> cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2ebits__lt___24a2(Vvar__0___24Anonymous__29525,Vvar__0___24Anonymous__29530) ) )
                  | ( 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__29531] :
                  ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__29531)
                  & V2__q = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__29531)
                  & ( cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2ebits__lt___24a2(V1__p,V2__q)
                  <=> p(c_24True) ) )
              | ? [Vvar__0___24Anonymous__29532] :
                  ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__29532)
                  & V2__q = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__29532)
                  & ( 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__29517] :
      ( cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2et___24t(Vvar__29517)
    <=> cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__29517) ) ).

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__29689] :
      ( cCoq_2eStructures_2eOrderedTypeEx_2ePositive__as__OT_2et___24t(Vvar__29689)
    <=> cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__29689) ) ).

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__25149] :
      ( cCoq_2eStructures_2eOrderedTypeEx_2eString__as__OT_2et___24t(Vvar__25149)
    <=> cCoq_2eStrings_2eString_2estring___24t(Vvar__25149) ) ).

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__29691] :
      ( cCoq_2eStructures_2eOrderedTypeEx_2eZ__as__OT_2et___24t(Vvar__29691)
    <=> cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__29691) ) ).

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.b2z',axiom,
    ! [V0__b] :
      ( cCoq_2eInit_2eDatatypes_2ebool___24t(V0__b)
     => ( ( V0__b = cCoq_2eInit_2eDatatypes_2etrue
          & cCoq_2eZArith_2eBinInt_2eZ_2eb2z___24a1(V0__b) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH) )
        | ( V0__b = cCoq_2eInit_2eDatatypes_2efalse
          & cCoq_2eZArith_2eBinInt_2eZ_2eb2z___24a1(V0__b) = cCoq_2eNumbers_2eBinNums_2eZ0 ) ) ) ).

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.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] :
      ( p(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__25154] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__25154)
            & V0__z = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__25154)
            & cCoq_2eZArith_2eBinIntDef_2eZ_2eabs___24a1(V0__z) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__25154) )
        | ? [Vvar__0___24Anonymous__25155] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__25155)
            & V0__z = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__25155)
            & cCoq_2eZArith_2eBinIntDef_2eZ_2eabs___24a1(V0__z) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__25155) ) ) ) ).

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__25158] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__25158)
            & V0__z = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__25158)
            & cCoq_2eZArith_2eBinIntDef_2eZ_2eabs__N___24a1(V0__z) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__25158) )
        | ? [Vvar__0___24Anonymous__25159] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__25159)
            & V0__z = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__25159)
            & cCoq_2eZArith_2eBinIntDef_2eZ_2eabs__N___24a1(V0__z) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__25159) ) ) ) ).

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__25156] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__25156)
            & V0__z = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__25156)
            & cCoq_2eZArith_2eBinIntDef_2eZ_2eabs__nat___24a1(V0__z) = cCoq_2ePArith_2eBinPosDef_2ePos_2eto__nat___24a1(Vvar__0___24Anonymous__25156) )
        | ? [Vvar__0___24Anonymous__25157] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__25157)
            & V0__z = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__25157)
            & cCoq_2eZArith_2eBinIntDef_2eZ_2eabs__nat___24a1(V0__z) = cCoq_2ePArith_2eBinPosDef_2ePos_2eto__nat___24a1(Vvar__0___24Anonymous__25157) ) ) ) ).

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__10804] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__10804)
            & ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
             => ( V0__x = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__10804)
                & ( ( V1__y = cCoq_2eNumbers_2eBinNums_2eZ0
                    & cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__x,V1__y) = V0__x )
                  | ? [Vvar__0___24Anonymous__10808] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__10808)
                      & V1__y = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__10808)
                      & cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(Vvar__0___24Anonymous__10804,Vvar__0___24Anonymous__10808)) )
                  | ? [Vvar__0___24Anonymous__10809] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__10809)
                      & V1__y = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__10809)
                      & cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__x,V1__y) = cCoq_2eZArith_2eBinIntDef_2eZ_2epos__sub___24a2(Vvar__0___24Anonymous__10804,Vvar__0___24Anonymous__10809) ) ) ) ) )
        | ? [Vvar__0___24Anonymous__10810] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__10810)
            & ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
             => ( V0__x = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__10810)
                & ( ( V1__y = cCoq_2eNumbers_2eBinNums_2eZ0
                    & cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__x,V1__y) = V0__x )
                  | ? [Vvar__0___24Anonymous__10814] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__10814)
                      & V1__y = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__10814)
                      & cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__x,V1__y) = cCoq_2eZArith_2eBinIntDef_2eZ_2epos__sub___24a2(Vvar__0___24Anonymous__10814,Vvar__0___24Anonymous__10810) )
                  | ? [Vvar__0___24Anonymous__10815] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__10815)
                      & V1__y = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__10815)
                      & cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(Vvar__0___24Anonymous__10810,Vvar__0___24Anonymous__10815)) ) ) ) ) ) ) ) ).

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__2540] :
                  ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__2540)
                  & V1__y = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__2540)
                  & cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eLt )
              | ? [Vvar__0___24Anonymous__2541] :
                  ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__2541)
                  & V1__y = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__2541)
                  & cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eGt ) ) ) )
        | ? [Vvar__0___24Anonymous__2542] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__2542)
            & ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
             => ( V0__x = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__2542)
                & ( ( V1__y = cCoq_2eNumbers_2eBinNums_2eZ0
                    & cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eGt )
                  | ? [Vvar__0___24Anonymous__2546] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__2546)
                      & V1__y = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__2546)
                      & cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare___24a2(Vvar__0___24Anonymous__2542,Vvar__0___24Anonymous__2546) )
                  | ? [Vvar__0___24Anonymous__2547] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__2547)
                      & V1__y = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__2547)
                      & cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eGt ) ) ) ) )
        | ? [Vvar__0___24Anonymous__2548] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__2548)
            & ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
             => ( V0__x = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__2548)
                & ( ( V1__y = cCoq_2eNumbers_2eBinNums_2eZ0
                    & cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eLt )
                  | ? [Vvar__0___24Anonymous__2552] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__2552)
                      & V1__y = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__2552)
                      & cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eLt )
                  | ? [Vvar__0___24Anonymous__2553] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__2553)
                      & V1__y = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__2553)
                      & cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eCompOpp___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare___24a2(Vvar__0___24Anonymous__2548,Vvar__0___24Anonymous__2553)) ) ) ) ) ) ) ) ).

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__25173] :
            ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__2___24Anonymous__25173)
            & ? [Vvar__3___24Anonymous__25174] :
                ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__3___24Anonymous__25174)
                & 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__25173,Vvar__3___24Anonymous__25174)
                & cCoq_2eZArith_2eBinIntDef_2eZ_2ediv___24a2(V0__a,V1__b) = Vvar__2___24Anonymous__25173 ) ) ) ) ).

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__33106] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__33106)
            & ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__33106)
             => ( V0__z = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__33106)
                & ( ? [Vvar__0___24Anonymous__33110] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__33110)
                      & Vvar__0___24Anonymous__33106 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__33110)
                      & cCoq_2eZArith_2eBinIntDef_2eZ_2eeven___24a1(V0__z) = cCoq_2eInit_2eDatatypes_2efalse )
                  | ? [Vvar__0___24Anonymous__33111] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__33111)
                      & Vvar__0___24Anonymous__33106 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__33111)
                      & cCoq_2eZArith_2eBinIntDef_2eZ_2eeven___24a1(V0__z) = cCoq_2eInit_2eDatatypes_2etrue )
                  | ( Vvar__0___24Anonymous__33106 = cCoq_2eNumbers_2eBinNums_2exH
                    & cCoq_2eZArith_2eBinIntDef_2eZ_2eeven___24a1(V0__z) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) )
        | ? [Vvar__0___24Anonymous__33112] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__33112)
            & ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__33112)
             => ( V0__z = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__33112)
                & ( ? [Vvar__0___24Anonymous__33116] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__33116)
                      & Vvar__0___24Anonymous__33112 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__33116)
                      & cCoq_2eZArith_2eBinIntDef_2eZ_2eeven___24a1(V0__z) = cCoq_2eInit_2eDatatypes_2efalse )
                  | ? [Vvar__0___24Anonymous__33117] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__33117)
                      & Vvar__0___24Anonymous__33112 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__33117)
                      & cCoq_2eZArith_2eBinIntDef_2eZ_2eeven___24a1(V0__z) = cCoq_2eInit_2eDatatypes_2etrue )
                  | ( Vvar__0___24Anonymous__33112 = 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__10845] :
            ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__2___24Anonymous__10845)
            & ? [Vvar__3___24Anonymous__10846] :
                ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__3___24Anonymous__10846)
                & 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__10845,Vvar__3___24Anonymous__10846)
                & cCoq_2eZArith_2eBinIntDef_2eZ_2emodulo___24a2(V0__a,V1__b) = Vvar__3___24Anonymous__10846 ) ) ) ) ).

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__10822] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__10822)
            & ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
             => ( V0__x = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__10822)
                & ( ( V1__y = cCoq_2eNumbers_2eBinNums_2eZ0
                    & cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZ0 )
                  | ? [Vvar__0___24Anonymous__10826] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__10826)
                      & V1__y = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__10826)
                      & cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2emul___24a2(Vvar__0___24Anonymous__10822,Vvar__0___24Anonymous__10826)) )
                  | ? [Vvar__0___24Anonymous__10827] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__10827)
                      & V1__y = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__10827)
                      & cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2emul___24a2(Vvar__0___24Anonymous__10822,Vvar__0___24Anonymous__10827)) ) ) ) ) )
        | ? [Vvar__0___24Anonymous__10828] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__10828)
            & ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
             => ( V0__x = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__10828)
                & ( ( V1__y = cCoq_2eNumbers_2eBinNums_2eZ0
                    & cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZ0 )
                  | ? [Vvar__0___24Anonymous__10832] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__10832)
                      & V1__y = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__10832)
                      & cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2emul___24a2(Vvar__0___24Anonymous__10828,Vvar__0___24Anonymous__10832)) )
                  | ? [Vvar__0___24Anonymous__10833] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__10833)
                      & V1__y = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__10833)
                      & cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2emul___24a2(Vvar__0___24Anonymous__10828,Vvar__0___24Anonymous__10833)) ) ) ) ) ) ) ) ).

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__25179] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__25179)
            & ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__25179)
             => ( V0__z = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__25179)
                & ( ? [Vvar__0___24Anonymous__25183] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__25183)
                      & Vvar__0___24Anonymous__25179 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__25183)
                      & cCoq_2eZArith_2eBinIntDef_2eZ_2eodd___24a1(V0__z) = cCoq_2eInit_2eDatatypes_2etrue )
                  | ? [Vvar__0___24Anonymous__25184] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__25184)
                      & Vvar__0___24Anonymous__25179 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__25184)
                      & cCoq_2eZArith_2eBinIntDef_2eZ_2eodd___24a1(V0__z) = cCoq_2eInit_2eDatatypes_2efalse )
                  | ( Vvar__0___24Anonymous__25179 = cCoq_2eNumbers_2eBinNums_2exH
                    & cCoq_2eZArith_2eBinIntDef_2eZ_2eodd___24a1(V0__z) = cCoq_2eInit_2eDatatypes_2etrue ) ) ) ) )
        | ? [Vvar__0___24Anonymous__25185] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__25185)
            & ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__25185)
             => ( V0__z = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__25185)
                & ( ? [Vvar__0___24Anonymous__25189] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__25189)
                      & Vvar__0___24Anonymous__25185 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__25189)
                      & cCoq_2eZArith_2eBinIntDef_2eZ_2eodd___24a1(V0__z) = cCoq_2eInit_2eDatatypes_2etrue )
                  | ? [Vvar__0___24Anonymous__25190] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__25190)
                      & Vvar__0___24Anonymous__25185 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__25190)
                      & cCoq_2eZArith_2eBinIntDef_2eZ_2eodd___24a1(V0__z) = cCoq_2eInit_2eDatatypes_2efalse )
                  | ( Vvar__0___24Anonymous__25185 = 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__10838] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__10838)
            & V0__n = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__10838)
            & cCoq_2eZArith_2eBinIntDef_2eZ_2eof__N___24a1(V0__n) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__10838) ) ) ) ).

fof('$_def_Coq.ZArith.BinIntDef.Z.of_nat',axiom,
    ! [V0__n] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
     => ( ( V0__n = cCoq_2eInit_2eDatatypes_2eO
          & cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat___24a1(V0__n) = cCoq_2eNumbers_2eBinNums_2eZ0 )
        | ? [Vvar__0___24Anonymous__25162] :
            ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__25162)
            & V0__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__25162)
            & cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat___24a1(V0__n) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eof__succ__nat___24a1(Vvar__0___24Anonymous__25162)) ) ) ) ).

fof('$_def_Coq.ZArith.BinIntDef.Z.one',axiom,
    cCoq_2eZArith_2eBinIntDef_2eZ_2eone = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH) ).

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__10819] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__10819)
            & V0__x = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__10819)
            & cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V0__x) = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__10819) )
        | ? [Vvar__0___24Anonymous__10820] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__10820)
            & V0__x = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__10820)
            & cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V0__x) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__10820) ) ) ) ).

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__10835] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__10835)
            & V1__y = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__10835)
            & cCoq_2eZArith_2eBinIntDef_2eZ_2epow___24a2(V0__x,V1__y) = cCoq_2eZArith_2eBinIntDef_2eZ_2epow__pos___24a2(V0__x,Vvar__0___24Anonymous__10835) )
        | ? [Vvar__0___24Anonymous__10836] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__10836)
            & V1__y = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__10836)
            & 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__29690] :
      ( cCoq_2eZArith_2eBinIntDef_2eZ_2et___24t(Vvar__29690)
    <=> cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__29690) ) ).

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__33104] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__33104)
            & V0__z = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__33104)
            & cCoq_2eZArith_2eBinIntDef_2eZ_2eto__N___24a1(V0__z) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__33104) )
        | ? [Vvar__0___24Anonymous__33105] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__33105)
            & V0__z = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__33105)
            & 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__2557] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__2557)
            & V0__z = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__2557)
            & cCoq_2eZArith_2eBinIntDef_2eZ_2eto__nat___24a1(V0__z) = cCoq_2ePArith_2eBinPosDef_2ePos_2eto__nat___24a1(Vvar__0___24Anonymous__2557) )
        | ? [Vvar__0___24Anonymous__2558] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__2558)
            & V0__z = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__2558)
            & 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__25165] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__25165)
            & V0__z = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__25165)
            & cCoq_2eZArith_2eBinIntDef_2eZ_2eto__pos___24a1(V0__z) = Vvar__0___24Anonymous__25165 )
        | ? [Vvar__0___24Anonymous__25166] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__25166)
            & V0__z = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__25166)
            & 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.Zcomplements.floor_pos',axiom,
    ! [V1__a] :
      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__a)
     => ( ? [Vvar__0___24Anonymous__32900] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__32900)
            & V1__a = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__32900)
            & cCoq_2eZArith_2eZcomplements_2efloor__pos___24a1(V1__a) = cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2eZArith_2eZcomplements_2efloor__pos___24a1(Vvar__0___24Anonymous__32900)) )
        | ? [Vvar__0___24Anonymous__32901] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__32901)
            & V1__a = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__32901)
            & cCoq_2eZArith_2eZcomplements_2efloor__pos___24a1(V1__a) = cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2eZArith_2eZcomplements_2efloor__pos___24a1(Vvar__0___24Anonymous__32901)) )
        | ( V1__a = cCoq_2eNumbers_2eBinNums_2exH
          & cCoq_2eZArith_2eZcomplements_2efloor__pos___24a1(V1__a) = cCoq_2eNumbers_2eBinNums_2exH ) ) ) ).

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__29427] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__29427)
            & ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__29427)
             => ( V0__z = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__29427)
                & ( ? [Vvar__0___24Anonymous__29431] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__29431)
                      & Vvar__0___24Anonymous__29427 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__29431)
                      & ( cCoq_2eZArith_2eZeven_2eZeven___24a1(V0__z)
                      <=> p(c_24False) ) )
                  | ? [Vvar__0___24Anonymous__29432] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__29432)
                      & Vvar__0___24Anonymous__29427 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__29432)
                      & ( cCoq_2eZArith_2eZeven_2eZeven___24a1(V0__z)
                      <=> p(c_24True) ) )
                  | ( Vvar__0___24Anonymous__29427 = cCoq_2eNumbers_2eBinNums_2exH
                    & ( cCoq_2eZArith_2eZeven_2eZeven___24a1(V0__z)
                    <=> p(c_24False) ) ) ) ) ) )
        | ? [Vvar__0___24Anonymous__29433] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__29433)
            & ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__29433)
             => ( V0__z = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__29433)
                & ( ? [Vvar__0___24Anonymous__29437] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__29437)
                      & Vvar__0___24Anonymous__29433 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__29437)
                      & ( cCoq_2eZArith_2eZeven_2eZeven___24a1(V0__z)
                      <=> p(c_24False) ) )
                  | ? [Vvar__0___24Anonymous__29438] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__29438)
                      & Vvar__0___24Anonymous__29433 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__29438)
                      & ( cCoq_2eZArith_2eZeven_2eZeven___24a1(V0__z)
                      <=> p(c_24True) ) )
                  | ( Vvar__0___24Anonymous__29433 = 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__24103] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__24103)
            & ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__24103)
             => ( V0__z = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__24103)
                & ( ? [Vvar__0___24Anonymous__24107] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__24107)
                      & Vvar__0___24Anonymous__24103 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__24107)
                      & ( cCoq_2eZArith_2eZeven_2eZodd___24a1(V0__z)
                      <=> p(c_24True) ) )
                  | ? [Vvar__0___24Anonymous__24108] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__24108)
                      & Vvar__0___24Anonymous__24103 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__24108)
                      & ( cCoq_2eZArith_2eZeven_2eZodd___24a1(V0__z)
                      <=> p(c_24False) ) )
                  | ( Vvar__0___24Anonymous__24103 = cCoq_2eNumbers_2eBinNums_2exH
                    & ( cCoq_2eZArith_2eZeven_2eZodd___24a1(V0__z)
                    <=> p(c_24True) ) ) ) ) ) )
        | ? [Vvar__0___24Anonymous__24109] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__24109)
            & ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__24109)
             => ( V0__z = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__24109)
                & ( ? [Vvar__0___24Anonymous__24113] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__24113)
                      & Vvar__0___24Anonymous__24109 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__24113)
                      & ( cCoq_2eZArith_2eZeven_2eZodd___24a1(V0__z)
                      <=> p(c_24True) ) )
                  | ? [Vvar__0___24Anonymous__24114] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__24114)
                      & Vvar__0___24Anonymous__24109 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__24114)
                      & ( cCoq_2eZArith_2eZeven_2eZodd___24a1(V0__z)
                      <=> p(c_24False) ) )
                  | ( Vvar__0___24Anonymous__24109 = 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__29440] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__29440)
            & V1__p = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__29440)
            & ( cCoq_2eZArith_2eZlogarithm_2eIs__power___24a1(V1__p)
            <=> p(c_24False) ) )
        | ? [Vvar__0___24Anonymous__29441] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__29441)
            & V1__p = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__29441)
            & ( cCoq_2eZArith_2eZlogarithm_2eIs__power___24a1(V1__p)
            <=> cCoq_2eZArith_2eZlogarithm_2eIs__power___24a1(Vvar__0___24Anonymous__29441) ) )
        | ( 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__32904] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__32904)
            & V1__p = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__32904)
            & cCoq_2eZArith_2eZlogarithm_2elog__inf___24a1(V1__p) = cCoq_2eZArith_2eBinIntDef_2eZ_2esucc___24a1(cCoq_2eZArith_2eZlogarithm_2elog__inf___24a1(Vvar__0___24Anonymous__32904)) )
        | ? [Vvar__0___24Anonymous__32905] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__32905)
            & V1__p = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__32905)
            & cCoq_2eZArith_2eZlogarithm_2elog__inf___24a1(V1__p) = cCoq_2eZArith_2eBinIntDef_2eZ_2esucc___24a1(cCoq_2eZArith_2eZlogarithm_2elog__inf___24a1(Vvar__0___24Anonymous__32905)) )
        | ( V1__p = cCoq_2eNumbers_2eBinNums_2exH
          & cCoq_2eZArith_2eZlogarithm_2elog__inf___24a1(V1__p) = cCoq_2eNumbers_2eBinNums_2eZ0 ) ) ) ).

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

fof('$_def_Coq.micromega.Env.Env',axiom,
    ! [V0__D] : cCoq_2emicromega_2eEnv_2eEnv___24a1(V0__D) = c_24__type__26145___24a1(V0__D) ).

fof('$_def_Coq.micromega.Refl.make_conj',axiom,
    ! [V1__A,V2__eval,V3__l] :
      ( cType___24t(V1__A)
     => ( cCoq_2eInit_2eDatatypes_2elist___24t(V1__A,V3__l)
       => ( ( V3__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V1__A)
            & ( cCoq_2emicromega_2eRefl_2emake__conj___24a3(V1__A,V2__eval,V3__l)
            <=> p(c_24True) ) )
          | ? [Vvar__1___24Anonymous__16799] :
              ( t(Vvar__1___24Anonymous__16799,V1__A)
              & ? [Vvar__2___24Anonymous__16800] :
                  ( cCoq_2eInit_2eDatatypes_2elist___24t(V1__A,Vvar__2___24Anonymous__16800)
                  & ( cType___24t(V1__A)
                   => ( cCoq_2eInit_2eDatatypes_2elist___24t(V1__A,Vvar__2___24Anonymous__16800)
                     => ( V3__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V1__A,Vvar__1___24Anonymous__16799,Vvar__2___24Anonymous__16800)
                        & ( ( Vvar__2___24Anonymous__16800 = 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__16799)) ) )
                          | ? [Vvar__1___24Anonymous__16811] :
                              ( t(Vvar__1___24Anonymous__16811,V1__A)
                              & ? [Vvar__2___24Anonymous__16812] :
                                  ( cCoq_2eInit_2eDatatypes_2elist___24t(V1__A,Vvar__2___24Anonymous__16812)
                                  & Vvar__2___24Anonymous__16800 = cCoq_2eInit_2eDatatypes_2econs___24a3(V1__A,Vvar__1___24Anonymous__16811,Vvar__2___24Anonymous__16812)
                                  & ( cCoq_2emicromega_2eRefl_2emake__conj___24a3(V1__A,V2__eval,V3__l)
                                  <=> ( p(happ(V2__eval,Vvar__1___24Anonymous__16799))
                                      & cCoq_2emicromega_2eRefl_2emake__conj___24a3(V1__A,V2__eval,Vvar__2___24Anonymous__16800) ) ) ) ) ) ) ) ) ) ) ) ) ) ).

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__16780] :
              ( t(Vvar__1___24Anonymous__16780,V1__A)
              & ? [Vvar__2___24Anonymous__16781] :
                  ( cCoq_2eInit_2eDatatypes_2elist___24t(V1__A,Vvar__2___24Anonymous__16781)
                  & V3__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V1__A,Vvar__1___24Anonymous__16780,Vvar__2___24Anonymous__16781)
                  & ( cCoq_2emicromega_2eRefl_2emake__impl___24a4(V1__A,V2__eval,V3__l,V4__goal)
                  <=> ( p(happ(V2__eval,Vvar__1___24Anonymous__16780))
                     => cCoq_2emicromega_2eRefl_2emake__impl___24a4(V1__A,V2__eval,Vvar__2___24Anonymous__16781,V4__goal) ) ) ) ) ) ) ) ).

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

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

fof('$_def_Coq.micromega.RingMicromega.cneqb',axiom,
    ! [V0__C,V1__ceqb,V2__x,V3__y] : cCoq_2emicromega_2eRingMicromega_2ecneqb___24a4(V0__C,V1__ceqb,V2__x,V3__y) = cCoq_2eInit_2eDatatypes_2enegb___24a1(happ(happ(V1__ceqb,V2__x),V3__y)) ).

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__31829___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__31837___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__31845___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__31853___24a3(V0__R,V1__rO,V3__rle) ) ) ) ) ).

fof('$_def_Coq.micromega.RingMicromega.eval_op2',axiom,
    ! [V0__R,V1__req,V2__rle,V3__rlt,V4__o] :
      ( cType___24t(V0__R)
     => ( cCoq_2emicromega_2eRingMicromega_2eOp2___24t(V4__o)
       => ( ( V4__o = cCoq_2emicromega_2eRingMicromega_2eOpEq
            & cCoq_2emicromega_2eRingMicromega_2eeval__op2___24a5(V0__R,V1__req,V2__rle,V3__rlt,V4__o) = V1__req )
          | ( V4__o = cCoq_2emicromega_2eRingMicromega_2eOpNEq
            & cCoq_2emicromega_2eRingMicromega_2eeval__op2___24a5(V0__R,V1__req,V2__rle,V3__rlt,V4__o) = c_24__lam__31926___24a2(V0__R,V1__req) )
          | ( V4__o = cCoq_2emicromega_2eRingMicromega_2eOpLe
            & cCoq_2emicromega_2eRingMicromega_2eeval__op2___24a5(V0__R,V1__req,V2__rle,V3__rlt,V4__o) = V2__rle )
          | ( V4__o = cCoq_2emicromega_2eRingMicromega_2eOpGe
            & cCoq_2emicromega_2eRingMicromega_2eeval__op2___24a5(V0__R,V1__req,V2__rle,V3__rlt,V4__o) = c_24__lam__31934___24a2(V0__R,V2__rle) )
          | ( V4__o = cCoq_2emicromega_2eRingMicromega_2eOpLt
            & cCoq_2emicromega_2eRingMicromega_2eeval__op2___24a5(V0__R,V1__req,V2__rle,V3__rlt,V4__o) = c_24__lam__31942___24a2(V0__R,V3__rlt) )
          | ( V4__o = cCoq_2emicromega_2eRingMicromega_2eOpGt
            & cCoq_2emicromega_2eRingMicromega_2eeval__op2___24a5(V0__R,V1__req,V2__rle,V3__rlt,V4__o) = c_24__lam__31950___24a2(V0__R,V3__rlt) ) ) ) ) ).

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__31913] :
                  ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__31913)
                  & V2__m = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__31913)
                  & cCoq_2emicromega_2eRingMicromega_2ege__bool___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) )
        | ? [Vvar__0___24Anonymous__31914] :
            ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__31914)
            & ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__m)
             => ( V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__31914)
                & ( ( V2__m = cCoq_2eInit_2eDatatypes_2eO
                    & cCoq_2emicromega_2eRingMicromega_2ege__bool___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2etrue )
                  | ? [Vvar__0___24Anonymous__31917] :
                      ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__31917)
                      & V2__m = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__31917)
                      & cCoq_2emicromega_2eRingMicromega_2ege__bool___24a2(V1__n,V2__m) = cCoq_2emicromega_2eRingMicromega_2ege__bool___24a2(Vvar__0___24Anonymous__31914,Vvar__0___24Anonymous__31917) ) ) ) ) ) ) ) ).

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.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.ZCoeff.gen_order_phi_Z',axiom,
    ! [V0__R,V1__rO,V2__rI,V3__rplus,V4__rtimes,V5__ropp] : cCoq_2emicromega_2eZCoeff_2egen__order__phi__Z___24a6(V0__R,V1__rO,V2__rI,V3__rplus,V4__rtimes,V5__ropp) = cCoq_2esetoid__ring_2eInitialRing_2egen__phiZ___24a6(V0__R,V1__rO,V2__rI,V3__rplus,V4__rtimes,V5__ropp) ).

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.ZWitness',axiom,
    ! [Vvar__32879] :
      ( cCoq_2emicromega_2eZMicromega_2eZWitness___24t(Vvar__32879)
    <=> cCoq_2emicromega_2eRingMicromega_2ePsatz___24t(cCoq_2eNumbers_2eBinNums_2eZ,Vvar__32879) ) ).

fof('$_def_Coq.micromega.ZMicromega.coneMember',axiom,
    ! [Vvar__32898] :
      ( cCoq_2emicromega_2eZMicromega_2econeMember___24t(Vvar__32898)
    <=> cCoq_2emicromega_2eZMicromega_2eZWitness___24t(Vvar__32898) ) ).

fof('$_def_Coq.micromega.ZMicromega.isZ0',axiom,
    ! [V0__x] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
     => ( ( V0__x = cCoq_2eNumbers_2eBinNums_2eZ0
          & cCoq_2emicromega_2eZMicromega_2eisZ0___24a1(V0__x) = cCoq_2eInit_2eDatatypes_2etrue )
        | ? [Vvar__0___24Anonymous__32880] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__32880)
            & V0__x = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__32880)
            & cCoq_2emicromega_2eZMicromega_2eisZ0___24a1(V0__x) = cCoq_2eInit_2eDatatypes_2efalse )
        | ? [Vvar__0___24Anonymous__32881] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__32881)
            & V0__x = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__32881)
            & cCoq_2emicromega_2eZMicromega_2eisZ0___24a1(V0__x) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ).

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__14716] :
      ( cCoq_2esetoid__ring_2eInitialRing_2eNword___24t(Vvar__14716)
    <=> cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eNumbers_2eBinNums_2eN,Vvar__14716) ) ).

fof('$_def_Coq.setoid_ring.InitialRing.gen_phiN',axiom,
    ! [V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__x] :
      ( cType___24t(V0__R)
     => ( cCoq_2eNumbers_2eBinNums_2eN___24t(V5__x)
       => ( ( V5__x = cCoq_2eNumbers_2eBinNums_2eN0
            & cCoq_2esetoid__ring_2eInitialRing_2egen__phiN___24a6(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__x) = V1__rO )
          | ? [Vvar__0___24Anonymous__14676] :
              ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__14676)
              & V5__x = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__14676)
              & cCoq_2esetoid__ring_2eInitialRing_2egen__phiN___24a6(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__x) = cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS___24a5(V0__R,V2__rI,V3__radd,V4__rmul,Vvar__0___24Anonymous__14676) ) ) ) ) ).

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__26997] :
              ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__26997)
              & ( cType___24t(V0__R)
               => ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__26997)
                 => ( V5__p = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__26997)
                    & ( ? [Vvar__0___24Anonymous__27001] :
                          ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__27001)
                          & Vvar__0___24Anonymous__26997 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__27001)
                          & 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__26997))) )
                      | ? [Vvar__0___24Anonymous__27002] :
                          ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__27002)
                          & Vvar__0___24Anonymous__26997 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__27002)
                          & 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__26997))) )
                      | ( Vvar__0___24Anonymous__26997 = 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__27003] :
              ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__27003)
              & ( cType___24t(V0__R)
               => ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__27003)
                 => ( V5__p = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__27003)
                    & ( ? [Vvar__0___24Anonymous__27007] :
                          ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__27007)
                          & Vvar__0___24Anonymous__27003 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__27007)
                          & 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__27003)) )
                      | ? [Vvar__0___24Anonymous__27008] :
                          ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__27008)
                          & Vvar__0___24Anonymous__27003 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__27008)
                          & 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__27003)) )
                      | ( Vvar__0___24Anonymous__27003 = 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__26964] :
              ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__26964)
              & V5__p = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__26964)
              & 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__26964))) )
          | ? [Vvar__0___24Anonymous__26965] :
              ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__26965)
              & V5__p = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__26965)
              & 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__26965)) )
          | ( 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.InitialRing.gen_phiZ',axiom,
    ! [V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__ropp,V6__z] :
      ( cType___24t(V0__R)
     => ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V6__z)
       => ( ( V6__z = cCoq_2eNumbers_2eBinNums_2eZ0
            & cCoq_2esetoid__ring_2eInitialRing_2egen__phiZ___24a7(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__ropp,V6__z) = V1__rO )
          | ? [Vvar__0___24Anonymous__14601] :
              ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__14601)
              & V6__z = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__14601)
              & cCoq_2esetoid__ring_2eInitialRing_2egen__phiZ___24a7(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__ropp,V6__z) = cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS___24a5(V0__R,V2__rI,V3__radd,V4__rmul,Vvar__0___24Anonymous__14601) )
          | ? [Vvar__0___24Anonymous__14602] :
              ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__14602)
              & V6__z = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__14602)
              & cCoq_2esetoid__ring_2eInitialRing_2egen__phiZ___24a7(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__ropp,V6__z) = happ(V5__ropp,cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS___24a5(V0__R,V2__rI,V3__radd,V4__rmul,Vvar__0___24Anonymous__14602)) ) ) ) ) ).

fof('$_def_Coq.setoid_ring.InitialRing.hypo_type',axiom,
    ! [V0__h] :
      ( cCoq_2esetoid__ring_2eInitialRing_2ehypo___24t(V0__h)
     => ? [Vvar__0__hypo__type__29874] :
          ( cType___24t(Vvar__0__hypo__type__29874)
          & ? [Vvar__1__hypo__proof__29875] :
              ( t(Vvar__1__hypo__proof__29875,Vvar__0__hypo__type__29874)
              & V0__h = cCoq_2esetoid__ring_2eInitialRing_2emkhypo___24a2(Vvar__0__hypo__type__29874,Vvar__1__hypo__proof__29875)
              & cCoq_2esetoid__ring_2eInitialRing_2ehypo__type___24a1(V0__h) = Vvar__0__hypo__type__29874 ) ) ) ).

fof('$_def_Coq.setoid_ring.Ring.bool_eq',axiom,
    ! [V0__b1,V1__b2] :
      ( cCoq_2eInit_2eDatatypes_2ebool___24t(V0__b1)
     => ( ( V0__b1 = cCoq_2eInit_2eDatatypes_2etrue
          & cCoq_2esetoid__ring_2eRing_2ebool__eq___24a2(V0__b1,V1__b2) = V1__b2 )
        | ( V0__b1 = cCoq_2eInit_2eDatatypes_2efalse
          & cCoq_2esetoid__ring_2eRing_2ebool__eq___24a2(V0__b1,V1__b2) = cCoq_2eInit_2eDatatypes_2enegb___24a1(V1__b2) ) ) ) ).

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__23080] :
              ( t(Vvar__1___24Anonymous__23080,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__23080)
                    & ( ? [Vvar__1___24Anonymous__23090] :
                          ( t(Vvar__1___24Anonymous__23090,V0__C)
                          & V4__P_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePc___24a2(V0__C,Vvar__1___24Anonymous__23090)
                          & cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,V3__P,V4__P_27) = happ(happ(V1__ceqb,Vvar__1___24Anonymous__23080),Vvar__1___24Anonymous__23090) )
                      | ? [Vvar__1___24Anonymous__23092] :
                          ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__23092)
                          & ? [Vvar__2___24Anonymous__23093] :
                              ( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__2___24Anonymous__23093)
                              & V4__P_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePinj___24a3(V0__C,Vvar__1___24Anonymous__23092,Vvar__2___24Anonymous__23093)
                              & cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,V3__P,V4__P_27) = cCoq_2eInit_2eDatatypes_2efalse ) )
                      | ? [Vvar__1___24Anonymous__23096] :
                          ( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__1___24Anonymous__23096)
                          & ? [Vvar__2___24Anonymous__23097] :
                              ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2___24Anonymous__23097)
                              & ? [Vvar__3___24Anonymous__23098] :
                                  ( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__3___24Anonymous__23098)
                                  & V4__P_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePX___24a4(V0__C,Vvar__1___24Anonymous__23096,Vvar__2___24Anonymous__23097,Vvar__3___24Anonymous__23098)
                                  & cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,V3__P,V4__P_27) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ) ) ) )
          | ? [Vvar__1___24Anonymous__23103] :
              ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__23103)
              & ? [Vvar__2___24Anonymous__23104] :
                  ( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__2___24Anonymous__23104)
                  & ( 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__23103,Vvar__2___24Anonymous__23104)
                        & ( ? [Vvar__1___24Anonymous__23124] :
                              ( t(Vvar__1___24Anonymous__23124,V0__C)
                              & V4__P_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePc___24a2(V0__C,Vvar__1___24Anonymous__23124)
                              & cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,V3__P,V4__P_27) = cCoq_2eInit_2eDatatypes_2efalse )
                          | ? [Vvar__1___24Anonymous__23126] :
                              ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__23126)
                              & ? [Vvar__2___24Anonymous__23127] :
                                  ( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__2___24Anonymous__23127)
                                  & ( cType___24t(V0__C)
                                   => ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__23103)
                                     => ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__23126)
                                       => ( V4__P_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePinj___24a3(V0__C,Vvar__1___24Anonymous__23126,Vvar__2___24Anonymous__23127)
                                          & ( ( cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare___24a2(Vvar__1___24Anonymous__23103,Vvar__1___24Anonymous__23126) = 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__23104,Vvar__2___24Anonymous__23127) )
                                            | ( cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare___24a2(Vvar__1___24Anonymous__23103,Vvar__1___24Anonymous__23126) = 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__23103,Vvar__1___24Anonymous__23126) = 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__23132] :
                              ( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__1___24Anonymous__23132)
                              & ? [Vvar__2___24Anonymous__23133] :
                                  ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2___24Anonymous__23133)
                                  & ? [Vvar__3___24Anonymous__23134] :
                                      ( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__3___24Anonymous__23134)
                                      & V4__P_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePX___24a4(V0__C,Vvar__1___24Anonymous__23132,Vvar__2___24Anonymous__23133,Vvar__3___24Anonymous__23134)
                                      & cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,V3__P,V4__P_27) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ) ) ) ) )
          | ? [Vvar__1___24Anonymous__23139] :
              ( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__1___24Anonymous__23139)
              & ? [Vvar__2___24Anonymous__23140] :
                  ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2___24Anonymous__23140)
                  & ? [Vvar__3___24Anonymous__23141] :
                      ( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__3___24Anonymous__23141)
                      & ( 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__23139,Vvar__2___24Anonymous__23140,Vvar__3___24Anonymous__23141)
                            & ( ? [Vvar__1___24Anonymous__23174] :
                                  ( t(Vvar__1___24Anonymous__23174,V0__C)
                                  & V4__P_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePc___24a2(V0__C,Vvar__1___24Anonymous__23174)
                                  & cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,V3__P,V4__P_27) = cCoq_2eInit_2eDatatypes_2efalse )
                              | ? [Vvar__1___24Anonymous__23176] :
                                  ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__23176)
                                  & ? [Vvar__2___24Anonymous__23177] :
                                      ( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__2___24Anonymous__23177)
                                      & V4__P_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePinj___24a3(V0__C,Vvar__1___24Anonymous__23176,Vvar__2___24Anonymous__23177)
                                      & cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,V3__P,V4__P_27) = cCoq_2eInit_2eDatatypes_2efalse ) )
                              | ? [Vvar__1___24Anonymous__23180] :
                                  ( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__1___24Anonymous__23180)
                                  & ? [Vvar__2___24Anonymous__23181] :
                                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2___24Anonymous__23181)
                                      & ? [Vvar__3___24Anonymous__23182] :
                                          ( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__3___24Anonymous__23182)
                                          & ( cType___24t(V0__C)
                                           => ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2___24Anonymous__23140)
                                             => ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2___24Anonymous__23181)
                                               => ( V4__P_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePX___24a4(V0__C,Vvar__1___24Anonymous__23180,Vvar__2___24Anonymous__23181,Vvar__3___24Anonymous__23182)
                                                  & ( ( cType___24t(V0__C)
                                                     => ( c_24__type__4310___24t(V0__C,V1__ceqb)
                                                       => ( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__1___24Anonymous__23139)
                                                         => ( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__1___24Anonymous__23180)
                                                           => ( cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare___24a2(Vvar__2___24Anonymous__23140,Vvar__2___24Anonymous__23181) = cCoq_2eInit_2eDatatypes_2eEq
                                                              & ( ( cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,Vvar__1___24Anonymous__23139,Vvar__1___24Anonymous__23180) = 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__23141,Vvar__3___24Anonymous__23182) )
                                                                | ( cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,Vvar__1___24Anonymous__23139,Vvar__1___24Anonymous__23180) = 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__23140,Vvar__2___24Anonymous__23181) = 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__23140,Vvar__2___24Anonymous__23181) = 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__27077] :
              ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__27077)
              & V5__p = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__27077)
              & 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__27077),V4__x,Vvar__0___24Anonymous__27077) )
          | ? [Vvar__0___24Anonymous__27078] :
              ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__27078)
              & V5__p = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__27078)
              & 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__27078),V4__x,Vvar__0___24Anonymous__27078) )
          | ( 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__6440] :
              ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__6440)
              & V4__p = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__6440)
              & 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__6440) ) ) ) ) ).

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__27098] :
              ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__27098)
              & V4__i = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__27098)
              & 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__27099__27102___24a4(V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__27098)),c_24__let__var__6__p__27099__27102___24a4(V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__27098))) )
          | ? [Vvar__0___24Anonymous__27100] :
              ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__27100)
              & V4__i = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__27100)
              & 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__27101__27103___24a4(V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__27100)),c_24__let__var__6__p__27101__27103___24a4(V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__27100)) )
          | ( 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('$_discrim_Coq.Bool.Bool.ReflectT$Coq.Bool.Bool.ReflectF',axiom,
    ! [Vvar__0__P__10955,Vvar__1___24Anonymous__10956,Vvar__0__P__10957,Vvar__1___24Anonymous__10958] : cCoq_2eBool_2eBool_2eReflectT___24a1(Vvar__0__P__10955) != cCoq_2eBool_2eBool_2eReflectF___24a1(Vvar__0__P__10957) ).

fof('$_discrim_Coq.FSets.FSetPositive.PositiveSet.Leaf$Coq.FSets.FSetPositive.PositiveSet.Node',axiom,
    ! [Vvar__0___24Anonymous__25992,Vvar__1___24Anonymous__25993,Vvar__2___24Anonymous__25994] : cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eLeaf != cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eNode___24a3(Vvar__0___24Anonymous__25992,Vvar__1___24Anonymous__25993,Vvar__2___24Anonymous__25994) ).

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__12005,Vvar__1__Plt__12006,Vvar__2__Pgt__12007,Vvar__3___24Anonymous__12008,Vvar__0__Peq__12009,Vvar__1__Plt__12010,Vvar__2__Pgt__12011,Vvar__3___24Anonymous__12012] : cCoq_2eInit_2eDatatypes_2eCompEqT___24a3(Vvar__0__Peq__12005,Vvar__1__Plt__12006,Vvar__2__Pgt__12007) != cCoq_2eInit_2eDatatypes_2eCompLtT___24a3(Vvar__0__Peq__12009,Vvar__1__Plt__12010,Vvar__2__Pgt__12011) ).

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__32] : cCoq_2eInit_2eDatatypes_2eO != cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__32) ).

fof('$_discrim_Coq.Init.Datatypes.Some$Coq.Init.Datatypes.None',axiom,
    ! [Vvar__0__A__11811,Vvar__1___24Anonymous__11812,Vvar__0__A__11813] : cCoq_2eInit_2eDatatypes_2eSome___24a2(Vvar__0__A__11811,Vvar__1___24Anonymous__11812) != cCoq_2eInit_2eDatatypes_2eNone___24a1(Vvar__0__A__11813) ).

fof('$_discrim_Coq.Init.Datatypes.inl$Coq.Init.Datatypes.inr',axiom,
    ! [Vvar__0__A__11835,Vvar__1__B__11836,Vvar__2___24Anonymous__11837,Vvar__0__A__11838,Vvar__1__B__11839,Vvar__2___24Anonymous__11840] : cCoq_2eInit_2eDatatypes_2einl___24a3(Vvar__0__A__11835,Vvar__1__B__11836,Vvar__2___24Anonymous__11837) != cCoq_2eInit_2eDatatypes_2einr___24a3(Vvar__0__A__11838,Vvar__1__B__11839,Vvar__2___24Anonymous__11840) ).

fof('$_discrim_Coq.Init.Datatypes.nil$Coq.Init.Datatypes.cons',axiom,
    ! [Vvar__0__A__3244,Vvar__0__A__3245,Vvar__1___24Anonymous__3246,Vvar__2___24Anonymous__3247] : cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__3244) != cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__3245,Vvar__1___24Anonymous__3246,Vvar__2___24Anonymous__3247) ).

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__26124,Vvar__1__f__26125,Vvar__0__i__26126,Vvar__1__f__26127,Vvar__2__e__26128] : cCoq_2eInit_2eDecimal_2eDecimal___24a2(Vvar__0__i__26124,Vvar__1__f__26125) != cCoq_2eInit_2eDecimal_2eDecimalExp___24a3(Vvar__0__i__26126,Vvar__1__f__26127,Vvar__2__e__26128) ).

fof('$_discrim_Coq.Init.Decimal.Nil$Coq.Init.Decimal.D0',axiom,
    ! [Vvar__0___24Anonymous__12244] : cCoq_2eInit_2eDecimal_2eNil != cCoq_2eInit_2eDecimal_2eD0___24a1(Vvar__0___24Anonymous__12244) ).

fof('$_discrim_Coq.Init.Decimal.Pos$Coq.Init.Decimal.Neg',axiom,
    ! [Vvar__0__d__12270,Vvar__0__d__12271] : cCoq_2eInit_2eDecimal_2ePos___24a1(Vvar__0__d__12270) != cCoq_2eInit_2eDecimal_2eNeg___24a1(Vvar__0__d__12271) ).

fof('$_discrim_Coq.Init.Specif.inleft$Coq.Init.Specif.inright',axiom,
    ! [Vvar__0__A__28882,Vvar__1__B__28883,Vvar__2___24Anonymous__28884,Vvar__0__A__28885,Vvar__1__B__28886,Vvar__2___24Anonymous__28887] : cCoq_2eInit_2eSpecif_2einleft___24a3(Vvar__0__A__28882,Vvar__1__B__28883,Vvar__2___24Anonymous__28884) != cCoq_2eInit_2eSpecif_2einright___24a2(Vvar__0__A__28885,Vvar__1__B__28886) ).

fof('$_discrim_Coq.Init.Specif.left$Coq.Init.Specif.right',axiom,
    ! [Vvar__0__A__2605,Vvar__1__B__2606,Vvar__2___24Anonymous__2607,Vvar__0__A__2608,Vvar__1__B__2609,Vvar__2___24Anonymous__2610] : cCoq_2eInit_2eSpecif_2eleft___24a2(Vvar__0__A__2605,Vvar__1__B__2606) != cCoq_2eInit_2eSpecif_2eright___24a2(Vvar__0__A__2608,Vvar__1__B__2609) ).

fof('$_discrim_Coq.Numbers.BinNums.N0$Coq.Numbers.BinNums.Npos',axiom,
    ! [Vvar__0___24Anonymous__2583] : cCoq_2eNumbers_2eBinNums_2eN0 != cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__2583) ).

fof('$_discrim_Coq.Numbers.BinNums.Z0$Coq.Numbers.BinNums.Zpos',axiom,
    ! [Vvar__0___24Anonymous__1420] : cCoq_2eNumbers_2eBinNums_2eZ0 != cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__1420) ).

fof('$_discrim_Coq.Numbers.BinNums.xI$Coq.Numbers.BinNums.xO',axiom,
    ! [Vvar__0___24Anonymous__1408,Vvar__0___24Anonymous__1409] : cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__1408) != cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__1409) ).

fof('$_discrim_Coq.PArith.BinPos.Pos.PeanoOne$Coq.PArith.BinPos.Pos.PeanoSucc',axiom,
    ! [Vvar__0__p__29674,Vvar__1___24Anonymous__29675] : cCoq_2ePArith_2eBinPos_2ePos_2ePeanoOne != cCoq_2ePArith_2eBinPos_2ePos_2ePeanoSucc___24a2(Vvar__0__p__29674,Vvar__1___24Anonymous__29675) ).

fof('$_discrim_Coq.PArith.BinPosDef.Pos.IsNul$Coq.PArith.BinPosDef.Pos.IsPos',axiom,
    ! [Vvar__0___24Anonymous__25985] : cCoq_2ePArith_2eBinPosDef_2ePos_2eIsNul != cCoq_2ePArith_2eBinPosDef_2ePos_2eIsPos___24a1(Vvar__0___24Anonymous__25985) ).

fof('$_discrim_Coq.Reals.Rfunctions.ZintNull$Coq.Reals.Rfunctions.ZintPos',axiom,
    ! [Vvar__0__x__17110,Vvar__1___24Anonymous__17111,Vvar__0__x__17112,Vvar__1__n__17113,Vvar__2___24Anonymous__17114] : cCoq_2eReals_2eRfunctions_2eZintNull___24a1(Vvar__0__x__17110) != cCoq_2eReals_2eRfunctions_2eZintPos___24a2(Vvar__0__x__17112,Vvar__1__n__17113) ).

fof('$_discrim_Coq.Strings.String.EmptyString$Coq.Strings.String.String',axiom,
    ! [Vvar__0___24Anonymous__25976,Vvar__1___24Anonymous__25977] : cCoq_2eStrings_2eString_2eEmptyString != cCoq_2eStrings_2eString_2eString___24a2(Vvar__0___24Anonymous__25976,Vvar__1___24Anonymous__25977) ).

fof('$_discrim_Coq.Structures.OrderedType.LT$Coq.Structures.OrderedType.EQ',axiom,
    ! [Vvar__0__X__16378,Vvar__1__lt__16379,Vvar__2__eq__16380,Vvar__3__x__16381,Vvar__4__y__16382,Vvar__5___24Anonymous__16383,Vvar__0__X__16384,Vvar__1__lt__16385,Vvar__2__eq__16386,Vvar__3__x__16387,Vvar__4__y__16388,Vvar__5___24Anonymous__16389] : cCoq_2eStructures_2eOrderedType_2eLT___24a5(Vvar__0__X__16378,Vvar__1__lt__16379,Vvar__2__eq__16380,Vvar__3__x__16381,Vvar__4__y__16382) != cCoq_2eStructures_2eOrderedType_2eEQ___24a5(Vvar__0__X__16384,Vvar__1__lt__16385,Vvar__2__eq__16386,Vvar__3__x__16387,Vvar__4__y__16388) ).

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__14589,Vvar__0__n__14590,Vvar__1___24Anonymous__14591] : cCoq_2eVectors_2eFin_2eF1___24a1(Vvar__0__n__14589) != cCoq_2eVectors_2eFin_2eFS___24a2(Vvar__0__n__14590,Vvar__1___24Anonymous__14591) ).

fof('$_discrim_Coq.Vectors.VectorDef.nil$Coq.Vectors.VectorDef.cons',axiom,
    ! [Vvar__0__A__23996,Vvar__0__A__23997,Vvar__1__h__23998,Vvar__2__n__23999,Vvar__3___24Anonymous__24000] : cCoq_2eVectors_2eVectorDef_2enil___24a1(Vvar__0__A__23996) != cCoq_2eVectors_2eVectorDef_2econs___24a4(Vvar__0__A__23997,Vvar__1__h__23998,Vvar__2__n__23999,Vvar__3___24Anonymous__24000) ).

fof('$_discrim_Coq.micromega.EnvRing.PEc$Coq.micromega.EnvRing.PEX',axiom,
    ! [Vvar__0__C__25446,Vvar__1___24Anonymous__25447,Vvar__0__C__25448,Vvar__1___24Anonymous__25449] : cCoq_2emicromega_2eEnvRing_2ePEc___24a2(Vvar__0__C__25446,Vvar__1___24Anonymous__25447) != cCoq_2emicromega_2eEnvRing_2ePEX___24a2(Vvar__0__C__25448,Vvar__1___24Anonymous__25449) ).

fof('$_discrim_Coq.micromega.EnvRing.Pc$Coq.micromega.EnvRing.Pinj',axiom,
    ! [Vvar__0__C__12307,Vvar__1___24Anonymous__12308,Vvar__0__C__12309,Vvar__1___24Anonymous__12310,Vvar__2___24Anonymous__12311] : cCoq_2emicromega_2eEnvRing_2ePc___24a2(Vvar__0__C__12307,Vvar__1___24Anonymous__12308) != cCoq_2emicromega_2eEnvRing_2ePinj___24a3(Vvar__0__C__12309,Vvar__1___24Anonymous__12310,Vvar__2___24Anonymous__12311) ).

fof('$_discrim_Coq.micromega.EnvRing.mon0$Coq.micromega.EnvRing.zmon',axiom,
    ! [Vvar__0___24Anonymous__26158,Vvar__1___24Anonymous__26159] : cCoq_2emicromega_2eEnvRing_2emon0 != cCoq_2emicromega_2eEnvRing_2ezmon___24a2(Vvar__0___24Anonymous__26158,Vvar__1___24Anonymous__26159) ).

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__22683,Vvar__1___24Anonymous__22684,Vvar__0__C__22685,Vvar__1___24Anonymous__22686] : cCoq_2emicromega_2eRingMicromega_2ePsatzIn___24a2(Vvar__0__C__22683,Vvar__1___24Anonymous__22684) != cCoq_2emicromega_2eRingMicromega_2ePsatzSquare___24a2(Vvar__0__C__22685,Vvar__1___24Anonymous__22686) ).

fof('$_discrim_Coq.micromega.Tauto.TT$Coq.micromega.Tauto.FF',axiom,
    ! [Vvar__0__TA__29253,Vvar__1__TX__29254,Vvar__2__AA__29255,Vvar__3__AF__29256,Vvar__0__TA__29257,Vvar__1__TX__29258,Vvar__2__AA__29259,Vvar__3__AF__29260] : cCoq_2emicromega_2eTauto_2eTT___24a4(Vvar__0__TA__29253,Vvar__1__TX__29254,Vvar__2__AA__29255,Vvar__3__AF__29256) != cCoq_2emicromega_2eTauto_2eFF___24a4(Vvar__0__TA__29257,Vvar__1__TX__29258,Vvar__2__AA__29259,Vvar__3__AF__29260) ).

fof('$_discrim_Coq.micromega.VarMap.Empty$Coq.micromega.VarMap.Elt',axiom,
    ! [Vvar__0__A__29367,Vvar__0__A__29368,Vvar__1___24Anonymous__29369] : cCoq_2emicromega_2eVarMap_2eEmpty___24a1(Vvar__0__A__29367) != cCoq_2emicromega_2eVarMap_2eElt___24a2(Vvar__0__A__29368,Vvar__1___24Anonymous__29369) ).

fof('$_discrim_Coq.micromega.ZMicromega.DoneProof$Coq.micromega.ZMicromega.RatProof',axiom,
    ! [Vvar__0___24Anonymous__29411,Vvar__1___24Anonymous__29412] : cCoq_2emicromega_2eZMicromega_2eDoneProof != cCoq_2emicromega_2eZMicromega_2eRatProof___24a2(Vvar__0___24Anonymous__29411,Vvar__1___24Anonymous__29412) ).

fof('$_discrim_Coq.setoid_ring.Field_theory.FEO$Coq.setoid_ring.Field_theory.FEI',axiom,
    ! [Vvar__0__C__3601,Vvar__0__C__3602] : cCoq_2esetoid__ring_2eField__theory_2eFEO___24a1(Vvar__0__C__3601) != cCoq_2esetoid__ring_2eField__theory_2eFEI___24a1(Vvar__0__C__3602) ).

fof('$_discrim_Coq.setoid_ring.Ring_polynom.PEO$Coq.setoid_ring.Ring_polynom.PEI',axiom,
    ! [Vvar__0__C__5033,Vvar__0__C__5034] : cCoq_2esetoid__ring_2eRing__polynom_2ePEO___24a1(Vvar__0__C__5033) != cCoq_2esetoid__ring_2eRing__polynom_2ePEI___24a1(Vvar__0__C__5034) ).

fof('$_discrim_Coq.setoid_ring.Ring_polynom.Pc$Coq.setoid_ring.Ring_polynom.Pinj',axiom,
    ! [Vvar__0__C__4793,Vvar__1___24Anonymous__4794,Vvar__0__C__4795,Vvar__1___24Anonymous__4796,Vvar__2___24Anonymous__4797] : cCoq_2esetoid__ring_2eRing__polynom_2ePc___24a2(Vvar__0__C__4793,Vvar__1___24Anonymous__4794) != cCoq_2esetoid__ring_2eRing__polynom_2ePinj___24a3(Vvar__0__C__4795,Vvar__1___24Anonymous__4796,Vvar__2___24Anonymous__4797) ).

fof('$_discrim_Coq.setoid_ring.Ring_polynom.mon0$Coq.setoid_ring.Ring_polynom.zmon',axiom,
    ! [Vvar__0___24Anonymous__4843,Vvar__1___24Anonymous__4844] : cCoq_2esetoid__ring_2eRing__polynom_2emon0 != cCoq_2esetoid__ring_2eRing__polynom_2ezmon___24a2(Vvar__0___24Anonymous__4843,Vvar__1___24Anonymous__4844) ).

fof('$_discrim_Coq.setoid_ring.Ring_theory.Abstract$Coq.setoid_ring.Ring_theory.Computational',axiom,
    ! [Vvar__0__R__28541,Vvar__1__req__28542,Vvar__2__reqb__28543,Vvar__3___24Anonymous__28544] : cCoq_2esetoid__ring_2eRing__theory_2eAbstract != cCoq_2esetoid__ring_2eRing__theory_2eComputational___24a3(Vvar__0__R__28541,Vvar__1__req__28542,Vvar__2__reqb__28543) ).

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

fof('$_fix_29669_v_CANONICAL_0',axiom,
    ! [Vv__CANONICAL__1] :
      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__1)
     => ( ? [Vvar__0___24Anonymous__29670] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__29670)
            & Vv__CANONICAL__1 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__29670)
            & c_24__fix__29669__v__CANONICAL__0___24a1(Vv__CANONICAL__1) = cCoq_2eNumbers_2eBinNums_2exO___24a1(c_24__fix__29669__v__CANONICAL__0___24a1(Vvar__0___24Anonymous__29670)) )
        | ? [Vvar__0___24Anonymous__29671] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__29671)
            & Vv__CANONICAL__1 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__29671)
            & c_24__fix__29669__v__CANONICAL__0___24a1(Vv__CANONICAL__1) = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__29671) )
        | ( Vv__CANONICAL__1 = cCoq_2eNumbers_2eBinNums_2exH
          & c_24__fix__29669__v__CANONICAL__0___24a1(Vv__CANONICAL__1) = cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2eNumbers_2eBinNums_2exH) ) ) ) ).

fof('$_fix_31684_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__31684__v__CANONICAL__1___24a3(Vv__CANONICAL__0,Vv__CANONICAL__2,Vv__CANONICAL__3) = Vv__CANONICAL__3 )
          | ? [Vvar__1___24Anonymous__31688] :
              ( t(Vvar__1___24Anonymous__31688,Vv__CANONICAL__0)
              & ? [Vvar__2___24Anonymous__31689] :
                  ( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vvar__2___24Anonymous__31689)
                  & Vv__CANONICAL__2 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vv__CANONICAL__0,Vvar__1___24Anonymous__31688,Vvar__2___24Anonymous__31689)
                  & c_24__fix__31684__v__CANONICAL__1___24a3(Vv__CANONICAL__0,Vv__CANONICAL__2,Vv__CANONICAL__3) = cCoq_2eInit_2eDatatypes_2econs___24a3(Vv__CANONICAL__0,Vvar__1___24Anonymous__31688,c_24__fix__31684__v__CANONICAL__1___24a3(Vv__CANONICAL__0,Vvar__2___24Anonymous__31689,Vv__CANONICAL__3)) ) ) ) ) ) ).

fof('$_inj_Coq.Bool.Bool.ReflectF',axiom,
    ! [Vvar__0__P__10963,Vvar__0__P__10964,Vvar__1___24Anonymous__10965,Vvar__1___24Anonymous__10966] :
      ( cCoq_2eBool_2eBool_2eReflectF___24a1(Vvar__0__P__10963) = cCoq_2eBool_2eBool_2eReflectF___24a1(Vvar__0__P__10964)
     => ( c_24Proof = c_24Proof
        & Vvar__0__P__10963 = Vvar__0__P__10964 ) ) ).

fof('$_inj_Coq.Bool.Bool.ReflectT',axiom,
    ! [Vvar__0__P__10959,Vvar__0__P__10960,Vvar__1___24Anonymous__10961,Vvar__1___24Anonymous__10962] :
      ( cCoq_2eBool_2eBool_2eReflectT___24a1(Vvar__0__P__10959) = cCoq_2eBool_2eBool_2eReflectT___24a1(Vvar__0__P__10960)
     => ( c_24Proof = c_24Proof
        & Vvar__0__P__10959 = Vvar__0__P__10960 ) ) ).

fof('$_inj_Coq.FSets.FSetPositive.PositiveSet.Node',axiom,
    ! [Vvar__0___24Anonymous__25995,Vvar__0___24Anonymous__25996,Vvar__1___24Anonymous__25997,Vvar__1___24Anonymous__25998,Vvar__2___24Anonymous__25999,Vvar__2___24Anonymous__26000] :
      ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eNode___24a3(Vvar__0___24Anonymous__25995,Vvar__1___24Anonymous__25997,Vvar__2___24Anonymous__25999) = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eNode___24a3(Vvar__0___24Anonymous__25996,Vvar__1___24Anonymous__25998,Vvar__2___24Anonymous__26000)
     => ( Vvar__2___24Anonymous__25999 = Vvar__2___24Anonymous__26000
        & Vvar__1___24Anonymous__25997 = Vvar__1___24Anonymous__25998
        & Vvar__0___24Anonymous__25995 = Vvar__0___24Anonymous__25996 ) ) ).

fof('$_inj_Coq.Init.Datatypes.CompEqT',axiom,
    ! [Vvar__0__Peq__12013,Vvar__0__Peq__12014,Vvar__1__Plt__12015,Vvar__1__Plt__12016,Vvar__2__Pgt__12017,Vvar__2__Pgt__12018,Vvar__3___24Anonymous__12019,Vvar__3___24Anonymous__12020] :
      ( cCoq_2eInit_2eDatatypes_2eCompEqT___24a3(Vvar__0__Peq__12013,Vvar__1__Plt__12015,Vvar__2__Pgt__12017) = cCoq_2eInit_2eDatatypes_2eCompEqT___24a3(Vvar__0__Peq__12014,Vvar__1__Plt__12016,Vvar__2__Pgt__12018)
     => ( c_24Proof = c_24Proof
        & Vvar__2__Pgt__12017 = Vvar__2__Pgt__12018
        & Vvar__1__Plt__12015 = Vvar__1__Plt__12016
        & Vvar__0__Peq__12013 = Vvar__0__Peq__12014 ) ) ).

fof('$_inj_Coq.Init.Datatypes.CompGtT',axiom,
    ! [Vvar__0__Peq__12029,Vvar__0__Peq__12030,Vvar__1__Plt__12031,Vvar__1__Plt__12032,Vvar__2__Pgt__12033,Vvar__2__Pgt__12034,Vvar__3___24Anonymous__12035,Vvar__3___24Anonymous__12036] :
      ( cCoq_2eInit_2eDatatypes_2eCompGtT___24a3(Vvar__0__Peq__12029,Vvar__1__Plt__12031,Vvar__2__Pgt__12033) = cCoq_2eInit_2eDatatypes_2eCompGtT___24a3(Vvar__0__Peq__12030,Vvar__1__Plt__12032,Vvar__2__Pgt__12034)
     => ( c_24Proof = c_24Proof
        & Vvar__2__Pgt__12033 = Vvar__2__Pgt__12034
        & Vvar__1__Plt__12031 = Vvar__1__Plt__12032
        & Vvar__0__Peq__12029 = Vvar__0__Peq__12030 ) ) ).

fof('$_inj_Coq.Init.Datatypes.CompLtT',axiom,
    ! [Vvar__0__Peq__12021,Vvar__0__Peq__12022,Vvar__1__Plt__12023,Vvar__1__Plt__12024,Vvar__2__Pgt__12025,Vvar__2__Pgt__12026,Vvar__3___24Anonymous__12027,Vvar__3___24Anonymous__12028] :
      ( cCoq_2eInit_2eDatatypes_2eCompLtT___24a3(Vvar__0__Peq__12021,Vvar__1__Plt__12023,Vvar__2__Pgt__12025) = cCoq_2eInit_2eDatatypes_2eCompLtT___24a3(Vvar__0__Peq__12022,Vvar__1__Plt__12024,Vvar__2__Pgt__12026)
     => ( c_24Proof = c_24Proof
        & Vvar__2__Pgt__12025 = Vvar__2__Pgt__12026
        & Vvar__1__Plt__12023 = Vvar__1__Plt__12024
        & Vvar__0__Peq__12021 = Vvar__0__Peq__12022 ) ) ).

fof('$_inj_Coq.Init.Datatypes.None',axiom,
    ! [Vvar__0__A__11818,Vvar__0__A__11819] :
      ( cCoq_2eInit_2eDatatypes_2eNone___24a1(Vvar__0__A__11818) = cCoq_2eInit_2eDatatypes_2eNone___24a1(Vvar__0__A__11819)
     => Vvar__0__A__11818 = Vvar__0__A__11819 ) ).

fof('$_inj_Coq.Init.Datatypes.S',axiom,
    ! [Vvar__0___24Anonymous__33,Vvar__0___24Anonymous__34] :
      ( cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__33) = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__34)
     => Vvar__0___24Anonymous__33 = Vvar__0___24Anonymous__34 ) ).

fof('$_inj_Coq.Init.Datatypes.Some',axiom,
    ! [Vvar__0__A__11814,Vvar__0__A__11815,Vvar__1___24Anonymous__11816,Vvar__1___24Anonymous__11817] :
      ( cCoq_2eInit_2eDatatypes_2eSome___24a2(Vvar__0__A__11814,Vvar__1___24Anonymous__11816) = cCoq_2eInit_2eDatatypes_2eSome___24a2(Vvar__0__A__11815,Vvar__1___24Anonymous__11817)
     => ( Vvar__1___24Anonymous__11816 = Vvar__1___24Anonymous__11817
        & Vvar__0__A__11814 = Vvar__0__A__11815 ) ) ).

fof('$_inj_Coq.Init.Datatypes.cons',axiom,
    ! [Vvar__0__A__3250,Vvar__0__A__3251,Vvar__1___24Anonymous__3252,Vvar__1___24Anonymous__3253,Vvar__2___24Anonymous__3254,Vvar__2___24Anonymous__3255] :
      ( cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__3250,Vvar__1___24Anonymous__3252,Vvar__2___24Anonymous__3254) = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__3251,Vvar__1___24Anonymous__3253,Vvar__2___24Anonymous__3255)
     => ( Vvar__2___24Anonymous__3254 = Vvar__2___24Anonymous__3255
        & Vvar__1___24Anonymous__3252 = Vvar__1___24Anonymous__3253
        & Vvar__0__A__3250 = Vvar__0__A__3251 ) ) ).

fof('$_inj_Coq.Init.Datatypes.inl',axiom,
    ! [Vvar__0__A__11841,Vvar__0__A__11842,Vvar__1__B__11843,Vvar__1__B__11844,Vvar__2___24Anonymous__11845,Vvar__2___24Anonymous__11846] :
      ( cCoq_2eInit_2eDatatypes_2einl___24a3(Vvar__0__A__11841,Vvar__1__B__11843,Vvar__2___24Anonymous__11845) = cCoq_2eInit_2eDatatypes_2einl___24a3(Vvar__0__A__11842,Vvar__1__B__11844,Vvar__2___24Anonymous__11846)
     => ( Vvar__2___24Anonymous__11845 = Vvar__2___24Anonymous__11846
        & Vvar__1__B__11843 = Vvar__1__B__11844
        & Vvar__0__A__11841 = Vvar__0__A__11842 ) ) ).

fof('$_inj_Coq.Init.Datatypes.inr',axiom,
    ! [Vvar__0__A__11847,Vvar__0__A__11848,Vvar__1__B__11849,Vvar__1__B__11850,Vvar__2___24Anonymous__11851,Vvar__2___24Anonymous__11852] :
      ( cCoq_2eInit_2eDatatypes_2einr___24a3(Vvar__0__A__11847,Vvar__1__B__11849,Vvar__2___24Anonymous__11851) = cCoq_2eInit_2eDatatypes_2einr___24a3(Vvar__0__A__11848,Vvar__1__B__11850,Vvar__2___24Anonymous__11852)
     => ( Vvar__2___24Anonymous__11851 = Vvar__2___24Anonymous__11852
        & Vvar__1__B__11849 = Vvar__1__B__11850
        & Vvar__0__A__11847 = Vvar__0__A__11848 ) ) ).

fof('$_inj_Coq.Init.Datatypes.nil',axiom,
    ! [Vvar__0__A__3248,Vvar__0__A__3249] :
      ( cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__3248) = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__3249)
     => Vvar__0__A__3248 = Vvar__0__A__3249 ) ).

fof('$_inj_Coq.Init.Datatypes.pair',axiom,
    ! [Vvar__0__A__49,Vvar__0__A__50,Vvar__1__B__51,Vvar__1__B__52,Vvar__2___24Anonymous__53,Vvar__2___24Anonymous__54,Vvar__3___24Anonymous__55,Vvar__3___24Anonymous__56] :
      ( cCoq_2eInit_2eDatatypes_2epair___24a4(Vvar__0__A__49,Vvar__1__B__51,Vvar__2___24Anonymous__53,Vvar__3___24Anonymous__55) = cCoq_2eInit_2eDatatypes_2epair___24a4(Vvar__0__A__50,Vvar__1__B__52,Vvar__2___24Anonymous__54,Vvar__3___24Anonymous__56)
     => ( Vvar__3___24Anonymous__55 = Vvar__3___24Anonymous__56
        & Vvar__2___24Anonymous__53 = Vvar__2___24Anonymous__54
        & Vvar__1__B__51 = Vvar__1__B__52
        & Vvar__0__A__49 = Vvar__0__A__50 ) ) ).

fof('$_inj_Coq.Init.Decimal.D0',axiom,
    ! [Vvar__0___24Anonymous__12245,Vvar__0___24Anonymous__12246] :
      ( cCoq_2eInit_2eDecimal_2eD0___24a1(Vvar__0___24Anonymous__12245) = cCoq_2eInit_2eDecimal_2eD0___24a1(Vvar__0___24Anonymous__12246)
     => Vvar__0___24Anonymous__12245 = Vvar__0___24Anonymous__12246 ) ).

fof('$_inj_Coq.Init.Decimal.D1',axiom,
    ! [Vvar__0___24Anonymous__12247,Vvar__0___24Anonymous__12248] :
      ( cCoq_2eInit_2eDecimal_2eD1___24a1(Vvar__0___24Anonymous__12247) = cCoq_2eInit_2eDecimal_2eD1___24a1(Vvar__0___24Anonymous__12248)
     => Vvar__0___24Anonymous__12247 = Vvar__0___24Anonymous__12248 ) ).

fof('$_inj_Coq.Init.Decimal.D2',axiom,
    ! [Vvar__0___24Anonymous__12249,Vvar__0___24Anonymous__12250] :
      ( cCoq_2eInit_2eDecimal_2eD2___24a1(Vvar__0___24Anonymous__12249) = cCoq_2eInit_2eDecimal_2eD2___24a1(Vvar__0___24Anonymous__12250)
     => Vvar__0___24Anonymous__12249 = Vvar__0___24Anonymous__12250 ) ).

fof('$_inj_Coq.Init.Decimal.D3',axiom,
    ! [Vvar__0___24Anonymous__12251,Vvar__0___24Anonymous__12252] :
      ( cCoq_2eInit_2eDecimal_2eD3___24a1(Vvar__0___24Anonymous__12251) = cCoq_2eInit_2eDecimal_2eD3___24a1(Vvar__0___24Anonymous__12252)
     => Vvar__0___24Anonymous__12251 = Vvar__0___24Anonymous__12252 ) ).

fof('$_inj_Coq.Init.Decimal.D4',axiom,
    ! [Vvar__0___24Anonymous__12253,Vvar__0___24Anonymous__12254] :
      ( cCoq_2eInit_2eDecimal_2eD4___24a1(Vvar__0___24Anonymous__12253) = cCoq_2eInit_2eDecimal_2eD4___24a1(Vvar__0___24Anonymous__12254)
     => Vvar__0___24Anonymous__12253 = Vvar__0___24Anonymous__12254 ) ).

fof('$_inj_Coq.Init.Decimal.D5',axiom,
    ! [Vvar__0___24Anonymous__12255,Vvar__0___24Anonymous__12256] :
      ( cCoq_2eInit_2eDecimal_2eD5___24a1(Vvar__0___24Anonymous__12255) = cCoq_2eInit_2eDecimal_2eD5___24a1(Vvar__0___24Anonymous__12256)
     => Vvar__0___24Anonymous__12255 = Vvar__0___24Anonymous__12256 ) ).

fof('$_inj_Coq.Init.Decimal.D6',axiom,
    ! [Vvar__0___24Anonymous__12257,Vvar__0___24Anonymous__12258] :
      ( cCoq_2eInit_2eDecimal_2eD6___24a1(Vvar__0___24Anonymous__12257) = cCoq_2eInit_2eDecimal_2eD6___24a1(Vvar__0___24Anonymous__12258)
     => Vvar__0___24Anonymous__12257 = Vvar__0___24Anonymous__12258 ) ).

fof('$_inj_Coq.Init.Decimal.D7',axiom,
    ! [Vvar__0___24Anonymous__12259,Vvar__0___24Anonymous__12260] :
      ( cCoq_2eInit_2eDecimal_2eD7___24a1(Vvar__0___24Anonymous__12259) = cCoq_2eInit_2eDecimal_2eD7___24a1(Vvar__0___24Anonymous__12260)
     => Vvar__0___24Anonymous__12259 = Vvar__0___24Anonymous__12260 ) ).

fof('$_inj_Coq.Init.Decimal.D8',axiom,
    ! [Vvar__0___24Anonymous__12261,Vvar__0___24Anonymous__12262] :
      ( cCoq_2eInit_2eDecimal_2eD8___24a1(Vvar__0___24Anonymous__12261) = cCoq_2eInit_2eDecimal_2eD8___24a1(Vvar__0___24Anonymous__12262)
     => Vvar__0___24Anonymous__12261 = Vvar__0___24Anonymous__12262 ) ).

fof('$_inj_Coq.Init.Decimal.D9',axiom,
    ! [Vvar__0___24Anonymous__12263,Vvar__0___24Anonymous__12264] :
      ( cCoq_2eInit_2eDecimal_2eD9___24a1(Vvar__0___24Anonymous__12263) = cCoq_2eInit_2eDecimal_2eD9___24a1(Vvar__0___24Anonymous__12264)
     => Vvar__0___24Anonymous__12263 = Vvar__0___24Anonymous__12264 ) ).

fof('$_inj_Coq.Init.Decimal.Decimal',axiom,
    ! [Vvar__0__i__26129,Vvar__0__i__26130,Vvar__1__f__26131,Vvar__1__f__26132] :
      ( cCoq_2eInit_2eDecimal_2eDecimal___24a2(Vvar__0__i__26129,Vvar__1__f__26131) = cCoq_2eInit_2eDecimal_2eDecimal___24a2(Vvar__0__i__26130,Vvar__1__f__26132)
     => ( Vvar__1__f__26131 = Vvar__1__f__26132
        & Vvar__0__i__26129 = Vvar__0__i__26130 ) ) ).

fof('$_inj_Coq.Init.Decimal.DecimalExp',axiom,
    ! [Vvar__0__i__26133,Vvar__0__i__26134,Vvar__1__f__26135,Vvar__1__f__26136,Vvar__2__e__26137,Vvar__2__e__26138] :
      ( cCoq_2eInit_2eDecimal_2eDecimalExp___24a3(Vvar__0__i__26133,Vvar__1__f__26135,Vvar__2__e__26137) = cCoq_2eInit_2eDecimal_2eDecimalExp___24a3(Vvar__0__i__26134,Vvar__1__f__26136,Vvar__2__e__26138)
     => ( Vvar__2__e__26137 = Vvar__2__e__26138
        & Vvar__1__f__26135 = Vvar__1__f__26136
        & Vvar__0__i__26133 = Vvar__0__i__26134 ) ) ).

fof('$_inj_Coq.Init.Decimal.Neg',axiom,
    ! [Vvar__0__d__12274,Vvar__0__d__12275] :
      ( cCoq_2eInit_2eDecimal_2eNeg___24a1(Vvar__0__d__12274) = cCoq_2eInit_2eDecimal_2eNeg___24a1(Vvar__0__d__12275)
     => Vvar__0__d__12274 = Vvar__0__d__12275 ) ).

fof('$_inj_Coq.Init.Decimal.Pos',axiom,
    ! [Vvar__0__d__12272,Vvar__0__d__12273] :
      ( cCoq_2eInit_2eDecimal_2ePos___24a1(Vvar__0__d__12272) = cCoq_2eInit_2eDecimal_2ePos___24a1(Vvar__0__d__12273)
     => Vvar__0__d__12272 = Vvar__0__d__12273 ) ).

fof('$_inj_Coq.Init.Specif.exist',axiom,
    ! [Vvar__0__A__23545,Vvar__0__A__23546,Vvar__1__P__23547,Vvar__1__P__23548,Vvar__2__x__23549,Vvar__2__x__23550,Vvar__3___24Anonymous__23551,Vvar__3___24Anonymous__23552] :
      ( cCoq_2eInit_2eSpecif_2eexist___24a3(Vvar__0__A__23545,Vvar__1__P__23547,Vvar__2__x__23549) = cCoq_2eInit_2eSpecif_2eexist___24a3(Vvar__0__A__23546,Vvar__1__P__23548,Vvar__2__x__23550)
     => ( c_24Proof = c_24Proof
        & Vvar__2__x__23549 = Vvar__2__x__23550
        & Vvar__1__P__23547 = Vvar__1__P__23548
        & Vvar__0__A__23545 = Vvar__0__A__23546 ) ) ).

fof('$_inj_Coq.Init.Specif.exist2',axiom,
    ! [Vvar__0__A__28802,Vvar__0__A__28803,Vvar__1__P__28804,Vvar__1__P__28805,Vvar__2__Q__28806,Vvar__2__Q__28807,Vvar__3__x__28808,Vvar__3__x__28809,Vvar__4___24Anonymous__28810,Vvar__4___24Anonymous__28811,Vvar__5___24Anonymous__28812,Vvar__5___24Anonymous__28813] :
      ( cCoq_2eInit_2eSpecif_2eexist2___24a4(Vvar__0__A__28802,Vvar__1__P__28804,Vvar__2__Q__28806,Vvar__3__x__28808) = cCoq_2eInit_2eSpecif_2eexist2___24a4(Vvar__0__A__28803,Vvar__1__P__28805,Vvar__2__Q__28807,Vvar__3__x__28809)
     => ( c_24Proof = c_24Proof
        & c_24Proof = c_24Proof
        & Vvar__3__x__28808 = Vvar__3__x__28809
        & Vvar__2__Q__28806 = Vvar__2__Q__28807
        & Vvar__1__P__28804 = Vvar__1__P__28805
        & Vvar__0__A__28802 = Vvar__0__A__28803 ) ) ).

fof('$_inj_Coq.Init.Specif.existT',axiom,
    ! [Vvar__0__A__23584,Vvar__0__A__23585,Vvar__1__P__23586,Vvar__1__P__23587,Vvar__2__x__23588,Vvar__2__x__23589,Vvar__3___24Anonymous__23590,Vvar__3___24Anonymous__23591] :
      ( cCoq_2eInit_2eSpecif_2eexistT___24a4(Vvar__0__A__23584,Vvar__1__P__23586,Vvar__2__x__23588,Vvar__3___24Anonymous__23590) = cCoq_2eInit_2eSpecif_2eexistT___24a4(Vvar__0__A__23585,Vvar__1__P__23587,Vvar__2__x__23589,Vvar__3___24Anonymous__23591)
     => ( Vvar__3___24Anonymous__23590 = Vvar__3___24Anonymous__23591
        & Vvar__2__x__23588 = Vvar__2__x__23589
        & Vvar__1__P__23586 = Vvar__1__P__23587
        & Vvar__0__A__23584 = Vvar__0__A__23585 ) ) ).

fof('$_inj_Coq.Init.Specif.existT2',axiom,
    ! [Vvar__0__A__28858,Vvar__0__A__28859,Vvar__1__P__28860,Vvar__1__P__28861,Vvar__2__Q__28862,Vvar__2__Q__28863,Vvar__3__x__28864,Vvar__3__x__28865,Vvar__4___24Anonymous__28866,Vvar__4___24Anonymous__28867,Vvar__5___24Anonymous__28868,Vvar__5___24Anonymous__28869] :
      ( cCoq_2eInit_2eSpecif_2eexistT2___24a6(Vvar__0__A__28858,Vvar__1__P__28860,Vvar__2__Q__28862,Vvar__3__x__28864,Vvar__4___24Anonymous__28866,Vvar__5___24Anonymous__28868) = cCoq_2eInit_2eSpecif_2eexistT2___24a6(Vvar__0__A__28859,Vvar__1__P__28861,Vvar__2__Q__28863,Vvar__3__x__28865,Vvar__4___24Anonymous__28867,Vvar__5___24Anonymous__28869)
     => ( Vvar__5___24Anonymous__28868 = Vvar__5___24Anonymous__28869
        & Vvar__4___24Anonymous__28866 = Vvar__4___24Anonymous__28867
        & Vvar__3__x__28864 = Vvar__3__x__28865
        & Vvar__2__Q__28862 = Vvar__2__Q__28863
        & Vvar__1__P__28860 = Vvar__1__P__28861
        & Vvar__0__A__28858 = Vvar__0__A__28859 ) ) ).

fof('$_inj_Coq.Init.Specif.inleft',axiom,
    ! [Vvar__0__A__28888,Vvar__0__A__28889,Vvar__1__B__28890,Vvar__1__B__28891,Vvar__2___24Anonymous__28892,Vvar__2___24Anonymous__28893] :
      ( cCoq_2eInit_2eSpecif_2einleft___24a3(Vvar__0__A__28888,Vvar__1__B__28890,Vvar__2___24Anonymous__28892) = cCoq_2eInit_2eSpecif_2einleft___24a3(Vvar__0__A__28889,Vvar__1__B__28891,Vvar__2___24Anonymous__28893)
     => ( Vvar__2___24Anonymous__28892 = Vvar__2___24Anonymous__28893
        & Vvar__1__B__28890 = Vvar__1__B__28891
        & Vvar__0__A__28888 = Vvar__0__A__28889 ) ) ).

fof('$_inj_Coq.Init.Specif.inright',axiom,
    ! [Vvar__0__A__28894,Vvar__0__A__28895,Vvar__1__B__28896,Vvar__1__B__28897,Vvar__2___24Anonymous__28898,Vvar__2___24Anonymous__28899] :
      ( cCoq_2eInit_2eSpecif_2einright___24a2(Vvar__0__A__28894,Vvar__1__B__28896) = cCoq_2eInit_2eSpecif_2einright___24a2(Vvar__0__A__28895,Vvar__1__B__28897)
     => ( c_24Proof = c_24Proof
        & Vvar__1__B__28896 = Vvar__1__B__28897
        & Vvar__0__A__28894 = Vvar__0__A__28895 ) ) ).

fof('$_inj_Coq.Init.Specif.left',axiom,
    ! [Vvar__0__A__2611,Vvar__0__A__2612,Vvar__1__B__2613,Vvar__1__B__2614,Vvar__2___24Anonymous__2615,Vvar__2___24Anonymous__2616] :
      ( cCoq_2eInit_2eSpecif_2eleft___24a2(Vvar__0__A__2611,Vvar__1__B__2613) = cCoq_2eInit_2eSpecif_2eleft___24a2(Vvar__0__A__2612,Vvar__1__B__2614)
     => ( c_24Proof = c_24Proof
        & Vvar__1__B__2613 = Vvar__1__B__2614
        & Vvar__0__A__2611 = Vvar__0__A__2612 ) ) ).

fof('$_inj_Coq.Init.Specif.right',axiom,
    ! [Vvar__0__A__2617,Vvar__0__A__2618,Vvar__1__B__2619,Vvar__1__B__2620,Vvar__2___24Anonymous__2621,Vvar__2___24Anonymous__2622] :
      ( cCoq_2eInit_2eSpecif_2eright___24a2(Vvar__0__A__2617,Vvar__1__B__2619) = cCoq_2eInit_2eSpecif_2eright___24a2(Vvar__0__A__2618,Vvar__1__B__2620)
     => ( c_24Proof = c_24Proof
        & Vvar__1__B__2619 = Vvar__1__B__2620
        & Vvar__0__A__2617 = Vvar__0__A__2618 ) ) ).

fof('$_inj_Coq.Numbers.BinNums.Npos',axiom,
    ! [Vvar__0___24Anonymous__2584,Vvar__0___24Anonymous__2585] :
      ( cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__2584) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__2585)
     => Vvar__0___24Anonymous__2584 = Vvar__0___24Anonymous__2585 ) ).

fof('$_inj_Coq.Numbers.BinNums.Zneg',axiom,
    ! [Vvar__0___24Anonymous__1423,Vvar__0___24Anonymous__1424] :
      ( cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__1423) = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__1424)
     => Vvar__0___24Anonymous__1423 = Vvar__0___24Anonymous__1424 ) ).

fof('$_inj_Coq.Numbers.BinNums.Zpos',axiom,
    ! [Vvar__0___24Anonymous__1421,Vvar__0___24Anonymous__1422] :
      ( cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__1421) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__1422)
     => Vvar__0___24Anonymous__1421 = Vvar__0___24Anonymous__1422 ) ).

fof('$_inj_Coq.Numbers.BinNums.xI',axiom,
    ! [Vvar__0___24Anonymous__1410,Vvar__0___24Anonymous__1411] :
      ( cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__1410) = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__1411)
     => Vvar__0___24Anonymous__1410 = Vvar__0___24Anonymous__1411 ) ).

fof('$_inj_Coq.Numbers.BinNums.xO',axiom,
    ! [Vvar__0___24Anonymous__1412,Vvar__0___24Anonymous__1413] :
      ( cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__1412) = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__1413)
     => Vvar__0___24Anonymous__1412 = Vvar__0___24Anonymous__1413 ) ).

fof('$_inj_Coq.PArith.BinPos.Pos.PeanoSucc',axiom,
    ! [Vvar__0__p__29676,Vvar__0__p__29677,Vvar__1___24Anonymous__29678,Vvar__1___24Anonymous__29679] :
      ( cCoq_2ePArith_2eBinPos_2ePos_2ePeanoSucc___24a2(Vvar__0__p__29676,Vvar__1___24Anonymous__29678) = cCoq_2ePArith_2eBinPos_2ePos_2ePeanoSucc___24a2(Vvar__0__p__29677,Vvar__1___24Anonymous__29679)
     => ( Vvar__1___24Anonymous__29678 = Vvar__1___24Anonymous__29679
        & Vvar__0__p__29676 = Vvar__0__p__29677 ) ) ).

fof('$_inj_Coq.PArith.BinPosDef.Pos.IsPos',axiom,
    ! [Vvar__0___24Anonymous__25986,Vvar__0___24Anonymous__25987] :
      ( cCoq_2ePArith_2eBinPosDef_2ePos_2eIsPos___24a1(Vvar__0___24Anonymous__25986) = cCoq_2ePArith_2eBinPosDef_2ePos_2eIsPos___24a1(Vvar__0___24Anonymous__25987)
     => Vvar__0___24Anonymous__25986 = Vvar__0___24Anonymous__25987 ) ).

fof('$_inj_Coq.QArith.QArith_base.Qmake',axiom,
    ! [Vvar__0__Qnum__16465,Vvar__0__Qnum__16466,Vvar__1__Qden__16467,Vvar__1__Qden__16468] :
      ( cCoq_2eQArith_2eQArith__base_2eQmake___24a2(Vvar__0__Qnum__16465,Vvar__1__Qden__16467) = cCoq_2eQArith_2eQArith__base_2eQmake___24a2(Vvar__0__Qnum__16466,Vvar__1__Qden__16468)
     => ( Vvar__1__Qden__16467 = Vvar__1__Qden__16468
        & Vvar__0__Qnum__16465 = Vvar__0__Qnum__16466 ) ) ).

fof('$_inj_Coq.Reals.RIneq.mknegreal',axiom,
    ! [Vvar__0__neg__27059,Vvar__0__neg__27060,Vvar__1__cond__neg__27061,Vvar__1__cond__neg__27062] :
      ( cCoq_2eReals_2eRIneq_2emknegreal___24a1(Vvar__0__neg__27059) = cCoq_2eReals_2eRIneq_2emknegreal___24a1(Vvar__0__neg__27060)
     => ( c_24Proof = c_24Proof
        & Vvar__0__neg__27059 = Vvar__0__neg__27060 ) ) ).

fof('$_inj_Coq.Reals.RIneq.mknonnegreal',axiom,
    ! [Vvar__0__nonneg__27045,Vvar__0__nonneg__27046,Vvar__1__cond__nonneg__27047,Vvar__1__cond__nonneg__27048] :
      ( cCoq_2eReals_2eRIneq_2emknonnegreal___24a1(Vvar__0__nonneg__27045) = cCoq_2eReals_2eRIneq_2emknonnegreal___24a1(Vvar__0__nonneg__27046)
     => ( c_24Proof = c_24Proof
        & Vvar__0__nonneg__27045 = Vvar__0__nonneg__27046 ) ) ).

fof('$_inj_Coq.Reals.RIneq.mknonposreal',axiom,
    ! [Vvar__0__nonpos__16532,Vvar__0__nonpos__16533,Vvar__1__cond__nonpos__16534,Vvar__1__cond__nonpos__16535] :
      ( cCoq_2eReals_2eRIneq_2emknonposreal___24a1(Vvar__0__nonpos__16532) = cCoq_2eReals_2eRIneq_2emknonposreal___24a1(Vvar__0__nonpos__16533)
     => ( c_24Proof = c_24Proof
        & Vvar__0__nonpos__16532 = Vvar__0__nonpos__16533 ) ) ).

fof('$_inj_Coq.Reals.RIneq.mknonzeroreal',axiom,
    ! [Vvar__0__nonzero__27066,Vvar__0__nonzero__27067,Vvar__1__cond__nonzero__27068,Vvar__1__cond__nonzero__27069] :
      ( cCoq_2eReals_2eRIneq_2emknonzeroreal___24a1(Vvar__0__nonzero__27066) = cCoq_2eReals_2eRIneq_2emknonzeroreal___24a1(Vvar__0__nonzero__27067)
     => ( c_24Proof = c_24Proof
        & Vvar__0__nonzero__27066 = Vvar__0__nonzero__27067 ) ) ).

fof('$_inj_Coq.Reals.RIneq.mkposreal',axiom,
    ! [Vvar__0__pos__27052,Vvar__0__pos__27053,Vvar__1__cond__pos__27054,Vvar__1__cond__pos__27055] :
      ( cCoq_2eReals_2eRIneq_2emkposreal___24a1(Vvar__0__pos__27052) = cCoq_2eReals_2eRIneq_2emkposreal___24a1(Vvar__0__pos__27053)
     => ( c_24Proof = c_24Proof
        & Vvar__0__pos__27052 = Vvar__0__pos__27053 ) ) ).

fof('$_inj_Coq.Reals.Rfunctions.ZintNeg',axiom,
    ! [Vvar__0__x__17125,Vvar__0__x__17126,Vvar__1__n__17127,Vvar__1__n__17128,Vvar__2___24Anonymous__17129,Vvar__2___24Anonymous__17130] :
      ( cCoq_2eReals_2eRfunctions_2eZintNeg___24a2(Vvar__0__x__17125,Vvar__1__n__17127) = cCoq_2eReals_2eRfunctions_2eZintNeg___24a2(Vvar__0__x__17126,Vvar__1__n__17128)
     => ( c_24Proof = c_24Proof
        & Vvar__1__n__17127 = Vvar__1__n__17128
        & Vvar__0__x__17125 = Vvar__0__x__17126 ) ) ).

fof('$_inj_Coq.Reals.Rfunctions.ZintNull',axiom,
    ! [Vvar__0__x__17115,Vvar__0__x__17116,Vvar__1___24Anonymous__17117,Vvar__1___24Anonymous__17118] :
      ( cCoq_2eReals_2eRfunctions_2eZintNull___24a1(Vvar__0__x__17115) = cCoq_2eReals_2eRfunctions_2eZintNull___24a1(Vvar__0__x__17116)
     => ( c_24Proof = c_24Proof
        & Vvar__0__x__17115 = Vvar__0__x__17116 ) ) ).

fof('$_inj_Coq.Reals.Rfunctions.ZintPos',axiom,
    ! [Vvar__0__x__17119,Vvar__0__x__17120,Vvar__1__n__17121,Vvar__1__n__17122,Vvar__2___24Anonymous__17123,Vvar__2___24Anonymous__17124] :
      ( cCoq_2eReals_2eRfunctions_2eZintPos___24a2(Vvar__0__x__17119,Vvar__1__n__17121) = cCoq_2eReals_2eRfunctions_2eZintPos___24a2(Vvar__0__x__17120,Vvar__1__n__17122)
     => ( c_24Proof = c_24Proof
        & Vvar__1__n__17121 = Vvar__1__n__17122
        & Vvar__0__x__17119 = Vvar__0__x__17120 ) ) ).

fof('$_inj_Coq.Strings.Ascii.Ascii',axiom,
    ! [Vvar__0___24Anonymous__25306,Vvar__0___24Anonymous__25307,Vvar__1___24Anonymous__25308,Vvar__1___24Anonymous__25309,Vvar__2___24Anonymous__25310,Vvar__2___24Anonymous__25311,Vvar__3___24Anonymous__25312,Vvar__3___24Anonymous__25313,Vvar__4___24Anonymous__25314,Vvar__4___24Anonymous__25315,Vvar__5___24Anonymous__25316,Vvar__5___24Anonymous__25317,Vvar__6___24Anonymous__25318,Vvar__6___24Anonymous__25319,Vvar__7___24Anonymous__25320,Vvar__7___24Anonymous__25321] :
      ( cCoq_2eStrings_2eAscii_2eAscii___24a8(Vvar__0___24Anonymous__25306,Vvar__1___24Anonymous__25308,Vvar__2___24Anonymous__25310,Vvar__3___24Anonymous__25312,Vvar__4___24Anonymous__25314,Vvar__5___24Anonymous__25316,Vvar__6___24Anonymous__25318,Vvar__7___24Anonymous__25320) = cCoq_2eStrings_2eAscii_2eAscii___24a8(Vvar__0___24Anonymous__25307,Vvar__1___24Anonymous__25309,Vvar__2___24Anonymous__25311,Vvar__3___24Anonymous__25313,Vvar__4___24Anonymous__25315,Vvar__5___24Anonymous__25317,Vvar__6___24Anonymous__25319,Vvar__7___24Anonymous__25321)
     => ( Vvar__7___24Anonymous__25320 = Vvar__7___24Anonymous__25321
        & Vvar__6___24Anonymous__25318 = Vvar__6___24Anonymous__25319
        & Vvar__5___24Anonymous__25316 = Vvar__5___24Anonymous__25317
        & Vvar__4___24Anonymous__25314 = Vvar__4___24Anonymous__25315
        & Vvar__3___24Anonymous__25312 = Vvar__3___24Anonymous__25313
        & Vvar__2___24Anonymous__25310 = Vvar__2___24Anonymous__25311
        & Vvar__1___24Anonymous__25308 = Vvar__1___24Anonymous__25309
        & Vvar__0___24Anonymous__25306 = Vvar__0___24Anonymous__25307 ) ) ).

fof('$_inj_Coq.Strings.String.String',axiom,
    ! [Vvar__0___24Anonymous__25978,Vvar__0___24Anonymous__25979,Vvar__1___24Anonymous__25980,Vvar__1___24Anonymous__25981] :
      ( cCoq_2eStrings_2eString_2eString___24a2(Vvar__0___24Anonymous__25978,Vvar__1___24Anonymous__25980) = cCoq_2eStrings_2eString_2eString___24a2(Vvar__0___24Anonymous__25979,Vvar__1___24Anonymous__25981)
     => ( Vvar__1___24Anonymous__25980 = Vvar__1___24Anonymous__25981
        & Vvar__0___24Anonymous__25978 = Vvar__0___24Anonymous__25979 ) ) ).

fof('$_inj_Coq.Structures.OrderedType.EQ',axiom,
    ! [Vvar__0__X__16402,Vvar__0__X__16403,Vvar__1__lt__16404,Vvar__1__lt__16405,Vvar__2__eq__16406,Vvar__2__eq__16407,Vvar__3__x__16408,Vvar__3__x__16409,Vvar__4__y__16410,Vvar__4__y__16411,Vvar__5___24Anonymous__16412,Vvar__5___24Anonymous__16413] :
      ( cCoq_2eStructures_2eOrderedType_2eEQ___24a5(Vvar__0__X__16402,Vvar__1__lt__16404,Vvar__2__eq__16406,Vvar__3__x__16408,Vvar__4__y__16410) = cCoq_2eStructures_2eOrderedType_2eEQ___24a5(Vvar__0__X__16403,Vvar__1__lt__16405,Vvar__2__eq__16407,Vvar__3__x__16409,Vvar__4__y__16411)
     => ( c_24Proof = c_24Proof
        & Vvar__4__y__16410 = Vvar__4__y__16411
        & Vvar__3__x__16408 = Vvar__3__x__16409
        & Vvar__2__eq__16406 = Vvar__2__eq__16407
        & Vvar__1__lt__16404 = Vvar__1__lt__16405
        & Vvar__0__X__16402 = Vvar__0__X__16403 ) ) ).

fof('$_inj_Coq.Structures.OrderedType.GT',axiom,
    ! [Vvar__0__X__16414,Vvar__0__X__16415,Vvar__1__lt__16416,Vvar__1__lt__16417,Vvar__2__eq__16418,Vvar__2__eq__16419,Vvar__3__x__16420,Vvar__3__x__16421,Vvar__4__y__16422,Vvar__4__y__16423,Vvar__5___24Anonymous__16424,Vvar__5___24Anonymous__16425] :
      ( cCoq_2eStructures_2eOrderedType_2eGT___24a5(Vvar__0__X__16414,Vvar__1__lt__16416,Vvar__2__eq__16418,Vvar__3__x__16420,Vvar__4__y__16422) = cCoq_2eStructures_2eOrderedType_2eGT___24a5(Vvar__0__X__16415,Vvar__1__lt__16417,Vvar__2__eq__16419,Vvar__3__x__16421,Vvar__4__y__16423)
     => ( c_24Proof = c_24Proof
        & Vvar__4__y__16422 = Vvar__4__y__16423
        & Vvar__3__x__16420 = Vvar__3__x__16421
        & Vvar__2__eq__16418 = Vvar__2__eq__16419
        & Vvar__1__lt__16416 = Vvar__1__lt__16417
        & Vvar__0__X__16414 = Vvar__0__X__16415 ) ) ).

fof('$_inj_Coq.Structures.OrderedType.LT',axiom,
    ! [Vvar__0__X__16390,Vvar__0__X__16391,Vvar__1__lt__16392,Vvar__1__lt__16393,Vvar__2__eq__16394,Vvar__2__eq__16395,Vvar__3__x__16396,Vvar__3__x__16397,Vvar__4__y__16398,Vvar__4__y__16399,Vvar__5___24Anonymous__16400,Vvar__5___24Anonymous__16401] :
      ( cCoq_2eStructures_2eOrderedType_2eLT___24a5(Vvar__0__X__16390,Vvar__1__lt__16392,Vvar__2__eq__16394,Vvar__3__x__16396,Vvar__4__y__16398) = cCoq_2eStructures_2eOrderedType_2eLT___24a5(Vvar__0__X__16391,Vvar__1__lt__16393,Vvar__2__eq__16395,Vvar__3__x__16397,Vvar__4__y__16399)
     => ( c_24Proof = c_24Proof
        & Vvar__4__y__16398 = Vvar__4__y__16399
        & Vvar__3__x__16396 = Vvar__3__x__16397
        & Vvar__2__eq__16394 = Vvar__2__eq__16395
        & Vvar__1__lt__16392 = Vvar__1__lt__16393
        & Vvar__0__X__16390 = Vvar__0__X__16391 ) ) ).

fof('$_inj_Coq.Vectors.Fin.F1',axiom,
    ! [Vvar__0__n__14592,Vvar__0__n__14593] :
      ( cCoq_2eVectors_2eFin_2eF1___24a1(Vvar__0__n__14592) = cCoq_2eVectors_2eFin_2eF1___24a1(Vvar__0__n__14593)
     => Vvar__0__n__14592 = Vvar__0__n__14593 ) ).

fof('$_inj_Coq.Vectors.Fin.FS',axiom,
    ! [Vvar__0__n__14594,Vvar__0__n__14595,Vvar__1___24Anonymous__14596,Vvar__1___24Anonymous__14597] :
      ( cCoq_2eVectors_2eFin_2eFS___24a2(Vvar__0__n__14594,Vvar__1___24Anonymous__14596) = cCoq_2eVectors_2eFin_2eFS___24a2(Vvar__0__n__14595,Vvar__1___24Anonymous__14597)
     => ( Vvar__1___24Anonymous__14596 = Vvar__1___24Anonymous__14597
        & Vvar__0__n__14594 = Vvar__0__n__14595 ) ) ).

fof('$_inj_Coq.Vectors.VectorDef.cons',axiom,
    ! [Vvar__0__A__24003,Vvar__0__A__24004,Vvar__1__h__24005,Vvar__1__h__24006,Vvar__2__n__24007,Vvar__2__n__24008,Vvar__3___24Anonymous__24009,Vvar__3___24Anonymous__24010] :
      ( cCoq_2eVectors_2eVectorDef_2econs___24a4(Vvar__0__A__24003,Vvar__1__h__24005,Vvar__2__n__24007,Vvar__3___24Anonymous__24009) = cCoq_2eVectors_2eVectorDef_2econs___24a4(Vvar__0__A__24004,Vvar__1__h__24006,Vvar__2__n__24008,Vvar__3___24Anonymous__24010)
     => ( Vvar__3___24Anonymous__24009 = Vvar__3___24Anonymous__24010
        & Vvar__2__n__24007 = Vvar__2__n__24008
        & Vvar__1__h__24005 = Vvar__1__h__24006
        & Vvar__0__A__24003 = Vvar__0__A__24004 ) ) ).

fof('$_inj_Coq.Vectors.VectorDef.nil',axiom,
    ! [Vvar__0__A__24001,Vvar__0__A__24002] :
      ( cCoq_2eVectors_2eVectorDef_2enil___24a1(Vvar__0__A__24001) = cCoq_2eVectors_2eVectorDef_2enil___24a1(Vvar__0__A__24002)
     => Vvar__0__A__24001 = Vvar__0__A__24002 ) ).

fof('$_inj_Coq.ZArith.Znumtheory.Euclid_intro',axiom,
    ! [Vvar__0__a__29455,Vvar__0__a__29456,Vvar__1__b__29457,Vvar__1__b__29458,Vvar__2__u__29459,Vvar__2__u__29460,Vvar__3__v__29461,Vvar__3__v__29462,Vvar__4__d__29463,Vvar__4__d__29464,Vvar__5___24Anonymous__29465,Vvar__5___24Anonymous__29466,Vvar__6___24Anonymous__29467,Vvar__6___24Anonymous__29468] :
      ( cCoq_2eZArith_2eZnumtheory_2eEuclid__intro___24a5(Vvar__0__a__29455,Vvar__1__b__29457,Vvar__2__u__29459,Vvar__3__v__29461,Vvar__4__d__29463) = cCoq_2eZArith_2eZnumtheory_2eEuclid__intro___24a5(Vvar__0__a__29456,Vvar__1__b__29458,Vvar__2__u__29460,Vvar__3__v__29462,Vvar__4__d__29464)
     => ( c_24Proof = c_24Proof
        & c_24Proof = c_24Proof
        & Vvar__4__d__29463 = Vvar__4__d__29464
        & Vvar__3__v__29461 = Vvar__3__v__29462
        & Vvar__2__u__29459 = Vvar__2__u__29460
        & Vvar__1__b__29457 = Vvar__1__b__29458
        & Vvar__0__a__29455 = Vvar__0__a__29456 ) ) ).

fof('$_inj_Coq.ZArith.Zpower.Zdiv_rest_proof',axiom,
    ! [Vvar__0__x__29503,Vvar__0__x__29504,Vvar__1__p__29505,Vvar__1__p__29506,Vvar__2__q__29507,Vvar__2__q__29508,Vvar__3__r__29509,Vvar__3__r__29510,Vvar__4___24Anonymous__29511,Vvar__4___24Anonymous__29512,Vvar__5___24Anonymous__29513,Vvar__5___24Anonymous__29514,Vvar__6___24Anonymous__29515,Vvar__6___24Anonymous__29516] :
      ( cCoq_2eZArith_2eZpower_2eZdiv__rest__proof___24a4(Vvar__0__x__29503,Vvar__1__p__29505,Vvar__2__q__29507,Vvar__3__r__29509) = cCoq_2eZArith_2eZpower_2eZdiv__rest__proof___24a4(Vvar__0__x__29504,Vvar__1__p__29506,Vvar__2__q__29508,Vvar__3__r__29510)
     => ( c_24Proof = c_24Proof
        & c_24Proof = c_24Proof
        & c_24Proof = c_24Proof
        & Vvar__3__r__29509 = Vvar__3__r__29510
        & Vvar__2__q__29507 = Vvar__2__q__29508
        & Vvar__1__p__29505 = Vvar__1__p__29506
        & Vvar__0__x__29503 = Vvar__0__x__29504 ) ) ).

fof('$_inj_Coq.micromega.EnvRing.PEX',axiom,
    ! [Vvar__0__C__25454,Vvar__0__C__25455,Vvar__1___24Anonymous__25456,Vvar__1___24Anonymous__25457] :
      ( cCoq_2emicromega_2eEnvRing_2ePEX___24a2(Vvar__0__C__25454,Vvar__1___24Anonymous__25456) = cCoq_2emicromega_2eEnvRing_2ePEX___24a2(Vvar__0__C__25455,Vvar__1___24Anonymous__25457)
     => ( Vvar__1___24Anonymous__25456 = Vvar__1___24Anonymous__25457
        & Vvar__0__C__25454 = Vvar__0__C__25455 ) ) ).

fof('$_inj_Coq.micromega.EnvRing.PEadd',axiom,
    ! [Vvar__0__C__25458,Vvar__0__C__25459,Vvar__1___24Anonymous__25460,Vvar__1___24Anonymous__25461,Vvar__2___24Anonymous__25462,Vvar__2___24Anonymous__25463] :
      ( cCoq_2emicromega_2eEnvRing_2ePEadd___24a3(Vvar__0__C__25458,Vvar__1___24Anonymous__25460,Vvar__2___24Anonymous__25462) = cCoq_2emicromega_2eEnvRing_2ePEadd___24a3(Vvar__0__C__25459,Vvar__1___24Anonymous__25461,Vvar__2___24Anonymous__25463)
     => ( Vvar__2___24Anonymous__25462 = Vvar__2___24Anonymous__25463
        & Vvar__1___24Anonymous__25460 = Vvar__1___24Anonymous__25461
        & Vvar__0__C__25458 = Vvar__0__C__25459 ) ) ).

fof('$_inj_Coq.micromega.EnvRing.PEc',axiom,
    ! [Vvar__0__C__25450,Vvar__0__C__25451,Vvar__1___24Anonymous__25452,Vvar__1___24Anonymous__25453] :
      ( cCoq_2emicromega_2eEnvRing_2ePEc___24a2(Vvar__0__C__25450,Vvar__1___24Anonymous__25452) = cCoq_2emicromega_2eEnvRing_2ePEc___24a2(Vvar__0__C__25451,Vvar__1___24Anonymous__25453)
     => ( Vvar__1___24Anonymous__25452 = Vvar__1___24Anonymous__25453
        & Vvar__0__C__25450 = Vvar__0__C__25451 ) ) ).

fof('$_inj_Coq.micromega.EnvRing.PEmul',axiom,
    ! [Vvar__0__C__25470,Vvar__0__C__25471,Vvar__1___24Anonymous__25472,Vvar__1___24Anonymous__25473,Vvar__2___24Anonymous__25474,Vvar__2___24Anonymous__25475] :
      ( cCoq_2emicromega_2eEnvRing_2ePEmul___24a3(Vvar__0__C__25470,Vvar__1___24Anonymous__25472,Vvar__2___24Anonymous__25474) = cCoq_2emicromega_2eEnvRing_2ePEmul___24a3(Vvar__0__C__25471,Vvar__1___24Anonymous__25473,Vvar__2___24Anonymous__25475)
     => ( Vvar__2___24Anonymous__25474 = Vvar__2___24Anonymous__25475
        & Vvar__1___24Anonymous__25472 = Vvar__1___24Anonymous__25473
        & Vvar__0__C__25470 = Vvar__0__C__25471 ) ) ).

fof('$_inj_Coq.micromega.EnvRing.PEopp',axiom,
    ! [Vvar__0__C__25476,Vvar__0__C__25477,Vvar__1___24Anonymous__25478,Vvar__1___24Anonymous__25479] :
      ( cCoq_2emicromega_2eEnvRing_2ePEopp___24a2(Vvar__0__C__25476,Vvar__1___24Anonymous__25478) = cCoq_2emicromega_2eEnvRing_2ePEopp___24a2(Vvar__0__C__25477,Vvar__1___24Anonymous__25479)
     => ( Vvar__1___24Anonymous__25478 = Vvar__1___24Anonymous__25479
        & Vvar__0__C__25476 = Vvar__0__C__25477 ) ) ).

fof('$_inj_Coq.micromega.EnvRing.PEpow',axiom,
    ! [Vvar__0__C__25480,Vvar__0__C__25481,Vvar__1___24Anonymous__25482,Vvar__1___24Anonymous__25483,Vvar__2___24Anonymous__25484,Vvar__2___24Anonymous__25485] :
      ( cCoq_2emicromega_2eEnvRing_2ePEpow___24a3(Vvar__0__C__25480,Vvar__1___24Anonymous__25482,Vvar__2___24Anonymous__25484) = cCoq_2emicromega_2eEnvRing_2ePEpow___24a3(Vvar__0__C__25481,Vvar__1___24Anonymous__25483,Vvar__2___24Anonymous__25485)
     => ( Vvar__2___24Anonymous__25484 = Vvar__2___24Anonymous__25485
        & Vvar__1___24Anonymous__25482 = Vvar__1___24Anonymous__25483
        & Vvar__0__C__25480 = Vvar__0__C__25481 ) ) ).

fof('$_inj_Coq.micromega.EnvRing.PEsub',axiom,
    ! [Vvar__0__C__25464,Vvar__0__C__25465,Vvar__1___24Anonymous__25466,Vvar__1___24Anonymous__25467,Vvar__2___24Anonymous__25468,Vvar__2___24Anonymous__25469] :
      ( cCoq_2emicromega_2eEnvRing_2ePEsub___24a3(Vvar__0__C__25464,Vvar__1___24Anonymous__25466,Vvar__2___24Anonymous__25468) = cCoq_2emicromega_2eEnvRing_2ePEsub___24a3(Vvar__0__C__25465,Vvar__1___24Anonymous__25467,Vvar__2___24Anonymous__25469)
     => ( Vvar__2___24Anonymous__25468 = Vvar__2___24Anonymous__25469
        & Vvar__1___24Anonymous__25466 = Vvar__1___24Anonymous__25467
        & Vvar__0__C__25464 = Vvar__0__C__25465 ) ) ).

fof('$_inj_Coq.micromega.EnvRing.PX',axiom,
    ! [Vvar__0__C__12322,Vvar__0__C__12323,Vvar__1___24Anonymous__12324,Vvar__1___24Anonymous__12325,Vvar__2___24Anonymous__12326,Vvar__2___24Anonymous__12327,Vvar__3___24Anonymous__12328,Vvar__3___24Anonymous__12329] :
      ( cCoq_2emicromega_2eEnvRing_2ePX___24a4(Vvar__0__C__12322,Vvar__1___24Anonymous__12324,Vvar__2___24Anonymous__12326,Vvar__3___24Anonymous__12328) = cCoq_2emicromega_2eEnvRing_2ePX___24a4(Vvar__0__C__12323,Vvar__1___24Anonymous__12325,Vvar__2___24Anonymous__12327,Vvar__3___24Anonymous__12329)
     => ( Vvar__3___24Anonymous__12328 = Vvar__3___24Anonymous__12329
        & Vvar__2___24Anonymous__12326 = Vvar__2___24Anonymous__12327
        & Vvar__1___24Anonymous__12324 = Vvar__1___24Anonymous__12325
        & Vvar__0__C__12322 = Vvar__0__C__12323 ) ) ).

fof('$_inj_Coq.micromega.EnvRing.Pc',axiom,
    ! [Vvar__0__C__12312,Vvar__0__C__12313,Vvar__1___24Anonymous__12314,Vvar__1___24Anonymous__12315] :
      ( cCoq_2emicromega_2eEnvRing_2ePc___24a2(Vvar__0__C__12312,Vvar__1___24Anonymous__12314) = cCoq_2emicromega_2eEnvRing_2ePc___24a2(Vvar__0__C__12313,Vvar__1___24Anonymous__12315)
     => ( Vvar__1___24Anonymous__12314 = Vvar__1___24Anonymous__12315
        & Vvar__0__C__12312 = Vvar__0__C__12313 ) ) ).

fof('$_inj_Coq.micromega.EnvRing.Pinj',axiom,
    ! [Vvar__0__C__12316,Vvar__0__C__12317,Vvar__1___24Anonymous__12318,Vvar__1___24Anonymous__12319,Vvar__2___24Anonymous__12320,Vvar__2___24Anonymous__12321] :
      ( cCoq_2emicromega_2eEnvRing_2ePinj___24a3(Vvar__0__C__12316,Vvar__1___24Anonymous__12318,Vvar__2___24Anonymous__12320) = cCoq_2emicromega_2eEnvRing_2ePinj___24a3(Vvar__0__C__12317,Vvar__1___24Anonymous__12319,Vvar__2___24Anonymous__12321)
     => ( Vvar__2___24Anonymous__12320 = Vvar__2___24Anonymous__12321
        & Vvar__1___24Anonymous__12318 = Vvar__1___24Anonymous__12319
        & Vvar__0__C__12316 = Vvar__0__C__12317 ) ) ).

fof('$_inj_Coq.micromega.EnvRing.vmon',axiom,
    ! [Vvar__0___24Anonymous__26164,Vvar__0___24Anonymous__26165,Vvar__1___24Anonymous__26166,Vvar__1___24Anonymous__26167] :
      ( cCoq_2emicromega_2eEnvRing_2evmon___24a2(Vvar__0___24Anonymous__26164,Vvar__1___24Anonymous__26166) = cCoq_2emicromega_2eEnvRing_2evmon___24a2(Vvar__0___24Anonymous__26165,Vvar__1___24Anonymous__26167)
     => ( Vvar__1___24Anonymous__26166 = Vvar__1___24Anonymous__26167
        & Vvar__0___24Anonymous__26164 = Vvar__0___24Anonymous__26165 ) ) ).

fof('$_inj_Coq.micromega.EnvRing.zmon',axiom,
    ! [Vvar__0___24Anonymous__26160,Vvar__0___24Anonymous__26161,Vvar__1___24Anonymous__26162,Vvar__1___24Anonymous__26163] :
      ( cCoq_2emicromega_2eEnvRing_2ezmon___24a2(Vvar__0___24Anonymous__26160,Vvar__1___24Anonymous__26162) = cCoq_2emicromega_2eEnvRing_2ezmon___24a2(Vvar__0___24Anonymous__26161,Vvar__1___24Anonymous__26163)
     => ( Vvar__1___24Anonymous__26162 = Vvar__1___24Anonymous__26163
        & Vvar__0___24Anonymous__26160 = Vvar__0___24Anonymous__26161 ) ) ).

fof('$_inj_Coq.micromega.RMicromega.CInv',axiom,
    ! [Vvar__0__r__16682,Vvar__0__r__16683] :
      ( cCoq_2emicromega_2eRMicromega_2eCInv___24a1(Vvar__0__r__16682) = cCoq_2emicromega_2eRMicromega_2eCInv___24a1(Vvar__0__r__16683)
     => Vvar__0__r__16682 = Vvar__0__r__16683 ) ).

fof('$_inj_Coq.micromega.RMicromega.CMinus',axiom,
    ! [Vvar__0__r1__16670,Vvar__0__r1__16671,Vvar__1__r2__16672,Vvar__1__r2__16673] :
      ( cCoq_2emicromega_2eRMicromega_2eCMinus___24a2(Vvar__0__r1__16670,Vvar__1__r2__16672) = cCoq_2emicromega_2eRMicromega_2eCMinus___24a2(Vvar__0__r1__16671,Vvar__1__r2__16673)
     => ( Vvar__1__r2__16672 = Vvar__1__r2__16673
        & Vvar__0__r1__16670 = Vvar__0__r1__16671 ) ) ).

fof('$_inj_Coq.micromega.RMicromega.CMult',axiom,
    ! [Vvar__0__r1__16674,Vvar__0__r1__16675,Vvar__1__r2__16676,Vvar__1__r2__16677] :
      ( cCoq_2emicromega_2eRMicromega_2eCMult___24a2(Vvar__0__r1__16674,Vvar__1__r2__16676) = cCoq_2emicromega_2eRMicromega_2eCMult___24a2(Vvar__0__r1__16675,Vvar__1__r2__16677)
     => ( Vvar__1__r2__16676 = Vvar__1__r2__16677
        & Vvar__0__r1__16674 = Vvar__0__r1__16675 ) ) ).

fof('$_inj_Coq.micromega.RMicromega.COpp',axiom,
    ! [Vvar__0__r__16684,Vvar__0__r__16685] :
      ( cCoq_2emicromega_2eRMicromega_2eCOpp___24a1(Vvar__0__r__16684) = cCoq_2emicromega_2eRMicromega_2eCOpp___24a1(Vvar__0__r__16685)
     => Vvar__0__r__16684 = Vvar__0__r__16685 ) ).

fof('$_inj_Coq.micromega.RMicromega.CPlus',axiom,
    ! [Vvar__0__r1__16666,Vvar__0__r1__16667,Vvar__1__r2__16668,Vvar__1__r2__16669] :
      ( cCoq_2emicromega_2eRMicromega_2eCPlus___24a2(Vvar__0__r1__16666,Vvar__1__r2__16668) = cCoq_2emicromega_2eRMicromega_2eCPlus___24a2(Vvar__0__r1__16667,Vvar__1__r2__16669)
     => ( Vvar__1__r2__16668 = Vvar__1__r2__16669
        & Vvar__0__r1__16666 = Vvar__0__r1__16667 ) ) ).

fof('$_inj_Coq.micromega.RMicromega.CPow',axiom,
    ! [Vvar__0__r1__16678,Vvar__0__r1__16679,Vvar__1__z__16680,Vvar__1__z__16681] :
      ( cCoq_2emicromega_2eRMicromega_2eCPow___24a2(Vvar__0__r1__16678,Vvar__1__z__16680) = cCoq_2emicromega_2eRMicromega_2eCPow___24a2(Vvar__0__r1__16679,Vvar__1__z__16681)
     => ( Vvar__1__z__16680 = Vvar__1__z__16681
        & Vvar__0__r1__16678 = Vvar__0__r1__16679 ) ) ).

fof('$_inj_Coq.micromega.RMicromega.CQ',axiom,
    ! [Vvar__0__r__16662,Vvar__0__r__16663] :
      ( cCoq_2emicromega_2eRMicromega_2eCQ___24a1(Vvar__0__r__16662) = cCoq_2emicromega_2eRMicromega_2eCQ___24a1(Vvar__0__r__16663)
     => Vvar__0__r__16662 = Vvar__0__r__16663 ) ).

fof('$_inj_Coq.micromega.RMicromega.CZ',axiom,
    ! [Vvar__0__r__16664,Vvar__0__r__16665] :
      ( cCoq_2emicromega_2eRMicromega_2eCZ___24a1(Vvar__0__r__16664) = cCoq_2emicromega_2eRMicromega_2eCZ___24a1(Vvar__0__r__16665)
     => Vvar__0__r__16664 = Vvar__0__r__16665 ) ).

fof('$_inj_Coq.micromega.RingMicromega.Build_Formula',axiom,
    ! [Vvar__0__T__22945,Vvar__0__T__22946,Vvar__1__Flhs__22947,Vvar__1__Flhs__22948,Vvar__2__Fop__22949,Vvar__2__Fop__22950,Vvar__3__Frhs__22951,Vvar__3__Frhs__22952] :
      ( cCoq_2emicromega_2eRingMicromega_2eBuild__Formula___24a4(Vvar__0__T__22945,Vvar__1__Flhs__22947,Vvar__2__Fop__22949,Vvar__3__Frhs__22951) = cCoq_2emicromega_2eRingMicromega_2eBuild__Formula___24a4(Vvar__0__T__22946,Vvar__1__Flhs__22948,Vvar__2__Fop__22950,Vvar__3__Frhs__22952)
     => ( Vvar__3__Frhs__22951 = Vvar__3__Frhs__22952
        & Vvar__2__Fop__22949 = Vvar__2__Fop__22950
        & Vvar__1__Flhs__22947 = Vvar__1__Flhs__22948
        & Vvar__0__T__22945 = Vvar__0__T__22946 ) ) ).

fof('$_inj_Coq.micromega.RingMicromega.PsatzAdd',axiom,
    ! [Vvar__0__C__22707,Vvar__0__C__22708,Vvar__1___24Anonymous__22709,Vvar__1___24Anonymous__22710,Vvar__2___24Anonymous__22711,Vvar__2___24Anonymous__22712] :
      ( cCoq_2emicromega_2eRingMicromega_2ePsatzAdd___24a3(Vvar__0__C__22707,Vvar__1___24Anonymous__22709,Vvar__2___24Anonymous__22711) = cCoq_2emicromega_2eRingMicromega_2ePsatzAdd___24a3(Vvar__0__C__22708,Vvar__1___24Anonymous__22710,Vvar__2___24Anonymous__22712)
     => ( Vvar__2___24Anonymous__22711 = Vvar__2___24Anonymous__22712
        & Vvar__1___24Anonymous__22709 = Vvar__1___24Anonymous__22710
        & Vvar__0__C__22707 = Vvar__0__C__22708 ) ) ).

fof('$_inj_Coq.micromega.RingMicromega.PsatzC',axiom,
    ! [Vvar__0__C__22713,Vvar__0__C__22714,Vvar__1___24Anonymous__22715,Vvar__1___24Anonymous__22716] :
      ( cCoq_2emicromega_2eRingMicromega_2ePsatzC___24a2(Vvar__0__C__22713,Vvar__1___24Anonymous__22715) = cCoq_2emicromega_2eRingMicromega_2ePsatzC___24a2(Vvar__0__C__22714,Vvar__1___24Anonymous__22716)
     => ( Vvar__1___24Anonymous__22715 = Vvar__1___24Anonymous__22716
        & Vvar__0__C__22713 = Vvar__0__C__22714 ) ) ).

fof('$_inj_Coq.micromega.RingMicromega.PsatzIn',axiom,
    ! [Vvar__0__C__22687,Vvar__0__C__22688,Vvar__1___24Anonymous__22689,Vvar__1___24Anonymous__22690] :
      ( cCoq_2emicromega_2eRingMicromega_2ePsatzIn___24a2(Vvar__0__C__22687,Vvar__1___24Anonymous__22689) = cCoq_2emicromega_2eRingMicromega_2ePsatzIn___24a2(Vvar__0__C__22688,Vvar__1___24Anonymous__22690)
     => ( Vvar__1___24Anonymous__22689 = Vvar__1___24Anonymous__22690
        & Vvar__0__C__22687 = Vvar__0__C__22688 ) ) ).

fof('$_inj_Coq.micromega.RingMicromega.PsatzMulC',axiom,
    ! [Vvar__0__C__22695,Vvar__0__C__22696,Vvar__1___24Anonymous__22697,Vvar__1___24Anonymous__22698,Vvar__2___24Anonymous__22699,Vvar__2___24Anonymous__22700] :
      ( cCoq_2emicromega_2eRingMicromega_2ePsatzMulC___24a3(Vvar__0__C__22695,Vvar__1___24Anonymous__22697,Vvar__2___24Anonymous__22699) = cCoq_2emicromega_2eRingMicromega_2ePsatzMulC___24a3(Vvar__0__C__22696,Vvar__1___24Anonymous__22698,Vvar__2___24Anonymous__22700)
     => ( Vvar__2___24Anonymous__22699 = Vvar__2___24Anonymous__22700
        & Vvar__1___24Anonymous__22697 = Vvar__1___24Anonymous__22698
        & Vvar__0__C__22695 = Vvar__0__C__22696 ) ) ).

fof('$_inj_Coq.micromega.RingMicromega.PsatzMulE',axiom,
    ! [Vvar__0__C__22701,Vvar__0__C__22702,Vvar__1___24Anonymous__22703,Vvar__1___24Anonymous__22704,Vvar__2___24Anonymous__22705,Vvar__2___24Anonymous__22706] :
      ( cCoq_2emicromega_2eRingMicromega_2ePsatzMulE___24a3(Vvar__0__C__22701,Vvar__1___24Anonymous__22703,Vvar__2___24Anonymous__22705) = cCoq_2emicromega_2eRingMicromega_2ePsatzMulE___24a3(Vvar__0__C__22702,Vvar__1___24Anonymous__22704,Vvar__2___24Anonymous__22706)
     => ( Vvar__2___24Anonymous__22705 = Vvar__2___24Anonymous__22706
        & Vvar__1___24Anonymous__22703 = Vvar__1___24Anonymous__22704
        & Vvar__0__C__22701 = Vvar__0__C__22702 ) ) ).

fof('$_inj_Coq.micromega.RingMicromega.PsatzSquare',axiom,
    ! [Vvar__0__C__22691,Vvar__0__C__22692,Vvar__1___24Anonymous__22693,Vvar__1___24Anonymous__22694] :
      ( cCoq_2emicromega_2eRingMicromega_2ePsatzSquare___24a2(Vvar__0__C__22691,Vvar__1___24Anonymous__22693) = cCoq_2emicromega_2eRingMicromega_2ePsatzSquare___24a2(Vvar__0__C__22692,Vvar__1___24Anonymous__22694)
     => ( Vvar__1___24Anonymous__22693 = Vvar__1___24Anonymous__22694
        & Vvar__0__C__22691 = Vvar__0__C__22692 ) ) ).

fof('$_inj_Coq.micromega.RingMicromega.PsatzZ',axiom,
    ! [Vvar__0__C__22717,Vvar__0__C__22718] :
      ( cCoq_2emicromega_2eRingMicromega_2ePsatzZ___24a1(Vvar__0__C__22717) = cCoq_2emicromega_2eRingMicromega_2ePsatzZ___24a1(Vvar__0__C__22718)
     => Vvar__0__C__22717 = Vvar__0__C__22718 ) ).

fof('$_inj_Coq.micromega.Tauto.A',axiom,
    ! [Vvar__0__TA__29287,Vvar__0__TA__29288,Vvar__1__TX__29289,Vvar__1__TX__29290,Vvar__2__AA__29291,Vvar__2__AA__29292,Vvar__3__AF__29293,Vvar__3__AF__29294,Vvar__4___24Anonymous__29295,Vvar__4___24Anonymous__29296,Vvar__5___24Anonymous__29297,Vvar__5___24Anonymous__29298] :
      ( cCoq_2emicromega_2eTauto_2eA___24a6(Vvar__0__TA__29287,Vvar__1__TX__29289,Vvar__2__AA__29291,Vvar__3__AF__29293,Vvar__4___24Anonymous__29295,Vvar__5___24Anonymous__29297) = cCoq_2emicromega_2eTauto_2eA___24a6(Vvar__0__TA__29288,Vvar__1__TX__29290,Vvar__2__AA__29292,Vvar__3__AF__29294,Vvar__4___24Anonymous__29296,Vvar__5___24Anonymous__29298)
     => ( Vvar__5___24Anonymous__29297 = Vvar__5___24Anonymous__29298
        & Vvar__4___24Anonymous__29295 = Vvar__4___24Anonymous__29296
        & Vvar__3__AF__29293 = Vvar__3__AF__29294
        & Vvar__2__AA__29291 = Vvar__2__AA__29292
        & Vvar__1__TX__29289 = Vvar__1__TX__29290
        & Vvar__0__TA__29287 = Vvar__0__TA__29288 ) ) ).

fof('$_inj_Coq.micromega.Tauto.Cj',axiom,
    ! [Vvar__0__TA__29299,Vvar__0__TA__29300,Vvar__1__TX__29301,Vvar__1__TX__29302,Vvar__2__AA__29303,Vvar__2__AA__29304,Vvar__3__AF__29305,Vvar__3__AF__29306,Vvar__4___24Anonymous__29307,Vvar__4___24Anonymous__29308,Vvar__5___24Anonymous__29309,Vvar__5___24Anonymous__29310] :
      ( cCoq_2emicromega_2eTauto_2eCj___24a6(Vvar__0__TA__29299,Vvar__1__TX__29301,Vvar__2__AA__29303,Vvar__3__AF__29305,Vvar__4___24Anonymous__29307,Vvar__5___24Anonymous__29309) = cCoq_2emicromega_2eTauto_2eCj___24a6(Vvar__0__TA__29300,Vvar__1__TX__29302,Vvar__2__AA__29304,Vvar__3__AF__29306,Vvar__4___24Anonymous__29308,Vvar__5___24Anonymous__29310)
     => ( Vvar__5___24Anonymous__29309 = Vvar__5___24Anonymous__29310
        & Vvar__4___24Anonymous__29307 = Vvar__4___24Anonymous__29308
        & Vvar__3__AF__29305 = Vvar__3__AF__29306
        & Vvar__2__AA__29303 = Vvar__2__AA__29304
        & Vvar__1__TX__29301 = Vvar__1__TX__29302
        & Vvar__0__TA__29299 = Vvar__0__TA__29300 ) ) ).

fof('$_inj_Coq.micromega.Tauto.D',axiom,
    ! [Vvar__0__TA__29311,Vvar__0__TA__29312,Vvar__1__TX__29313,Vvar__1__TX__29314,Vvar__2__AA__29315,Vvar__2__AA__29316,Vvar__3__AF__29317,Vvar__3__AF__29318,Vvar__4___24Anonymous__29319,Vvar__4___24Anonymous__29320,Vvar__5___24Anonymous__29321,Vvar__5___24Anonymous__29322] :
      ( cCoq_2emicromega_2eTauto_2eD___24a6(Vvar__0__TA__29311,Vvar__1__TX__29313,Vvar__2__AA__29315,Vvar__3__AF__29317,Vvar__4___24Anonymous__29319,Vvar__5___24Anonymous__29321) = cCoq_2emicromega_2eTauto_2eD___24a6(Vvar__0__TA__29312,Vvar__1__TX__29314,Vvar__2__AA__29316,Vvar__3__AF__29318,Vvar__4___24Anonymous__29320,Vvar__5___24Anonymous__29322)
     => ( Vvar__5___24Anonymous__29321 = Vvar__5___24Anonymous__29322
        & Vvar__4___24Anonymous__29319 = Vvar__4___24Anonymous__29320
        & Vvar__3__AF__29317 = Vvar__3__AF__29318
        & Vvar__2__AA__29315 = Vvar__2__AA__29316
        & Vvar__1__TX__29313 = Vvar__1__TX__29314
        & Vvar__0__TA__29311 = Vvar__0__TA__29312 ) ) ).

fof('$_inj_Coq.micromega.Tauto.FF',axiom,
    ! [Vvar__0__TA__29269,Vvar__0__TA__29270,Vvar__1__TX__29271,Vvar__1__TX__29272,Vvar__2__AA__29273,Vvar__2__AA__29274,Vvar__3__AF__29275,Vvar__3__AF__29276] :
      ( cCoq_2emicromega_2eTauto_2eFF___24a4(Vvar__0__TA__29269,Vvar__1__TX__29271,Vvar__2__AA__29273,Vvar__3__AF__29275) = cCoq_2emicromega_2eTauto_2eFF___24a4(Vvar__0__TA__29270,Vvar__1__TX__29272,Vvar__2__AA__29274,Vvar__3__AF__29276)
     => ( Vvar__3__AF__29275 = Vvar__3__AF__29276
        & Vvar__2__AA__29273 = Vvar__2__AA__29274
        & Vvar__1__TX__29271 = Vvar__1__TX__29272
        & Vvar__0__TA__29269 = Vvar__0__TA__29270 ) ) ).

fof('$_inj_Coq.micromega.Tauto.I',axiom,
    ! [Vvar__0__TA__29333,Vvar__0__TA__29334,Vvar__1__TX__29335,Vvar__1__TX__29336,Vvar__2__AA__29337,Vvar__2__AA__29338,Vvar__3__AF__29339,Vvar__3__AF__29340,Vvar__4___24Anonymous__29341,Vvar__4___24Anonymous__29342,Vvar__5___24Anonymous__29343,Vvar__5___24Anonymous__29344,Vvar__6___24Anonymous__29345,Vvar__6___24Anonymous__29346] :
      ( cCoq_2emicromega_2eTauto_2eI___24a7(Vvar__0__TA__29333,Vvar__1__TX__29335,Vvar__2__AA__29337,Vvar__3__AF__29339,Vvar__4___24Anonymous__29341,Vvar__5___24Anonymous__29343,Vvar__6___24Anonymous__29345) = cCoq_2emicromega_2eTauto_2eI___24a7(Vvar__0__TA__29334,Vvar__1__TX__29336,Vvar__2__AA__29338,Vvar__3__AF__29340,Vvar__4___24Anonymous__29342,Vvar__5___24Anonymous__29344,Vvar__6___24Anonymous__29346)
     => ( Vvar__6___24Anonymous__29345 = Vvar__6___24Anonymous__29346
        & Vvar__5___24Anonymous__29343 = Vvar__5___24Anonymous__29344
        & Vvar__4___24Anonymous__29341 = Vvar__4___24Anonymous__29342
        & Vvar__3__AF__29339 = Vvar__3__AF__29340
        & Vvar__2__AA__29337 = Vvar__2__AA__29338
        & Vvar__1__TX__29335 = Vvar__1__TX__29336
        & Vvar__0__TA__29333 = Vvar__0__TA__29334 ) ) ).

fof('$_inj_Coq.micromega.Tauto.N',axiom,
    ! [Vvar__0__TA__29323,Vvar__0__TA__29324,Vvar__1__TX__29325,Vvar__1__TX__29326,Vvar__2__AA__29327,Vvar__2__AA__29328,Vvar__3__AF__29329,Vvar__3__AF__29330,Vvar__4___24Anonymous__29331,Vvar__4___24Anonymous__29332] :
      ( cCoq_2emicromega_2eTauto_2eN___24a5(Vvar__0__TA__29323,Vvar__1__TX__29325,Vvar__2__AA__29327,Vvar__3__AF__29329,Vvar__4___24Anonymous__29331) = cCoq_2emicromega_2eTauto_2eN___24a5(Vvar__0__TA__29324,Vvar__1__TX__29326,Vvar__2__AA__29328,Vvar__3__AF__29330,Vvar__4___24Anonymous__29332)
     => ( Vvar__4___24Anonymous__29331 = Vvar__4___24Anonymous__29332
        & Vvar__3__AF__29329 = Vvar__3__AF__29330
        & Vvar__2__AA__29327 = Vvar__2__AA__29328
        & Vvar__1__TX__29325 = Vvar__1__TX__29326
        & Vvar__0__TA__29323 = Vvar__0__TA__29324 ) ) ).

fof('$_inj_Coq.micromega.Tauto.TT',axiom,
    ! [Vvar__0__TA__29261,Vvar__0__TA__29262,Vvar__1__TX__29263,Vvar__1__TX__29264,Vvar__2__AA__29265,Vvar__2__AA__29266,Vvar__3__AF__29267,Vvar__3__AF__29268] :
      ( cCoq_2emicromega_2eTauto_2eTT___24a4(Vvar__0__TA__29261,Vvar__1__TX__29263,Vvar__2__AA__29265,Vvar__3__AF__29267) = cCoq_2emicromega_2eTauto_2eTT___24a4(Vvar__0__TA__29262,Vvar__1__TX__29264,Vvar__2__AA__29266,Vvar__3__AF__29268)
     => ( Vvar__3__AF__29267 = Vvar__3__AF__29268
        & Vvar__2__AA__29265 = Vvar__2__AA__29266
        & Vvar__1__TX__29263 = Vvar__1__TX__29264
        & Vvar__0__TA__29261 = Vvar__0__TA__29262 ) ) ).

fof('$_inj_Coq.micromega.Tauto.X',axiom,
    ! [Vvar__0__TA__29277,Vvar__0__TA__29278,Vvar__1__TX__29279,Vvar__1__TX__29280,Vvar__2__AA__29281,Vvar__2__AA__29282,Vvar__3__AF__29283,Vvar__3__AF__29284,Vvar__4___24Anonymous__29285,Vvar__4___24Anonymous__29286] :
      ( cCoq_2emicromega_2eTauto_2eX___24a5(Vvar__0__TA__29277,Vvar__1__TX__29279,Vvar__2__AA__29281,Vvar__3__AF__29283,Vvar__4___24Anonymous__29285) = cCoq_2emicromega_2eTauto_2eX___24a5(Vvar__0__TA__29278,Vvar__1__TX__29280,Vvar__2__AA__29282,Vvar__3__AF__29284,Vvar__4___24Anonymous__29286)
     => ( Vvar__4___24Anonymous__29285 = Vvar__4___24Anonymous__29286
        & Vvar__3__AF__29283 = Vvar__3__AF__29284
        & Vvar__2__AA__29281 = Vvar__2__AA__29282
        & Vvar__1__TX__29279 = Vvar__1__TX__29280
        & Vvar__0__TA__29277 = Vvar__0__TA__29278 ) ) ).

fof('$_inj_Coq.micromega.VarMap.Branch',axiom,
    ! [Vvar__0__A__29376,Vvar__0__A__29377,Vvar__1___24Anonymous__29378,Vvar__1___24Anonymous__29379,Vvar__2___24Anonymous__29380,Vvar__2___24Anonymous__29381,Vvar__3___24Anonymous__29382,Vvar__3___24Anonymous__29383] :
      ( cCoq_2emicromega_2eVarMap_2eBranch___24a4(Vvar__0__A__29376,Vvar__1___24Anonymous__29378,Vvar__2___24Anonymous__29380,Vvar__3___24Anonymous__29382) = cCoq_2emicromega_2eVarMap_2eBranch___24a4(Vvar__0__A__29377,Vvar__1___24Anonymous__29379,Vvar__2___24Anonymous__29381,Vvar__3___24Anonymous__29383)
     => ( Vvar__3___24Anonymous__29382 = Vvar__3___24Anonymous__29383
        & Vvar__2___24Anonymous__29380 = Vvar__2___24Anonymous__29381
        & Vvar__1___24Anonymous__29378 = Vvar__1___24Anonymous__29379
        & Vvar__0__A__29376 = Vvar__0__A__29377 ) ) ).

fof('$_inj_Coq.micromega.VarMap.Elt',axiom,
    ! [Vvar__0__A__29372,Vvar__0__A__29373,Vvar__1___24Anonymous__29374,Vvar__1___24Anonymous__29375] :
      ( cCoq_2emicromega_2eVarMap_2eElt___24a2(Vvar__0__A__29372,Vvar__1___24Anonymous__29374) = cCoq_2emicromega_2eVarMap_2eElt___24a2(Vvar__0__A__29373,Vvar__1___24Anonymous__29375)
     => ( Vvar__1___24Anonymous__29374 = Vvar__1___24Anonymous__29375
        & Vvar__0__A__29372 = Vvar__0__A__29373 ) ) ).

fof('$_inj_Coq.micromega.VarMap.Empty',axiom,
    ! [Vvar__0__A__29370,Vvar__0__A__29371] :
      ( cCoq_2emicromega_2eVarMap_2eEmpty___24a1(Vvar__0__A__29370) = cCoq_2emicromega_2eVarMap_2eEmpty___24a1(Vvar__0__A__29371)
     => Vvar__0__A__29370 = Vvar__0__A__29371 ) ).

fof('$_inj_Coq.micromega.ZMicromega.CutProof',axiom,
    ! [Vvar__0___24Anonymous__29417,Vvar__0___24Anonymous__29418,Vvar__1___24Anonymous__29419,Vvar__1___24Anonymous__29420] :
      ( cCoq_2emicromega_2eZMicromega_2eCutProof___24a2(Vvar__0___24Anonymous__29417,Vvar__1___24Anonymous__29419) = cCoq_2emicromega_2eZMicromega_2eCutProof___24a2(Vvar__0___24Anonymous__29418,Vvar__1___24Anonymous__29420)
     => ( Vvar__1___24Anonymous__29419 = Vvar__1___24Anonymous__29420
        & Vvar__0___24Anonymous__29417 = Vvar__0___24Anonymous__29418 ) ) ).

fof('$_inj_Coq.micromega.ZMicromega.EnumProof',axiom,
    ! [Vvar__0___24Anonymous__29421,Vvar__0___24Anonymous__29422,Vvar__1___24Anonymous__29423,Vvar__1___24Anonymous__29424,Vvar__2___24Anonymous__29425,Vvar__2___24Anonymous__29426] :
      ( cCoq_2emicromega_2eZMicromega_2eEnumProof___24a3(Vvar__0___24Anonymous__29421,Vvar__1___24Anonymous__29423,Vvar__2___24Anonymous__29425) = cCoq_2emicromega_2eZMicromega_2eEnumProof___24a3(Vvar__0___24Anonymous__29422,Vvar__1___24Anonymous__29424,Vvar__2___24Anonymous__29426)
     => ( Vvar__2___24Anonymous__29425 = Vvar__2___24Anonymous__29426
        & Vvar__1___24Anonymous__29423 = Vvar__1___24Anonymous__29424
        & Vvar__0___24Anonymous__29421 = Vvar__0___24Anonymous__29422 ) ) ).

fof('$_inj_Coq.micromega.ZMicromega.RatProof',axiom,
    ! [Vvar__0___24Anonymous__29413,Vvar__0___24Anonymous__29414,Vvar__1___24Anonymous__29415,Vvar__1___24Anonymous__29416] :
      ( cCoq_2emicromega_2eZMicromega_2eRatProof___24a2(Vvar__0___24Anonymous__29413,Vvar__1___24Anonymous__29415) = cCoq_2emicromega_2eZMicromega_2eRatProof___24a2(Vvar__0___24Anonymous__29414,Vvar__1___24Anonymous__29416)
     => ( Vvar__1___24Anonymous__29415 = Vvar__1___24Anonymous__29416
        & Vvar__0___24Anonymous__29413 = Vvar__0___24Anonymous__29414 ) ) ).

fof('$_inj_Coq.setoid_ring.Field_theory.FEI',axiom,
    ! [Vvar__0__C__3605,Vvar__0__C__3606] :
      ( cCoq_2esetoid__ring_2eField__theory_2eFEI___24a1(Vvar__0__C__3605) = cCoq_2esetoid__ring_2eField__theory_2eFEI___24a1(Vvar__0__C__3606)
     => Vvar__0__C__3605 = Vvar__0__C__3606 ) ).

fof('$_inj_Coq.setoid_ring.Field_theory.FEO',axiom,
    ! [Vvar__0__C__3603,Vvar__0__C__3604] :
      ( cCoq_2esetoid__ring_2eField__theory_2eFEO___24a1(Vvar__0__C__3603) = cCoq_2esetoid__ring_2eField__theory_2eFEO___24a1(Vvar__0__C__3604)
     => Vvar__0__C__3603 = Vvar__0__C__3604 ) ).

fof('$_inj_Coq.setoid_ring.Field_theory.FEX',axiom,
    ! [Vvar__0__C__3611,Vvar__0__C__3612,Vvar__1___24Anonymous__3613,Vvar__1___24Anonymous__3614] :
      ( cCoq_2esetoid__ring_2eField__theory_2eFEX___24a2(Vvar__0__C__3611,Vvar__1___24Anonymous__3613) = cCoq_2esetoid__ring_2eField__theory_2eFEX___24a2(Vvar__0__C__3612,Vvar__1___24Anonymous__3614)
     => ( Vvar__1___24Anonymous__3613 = Vvar__1___24Anonymous__3614
        & Vvar__0__C__3611 = Vvar__0__C__3612 ) ) ).

fof('$_inj_Coq.setoid_ring.Field_theory.FEadd',axiom,
    ! [Vvar__0__C__3615,Vvar__0__C__3616,Vvar__1___24Anonymous__3617,Vvar__1___24Anonymous__3618,Vvar__2___24Anonymous__3619,Vvar__2___24Anonymous__3620] :
      ( cCoq_2esetoid__ring_2eField__theory_2eFEadd___24a3(Vvar__0__C__3615,Vvar__1___24Anonymous__3617,Vvar__2___24Anonymous__3619) = cCoq_2esetoid__ring_2eField__theory_2eFEadd___24a3(Vvar__0__C__3616,Vvar__1___24Anonymous__3618,Vvar__2___24Anonymous__3620)
     => ( Vvar__2___24Anonymous__3619 = Vvar__2___24Anonymous__3620
        & Vvar__1___24Anonymous__3617 = Vvar__1___24Anonymous__3618
        & Vvar__0__C__3615 = Vvar__0__C__3616 ) ) ).

fof('$_inj_Coq.setoid_ring.Field_theory.FEc',axiom,
    ! [Vvar__0__C__3607,Vvar__0__C__3608,Vvar__1___24Anonymous__3609,Vvar__1___24Anonymous__3610] :
      ( cCoq_2esetoid__ring_2eField__theory_2eFEc___24a2(Vvar__0__C__3607,Vvar__1___24Anonymous__3609) = cCoq_2esetoid__ring_2eField__theory_2eFEc___24a2(Vvar__0__C__3608,Vvar__1___24Anonymous__3610)
     => ( Vvar__1___24Anonymous__3609 = Vvar__1___24Anonymous__3610
        & Vvar__0__C__3607 = Vvar__0__C__3608 ) ) ).

fof('$_inj_Coq.setoid_ring.Field_theory.FEdiv',axiom,
    ! [Vvar__0__C__3641,Vvar__0__C__3642,Vvar__1___24Anonymous__3643,Vvar__1___24Anonymous__3644,Vvar__2___24Anonymous__3645,Vvar__2___24Anonymous__3646] :
      ( cCoq_2esetoid__ring_2eField__theory_2eFEdiv___24a3(Vvar__0__C__3641,Vvar__1___24Anonymous__3643,Vvar__2___24Anonymous__3645) = cCoq_2esetoid__ring_2eField__theory_2eFEdiv___24a3(Vvar__0__C__3642,Vvar__1___24Anonymous__3644,Vvar__2___24Anonymous__3646)
     => ( Vvar__2___24Anonymous__3645 = Vvar__2___24Anonymous__3646
        & Vvar__1___24Anonymous__3643 = Vvar__1___24Anonymous__3644
        & Vvar__0__C__3641 = Vvar__0__C__3642 ) ) ).

fof('$_inj_Coq.setoid_ring.Field_theory.FEinv',axiom,
    ! [Vvar__0__C__3637,Vvar__0__C__3638,Vvar__1___24Anonymous__3639,Vvar__1___24Anonymous__3640] :
      ( cCoq_2esetoid__ring_2eField__theory_2eFEinv___24a2(Vvar__0__C__3637,Vvar__1___24Anonymous__3639) = cCoq_2esetoid__ring_2eField__theory_2eFEinv___24a2(Vvar__0__C__3638,Vvar__1___24Anonymous__3640)
     => ( Vvar__1___24Anonymous__3639 = Vvar__1___24Anonymous__3640
        & Vvar__0__C__3637 = Vvar__0__C__3638 ) ) ).

fof('$_inj_Coq.setoid_ring.Field_theory.FEmul',axiom,
    ! [Vvar__0__C__3627,Vvar__0__C__3628,Vvar__1___24Anonymous__3629,Vvar__1___24Anonymous__3630,Vvar__2___24Anonymous__3631,Vvar__2___24Anonymous__3632] :
      ( cCoq_2esetoid__ring_2eField__theory_2eFEmul___24a3(Vvar__0__C__3627,Vvar__1___24Anonymous__3629,Vvar__2___24Anonymous__3631) = cCoq_2esetoid__ring_2eField__theory_2eFEmul___24a3(Vvar__0__C__3628,Vvar__1___24Anonymous__3630,Vvar__2___24Anonymous__3632)
     => ( Vvar__2___24Anonymous__3631 = Vvar__2___24Anonymous__3632
        & Vvar__1___24Anonymous__3629 = Vvar__1___24Anonymous__3630
        & Vvar__0__C__3627 = Vvar__0__C__3628 ) ) ).

fof('$_inj_Coq.setoid_ring.Field_theory.FEopp',axiom,
    ! [Vvar__0__C__3633,Vvar__0__C__3634,Vvar__1___24Anonymous__3635,Vvar__1___24Anonymous__3636] :
      ( cCoq_2esetoid__ring_2eField__theory_2eFEopp___24a2(Vvar__0__C__3633,Vvar__1___24Anonymous__3635) = cCoq_2esetoid__ring_2eField__theory_2eFEopp___24a2(Vvar__0__C__3634,Vvar__1___24Anonymous__3636)
     => ( Vvar__1___24Anonymous__3635 = Vvar__1___24Anonymous__3636
        & Vvar__0__C__3633 = Vvar__0__C__3634 ) ) ).

fof('$_inj_Coq.setoid_ring.Field_theory.FEpow',axiom,
    ! [Vvar__0__C__3647,Vvar__0__C__3648,Vvar__1___24Anonymous__3649,Vvar__1___24Anonymous__3650,Vvar__2___24Anonymous__3651,Vvar__2___24Anonymous__3652] :
      ( cCoq_2esetoid__ring_2eField__theory_2eFEpow___24a3(Vvar__0__C__3647,Vvar__1___24Anonymous__3649,Vvar__2___24Anonymous__3651) = cCoq_2esetoid__ring_2eField__theory_2eFEpow___24a3(Vvar__0__C__3648,Vvar__1___24Anonymous__3650,Vvar__2___24Anonymous__3652)
     => ( Vvar__2___24Anonymous__3651 = Vvar__2___24Anonymous__3652
        & Vvar__1___24Anonymous__3649 = Vvar__1___24Anonymous__3650
        & Vvar__0__C__3647 = Vvar__0__C__3648 ) ) ).

fof('$_inj_Coq.setoid_ring.Field_theory.FEsub',axiom,
    ! [Vvar__0__C__3621,Vvar__0__C__3622,Vvar__1___24Anonymous__3623,Vvar__1___24Anonymous__3624,Vvar__2___24Anonymous__3625,Vvar__2___24Anonymous__3626] :
      ( cCoq_2esetoid__ring_2eField__theory_2eFEsub___24a3(Vvar__0__C__3621,Vvar__1___24Anonymous__3623,Vvar__2___24Anonymous__3625) = cCoq_2esetoid__ring_2eField__theory_2eFEsub___24a3(Vvar__0__C__3622,Vvar__1___24Anonymous__3624,Vvar__2___24Anonymous__3626)
     => ( Vvar__2___24Anonymous__3625 = Vvar__2___24Anonymous__3626
        & Vvar__1___24Anonymous__3623 = Vvar__1___24Anonymous__3624
        & Vvar__0__C__3621 = Vvar__0__C__3622 ) ) ).

fof('$_inj_Coq.setoid_ring.Field_theory.mk_linear',axiom,
    ! [Vvar__0__C__3950,Vvar__0__C__3951,Vvar__1__num__3952,Vvar__1__num__3953,Vvar__2__denum__3954,Vvar__2__denum__3955,Vvar__3__condition__3956,Vvar__3__condition__3957] :
      ( cCoq_2esetoid__ring_2eField__theory_2emk__linear___24a4(Vvar__0__C__3950,Vvar__1__num__3952,Vvar__2__denum__3954,Vvar__3__condition__3956) = cCoq_2esetoid__ring_2eField__theory_2emk__linear___24a4(Vvar__0__C__3951,Vvar__1__num__3953,Vvar__2__denum__3955,Vvar__3__condition__3957)
     => ( Vvar__3__condition__3956 = Vvar__3__condition__3957
        & Vvar__2__denum__3954 = Vvar__2__denum__3955
        & Vvar__1__num__3952 = Vvar__1__num__3953
        & Vvar__0__C__3950 = Vvar__0__C__3951 ) ) ).

fof('$_inj_Coq.setoid_ring.Field_theory.mk_rsplit',axiom,
    ! [Vvar__0__C__4228,Vvar__0__C__4229,Vvar__1__rsplit__left__4230,Vvar__1__rsplit__left__4231,Vvar__2__rsplit__common__4232,Vvar__2__rsplit__common__4233,Vvar__3__rsplit__right__4234,Vvar__3__rsplit__right__4235] :
      ( cCoq_2esetoid__ring_2eField__theory_2emk__rsplit___24a4(Vvar__0__C__4228,Vvar__1__rsplit__left__4230,Vvar__2__rsplit__common__4232,Vvar__3__rsplit__right__4234) = cCoq_2esetoid__ring_2eField__theory_2emk__rsplit___24a4(Vvar__0__C__4229,Vvar__1__rsplit__left__4231,Vvar__2__rsplit__common__4233,Vvar__3__rsplit__right__4235)
     => ( Vvar__3__rsplit__right__4234 = Vvar__3__rsplit__right__4235
        & Vvar__2__rsplit__common__4232 = Vvar__2__rsplit__common__4233
        & Vvar__1__rsplit__left__4230 = Vvar__1__rsplit__left__4231
        & Vvar__0__C__4228 = Vvar__0__C__4229 ) ) ).

fof('$_inj_Coq.setoid_ring.InitialRing.mkhypo',axiom,
    ! [Vvar__0__hypo__type__27034,Vvar__0__hypo__type__27035,Vvar__1__hypo__proof__27036,Vvar__1__hypo__proof__27037] :
      ( cCoq_2esetoid__ring_2eInitialRing_2emkhypo___24a2(Vvar__0__hypo__type__27034,Vvar__1__hypo__proof__27036) = cCoq_2esetoid__ring_2eInitialRing_2emkhypo___24a2(Vvar__0__hypo__type__27035,Vvar__1__hypo__proof__27037)
     => ( Vvar__1__hypo__proof__27036 = Vvar__1__hypo__proof__27037
        & Vvar__0__hypo__type__27034 = Vvar__0__hypo__type__27035 ) ) ).

fof('$_inj_Coq.setoid_ring.Ring_polynom.PEI',axiom,
    ! [Vvar__0__C__5037,Vvar__0__C__5038] :
      ( cCoq_2esetoid__ring_2eRing__polynom_2ePEI___24a1(Vvar__0__C__5037) = cCoq_2esetoid__ring_2eRing__polynom_2ePEI___24a1(Vvar__0__C__5038)
     => Vvar__0__C__5037 = Vvar__0__C__5038 ) ).

fof('$_inj_Coq.setoid_ring.Ring_polynom.PEO',axiom,
    ! [Vvar__0__C__5035,Vvar__0__C__5036] :
      ( cCoq_2esetoid__ring_2eRing__polynom_2ePEO___24a1(Vvar__0__C__5035) = cCoq_2esetoid__ring_2eRing__polynom_2ePEO___24a1(Vvar__0__C__5036)
     => Vvar__0__C__5035 = Vvar__0__C__5036 ) ).

fof('$_inj_Coq.setoid_ring.Ring_polynom.PEX',axiom,
    ! [Vvar__0__C__5043,Vvar__0__C__5044,Vvar__1___24Anonymous__5045,Vvar__1___24Anonymous__5046] :
      ( cCoq_2esetoid__ring_2eRing__polynom_2ePEX___24a2(Vvar__0__C__5043,Vvar__1___24Anonymous__5045) = cCoq_2esetoid__ring_2eRing__polynom_2ePEX___24a2(Vvar__0__C__5044,Vvar__1___24Anonymous__5046)
     => ( Vvar__1___24Anonymous__5045 = Vvar__1___24Anonymous__5046
        & Vvar__0__C__5043 = Vvar__0__C__5044 ) ) ).

fof('$_inj_Coq.setoid_ring.Ring_polynom.PEadd',axiom,
    ! [Vvar__0__C__5047,Vvar__0__C__5048,Vvar__1___24Anonymous__5049,Vvar__1___24Anonymous__5050,Vvar__2___24Anonymous__5051,Vvar__2___24Anonymous__5052] :
      ( cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(Vvar__0__C__5047,Vvar__1___24Anonymous__5049,Vvar__2___24Anonymous__5051) = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(Vvar__0__C__5048,Vvar__1___24Anonymous__5050,Vvar__2___24Anonymous__5052)
     => ( Vvar__2___24Anonymous__5051 = Vvar__2___24Anonymous__5052
        & Vvar__1___24Anonymous__5049 = Vvar__1___24Anonymous__5050
        & Vvar__0__C__5047 = Vvar__0__C__5048 ) ) ).

fof('$_inj_Coq.setoid_ring.Ring_polynom.PEc',axiom,
    ! [Vvar__0__C__5039,Vvar__0__C__5040,Vvar__1___24Anonymous__5041,Vvar__1___24Anonymous__5042] :
      ( cCoq_2esetoid__ring_2eRing__polynom_2ePEc___24a2(Vvar__0__C__5039,Vvar__1___24Anonymous__5041) = cCoq_2esetoid__ring_2eRing__polynom_2ePEc___24a2(Vvar__0__C__5040,Vvar__1___24Anonymous__5042)
     => ( Vvar__1___24Anonymous__5041 = Vvar__1___24Anonymous__5042
        & Vvar__0__C__5039 = Vvar__0__C__5040 ) ) ).

fof('$_inj_Coq.setoid_ring.Ring_polynom.PEmul',axiom,
    ! [Vvar__0__C__5059,Vvar__0__C__5060,Vvar__1___24Anonymous__5061,Vvar__1___24Anonymous__5062,Vvar__2___24Anonymous__5063,Vvar__2___24Anonymous__5064] :
      ( cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(Vvar__0__C__5059,Vvar__1___24Anonymous__5061,Vvar__2___24Anonymous__5063) = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(Vvar__0__C__5060,Vvar__1___24Anonymous__5062,Vvar__2___24Anonymous__5064)
     => ( Vvar__2___24Anonymous__5063 = Vvar__2___24Anonymous__5064
        & Vvar__1___24Anonymous__5061 = Vvar__1___24Anonymous__5062
        & Vvar__0__C__5059 = Vvar__0__C__5060 ) ) ).

fof('$_inj_Coq.setoid_ring.Ring_polynom.PEopp',axiom,
    ! [Vvar__0__C__5065,Vvar__0__C__5066,Vvar__1___24Anonymous__5067,Vvar__1___24Anonymous__5068] :
      ( cCoq_2esetoid__ring_2eRing__polynom_2ePEopp___24a2(Vvar__0__C__5065,Vvar__1___24Anonymous__5067) = cCoq_2esetoid__ring_2eRing__polynom_2ePEopp___24a2(Vvar__0__C__5066,Vvar__1___24Anonymous__5068)
     => ( Vvar__1___24Anonymous__5067 = Vvar__1___24Anonymous__5068
        & Vvar__0__C__5065 = Vvar__0__C__5066 ) ) ).

fof('$_inj_Coq.setoid_ring.Ring_polynom.PEpow',axiom,
    ! [Vvar__0__C__5069,Vvar__0__C__5070,Vvar__1___24Anonymous__5071,Vvar__1___24Anonymous__5072,Vvar__2___24Anonymous__5073,Vvar__2___24Anonymous__5074] :
      ( cCoq_2esetoid__ring_2eRing__polynom_2ePEpow___24a3(Vvar__0__C__5069,Vvar__1___24Anonymous__5071,Vvar__2___24Anonymous__5073) = cCoq_2esetoid__ring_2eRing__polynom_2ePEpow___24a3(Vvar__0__C__5070,Vvar__1___24Anonymous__5072,Vvar__2___24Anonymous__5074)
     => ( Vvar__2___24Anonymous__5073 = Vvar__2___24Anonymous__5074
        & Vvar__1___24Anonymous__5071 = Vvar__1___24Anonymous__5072
        & Vvar__0__C__5069 = Vvar__0__C__5070 ) ) ).

fof('$_inj_Coq.setoid_ring.Ring_polynom.PEsub',axiom,
    ! [Vvar__0__C__5053,Vvar__0__C__5054,Vvar__1___24Anonymous__5055,Vvar__1___24Anonymous__5056,Vvar__2___24Anonymous__5057,Vvar__2___24Anonymous__5058] :
      ( cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(Vvar__0__C__5053,Vvar__1___24Anonymous__5055,Vvar__2___24Anonymous__5057) = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(Vvar__0__C__5054,Vvar__1___24Anonymous__5056,Vvar__2___24Anonymous__5058)
     => ( Vvar__2___24Anonymous__5057 = Vvar__2___24Anonymous__5058
        & Vvar__1___24Anonymous__5055 = Vvar__1___24Anonymous__5056
        & Vvar__0__C__5053 = Vvar__0__C__5054 ) ) ).

fof('$_inj_Coq.setoid_ring.Ring_polynom.PX',axiom,
    ! [Vvar__0__C__4808,Vvar__0__C__4809,Vvar__1___24Anonymous__4810,Vvar__1___24Anonymous__4811,Vvar__2___24Anonymous__4812,Vvar__2___24Anonymous__4813,Vvar__3___24Anonymous__4814,Vvar__3___24Anonymous__4815] :
      ( cCoq_2esetoid__ring_2eRing__polynom_2ePX___24a4(Vvar__0__C__4808,Vvar__1___24Anonymous__4810,Vvar__2___24Anonymous__4812,Vvar__3___24Anonymous__4814) = cCoq_2esetoid__ring_2eRing__polynom_2ePX___24a4(Vvar__0__C__4809,Vvar__1___24Anonymous__4811,Vvar__2___24Anonymous__4813,Vvar__3___24Anonymous__4815)
     => ( Vvar__3___24Anonymous__4814 = Vvar__3___24Anonymous__4815
        & Vvar__2___24Anonymous__4812 = Vvar__2___24Anonymous__4813
        & Vvar__1___24Anonymous__4810 = Vvar__1___24Anonymous__4811
        & Vvar__0__C__4808 = Vvar__0__C__4809 ) ) ).

fof('$_inj_Coq.setoid_ring.Ring_polynom.Pc',axiom,
    ! [Vvar__0__C__4798,Vvar__0__C__4799,Vvar__1___24Anonymous__4800,Vvar__1___24Anonymous__4801] :
      ( cCoq_2esetoid__ring_2eRing__polynom_2ePc___24a2(Vvar__0__C__4798,Vvar__1___24Anonymous__4800) = cCoq_2esetoid__ring_2eRing__polynom_2ePc___24a2(Vvar__0__C__4799,Vvar__1___24Anonymous__4801)
     => ( Vvar__1___24Anonymous__4800 = Vvar__1___24Anonymous__4801
        & Vvar__0__C__4798 = Vvar__0__C__4799 ) ) ).

fof('$_inj_Coq.setoid_ring.Ring_polynom.Pinj',axiom,
    ! [Vvar__0__C__4802,Vvar__0__C__4803,Vvar__1___24Anonymous__4804,Vvar__1___24Anonymous__4805,Vvar__2___24Anonymous__4806,Vvar__2___24Anonymous__4807] :
      ( cCoq_2esetoid__ring_2eRing__polynom_2ePinj___24a3(Vvar__0__C__4802,Vvar__1___24Anonymous__4804,Vvar__2___24Anonymous__4806) = cCoq_2esetoid__ring_2eRing__polynom_2ePinj___24a3(Vvar__0__C__4803,Vvar__1___24Anonymous__4805,Vvar__2___24Anonymous__4807)
     => ( Vvar__2___24Anonymous__4806 = Vvar__2___24Anonymous__4807
        & Vvar__1___24Anonymous__4804 = Vvar__1___24Anonymous__4805
        & Vvar__0__C__4802 = Vvar__0__C__4803 ) ) ).

fof('$_inj_Coq.setoid_ring.Ring_polynom.vmon',axiom,
    ! [Vvar__0___24Anonymous__4849,Vvar__0___24Anonymous__4850,Vvar__1___24Anonymous__4851,Vvar__1___24Anonymous__4852] :
      ( cCoq_2esetoid__ring_2eRing__polynom_2evmon___24a2(Vvar__0___24Anonymous__4849,Vvar__1___24Anonymous__4851) = cCoq_2esetoid__ring_2eRing__polynom_2evmon___24a2(Vvar__0___24Anonymous__4850,Vvar__1___24Anonymous__4852)
     => ( Vvar__1___24Anonymous__4851 = Vvar__1___24Anonymous__4852
        & Vvar__0___24Anonymous__4849 = Vvar__0___24Anonymous__4850 ) ) ).

fof('$_inj_Coq.setoid_ring.Ring_polynom.zmon',axiom,
    ! [Vvar__0___24Anonymous__4845,Vvar__0___24Anonymous__4846,Vvar__1___24Anonymous__4847,Vvar__1___24Anonymous__4848] :
      ( cCoq_2esetoid__ring_2eRing__polynom_2ezmon___24a2(Vvar__0___24Anonymous__4845,Vvar__1___24Anonymous__4847) = cCoq_2esetoid__ring_2eRing__polynom_2ezmon___24a2(Vvar__0___24Anonymous__4846,Vvar__1___24Anonymous__4848)
     => ( Vvar__1___24Anonymous__4847 = Vvar__1___24Anonymous__4848
        & Vvar__0___24Anonymous__4845 = Vvar__0___24Anonymous__4846 ) ) ).

fof('$_inj_Coq.setoid_ring.Ring_theory.Computational',axiom,
    ! [Vvar__0__R__28545,Vvar__0__R__28546,Vvar__1__req__28547,Vvar__1__req__28548,Vvar__2__reqb__28549,Vvar__2__reqb__28550,Vvar__3___24Anonymous__28551,Vvar__3___24Anonymous__28552] :
      ( cCoq_2esetoid__ring_2eRing__theory_2eComputational___24a3(Vvar__0__R__28545,Vvar__1__req__28547,Vvar__2__reqb__28549) = cCoq_2esetoid__ring_2eRing__theory_2eComputational___24a3(Vvar__0__R__28546,Vvar__1__req__28548,Vvar__2__reqb__28550)
     => ( c_24Proof = c_24Proof
        & Vvar__2__reqb__28549 = Vvar__2__reqb__28550
        & Vvar__1__req__28547 = Vvar__1__req__28548
        & Vvar__0__R__28545 = Vvar__0__R__28546 ) ) ).

fof('$_inj_Coq.setoid_ring.Ring_theory.Morphism',axiom,
    ! [Vvar__0__R__28553,Vvar__0__R__28554,Vvar__1__rO__28555,Vvar__1__rO__28556,Vvar__2__rI__28557,Vvar__2__rI__28558,Vvar__3__radd__28559,Vvar__3__radd__28560,Vvar__4__rmul__28561,Vvar__4__rmul__28562,Vvar__5__rsub__28563,Vvar__5__rsub__28564,Vvar__6__ropp__28565,Vvar__6__ropp__28566,Vvar__7__req__28567,Vvar__7__req__28568,Vvar__8__C__28569,Vvar__8__C__28570,Vvar__9__cO__28571,Vvar__9__cO__28572,Vvar__10__cI__28573,Vvar__10__cI__28574,Vvar__11__cadd__28575,Vvar__11__cadd__28576,Vvar__12__cmul__28577,Vvar__12__cmul__28578,Vvar__13__csub__28579,Vvar__13__csub__28580,Vvar__14__copp__28581,Vvar__14__copp__28582,Vvar__15__ceqb__28583,Vvar__15__ceqb__28584,Vvar__16__phi__28585,Vvar__16__phi__28586,Vvar__17___24Anonymous__28587,Vvar__17___24Anonymous__28588] :
      ( cCoq_2esetoid__ring_2eRing__theory_2eMorphism___24a17(Vvar__0__R__28553,Vvar__1__rO__28555,Vvar__2__rI__28557,Vvar__3__radd__28559,Vvar__4__rmul__28561,Vvar__5__rsub__28563,Vvar__6__ropp__28565,Vvar__7__req__28567,Vvar__8__C__28569,Vvar__9__cO__28571,Vvar__10__cI__28573,Vvar__11__cadd__28575,Vvar__12__cmul__28577,Vvar__13__csub__28579,Vvar__14__copp__28581,Vvar__15__ceqb__28583,Vvar__16__phi__28585) = cCoq_2esetoid__ring_2eRing__theory_2eMorphism___24a17(Vvar__0__R__28554,Vvar__1__rO__28556,Vvar__2__rI__28558,Vvar__3__radd__28560,Vvar__4__rmul__28562,Vvar__5__rsub__28564,Vvar__6__ropp__28566,Vvar__7__req__28568,Vvar__8__C__28570,Vvar__9__cO__28572,Vvar__10__cI__28574,Vvar__11__cadd__28576,Vvar__12__cmul__28578,Vvar__13__csub__28580,Vvar__14__copp__28582,Vvar__15__ceqb__28584,Vvar__16__phi__28586)
     => ( c_24Proof = c_24Proof
        & Vvar__16__phi__28585 = Vvar__16__phi__28586
        & Vvar__15__ceqb__28583 = Vvar__15__ceqb__28584
        & Vvar__14__copp__28581 = Vvar__14__copp__28582
        & Vvar__13__csub__28579 = Vvar__13__csub__28580
        & Vvar__12__cmul__28577 = Vvar__12__cmul__28578
        & Vvar__11__cadd__28575 = Vvar__11__cadd__28576
        & Vvar__10__cI__28573 = Vvar__10__cI__28574
        & Vvar__9__cO__28571 = Vvar__9__cO__28572
        & Vvar__8__C__28569 = Vvar__8__C__28570
        & Vvar__7__req__28567 = Vvar__7__req__28568
        & Vvar__6__ropp__28565 = Vvar__6__ropp__28566
        & Vvar__5__rsub__28563 = Vvar__5__rsub__28564
        & Vvar__4__rmul__28561 = Vvar__4__rmul__28562
        & Vvar__3__radd__28559 = Vvar__3__radd__28560
        & Vvar__2__rI__28557 = Vvar__2__rI__28558
        & Vvar__1__rO__28555 = Vvar__1__rO__28556
        & Vvar__0__R__28553 = Vvar__0__R__28554 ) ) ).

fof('$_inversion_Coq.Arith.Between.P_nth',axiom,
    ! [Vvar__0__P__26057,Vvar__1__Q__26059,Vvar__2__init__26062,Vvar__3___24Anonymous__26063,Vvar__4___24Anonymous__26064] :
      ( c_24__type__26090___24t(Vvar__0__P__26057,Vvar__1__Q__26059,Vvar__2__init__26062,Vvar__3___24Anonymous__26063,Vvar__4___24Anonymous__26064,Vvar__0__P__26057)
     => ( c_24__type__26098___24t(Vvar__0__P__26057,Vvar__1__Q__26059,Vvar__2__init__26062,Vvar__3___24Anonymous__26063,Vvar__4___24Anonymous__26064,Vvar__1__Q__26059)
       => ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__2__init__26062)
         => ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__3___24Anonymous__26063)
           => ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__4___24Anonymous__26064)
             => ( cCoq_2eArith_2eBetween_2eP__nth___24a5(Vvar__0__P__26057,Vvar__1__Q__26059,Vvar__2__init__26062,Vvar__3___24Anonymous__26063,Vvar__4___24Anonymous__26064)
               => ( ( Vvar__4___24Anonymous__26064 = cCoq_2eInit_2eDatatypes_2eO
                    & Vvar__3___24Anonymous__26063 = Vvar__2__init__26062 )
                  | ? [Vvar__3__k__26078] :
                      ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__3__k__26078)
                      & ? [Vvar__4__l__26079] :
                          ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__4__l__26079)
                          & ? [Vvar__5__n__26080] :
                              ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__5__n__26080)
                              & cCoq_2eArith_2eBetween_2eP__nth___24a5(Vvar__0__P__26057,Vvar__1__Q__26059,Vvar__2__init__26062,Vvar__3__k__26078,Vvar__5__n__26080)
                              & cCoq_2eArith_2eBetween_2ebetween___24a3(Vvar__0__P__26057,cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__3__k__26078),Vvar__4__l__26079)
                              & p(happ(Vvar__1__Q__26059,Vvar__4__l__26079))
                              & Vvar__4___24Anonymous__26064 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__5__n__26080)
                              & Vvar__3___24Anonymous__26063 = Vvar__4__l__26079 ) ) ) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.Arith.Between.between',axiom,
    ! [Vvar__0__P__26017,Vvar__1__k__26019,Vvar__2___24Anonymous__26020] :
      ( c_24__type__26034___24t(Vvar__0__P__26017,Vvar__1__k__26019,Vvar__2___24Anonymous__26020,Vvar__0__P__26017)
     => ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__1__k__26019)
       => ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__2___24Anonymous__26020)
         => ( cCoq_2eArith_2eBetween_2ebetween___24a3(Vvar__0__P__26017,Vvar__1__k__26019,Vvar__2___24Anonymous__26020)
           => ( Vvar__2___24Anonymous__26020 = Vvar__1__k__26019
              | ? [Vvar__2__l__26028] :
                  ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__2__l__26028)
                  & cCoq_2eArith_2eBetween_2ebetween___24a3(Vvar__0__P__26017,Vvar__1__k__26019,Vvar__2__l__26028)
                  & p(happ(Vvar__0__P__26017,Vvar__2__l__26028))
                  & Vvar__2___24Anonymous__26020 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__2__l__26028) ) ) ) ) ) ) ).

fof('$_inversion_Coq.Arith.Between.exists_between',axiom,
    ! [Vvar__0__Q__26036,Vvar__1__k__26038,Vvar__2___24Anonymous__26039] :
      ( c_24__type__26055___24t(Vvar__0__Q__26036,Vvar__1__k__26038,Vvar__2___24Anonymous__26039,Vvar__0__Q__26036)
     => ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__1__k__26038)
       => ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__2___24Anonymous__26039)
         => ( cCoq_2eArith_2eBetween_2eexists__between___24a3(Vvar__0__Q__26036,Vvar__1__k__26038,Vvar__2___24Anonymous__26039)
           => ( ? [Vvar__2__l__26044] :
                  ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__2__l__26044)
                  & cCoq_2eArith_2eBetween_2eexists__between___24a3(Vvar__0__Q__26036,Vvar__1__k__26038,Vvar__2__l__26044)
                  & Vvar__2___24Anonymous__26039 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__2__l__26044) )
              | ? [Vvar__2__l__26049] :
                  ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__2__l__26049)
                  & cCoq_2eInit_2ePeano_2ele___24a2(Vvar__1__k__26038,Vvar__2__l__26049)
                  & p(happ(Vvar__0__Q__26036,Vvar__2__l__26049))
                  & Vvar__2___24Anonymous__26039 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__2__l__26049) ) ) ) ) ) ) ).

fof('$_inversion_Coq.Arith.Even.even',axiom,
    ! [Vvar__0___24Anonymous__12420] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__12420)
     => ( cCoq_2eArith_2eEven_2eeven___24a1(Vvar__0___24Anonymous__12420)
       => ( Vvar__0___24Anonymous__12420 = cCoq_2eInit_2eDatatypes_2eO
          | ? [Vvar__0__n__12422] :
              ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0__n__12422)
              & cCoq_2eArith_2eEven_2eodd___24a1(Vvar__0__n__12422)
              & Vvar__0___24Anonymous__12420 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0__n__12422) ) ) ) ) ).

fof('$_inversion_Coq.Arith.Even.odd',axiom,
    ! [Vvar__0___24Anonymous__12424] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__12424)
     => ( cCoq_2eArith_2eEven_2eodd___24a1(Vvar__0___24Anonymous__12424)
       => ? [Vvar__0__n__12426] :
            ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0__n__12426)
            & cCoq_2eArith_2eEven_2eeven___24a1(Vvar__0__n__12426)
            & Vvar__0___24Anonymous__12424 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0__n__12426) ) ) ) ).

fof('$_inversion_Coq.Bool.Bool.reflect',axiom,
    ! [Vvar__0__P__10945,Vvar__1___24Anonymous__10946,VX10947] :
      ( cProp___24t(Vvar__0__P__10945)
     => ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__1___24Anonymous__10946)
       => ( cCoq_2eBool_2eBool_2ereflect___24t(Vvar__0__P__10945,Vvar__1___24Anonymous__10946,VX10947)
         => ( ( p(Vvar__0__P__10945)
              & Vvar__1___24Anonymous__10946 = cCoq_2eInit_2eDatatypes_2etrue
              & VX10947 = cCoq_2eBool_2eBool_2eReflectT___24a1(Vvar__0__P__10945) )
            | ( ~ p(Vvar__0__P__10945)
              & Vvar__1___24Anonymous__10946 = cCoq_2eInit_2eDatatypes_2efalse
              & VX10947 = cCoq_2eBool_2eBool_2eReflectF___24a1(Vvar__0__P__10945) ) ) ) ) ) ).

fof('$_inversion_Coq.FSets.FSetPositive.PositiveSet.ct',axiom,
    ! [Vvar__0___24Anonymous__29680,Vvar__1___24Anonymous__29681,Vvar__2___24Anonymous__29682] :
      ( cCoq_2eInit_2eDatatypes_2ecomparison___24t(Vvar__0___24Anonymous__29680)
     => ( cCoq_2eInit_2eDatatypes_2ecomparison___24t(Vvar__1___24Anonymous__29681)
       => ( cCoq_2eInit_2eDatatypes_2ecomparison___24t(Vvar__2___24Anonymous__29682)
         => ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2ect___24a3(Vvar__0___24Anonymous__29680,Vvar__1___24Anonymous__29681,Vvar__2___24Anonymous__29682)
           => ( ? [Vvar__0__x__29684] :
                  ( cCoq_2eInit_2eDatatypes_2ecomparison___24t(Vvar__0__x__29684)
                  & Vvar__2___24Anonymous__29682 = Vvar__0__x__29684
                  & Vvar__1___24Anonymous__29681 = Vvar__0__x__29684
                  & Vvar__0___24Anonymous__29680 = Vvar__0__x__29684 )
              | ? [Vvar__0__x__29685] :
                  ( cCoq_2eInit_2eDatatypes_2ecomparison___24t(Vvar__0__x__29685)
                  & Vvar__2___24Anonymous__29682 = Vvar__0__x__29685
                  & Vvar__1___24Anonymous__29681 = cCoq_2eInit_2eDatatypes_2eEq
                  & Vvar__0___24Anonymous__29680 = Vvar__0__x__29685 )
              | ? [Vvar__0__x__29686] :
                  ( cCoq_2eInit_2eDatatypes_2ecomparison___24t(Vvar__0__x__29686)
                  & Vvar__2___24Anonymous__29682 = Vvar__0__x__29686
                  & Vvar__1___24Anonymous__29681 = Vvar__0__x__29686
                  & Vvar__0___24Anonymous__29680 = cCoq_2eInit_2eDatatypes_2eEq )
              | ? [Vvar__0__x__29687] :
                  ( cCoq_2eInit_2eDatatypes_2ecomparison___24t(Vvar__0__x__29687)
                  & Vvar__2___24Anonymous__29682 = Vvar__0__x__29687
                  & Vvar__1___24Anonymous__29681 = cCoq_2eInit_2eDatatypes_2eLt
                  & Vvar__0___24Anonymous__29680 = cCoq_2eInit_2eDatatypes_2eGt )
              | ? [Vvar__0__x__29688] :
                  ( cCoq_2eInit_2eDatatypes_2ecomparison___24t(Vvar__0__x__29688)
                  & Vvar__2___24Anonymous__29682 = Vvar__0__x__29688
                  & Vvar__1___24Anonymous__29681 = cCoq_2eInit_2eDatatypes_2eGt
                  & Vvar__0___24Anonymous__29680 = cCoq_2eInit_2eDatatypes_2eLt ) ) ) ) ) ) ).

fof('$_inversion_Coq.FSets.FSetPositive.PositiveSet.tree',axiom,
    ! [VX25988] :
      ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree___24t(VX25988)
     => ( VX25988 = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eLeaf
        | ? [Vvar__0___24Anonymous__25989] :
            ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree___24t(Vvar__0___24Anonymous__25989)
            & ? [Vvar__1___24Anonymous__25990] :
                ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__1___24Anonymous__25990)
                & ? [Vvar__2___24Anonymous__25991] :
                    ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree___24t(Vvar__2___24Anonymous__25991)
                    & VX25988 = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eNode___24a3(Vvar__0___24Anonymous__25989,Vvar__1___24Anonymous__25990,Vvar__2___24Anonymous__25991) ) ) ) ) ) ).

fof('$_inversion_Coq.Init.Byte.byte',axiom,
    ! [VX11123] :
      ( cCoq_2eInit_2eByte_2ebyte___24t(VX11123)
     => ( VX11123 = cCoq_2eInit_2eByte_2ex00
        | VX11123 = cCoq_2eInit_2eByte_2ex01
        | VX11123 = cCoq_2eInit_2eByte_2ex02
        | VX11123 = cCoq_2eInit_2eByte_2ex03
        | VX11123 = cCoq_2eInit_2eByte_2ex04
        | VX11123 = cCoq_2eInit_2eByte_2ex05
        | VX11123 = cCoq_2eInit_2eByte_2ex06
        | VX11123 = cCoq_2eInit_2eByte_2ex07
        | VX11123 = cCoq_2eInit_2eByte_2ex08
        | VX11123 = cCoq_2eInit_2eByte_2ex09
        | VX11123 = cCoq_2eInit_2eByte_2ex0a
        | VX11123 = cCoq_2eInit_2eByte_2ex0b
        | VX11123 = cCoq_2eInit_2eByte_2ex0c
        | VX11123 = cCoq_2eInit_2eByte_2ex0d
        | VX11123 = cCoq_2eInit_2eByte_2ex0e
        | VX11123 = cCoq_2eInit_2eByte_2ex0f
        | VX11123 = cCoq_2eInit_2eByte_2ex10
        | VX11123 = cCoq_2eInit_2eByte_2ex11
        | VX11123 = cCoq_2eInit_2eByte_2ex12
        | VX11123 = cCoq_2eInit_2eByte_2ex13
        | VX11123 = cCoq_2eInit_2eByte_2ex14
        | VX11123 = cCoq_2eInit_2eByte_2ex15
        | VX11123 = cCoq_2eInit_2eByte_2ex16
        | VX11123 = cCoq_2eInit_2eByte_2ex17
        | VX11123 = cCoq_2eInit_2eByte_2ex18
        | VX11123 = cCoq_2eInit_2eByte_2ex19
        | VX11123 = cCoq_2eInit_2eByte_2ex1a
        | VX11123 = cCoq_2eInit_2eByte_2ex1b
        | VX11123 = cCoq_2eInit_2eByte_2ex1c
        | VX11123 = cCoq_2eInit_2eByte_2ex1d
        | VX11123 = cCoq_2eInit_2eByte_2ex1e
        | VX11123 = cCoq_2eInit_2eByte_2ex1f
        | VX11123 = cCoq_2eInit_2eByte_2ex20
        | VX11123 = cCoq_2eInit_2eByte_2ex21
        | VX11123 = cCoq_2eInit_2eByte_2ex22
        | VX11123 = cCoq_2eInit_2eByte_2ex23
        | VX11123 = cCoq_2eInit_2eByte_2ex24
        | VX11123 = cCoq_2eInit_2eByte_2ex25
        | VX11123 = cCoq_2eInit_2eByte_2ex26
        | VX11123 = cCoq_2eInit_2eByte_2ex27
        | VX11123 = cCoq_2eInit_2eByte_2ex28
        | VX11123 = cCoq_2eInit_2eByte_2ex29
        | VX11123 = cCoq_2eInit_2eByte_2ex2a
        | VX11123 = cCoq_2eInit_2eByte_2ex2b
        | VX11123 = cCoq_2eInit_2eByte_2ex2c
        | VX11123 = cCoq_2eInit_2eByte_2ex2d
        | VX11123 = cCoq_2eInit_2eByte_2ex2e
        | VX11123 = cCoq_2eInit_2eByte_2ex2f
        | VX11123 = cCoq_2eInit_2eByte_2ex30
        | VX11123 = cCoq_2eInit_2eByte_2ex31
        | VX11123 = cCoq_2eInit_2eByte_2ex32
        | VX11123 = cCoq_2eInit_2eByte_2ex33
        | VX11123 = cCoq_2eInit_2eByte_2ex34
        | VX11123 = cCoq_2eInit_2eByte_2ex35
        | VX11123 = cCoq_2eInit_2eByte_2ex36
        | VX11123 = cCoq_2eInit_2eByte_2ex37
        | VX11123 = cCoq_2eInit_2eByte_2ex38
        | VX11123 = cCoq_2eInit_2eByte_2ex39
        | VX11123 = cCoq_2eInit_2eByte_2ex3a
        | VX11123 = cCoq_2eInit_2eByte_2ex3b
        | VX11123 = cCoq_2eInit_2eByte_2ex3c
        | VX11123 = cCoq_2eInit_2eByte_2ex3d
        | VX11123 = cCoq_2eInit_2eByte_2ex3e
        | VX11123 = cCoq_2eInit_2eByte_2ex3f
        | VX11123 = cCoq_2eInit_2eByte_2ex40
        | VX11123 = cCoq_2eInit_2eByte_2ex41
        | VX11123 = cCoq_2eInit_2eByte_2ex42
        | VX11123 = cCoq_2eInit_2eByte_2ex43
        | VX11123 = cCoq_2eInit_2eByte_2ex44
        | VX11123 = cCoq_2eInit_2eByte_2ex45
        | VX11123 = cCoq_2eInit_2eByte_2ex46
        | VX11123 = cCoq_2eInit_2eByte_2ex47
        | VX11123 = cCoq_2eInit_2eByte_2ex48
        | VX11123 = cCoq_2eInit_2eByte_2ex49
        | VX11123 = cCoq_2eInit_2eByte_2ex4a
        | VX11123 = cCoq_2eInit_2eByte_2ex4b
        | VX11123 = cCoq_2eInit_2eByte_2ex4c
        | VX11123 = cCoq_2eInit_2eByte_2ex4d
        | VX11123 = cCoq_2eInit_2eByte_2ex4e
        | VX11123 = cCoq_2eInit_2eByte_2ex4f
        | VX11123 = cCoq_2eInit_2eByte_2ex50
        | VX11123 = cCoq_2eInit_2eByte_2ex51
        | VX11123 = cCoq_2eInit_2eByte_2ex52
        | VX11123 = cCoq_2eInit_2eByte_2ex53
        | VX11123 = cCoq_2eInit_2eByte_2ex54
        | VX11123 = cCoq_2eInit_2eByte_2ex55
        | VX11123 = cCoq_2eInit_2eByte_2ex56
        | VX11123 = cCoq_2eInit_2eByte_2ex57
        | VX11123 = cCoq_2eInit_2eByte_2ex58
        | VX11123 = cCoq_2eInit_2eByte_2ex59
        | VX11123 = cCoq_2eInit_2eByte_2ex5a
        | VX11123 = cCoq_2eInit_2eByte_2ex5b
        | VX11123 = cCoq_2eInit_2eByte_2ex5c
        | VX11123 = cCoq_2eInit_2eByte_2ex5d
        | VX11123 = cCoq_2eInit_2eByte_2ex5e
        | VX11123 = cCoq_2eInit_2eByte_2ex5f
        | VX11123 = cCoq_2eInit_2eByte_2ex60
        | VX11123 = cCoq_2eInit_2eByte_2ex61
        | VX11123 = cCoq_2eInit_2eByte_2ex62
        | VX11123 = cCoq_2eInit_2eByte_2ex63
        | VX11123 = cCoq_2eInit_2eByte_2ex64
        | VX11123 = cCoq_2eInit_2eByte_2ex65
        | VX11123 = cCoq_2eInit_2eByte_2ex66
        | VX11123 = cCoq_2eInit_2eByte_2ex67
        | VX11123 = cCoq_2eInit_2eByte_2ex68
        | VX11123 = cCoq_2eInit_2eByte_2ex69
        | VX11123 = cCoq_2eInit_2eByte_2ex6a
        | VX11123 = cCoq_2eInit_2eByte_2ex6b
        | VX11123 = cCoq_2eInit_2eByte_2ex6c
        | VX11123 = cCoq_2eInit_2eByte_2ex6d
        | VX11123 = cCoq_2eInit_2eByte_2ex6e
        | VX11123 = cCoq_2eInit_2eByte_2ex6f
        | VX11123 = cCoq_2eInit_2eByte_2ex70
        | VX11123 = cCoq_2eInit_2eByte_2ex71
        | VX11123 = cCoq_2eInit_2eByte_2ex72
        | VX11123 = cCoq_2eInit_2eByte_2ex73
        | VX11123 = cCoq_2eInit_2eByte_2ex74
        | VX11123 = cCoq_2eInit_2eByte_2ex75
        | VX11123 = cCoq_2eInit_2eByte_2ex76
        | VX11123 = cCoq_2eInit_2eByte_2ex77
        | VX11123 = cCoq_2eInit_2eByte_2ex78
        | VX11123 = cCoq_2eInit_2eByte_2ex79
        | VX11123 = cCoq_2eInit_2eByte_2ex7a
        | VX11123 = cCoq_2eInit_2eByte_2ex7b
        | VX11123 = cCoq_2eInit_2eByte_2ex7c
        | VX11123 = cCoq_2eInit_2eByte_2ex7d
        | VX11123 = cCoq_2eInit_2eByte_2ex7e
        | VX11123 = cCoq_2eInit_2eByte_2ex7f
        | VX11123 = cCoq_2eInit_2eByte_2ex80
        | VX11123 = cCoq_2eInit_2eByte_2ex81
        | VX11123 = cCoq_2eInit_2eByte_2ex82
        | VX11123 = cCoq_2eInit_2eByte_2ex83
        | VX11123 = cCoq_2eInit_2eByte_2ex84
        | VX11123 = cCoq_2eInit_2eByte_2ex85
        | VX11123 = cCoq_2eInit_2eByte_2ex86
        | VX11123 = cCoq_2eInit_2eByte_2ex87
        | VX11123 = cCoq_2eInit_2eByte_2ex88
        | VX11123 = cCoq_2eInit_2eByte_2ex89
        | VX11123 = cCoq_2eInit_2eByte_2ex8a
        | VX11123 = cCoq_2eInit_2eByte_2ex8b
        | VX11123 = cCoq_2eInit_2eByte_2ex8c
        | VX11123 = cCoq_2eInit_2eByte_2ex8d
        | VX11123 = cCoq_2eInit_2eByte_2ex8e
        | VX11123 = cCoq_2eInit_2eByte_2ex8f
        | VX11123 = cCoq_2eInit_2eByte_2ex90
        | VX11123 = cCoq_2eInit_2eByte_2ex91
        | VX11123 = cCoq_2eInit_2eByte_2ex92
        | VX11123 = cCoq_2eInit_2eByte_2ex93
        | VX11123 = cCoq_2eInit_2eByte_2ex94
        | VX11123 = cCoq_2eInit_2eByte_2ex95
        | VX11123 = cCoq_2eInit_2eByte_2ex96
        | VX11123 = cCoq_2eInit_2eByte_2ex97
        | VX11123 = cCoq_2eInit_2eByte_2ex98
        | VX11123 = cCoq_2eInit_2eByte_2ex99
        | VX11123 = cCoq_2eInit_2eByte_2ex9a
        | VX11123 = cCoq_2eInit_2eByte_2ex9b
        | VX11123 = cCoq_2eInit_2eByte_2ex9c
        | VX11123 = cCoq_2eInit_2eByte_2ex9d
        | VX11123 = cCoq_2eInit_2eByte_2ex9e
        | VX11123 = cCoq_2eInit_2eByte_2ex9f
        | VX11123 = cCoq_2eInit_2eByte_2exa0
        | VX11123 = cCoq_2eInit_2eByte_2exa1
        | VX11123 = cCoq_2eInit_2eByte_2exa2
        | VX11123 = cCoq_2eInit_2eByte_2exa3
        | VX11123 = cCoq_2eInit_2eByte_2exa4
        | VX11123 = cCoq_2eInit_2eByte_2exa5
        | VX11123 = cCoq_2eInit_2eByte_2exa6
        | VX11123 = cCoq_2eInit_2eByte_2exa7
        | VX11123 = cCoq_2eInit_2eByte_2exa8
        | VX11123 = cCoq_2eInit_2eByte_2exa9
        | VX11123 = cCoq_2eInit_2eByte_2exaa
        | VX11123 = cCoq_2eInit_2eByte_2exab
        | VX11123 = cCoq_2eInit_2eByte_2exac
        | VX11123 = cCoq_2eInit_2eByte_2exad
        | VX11123 = cCoq_2eInit_2eByte_2exae
        | VX11123 = cCoq_2eInit_2eByte_2exaf
        | VX11123 = cCoq_2eInit_2eByte_2exb0
        | VX11123 = cCoq_2eInit_2eByte_2exb1
        | VX11123 = cCoq_2eInit_2eByte_2exb2
        | VX11123 = cCoq_2eInit_2eByte_2exb3
        | VX11123 = cCoq_2eInit_2eByte_2exb4
        | VX11123 = cCoq_2eInit_2eByte_2exb5
        | VX11123 = cCoq_2eInit_2eByte_2exb6
        | VX11123 = cCoq_2eInit_2eByte_2exb7
        | VX11123 = cCoq_2eInit_2eByte_2exb8
        | VX11123 = cCoq_2eInit_2eByte_2exb9
        | VX11123 = cCoq_2eInit_2eByte_2exba
        | VX11123 = cCoq_2eInit_2eByte_2exbb
        | VX11123 = cCoq_2eInit_2eByte_2exbc
        | VX11123 = cCoq_2eInit_2eByte_2exbd
        | VX11123 = cCoq_2eInit_2eByte_2exbe
        | VX11123 = cCoq_2eInit_2eByte_2exbf
        | VX11123 = cCoq_2eInit_2eByte_2exc0
        | VX11123 = cCoq_2eInit_2eByte_2exc1
        | VX11123 = cCoq_2eInit_2eByte_2exc2
        | VX11123 = cCoq_2eInit_2eByte_2exc3
        | VX11123 = cCoq_2eInit_2eByte_2exc4
        | VX11123 = cCoq_2eInit_2eByte_2exc5
        | VX11123 = cCoq_2eInit_2eByte_2exc6
        | VX11123 = cCoq_2eInit_2eByte_2exc7
        | VX11123 = cCoq_2eInit_2eByte_2exc8
        | VX11123 = cCoq_2eInit_2eByte_2exc9
        | VX11123 = cCoq_2eInit_2eByte_2exca
        | VX11123 = cCoq_2eInit_2eByte_2excb
        | VX11123 = cCoq_2eInit_2eByte_2excc
        | VX11123 = cCoq_2eInit_2eByte_2excd
        | VX11123 = cCoq_2eInit_2eByte_2exce
        | VX11123 = cCoq_2eInit_2eByte_2excf
        | VX11123 = cCoq_2eInit_2eByte_2exd0
        | VX11123 = cCoq_2eInit_2eByte_2exd1
        | VX11123 = cCoq_2eInit_2eByte_2exd2
        | VX11123 = cCoq_2eInit_2eByte_2exd3
        | VX11123 = cCoq_2eInit_2eByte_2exd4
        | VX11123 = cCoq_2eInit_2eByte_2exd5
        | VX11123 = cCoq_2eInit_2eByte_2exd6
        | VX11123 = cCoq_2eInit_2eByte_2exd7
        | VX11123 = cCoq_2eInit_2eByte_2exd8
        | VX11123 = cCoq_2eInit_2eByte_2exd9
        | VX11123 = cCoq_2eInit_2eByte_2exda
        | VX11123 = cCoq_2eInit_2eByte_2exdb
        | VX11123 = cCoq_2eInit_2eByte_2exdc
        | VX11123 = cCoq_2eInit_2eByte_2exdd
        | VX11123 = cCoq_2eInit_2eByte_2exde
        | VX11123 = cCoq_2eInit_2eByte_2exdf
        | VX11123 = cCoq_2eInit_2eByte_2exe0
        | VX11123 = cCoq_2eInit_2eByte_2exe1
        | VX11123 = cCoq_2eInit_2eByte_2exe2
        | VX11123 = cCoq_2eInit_2eByte_2exe3
        | VX11123 = cCoq_2eInit_2eByte_2exe4
        | VX11123 = cCoq_2eInit_2eByte_2exe5
        | VX11123 = cCoq_2eInit_2eByte_2exe6
        | VX11123 = cCoq_2eInit_2eByte_2exe7
        | VX11123 = cCoq_2eInit_2eByte_2exe8
        | VX11123 = cCoq_2eInit_2eByte_2exe9
        | VX11123 = cCoq_2eInit_2eByte_2exea
        | VX11123 = cCoq_2eInit_2eByte_2exeb
        | VX11123 = cCoq_2eInit_2eByte_2exec
        | VX11123 = cCoq_2eInit_2eByte_2exed
        | VX11123 = cCoq_2eInit_2eByte_2exee
        | VX11123 = cCoq_2eInit_2eByte_2exef
        | VX11123 = cCoq_2eInit_2eByte_2exf0
        | VX11123 = cCoq_2eInit_2eByte_2exf1
        | VX11123 = cCoq_2eInit_2eByte_2exf2
        | VX11123 = cCoq_2eInit_2eByte_2exf3
        | VX11123 = cCoq_2eInit_2eByte_2exf4
        | VX11123 = cCoq_2eInit_2eByte_2exf5
        | VX11123 = cCoq_2eInit_2eByte_2exf6
        | VX11123 = cCoq_2eInit_2eByte_2exf7
        | VX11123 = cCoq_2eInit_2eByte_2exf8
        | VX11123 = cCoq_2eInit_2eByte_2exf9
        | VX11123 = cCoq_2eInit_2eByte_2exfa
        | VX11123 = cCoq_2eInit_2eByte_2exfb
        | VX11123 = cCoq_2eInit_2eByte_2exfc
        | VX11123 = cCoq_2eInit_2eByte_2exfd
        | VX11123 = cCoq_2eInit_2eByte_2exfe
        | VX11123 = cCoq_2eInit_2eByte_2exff ) ) ).

fof('$_inversion_Coq.Init.Datatypes.BoolSpec',axiom,
    ! [Vvar__0__P__26101,Vvar__1__Q__26102,Vvar__2___24Anonymous__26103] :
      ( cProp___24t(Vvar__0__P__26101)
     => ( cProp___24t(Vvar__1__Q__26102)
       => ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__2___24Anonymous__26103)
         => ( cCoq_2eInit_2eDatatypes_2eBoolSpec___24a3(Vvar__0__P__26101,Vvar__1__Q__26102,Vvar__2___24Anonymous__26103)
           => ( ( p(Vvar__0__P__26101)
                & Vvar__2___24Anonymous__26103 = cCoq_2eInit_2eDatatypes_2etrue )
              | ( p(Vvar__1__Q__26102)
                & Vvar__2___24Anonymous__26103 = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ) ) ).

fof('$_inversion_Coq.Init.Datatypes.CompareSpec',axiom,
    ! [Vvar__0__Peq__11947,Vvar__1__Plt__11948,Vvar__2__Pgt__11949,Vvar__3___24Anonymous__11950] :
      ( cProp___24t(Vvar__0__Peq__11947)
     => ( cProp___24t(Vvar__1__Plt__11948)
       => ( cProp___24t(Vvar__2__Pgt__11949)
         => ( cCoq_2eInit_2eDatatypes_2ecomparison___24t(Vvar__3___24Anonymous__11950)
           => ( cCoq_2eInit_2eDatatypes_2eCompareSpec___24a4(Vvar__0__Peq__11947,Vvar__1__Plt__11948,Vvar__2__Pgt__11949,Vvar__3___24Anonymous__11950)
             => ( ( p(Vvar__0__Peq__11947)
                  & Vvar__3___24Anonymous__11950 = cCoq_2eInit_2eDatatypes_2eEq )
                | ( p(Vvar__1__Plt__11948)
                  & Vvar__3___24Anonymous__11950 = cCoq_2eInit_2eDatatypes_2eLt )
                | ( p(Vvar__2__Pgt__11949)
                  & Vvar__3___24Anonymous__11950 = cCoq_2eInit_2eDatatypes_2eGt ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.Init.Datatypes.CompareSpecT',axiom,
    ! [Vvar__0__Peq__11964,Vvar__1__Plt__11965,Vvar__2__Pgt__11966,Vvar__3___24Anonymous__11967,VX11968] :
      ( cProp___24t(Vvar__0__Peq__11964)
     => ( cProp___24t(Vvar__1__Plt__11965)
       => ( cProp___24t(Vvar__2__Pgt__11966)
         => ( cCoq_2eInit_2eDatatypes_2ecomparison___24t(Vvar__3___24Anonymous__11967)
           => ( cCoq_2eInit_2eDatatypes_2eCompareSpecT___24t(Vvar__0__Peq__11964,Vvar__1__Plt__11965,Vvar__2__Pgt__11966,Vvar__3___24Anonymous__11967,VX11968)
             => ( ( p(Vvar__0__Peq__11964)
                  & Vvar__3___24Anonymous__11967 = cCoq_2eInit_2eDatatypes_2eEq
                  & VX11968 = cCoq_2eInit_2eDatatypes_2eCompEqT___24a3(Vvar__0__Peq__11964,Vvar__1__Plt__11965,Vvar__2__Pgt__11966) )
                | ( p(Vvar__1__Plt__11965)
                  & Vvar__3___24Anonymous__11967 = cCoq_2eInit_2eDatatypes_2eLt
                  & VX11968 = cCoq_2eInit_2eDatatypes_2eCompLtT___24a3(Vvar__0__Peq__11964,Vvar__1__Plt__11965,Vvar__2__Pgt__11966) )
                | ( p(Vvar__2__Pgt__11966)
                  & Vvar__3___24Anonymous__11967 = cCoq_2eInit_2eDatatypes_2eGt
                  & VX11968 = cCoq_2eInit_2eDatatypes_2eCompGtT___24a3(Vvar__0__Peq__11964,Vvar__1__Plt__11965,Vvar__2__Pgt__11966) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.Init.Datatypes.bool',axiom,
    ! [VX11771] :
      ( cCoq_2eInit_2eDatatypes_2ebool___24t(VX11771)
     => ( VX11771 = cCoq_2eInit_2eDatatypes_2etrue
        | VX11771 = cCoq_2eInit_2eDatatypes_2efalse ) ) ).

fof('$_inversion_Coq.Init.Datatypes.comparison',axiom,
    ! [VX1429] :
      ( cCoq_2eInit_2eDatatypes_2ecomparison___24t(VX1429)
     => ( VX1429 = cCoq_2eInit_2eDatatypes_2eEq
        | VX1429 = cCoq_2eInit_2eDatatypes_2eLt
        | VX1429 = cCoq_2eInit_2eDatatypes_2eGt ) ) ).

fof('$_inversion_Coq.Init.Datatypes.eq_true',axiom,
    ! [Vvar__0___24Anonymous__11777] :
      ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__0___24Anonymous__11777)
     => ( cCoq_2eInit_2eDatatypes_2eeq__true___24a1(Vvar__0___24Anonymous__11777)
       => Vvar__0___24Anonymous__11777 = cCoq_2eInit_2eDatatypes_2etrue ) ) ).

fof('$_inversion_Coq.Init.Datatypes.identity',axiom,
    ! [Vvar__0__A__26111,Vvar__1__a__26112,Vvar__2___24Anonymous__26113] :
      ( cType___24t(Vvar__0__A__26111)
     => ( t(Vvar__1__a__26112,Vvar__0__A__26111)
       => ( t(Vvar__2___24Anonymous__26113,Vvar__0__A__26111)
         => ( cCoq_2eInit_2eDatatypes_2eidentity___24a3(Vvar__0__A__26111,Vvar__1__a__26112,Vvar__2___24Anonymous__26113)
           => Vvar__2___24Anonymous__26113 = Vvar__1__a__26112 ) ) ) ) ).

fof('$_inversion_Coq.Init.Datatypes.list',axiom,
    ! [Vvar__0__A__3238,VX3239] :
      ( cType___24t(Vvar__0__A__3238)
     => ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__3238,VX3239)
       => ( VX3239 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__3238)
          | ? [Vvar__1___24Anonymous__3242] :
              ( t(Vvar__1___24Anonymous__3242,Vvar__0__A__3238)
              & ? [Vvar__2___24Anonymous__3243] :
                  ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__3238,Vvar__2___24Anonymous__3243)
                  & VX3239 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__3238,Vvar__1___24Anonymous__3242,Vvar__2___24Anonymous__3243) ) ) ) ) ) ).

fof('$_inversion_Coq.Init.Datatypes.nat',axiom,
    ! [VX30] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(VX30)
     => ( VX30 = cCoq_2eInit_2eDatatypes_2eO
        | ? [Vvar__0___24Anonymous__31] :
            ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__31)
            & VX30 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__31) ) ) ) ).

fof('$_inversion_Coq.Init.Datatypes.option',axiom,
    ! [Vvar__0__A__11806,VX11807] :
      ( cType___24t(Vvar__0__A__11806)
     => ( cCoq_2eInit_2eDatatypes_2eoption___24t(Vvar__0__A__11806,VX11807)
       => ( ? [Vvar__1___24Anonymous__11809] :
              ( t(Vvar__1___24Anonymous__11809,Vvar__0__A__11806)
              & VX11807 = cCoq_2eInit_2eDatatypes_2eSome___24a2(Vvar__0__A__11806,Vvar__1___24Anonymous__11809) )
          | VX11807 = cCoq_2eInit_2eDatatypes_2eNone___24a1(Vvar__0__A__11806) ) ) ) ).

fof('$_inversion_Coq.Init.Datatypes.prod',axiom,
    ! [Vvar__0__A__39,Vvar__1__B__40,VX41] :
      ( cType___24t(Vvar__0__A__39)
     => ( cType___24t(Vvar__1__B__40)
       => ( cCoq_2eInit_2eDatatypes_2eprod___24t(Vvar__0__A__39,Vvar__1__B__40,VX41)
         => ? [Vvar__2___24Anonymous__44] :
              ( t(Vvar__2___24Anonymous__44,Vvar__0__A__39)
              & ? [Vvar__3___24Anonymous__45] :
                  ( t(Vvar__3___24Anonymous__45,Vvar__1__B__40)
                  & VX41 = cCoq_2eInit_2eDatatypes_2epair___24a4(Vvar__0__A__39,Vvar__1__B__40,Vvar__2___24Anonymous__44,Vvar__3___24Anonymous__45) ) ) ) ) ) ).

fof('$_inversion_Coq.Init.Datatypes.sum',axiom,
    ! [Vvar__0__A__11825,Vvar__1__B__11826,VX11827] :
      ( cType___24t(Vvar__0__A__11825)
     => ( cType___24t(Vvar__1__B__11826)
       => ( cCoq_2eInit_2eDatatypes_2esum___24t(Vvar__0__A__11825,Vvar__1__B__11826,VX11827)
         => ( ? [Vvar__2___24Anonymous__11830] :
                ( t(Vvar__2___24Anonymous__11830,Vvar__0__A__11825)
                & VX11827 = cCoq_2eInit_2eDatatypes_2einl___24a3(Vvar__0__A__11825,Vvar__1__B__11826,Vvar__2___24Anonymous__11830) )
            | ? [Vvar__2___24Anonymous__11833] :
                ( t(Vvar__2___24Anonymous__11833,Vvar__1__B__11826)
                & VX11827 = cCoq_2eInit_2eDatatypes_2einr___24a3(Vvar__0__A__11825,Vvar__1__B__11826,Vvar__2___24Anonymous__11833) ) ) ) ) ) ).

fof('$_inversion_Coq.Init.Datatypes.unit',axiom,
    ! [VX2586] :
      ( cCoq_2eInit_2eDatatypes_2eunit___24t(VX2586)
     => VX2586 = cCoq_2eInit_2eDatatypes_2ett ) ).

fof('$_inversion_Coq.Init.Decimal.decimal',axiom,
    ! [VX26118] :
      ( cCoq_2eInit_2eDecimal_2edecimal___24t(VX26118)
     => ( ? [Vvar__0__i__26119] :
            ( cCoq_2eInit_2eDecimal_2eint___24t(Vvar__0__i__26119)
            & ? [Vvar__1__f__26120] :
                ( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__1__f__26120)
                & VX26118 = cCoq_2eInit_2eDecimal_2eDecimal___24a2(Vvar__0__i__26119,Vvar__1__f__26120) ) )
        | ? [Vvar__0__i__26121] :
            ( cCoq_2eInit_2eDecimal_2eint___24t(Vvar__0__i__26121)
            & ? [Vvar__1__f__26122] :
                ( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__1__f__26122)
                & ? [Vvar__2__e__26123] :
                    ( cCoq_2eInit_2eDecimal_2eint___24t(Vvar__2__e__26123)
                    & VX26118 = cCoq_2eInit_2eDecimal_2eDecimalExp___24a3(Vvar__0__i__26121,Vvar__1__f__26122,Vvar__2__e__26123) ) ) ) ) ) ).

fof('$_inversion_Coq.Init.Decimal.int',axiom,
    ! [VX12267] :
      ( cCoq_2eInit_2eDecimal_2eint___24t(VX12267)
     => ( ? [Vvar__0__d__12268] :
            ( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0__d__12268)
            & VX12267 = cCoq_2eInit_2eDecimal_2ePos___24a1(Vvar__0__d__12268) )
        | ? [Vvar__0__d__12269] :
            ( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0__d__12269)
            & VX12267 = cCoq_2eInit_2eDecimal_2eNeg___24a1(Vvar__0__d__12269) ) ) ) ).

fof('$_inversion_Coq.Init.Decimal.uint',axiom,
    ! [VX12134] :
      ( cCoq_2eInit_2eDecimal_2euint___24t(VX12134)
     => ( VX12134 = cCoq_2eInit_2eDecimal_2eNil
        | ? [Vvar__0___24Anonymous__12135] :
            ( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0___24Anonymous__12135)
            & VX12134 = cCoq_2eInit_2eDecimal_2eD0___24a1(Vvar__0___24Anonymous__12135) )
        | ? [Vvar__0___24Anonymous__12136] :
            ( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0___24Anonymous__12136)
            & VX12134 = cCoq_2eInit_2eDecimal_2eD1___24a1(Vvar__0___24Anonymous__12136) )
        | ? [Vvar__0___24Anonymous__12137] :
            ( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0___24Anonymous__12137)
            & VX12134 = cCoq_2eInit_2eDecimal_2eD2___24a1(Vvar__0___24Anonymous__12137) )
        | ? [Vvar__0___24Anonymous__12138] :
            ( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0___24Anonymous__12138)
            & VX12134 = cCoq_2eInit_2eDecimal_2eD3___24a1(Vvar__0___24Anonymous__12138) )
        | ? [Vvar__0___24Anonymous__12139] :
            ( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0___24Anonymous__12139)
            & VX12134 = cCoq_2eInit_2eDecimal_2eD4___24a1(Vvar__0___24Anonymous__12139) )
        | ? [Vvar__0___24Anonymous__12140] :
            ( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0___24Anonymous__12140)
            & VX12134 = cCoq_2eInit_2eDecimal_2eD5___24a1(Vvar__0___24Anonymous__12140) )
        | ? [Vvar__0___24Anonymous__12141] :
            ( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0___24Anonymous__12141)
            & VX12134 = cCoq_2eInit_2eDecimal_2eD6___24a1(Vvar__0___24Anonymous__12141) )
        | ? [Vvar__0___24Anonymous__12142] :
            ( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0___24Anonymous__12142)
            & VX12134 = cCoq_2eInit_2eDecimal_2eD7___24a1(Vvar__0___24Anonymous__12142) )
        | ? [Vvar__0___24Anonymous__12143] :
            ( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0___24Anonymous__12143)
            & VX12134 = cCoq_2eInit_2eDecimal_2eD8___24a1(Vvar__0___24Anonymous__12143) )
        | ? [Vvar__0___24Anonymous__12144] :
            ( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0___24Anonymous__12144)
            & VX12134 = cCoq_2eInit_2eDecimal_2eD9___24a1(Vvar__0___24Anonymous__12144) ) ) ) ).

fof('$_inversion_Coq.Init.Peano.le',axiom,
    ! [Vvar__0__n__65,Vvar__1___24Anonymous__66] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0__n__65)
     => ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__1___24Anonymous__66)
       => ( cCoq_2eInit_2ePeano_2ele___24a2(Vvar__0__n__65,Vvar__1___24Anonymous__66)
         => ( Vvar__1___24Anonymous__66 = Vvar__0__n__65
            | ? [Vvar__1__m__70] :
                ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__1__m__70)
                & cCoq_2eInit_2ePeano_2ele___24a2(Vvar__0__n__65,Vvar__1__m__70)
                & Vvar__1___24Anonymous__66 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__1__m__70) ) ) ) ) ) ).

fof('$_inversion_Coq.Init.Specif.sig',axiom,
    ! [Vvar__0__A__23524,Vvar__1__P__23525,VX23528] :
      ( cType___24t(Vvar__0__A__23524)
     => ( c_24__type__23538___24t(Vvar__0__A__23524,Vvar__1__P__23525,Vvar__1__P__23525)
       => ( cCoq_2eInit_2eSpecif_2esig___24t(Vvar__0__A__23524,Vvar__1__P__23525,VX23528)
         => ? [Vvar__2__x__23533] :
              ( t(Vvar__2__x__23533,Vvar__0__A__23524)
              & p(happ(Vvar__1__P__23525,Vvar__2__x__23533))
              & VX23528 = cCoq_2eInit_2eSpecif_2eexist___24a3(Vvar__0__A__23524,Vvar__1__P__23525,Vvar__2__x__23533) ) ) ) ) ).

fof('$_inversion_Coq.Init.Specif.sig2',axiom,
    ! [Vvar__0__A__28758,Vvar__1__P__28759,Vvar__2__Q__28762,VX28765] :
      ( cType___24t(Vvar__0__A__28758)
     => ( c_24__type__28782___24t(Vvar__0__A__28758,Vvar__1__P__28759,Vvar__2__Q__28762,Vvar__1__P__28759)
       => ( c_24__type__28790___24t(Vvar__0__A__28758,Vvar__1__P__28759,Vvar__2__Q__28762,Vvar__2__Q__28762)
         => ( cCoq_2eInit_2eSpecif_2esig2___24t(Vvar__0__A__28758,Vvar__1__P__28759,Vvar__2__Q__28762,VX28765)
           => ? [Vvar__3__x__28773] :
                ( t(Vvar__3__x__28773,Vvar__0__A__28758)
                & p(happ(Vvar__1__P__28759,Vvar__3__x__28773))
                & p(happ(Vvar__2__Q__28762,Vvar__3__x__28773))
                & VX28765 = cCoq_2eInit_2eSpecif_2eexist2___24a4(Vvar__0__A__28758,Vvar__1__P__28759,Vvar__2__Q__28762,Vvar__3__x__28773) ) ) ) ) ) ).

fof('$_inversion_Coq.Init.Specif.sigT',axiom,
    ! [Vvar__0__A__23563,Vvar__1__P__23564,VX23567] :
      ( cType___24t(Vvar__0__A__23563)
     => ( c_24__type__23577___24t(Vvar__0__A__23563,Vvar__1__P__23564,Vvar__1__P__23564)
       => ( cCoq_2eInit_2eSpecif_2esigT___24t(Vvar__0__A__23563,Vvar__1__P__23564,VX23567)
         => ? [Vvar__2__x__23572] :
              ( t(Vvar__2__x__23572,Vvar__0__A__23563)
              & ? [Vvar__3___24Anonymous__23573] :
                  ( t(Vvar__3___24Anonymous__23573,happ(Vvar__1__P__23564,Vvar__2__x__23572))
                  & VX23567 = cCoq_2eInit_2eSpecif_2eexistT___24a4(Vvar__0__A__23563,Vvar__1__P__23564,Vvar__2__x__23572,Vvar__3___24Anonymous__23573) ) ) ) ) ) ).

fof('$_inversion_Coq.Init.Specif.sigT2',axiom,
    ! [Vvar__0__A__28814,Vvar__1__P__28815,Vvar__2__Q__28818,VX28821] :
      ( cType___24t(Vvar__0__A__28814)
     => ( c_24__type__28838___24t(Vvar__0__A__28814,Vvar__1__P__28815,Vvar__2__Q__28818,Vvar__1__P__28815)
       => ( c_24__type__28846___24t(Vvar__0__A__28814,Vvar__1__P__28815,Vvar__2__Q__28818,Vvar__2__Q__28818)
         => ( cCoq_2eInit_2eSpecif_2esigT2___24t(Vvar__0__A__28814,Vvar__1__P__28815,Vvar__2__Q__28818,VX28821)
           => ? [Vvar__3__x__28829] :
                ( t(Vvar__3__x__28829,Vvar__0__A__28814)
                & ? [Vvar__4___24Anonymous__28830] :
                    ( t(Vvar__4___24Anonymous__28830,happ(Vvar__1__P__28815,Vvar__3__x__28829))
                    & ? [Vvar__5___24Anonymous__28831] :
                        ( t(Vvar__5___24Anonymous__28831,happ(Vvar__2__Q__28818,Vvar__3__x__28829))
                        & VX28821 = cCoq_2eInit_2eSpecif_2eexistT2___24a6(Vvar__0__A__28814,Vvar__1__P__28815,Vvar__2__Q__28818,Vvar__3__x__28829,Vvar__4___24Anonymous__28830,Vvar__5___24Anonymous__28831) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.Init.Specif.sumbool',axiom,
    ! [Vvar__0__A__2593,Vvar__1__B__2594,VX2595] :
      ( cProp___24t(Vvar__0__A__2593)
     => ( cProp___24t(Vvar__1__B__2594)
       => ( cCoq_2eInit_2eSpecif_2esumbool___24t(Vvar__0__A__2593,Vvar__1__B__2594,VX2595)
         => ( ( p(Vvar__0__A__2593)
              & VX2595 = cCoq_2eInit_2eSpecif_2eleft___24a2(Vvar__0__A__2593,Vvar__1__B__2594) )
            | ( p(Vvar__1__B__2594)
              & VX2595 = cCoq_2eInit_2eSpecif_2eright___24a2(Vvar__0__A__2593,Vvar__1__B__2594) ) ) ) ) ) ).

fof('$_inversion_Coq.Init.Specif.sumor',axiom,
    ! [Vvar__0__A__28870,Vvar__1__B__28871,VX28872] :
      ( cType___24t(Vvar__0__A__28870)
     => ( cProp___24t(Vvar__1__B__28871)
       => ( cCoq_2eInit_2eSpecif_2esumor___24t(Vvar__0__A__28870,Vvar__1__B__28871,VX28872)
         => ( ? [Vvar__2___24Anonymous__28875] :
                ( t(Vvar__2___24Anonymous__28875,Vvar__0__A__28870)
                & VX28872 = cCoq_2eInit_2eSpecif_2einleft___24a3(Vvar__0__A__28870,Vvar__1__B__28871,Vvar__2___24Anonymous__28875) )
            | ( p(Vvar__1__B__28871)
              & VX28872 = cCoq_2eInit_2eSpecif_2einright___24a2(Vvar__0__A__28870,Vvar__1__B__28871) ) ) ) ) ) ).

fof('$_inversion_Coq.Init.Wf.Acc',axiom,
    ! [Vvar__0__A__75,Vvar__1__R__76,Vvar__2__x__81] :
      ( cType___24t(Vvar__0__A__75)
     => ( c_24__type__110___24t(Vvar__0__A__75,Vvar__1__R__76,Vvar__2__x__81,Vvar__1__R__76)
       => ( t(Vvar__2__x__81,Vvar__0__A__75)
         => ( cCoq_2eInit_2eWf_2eAcc___24a3(Vvar__0__A__75,Vvar__1__R__76,Vvar__2__x__81)
           => ( ! [Vvar__var__var__var__var__3__y__91__93__95__97__99] :
                  ( t(Vvar__var__var__var__var__3__y__91__93__95__97__99,Vvar__0__A__75)
                 => ( p(happ(happ(Vvar__1__R__76,Vvar__var__var__var__var__3__y__91__93__95__97__99),Vvar__2__x__81))
                   => cCoq_2eInit_2eWf_2eAcc___24a3(Vvar__0__A__75,Vvar__1__R__76,Vvar__var__var__var__var__3__y__91__93__95__97__99) ) )
              & p(c_24True) ) ) ) ) ) ).

fof('$_inversion_Coq.Lists.List.Add',axiom,
    ! [Vvar__0__A__29983,Vvar__1__a__29984,Vvar__2___24Anonymous__29985,Vvar__3___24Anonymous__29986] :
      ( cType___24t(Vvar__0__A__29983)
     => ( t(Vvar__1__a__29984,Vvar__0__A__29983)
       => ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__29983,Vvar__2___24Anonymous__29985)
         => ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__29983,Vvar__3___24Anonymous__29986)
           => ( cCoq_2eLists_2eList_2eAdd___24a4(Vvar__0__A__29983,Vvar__1__a__29984,Vvar__2___24Anonymous__29985,Vvar__3___24Anonymous__29986)
             => ( ? [Vvar__2__l__29990] :
                    ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__29983,Vvar__2__l__29990)
                    & Vvar__3___24Anonymous__29986 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__29983,Vvar__1__a__29984,Vvar__2__l__29990)
                    & Vvar__2___24Anonymous__29985 = Vvar__2__l__29990 )
                | ? [Vvar__2__x__29993] :
                    ( t(Vvar__2__x__29993,Vvar__0__A__29983)
                    & ? [Vvar__3__l__29994] :
                        ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__29983,Vvar__3__l__29994)
                        & ? [Vvar__4__l_27__29995] :
                            ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__29983,Vvar__4__l_27__29995)
                            & cCoq_2eLists_2eList_2eAdd___24a4(Vvar__0__A__29983,Vvar__1__a__29984,Vvar__3__l__29994,Vvar__4__l_27__29995)
                            & Vvar__3___24Anonymous__29986 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__29983,Vvar__2__x__29993,Vvar__4__l_27__29995)
                            & Vvar__2___24Anonymous__29985 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__29983,Vvar__2__x__29993,Vvar__3__l__29994) ) ) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.Lists.List.Exists',axiom,
    ! [Vvar__0__A__29997,Vvar__1__P__29998,Vvar__2___24Anonymous__30001] :
      ( cType___24t(Vvar__0__A__29997)
     => ( c_24__type__30021___24t(Vvar__0__A__29997,Vvar__1__P__29998,Vvar__2___24Anonymous__30001,Vvar__1__P__29998)
       => ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__29997,Vvar__2___24Anonymous__30001)
         => ( cCoq_2eLists_2eList_2eExists___24a3(Vvar__0__A__29997,Vvar__1__P__29998,Vvar__2___24Anonymous__30001)
           => ( ? [Vvar__2__x__30007] :
                  ( t(Vvar__2__x__30007,Vvar__0__A__29997)
                  & ? [Vvar__3__l__30008] :
                      ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__29997,Vvar__3__l__30008)
                      & p(happ(Vvar__1__P__29998,Vvar__2__x__30007))
                      & Vvar__2___24Anonymous__30001 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__29997,Vvar__2__x__30007,Vvar__3__l__30008) ) )
              | ? [Vvar__2__x__30014] :
                  ( t(Vvar__2__x__30014,Vvar__0__A__29997)
                  & ? [Vvar__3__l__30015] :
                      ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__29997,Vvar__3__l__30015)
                      & cCoq_2eLists_2eList_2eExists___24a3(Vvar__0__A__29997,Vvar__1__P__29998,Vvar__3__l__30015)
                      & Vvar__2___24Anonymous__30001 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__29997,Vvar__2__x__30014,Vvar__3__l__30015) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.Lists.List.Forall',axiom,
    ! [Vvar__0__A__30023,Vvar__1__P__30024,Vvar__2___24Anonymous__30027] :
      ( cType___24t(Vvar__0__A__30023)
     => ( c_24__type__30045___24t(Vvar__0__A__30023,Vvar__1__P__30024,Vvar__2___24Anonymous__30027,Vvar__1__P__30024)
       => ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__30023,Vvar__2___24Anonymous__30027)
         => ( cCoq_2eLists_2eList_2eForall___24a3(Vvar__0__A__30023,Vvar__1__P__30024,Vvar__2___24Anonymous__30027)
           => ( Vvar__2___24Anonymous__30027 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__30023)
              | ? [Vvar__2__x__30037] :
                  ( t(Vvar__2__x__30037,Vvar__0__A__30023)
                  & ? [Vvar__3__l__30038] :
                      ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__30023,Vvar__3__l__30038)
                      & p(happ(Vvar__1__P__30024,Vvar__2__x__30037))
                      & cCoq_2eLists_2eList_2eForall___24a3(Vvar__0__A__30023,Vvar__1__P__30024,Vvar__3__l__30038)
                      & Vvar__2___24Anonymous__30027 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__30023,Vvar__2__x__30037,Vvar__3__l__30038) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.Lists.List.Forall2',axiom,
    ! [Vvar__0__A__30047,Vvar__1__B__30048,Vvar__2__R__30049,Vvar__3___24Anonymous__30054,Vvar__4___24Anonymous__30055] :
      ( cType___24t(Vvar__0__A__30047)
     => ( cType___24t(Vvar__1__B__30048)
       => ( c_24__type__30092___24t(Vvar__0__A__30047,Vvar__1__B__30048,Vvar__2__R__30049,Vvar__3___24Anonymous__30054,Vvar__4___24Anonymous__30055,Vvar__2__R__30049)
         => ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__30047,Vvar__3___24Anonymous__30054)
           => ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__1__B__30048,Vvar__4___24Anonymous__30055)
             => ( cCoq_2eLists_2eList_2eForall2___24a5(Vvar__0__A__30047,Vvar__1__B__30048,Vvar__2__R__30049,Vvar__3___24Anonymous__30054,Vvar__4___24Anonymous__30055)
               => ( ( Vvar__4___24Anonymous__30055 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__1__B__30048)
                    & Vvar__3___24Anonymous__30054 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__30047) )
                  | ? [Vvar__3__x__30071] :
                      ( t(Vvar__3__x__30071,Vvar__0__A__30047)
                      & ? [Vvar__4__y__30072] :
                          ( t(Vvar__4__y__30072,Vvar__1__B__30048)
                          & ? [Vvar__5__l__30073] :
                              ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__30047,Vvar__5__l__30073)
                              & ? [Vvar__6__l_27__30074] :
                                  ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__1__B__30048,Vvar__6__l_27__30074)
                                  & p(happ(happ(Vvar__2__R__30049,Vvar__3__x__30071),Vvar__4__y__30072))
                                  & cCoq_2eLists_2eList_2eForall2___24a5(Vvar__0__A__30047,Vvar__1__B__30048,Vvar__2__R__30049,Vvar__5__l__30073,Vvar__6__l_27__30074)
                                  & Vvar__4___24Anonymous__30055 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__1__B__30048,Vvar__4__y__30072,Vvar__6__l_27__30074)
                                  & Vvar__3___24Anonymous__30054 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__30047,Vvar__3__x__30071,Vvar__5__l__30073) ) ) ) ) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.Lists.List.ForallOrdPairs',axiom,
    ! [Vvar__0__A__30094,Vvar__1__R__30095,Vvar__2___24Anonymous__30100] :
      ( cType___24t(Vvar__0__A__30094)
     => ( c_24__type__30127___24t(Vvar__0__A__30094,Vvar__1__R__30095,Vvar__2___24Anonymous__30100,Vvar__1__R__30095)
       => ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__30094,Vvar__2___24Anonymous__30100)
         => ( cCoq_2eLists_2eList_2eForallOrdPairs___24a3(Vvar__0__A__30094,Vvar__1__R__30095,Vvar__2___24Anonymous__30100)
           => ( Vvar__2___24Anonymous__30100 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__30094)
              | ? [Vvar__2__a__30114] :
                  ( t(Vvar__2__a__30114,Vvar__0__A__30094)
                  & ? [Vvar__3__l__30115] :
                      ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__30094,Vvar__3__l__30115)
                      & cCoq_2eLists_2eList_2eForall___24a3(Vvar__0__A__30094,happ(Vvar__1__R__30095,Vvar__2__a__30114),Vvar__3__l__30115)
                      & cCoq_2eLists_2eList_2eForallOrdPairs___24a3(Vvar__0__A__30094,Vvar__1__R__30095,Vvar__3__l__30115)
                      & Vvar__2___24Anonymous__30100 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__30094,Vvar__2__a__30114,Vvar__3__l__30115) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.Lists.List.NoDup',axiom,
    ! [Vvar__0__A__14952,Vvar__1___24Anonymous__14953] :
      ( cType___24t(Vvar__0__A__14952)
     => ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__14952,Vvar__1___24Anonymous__14953)
       => ( cCoq_2eLists_2eList_2eNoDup___24a2(Vvar__0__A__14952,Vvar__1___24Anonymous__14953)
         => ( Vvar__1___24Anonymous__14953 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__14952)
            | ? [Vvar__1__x__14957] :
                ( t(Vvar__1__x__14957,Vvar__0__A__14952)
                & ? [Vvar__2__l__14958] :
                    ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__14952,Vvar__2__l__14958)
                    & ~ cCoq_2eLists_2eList_2eIn___24a3(Vvar__0__A__14952,Vvar__1__x__14957,Vvar__2__l__14958)
                    & cCoq_2eLists_2eList_2eNoDup___24a2(Vvar__0__A__14952,Vvar__2__l__14958)
                    & Vvar__1___24Anonymous__14953 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__14952,Vvar__1__x__14957,Vvar__2__l__14958) ) ) ) ) ) ) ).

fof('$_inversion_Coq.Lists.SetoidList.InA',axiom,
    ! [Vvar__0__A__28589,Vvar__1__eqA__28590,Vvar__2__x__28595,Vvar__3___24Anonymous__28596] :
      ( cType___24t(Vvar__0__A__28589)
     => ( c_24__type__28629___24t(Vvar__0__A__28589,Vvar__1__eqA__28590,Vvar__2__x__28595,Vvar__3___24Anonymous__28596,Vvar__1__eqA__28590)
       => ( t(Vvar__2__x__28595,Vvar__0__A__28589)
         => ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__28589,Vvar__3___24Anonymous__28596)
           => ( cCoq_2eLists_2eSetoidList_2eInA___24a4(Vvar__0__A__28589,Vvar__1__eqA__28590,Vvar__2__x__28595,Vvar__3___24Anonymous__28596)
             => ( ? [Vvar__3__y__28605] :
                    ( t(Vvar__3__y__28605,Vvar__0__A__28589)
                    & ? [Vvar__4__l__28606] :
                        ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__28589,Vvar__4__l__28606)
                        & p(happ(happ(Vvar__1__eqA__28590,Vvar__2__x__28595),Vvar__3__y__28605))
                        & Vvar__3___24Anonymous__28596 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__28589,Vvar__3__y__28605,Vvar__4__l__28606) ) )
                | ? [Vvar__3__y__28615] :
                    ( t(Vvar__3__y__28615,Vvar__0__A__28589)
                    & ? [Vvar__4__l__28616] :
                        ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__28589,Vvar__4__l__28616)
                        & cCoq_2eLists_2eSetoidList_2eInA___24a4(Vvar__0__A__28589,Vvar__1__eqA__28590,Vvar__2__x__28595,Vvar__4__l__28616)
                        & Vvar__3___24Anonymous__28596 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__28589,Vvar__3__y__28615,Vvar__4__l__28616) ) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.Lists.SetoidList.NoDupA',axiom,
    ! [Vvar__0__A__32179,Vvar__1__eqA__32180,Vvar__2___24Anonymous__32185] :
      ( cType___24t(Vvar__0__A__32179)
     => ( c_24__type__32212___24t(Vvar__0__A__32179,Vvar__1__eqA__32180,Vvar__2___24Anonymous__32185,Vvar__1__eqA__32180)
       => ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__32179,Vvar__2___24Anonymous__32185)
         => ( cCoq_2eLists_2eSetoidList_2eNoDupA___24a3(Vvar__0__A__32179,Vvar__1__eqA__32180,Vvar__2___24Anonymous__32185)
           => ( Vvar__2___24Anonymous__32185 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__32179)
              | ? [Vvar__2__x__32199] :
                  ( t(Vvar__2__x__32199,Vvar__0__A__32179)
                  & ? [Vvar__3__l__32200] :
                      ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__32179,Vvar__3__l__32200)
                      & ~ cCoq_2eLists_2eSetoidList_2eInA___24a4(Vvar__0__A__32179,Vvar__1__eqA__32180,Vvar__2__x__32199,Vvar__3__l__32200)
                      & cCoq_2eLists_2eSetoidList_2eNoDupA___24a3(Vvar__0__A__32179,Vvar__1__eqA__32180,Vvar__3__l__32200)
                      & Vvar__2___24Anonymous__32185 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__32179,Vvar__2__x__32199,Vvar__3__l__32200) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.Lists.SetoidList.eqlistA',axiom,
    ! [Vvar__0__A__32214,Vvar__1__eqA__32215,Vvar__2___24Anonymous__32220,Vvar__3___24Anonymous__32221] :
      ( cType___24t(Vvar__0__A__32214)
     => ( c_24__type__32252___24t(Vvar__0__A__32214,Vvar__1__eqA__32215,Vvar__2___24Anonymous__32220,Vvar__3___24Anonymous__32221,Vvar__1__eqA__32215)
       => ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__32214,Vvar__2___24Anonymous__32220)
         => ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__32214,Vvar__3___24Anonymous__32221)
           => ( cCoq_2eLists_2eSetoidList_2eeqlistA___24a4(Vvar__0__A__32214,Vvar__1__eqA__32215,Vvar__2___24Anonymous__32220,Vvar__3___24Anonymous__32221)
             => ( ( Vvar__3___24Anonymous__32221 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__32214)
                  & Vvar__2___24Anonymous__32220 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__32214) )
                | ? [Vvar__2__x__32235] :
                    ( t(Vvar__2__x__32235,Vvar__0__A__32214)
                    & ? [Vvar__3__x_27__32236] :
                        ( t(Vvar__3__x_27__32236,Vvar__0__A__32214)
                        & ? [Vvar__4__l__32237] :
                            ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__32214,Vvar__4__l__32237)
                            & ? [Vvar__5__l_27__32238] :
                                ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__32214,Vvar__5__l_27__32238)
                                & p(happ(happ(Vvar__1__eqA__32215,Vvar__2__x__32235),Vvar__3__x_27__32236))
                                & cCoq_2eLists_2eSetoidList_2eeqlistA___24a4(Vvar__0__A__32214,Vvar__1__eqA__32215,Vvar__4__l__32237,Vvar__5__l_27__32238)
                                & Vvar__3___24Anonymous__32221 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__32214,Vvar__3__x_27__32236,Vvar__5__l_27__32238)
                                & Vvar__2___24Anonymous__32220 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__32214,Vvar__2__x__32235,Vvar__4__l__32237) ) ) ) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.Logic.EqdepFacts.eq_dep',axiom,
    ! [Vvar__0__U__26175,Vvar__1__P__26176,Vvar__2__p__26179,Vvar__3__x__26180,Vvar__4__q__26181,Vvar__5___24Anonymous__26182] :
      ( cType___24t(Vvar__0__U__26175)
     => ( c_24__type__26197___24t(Vvar__0__U__26175,Vvar__1__P__26176,Vvar__2__p__26179,Vvar__3__x__26180,Vvar__4__q__26181,Vvar__5___24Anonymous__26182,Vvar__1__P__26176)
       => ( t(Vvar__2__p__26179,Vvar__0__U__26175)
         => ( t(Vvar__3__x__26180,happ(Vvar__1__P__26176,Vvar__2__p__26179))
           => ( t(Vvar__4__q__26181,Vvar__0__U__26175)
             => ( t(Vvar__5___24Anonymous__26182,happ(Vvar__1__P__26176,Vvar__4__q__26181))
               => ( cCoq_2eLogic_2eEqdepFacts_2eeq__dep___24a6(Vvar__0__U__26175,Vvar__1__P__26176,Vvar__2__p__26179,Vvar__3__x__26180,Vvar__4__q__26181,Vvar__5___24Anonymous__26182)
                 => ( Vvar__5___24Anonymous__26182 = Vvar__3__x__26180
                    & Vvar__4__q__26181 = Vvar__2__p__26179 ) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.Logic.EqdepFacts.eq_dep1',axiom,
    ! [Vvar__0__U__26199,Vvar__1__P__26200,Vvar__2__p__26203,Vvar__3__x__26204,Vvar__4__q__26205,Vvar__5__y__26206] :
      ( cType___24t(Vvar__0__U__26199)
     => ( c_24__type__26225___24t(Vvar__0__U__26199,Vvar__1__P__26200,Vvar__2__p__26203,Vvar__3__x__26204,Vvar__4__q__26205,Vvar__5__y__26206,Vvar__1__P__26200)
       => ( t(Vvar__2__p__26203,Vvar__0__U__26199)
         => ( t(Vvar__3__x__26204,happ(Vvar__1__P__26200,Vvar__2__p__26203))
           => ( t(Vvar__4__q__26205,Vvar__0__U__26199)
             => ( t(Vvar__5__y__26206,happ(Vvar__1__P__26200,Vvar__4__q__26205))
               => ( cCoq_2eLogic_2eEqdepFacts_2eeq__dep1___24a6(Vvar__0__U__26199,Vvar__1__P__26200,Vvar__2__p__26203,Vvar__3__x__26204,Vvar__4__q__26205,Vvar__5__y__26206)
                 => ( Vvar__4__q__26205 = Vvar__2__p__26203
                    & Vvar__3__x__26204 = cCoq_2eInit_2eLogic_2eeq__rect___24a5(Vvar__0__U__26199,Vvar__4__q__26205,Vvar__1__P__26200,Vvar__5__y__26206,Vvar__2__p__26203)
                    & p(c_24True) ) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.Numbers.BinNums.N',axiom,
    ! [VX2581] :
      ( cCoq_2eNumbers_2eBinNums_2eN___24t(VX2581)
     => ( VX2581 = cCoq_2eNumbers_2eBinNums_2eN0
        | ? [Vvar__0___24Anonymous__2582] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__2582)
            & VX2581 = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__2582) ) ) ) ).

fof('$_inversion_Coq.Numbers.BinNums.Z',axiom,
    ! [VX1414] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(VX1414)
     => ( VX1414 = cCoq_2eNumbers_2eBinNums_2eZ0
        | ? [Vvar__0___24Anonymous__1415] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__1415)
            & VX1414 = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__1415) )
        | ? [Vvar__0___24Anonymous__1416] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__1416)
            & VX1414 = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__1416) ) ) ) ).

fof('$_inversion_Coq.Numbers.BinNums.positive',axiom,
    ! [VX1403] :
      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(VX1403)
     => ( ? [Vvar__0___24Anonymous__1404] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__1404)
            & VX1403 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__1404) )
        | ? [Vvar__0___24Anonymous__1405] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__1405)
            & VX1403 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__1405) )
        | VX1403 = cCoq_2eNumbers_2eBinNums_2exH ) ) ).

fof('$_inversion_Coq.PArith.BinPos.Pos.PeanoView',axiom,
    ! [Vvar__0___24Anonymous__29615,VX29616] :
      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__29615)
     => ( cCoq_2ePArith_2eBinPos_2ePos_2ePeanoView___24t(Vvar__0___24Anonymous__29615,VX29616)
       => ( ( Vvar__0___24Anonymous__29615 = cCoq_2eNumbers_2eBinNums_2exH
            & VX29616 = cCoq_2ePArith_2eBinPos_2ePos_2ePeanoOne )
          | ? [Vvar__0__p__29617] :
              ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0__p__29617)
              & ? [Vvar__1___24Anonymous__29618] :
                  ( cCoq_2ePArith_2eBinPos_2ePos_2ePeanoView___24t(Vvar__0__p__29617,Vvar__1___24Anonymous__29618)
                  & Vvar__0___24Anonymous__29615 = c_24__case__Coq_2eNumbers_2eBinNums_2epositive_2429653___24a2(Vvar__0___24Anonymous__29615,Vvar__0__p__29617)
                  & VX29616 = cCoq_2ePArith_2eBinPos_2ePos_2ePeanoSucc___24a2(Vvar__0__p__29617,Vvar__1___24Anonymous__29618) ) ) ) ) ) ).

fof('$_inversion_Coq.PArith.BinPos.Pos.SubMaskSpec',axiom,
    ! [Vvar__0__p__33058,Vvar__1__q__33059,Vvar__2___24Anonymous__33060] :
      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0__p__33058)
     => ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1__q__33059)
       => ( cCoq_2ePArith_2eBinPosDef_2ePos_2emask___24t(Vvar__2___24Anonymous__33060)
         => ( cCoq_2ePArith_2eBinPos_2ePos_2eSubMaskSpec___24a3(Vvar__0__p__33058,Vvar__1__q__33059,Vvar__2___24Anonymous__33060)
           => ( ( Vvar__0__p__33058 = Vvar__1__q__33059
                & Vvar__2___24Anonymous__33060 = cCoq_2ePArith_2eBinPosDef_2ePos_2eIsNul )
              | ? [Vvar__2__r__33067] :
                  ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2__r__33067)
                  & cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(Vvar__1__q__33059,Vvar__2__r__33067) = Vvar__0__p__33058
                  & Vvar__2___24Anonymous__33060 = cCoq_2ePArith_2eBinPosDef_2ePos_2eIsPos___24a1(Vvar__2__r__33067) )
              | ? [Vvar__2__r__33071] :
                  ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2__r__33071)
                  & cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(Vvar__0__p__33058,Vvar__2__r__33071) = Vvar__1__q__33059
                  & Vvar__2___24Anonymous__33060 = cCoq_2ePArith_2eBinPosDef_2ePos_2eIsNeg ) ) ) ) ) ) ).

fof('$_inversion_Coq.PArith.BinPosDef.Pos.mask',axiom,
    ! [VX25982] :
      ( cCoq_2ePArith_2eBinPosDef_2ePos_2emask___24t(VX25982)
     => ( VX25982 = cCoq_2ePArith_2eBinPosDef_2ePos_2eIsNul
        | ? [Vvar__0___24Anonymous__25983] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__25983)
            & VX25982 = cCoq_2ePArith_2eBinPosDef_2ePos_2eIsPos___24a1(Vvar__0___24Anonymous__25983) )
        | VX25982 = cCoq_2ePArith_2eBinPosDef_2ePos_2eIsNeg ) ) ).

fof('$_inversion_Coq.QArith.QArith_base.Q',axiom,
    ! [VX16462] :
      ( cCoq_2eQArith_2eQArith__base_2eQ___24t(VX16462)
     => ? [Vvar__0__Qnum__16463] :
          ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__0__Qnum__16463)
          & ? [Vvar__1__Qden__16464] :
              ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1__Qden__16464)
              & VX16462 = cCoq_2eQArith_2eQArith__base_2eQmake___24a2(Vvar__0__Qnum__16463,Vvar__1__Qden__16464) ) ) ) ).

fof('$_inversion_Coq.Reals.RIneq.negreal',axiom,
    ! [VX27056] :
      ( cCoq_2eReals_2eRIneq_2enegreal___24t(VX27056)
     => ? [Vvar__0__neg__27057] :
          ( cCoq_2eReals_2eRdefinitions_2eR___24t(Vvar__0__neg__27057)
          & cCoq_2eReals_2eRdefinitions_2eRlt___24a2(Vvar__0__neg__27057,cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0))
          & VX27056 = cCoq_2eReals_2eRIneq_2emknegreal___24a1(Vvar__0__neg__27057) ) ) ).

fof('$_inversion_Coq.Reals.RIneq.nonnegreal',axiom,
    ! [VX27042] :
      ( cCoq_2eReals_2eRIneq_2enonnegreal___24t(VX27042)
     => ? [Vvar__0__nonneg__27043] :
          ( cCoq_2eReals_2eRdefinitions_2eR___24t(Vvar__0__nonneg__27043)
          & cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),Vvar__0__nonneg__27043)
          & VX27042 = cCoq_2eReals_2eRIneq_2emknonnegreal___24a1(Vvar__0__nonneg__27043) ) ) ).

fof('$_inversion_Coq.Reals.RIneq.nonposreal',axiom,
    ! [VX16529] :
      ( cCoq_2eReals_2eRIneq_2enonposreal___24t(VX16529)
     => ? [Vvar__0__nonpos__16530] :
          ( cCoq_2eReals_2eRdefinitions_2eR___24t(Vvar__0__nonpos__16530)
          & cCoq_2eReals_2eRdefinitions_2eRle___24a2(Vvar__0__nonpos__16530,cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0))
          & VX16529 = cCoq_2eReals_2eRIneq_2emknonposreal___24a1(Vvar__0__nonpos__16530) ) ) ).

fof('$_inversion_Coq.Reals.RIneq.nonzeroreal',axiom,
    ! [VX27063] :
      ( cCoq_2eReals_2eRIneq_2enonzeroreal___24t(VX27063)
     => ? [Vvar__0__nonzero__27064] :
          ( cCoq_2eReals_2eRdefinitions_2eR___24t(Vvar__0__nonzero__27064)
          & Vvar__0__nonzero__27064 != cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)
          & VX27063 = cCoq_2eReals_2eRIneq_2emknonzeroreal___24a1(Vvar__0__nonzero__27064) ) ) ).

fof('$_inversion_Coq.Reals.RIneq.posreal',axiom,
    ! [VX27049] :
      ( cCoq_2eReals_2eRIneq_2eposreal___24t(VX27049)
     => ? [Vvar__0__pos__27050] :
          ( cCoq_2eReals_2eRdefinitions_2eR___24t(Vvar__0__pos__27050)
          & cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),Vvar__0__pos__27050)
          & VX27049 = cCoq_2eReals_2eRIneq_2emkposreal___24a1(Vvar__0__pos__27050) ) ) ).

fof('$_inversion_Coq.Reals.Rfunctions.Z_spec',axiom,
    ! [Vvar__0__x__17042,Vvar__1___24Anonymous__17043,VX17044] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__0__x__17042)
     => ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__1___24Anonymous__17043)
       => ( cCoq_2eReals_2eRfunctions_2eZ__spec___24t(Vvar__0__x__17042,Vvar__1___24Anonymous__17043,VX17044)
         => ( ( Vvar__0__x__17042 = cCoq_2eNumbers_2eBinNums_2eZ0
              & Vvar__1___24Anonymous__17043 = cCoq_2eNumbers_2eBinNums_2eZ0
              & VX17044 = cCoq_2eReals_2eRfunctions_2eZintNull___24a1(Vvar__0__x__17042) )
            | ? [Vvar__1__n__17048] :
                ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__1__n__17048)
                & Vvar__0__x__17042 = cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat___24a1(Vvar__1__n__17048)
                & Vvar__1___24Anonymous__17043 = c_24__case__Coq_2eInit_2eDatatypes_2enat_2417068___24a3(Vvar__0__x__17042,Vvar__1___24Anonymous__17043,Vvar__1__n__17048)
                & VX17044 = cCoq_2eReals_2eRfunctions_2eZintPos___24a2(Vvar__0__x__17042,Vvar__1__n__17048) )
            | ? [Vvar__1__n__17053] :
                ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__1__n__17053)
                & Vvar__0__x__17042 = cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat___24a1(Vvar__1__n__17053))
                & Vvar__1___24Anonymous__17043 = c_24__case__Coq_2eNumbers_2eBinNums_2eZ_2417085___24a3(Vvar__0__x__17042,Vvar__1___24Anonymous__17043,Vvar__1__n__17053)
                & VX17044 = cCoq_2eReals_2eRfunctions_2eZintNeg___24a2(Vvar__0__x__17042,Vvar__1__n__17053) ) ) ) ) ) ).

fof('$_inversion_Coq.Relations.Relation_Definitions.PER',axiom,
    ! [Vvar__0__A__30815,Vvar__1__R__30816] :
      ( cType___24t(Vvar__0__A__30815)
     => ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vvar__0__A__30815,Vvar__1__R__30816)
       => ( cCoq_2eRelations_2eRelation__Definitions_2ePER___24a2(Vvar__0__A__30815,Vvar__1__R__30816)
         => ( cCoq_2eRelations_2eRelation__Definitions_2esymmetric___24a2(Vvar__0__A__30815,Vvar__1__R__30816)
            & cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2(Vvar__0__A__30815,Vvar__1__R__30816)
            & p(c_24True) ) ) ) ) ).

fof('$_inversion_Coq.Relations.Relation_Definitions.equivalence',axiom,
    ! [Vvar__0__A__30807,Vvar__1__R__30808] :
      ( cType___24t(Vvar__0__A__30807)
     => ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vvar__0__A__30807,Vvar__1__R__30808)
       => ( cCoq_2eRelations_2eRelation__Definitions_2eequivalence___24a2(Vvar__0__A__30807,Vvar__1__R__30808)
         => ( cCoq_2eRelations_2eRelation__Definitions_2ereflexive___24a2(Vvar__0__A__30807,Vvar__1__R__30808)
            & cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2(Vvar__0__A__30807,Vvar__1__R__30808)
            & cCoq_2eRelations_2eRelation__Definitions_2esymmetric___24a2(Vvar__0__A__30807,Vvar__1__R__30808)
            & p(c_24True) ) ) ) ) ).

fof('$_inversion_Coq.Relations.Relation_Definitions.order',axiom,
    ! [Vvar__0__A__30799,Vvar__1__R__30800] :
      ( cType___24t(Vvar__0__A__30799)
     => ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vvar__0__A__30799,Vvar__1__R__30800)
       => ( cCoq_2eRelations_2eRelation__Definitions_2eorder___24a2(Vvar__0__A__30799,Vvar__1__R__30800)
         => ( cCoq_2eRelations_2eRelation__Definitions_2ereflexive___24a2(Vvar__0__A__30799,Vvar__1__R__30800)
            & cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2(Vvar__0__A__30799,Vvar__1__R__30800)
            & cCoq_2eRelations_2eRelation__Definitions_2eantisymmetric___24a2(Vvar__0__A__30799,Vvar__1__R__30800)
            & p(c_24True) ) ) ) ) ).

fof('$_inversion_Coq.Relations.Relation_Definitions.preorder',axiom,
    ! [Vvar__0__A__30792,Vvar__1__R__30793] :
      ( cType___24t(Vvar__0__A__30792)
     => ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vvar__0__A__30792,Vvar__1__R__30793)
       => ( cCoq_2eRelations_2eRelation__Definitions_2epreorder___24a2(Vvar__0__A__30792,Vvar__1__R__30793)
         => ( cCoq_2eRelations_2eRelation__Definitions_2ereflexive___24a2(Vvar__0__A__30792,Vvar__1__R__30793)
            & cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2(Vvar__0__A__30792,Vvar__1__R__30793)
            & p(c_24True) ) ) ) ) ).

fof('$_inversion_Coq.Relations.Relation_Operators.Desc',axiom,
    ! [Vvar__0__A__31258,Vvar__1__leA__31259,Vvar__2___24Anonymous__31264] :
      ( cType___24t(Vvar__0__A__31258)
     => ( c_24__type__31354___24t(Vvar__0__A__31258,Vvar__1__leA__31259,Vvar__2___24Anonymous__31264,Vvar__1__leA__31259)
       => ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__31258,Vvar__2___24Anonymous__31264)
         => ( cCoq_2eRelations_2eRelation__Operators_2eDesc___24a3(Vvar__0__A__31258,Vvar__1__leA__31259,Vvar__2___24Anonymous__31264)
           => ( Vvar__2___24Anonymous__31264 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__31258)
              | ? [Vvar__2__x__31278] :
                  ( t(Vvar__2__x__31278,Vvar__0__A__31258)
                  & Vvar__2___24Anonymous__31264 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__31258,Vvar__2__x__31278,cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__31258)) )
              | ? [Vvar__2__x__31285] :
                  ( t(Vvar__2__x__31285,Vvar__0__A__31258)
                  & ? [Vvar__3__y__31286] :
                      ( t(Vvar__3__y__31286,Vvar__0__A__31258)
                      & ? [Vvar__4__l__31287] :
                          ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__31258,Vvar__4__l__31287)
                          & cCoq_2eRelations_2eRelation__Operators_2eclos__refl___24a4(Vvar__0__A__31258,Vvar__1__leA__31259,Vvar__2__x__31285,Vvar__3__y__31286)
                          & cCoq_2eRelations_2eRelation__Operators_2eDesc___24a3(Vvar__0__A__31258,Vvar__1__leA__31259,cCoq_2eInit_2eDatatypes_2eapp___24a3(Vvar__0__A__31258,Vvar__4__l__31287,cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__31258,Vvar__3__y__31286,cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__31258))))
                          & Vvar__2___24Anonymous__31264 = c_24__case__Coq_2eInit_2eDatatypes_2elist_2431552___24a6(Vvar__0__A__31258,Vvar__1__leA__31259,Vvar__2___24Anonymous__31264,Vvar__2__x__31285,Vvar__3__y__31286,Vvar__4__l__31287) ) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.Relations.Relation_Operators.Ltl',axiom,
    ! [Vvar__0__A__31207,Vvar__1__leA__31208,Vvar__2___24Anonymous__31213,Vvar__3___24Anonymous__31214] :
      ( cType___24t(Vvar__0__A__31207)
     => ( c_24__type__31256___24t(Vvar__0__A__31207,Vvar__1__leA__31208,Vvar__2___24Anonymous__31213,Vvar__3___24Anonymous__31214,Vvar__1__leA__31208)
       => ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__31207,Vvar__2___24Anonymous__31213)
         => ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__31207,Vvar__3___24Anonymous__31214)
           => ( cCoq_2eRelations_2eRelation__Operators_2eLtl___24a4(Vvar__0__A__31207,Vvar__1__leA__31208,Vvar__2___24Anonymous__31213,Vvar__3___24Anonymous__31214)
             => ( ? [Vvar__2__a__31222] :
                    ( t(Vvar__2__a__31222,Vvar__0__A__31207)
                    & ? [Vvar__3__x__31223] :
                        ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__31207,Vvar__3__x__31223)
                        & Vvar__3___24Anonymous__31214 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__31207,Vvar__2__a__31222,Vvar__3__x__31223)
                        & Vvar__2___24Anonymous__31213 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__31207) ) )
                | ? [Vvar__2__a__31230] :
                    ( t(Vvar__2__a__31230,Vvar__0__A__31207)
                    & ? [Vvar__3__b__31231] :
                        ( t(Vvar__3__b__31231,Vvar__0__A__31207)
                        & p(happ(happ(Vvar__1__leA__31208,Vvar__2__a__31230),Vvar__3__b__31231))
                        & ? [Vvar__5__x__31233] :
                            ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__31207,Vvar__5__x__31233)
                            & ? [Vvar__6__y__31234] :
                                ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__31207,Vvar__6__y__31234)
                                & Vvar__3___24Anonymous__31214 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__31207,Vvar__3__b__31231,Vvar__6__y__31234)
                                & Vvar__2___24Anonymous__31213 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__31207,Vvar__2__a__31230,Vvar__5__x__31233) ) ) ) )
                | ? [Vvar__2__a__31241] :
                    ( t(Vvar__2__a__31241,Vvar__0__A__31207)
                    & ? [Vvar__3__x__31242] :
                        ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__31207,Vvar__3__x__31242)
                        & ? [Vvar__4__y__31243] :
                            ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__31207,Vvar__4__y__31243)
                            & cCoq_2eRelations_2eRelation__Operators_2eLtl___24a4(Vvar__0__A__31207,Vvar__1__leA__31208,Vvar__3__x__31242,Vvar__4__y__31243)
                            & Vvar__3___24Anonymous__31214 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__31207,Vvar__2__a__31241,Vvar__4__y__31243)
                            & Vvar__2___24Anonymous__31213 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__31207,Vvar__2__a__31241,Vvar__3__x__31242) ) ) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.Relations.Relation_Operators.clos_refl',axiom,
    ! [Vvar__0__A__30856,Vvar__1__R__30857,Vvar__2__x__30858,Vvar__3___24Anonymous__30859] :
      ( cType___24t(Vvar__0__A__30856)
     => ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vvar__0__A__30856,Vvar__1__R__30857)
       => ( t(Vvar__2__x__30858,Vvar__0__A__30856)
         => ( t(Vvar__3___24Anonymous__30859,Vvar__0__A__30856)
           => ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl___24a4(Vvar__0__A__30856,Vvar__1__R__30857,Vvar__2__x__30858,Vvar__3___24Anonymous__30859)
             => ( ? [Vvar__3__y__30864] :
                    ( t(Vvar__3__y__30864,Vvar__0__A__30856)
                    & p(happ(happ(Vvar__1__R__30857,Vvar__2__x__30858),Vvar__3__y__30864))
                    & Vvar__3___24Anonymous__30859 = Vvar__3__y__30864 )
                | Vvar__3___24Anonymous__30859 = Vvar__2__x__30858 ) ) ) ) ) ) ).

fof('$_inversion_Coq.Relations.Relation_Operators.clos_refl_sym_trans',axiom,
    ! [Vvar__0__A__30904,Vvar__1__R__30905,Vvar__1___24Anonymous__30906,Vvar__2___24Anonymous__30907] :
      ( cType___24t(Vvar__0__A__30904)
     => ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vvar__0__A__30904,Vvar__1__R__30905)
       => ( t(Vvar__1___24Anonymous__30906,Vvar__0__A__30904)
         => ( t(Vvar__2___24Anonymous__30907,Vvar__0__A__30904)
           => ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans___24a4(Vvar__0__A__30904,Vvar__1__R__30905,Vvar__1___24Anonymous__30906,Vvar__2___24Anonymous__30907)
             => ( ? [Vvar__2__x__30911] :
                    ( t(Vvar__2__x__30911,Vvar__0__A__30904)
                    & ? [Vvar__3__y__30912] :
                        ( t(Vvar__3__y__30912,Vvar__0__A__30904)
                        & p(happ(happ(Vvar__1__R__30905,Vvar__2__x__30911),Vvar__3__y__30912))
                        & Vvar__2___24Anonymous__30907 = Vvar__3__y__30912
                        & Vvar__1___24Anonymous__30906 = Vvar__2__x__30911 ) )
                | ? [Vvar__2__x__30916] :
                    ( t(Vvar__2__x__30916,Vvar__0__A__30904)
                    & Vvar__2___24Anonymous__30907 = Vvar__2__x__30916
                    & Vvar__1___24Anonymous__30906 = Vvar__2__x__30916 )
                | ? [Vvar__2__x__30919] :
                    ( t(Vvar__2__x__30919,Vvar__0__A__30904)
                    & ? [Vvar__3__y__30920] :
                        ( t(Vvar__3__y__30920,Vvar__0__A__30904)
                        & cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans___24a4(Vvar__0__A__30904,Vvar__1__R__30905,Vvar__2__x__30919,Vvar__3__y__30920)
                        & Vvar__2___24Anonymous__30907 = Vvar__2__x__30919
                        & Vvar__1___24Anonymous__30906 = Vvar__3__y__30920 ) )
                | ? [Vvar__2__x__30924] :
                    ( t(Vvar__2__x__30924,Vvar__0__A__30904)
                    & ? [Vvar__3__y__30925] :
                        ( t(Vvar__3__y__30925,Vvar__0__A__30904)
                        & ? [Vvar__4__z__30926] :
                            ( t(Vvar__4__z__30926,Vvar__0__A__30904)
                            & cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans___24a4(Vvar__0__A__30904,Vvar__1__R__30905,Vvar__2__x__30924,Vvar__3__y__30925)
                            & cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans___24a4(Vvar__0__A__30904,Vvar__1__R__30905,Vvar__3__y__30925,Vvar__4__z__30926)
                            & Vvar__2___24Anonymous__30907 = Vvar__4__z__30926
                            & Vvar__1___24Anonymous__30906 = Vvar__2__x__30924 ) ) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.Relations.Relation_Operators.clos_refl_sym_trans_1n',axiom,
    ! [Vvar__0__A__30929,Vvar__1__R__30930,Vvar__2__x__30931,Vvar__3___24Anonymous__30932] :
      ( cType___24t(Vvar__0__A__30929)
     => ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vvar__0__A__30929,Vvar__1__R__30930)
       => ( t(Vvar__2__x__30931,Vvar__0__A__30929)
         => ( t(Vvar__3___24Anonymous__30932,Vvar__0__A__30929)
           => ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans__1n___24a4(Vvar__0__A__30929,Vvar__1__R__30930,Vvar__2__x__30931,Vvar__3___24Anonymous__30932)
             => ( Vvar__3___24Anonymous__30932 = Vvar__2__x__30931
                | ? [Vvar__3__y__30940] :
                    ( t(Vvar__3__y__30940,Vvar__0__A__30929)
                    & ? [Vvar__4__z__30941] :
                        ( t(Vvar__4__z__30941,Vvar__0__A__30929)
                        & ( p(happ(happ(Vvar__1__R__30930,Vvar__2__x__30931),Vvar__3__y__30940))
                          | p(happ(happ(Vvar__1__R__30930,Vvar__3__y__30940),Vvar__2__x__30931)) )
                        & cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans__1n___24a4(Vvar__0__A__30929,Vvar__1__R__30930,Vvar__3__y__30940,Vvar__4__z__30941)
                        & Vvar__3___24Anonymous__30932 = Vvar__4__z__30941 ) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.Relations.Relation_Operators.clos_refl_sym_trans_n1',axiom,
    ! [Vvar__0__A__30944,Vvar__1__R__30945,Vvar__2__x__30946,Vvar__3___24Anonymous__30947] :
      ( cType___24t(Vvar__0__A__30944)
     => ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vvar__0__A__30944,Vvar__1__R__30945)
       => ( t(Vvar__2__x__30946,Vvar__0__A__30944)
         => ( t(Vvar__3___24Anonymous__30947,Vvar__0__A__30944)
           => ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans__n1___24a4(Vvar__0__A__30944,Vvar__1__R__30945,Vvar__2__x__30946,Vvar__3___24Anonymous__30947)
             => ( Vvar__3___24Anonymous__30947 = Vvar__2__x__30946
                | ? [Vvar__3__y__30955] :
                    ( t(Vvar__3__y__30955,Vvar__0__A__30944)
                    & ? [Vvar__4__z__30956] :
                        ( t(Vvar__4__z__30956,Vvar__0__A__30944)
                        & ( p(happ(happ(Vvar__1__R__30945,Vvar__3__y__30955),Vvar__4__z__30956))
                          | p(happ(happ(Vvar__1__R__30945,Vvar__4__z__30956),Vvar__3__y__30955)) )
                        & cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans__n1___24a4(Vvar__0__A__30944,Vvar__1__R__30945,Vvar__2__x__30946,Vvar__3__y__30955)
                        & Vvar__3___24Anonymous__30947 = Vvar__4__z__30956 ) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.Relations.Relation_Operators.clos_refl_trans',axiom,
    ! [Vvar__0__A__30869,Vvar__1__R__30870,Vvar__2__x__30871,Vvar__3___24Anonymous__30872] :
      ( cType___24t(Vvar__0__A__30869)
     => ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vvar__0__A__30869,Vvar__1__R__30870)
       => ( t(Vvar__2__x__30871,Vvar__0__A__30869)
         => ( t(Vvar__3___24Anonymous__30872,Vvar__0__A__30869)
           => ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a4(Vvar__0__A__30869,Vvar__1__R__30870,Vvar__2__x__30871,Vvar__3___24Anonymous__30872)
             => ( ? [Vvar__3__y__30877] :
                    ( t(Vvar__3__y__30877,Vvar__0__A__30869)
                    & p(happ(happ(Vvar__1__R__30870,Vvar__2__x__30871),Vvar__3__y__30877))
                    & Vvar__3___24Anonymous__30872 = Vvar__3__y__30877 )
                | Vvar__3___24Anonymous__30872 = Vvar__2__x__30871
                | ? [Vvar__3__y__30885] :
                    ( t(Vvar__3__y__30885,Vvar__0__A__30869)
                    & ? [Vvar__4__z__30886] :
                        ( t(Vvar__4__z__30886,Vvar__0__A__30869)
                        & cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a4(Vvar__0__A__30869,Vvar__1__R__30870,Vvar__2__x__30871,Vvar__3__y__30885)
                        & cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a4(Vvar__0__A__30869,Vvar__1__R__30870,Vvar__3__y__30885,Vvar__4__z__30886)
                        & Vvar__3___24Anonymous__30872 = Vvar__4__z__30886 ) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.Relations.Relation_Operators.clos_refl_trans_1n',axiom,
    ! [Vvar__0__A__30889,Vvar__1__R__30890,Vvar__2__x__30891,Vvar__3___24Anonymous__30892] :
      ( cType___24t(Vvar__0__A__30889)
     => ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vvar__0__A__30889,Vvar__1__R__30890)
       => ( t(Vvar__2__x__30891,Vvar__0__A__30889)
         => ( t(Vvar__3___24Anonymous__30892,Vvar__0__A__30889)
           => ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans__1n___24a4(Vvar__0__A__30889,Vvar__1__R__30890,Vvar__2__x__30891,Vvar__3___24Anonymous__30892)
             => ( Vvar__3___24Anonymous__30892 = Vvar__2__x__30891
                | ? [Vvar__3__y__30900] :
                    ( t(Vvar__3__y__30900,Vvar__0__A__30889)
                    & ? [Vvar__4__z__30901] :
                        ( t(Vvar__4__z__30901,Vvar__0__A__30889)
                        & p(happ(happ(Vvar__1__R__30890,Vvar__2__x__30891),Vvar__3__y__30900))
                        & cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans__1n___24a4(Vvar__0__A__30889,Vvar__1__R__30890,Vvar__3__y__30900,Vvar__4__z__30901)
                        & Vvar__3___24Anonymous__30892 = Vvar__4__z__30901 ) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.Relations.Relation_Operators.clos_refl_trans_n1',axiom,
    ! [Vvar__0__A__16840,Vvar__1__R__16841,Vvar__2__x__16842,Vvar__3___24Anonymous__16843] :
      ( cType___24t(Vvar__0__A__16840)
     => ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vvar__0__A__16840,Vvar__1__R__16841)
       => ( t(Vvar__2__x__16842,Vvar__0__A__16840)
         => ( t(Vvar__3___24Anonymous__16843,Vvar__0__A__16840)
           => ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans__n1___24a4(Vvar__0__A__16840,Vvar__1__R__16841,Vvar__2__x__16842,Vvar__3___24Anonymous__16843)
             => ( Vvar__3___24Anonymous__16843 = Vvar__2__x__16842
                | ? [Vvar__3__y__16851] :
                    ( t(Vvar__3__y__16851,Vvar__0__A__16840)
                    & ? [Vvar__4__z__16852] :
                        ( t(Vvar__4__z__16852,Vvar__0__A__16840)
                        & p(happ(happ(Vvar__1__R__16841,Vvar__3__y__16851),Vvar__4__z__16852))
                        & cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans__n1___24a4(Vvar__0__A__16840,Vvar__1__R__16841,Vvar__2__x__16842,Vvar__3__y__16851)
                        & Vvar__3___24Anonymous__16843 = Vvar__4__z__16852 ) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.Relations.Relation_Operators.clos_trans',axiom,
    ! [Vvar__0__A__16823,Vvar__1__R__16824,Vvar__2__x__16825,Vvar__3___24Anonymous__16826] :
      ( cType___24t(Vvar__0__A__16823)
     => ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vvar__0__A__16823,Vvar__1__R__16824)
       => ( t(Vvar__2__x__16825,Vvar__0__A__16823)
         => ( t(Vvar__3___24Anonymous__16826,Vvar__0__A__16823)
           => ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a4(Vvar__0__A__16823,Vvar__1__R__16824,Vvar__2__x__16825,Vvar__3___24Anonymous__16826)
             => ( ? [Vvar__3__y__16831] :
                    ( t(Vvar__3__y__16831,Vvar__0__A__16823)
                    & p(happ(happ(Vvar__1__R__16824,Vvar__2__x__16825),Vvar__3__y__16831))
                    & Vvar__3___24Anonymous__16826 = Vvar__3__y__16831 )
                | ? [Vvar__3__y__16836] :
                    ( t(Vvar__3__y__16836,Vvar__0__A__16823)
                    & ? [Vvar__4__z__16837] :
                        ( t(Vvar__4__z__16837,Vvar__0__A__16823)
                        & cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a4(Vvar__0__A__16823,Vvar__1__R__16824,Vvar__2__x__16825,Vvar__3__y__16836)
                        & cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a4(Vvar__0__A__16823,Vvar__1__R__16824,Vvar__3__y__16836,Vvar__4__z__16837)
                        & Vvar__3___24Anonymous__16826 = Vvar__4__z__16837 ) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.Relations.Relation_Operators.clos_trans_1n',axiom,
    ! [Vvar__0__A__30822,Vvar__1__R__30823,Vvar__2__x__30824,Vvar__3___24Anonymous__30825] :
      ( cType___24t(Vvar__0__A__30822)
     => ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vvar__0__A__30822,Vvar__1__R__30823)
       => ( t(Vvar__2__x__30824,Vvar__0__A__30822)
         => ( t(Vvar__3___24Anonymous__30825,Vvar__0__A__30822)
           => ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans__1n___24a4(Vvar__0__A__30822,Vvar__1__R__30823,Vvar__2__x__30824,Vvar__3___24Anonymous__30825)
             => ( ? [Vvar__3__y__30830] :
                    ( t(Vvar__3__y__30830,Vvar__0__A__30822)
                    & p(happ(happ(Vvar__1__R__30823,Vvar__2__x__30824),Vvar__3__y__30830))
                    & Vvar__3___24Anonymous__30825 = Vvar__3__y__30830 )
                | ? [Vvar__3__y__30835] :
                    ( t(Vvar__3__y__30835,Vvar__0__A__30822)
                    & ? [Vvar__4__z__30836] :
                        ( t(Vvar__4__z__30836,Vvar__0__A__30822)
                        & p(happ(happ(Vvar__1__R__30823,Vvar__2__x__30824),Vvar__3__y__30835))
                        & cCoq_2eRelations_2eRelation__Operators_2eclos__trans__1n___24a4(Vvar__0__A__30822,Vvar__1__R__30823,Vvar__3__y__30835,Vvar__4__z__30836)
                        & Vvar__3___24Anonymous__30825 = Vvar__4__z__30836 ) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.Relations.Relation_Operators.clos_trans_n1',axiom,
    ! [Vvar__0__A__30839,Vvar__1__R__30840,Vvar__2__x__30841,Vvar__3___24Anonymous__30842] :
      ( cType___24t(Vvar__0__A__30839)
     => ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vvar__0__A__30839,Vvar__1__R__30840)
       => ( t(Vvar__2__x__30841,Vvar__0__A__30839)
         => ( t(Vvar__3___24Anonymous__30842,Vvar__0__A__30839)
           => ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans__n1___24a4(Vvar__0__A__30839,Vvar__1__R__30840,Vvar__2__x__30841,Vvar__3___24Anonymous__30842)
             => ( ? [Vvar__3__y__30847] :
                    ( t(Vvar__3__y__30847,Vvar__0__A__30839)
                    & p(happ(happ(Vvar__1__R__30840,Vvar__2__x__30841),Vvar__3__y__30847))
                    & Vvar__3___24Anonymous__30842 = Vvar__3__y__30847 )
                | ? [Vvar__3__y__30852] :
                    ( t(Vvar__3__y__30852,Vvar__0__A__30839)
                    & ? [Vvar__4__z__30853] :
                        ( t(Vvar__4__z__30853,Vvar__0__A__30839)
                        & p(happ(happ(Vvar__1__R__30840,Vvar__3__y__30852),Vvar__4__z__30853))
                        & cCoq_2eRelations_2eRelation__Operators_2eclos__trans__n1___24a4(Vvar__0__A__30839,Vvar__1__R__30840,Vvar__2__x__30841,Vvar__3__y__30852)
                        & Vvar__3___24Anonymous__30842 = Vvar__4__z__30853 ) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.Relations.Relation_Operators.le_AsB',axiom,
    ! [Vvar__0__A__30959,Vvar__1__B__30960,Vvar__2__leA__30961,Vvar__3__leB__30966,Vvar__4___24Anonymous__30971,Vvar__5___24Anonymous__30972] :
      ( cType___24t(Vvar__0__A__30959)
     => ( cType___24t(Vvar__1__B__30960)
       => ( c_24__type__31041___24t(Vvar__0__A__30959,Vvar__1__B__30960,Vvar__2__leA__30961,Vvar__3__leB__30966,Vvar__4___24Anonymous__30971,Vvar__5___24Anonymous__30972,Vvar__2__leA__30961)
         => ( c_24__type__31066___24t(Vvar__0__A__30959,Vvar__1__B__30960,Vvar__2__leA__30961,Vvar__3__leB__30966,Vvar__4___24Anonymous__30971,Vvar__5___24Anonymous__30972,Vvar__3__leB__30966)
           => ( cCoq_2eInit_2eDatatypes_2esum___24t(Vvar__0__A__30959,Vvar__1__B__30960,Vvar__4___24Anonymous__30971)
             => ( cCoq_2eInit_2eDatatypes_2esum___24t(Vvar__0__A__30959,Vvar__1__B__30960,Vvar__5___24Anonymous__30972)
               => ( cCoq_2eRelations_2eRelation__Operators_2ele__AsB___24a6(Vvar__0__A__30959,Vvar__1__B__30960,Vvar__2__leA__30961,Vvar__3__leB__30966,Vvar__4___24Anonymous__30971,Vvar__5___24Anonymous__30972)
                 => ( ? [Vvar__4__x__30986] :
                        ( t(Vvar__4__x__30986,Vvar__0__A__30959)
                        & ? [Vvar__5__y__30987] :
                            ( t(Vvar__5__y__30987,Vvar__0__A__30959)
                            & p(happ(happ(Vvar__2__leA__30961,Vvar__4__x__30986),Vvar__5__y__30987))
                            & Vvar__5___24Anonymous__30972 = cCoq_2eInit_2eDatatypes_2einl___24a3(Vvar__0__A__30959,Vvar__1__B__30960,Vvar__5__y__30987)
                            & Vvar__4___24Anonymous__30971 = cCoq_2eInit_2eDatatypes_2einl___24a3(Vvar__0__A__30959,Vvar__1__B__30960,Vvar__4__x__30986) ) )
                    | ? [Vvar__4__x__31001] :
                        ( t(Vvar__4__x__31001,Vvar__0__A__30959)
                        & ? [Vvar__5__y__31002] :
                            ( t(Vvar__5__y__31002,Vvar__1__B__30960)
                            & Vvar__5___24Anonymous__30972 = cCoq_2eInit_2eDatatypes_2einr___24a3(Vvar__0__A__30959,Vvar__1__B__30960,Vvar__5__y__31002)
                            & Vvar__4___24Anonymous__30971 = cCoq_2eInit_2eDatatypes_2einl___24a3(Vvar__0__A__30959,Vvar__1__B__30960,Vvar__4__x__31001) ) )
                    | ? [Vvar__4__x__31015] :
                        ( t(Vvar__4__x__31015,Vvar__1__B__30960)
                        & ? [Vvar__5__y__31016] :
                            ( t(Vvar__5__y__31016,Vvar__1__B__30960)
                            & p(happ(happ(Vvar__3__leB__30966,Vvar__4__x__31015),Vvar__5__y__31016))
                            & Vvar__5___24Anonymous__30972 = cCoq_2eInit_2eDatatypes_2einr___24a3(Vvar__0__A__30959,Vvar__1__B__30960,Vvar__5__y__31016)
                            & Vvar__4___24Anonymous__30971 = cCoq_2eInit_2eDatatypes_2einr___24a3(Vvar__0__A__30959,Vvar__1__B__30960,Vvar__4__x__31015) ) ) ) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.Relations.Relation_Operators.lexprod',axiom,
    ! [Vvar__0__A__16855,Vvar__1__B__16856,Vvar__2__leA__16859,Vvar__3__leB__16864,Vvar__4___24Anonymous__16871,Vvar__5___24Anonymous__16872] :
      ( cType___24t(Vvar__0__A__16855)
     => ( c_24__type__16935___24t(Vvar__0__A__16855,Vvar__1__B__16856,Vvar__2__leA__16859,Vvar__3__leB__16864,Vvar__4___24Anonymous__16871,Vvar__5___24Anonymous__16872,Vvar__1__B__16856)
       => ( c_24__type__16964___24t(Vvar__0__A__16855,Vvar__1__B__16856,Vvar__2__leA__16859,Vvar__3__leB__16864,Vvar__4___24Anonymous__16871,Vvar__5___24Anonymous__16872,Vvar__2__leA__16859)
         => ( c_24__type__17001___24t(Vvar__0__A__16855,Vvar__1__B__16856,Vvar__2__leA__16859,Vvar__3__leB__16864,Vvar__4___24Anonymous__16871,Vvar__5___24Anonymous__16872,Vvar__3__leB__16864)
           => ( cCoq_2eInit_2eSpecif_2esigT___24t(Vvar__0__A__16855,Vvar__1__B__16856,Vvar__4___24Anonymous__16871)
             => ( cCoq_2eInit_2eSpecif_2esigT___24t(Vvar__0__A__16855,Vvar__1__B__16856,Vvar__5___24Anonymous__16872)
               => ( cCoq_2eRelations_2eRelation__Operators_2elexprod___24a6(Vvar__0__A__16855,Vvar__1__B__16856,Vvar__2__leA__16859,Vvar__3__leB__16864,Vvar__4___24Anonymous__16871,Vvar__5___24Anonymous__16872)
                 => ( ? [Vvar__4__x__16890] :
                        ( t(Vvar__4__x__16890,Vvar__0__A__16855)
                        & ? [Vvar__5__x_27__16891] :
                            ( t(Vvar__5__x_27__16891,Vvar__0__A__16855)
                            & ? [Vvar__6__y__16892] :
                                ( t(Vvar__6__y__16892,happ(Vvar__1__B__16856,Vvar__4__x__16890))
                                & ? [Vvar__7__y_27__16893] :
                                    ( t(Vvar__7__y_27__16893,happ(Vvar__1__B__16856,Vvar__5__x_27__16891))
                                    & p(happ(happ(Vvar__2__leA__16859,Vvar__4__x__16890),Vvar__5__x_27__16891))
                                    & Vvar__5___24Anonymous__16872 = cCoq_2eInit_2eSpecif_2eexistT___24a4(Vvar__0__A__16855,Vvar__1__B__16856,Vvar__5__x_27__16891,Vvar__7__y_27__16893)
                                    & Vvar__4___24Anonymous__16871 = cCoq_2eInit_2eSpecif_2eexistT___24a4(Vvar__0__A__16855,Vvar__1__B__16856,Vvar__4__x__16890,Vvar__6__y__16892) ) ) ) )
                    | ? [Vvar__4__x__16911] :
                        ( t(Vvar__4__x__16911,Vvar__0__A__16855)
                        & ? [Vvar__5__y__16912] :
                            ( t(Vvar__5__y__16912,happ(Vvar__1__B__16856,Vvar__4__x__16911))
                            & ? [Vvar__6__y_27__16913] :
                                ( t(Vvar__6__y_27__16913,happ(Vvar__1__B__16856,Vvar__4__x__16911))
                                & p(happ(happ(happ(Vvar__3__leB__16864,Vvar__4__x__16911),Vvar__5__y__16912),Vvar__6__y_27__16913))
                                & Vvar__5___24Anonymous__16872 = cCoq_2eInit_2eSpecif_2eexistT___24a4(Vvar__0__A__16855,Vvar__1__B__16856,Vvar__4__x__16911,Vvar__6__y_27__16913)
                                & Vvar__4___24Anonymous__16871 = cCoq_2eInit_2eSpecif_2eexistT___24a4(Vvar__0__A__16855,Vvar__1__B__16856,Vvar__4__x__16911,Vvar__5__y__16912) ) ) ) ) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.Relations.Relation_Operators.swapprod',axiom,
    ! [Vvar__0__A__31165,Vvar__1__R__31166,Vvar__2___24Anonymous__31171,Vvar__3___24Anonymous__31172] :
      ( cType___24t(Vvar__0__A__31165)
     => ( c_24__type__31205___24t(Vvar__0__A__31165,Vvar__1__R__31166,Vvar__2___24Anonymous__31171,Vvar__3___24Anonymous__31172,Vvar__1__R__31166)
       => ( cCoq_2eInit_2eDatatypes_2eprod___24t(Vvar__0__A__31165,Vvar__0__A__31165,Vvar__2___24Anonymous__31171)
         => ( cCoq_2eInit_2eDatatypes_2eprod___24t(Vvar__0__A__31165,Vvar__0__A__31165,Vvar__3___24Anonymous__31172)
           => ( cCoq_2eRelations_2eRelation__Operators_2eswapprod___24a4(Vvar__0__A__31165,Vvar__1__R__31166,Vvar__2___24Anonymous__31171,Vvar__3___24Anonymous__31172)
             => ( ? [Vvar__2__x__31180] :
                    ( t(Vvar__2__x__31180,Vvar__0__A__31165)
                    & ? [Vvar__3__y__31181] :
                        ( t(Vvar__3__y__31181,Vvar__0__A__31165)
                        & ? [Vvar__4__p__31182] :
                            ( cCoq_2eInit_2eDatatypes_2eprod___24t(Vvar__0__A__31165,Vvar__0__A__31165,Vvar__4__p__31182)
                            & cCoq_2eRelations_2eRelation__Operators_2esymprod___24a6(Vvar__0__A__31165,Vvar__0__A__31165,Vvar__1__R__31166,Vvar__1__R__31166,cCoq_2eInit_2eDatatypes_2epair___24a4(Vvar__0__A__31165,Vvar__0__A__31165,Vvar__2__x__31180,Vvar__3__y__31181),Vvar__4__p__31182)
                            & Vvar__3___24Anonymous__31172 = Vvar__4__p__31182
                            & Vvar__2___24Anonymous__31171 = cCoq_2eInit_2eDatatypes_2epair___24a4(Vvar__0__A__31165,Vvar__0__A__31165,Vvar__2__x__31180,Vvar__3__y__31181) ) ) )
                | ? [Vvar__2__x__31190] :
                    ( t(Vvar__2__x__31190,Vvar__0__A__31165)
                    & ? [Vvar__3__y__31191] :
                        ( t(Vvar__3__y__31191,Vvar__0__A__31165)
                        & ? [Vvar__4__p__31192] :
                            ( cCoq_2eInit_2eDatatypes_2eprod___24t(Vvar__0__A__31165,Vvar__0__A__31165,Vvar__4__p__31192)
                            & cCoq_2eRelations_2eRelation__Operators_2esymprod___24a6(Vvar__0__A__31165,Vvar__0__A__31165,Vvar__1__R__31166,Vvar__1__R__31166,cCoq_2eInit_2eDatatypes_2epair___24a4(Vvar__0__A__31165,Vvar__0__A__31165,Vvar__2__x__31190,Vvar__3__y__31191),Vvar__4__p__31192)
                            & Vvar__3___24Anonymous__31172 = Vvar__4__p__31192
                            & Vvar__2___24Anonymous__31171 = cCoq_2eInit_2eDatatypes_2epair___24a4(Vvar__0__A__31165,Vvar__0__A__31165,Vvar__3__y__31191,Vvar__2__x__31190) ) ) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.Relations.Relation_Operators.symprod',axiom,
    ! [Vvar__0__A__31068,Vvar__1__B__31069,Vvar__2__leA__31070,Vvar__3__leB__31075,Vvar__4___24Anonymous__31080,Vvar__5___24Anonymous__31081] :
      ( cType___24t(Vvar__0__A__31068)
     => ( cType___24t(Vvar__1__B__31069)
       => ( c_24__type__31138___24t(Vvar__0__A__31068,Vvar__1__B__31069,Vvar__2__leA__31070,Vvar__3__leB__31075,Vvar__4___24Anonymous__31080,Vvar__5___24Anonymous__31081,Vvar__2__leA__31070)
         => ( c_24__type__31163___24t(Vvar__0__A__31068,Vvar__1__B__31069,Vvar__2__leA__31070,Vvar__3__leB__31075,Vvar__4___24Anonymous__31080,Vvar__5___24Anonymous__31081,Vvar__3__leB__31075)
           => ( cCoq_2eInit_2eDatatypes_2eprod___24t(Vvar__0__A__31068,Vvar__1__B__31069,Vvar__4___24Anonymous__31080)
             => ( cCoq_2eInit_2eDatatypes_2eprod___24t(Vvar__0__A__31068,Vvar__1__B__31069,Vvar__5___24Anonymous__31081)
               => ( cCoq_2eRelations_2eRelation__Operators_2esymprod___24a6(Vvar__0__A__31068,Vvar__1__B__31069,Vvar__2__leA__31070,Vvar__3__leB__31075,Vvar__4___24Anonymous__31080,Vvar__5___24Anonymous__31081)
                 => ( ? [Vvar__4__x__31095] :
                        ( t(Vvar__4__x__31095,Vvar__0__A__31068)
                        & ? [Vvar__5__x_27__31096] :
                            ( t(Vvar__5__x_27__31096,Vvar__0__A__31068)
                            & p(happ(happ(Vvar__2__leA__31070,Vvar__4__x__31095),Vvar__5__x_27__31096))
                            & ? [Vvar__7__y__31098] :
                                ( t(Vvar__7__y__31098,Vvar__1__B__31069)
                                & Vvar__5___24Anonymous__31081 = cCoq_2eInit_2eDatatypes_2epair___24a4(Vvar__0__A__31068,Vvar__1__B__31069,Vvar__5__x_27__31096,Vvar__7__y__31098)
                                & Vvar__4___24Anonymous__31080 = cCoq_2eInit_2eDatatypes_2epair___24a4(Vvar__0__A__31068,Vvar__1__B__31069,Vvar__4__x__31095,Vvar__7__y__31098) ) ) )
                    | ? [Vvar__4__y__31111] :
                        ( t(Vvar__4__y__31111,Vvar__1__B__31069)
                        & ? [Vvar__5__y_27__31112] :
                            ( t(Vvar__5__y_27__31112,Vvar__1__B__31069)
                            & p(happ(happ(Vvar__3__leB__31075,Vvar__4__y__31111),Vvar__5__y_27__31112))
                            & ? [Vvar__7__x__31114] :
                                ( t(Vvar__7__x__31114,Vvar__0__A__31068)
                                & Vvar__5___24Anonymous__31081 = cCoq_2eInit_2eDatatypes_2epair___24a4(Vvar__0__A__31068,Vvar__1__B__31069,Vvar__7__x__31114,Vvar__5__y_27__31112)
                                & Vvar__4___24Anonymous__31080 = cCoq_2eInit_2eDatatypes_2epair___24a4(Vvar__0__A__31068,Vvar__1__B__31069,Vvar__7__x__31114,Vvar__4__y__31111) ) ) ) ) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.Sets.Relations_1.Equivalence',axiom,
    ! [Vvar__0__U__31792,Vvar__1__R__31793] :
      ( cType___24t(Vvar__0__U__31792)
     => ( cCoq_2eSets_2eRelations__1_2eRelation___24t(Vvar__0__U__31792,Vvar__1__R__31793)
       => ( cCoq_2eSets_2eRelations__1_2eEquivalence___24a2(Vvar__0__U__31792,Vvar__1__R__31793)
         => ( cCoq_2eSets_2eRelations__1_2eReflexive___24a2(Vvar__0__U__31792,Vvar__1__R__31793)
            & cCoq_2eSets_2eRelations__1_2eTransitive___24a2(Vvar__0__U__31792,Vvar__1__R__31793)
            & cCoq_2eSets_2eRelations__1_2eSymmetric___24a2(Vvar__0__U__31792,Vvar__1__R__31793)
            & p(c_24True) ) ) ) ) ).

fof('$_inversion_Coq.Sets.Relations_1.Order',axiom,
    ! [Vvar__0__U__31784,Vvar__1__R__31785] :
      ( cType___24t(Vvar__0__U__31784)
     => ( cCoq_2eSets_2eRelations__1_2eRelation___24t(Vvar__0__U__31784,Vvar__1__R__31785)
       => ( cCoq_2eSets_2eRelations__1_2eOrder___24a2(Vvar__0__U__31784,Vvar__1__R__31785)
         => ( cCoq_2eSets_2eRelations__1_2eReflexive___24a2(Vvar__0__U__31784,Vvar__1__R__31785)
            & cCoq_2eSets_2eRelations__1_2eTransitive___24a2(Vvar__0__U__31784,Vvar__1__R__31785)
            & cCoq_2eSets_2eRelations__1_2eAntisymmetric___24a2(Vvar__0__U__31784,Vvar__1__R__31785)
            & p(c_24True) ) ) ) ) ).

fof('$_inversion_Coq.Sets.Relations_1.PER',axiom,
    ! [Vvar__0__U__31800,Vvar__1__R__31801] :
      ( cType___24t(Vvar__0__U__31800)
     => ( cCoq_2eSets_2eRelations__1_2eRelation___24t(Vvar__0__U__31800,Vvar__1__R__31801)
       => ( cCoq_2eSets_2eRelations__1_2ePER___24a2(Vvar__0__U__31800,Vvar__1__R__31801)
         => ( cCoq_2eSets_2eRelations__1_2eSymmetric___24a2(Vvar__0__U__31800,Vvar__1__R__31801)
            & cCoq_2eSets_2eRelations__1_2eTransitive___24a2(Vvar__0__U__31800,Vvar__1__R__31801)
            & p(c_24True) ) ) ) ) ).

fof('$_inversion_Coq.Sets.Relations_1.Preorder',axiom,
    ! [Vvar__0__U__31777,Vvar__1__R__31778] :
      ( cType___24t(Vvar__0__U__31777)
     => ( cCoq_2eSets_2eRelations__1_2eRelation___24t(Vvar__0__U__31777,Vvar__1__R__31778)
       => ( cCoq_2eSets_2eRelations__1_2ePreorder___24a2(Vvar__0__U__31777,Vvar__1__R__31778)
         => ( cCoq_2eSets_2eRelations__1_2eReflexive___24a2(Vvar__0__U__31777,Vvar__1__R__31778)
            & cCoq_2eSets_2eRelations__1_2eTransitive___24a2(Vvar__0__U__31777,Vvar__1__R__31778)
            & p(c_24True) ) ) ) ) ).

fof('$_inversion_Coq.Sorting.Sorted.HdRel',axiom,
    ! [Vvar__0__A__32352,Vvar__1__R__32353,Vvar__2__a__32358,Vvar__3___24Anonymous__32359] :
      ( cType___24t(Vvar__0__A__32352)
     => ( c_24__type__32389___24t(Vvar__0__A__32352,Vvar__1__R__32353,Vvar__2__a__32358,Vvar__3___24Anonymous__32359,Vvar__1__R__32353)
       => ( t(Vvar__2__a__32358,Vvar__0__A__32352)
         => ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__32352,Vvar__3___24Anonymous__32359)
           => ( cCoq_2eSorting_2eSorted_2eHdRel___24a4(Vvar__0__A__32352,Vvar__1__R__32353,Vvar__2__a__32358,Vvar__3___24Anonymous__32359)
             => ( Vvar__3___24Anonymous__32359 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__32352)
                | ? [Vvar__3__b__32375] :
                    ( t(Vvar__3__b__32375,Vvar__0__A__32352)
                    & ? [Vvar__4__l__32376] :
                        ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__32352,Vvar__4__l__32376)
                        & p(happ(happ(Vvar__1__R__32353,Vvar__2__a__32358),Vvar__3__b__32375))
                        & Vvar__3___24Anonymous__32359 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__32352,Vvar__3__b__32375,Vvar__4__l__32376) ) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.Sorting.Sorted.LocallySorted',axiom,
    ! [Vvar__0__A__32309,Vvar__1__R__32310,Vvar__2___24Anonymous__32315] :
      ( cType___24t(Vvar__0__A__32309)
     => ( c_24__type__32350___24t(Vvar__0__A__32309,Vvar__1__R__32310,Vvar__2___24Anonymous__32315,Vvar__1__R__32310)
       => ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__32309,Vvar__2___24Anonymous__32315)
         => ( cCoq_2eSorting_2eSorted_2eLocallySorted___24a3(Vvar__0__A__32309,Vvar__1__R__32310,Vvar__2___24Anonymous__32315)
           => ( Vvar__2___24Anonymous__32315 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__32309)
              | ? [Vvar__2__a__32329] :
                  ( t(Vvar__2__a__32329,Vvar__0__A__32309)
                  & Vvar__2___24Anonymous__32315 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__32309,Vvar__2__a__32329,cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__32309)) )
              | ? [Vvar__2__a__32336] :
                  ( t(Vvar__2__a__32336,Vvar__0__A__32309)
                  & ? [Vvar__3__b__32337] :
                      ( t(Vvar__3__b__32337,Vvar__0__A__32309)
                      & ? [Vvar__4__l__32338] :
                          ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__32309,Vvar__4__l__32338)
                          & cCoq_2eSorting_2eSorted_2eLocallySorted___24a3(Vvar__0__A__32309,Vvar__1__R__32310,cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__32309,Vvar__3__b__32337,Vvar__4__l__32338))
                          & p(happ(happ(Vvar__1__R__32310,Vvar__2__a__32336),Vvar__3__b__32337))
                          & Vvar__2___24Anonymous__32315 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__32309,Vvar__2__a__32336,cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__32309,Vvar__3__b__32337,Vvar__4__l__32338)) ) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.Sorting.Sorted.Sorted',axiom,
    ! [Vvar__0__A__32391,Vvar__1__R__32392,Vvar__2___24Anonymous__32397] :
      ( cType___24t(Vvar__0__A__32391)
     => ( c_24__type__32424___24t(Vvar__0__A__32391,Vvar__1__R__32392,Vvar__2___24Anonymous__32397,Vvar__1__R__32392)
       => ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__32391,Vvar__2___24Anonymous__32397)
         => ( cCoq_2eSorting_2eSorted_2eSorted___24a3(Vvar__0__A__32391,Vvar__1__R__32392,Vvar__2___24Anonymous__32397)
           => ( Vvar__2___24Anonymous__32397 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__32391)
              | ? [Vvar__2__a__32411] :
                  ( t(Vvar__2__a__32411,Vvar__0__A__32391)
                  & ? [Vvar__3__l__32412] :
                      ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__32391,Vvar__3__l__32412)
                      & cCoq_2eSorting_2eSorted_2eSorted___24a3(Vvar__0__A__32391,Vvar__1__R__32392,Vvar__3__l__32412)
                      & cCoq_2eSorting_2eSorted_2eHdRel___24a4(Vvar__0__A__32391,Vvar__1__R__32392,Vvar__2__a__32411,Vvar__3__l__32412)
                      & Vvar__2___24Anonymous__32397 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__32391,Vvar__2__a__32411,Vvar__3__l__32412) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.Sorting.Sorted.StronglySorted',axiom,
    ! [Vvar__0__A__32426,Vvar__1__R__32427,Vvar__2___24Anonymous__32432] :
      ( cType___24t(Vvar__0__A__32426)
     => ( c_24__type__32459___24t(Vvar__0__A__32426,Vvar__1__R__32427,Vvar__2___24Anonymous__32432,Vvar__1__R__32427)
       => ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__32426,Vvar__2___24Anonymous__32432)
         => ( cCoq_2eSorting_2eSorted_2eStronglySorted___24a3(Vvar__0__A__32426,Vvar__1__R__32427,Vvar__2___24Anonymous__32432)
           => ( Vvar__2___24Anonymous__32432 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__32426)
              | ? [Vvar__2__a__32446] :
                  ( t(Vvar__2__a__32446,Vvar__0__A__32426)
                  & ? [Vvar__3__l__32447] :
                      ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__32426,Vvar__3__l__32447)
                      & cCoq_2eSorting_2eSorted_2eStronglySorted___24a3(Vvar__0__A__32426,Vvar__1__R__32427,Vvar__3__l__32447)
                      & cCoq_2eLists_2eList_2eForall___24a3(Vvar__0__A__32426,happ(Vvar__1__R__32427,Vvar__2__a__32446),Vvar__3__l__32447)
                      & Vvar__2___24Anonymous__32432 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__32426,Vvar__2__a__32446,Vvar__3__l__32447) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.Strings.Ascii.ascii',axiom,
    ! [VX25297] :
      ( cCoq_2eStrings_2eAscii_2eascii___24t(VX25297)
     => ? [Vvar__0___24Anonymous__25298] :
          ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__0___24Anonymous__25298)
          & ? [Vvar__1___24Anonymous__25299] :
              ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__1___24Anonymous__25299)
              & ? [Vvar__2___24Anonymous__25300] :
                  ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__2___24Anonymous__25300)
                  & ? [Vvar__3___24Anonymous__25301] :
                      ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__3___24Anonymous__25301)
                      & ? [Vvar__4___24Anonymous__25302] :
                          ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__4___24Anonymous__25302)
                          & ? [Vvar__5___24Anonymous__25303] :
                              ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__5___24Anonymous__25303)
                              & ? [Vvar__6___24Anonymous__25304] :
                                  ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__6___24Anonymous__25304)
                                  & ? [Vvar__7___24Anonymous__25305] :
                                      ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__7___24Anonymous__25305)
                                      & VX25297 = cCoq_2eStrings_2eAscii_2eAscii___24a8(Vvar__0___24Anonymous__25298,Vvar__1___24Anonymous__25299,Vvar__2___24Anonymous__25300,Vvar__3___24Anonymous__25301,Vvar__4___24Anonymous__25302,Vvar__5___24Anonymous__25303,Vvar__6___24Anonymous__25304,Vvar__7___24Anonymous__25305) ) ) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.Strings.String.string',axiom,
    ! [VX25973] :
      ( cCoq_2eStrings_2eString_2estring___24t(VX25973)
     => ( VX25973 = cCoq_2eStrings_2eString_2eEmptyString
        | ? [Vvar__0___24Anonymous__25974] :
            ( cCoq_2eStrings_2eAscii_2eascii___24t(Vvar__0___24Anonymous__25974)
            & ? [Vvar__1___24Anonymous__25975] :
                ( cCoq_2eStrings_2eString_2estring___24t(Vvar__1___24Anonymous__25975)
                & VX25973 = cCoq_2eStrings_2eString_2eString___24a2(Vvar__0___24Anonymous__25974,Vvar__1___24Anonymous__25975) ) ) ) ) ).

fof('$_inversion_Coq.Structures.OrderedType.Compare',axiom,
    ! [Vvar__0__X__16234,Vvar__1__lt__16235,Vvar__2__eq__16240,Vvar__3__x__16245,Vvar__4__y__16246,VX16247] :
      ( cType___24t(Vvar__0__X__16234)
     => ( c_24__type__16307___24t(Vvar__0__X__16234,Vvar__1__lt__16235,Vvar__2__eq__16240,Vvar__3__x__16245,Vvar__4__y__16246,Vvar__1__lt__16235)
       => ( c_24__type__16326___24t(Vvar__0__X__16234,Vvar__1__lt__16235,Vvar__2__eq__16240,Vvar__3__x__16245,Vvar__4__y__16246,Vvar__2__eq__16240)
         => ( t(Vvar__3__x__16245,Vvar__0__X__16234)
           => ( t(Vvar__4__y__16246,Vvar__0__X__16234)
             => ( cCoq_2eStructures_2eOrderedType_2eCompare___24t(Vvar__0__X__16234,Vvar__1__lt__16235,Vvar__2__eq__16240,Vvar__3__x__16245,Vvar__4__y__16246,VX16247)
               => ( ( p(happ(happ(Vvar__1__lt__16235,Vvar__3__x__16245),Vvar__4__y__16246))
                    & VX16247 = cCoq_2eStructures_2eOrderedType_2eLT___24a5(Vvar__0__X__16234,Vvar__1__lt__16235,Vvar__2__eq__16240,Vvar__3__x__16245,Vvar__4__y__16246) )
                  | ( p(happ(happ(Vvar__2__eq__16240,Vvar__3__x__16245),Vvar__4__y__16246))
                    & VX16247 = cCoq_2eStructures_2eOrderedType_2eEQ___24a5(Vvar__0__X__16234,Vvar__1__lt__16235,Vvar__2__eq__16240,Vvar__3__x__16245,Vvar__4__y__16246) )
                  | ( p(happ(happ(Vvar__1__lt__16235,Vvar__4__y__16246),Vvar__3__x__16245))
                    & VX16247 = cCoq_2eStructures_2eOrderedType_2eGT___24a5(Vvar__0__X__16234,Vvar__1__lt__16235,Vvar__2__eq__16240,Vvar__3__x__16245,Vvar__4__y__16246) ) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.Structures.OrderedTypeEx.String_as_OT.lts',axiom,
    ! [Vvar__0___24Anonymous__33086,Vvar__1___24Anonymous__33087] :
      ( cCoq_2eStrings_2eString_2estring___24t(Vvar__0___24Anonymous__33086)
     => ( cCoq_2eStrings_2eString_2estring___24t(Vvar__1___24Anonymous__33087)
       => ( cCoq_2eStructures_2eOrderedTypeEx_2eString__as__OT_2elts___24a2(Vvar__0___24Anonymous__33086,Vvar__1___24Anonymous__33087)
         => ( ? [Vvar__0__a__33089] :
                ( cCoq_2eStrings_2eAscii_2eascii___24t(Vvar__0__a__33089)
                & ? [Vvar__1__s__33090] :
                    ( cCoq_2eStrings_2eString_2estring___24t(Vvar__1__s__33090)
                    & Vvar__1___24Anonymous__33087 = cCoq_2eStrings_2eString_2eString___24a2(Vvar__0__a__33089,Vvar__1__s__33090)
                    & Vvar__0___24Anonymous__33086 = cCoq_2eStrings_2eString_2eEmptyString ) )
            | ? [Vvar__0__a__33091] :
                ( cCoq_2eStrings_2eAscii_2eascii___24t(Vvar__0__a__33091)
                & ? [Vvar__1__s1__33092] :
                    ( cCoq_2eStrings_2eString_2estring___24t(Vvar__1__s1__33092)
                    & ? [Vvar__2__s2__33093] :
                        ( cCoq_2eStrings_2eString_2estring___24t(Vvar__2__s2__33093)
                        & cCoq_2eStructures_2eOrderedTypeEx_2eString__as__OT_2elts___24a2(Vvar__1__s1__33092,Vvar__2__s2__33093)
                        & Vvar__1___24Anonymous__33087 = cCoq_2eStrings_2eString_2eString___24a2(Vvar__0__a__33091,Vvar__2__s2__33093)
                        & Vvar__0___24Anonymous__33086 = cCoq_2eStrings_2eString_2eString___24a2(Vvar__0__a__33091,Vvar__1__s1__33092) ) ) )
            | ? [Vvar__0__a__33095] :
                ( cCoq_2eStrings_2eAscii_2eascii___24t(Vvar__0__a__33095)
                & ? [Vvar__1__b__33096] :
                    ( cCoq_2eStrings_2eAscii_2eascii___24t(Vvar__1__b__33096)
                    & ? [Vvar__2__s1__33097] :
                        ( cCoq_2eStrings_2eString_2estring___24t(Vvar__2__s1__33097)
                        & ? [Vvar__3__s2__33098] :
                            ( cCoq_2eStrings_2eString_2estring___24t(Vvar__3__s2__33098)
                            & cCoq_2eInit_2ePeano_2elt___24a2(cCoq_2eStrings_2eAscii_2enat__of__ascii___24a1(Vvar__0__a__33095),cCoq_2eStrings_2eAscii_2enat__of__ascii___24a1(Vvar__1__b__33096))
                            & Vvar__1___24Anonymous__33087 = cCoq_2eStrings_2eString_2eString___24a2(Vvar__1__b__33096,Vvar__3__s2__33098)
                            & Vvar__0___24Anonymous__33086 = cCoq_2eStrings_2eString_2eString___24a2(Vvar__0__a__33095,Vvar__2__s1__33097) ) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.Structures.OrdersTac.ord',axiom,
    ! [VX2587] :
      ( cCoq_2eStructures_2eOrdersTac_2eord___24t(VX2587)
     => ( VX2587 = cCoq_2eStructures_2eOrdersTac_2eOEQ
        | VX2587 = cCoq_2eStructures_2eOrdersTac_2eOLT
        | VX2587 = cCoq_2eStructures_2eOrdersTac_2eOLE ) ) ).

fof('$_inversion_Coq.Vectors.Fin.t',axiom,
    ! [Vvar__0___24Anonymous__14584,VX14585] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__14584)
     => ( cCoq_2eVectors_2eFin_2et___24t(Vvar__0___24Anonymous__14584,VX14585)
       => ( ? [Vvar__0__n__14586] :
              ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0__n__14586)
              & Vvar__0___24Anonymous__14584 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0__n__14586)
              & VX14585 = cCoq_2eVectors_2eFin_2eF1___24a1(Vvar__0__n__14586) )
          | ? [Vvar__0__n__14587] :
              ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0__n__14587)
              & ? [Vvar__1___24Anonymous__14588] :
                  ( cCoq_2eVectors_2eFin_2et___24t(Vvar__0__n__14587,Vvar__1___24Anonymous__14588)
                  & Vvar__0___24Anonymous__14584 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0__n__14587)
                  & VX14585 = cCoq_2eVectors_2eFin_2eFS___24a2(Vvar__0__n__14587,Vvar__1___24Anonymous__14588) ) ) ) ) ) ).

fof('$_inversion_Coq.Vectors.VectorDef.Exists',axiom,
    ! [Vvar__0__A__32613,Vvar__1__P__32614,Vvar__2__n__32617,Vvar__3___24Anonymous__32618] :
      ( cType___24t(Vvar__0__A__32613)
     => ( c_24__type__32641___24t(Vvar__0__A__32613,Vvar__1__P__32614,Vvar__2__n__32617,Vvar__3___24Anonymous__32618,Vvar__1__P__32614)
       => ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__2__n__32617)
         => ( cCoq_2eVectors_2eVectorDef_2et___24t(Vvar__0__A__32613,Vvar__2__n__32617,Vvar__3___24Anonymous__32618)
           => ( cCoq_2eVectors_2eVectorDef_2eExists___24a4(Vvar__0__A__32613,Vvar__1__P__32614,Vvar__2__n__32617,Vvar__3___24Anonymous__32618)
             => ( ? [Vvar__2__m__32624] :
                    ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__2__m__32624)
                    & ? [Vvar__3__x__32625] :
                        ( t(Vvar__3__x__32625,Vvar__0__A__32613)
                        & ? [Vvar__4__v__32626] :
                            ( cCoq_2eVectors_2eVectorDef_2et___24t(Vvar__0__A__32613,Vvar__2__m__32624,Vvar__4__v__32626)
                            & p(happ(Vvar__1__P__32614,Vvar__3__x__32625))
                            & Vvar__3___24Anonymous__32618 = cCoq_2eVectors_2eVectorDef_2econs___24a4(Vvar__0__A__32613,Vvar__3__x__32625,Vvar__2__m__32624,Vvar__4__v__32626)
                            & Vvar__2__n__32617 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__2__m__32624) ) ) )
                | ? [Vvar__2__m__32632] :
                    ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__2__m__32632)
                    & ? [Vvar__3__x__32633] :
                        ( t(Vvar__3__x__32633,Vvar__0__A__32613)
                        & ? [Vvar__4__v__32634] :
                            ( cCoq_2eVectors_2eVectorDef_2et___24t(Vvar__0__A__32613,Vvar__2__m__32632,Vvar__4__v__32634)
                            & cCoq_2eVectors_2eVectorDef_2eExists___24a4(Vvar__0__A__32613,Vvar__1__P__32614,Vvar__2__m__32632,Vvar__4__v__32634)
                            & Vvar__3___24Anonymous__32618 = cCoq_2eVectors_2eVectorDef_2econs___24a4(Vvar__0__A__32613,Vvar__3__x__32633,Vvar__2__m__32632,Vvar__4__v__32634)
                            & Vvar__2__n__32617 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__2__m__32632) ) ) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.Vectors.VectorDef.Exists2',axiom,
    ! [Vvar__0__A__32709,Vvar__1__B__32710,Vvar__2__P__32711,Vvar__3__n__32716,Vvar__4___24Anonymous__32717,Vvar__5___24Anonymous__32718] :
      ( cType___24t(Vvar__0__A__32709)
     => ( cType___24t(Vvar__1__B__32710)
       => ( c_24__type__32763___24t(Vvar__0__A__32709,Vvar__1__B__32710,Vvar__2__P__32711,Vvar__3__n__32716,Vvar__4___24Anonymous__32717,Vvar__5___24Anonymous__32718,Vvar__2__P__32711)
         => ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__3__n__32716)
           => ( cCoq_2eVectors_2eVectorDef_2et___24t(Vvar__0__A__32709,Vvar__3__n__32716,Vvar__4___24Anonymous__32717)
             => ( cCoq_2eVectors_2eVectorDef_2et___24t(Vvar__1__B__32710,Vvar__3__n__32716,Vvar__5___24Anonymous__32718)
               => ( cCoq_2eVectors_2eVectorDef_2eExists2___24a6(Vvar__0__A__32709,Vvar__1__B__32710,Vvar__2__P__32711,Vvar__3__n__32716,Vvar__4___24Anonymous__32717,Vvar__5___24Anonymous__32718)
                 => ( ? [Vvar__3__m__32727] :
                        ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__3__m__32727)
                        & ? [Vvar__4__x1__32728] :
                            ( t(Vvar__4__x1__32728,Vvar__0__A__32709)
                            & ? [Vvar__5__x2__32729] :
                                ( t(Vvar__5__x2__32729,Vvar__1__B__32710)
                                & ? [Vvar__6__v1__32730] :
                                    ( cCoq_2eVectors_2eVectorDef_2et___24t(Vvar__0__A__32709,Vvar__3__m__32727,Vvar__6__v1__32730)
                                    & ? [Vvar__7__v2__32731] :
                                        ( cCoq_2eVectors_2eVectorDef_2et___24t(Vvar__1__B__32710,Vvar__3__m__32727,Vvar__7__v2__32731)
                                        & p(happ(happ(Vvar__2__P__32711,Vvar__4__x1__32728),Vvar__5__x2__32729))
                                        & Vvar__5___24Anonymous__32718 = cCoq_2eVectors_2eVectorDef_2econs___24a4(Vvar__1__B__32710,Vvar__5__x2__32729,Vvar__3__m__32727,Vvar__7__v2__32731)
                                        & Vvar__4___24Anonymous__32717 = cCoq_2eVectors_2eVectorDef_2econs___24a4(Vvar__0__A__32709,Vvar__4__x1__32728,Vvar__3__m__32727,Vvar__6__v1__32730)
                                        & Vvar__3__n__32716 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__3__m__32727) ) ) ) ) )
                    | ? [Vvar__3__m__32740] :
                        ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__3__m__32740)
                        & ? [Vvar__4__x1__32741] :
                            ( t(Vvar__4__x1__32741,Vvar__0__A__32709)
                            & ? [Vvar__5__x2__32742] :
                                ( t(Vvar__5__x2__32742,Vvar__1__B__32710)
                                & ? [Vvar__6__v1__32743] :
                                    ( cCoq_2eVectors_2eVectorDef_2et___24t(Vvar__0__A__32709,Vvar__3__m__32740,Vvar__6__v1__32743)
                                    & ? [Vvar__7__v2__32744] :
                                        ( cCoq_2eVectors_2eVectorDef_2et___24t(Vvar__1__B__32710,Vvar__3__m__32740,Vvar__7__v2__32744)
                                        & cCoq_2eVectors_2eVectorDef_2eExists2___24a6(Vvar__0__A__32709,Vvar__1__B__32710,Vvar__2__P__32711,Vvar__3__m__32740,Vvar__6__v1__32743,Vvar__7__v2__32744)
                                        & Vvar__5___24Anonymous__32718 = cCoq_2eVectors_2eVectorDef_2econs___24a4(Vvar__1__B__32710,Vvar__5__x2__32742,Vvar__3__m__32740,Vvar__7__v2__32744)
                                        & Vvar__4___24Anonymous__32717 = cCoq_2eVectors_2eVectorDef_2econs___24a4(Vvar__0__A__32709,Vvar__4__x1__32741,Vvar__3__m__32740,Vvar__6__v1__32743)
                                        & Vvar__3__n__32716 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__3__m__32740) ) ) ) ) ) ) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.Vectors.VectorDef.Forall',axiom,
    ! [Vvar__0__A__24021,Vvar__1__P__24022,Vvar__2__n__24025,Vvar__3__v__24026] :
      ( cType___24t(Vvar__0__A__24021)
     => ( c_24__type__24046___24t(Vvar__0__A__24021,Vvar__1__P__24022,Vvar__2__n__24025,Vvar__3__v__24026,Vvar__1__P__24022)
       => ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__2__n__24025)
         => ( cCoq_2eVectors_2eVectorDef_2et___24t(Vvar__0__A__24021,Vvar__2__n__24025,Vvar__3__v__24026)
           => ( cCoq_2eVectors_2eVectorDef_2eForall___24a4(Vvar__0__A__24021,Vvar__1__P__24022,Vvar__2__n__24025,Vvar__3__v__24026)
             => ( ( Vvar__3__v__24026 = cCoq_2eVectors_2eVectorDef_2enil___24a1(Vvar__0__A__24021)
                  & Vvar__2__n__24025 = cCoq_2eInit_2eDatatypes_2eO )
                | ? [Vvar__2__n__24036] :
                    ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__2__n__24036)
                    & ? [Vvar__3__x__24037] :
                        ( t(Vvar__3__x__24037,Vvar__0__A__24021)
                        & ? [Vvar__4__v__24038] :
                            ( cCoq_2eVectors_2eVectorDef_2et___24t(Vvar__0__A__24021,Vvar__2__n__24036,Vvar__4__v__24038)
                            & p(happ(Vvar__1__P__24022,Vvar__3__x__24037))
                            & cCoq_2eVectors_2eVectorDef_2eForall___24a4(Vvar__0__A__24021,Vvar__1__P__24022,Vvar__2__n__24036,Vvar__4__v__24038)
                            & Vvar__3__v__24026 = cCoq_2eVectors_2eVectorDef_2econs___24a4(Vvar__0__A__24021,Vvar__3__x__24037,Vvar__2__n__24036,Vvar__4__v__24038)
                            & Vvar__2__n__24025 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__2__n__24036) ) ) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.Vectors.VectorDef.Forall2',axiom,
    ! [Vvar__0__A__32658,Vvar__1__B__32659,Vvar__2__P__32660,Vvar__3__n__32665,Vvar__4___24Anonymous__32666,Vvar__5___24Anonymous__32667] :
      ( cType___24t(Vvar__0__A__32658)
     => ( cType___24t(Vvar__1__B__32659)
       => ( c_24__type__32707___24t(Vvar__0__A__32658,Vvar__1__B__32659,Vvar__2__P__32660,Vvar__3__n__32665,Vvar__4___24Anonymous__32666,Vvar__5___24Anonymous__32667,Vvar__2__P__32660)
         => ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__3__n__32665)
           => ( cCoq_2eVectors_2eVectorDef_2et___24t(Vvar__0__A__32658,Vvar__3__n__32665,Vvar__4___24Anonymous__32666)
             => ( cCoq_2eVectors_2eVectorDef_2et___24t(Vvar__1__B__32659,Vvar__3__n__32665,Vvar__5___24Anonymous__32667)
               => ( cCoq_2eVectors_2eVectorDef_2eForall2___24a6(Vvar__0__A__32658,Vvar__1__B__32659,Vvar__2__P__32660,Vvar__3__n__32665,Vvar__4___24Anonymous__32666,Vvar__5___24Anonymous__32667)
                 => ( ( Vvar__5___24Anonymous__32667 = cCoq_2eVectors_2eVectorDef_2enil___24a1(Vvar__1__B__32659)
                      & Vvar__4___24Anonymous__32666 = cCoq_2eVectors_2eVectorDef_2enil___24a1(Vvar__0__A__32658)
                      & Vvar__3__n__32665 = cCoq_2eInit_2eDatatypes_2eO )
                    | ? [Vvar__3__m__32683] :
                        ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__3__m__32683)
                        & ? [Vvar__4__x1__32684] :
                            ( t(Vvar__4__x1__32684,Vvar__0__A__32658)
                            & ? [Vvar__5__x2__32685] :
                                ( t(Vvar__5__x2__32685,Vvar__1__B__32659)
                                & ? [Vvar__6__v1__32686] :
                                    ( cCoq_2eVectors_2eVectorDef_2et___24t(Vvar__0__A__32658,Vvar__3__m__32683,Vvar__6__v1__32686)
                                    & ? [Vvar__7__v2__32687] :
                                        ( cCoq_2eVectors_2eVectorDef_2et___24t(Vvar__1__B__32659,Vvar__3__m__32683,Vvar__7__v2__32687)
                                        & p(happ(happ(Vvar__2__P__32660,Vvar__4__x1__32684),Vvar__5__x2__32685))
                                        & cCoq_2eVectors_2eVectorDef_2eForall2___24a6(Vvar__0__A__32658,Vvar__1__B__32659,Vvar__2__P__32660,Vvar__3__m__32683,Vvar__6__v1__32686,Vvar__7__v2__32687)
                                        & Vvar__5___24Anonymous__32667 = cCoq_2eVectors_2eVectorDef_2econs___24a4(Vvar__1__B__32659,Vvar__5__x2__32685,Vvar__3__m__32683,Vvar__7__v2__32687)
                                        & Vvar__4___24Anonymous__32666 = cCoq_2eVectors_2eVectorDef_2econs___24a4(Vvar__0__A__32658,Vvar__4__x1__32684,Vvar__3__m__32683,Vvar__6__v1__32686)
                                        & Vvar__3__n__32665 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__3__m__32683) ) ) ) ) ) ) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.Vectors.VectorDef.In',axiom,
    ! [Vvar__0__A__32643,Vvar__1__a__32644,Vvar__2__n__32645,Vvar__3___24Anonymous__32646] :
      ( cType___24t(Vvar__0__A__32643)
     => ( t(Vvar__1__a__32644,Vvar__0__A__32643)
       => ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__2__n__32645)
         => ( cCoq_2eVectors_2eVectorDef_2et___24t(Vvar__0__A__32643,Vvar__2__n__32645,Vvar__3___24Anonymous__32646)
           => ( cCoq_2eVectors_2eVectorDef_2eIn___24a4(Vvar__0__A__32643,Vvar__1__a__32644,Vvar__2__n__32645,Vvar__3___24Anonymous__32646)
             => ( ? [Vvar__2__m__32650] :
                    ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__2__m__32650)
                    & ? [Vvar__3__v__32651] :
                        ( cCoq_2eVectors_2eVectorDef_2et___24t(Vvar__0__A__32643,Vvar__2__m__32650,Vvar__3__v__32651)
                        & Vvar__3___24Anonymous__32646 = cCoq_2eVectors_2eVectorDef_2econs___24a4(Vvar__0__A__32643,Vvar__1__a__32644,Vvar__2__m__32650,Vvar__3__v__32651)
                        & Vvar__2__n__32645 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__2__m__32650) ) )
                | ? [Vvar__2__m__32654] :
                    ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__2__m__32654)
                    & ? [Vvar__3__x__32655] :
                        ( t(Vvar__3__x__32655,Vvar__0__A__32643)
                        & ? [Vvar__4__v__32656] :
                            ( cCoq_2eVectors_2eVectorDef_2et___24t(Vvar__0__A__32643,Vvar__2__m__32654,Vvar__4__v__32656)
                            & cCoq_2eVectors_2eVectorDef_2eIn___24a4(Vvar__0__A__32643,Vvar__1__a__32644,Vvar__2__m__32654,Vvar__4__v__32656)
                            & Vvar__3___24Anonymous__32646 = cCoq_2eVectors_2eVectorDef_2econs___24a4(Vvar__0__A__32643,Vvar__3__x__32655,Vvar__2__m__32654,Vvar__4__v__32656)
                            & Vvar__2__n__32645 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__2__m__32654) ) ) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.Vectors.VectorDef.t',axiom,
    ! [Vvar__0__A__23985,Vvar__1___24Anonymous__23986,VX23987] :
      ( cType___24t(Vvar__0__A__23985)
     => ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__1___24Anonymous__23986)
       => ( cCoq_2eVectors_2eVectorDef_2et___24t(Vvar__0__A__23985,Vvar__1___24Anonymous__23986,VX23987)
         => ( ( Vvar__1___24Anonymous__23986 = cCoq_2eInit_2eDatatypes_2eO
              & VX23987 = cCoq_2eVectors_2eVectorDef_2enil___24a1(Vvar__0__A__23985) )
            | ? [Vvar__1__h__23990] :
                ( t(Vvar__1__h__23990,Vvar__0__A__23985)
                & ? [Vvar__2__n__23991] :
                    ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__2__n__23991)
                    & ? [Vvar__3___24Anonymous__23992] :
                        ( cCoq_2eVectors_2eVectorDef_2et___24t(Vvar__0__A__23985,Vvar__2__n__23991,Vvar__3___24Anonymous__23992)
                        & Vvar__1___24Anonymous__23986 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__2__n__23991)
                        & VX23987 = cCoq_2eVectors_2eVectorDef_2econs___24a4(Vvar__0__A__23985,Vvar__1__h__23990,Vvar__2__n__23991,Vvar__3___24Anonymous__23992) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.ZArith.Znumtheory.Bezout',axiom,
    ! [Vvar__0__a__29469,Vvar__1__b__29470,Vvar__2__d__29471] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__0__a__29469)
     => ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__1__b__29470)
       => ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__2__d__29471)
         => ( cCoq_2eZArith_2eZnumtheory_2eBezout___24a3(Vvar__0__a__29469,Vvar__1__b__29470,Vvar__2__d__29471)
           => ? [Vvar__3__u__29476] :
                ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__3__u__29476)
                & ? [Vvar__4__v__29477] :
                    ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__4__v__29477)
                    & cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(Vvar__3__u__29476,Vvar__0__a__29469),cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(Vvar__4__v__29477,Vvar__1__b__29470)) = Vvar__2__d__29471
                    & p(c_24True) ) ) ) ) ) ) ).

fof('$_inversion_Coq.ZArith.Znumtheory.Euclid',axiom,
    ! [Vvar__0__a__29444,Vvar__1__b__29445,VX29446] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__0__a__29444)
     => ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__1__b__29445)
       => ( cCoq_2eZArith_2eZnumtheory_2eEuclid___24t(Vvar__0__a__29444,Vvar__1__b__29445,VX29446)
         => ? [Vvar__2__u__29449] :
              ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__2__u__29449)
              & ? [Vvar__3__v__29450] :
                  ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__3__v__29450)
                  & ? [Vvar__4__d__29451] :
                      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__4__d__29451)
                      & cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(Vvar__2__u__29449,Vvar__0__a__29444),cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(Vvar__3__v__29450,Vvar__1__b__29445)) = Vvar__4__d__29451
                      & cCoq_2eZArith_2eZnumtheory_2eZis__gcd___24a3(Vvar__0__a__29444,Vvar__1__b__29445,Vvar__4__d__29451)
                      & VX29446 = cCoq_2eZArith_2eZnumtheory_2eEuclid__intro___24a5(Vvar__0__a__29444,Vvar__1__b__29445,Vvar__2__u__29449,Vvar__3__v__29450,Vvar__4__d__29451) ) ) ) ) ) ) ).

fof('$_inversion_Coq.ZArith.Znumtheory.Zis_gcd',axiom,
    ! [Vvar__0__a__10757,Vvar__1__b__10758,Vvar__2__g__10759] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__0__a__10757)
     => ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__1__b__10758)
       => ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__2__g__10759)
         => ( cCoq_2eZArith_2eZnumtheory_2eZis__gcd___24a3(Vvar__0__a__10757,Vvar__1__b__10758,Vvar__2__g__10759)
           => ( cCoq_2eZArith_2eBinInt_2eZ_2edivide___24a2(Vvar__2__g__10759,Vvar__0__a__10757)
              & cCoq_2eZArith_2eBinInt_2eZ_2edivide___24a2(Vvar__2__g__10759,Vvar__1__b__10758)
              & ! [Vvar__var__var__var__var__5__x__10767__10770__10773__10776__10779] :
                  ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__var__var__var__var__5__x__10767__10770__10773__10776__10779)
                 => ( cCoq_2eZArith_2eBinInt_2eZ_2edivide___24a2(Vvar__var__var__var__var__5__x__10767__10770__10773__10776__10779,Vvar__0__a__10757)
                   => ( cCoq_2eZArith_2eBinInt_2eZ_2edivide___24a2(Vvar__var__var__var__var__5__x__10767__10770__10773__10776__10779,Vvar__1__b__10758)
                     => cCoq_2eZArith_2eBinInt_2eZ_2edivide___24a2(Vvar__var__var__var__var__5__x__10767__10770__10773__10776__10779,Vvar__2__g__10759) ) ) )
              & p(c_24True) ) ) ) ) ) ).

fof('$_inversion_Coq.ZArith.Znumtheory.prime',axiom,
    ! [Vvar__0__p__10789] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__0__p__10789)
     => ( cCoq_2eZArith_2eZnumtheory_2eprime___24a1(Vvar__0__p__10789)
       => ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH),Vvar__0__p__10789))
          & ! [Vvar__var__var__2__n__10794__10796__10798] :
              ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__var__var__2__n__10794__10796__10798)
             => ( ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH),Vvar__var__var__2__n__10794__10796__10798))
                  & p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(Vvar__var__var__2__n__10794__10796__10798,Vvar__0__p__10789)) )
               => cCoq_2eZArith_2eZnumtheory_2erel__prime___24a2(Vvar__var__var__2__n__10794__10796__10798,Vvar__0__p__10789) ) )
          & p(c_24True) ) ) ) ).

fof('$_inversion_Coq.ZArith.Zpower.Zdiv_rest_proofs',axiom,
    ! [Vvar__0__x__29479,Vvar__1__p__29480,VX29481] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__0__x__29479)
     => ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1__p__29480)
       => ( cCoq_2eZArith_2eZpower_2eZdiv__rest__proofs___24t(Vvar__0__x__29479,Vvar__1__p__29480,VX29481)
         => ? [Vvar__2__q__29484] :
              ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__2__q__29484)
              & ? [Vvar__3__r__29485] :
                  ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__3__r__29485)
                  & Vvar__0__x__29479 = cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(Vvar__2__q__29484,cCoq_2eZArith_2eZpower_2etwo__power__pos___24a1(Vvar__1__p__29480)),Vvar__3__r__29485)
                  & p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,Vvar__3__r__29485))
                  & p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(Vvar__3__r__29485,cCoq_2eZArith_2eZpower_2etwo__power__pos___24a1(Vvar__1__p__29480)))
                  & VX29481 = cCoq_2eZArith_2eZpower_2eZdiv__rest__proof___24a4(Vvar__0__x__29479,Vvar__1__p__29480,Vvar__2__q__29484,Vvar__3__r__29485) ) ) ) ) ) ).

fof('$_inversion_Coq.micromega.DeclConstant.DeclaredConstant',axiom,
    ! [Vvar__0__T__12278,Vvar__1__F__12279] :
      ( cType___24t(Vvar__0__T__12278)
     => ( t(Vvar__1__F__12279,Vvar__0__T__12278)
       => ( cCoq_2emicromega_2eDeclConstant_2eDeclaredConstant___24a2(Vvar__0__T__12278,Vvar__1__F__12279)
         => p(c_24True) ) ) ) ).

fof('$_inversion_Coq.micromega.DeclConstant.GT',axiom,
    ! [Vvar__0__T__26139,Vvar__1__F__26140] :
      ( cType___24t(Vvar__0__T__26139)
     => ( t(Vvar__1__F__26140,Vvar__0__T__26139)
       => ( cCoq_2emicromega_2eDeclConstant_2eGT___24a2(Vvar__0__T__26139,Vvar__1__F__26140)
         => p(c_24True) ) ) ) ).

fof('$_inversion_Coq.micromega.EnvRing.Mon',axiom,
    ! [VX26147] :
      ( cCoq_2emicromega_2eEnvRing_2eMon___24t(VX26147)
     => ( VX26147 = cCoq_2emicromega_2eEnvRing_2emon0
        | ? [Vvar__0___24Anonymous__26148] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__26148)
            & ? [Vvar__1___24Anonymous__26149] :
                ( cCoq_2emicromega_2eEnvRing_2eMon___24t(Vvar__1___24Anonymous__26149)
                & VX26147 = cCoq_2emicromega_2eEnvRing_2ezmon___24a2(Vvar__0___24Anonymous__26148,Vvar__1___24Anonymous__26149) ) )
        | ? [Vvar__0___24Anonymous__26150] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__26150)
            & ? [Vvar__1___24Anonymous__26151] :
                ( cCoq_2emicromega_2eEnvRing_2eMon___24t(Vvar__1___24Anonymous__26151)
                & VX26147 = cCoq_2emicromega_2eEnvRing_2evmon___24a2(Vvar__0___24Anonymous__26150,Vvar__1___24Anonymous__26151) ) ) ) ) ).

fof('$_inversion_Coq.micromega.EnvRing.PExpr',axiom,
    ! [Vvar__0__C__25322,VX25323] :
      ( cType___24t(Vvar__0__C__25322)
     => ( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__C__25322,VX25323)
       => ( ? [Vvar__1___24Anonymous__25325] :
              ( t(Vvar__1___24Anonymous__25325,Vvar__0__C__25322)
              & VX25323 = cCoq_2emicromega_2eEnvRing_2ePEc___24a2(Vvar__0__C__25322,Vvar__1___24Anonymous__25325) )
          | ? [Vvar__1___24Anonymous__25327] :
              ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__25327)
              & VX25323 = cCoq_2emicromega_2eEnvRing_2ePEX___24a2(Vvar__0__C__25322,Vvar__1___24Anonymous__25327) )
          | ? [Vvar__1___24Anonymous__25329] :
              ( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__C__25322,Vvar__1___24Anonymous__25329)
              & ? [Vvar__2___24Anonymous__25330] :
                  ( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__C__25322,Vvar__2___24Anonymous__25330)
                  & VX25323 = cCoq_2emicromega_2eEnvRing_2ePEadd___24a3(Vvar__0__C__25322,Vvar__1___24Anonymous__25329,Vvar__2___24Anonymous__25330) ) )
          | ? [Vvar__1___24Anonymous__25332] :
              ( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__C__25322,Vvar__1___24Anonymous__25332)
              & ? [Vvar__2___24Anonymous__25333] :
                  ( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__C__25322,Vvar__2___24Anonymous__25333)
                  & VX25323 = cCoq_2emicromega_2eEnvRing_2ePEsub___24a3(Vvar__0__C__25322,Vvar__1___24Anonymous__25332,Vvar__2___24Anonymous__25333) ) )
          | ? [Vvar__1___24Anonymous__25335] :
              ( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__C__25322,Vvar__1___24Anonymous__25335)
              & ? [Vvar__2___24Anonymous__25336] :
                  ( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__C__25322,Vvar__2___24Anonymous__25336)
                  & VX25323 = cCoq_2emicromega_2eEnvRing_2ePEmul___24a3(Vvar__0__C__25322,Vvar__1___24Anonymous__25335,Vvar__2___24Anonymous__25336) ) )
          | ? [Vvar__1___24Anonymous__25338] :
              ( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__C__25322,Vvar__1___24Anonymous__25338)
              & VX25323 = cCoq_2emicromega_2eEnvRing_2ePEopp___24a2(Vvar__0__C__25322,Vvar__1___24Anonymous__25338) )
          | ? [Vvar__1___24Anonymous__25340] :
              ( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__C__25322,Vvar__1___24Anonymous__25340)
              & ? [Vvar__2___24Anonymous__25341] :
                  ( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__2___24Anonymous__25341)
                  & VX25323 = cCoq_2emicromega_2eEnvRing_2ePEpow___24a3(Vvar__0__C__25322,Vvar__1___24Anonymous__25340,Vvar__2___24Anonymous__25341) ) ) ) ) ) ).

fof('$_inversion_Coq.micromega.EnvRing.Pol',axiom,
    ! [Vvar__0__C__12283,VX12284] :
      ( cType___24t(Vvar__0__C__12283)
     => ( cCoq_2emicromega_2eEnvRing_2ePol___24t(Vvar__0__C__12283,VX12284)
       => ( ? [Vvar__1___24Anonymous__12286] :
              ( t(Vvar__1___24Anonymous__12286,Vvar__0__C__12283)
              & VX12284 = cCoq_2emicromega_2eEnvRing_2ePc___24a2(Vvar__0__C__12283,Vvar__1___24Anonymous__12286) )
          | ? [Vvar__1___24Anonymous__12288] :
              ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__12288)
              & ? [Vvar__2___24Anonymous__12289] :
                  ( cCoq_2emicromega_2eEnvRing_2ePol___24t(Vvar__0__C__12283,Vvar__2___24Anonymous__12289)
                  & VX12284 = cCoq_2emicromega_2eEnvRing_2ePinj___24a3(Vvar__0__C__12283,Vvar__1___24Anonymous__12288,Vvar__2___24Anonymous__12289) ) )
          | ? [Vvar__1___24Anonymous__12291] :
              ( cCoq_2emicromega_2eEnvRing_2ePol___24t(Vvar__0__C__12283,Vvar__1___24Anonymous__12291)
              & ? [Vvar__2___24Anonymous__12292] :
                  ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2___24Anonymous__12292)
                  & ? [Vvar__3___24Anonymous__12293] :
                      ( cCoq_2emicromega_2eEnvRing_2ePol___24t(Vvar__0__C__12283,Vvar__3___24Anonymous__12293)
                      & VX12284 = cCoq_2emicromega_2eEnvRing_2ePX___24a4(Vvar__0__C__12283,Vvar__1___24Anonymous__12291,Vvar__2___24Anonymous__12292,Vvar__3___24Anonymous__12293) ) ) ) ) ) ) ).

fof('$_inversion_Coq.micromega.OrderedRing.SOR',axiom,
    ! [Vvar__0__R__15038,Vvar__1__rO__15039,Vvar__2__rI__15040,Vvar__3__rplus__15041,Vvar__4__rtimes__15046,Vvar__5__rminus__15051,Vvar__6__ropp__15056,Vvar__7__req__15059,Vvar__8__rle__15064,Vvar__9__rlt__15069] :
      ( cType___24t(Vvar__0__R__15038)
     => ( t(Vvar__1__rO__15039,Vvar__0__R__15038)
       => ( t(Vvar__2__rI__15040,Vvar__0__R__15038)
         => ( c_24__type__15470___24t(Vvar__0__R__15038,Vvar__1__rO__15039,Vvar__2__rI__15040,Vvar__3__rplus__15041,Vvar__4__rtimes__15046,Vvar__5__rminus__15051,Vvar__6__ropp__15056,Vvar__7__req__15059,Vvar__8__rle__15064,Vvar__9__rlt__15069,Vvar__3__rplus__15041)
           => ( c_24__type__15571___24t(Vvar__0__R__15038,Vvar__1__rO__15039,Vvar__2__rI__15040,Vvar__3__rplus__15041,Vvar__4__rtimes__15046,Vvar__5__rminus__15051,Vvar__6__ropp__15056,Vvar__7__req__15059,Vvar__8__rle__15064,Vvar__9__rlt__15069,Vvar__4__rtimes__15046)
             => ( c_24__type__15672___24t(Vvar__0__R__15038,Vvar__1__rO__15039,Vvar__2__rI__15040,Vvar__3__rplus__15041,Vvar__4__rtimes__15046,Vvar__5__rminus__15051,Vvar__6__ropp__15056,Vvar__7__req__15059,Vvar__8__rle__15064,Vvar__9__rlt__15069,Vvar__5__rminus__15051)
               => ( c_24__type__15762___24t(Vvar__0__R__15038,Vvar__1__rO__15039,Vvar__2__rI__15040,Vvar__3__rplus__15041,Vvar__4__rtimes__15046,Vvar__5__rminus__15051,Vvar__6__ropp__15056,Vvar__7__req__15059,Vvar__8__rle__15064,Vvar__9__rlt__15069,Vvar__6__ropp__15056)
                 => ( c_24__type__15863___24t(Vvar__0__R__15038,Vvar__1__rO__15039,Vvar__2__rI__15040,Vvar__3__rplus__15041,Vvar__4__rtimes__15046,Vvar__5__rminus__15051,Vvar__6__ropp__15056,Vvar__7__req__15059,Vvar__8__rle__15064,Vvar__9__rlt__15069,Vvar__7__req__15059)
                   => ( c_24__type__15964___24t(Vvar__0__R__15038,Vvar__1__rO__15039,Vvar__2__rI__15040,Vvar__3__rplus__15041,Vvar__4__rtimes__15046,Vvar__5__rminus__15051,Vvar__6__ropp__15056,Vvar__7__req__15059,Vvar__8__rle__15064,Vvar__9__rlt__15069,Vvar__8__rle__15064)
                     => ( c_24__type__16065___24t(Vvar__0__R__15038,Vvar__1__rO__15039,Vvar__2__rI__15040,Vvar__3__rplus__15041,Vvar__4__rtimes__15046,Vvar__5__rminus__15051,Vvar__6__ropp__15056,Vvar__7__req__15059,Vvar__8__rle__15064,Vvar__9__rlt__15069,Vvar__9__rlt__15069)
                       => ( cCoq_2emicromega_2eOrderedRing_2eSOR___24a10(Vvar__0__R__15038,Vvar__1__rO__15039,Vvar__2__rI__15040,Vvar__3__rplus__15041,Vvar__4__rtimes__15046,Vvar__5__rminus__15051,Vvar__6__ropp__15056,Vvar__7__req__15059,Vvar__8__rle__15064,Vvar__9__rlt__15069)
                         => ( cCoq_2eSetoids_2eSetoid_2eSetoid__Theory___24a2(Vvar__0__R__15038,Vvar__7__req__15059)
                            & ! [Vvar__var__var__var__var__11__x1__15113__15119__15224__15230__15236] :
                                ( t(Vvar__var__var__var__var__11__x1__15113__15119__15224__15230__15236,Vvar__0__R__15038)
                               => ! [Vvar__var__var__var__var__12__x2__15114__15120__15225__15231__15237] :
                                    ( t(Vvar__var__var__var__var__12__x2__15114__15120__15225__15231__15237,Vvar__0__R__15038)
                                   => ( p(happ(happ(Vvar__7__req__15059,Vvar__var__var__var__var__11__x1__15113__15119__15224__15230__15236),Vvar__var__var__var__var__12__x2__15114__15120__15225__15231__15237))
                                     => ! [Vvar__var__var__var__var__14__y1__15115__15121__15226__15232__15238] :
                                          ( t(Vvar__var__var__var__var__14__y1__15115__15121__15226__15232__15238,Vvar__0__R__15038)
                                         => ! [Vvar__var__var__var__var__15__y2__15116__15122__15227__15233__15239] :
                                              ( t(Vvar__var__var__var__var__15__y2__15116__15122__15227__15233__15239,Vvar__0__R__15038)
                                             => ( p(happ(happ(Vvar__7__req__15059,Vvar__var__var__var__var__14__y1__15115__15121__15226__15232__15238),Vvar__var__var__var__var__15__y2__15116__15122__15227__15233__15239))
                                               => p(happ(happ(Vvar__7__req__15059,happ(happ(Vvar__3__rplus__15041,Vvar__var__var__var__var__11__x1__15113__15119__15224__15230__15236),Vvar__var__var__var__var__14__y1__15115__15121__15226__15232__15238)),happ(happ(Vvar__3__rplus__15041,Vvar__var__var__var__var__12__x2__15114__15120__15225__15231__15237),Vvar__var__var__var__var__15__y2__15116__15122__15227__15233__15239))) ) ) ) ) ) )
                            & ! [Vvar__var__var__var__var__12__x1__15126__15132__15242__15248__15254] :
                                ( t(Vvar__var__var__var__var__12__x1__15126__15132__15242__15248__15254,Vvar__0__R__15038)
                               => ! [Vvar__var__var__var__var__13__x2__15127__15133__15243__15249__15255] :
                                    ( t(Vvar__var__var__var__var__13__x2__15127__15133__15243__15249__15255,Vvar__0__R__15038)
                                   => ( p(happ(happ(Vvar__7__req__15059,Vvar__var__var__var__var__12__x1__15126__15132__15242__15248__15254),Vvar__var__var__var__var__13__x2__15127__15133__15243__15249__15255))
                                     => ! [Vvar__var__var__var__var__15__y1__15128__15134__15244__15250__15256] :
                                          ( t(Vvar__var__var__var__var__15__y1__15128__15134__15244__15250__15256,Vvar__0__R__15038)
                                         => ! [Vvar__var__var__var__var__16__y2__15129__15135__15245__15251__15257] :
                                              ( t(Vvar__var__var__var__var__16__y2__15129__15135__15245__15251__15257,Vvar__0__R__15038)
                                             => ( p(happ(happ(Vvar__7__req__15059,Vvar__var__var__var__var__15__y1__15128__15134__15244__15250__15256),Vvar__var__var__var__var__16__y2__15129__15135__15245__15251__15257))
                                               => p(happ(happ(Vvar__7__req__15059,happ(happ(Vvar__4__rtimes__15046,Vvar__var__var__var__var__12__x1__15126__15132__15242__15248__15254),Vvar__var__var__var__var__15__y1__15128__15134__15244__15250__15256)),happ(happ(Vvar__4__rtimes__15046,Vvar__var__var__var__var__13__x2__15127__15133__15243__15249__15255),Vvar__var__var__var__var__16__y2__15129__15135__15245__15251__15257))) ) ) ) ) ) )
                            & ! [Vvar__var__var__var__var__13__x1__15139__15142__15260__15263__15266] :
                                ( t(Vvar__var__var__var__var__13__x1__15139__15142__15260__15263__15266,Vvar__0__R__15038)
                               => ! [Vvar__var__var__var__var__14__x2__15140__15143__15261__15264__15267] :
                                    ( t(Vvar__var__var__var__var__14__x2__15140__15143__15261__15264__15267,Vvar__0__R__15038)
                                   => ( p(happ(happ(Vvar__7__req__15059,Vvar__var__var__var__var__13__x1__15139__15142__15260__15263__15266),Vvar__var__var__var__var__14__x2__15140__15143__15261__15264__15267))
                                     => p(happ(happ(Vvar__7__req__15059,happ(Vvar__6__ropp__15056,Vvar__var__var__var__var__13__x1__15139__15142__15260__15263__15266)),happ(Vvar__6__ropp__15056,Vvar__var__var__var__var__14__x2__15140__15143__15261__15264__15267))) ) ) )
                            & ! [Vvar__var__var__var__var__14__x1__15146__15152__15269__15275__15281] :
                                ( t(Vvar__var__var__var__var__14__x1__15146__15152__15269__15275__15281,Vvar__0__R__15038)
                               => ! [Vvar__var__var__var__var__15__x2__15147__15153__15270__15276__15282] :
                                    ( t(Vvar__var__var__var__var__15__x2__15147__15153__15270__15276__15282,Vvar__0__R__15038)
                                   => ( p(happ(happ(Vvar__7__req__15059,Vvar__var__var__var__var__14__x1__15146__15152__15269__15275__15281),Vvar__var__var__var__var__15__x2__15147__15153__15270__15276__15282))
                                     => ! [Vvar__var__var__var__var__17__y1__15148__15154__15271__15277__15283] :
                                          ( t(Vvar__var__var__var__var__17__y1__15148__15154__15271__15277__15283,Vvar__0__R__15038)
                                         => ! [Vvar__var__var__var__var__18__y2__15149__15155__15272__15278__15284] :
                                              ( t(Vvar__var__var__var__var__18__y2__15149__15155__15272__15278__15284,Vvar__0__R__15038)
                                             => ( p(happ(happ(Vvar__7__req__15059,Vvar__var__var__var__var__17__y1__15148__15154__15271__15277__15283),Vvar__var__var__var__var__18__y2__15149__15155__15272__15278__15284))
                                               => ( p(happ(happ(Vvar__8__rle__15064,Vvar__var__var__var__var__14__x1__15146__15152__15269__15275__15281),Vvar__var__var__var__var__17__y1__15148__15154__15271__15277__15283))
                                                <=> p(happ(happ(Vvar__8__rle__15064,Vvar__var__var__var__var__15__x2__15147__15153__15270__15276__15282),Vvar__var__var__var__var__18__y2__15149__15155__15272__15278__15284)) ) ) ) ) ) ) )
                            & ! [Vvar__var__var__var__var__15__x1__15159__15165__15287__15293__15299] :
                                ( t(Vvar__var__var__var__var__15__x1__15159__15165__15287__15293__15299,Vvar__0__R__15038)
                               => ! [Vvar__var__var__var__var__16__x2__15160__15166__15288__15294__15300] :
                                    ( t(Vvar__var__var__var__var__16__x2__15160__15166__15288__15294__15300,Vvar__0__R__15038)
                                   => ( p(happ(happ(Vvar__7__req__15059,Vvar__var__var__var__var__15__x1__15159__15165__15287__15293__15299),Vvar__var__var__var__var__16__x2__15160__15166__15288__15294__15300))
                                     => ! [Vvar__var__var__var__var__18__y1__15161__15167__15289__15295__15301] :
                                          ( t(Vvar__var__var__var__var__18__y1__15161__15167__15289__15295__15301,Vvar__0__R__15038)
                                         => ! [Vvar__var__var__var__var__19__y2__15162__15168__15290__15296__15302] :
                                              ( t(Vvar__var__var__var__var__19__y2__15162__15168__15290__15296__15302,Vvar__0__R__15038)
                                             => ( p(happ(happ(Vvar__7__req__15059,Vvar__var__var__var__var__18__y1__15161__15167__15289__15295__15301),Vvar__var__var__var__var__19__y2__15162__15168__15290__15296__15302))
                                               => ( p(happ(happ(Vvar__9__rlt__15069,Vvar__var__var__var__var__15__x1__15159__15165__15287__15293__15299),Vvar__var__var__var__var__18__y1__15161__15167__15289__15295__15301))
                                                <=> p(happ(happ(Vvar__9__rlt__15069,Vvar__var__var__var__var__16__x2__15160__15166__15288__15294__15300),Vvar__var__var__var__var__19__y2__15162__15168__15290__15296__15302)) ) ) ) ) ) ) )
                            & cCoq_2esetoid__ring_2eRing__theory_2ering__theory___24a8(Vvar__0__R__15038,Vvar__1__rO__15039,Vvar__2__rI__15040,Vvar__3__rplus__15041,Vvar__4__rtimes__15046,Vvar__5__rminus__15051,Vvar__6__ropp__15056,Vvar__7__req__15059)
                            & ! [Vvar__var__var__var__17__n__15173__15174__15305__15306] :
                                ( t(Vvar__var__var__var__17__n__15173__15174__15305__15306,Vvar__0__R__15038)
                               => p(happ(happ(Vvar__8__rle__15064,Vvar__var__var__var__17__n__15173__15174__15305__15306),Vvar__var__var__var__17__n__15173__15174__15305__15306)) )
                            & ! [Vvar__var__var__var__var__18__n__15176__15180__15307__15311__15315] :
                                ( t(Vvar__var__var__var__var__18__n__15176__15180__15307__15311__15315,Vvar__0__R__15038)
                               => ! [Vvar__var__var__var__var__19__m__15177__15181__15308__15312__15316] :
                                    ( t(Vvar__var__var__var__var__19__m__15177__15181__15308__15312__15316,Vvar__0__R__15038)
                                   => ( p(happ(happ(Vvar__8__rle__15064,Vvar__var__var__var__var__18__n__15176__15180__15307__15311__15315),Vvar__var__var__var__var__19__m__15177__15181__15308__15312__15316))
                                     => ( p(happ(happ(Vvar__8__rle__15064,Vvar__var__var__var__var__19__m__15177__15181__15308__15312__15316),Vvar__var__var__var__var__18__n__15176__15180__15307__15311__15315))
                                       => p(happ(happ(Vvar__7__req__15059,Vvar__var__var__var__var__18__n__15176__15180__15307__15311__15315),Vvar__var__var__var__var__19__m__15177__15181__15308__15312__15316)) ) ) ) )
                            & ! [Vvar__var__var__var__19__n__15185__15190__15319__15324] :
                                ( t(Vvar__var__var__var__19__n__15185__15190__15319__15324,Vvar__0__R__15038)
                               => ! [Vvar__var__var__var__20__m__15186__15191__15320__15325] :
                                    ( t(Vvar__var__var__var__20__m__15186__15191__15320__15325,Vvar__0__R__15038)
                                   => ! [Vvar__var__var__var__21__p__15187__15192__15321__15326] :
                                        ( t(Vvar__var__var__var__21__p__15187__15192__15321__15326,Vvar__0__R__15038)
                                       => ( p(happ(happ(Vvar__8__rle__15064,Vvar__var__var__var__19__n__15185__15190__15319__15324),Vvar__var__var__var__20__m__15186__15191__15320__15325))
                                         => ( p(happ(happ(Vvar__8__rle__15064,Vvar__var__var__var__20__m__15186__15191__15320__15325),Vvar__var__var__var__21__p__15187__15192__15321__15326))
                                           => p(happ(happ(Vvar__8__rle__15064,Vvar__var__var__var__19__n__15185__15190__15319__15324),Vvar__var__var__var__21__p__15187__15192__15321__15326)) ) ) ) ) )
                            & ! [Vvar__var__var__var__var__var__20__n__15196__15198__15329__15331__15333__15335] :
                                ( t(Vvar__var__var__var__var__var__20__n__15196__15198__15329__15331__15333__15335,Vvar__0__R__15038)
                               => ! [Vvar__var__var__var__var__var__21__m__15197__15199__15330__15332__15334__15336] :
                                    ( t(Vvar__var__var__var__var__var__21__m__15197__15199__15330__15332__15334__15336,Vvar__0__R__15038)
                                   => ( p(happ(happ(Vvar__9__rlt__15069,Vvar__var__var__var__var__var__20__n__15196__15198__15329__15331__15333__15335),Vvar__var__var__var__var__var__21__m__15197__15199__15330__15332__15334__15336))
                                    <=> ( p(happ(happ(Vvar__8__rle__15064,Vvar__var__var__var__var__var__20__n__15196__15198__15329__15331__15333__15335),Vvar__var__var__var__var__var__21__m__15197__15199__15330__15332__15334__15336))
                                        & ~ p(happ(happ(Vvar__7__req__15059,Vvar__var__var__var__var__var__20__n__15196__15198__15329__15331__15333__15335),Vvar__var__var__var__var__var__21__m__15197__15199__15330__15332__15334__15336)) ) ) ) )
                            & ! [Vvar__var__var__var__var__21__n__15201__15203__15337__15339__15341] :
                                ( t(Vvar__var__var__var__var__21__n__15201__15203__15337__15339__15341,Vvar__0__R__15038)
                               => ! [Vvar__var__var__var__var__22__m__15202__15204__15338__15340__15342] :
                                    ( t(Vvar__var__var__var__var__22__m__15202__15204__15338__15340__15342,Vvar__0__R__15038)
                                   => ( p(happ(happ(Vvar__9__rlt__15069,Vvar__var__var__var__var__21__n__15201__15203__15337__15339__15341),Vvar__var__var__var__var__22__m__15202__15204__15338__15340__15342))
                                      | p(happ(happ(Vvar__7__req__15059,Vvar__var__var__var__var__21__n__15201__15203__15337__15339__15341),Vvar__var__var__var__var__22__m__15202__15204__15338__15340__15342))
                                      | p(happ(happ(Vvar__9__rlt__15069,Vvar__var__var__var__var__22__m__15202__15204__15338__15340__15342),Vvar__var__var__var__var__21__n__15201__15203__15337__15339__15341)) ) ) )
                            & ! [Vvar__var__var__var__var__22__n__15206__15210__15343__15347__15351] :
                                ( t(Vvar__var__var__var__var__22__n__15206__15210__15343__15347__15351,Vvar__0__R__15038)
                               => ! [Vvar__var__var__var__var__23__m__15207__15211__15344__15348__15352] :
                                    ( t(Vvar__var__var__var__var__23__m__15207__15211__15344__15348__15352,Vvar__0__R__15038)
                                   => ! [Vvar__var__var__var__var__24__p__15208__15212__15345__15349__15353] :
                                        ( t(Vvar__var__var__var__var__24__p__15208__15212__15345__15349__15353,Vvar__0__R__15038)
                                       => ( p(happ(happ(Vvar__8__rle__15064,Vvar__var__var__var__var__22__n__15206__15210__15343__15347__15351),Vvar__var__var__var__var__23__m__15207__15211__15344__15348__15352))
                                         => p(happ(happ(Vvar__8__rle__15064,happ(happ(Vvar__3__rplus__15041,Vvar__var__var__var__var__24__p__15208__15212__15345__15349__15353),Vvar__var__var__var__var__22__n__15206__15210__15343__15347__15351)),happ(happ(Vvar__3__rplus__15041,Vvar__var__var__var__var__24__p__15208__15212__15345__15349__15353),Vvar__var__var__var__var__23__m__15207__15211__15344__15348__15352))) ) ) ) )
                            & ! [Vvar__var__var__var__var__var__23__n__15215__15219__15355__15359__15363__15367] :
                                ( t(Vvar__var__var__var__var__var__23__n__15215__15219__15355__15359__15363__15367,Vvar__0__R__15038)
                               => ! [Vvar__var__var__var__var__var__24__m__15216__15220__15356__15360__15364__15368] :
                                    ( t(Vvar__var__var__var__var__var__24__m__15216__15220__15356__15360__15364__15368,Vvar__0__R__15038)
                                   => ( p(happ(happ(Vvar__9__rlt__15069,Vvar__1__rO__15039),Vvar__var__var__var__var__var__23__n__15215__15219__15355__15359__15363__15367))
                                     => ( p(happ(happ(Vvar__9__rlt__15069,Vvar__1__rO__15039),Vvar__var__var__var__var__var__24__m__15216__15220__15356__15360__15364__15368))
                                       => p(happ(happ(Vvar__9__rlt__15069,Vvar__1__rO__15039),happ(happ(Vvar__4__rtimes__15046,Vvar__var__var__var__var__var__23__n__15215__15219__15355__15359__15363__15367),Vvar__var__var__var__var__var__24__m__15216__15220__15356__15360__15364__15368))) ) ) ) )
                            & ~ p(happ(happ(Vvar__7__req__15059,Vvar__1__rO__15039),Vvar__2__rI__15040))
                            & p(c_24True) ) ) ) ) ) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.micromega.RMicromega.Rcst',axiom,
    ! [VX16541] :
      ( cCoq_2emicromega_2eRMicromega_2eRcst___24t(VX16541)
     => ( VX16541 = cCoq_2emicromega_2eRMicromega_2eC0
        | VX16541 = cCoq_2emicromega_2eRMicromega_2eC1
        | ? [Vvar__0__r__16542] :
            ( cCoq_2eQArith_2eQArith__base_2eQ___24t(Vvar__0__r__16542)
            & VX16541 = cCoq_2emicromega_2eRMicromega_2eCQ___24a1(Vvar__0__r__16542) )
        | ? [Vvar__0__r__16543] :
            ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__0__r__16543)
            & VX16541 = cCoq_2emicromega_2eRMicromega_2eCZ___24a1(Vvar__0__r__16543) )
        | ? [Vvar__0__r1__16544] :
            ( cCoq_2emicromega_2eRMicromega_2eRcst___24t(Vvar__0__r1__16544)
            & ? [Vvar__1__r2__16545] :
                ( cCoq_2emicromega_2eRMicromega_2eRcst___24t(Vvar__1__r2__16545)
                & VX16541 = cCoq_2emicromega_2eRMicromega_2eCPlus___24a2(Vvar__0__r1__16544,Vvar__1__r2__16545) ) )
        | ? [Vvar__0__r1__16546] :
            ( cCoq_2emicromega_2eRMicromega_2eRcst___24t(Vvar__0__r1__16546)
            & ? [Vvar__1__r2__16547] :
                ( cCoq_2emicromega_2eRMicromega_2eRcst___24t(Vvar__1__r2__16547)
                & VX16541 = cCoq_2emicromega_2eRMicromega_2eCMinus___24a2(Vvar__0__r1__16546,Vvar__1__r2__16547) ) )
        | ? [Vvar__0__r1__16548] :
            ( cCoq_2emicromega_2eRMicromega_2eRcst___24t(Vvar__0__r1__16548)
            & ? [Vvar__1__r2__16549] :
                ( cCoq_2emicromega_2eRMicromega_2eRcst___24t(Vvar__1__r2__16549)
                & VX16541 = cCoq_2emicromega_2eRMicromega_2eCMult___24a2(Vvar__0__r1__16548,Vvar__1__r2__16549) ) )
        | ? [Vvar__0__r1__16550] :
            ( cCoq_2emicromega_2eRMicromega_2eRcst___24t(Vvar__0__r1__16550)
            & ? [Vvar__1__z__16551] :
                ( cCoq_2eInit_2eDatatypes_2esum___24t(cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eInit_2eDatatypes_2enat,Vvar__1__z__16551)
                & VX16541 = cCoq_2emicromega_2eRMicromega_2eCPow___24a2(Vvar__0__r1__16550,Vvar__1__z__16551) ) )
        | ? [Vvar__0__r__16552] :
            ( cCoq_2emicromega_2eRMicromega_2eRcst___24t(Vvar__0__r__16552)
            & VX16541 = cCoq_2emicromega_2eRMicromega_2eCInv___24a1(Vvar__0__r__16552) )
        | ? [Vvar__0__r__16553] :
            ( cCoq_2emicromega_2eRMicromega_2eRcst___24t(Vvar__0__r__16553)
            & VX16541 = cCoq_2emicromega_2eRMicromega_2eCOpp___24a1(Vvar__0__r__16553) ) ) ) ).

fof('$_inversion_Coq.micromega.RingMicromega.Formula',axiom,
    ! [Vvar__0__T__22939,VX22940] :
      ( cType___24t(Vvar__0__T__22939)
     => ( cCoq_2emicromega_2eRingMicromega_2eFormula___24t(Vvar__0__T__22939,VX22940)
       => ? [Vvar__1__Flhs__22942] :
            ( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__T__22939,Vvar__1__Flhs__22942)
            & ? [Vvar__2__Fop__22943] :
                ( cCoq_2emicromega_2eRingMicromega_2eOp2___24t(Vvar__2__Fop__22943)
                & ? [Vvar__3__Frhs__22944] :
                    ( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__T__22939,Vvar__3__Frhs__22944)
                    & VX22940 = cCoq_2emicromega_2eRingMicromega_2eBuild__Formula___24a4(Vvar__0__T__22939,Vvar__1__Flhs__22942,Vvar__2__Fop__22943,Vvar__3__Frhs__22944) ) ) ) ) ) ).

fof('$_inversion_Coq.micromega.RingMicromega.Op1',axiom,
    ! [VX27074] :
      ( cCoq_2emicromega_2eRingMicromega_2eOp1___24t(VX27074)
     => ( VX27074 = cCoq_2emicromega_2eRingMicromega_2eEqual
        | VX27074 = cCoq_2emicromega_2eRingMicromega_2eNonEqual
        | VX27074 = cCoq_2emicromega_2eRingMicromega_2eStrict
        | VX27074 = cCoq_2emicromega_2eRingMicromega_2eNonStrict ) ) ).

fof('$_inversion_Coq.micromega.RingMicromega.Op2',axiom,
    ! [VX27075] :
      ( cCoq_2emicromega_2eRingMicromega_2eOp2___24t(VX27075)
     => ( VX27075 = cCoq_2emicromega_2eRingMicromega_2eOpEq
        | VX27075 = cCoq_2emicromega_2eRingMicromega_2eOpNEq
        | VX27075 = cCoq_2emicromega_2eRingMicromega_2eOpLe
        | VX27075 = cCoq_2emicromega_2eRingMicromega_2eOpGe
        | VX27075 = cCoq_2emicromega_2eRingMicromega_2eOpLt
        | VX27075 = cCoq_2emicromega_2eRingMicromega_2eOpGt ) ) ).

fof('$_inversion_Coq.micromega.RingMicromega.Psatz',axiom,
    ! [Vvar__0__C__22573,VX22574] :
      ( cType___24t(Vvar__0__C__22573)
     => ( cCoq_2emicromega_2eRingMicromega_2ePsatz___24t(Vvar__0__C__22573,VX22574)
       => ( ? [Vvar__1___24Anonymous__22576] :
              ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__1___24Anonymous__22576)
              & VX22574 = cCoq_2emicromega_2eRingMicromega_2ePsatzIn___24a2(Vvar__0__C__22573,Vvar__1___24Anonymous__22576) )
          | ? [Vvar__1___24Anonymous__22578] :
              ( cCoq_2emicromega_2eRingMicromega_2ePolC___24t(Vvar__0__C__22573,Vvar__1___24Anonymous__22578)
              & VX22574 = cCoq_2emicromega_2eRingMicromega_2ePsatzSquare___24a2(Vvar__0__C__22573,Vvar__1___24Anonymous__22578) )
          | ? [Vvar__1___24Anonymous__22580] :
              ( cCoq_2emicromega_2eRingMicromega_2ePolC___24t(Vvar__0__C__22573,Vvar__1___24Anonymous__22580)
              & ? [Vvar__2___24Anonymous__22581] :
                  ( cCoq_2emicromega_2eRingMicromega_2ePsatz___24t(Vvar__0__C__22573,Vvar__2___24Anonymous__22581)
                  & VX22574 = cCoq_2emicromega_2eRingMicromega_2ePsatzMulC___24a3(Vvar__0__C__22573,Vvar__1___24Anonymous__22580,Vvar__2___24Anonymous__22581) ) )
          | ? [Vvar__1___24Anonymous__22583] :
              ( cCoq_2emicromega_2eRingMicromega_2ePsatz___24t(Vvar__0__C__22573,Vvar__1___24Anonymous__22583)
              & ? [Vvar__2___24Anonymous__22584] :
                  ( cCoq_2emicromega_2eRingMicromega_2ePsatz___24t(Vvar__0__C__22573,Vvar__2___24Anonymous__22584)
                  & VX22574 = cCoq_2emicromega_2eRingMicromega_2ePsatzMulE___24a3(Vvar__0__C__22573,Vvar__1___24Anonymous__22583,Vvar__2___24Anonymous__22584) ) )
          | ? [Vvar__1___24Anonymous__22586] :
              ( cCoq_2emicromega_2eRingMicromega_2ePsatz___24t(Vvar__0__C__22573,Vvar__1___24Anonymous__22586)
              & ? [Vvar__2___24Anonymous__22587] :
                  ( cCoq_2emicromega_2eRingMicromega_2ePsatz___24t(Vvar__0__C__22573,Vvar__2___24Anonymous__22587)
                  & VX22574 = cCoq_2emicromega_2eRingMicromega_2ePsatzAdd___24a3(Vvar__0__C__22573,Vvar__1___24Anonymous__22586,Vvar__2___24Anonymous__22587) ) )
          | ? [Vvar__1___24Anonymous__22589] :
              ( t(Vvar__1___24Anonymous__22589,Vvar__0__C__22573)
              & VX22574 = cCoq_2emicromega_2eRingMicromega_2ePsatzC___24a2(Vvar__0__C__22573,Vvar__1___24Anonymous__22589) )
          | VX22574 = cCoq_2emicromega_2eRingMicromega_2ePsatzZ___24a1(Vvar__0__C__22573) ) ) ) ).

fof('$_inversion_Coq.micromega.RingMicromega.SORaddon',axiom,
    ! [Vvar__0__R__17143,Vvar__1__rO__17144,Vvar__2__rI__17145,Vvar__3__rplus__17146,Vvar__4__rtimes__17151,Vvar__5__rminus__17156,Vvar__6__ropp__17161,Vvar__7__req__17164,Vvar__8__rle__17169,Vvar__9__C__17174,Vvar__10__cO__17175,Vvar__11__cI__17176,Vvar__12__cplus__17177,Vvar__13__ctimes__17182,Vvar__14__cminus__17187,Vvar__15__copp__17192,Vvar__16__ceqb__17195,Vvar__17__cleb__17200,Vvar__18__phi__17205,Vvar__19__E__17208,Vvar__20__pow__phi__17209,Vvar__21__rpow__17212] :
      ( cType___24t(Vvar__0__R__17143)
     => ( t(Vvar__1__rO__17144,Vvar__0__R__17143)
       => ( t(Vvar__2__rI__17145,Vvar__0__R__17143)
         => ( c_24__type__17676___24t(Vvar__0__R__17143,Vvar__1__rO__17144,Vvar__2__rI__17145,Vvar__3__rplus__17146,Vvar__4__rtimes__17151,Vvar__5__rminus__17156,Vvar__6__ropp__17161,Vvar__7__req__17164,Vvar__8__rle__17169,Vvar__9__C__17174,Vvar__10__cO__17175,Vvar__11__cI__17176,Vvar__12__cplus__17177,Vvar__13__ctimes__17182,Vvar__14__cminus__17187,Vvar__15__copp__17192,Vvar__16__ceqb__17195,Vvar__17__cleb__17200,Vvar__18__phi__17205,Vvar__19__E__17208,Vvar__20__pow__phi__17209,Vvar__21__rpow__17212,Vvar__3__rplus__17146)
           => ( c_24__type__18022___24t(Vvar__0__R__17143,Vvar__1__rO__17144,Vvar__2__rI__17145,Vvar__3__rplus__17146,Vvar__4__rtimes__17151,Vvar__5__rminus__17156,Vvar__6__ropp__17161,Vvar__7__req__17164,Vvar__8__rle__17169,Vvar__9__C__17174,Vvar__10__cO__17175,Vvar__11__cI__17176,Vvar__12__cplus__17177,Vvar__13__ctimes__17182,Vvar__14__cminus__17187,Vvar__15__copp__17192,Vvar__16__ceqb__17195,Vvar__17__cleb__17200,Vvar__18__phi__17205,Vvar__19__E__17208,Vvar__20__pow__phi__17209,Vvar__21__rpow__17212,Vvar__4__rtimes__17151)
             => ( c_24__type__18368___24t(Vvar__0__R__17143,Vvar__1__rO__17144,Vvar__2__rI__17145,Vvar__3__rplus__17146,Vvar__4__rtimes__17151,Vvar__5__rminus__17156,Vvar__6__ropp__17161,Vvar__7__req__17164,Vvar__8__rle__17169,Vvar__9__C__17174,Vvar__10__cO__17175,Vvar__11__cI__17176,Vvar__12__cplus__17177,Vvar__13__ctimes__17182,Vvar__14__cminus__17187,Vvar__15__copp__17192,Vvar__16__ceqb__17195,Vvar__17__cleb__17200,Vvar__18__phi__17205,Vvar__19__E__17208,Vvar__20__pow__phi__17209,Vvar__21__rpow__17212,Vvar__5__rminus__17156)
               => ( c_24__type__18691___24t(Vvar__0__R__17143,Vvar__1__rO__17144,Vvar__2__rI__17145,Vvar__3__rplus__17146,Vvar__4__rtimes__17151,Vvar__5__rminus__17156,Vvar__6__ropp__17161,Vvar__7__req__17164,Vvar__8__rle__17169,Vvar__9__C__17174,Vvar__10__cO__17175,Vvar__11__cI__17176,Vvar__12__cplus__17177,Vvar__13__ctimes__17182,Vvar__14__cminus__17187,Vvar__15__copp__17192,Vvar__16__ceqb__17195,Vvar__17__cleb__17200,Vvar__18__phi__17205,Vvar__19__E__17208,Vvar__20__pow__phi__17209,Vvar__21__rpow__17212,Vvar__6__ropp__17161)
                 => ( c_24__type__19037___24t(Vvar__0__R__17143,Vvar__1__rO__17144,Vvar__2__rI__17145,Vvar__3__rplus__17146,Vvar__4__rtimes__17151,Vvar__5__rminus__17156,Vvar__6__ropp__17161,Vvar__7__req__17164,Vvar__8__rle__17169,Vvar__9__C__17174,Vvar__10__cO__17175,Vvar__11__cI__17176,Vvar__12__cplus__17177,Vvar__13__ctimes__17182,Vvar__14__cminus__17187,Vvar__15__copp__17192,Vvar__16__ceqb__17195,Vvar__17__cleb__17200,Vvar__18__phi__17205,Vvar__19__E__17208,Vvar__20__pow__phi__17209,Vvar__21__rpow__17212,Vvar__7__req__17164)
                   => ( c_24__type__19383___24t(Vvar__0__R__17143,Vvar__1__rO__17144,Vvar__2__rI__17145,Vvar__3__rplus__17146,Vvar__4__rtimes__17151,Vvar__5__rminus__17156,Vvar__6__ropp__17161,Vvar__7__req__17164,Vvar__8__rle__17169,Vvar__9__C__17174,Vvar__10__cO__17175,Vvar__11__cI__17176,Vvar__12__cplus__17177,Vvar__13__ctimes__17182,Vvar__14__cminus__17187,Vvar__15__copp__17192,Vvar__16__ceqb__17195,Vvar__17__cleb__17200,Vvar__18__phi__17205,Vvar__19__E__17208,Vvar__20__pow__phi__17209,Vvar__21__rpow__17212,Vvar__8__rle__17169)
                     => ( cType___24t(Vvar__9__C__17174)
                       => ( t(Vvar__10__cO__17175,Vvar__9__C__17174)
                         => ( t(Vvar__11__cI__17176,Vvar__9__C__17174)
                           => ( c_24__type__19729___24t(Vvar__0__R__17143,Vvar__1__rO__17144,Vvar__2__rI__17145,Vvar__3__rplus__17146,Vvar__4__rtimes__17151,Vvar__5__rminus__17156,Vvar__6__ropp__17161,Vvar__7__req__17164,Vvar__8__rle__17169,Vvar__9__C__17174,Vvar__10__cO__17175,Vvar__11__cI__17176,Vvar__12__cplus__17177,Vvar__13__ctimes__17182,Vvar__14__cminus__17187,Vvar__15__copp__17192,Vvar__16__ceqb__17195,Vvar__17__cleb__17200,Vvar__18__phi__17205,Vvar__19__E__17208,Vvar__20__pow__phi__17209,Vvar__21__rpow__17212,Vvar__12__cplus__17177)
                             => ( c_24__type__20075___24t(Vvar__0__R__17143,Vvar__1__rO__17144,Vvar__2__rI__17145,Vvar__3__rplus__17146,Vvar__4__rtimes__17151,Vvar__5__rminus__17156,Vvar__6__ropp__17161,Vvar__7__req__17164,Vvar__8__rle__17169,Vvar__9__C__17174,Vvar__10__cO__17175,Vvar__11__cI__17176,Vvar__12__cplus__17177,Vvar__13__ctimes__17182,Vvar__14__cminus__17187,Vvar__15__copp__17192,Vvar__16__ceqb__17195,Vvar__17__cleb__17200,Vvar__18__phi__17205,Vvar__19__E__17208,Vvar__20__pow__phi__17209,Vvar__21__rpow__17212,Vvar__13__ctimes__17182)
                               => ( c_24__type__20421___24t(Vvar__0__R__17143,Vvar__1__rO__17144,Vvar__2__rI__17145,Vvar__3__rplus__17146,Vvar__4__rtimes__17151,Vvar__5__rminus__17156,Vvar__6__ropp__17161,Vvar__7__req__17164,Vvar__8__rle__17169,Vvar__9__C__17174,Vvar__10__cO__17175,Vvar__11__cI__17176,Vvar__12__cplus__17177,Vvar__13__ctimes__17182,Vvar__14__cminus__17187,Vvar__15__copp__17192,Vvar__16__ceqb__17195,Vvar__17__cleb__17200,Vvar__18__phi__17205,Vvar__19__E__17208,Vvar__20__pow__phi__17209,Vvar__21__rpow__17212,Vvar__14__cminus__17187)
                                 => ( c_24__type__20744___24t(Vvar__0__R__17143,Vvar__1__rO__17144,Vvar__2__rI__17145,Vvar__3__rplus__17146,Vvar__4__rtimes__17151,Vvar__5__rminus__17156,Vvar__6__ropp__17161,Vvar__7__req__17164,Vvar__8__rle__17169,Vvar__9__C__17174,Vvar__10__cO__17175,Vvar__11__cI__17176,Vvar__12__cplus__17177,Vvar__13__ctimes__17182,Vvar__14__cminus__17187,Vvar__15__copp__17192,Vvar__16__ceqb__17195,Vvar__17__cleb__17200,Vvar__18__phi__17205,Vvar__19__E__17208,Vvar__20__pow__phi__17209,Vvar__21__rpow__17212,Vvar__15__copp__17192)
                                   => ( c_24__type__21090___24t(Vvar__0__R__17143,Vvar__1__rO__17144,Vvar__2__rI__17145,Vvar__3__rplus__17146,Vvar__4__rtimes__17151,Vvar__5__rminus__17156,Vvar__6__ropp__17161,Vvar__7__req__17164,Vvar__8__rle__17169,Vvar__9__C__17174,Vvar__10__cO__17175,Vvar__11__cI__17176,Vvar__12__cplus__17177,Vvar__13__ctimes__17182,Vvar__14__cminus__17187,Vvar__15__copp__17192,Vvar__16__ceqb__17195,Vvar__17__cleb__17200,Vvar__18__phi__17205,Vvar__19__E__17208,Vvar__20__pow__phi__17209,Vvar__21__rpow__17212,Vvar__16__ceqb__17195)
                                     => ( c_24__type__21436___24t(Vvar__0__R__17143,Vvar__1__rO__17144,Vvar__2__rI__17145,Vvar__3__rplus__17146,Vvar__4__rtimes__17151,Vvar__5__rminus__17156,Vvar__6__ropp__17161,Vvar__7__req__17164,Vvar__8__rle__17169,Vvar__9__C__17174,Vvar__10__cO__17175,Vvar__11__cI__17176,Vvar__12__cplus__17177,Vvar__13__ctimes__17182,Vvar__14__cminus__17187,Vvar__15__copp__17192,Vvar__16__ceqb__17195,Vvar__17__cleb__17200,Vvar__18__phi__17205,Vvar__19__E__17208,Vvar__20__pow__phi__17209,Vvar__21__rpow__17212,Vvar__17__cleb__17200)
                                       => ( c_24__type__21759___24t(Vvar__0__R__17143,Vvar__1__rO__17144,Vvar__2__rI__17145,Vvar__3__rplus__17146,Vvar__4__rtimes__17151,Vvar__5__rminus__17156,Vvar__6__ropp__17161,Vvar__7__req__17164,Vvar__8__rle__17169,Vvar__9__C__17174,Vvar__10__cO__17175,Vvar__11__cI__17176,Vvar__12__cplus__17177,Vvar__13__ctimes__17182,Vvar__14__cminus__17187,Vvar__15__copp__17192,Vvar__16__ceqb__17195,Vvar__17__cleb__17200,Vvar__18__phi__17205,Vvar__19__E__17208,Vvar__20__pow__phi__17209,Vvar__21__rpow__17212,Vvar__18__phi__17205)
                                         => ( cType___24t(Vvar__19__E__17208)
                                           => ( c_24__type__22082___24t(Vvar__0__R__17143,Vvar__1__rO__17144,Vvar__2__rI__17145,Vvar__3__rplus__17146,Vvar__4__rtimes__17151,Vvar__5__rminus__17156,Vvar__6__ropp__17161,Vvar__7__req__17164,Vvar__8__rle__17169,Vvar__9__C__17174,Vvar__10__cO__17175,Vvar__11__cI__17176,Vvar__12__cplus__17177,Vvar__13__ctimes__17182,Vvar__14__cminus__17187,Vvar__15__copp__17192,Vvar__16__ceqb__17195,Vvar__17__cleb__17200,Vvar__18__phi__17205,Vvar__19__E__17208,Vvar__20__pow__phi__17209,Vvar__21__rpow__17212,Vvar__20__pow__phi__17209)
                                             => ( c_24__type__22428___24t(Vvar__0__R__17143,Vvar__1__rO__17144,Vvar__2__rI__17145,Vvar__3__rplus__17146,Vvar__4__rtimes__17151,Vvar__5__rminus__17156,Vvar__6__ropp__17161,Vvar__7__req__17164,Vvar__8__rle__17169,Vvar__9__C__17174,Vvar__10__cO__17175,Vvar__11__cI__17176,Vvar__12__cplus__17177,Vvar__13__ctimes__17182,Vvar__14__cminus__17187,Vvar__15__copp__17192,Vvar__16__ceqb__17195,Vvar__17__cleb__17200,Vvar__18__phi__17205,Vvar__19__E__17208,Vvar__20__pow__phi__17209,Vvar__21__rpow__17212,Vvar__21__rpow__17212)
                                               => ( cCoq_2emicromega_2eRingMicromega_2eSORaddon___24a22(Vvar__0__R__17143,Vvar__1__rO__17144,Vvar__2__rI__17145,Vvar__3__rplus__17146,Vvar__4__rtimes__17151,Vvar__5__rminus__17156,Vvar__6__ropp__17161,Vvar__7__req__17164,Vvar__8__rle__17169,Vvar__9__C__17174,Vvar__10__cO__17175,Vvar__11__cI__17176,Vvar__12__cplus__17177,Vvar__13__ctimes__17182,Vvar__14__cminus__17187,Vvar__15__copp__17192,Vvar__16__ceqb__17195,Vvar__17__cleb__17200,Vvar__18__phi__17205,Vvar__19__E__17208,Vvar__20__pow__phi__17209,Vvar__21__rpow__17212)
                                                 => ( cCoq_2esetoid__ring_2eRing__theory_2ering__morph___24a17(Vvar__0__R__17143,Vvar__1__rO__17144,Vvar__2__rI__17145,Vvar__3__rplus__17146,Vvar__4__rtimes__17151,Vvar__5__rminus__17156,Vvar__6__ropp__17161,Vvar__7__req__17164,Vvar__9__C__17174,Vvar__10__cO__17175,Vvar__11__cI__17176,Vvar__12__cplus__17177,Vvar__13__ctimes__17182,Vvar__14__cminus__17187,Vvar__15__copp__17192,Vvar__16__ceqb__17195,Vvar__18__phi__17205)
                                                    & cCoq_2esetoid__ring_2eRing__theory_2epower__theory___24a7(Vvar__0__R__17143,Vvar__2__rI__17145,Vvar__4__rtimes__17151,Vvar__7__req__17164,Vvar__19__E__17208,Vvar__20__pow__phi__17209,Vvar__21__rpow__17212)
                                                    & ! [Vvar__var__var__var__var__var__24__x__17295__17298__17308__17311__17314__17317] :
                                                        ( t(Vvar__var__var__var__var__var__24__x__17295__17298__17308__17311__17314__17317,Vvar__9__C__17174)
                                                       => ! [Vvar__var__var__var__var__var__25__y__17296__17299__17309__17312__17315__17318] :
                                                            ( t(Vvar__var__var__var__var__var__25__y__17296__17299__17309__17312__17315__17318,Vvar__9__C__17174)
                                                           => ( happ(happ(Vvar__16__ceqb__17195,Vvar__var__var__var__var__var__24__x__17295__17298__17308__17311__17314__17317),Vvar__var__var__var__var__var__25__y__17296__17299__17309__17312__17315__17318) = cCoq_2eInit_2eDatatypes_2efalse
                                                             => ~ p(happ(happ(Vvar__7__req__17164,happ(Vvar__18__phi__17205,Vvar__var__var__var__var__var__24__x__17295__17298__17308__17311__17314__17317)),happ(Vvar__18__phi__17205,Vvar__var__var__var__var__var__25__y__17296__17299__17309__17312__17315__17318))) ) ) )
                                                    & ! [Vvar__var__var__var__var__var__25__x__17302__17305__17320__17323__17326__17329] :
                                                        ( t(Vvar__var__var__var__var__var__25__x__17302__17305__17320__17323__17326__17329,Vvar__9__C__17174)
                                                       => ! [Vvar__var__var__var__var__var__26__y__17303__17306__17321__17324__17327__17330] :
                                                            ( t(Vvar__var__var__var__var__var__26__y__17303__17306__17321__17324__17327__17330,Vvar__9__C__17174)
                                                           => ( happ(happ(Vvar__17__cleb__17200,Vvar__var__var__var__var__var__25__x__17302__17305__17320__17323__17326__17329),Vvar__var__var__var__var__var__26__y__17303__17306__17321__17324__17327__17330) = cCoq_2eInit_2eDatatypes_2etrue
                                                             => p(happ(happ(Vvar__8__rle__17169,happ(Vvar__18__phi__17205,Vvar__var__var__var__var__var__25__x__17302__17305__17320__17323__17326__17329)),happ(Vvar__18__phi__17205,Vvar__var__var__var__var__var__26__y__17303__17306__17321__17324__17327__17330))) ) ) )
                                                    & p(c_24True) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.micromega.Tauto.GFormula',axiom,
    ! [Vvar__0__TA__28904,Vvar__1__TX__28905,Vvar__2__AA__28906,Vvar__3__AF__28907,VX28908] :
      ( cType___24t(Vvar__0__TA__28904)
     => ( cType___24t(Vvar__1__TX__28905)
       => ( cType___24t(Vvar__2__AA__28906)
         => ( cType___24t(Vvar__3__AF__28907)
           => ( cCoq_2emicromega_2eTauto_2eGFormula___24t(Vvar__0__TA__28904,Vvar__1__TX__28905,Vvar__2__AA__28906,Vvar__3__AF__28907,VX28908)
             => ( VX28908 = cCoq_2emicromega_2eTauto_2eTT___24a4(Vvar__0__TA__28904,Vvar__1__TX__28905,Vvar__2__AA__28906,Vvar__3__AF__28907)
                | VX28908 = cCoq_2emicromega_2eTauto_2eFF___24a4(Vvar__0__TA__28904,Vvar__1__TX__28905,Vvar__2__AA__28906,Vvar__3__AF__28907)
                | ? [Vvar__4___24Anonymous__28921] :
                    ( t(Vvar__4___24Anonymous__28921,Vvar__1__TX__28905)
                    & VX28908 = cCoq_2emicromega_2eTauto_2eX___24a5(Vvar__0__TA__28904,Vvar__1__TX__28905,Vvar__2__AA__28906,Vvar__3__AF__28907,Vvar__4___24Anonymous__28921) )
                | ? [Vvar__4___24Anonymous__28926] :
                    ( t(Vvar__4___24Anonymous__28926,Vvar__0__TA__28904)
                    & ? [Vvar__5___24Anonymous__28927] :
                        ( t(Vvar__5___24Anonymous__28927,Vvar__2__AA__28906)
                        & VX28908 = cCoq_2emicromega_2eTauto_2eA___24a6(Vvar__0__TA__28904,Vvar__1__TX__28905,Vvar__2__AA__28906,Vvar__3__AF__28907,Vvar__4___24Anonymous__28926,Vvar__5___24Anonymous__28927) ) )
                | ? [Vvar__4___24Anonymous__28932] :
                    ( cCoq_2emicromega_2eTauto_2eGFormula___24t(Vvar__0__TA__28904,Vvar__1__TX__28905,Vvar__2__AA__28906,Vvar__3__AF__28907,Vvar__4___24Anonymous__28932)
                    & ? [Vvar__5___24Anonymous__28933] :
                        ( cCoq_2emicromega_2eTauto_2eGFormula___24t(Vvar__0__TA__28904,Vvar__1__TX__28905,Vvar__2__AA__28906,Vvar__3__AF__28907,Vvar__5___24Anonymous__28933)
                        & VX28908 = cCoq_2emicromega_2eTauto_2eCj___24a6(Vvar__0__TA__28904,Vvar__1__TX__28905,Vvar__2__AA__28906,Vvar__3__AF__28907,Vvar__4___24Anonymous__28932,Vvar__5___24Anonymous__28933) ) )
                | ? [Vvar__4___24Anonymous__28938] :
                    ( cCoq_2emicromega_2eTauto_2eGFormula___24t(Vvar__0__TA__28904,Vvar__1__TX__28905,Vvar__2__AA__28906,Vvar__3__AF__28907,Vvar__4___24Anonymous__28938)
                    & ? [Vvar__5___24Anonymous__28939] :
                        ( cCoq_2emicromega_2eTauto_2eGFormula___24t(Vvar__0__TA__28904,Vvar__1__TX__28905,Vvar__2__AA__28906,Vvar__3__AF__28907,Vvar__5___24Anonymous__28939)
                        & VX28908 = cCoq_2emicromega_2eTauto_2eD___24a6(Vvar__0__TA__28904,Vvar__1__TX__28905,Vvar__2__AA__28906,Vvar__3__AF__28907,Vvar__4___24Anonymous__28938,Vvar__5___24Anonymous__28939) ) )
                | ? [Vvar__4___24Anonymous__28944] :
                    ( cCoq_2emicromega_2eTauto_2eGFormula___24t(Vvar__0__TA__28904,Vvar__1__TX__28905,Vvar__2__AA__28906,Vvar__3__AF__28907,Vvar__4___24Anonymous__28944)
                    & VX28908 = cCoq_2emicromega_2eTauto_2eN___24a5(Vvar__0__TA__28904,Vvar__1__TX__28905,Vvar__2__AA__28906,Vvar__3__AF__28907,Vvar__4___24Anonymous__28944) )
                | ? [Vvar__4___24Anonymous__28949] :
                    ( cCoq_2emicromega_2eTauto_2eGFormula___24t(Vvar__0__TA__28904,Vvar__1__TX__28905,Vvar__2__AA__28906,Vvar__3__AF__28907,Vvar__4___24Anonymous__28949)
                    & ? [Vvar__5___24Anonymous__28950] :
                        ( cCoq_2eInit_2eDatatypes_2eoption___24t(Vvar__3__AF__28907,Vvar__5___24Anonymous__28950)
                        & ? [Vvar__6___24Anonymous__28951] :
                            ( cCoq_2emicromega_2eTauto_2eGFormula___24t(Vvar__0__TA__28904,Vvar__1__TX__28905,Vvar__2__AA__28906,Vvar__3__AF__28907,Vvar__6___24Anonymous__28951)
                            & VX28908 = cCoq_2emicromega_2eTauto_2eI___24a7(Vvar__0__TA__28904,Vvar__1__TX__28905,Vvar__2__AA__28906,Vvar__3__AF__28907,Vvar__4___24Anonymous__28949,Vvar__5___24Anonymous__28950,Vvar__6___24Anonymous__28951) ) ) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.micromega.VarMap.t',axiom,
    ! [Vvar__0__A__29347,VX29348] :
      ( cType___24t(Vvar__0__A__29347)
     => ( cCoq_2emicromega_2eVarMap_2et___24t(Vvar__0__A__29347,VX29348)
       => ( VX29348 = cCoq_2emicromega_2eVarMap_2eEmpty___24a1(Vvar__0__A__29347)
          | ? [Vvar__1___24Anonymous__29351] :
              ( t(Vvar__1___24Anonymous__29351,Vvar__0__A__29347)
              & VX29348 = cCoq_2emicromega_2eVarMap_2eElt___24a2(Vvar__0__A__29347,Vvar__1___24Anonymous__29351) )
          | ? [Vvar__1___24Anonymous__29353] :
              ( cCoq_2emicromega_2eVarMap_2et___24t(Vvar__0__A__29347,Vvar__1___24Anonymous__29353)
              & ? [Vvar__2___24Anonymous__29354] :
                  ( t(Vvar__2___24Anonymous__29354,Vvar__0__A__29347)
                  & ? [Vvar__3___24Anonymous__29355] :
                      ( cCoq_2emicromega_2eVarMap_2et___24t(Vvar__0__A__29347,Vvar__3___24Anonymous__29355)
                      & VX29348 = cCoq_2emicromega_2eVarMap_2eBranch___24a4(Vvar__0__A__29347,Vvar__1___24Anonymous__29353,Vvar__2___24Anonymous__29354,Vvar__3___24Anonymous__29355) ) ) ) ) ) ) ).

fof('$_inversion_Coq.micromega.ZMicromega.Vars.Facts.MP.Dec.FSetDecideAuxiliary.FSet_Prop',axiom,
    ! [Vvar__0___24Anonymous__29565] :
      ( cProp___24t(Vvar__0___24Anonymous__29565)
     => ( cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__Prop___24a1(Vvar__0___24Anonymous__29565)
       => ( ? [Vvar__0__P__29567] :
              ( cProp___24t(Vvar__0__P__29567)
              & cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__elt__Prop___24a1(Vvar__0__P__29567)
              & Vvar__0___24Anonymous__29565 = Vvar__0__P__29567 )
          | ? [Vvar__0__s__29569] :
              ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(Vvar__0__s__29569)
              & Vvar__0___24Anonymous__29565 = c_24__prop__29578___24a2(Vvar__0___24Anonymous__29565,Vvar__0__s__29569) )
          | ? [Vvar__0__s1__29571] :
              ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(Vvar__0__s1__29571)
              & ? [Vvar__1__s2__29572] :
                  ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(Vvar__1__s2__29572)
                  & Vvar__0___24Anonymous__29565 = c_24__prop__29579___24a3(Vvar__0___24Anonymous__29565,Vvar__0__s1__29571,Vvar__1__s2__29572) ) )
          | ? [Vvar__0__s1__29575] :
              ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(Vvar__0__s1__29575)
              & ? [Vvar__1__s2__29576] :
                  ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(Vvar__1__s2__29576)
                  & Vvar__0___24Anonymous__29565 = c_24__prop__29580___24a3(Vvar__0___24Anonymous__29565,Vvar__0__s1__29575,Vvar__1__s2__29576) ) ) ) ) ) ).

fof('$_inversion_Coq.micromega.ZMicromega.Vars.Facts.MP.Dec.FSetDecideAuxiliary.FSet_elt_Prop',axiom,
    ! [Vvar__0___24Anonymous__29534] :
      ( cProp___24t(Vvar__0___24Anonymous__29534)
     => ( cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__elt__Prop___24a1(Vvar__0___24Anonymous__29534)
       => ( ? [Vvar__0__S__29536] :
              ( cType___24t(Vvar__0__S__29536)
              & ? [Vvar__1__x__29537] :
                  ( t(Vvar__1__x__29537,Vvar__0__S__29536)
                  & ? [Vvar__2__y__29538] :
                      ( t(Vvar__2__y__29538,Vvar__0__S__29536)
                      & Vvar__0___24Anonymous__29534 = c_24__prop__29558___24a4(Vvar__0___24Anonymous__29534,Vvar__0__S__29536,Vvar__1__x__29537,Vvar__2__y__29538) ) ) )
          | ? [Vvar__0__x__29539] :
              ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0__x__29539)
              & ? [Vvar__1__y__29540] :
                  ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1__y__29540)
                  & Vvar__0___24Anonymous__29534 = c_24__prop__29559___24a3(Vvar__0___24Anonymous__29534,Vvar__0__x__29539,Vvar__1__y__29540) ) )
          | ? [Vvar__0__x__29541] :
              ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(Vvar__0__x__29541)
              & ? [Vvar__1__s__29542] :
                  ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(Vvar__1__s__29542)
                  & Vvar__0___24Anonymous__29534 = c_24__prop__29560___24a3(Vvar__0___24Anonymous__29534,Vvar__0__x__29541,Vvar__1__s__29542) ) )
          | Vvar__0___24Anonymous__29534 = c_24True
          | Vvar__0___24Anonymous__29534 = c_24False
          | ? [Vvar__0__P__29543] :
              ( cProp___24t(Vvar__0__P__29543)
              & ? [Vvar__1__Q__29544] :
                  ( cProp___24t(Vvar__1__Q__29544)
                  & cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__elt__Prop___24a1(Vvar__0__P__29543)
                  & cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__elt__Prop___24a1(Vvar__1__Q__29544)
                  & Vvar__0___24Anonymous__29534 = c_24__prop__29561___24a3(Vvar__0___24Anonymous__29534,Vvar__0__P__29543,Vvar__1__Q__29544) ) )
          | ? [Vvar__0__P__29547] :
              ( cProp___24t(Vvar__0__P__29547)
              & ? [Vvar__1__Q__29548] :
                  ( cProp___24t(Vvar__1__Q__29548)
                  & cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__elt__Prop___24a1(Vvar__0__P__29547)
                  & cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__elt__Prop___24a1(Vvar__1__Q__29548)
                  & Vvar__0___24Anonymous__29534 = c_24__prop__29562___24a3(Vvar__0___24Anonymous__29534,Vvar__0__P__29547,Vvar__1__Q__29548) ) )
          | ? [Vvar__0__P__29551] :
              ( cProp___24t(Vvar__0__P__29551)
              & ? [Vvar__1__Q__29552] :
                  ( cProp___24t(Vvar__1__Q__29552)
                  & cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__elt__Prop___24a1(Vvar__0__P__29551)
                  & cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__elt__Prop___24a1(Vvar__1__Q__29552)
                  & Vvar__0___24Anonymous__29534 = c_24__prop__29563___24a3(Vvar__0___24Anonymous__29534,Vvar__0__P__29551,Vvar__1__Q__29552) ) )
          | ? [Vvar__0__P__29556] :
              ( cProp___24t(Vvar__0__P__29556)
              & cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__elt__Prop___24a1(Vvar__0__P__29556)
              & Vvar__0___24Anonymous__29534 = c_24__prop__29564___24a2(Vvar__0___24Anonymous__29534,Vvar__0__P__29556) ) ) ) ) ).

fof('$_inversion_Coq.micromega.ZMicromega.ZArithProof',axiom,
    ! [VX29384] :
      ( cCoq_2emicromega_2eZMicromega_2eZArithProof___24t(VX29384)
     => ( VX29384 = cCoq_2emicromega_2eZMicromega_2eDoneProof
        | ? [Vvar__0___24Anonymous__29385] :
            ( cCoq_2emicromega_2eZMicromega_2eZWitness___24t(Vvar__0___24Anonymous__29385)
            & ? [Vvar__1___24Anonymous__29386] :
                ( cCoq_2emicromega_2eZMicromega_2eZArithProof___24t(Vvar__1___24Anonymous__29386)
                & VX29384 = cCoq_2emicromega_2eZMicromega_2eRatProof___24a2(Vvar__0___24Anonymous__29385,Vvar__1___24Anonymous__29386) ) )
        | ? [Vvar__0___24Anonymous__29387] :
            ( cCoq_2emicromega_2eZMicromega_2eZWitness___24t(Vvar__0___24Anonymous__29387)
            & ? [Vvar__1___24Anonymous__29388] :
                ( cCoq_2emicromega_2eZMicromega_2eZArithProof___24t(Vvar__1___24Anonymous__29388)
                & VX29384 = cCoq_2emicromega_2eZMicromega_2eCutProof___24a2(Vvar__0___24Anonymous__29387,Vvar__1___24Anonymous__29388) ) )
        | ? [Vvar__0___24Anonymous__29389] :
            ( cCoq_2emicromega_2eZMicromega_2eZWitness___24t(Vvar__0___24Anonymous__29389)
            & ? [Vvar__1___24Anonymous__29390] :
                ( cCoq_2emicromega_2eZMicromega_2eZWitness___24t(Vvar__1___24Anonymous__29390)
                & ? [Vvar__2___24Anonymous__29391] :
                    ( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2emicromega_2eZMicromega_2eZArithProof,Vvar__2___24Anonymous__29391)
                    & VX29384 = cCoq_2emicromega_2eZMicromega_2eEnumProof___24a3(Vvar__0___24Anonymous__29389,Vvar__1___24Anonymous__29390,Vvar__2___24Anonymous__29391) ) ) ) ) ) ).

fof('$_inversion_Coq.micromega.ZMicromega.Zdivide_pol',axiom,
    ! [Vvar__0__x__32882,Vvar__1___24Anonymous__32883] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__0__x__32882)
     => ( cCoq_2emicromega_2eRingMicromega_2ePolC___24t(cCoq_2eNumbers_2eBinNums_2eZ,Vvar__1___24Anonymous__32883)
       => ( cCoq_2emicromega_2eZMicromega_2eZdivide__pol___24a2(Vvar__0__x__32882,Vvar__1___24Anonymous__32883)
         => ( ? [Vvar__1__c__32886] :
                ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__1__c__32886)
                & cCoq_2eZArith_2eBinInt_2eZ_2edivide___24a2(Vvar__0__x__32882,Vvar__1__c__32886)
                & Vvar__1___24Anonymous__32883 = cCoq_2emicromega_2eEnvRing_2ePc___24a2(cCoq_2eNumbers_2eBinNums_2eZ,Vvar__1__c__32886) )
            | ? [Vvar__1__p__32889] :
                ( cCoq_2emicromega_2eRingMicromega_2ePolC___24t(cCoq_2eNumbers_2eBinNums_2eZ,Vvar__1__p__32889)
                & cCoq_2emicromega_2eZMicromega_2eZdivide__pol___24a2(Vvar__0__x__32882,Vvar__1__p__32889)
                & ? [Vvar__3__j__32891] :
                    ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__3__j__32891)
                    & Vvar__1___24Anonymous__32883 = cCoq_2emicromega_2eEnvRing_2ePinj___24a3(cCoq_2eNumbers_2eBinNums_2eZ,Vvar__3__j__32891,Vvar__1__p__32889) ) )
            | ? [Vvar__1__p__32893] :
                ( cCoq_2emicromega_2eRingMicromega_2ePolC___24t(cCoq_2eNumbers_2eBinNums_2eZ,Vvar__1__p__32893)
                & ? [Vvar__2__q__32894] :
                    ( cCoq_2emicromega_2eRingMicromega_2ePolC___24t(cCoq_2eNumbers_2eBinNums_2eZ,Vvar__2__q__32894)
                    & cCoq_2emicromega_2eZMicromega_2eZdivide__pol___24a2(Vvar__0__x__32882,Vvar__1__p__32893)
                    & cCoq_2emicromega_2eZMicromega_2eZdivide__pol___24a2(Vvar__0__x__32882,Vvar__2__q__32894)
                    & ? [Vvar__5__j__32897] :
                        ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__5__j__32897)
                        & Vvar__1___24Anonymous__32883 = cCoq_2emicromega_2eEnvRing_2ePX___24a4(cCoq_2eNumbers_2eBinNums_2eZ,Vvar__1__p__32893,Vvar__5__j__32897,Vvar__2__q__32894) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.micromega.ZMicromega.is_diff_env_elt',axiom,
    ! [Vvar__0__fr__24062,Vvar__1__env__24063,Vvar__2__env_27__24066,Vvar__3__x__24069] :
      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0__fr__24062)
     => ( c_24__type__24090___24t(Vvar__0__fr__24062,Vvar__1__env__24063,Vvar__2__env_27__24066,Vvar__3__x__24069,Vvar__1__env__24063)
       => ( c_24__type__24099___24t(Vvar__0__fr__24062,Vvar__1__env__24063,Vvar__2__env_27__24066,Vvar__3__x__24069,Vvar__2__env_27__24066)
         => ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__3__x__24069)
           => ( cCoq_2emicromega_2eZMicromega_2eis__diff__env__elt___24a4(Vvar__0__fr__24062,Vvar__1__env__24063,Vvar__2__env_27__24066,Vvar__3__x__24069)
             => ( happ(Vvar__1__env__24063,Vvar__3__x__24069) = happ(Vvar__2__env_27__24066,Vvar__3__x__24069)
                & happ(Vvar__1__env__24063,Vvar__3__x__24069) = cCoq_2eZArith_2eBinIntDef_2eZ_2esub___24a2(happ(Vvar__2__env_27__24066,cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(Vvar__0__fr__24062,Vvar__3__x__24069))),happ(Vvar__2__env_27__24066,cCoq_2eNumbers_2eBinNums_2exI___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(Vvar__0__fr__24062,Vvar__3__x__24069))))
                & cCoq_2eZArith_2eBinInt_2eZ_2ege___24a2(happ(Vvar__2__env_27__24066,cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(Vvar__0__fr__24062,Vvar__3__x__24069))),cCoq_2eNumbers_2eBinNums_2eZ0)
                & cCoq_2eZArith_2eBinInt_2eZ_2ege___24a2(happ(Vvar__2__env_27__24066,cCoq_2eNumbers_2eBinNums_2exI___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(Vvar__0__fr__24062,Vvar__3__x__24069))),cCoq_2eNumbers_2eBinNums_2eZ0)
                & p(c_24True) ) ) ) ) ) ) ).

fof('$_inversion_Coq.setoid_ring.Field_theory.FExpr',axiom,
    ! [Vvar__0__C__3326,VX3327] :
      ( cType___24t(Vvar__0__C__3326)
     => ( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__3326,VX3327)
       => ( VX3327 = cCoq_2esetoid__ring_2eField__theory_2eFEO___24a1(Vvar__0__C__3326)
          | VX3327 = cCoq_2esetoid__ring_2eField__theory_2eFEI___24a1(Vvar__0__C__3326)
          | ? [Vvar__1___24Anonymous__3331] :
              ( t(Vvar__1___24Anonymous__3331,Vvar__0__C__3326)
              & VX3327 = cCoq_2esetoid__ring_2eField__theory_2eFEc___24a2(Vvar__0__C__3326,Vvar__1___24Anonymous__3331) )
          | ? [Vvar__1___24Anonymous__3333] :
              ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__3333)
              & VX3327 = cCoq_2esetoid__ring_2eField__theory_2eFEX___24a2(Vvar__0__C__3326,Vvar__1___24Anonymous__3333) )
          | ? [Vvar__1___24Anonymous__3335] :
              ( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__3326,Vvar__1___24Anonymous__3335)
              & ? [Vvar__2___24Anonymous__3336] :
                  ( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__3326,Vvar__2___24Anonymous__3336)
                  & VX3327 = cCoq_2esetoid__ring_2eField__theory_2eFEadd___24a3(Vvar__0__C__3326,Vvar__1___24Anonymous__3335,Vvar__2___24Anonymous__3336) ) )
          | ? [Vvar__1___24Anonymous__3338] :
              ( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__3326,Vvar__1___24Anonymous__3338)
              & ? [Vvar__2___24Anonymous__3339] :
                  ( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__3326,Vvar__2___24Anonymous__3339)
                  & VX3327 = cCoq_2esetoid__ring_2eField__theory_2eFEsub___24a3(Vvar__0__C__3326,Vvar__1___24Anonymous__3338,Vvar__2___24Anonymous__3339) ) )
          | ? [Vvar__1___24Anonymous__3341] :
              ( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__3326,Vvar__1___24Anonymous__3341)
              & ? [Vvar__2___24Anonymous__3342] :
                  ( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__3326,Vvar__2___24Anonymous__3342)
                  & VX3327 = cCoq_2esetoid__ring_2eField__theory_2eFEmul___24a3(Vvar__0__C__3326,Vvar__1___24Anonymous__3341,Vvar__2___24Anonymous__3342) ) )
          | ? [Vvar__1___24Anonymous__3344] :
              ( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__3326,Vvar__1___24Anonymous__3344)
              & VX3327 = cCoq_2esetoid__ring_2eField__theory_2eFEopp___24a2(Vvar__0__C__3326,Vvar__1___24Anonymous__3344) )
          | ? [Vvar__1___24Anonymous__3346] :
              ( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__3326,Vvar__1___24Anonymous__3346)
              & VX3327 = cCoq_2esetoid__ring_2eField__theory_2eFEinv___24a2(Vvar__0__C__3326,Vvar__1___24Anonymous__3346) )
          | ? [Vvar__1___24Anonymous__3348] :
              ( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__3326,Vvar__1___24Anonymous__3348)
              & ? [Vvar__2___24Anonymous__3349] :
                  ( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__3326,Vvar__2___24Anonymous__3349)
                  & VX3327 = cCoq_2esetoid__ring_2eField__theory_2eFEdiv___24a3(Vvar__0__C__3326,Vvar__1___24Anonymous__3348,Vvar__2___24Anonymous__3349) ) )
          | ? [Vvar__1___24Anonymous__3351] :
              ( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__3326,Vvar__1___24Anonymous__3351)
              & ? [Vvar__2___24Anonymous__3352] :
                  ( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__2___24Anonymous__3352)
                  & VX3327 = cCoq_2esetoid__ring_2eField__theory_2eFEpow___24a3(Vvar__0__C__3326,Vvar__1___24Anonymous__3351,Vvar__2___24Anonymous__3352) ) ) ) ) ) ).

fof('$_inversion_Coq.setoid_ring.Field_theory.almost_field_theory',axiom,
    ! [Vvar__0__R__12428,Vvar__1__rO__12429,Vvar__2__rI__12430,Vvar__3__radd__12431,Vvar__4__rmul__12436,Vvar__5__rsub__12441,Vvar__6__ropp__12446,Vvar__7__rdiv__12449,Vvar__8__rinv__12454,Vvar__9__req__12457] :
      ( cType___24t(Vvar__0__R__12428)
     => ( t(Vvar__1__rO__12429,Vvar__0__R__12428)
       => ( t(Vvar__2__rI__12430,Vvar__0__R__12428)
         => ( c_24__type__12622___24t(Vvar__0__R__12428,Vvar__1__rO__12429,Vvar__2__rI__12430,Vvar__3__radd__12431,Vvar__4__rmul__12436,Vvar__5__rsub__12441,Vvar__6__ropp__12446,Vvar__7__rdiv__12449,Vvar__8__rinv__12454,Vvar__9__req__12457,Vvar__3__radd__12431)
           => ( c_24__type__12715___24t(Vvar__0__R__12428,Vvar__1__rO__12429,Vvar__2__rI__12430,Vvar__3__radd__12431,Vvar__4__rmul__12436,Vvar__5__rsub__12441,Vvar__6__ropp__12446,Vvar__7__rdiv__12449,Vvar__8__rinv__12454,Vvar__9__req__12457,Vvar__4__rmul__12436)
             => ( c_24__type__12808___24t(Vvar__0__R__12428,Vvar__1__rO__12429,Vvar__2__rI__12430,Vvar__3__radd__12431,Vvar__4__rmul__12436,Vvar__5__rsub__12441,Vvar__6__ropp__12446,Vvar__7__rdiv__12449,Vvar__8__rinv__12454,Vvar__9__req__12457,Vvar__5__rsub__12441)
               => ( c_24__type__12890___24t(Vvar__0__R__12428,Vvar__1__rO__12429,Vvar__2__rI__12430,Vvar__3__radd__12431,Vvar__4__rmul__12436,Vvar__5__rsub__12441,Vvar__6__ropp__12446,Vvar__7__rdiv__12449,Vvar__8__rinv__12454,Vvar__9__req__12457,Vvar__6__ropp__12446)
                 => ( c_24__type__12983___24t(Vvar__0__R__12428,Vvar__1__rO__12429,Vvar__2__rI__12430,Vvar__3__radd__12431,Vvar__4__rmul__12436,Vvar__5__rsub__12441,Vvar__6__ropp__12446,Vvar__7__rdiv__12449,Vvar__8__rinv__12454,Vvar__9__req__12457,Vvar__7__rdiv__12449)
                   => ( c_24__type__13065___24t(Vvar__0__R__12428,Vvar__1__rO__12429,Vvar__2__rI__12430,Vvar__3__radd__12431,Vvar__4__rmul__12436,Vvar__5__rsub__12441,Vvar__6__ropp__12446,Vvar__7__rdiv__12449,Vvar__8__rinv__12454,Vvar__9__req__12457,Vvar__8__rinv__12454)
                     => ( c_24__type__13158___24t(Vvar__0__R__12428,Vvar__1__rO__12429,Vvar__2__rI__12430,Vvar__3__radd__12431,Vvar__4__rmul__12436,Vvar__5__rsub__12441,Vvar__6__ropp__12446,Vvar__7__rdiv__12449,Vvar__8__rinv__12454,Vvar__9__req__12457,Vvar__9__req__12457)
                       => ( cCoq_2esetoid__ring_2eField__theory_2ealmost__field__theory___24a10(Vvar__0__R__12428,Vvar__1__rO__12429,Vvar__2__rI__12430,Vvar__3__radd__12431,Vvar__4__rmul__12436,Vvar__5__rsub__12441,Vvar__6__ropp__12446,Vvar__7__rdiv__12449,Vvar__8__rinv__12454,Vvar__9__req__12457)
                         => ( cCoq_2esetoid__ring_2eRing__theory_2ealmost__ring__theory___24a8(Vvar__0__R__12428,Vvar__1__rO__12429,Vvar__2__rI__12430,Vvar__3__radd__12431,Vvar__4__rmul__12436,Vvar__5__rsub__12441,Vvar__6__ropp__12446,Vvar__9__req__12457)
                            & ~ p(happ(happ(Vvar__9__req__12457,Vvar__2__rI__12430),Vvar__1__rO__12429))
                            & ! [Vvar__var__var__var__var__var__var__12__p__12500__12502__12509__12511__12513__12515__12517] :
                                ( t(Vvar__var__var__var__var__var__var__12__p__12500__12502__12509__12511__12513__12515__12517,Vvar__0__R__12428)
                               => ! [Vvar__var__var__var__var__var__var__13__q__12501__12503__12510__12512__12514__12516__12518] :
                                    ( t(Vvar__var__var__var__var__var__var__13__q__12501__12503__12510__12512__12514__12516__12518,Vvar__0__R__12428)
                                   => p(happ(happ(Vvar__9__req__12457,happ(happ(Vvar__7__rdiv__12449,Vvar__var__var__var__var__var__var__12__p__12500__12502__12509__12511__12513__12515__12517),Vvar__var__var__var__var__var__var__13__q__12501__12503__12510__12512__12514__12516__12518)),happ(happ(Vvar__4__rmul__12436,Vvar__var__var__var__var__var__var__12__p__12500__12502__12509__12511__12513__12515__12517),happ(Vvar__8__rinv__12454,Vvar__var__var__var__var__var__var__13__q__12501__12503__12510__12512__12514__12516__12518)))) ) )
                            & ! [Vvar__var__var__var__var__var__var__var__13__p__12505__12507__12519__12521__12523__12525__12527__12529] :
                                ( t(Vvar__var__var__var__var__var__var__var__13__p__12505__12507__12519__12521__12523__12525__12527__12529,Vvar__0__R__12428)
                               => ( ~ p(happ(happ(Vvar__9__req__12457,Vvar__var__var__var__var__var__var__var__13__p__12505__12507__12519__12521__12523__12525__12527__12529),Vvar__1__rO__12429))
                                 => p(happ(happ(Vvar__9__req__12457,happ(happ(Vvar__4__rmul__12436,happ(Vvar__8__rinv__12454,Vvar__var__var__var__var__var__var__var__13__p__12505__12507__12519__12521__12523__12525__12527__12529)),Vvar__var__var__var__var__var__var__var__13__p__12505__12507__12519__12521__12523__12525__12527__12529)),Vvar__2__rI__12430)) ) )
                            & p(c_24True) ) ) ) ) ) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.setoid_ring.Field_theory.field_theory',axiom,
    ! [Vvar__0__R__26227,Vvar__1__rO__26228,Vvar__2__rI__26229,Vvar__3__radd__26230,Vvar__4__rmul__26235,Vvar__5__rsub__26240,Vvar__6__ropp__26245,Vvar__7__rdiv__26248,Vvar__8__rinv__26253,Vvar__9__req__26256] :
      ( cType___24t(Vvar__0__R__26227)
     => ( t(Vvar__1__rO__26228,Vvar__0__R__26227)
       => ( t(Vvar__2__rI__26229,Vvar__0__R__26227)
         => ( c_24__type__26421___24t(Vvar__0__R__26227,Vvar__1__rO__26228,Vvar__2__rI__26229,Vvar__3__radd__26230,Vvar__4__rmul__26235,Vvar__5__rsub__26240,Vvar__6__ropp__26245,Vvar__7__rdiv__26248,Vvar__8__rinv__26253,Vvar__9__req__26256,Vvar__3__radd__26230)
           => ( c_24__type__26514___24t(Vvar__0__R__26227,Vvar__1__rO__26228,Vvar__2__rI__26229,Vvar__3__radd__26230,Vvar__4__rmul__26235,Vvar__5__rsub__26240,Vvar__6__ropp__26245,Vvar__7__rdiv__26248,Vvar__8__rinv__26253,Vvar__9__req__26256,Vvar__4__rmul__26235)
             => ( c_24__type__26607___24t(Vvar__0__R__26227,Vvar__1__rO__26228,Vvar__2__rI__26229,Vvar__3__radd__26230,Vvar__4__rmul__26235,Vvar__5__rsub__26240,Vvar__6__ropp__26245,Vvar__7__rdiv__26248,Vvar__8__rinv__26253,Vvar__9__req__26256,Vvar__5__rsub__26240)
               => ( c_24__type__26689___24t(Vvar__0__R__26227,Vvar__1__rO__26228,Vvar__2__rI__26229,Vvar__3__radd__26230,Vvar__4__rmul__26235,Vvar__5__rsub__26240,Vvar__6__ropp__26245,Vvar__7__rdiv__26248,Vvar__8__rinv__26253,Vvar__9__req__26256,Vvar__6__ropp__26245)
                 => ( c_24__type__26782___24t(Vvar__0__R__26227,Vvar__1__rO__26228,Vvar__2__rI__26229,Vvar__3__radd__26230,Vvar__4__rmul__26235,Vvar__5__rsub__26240,Vvar__6__ropp__26245,Vvar__7__rdiv__26248,Vvar__8__rinv__26253,Vvar__9__req__26256,Vvar__7__rdiv__26248)
                   => ( c_24__type__26864___24t(Vvar__0__R__26227,Vvar__1__rO__26228,Vvar__2__rI__26229,Vvar__3__radd__26230,Vvar__4__rmul__26235,Vvar__5__rsub__26240,Vvar__6__ropp__26245,Vvar__7__rdiv__26248,Vvar__8__rinv__26253,Vvar__9__req__26256,Vvar__8__rinv__26253)
                     => ( c_24__type__26957___24t(Vvar__0__R__26227,Vvar__1__rO__26228,Vvar__2__rI__26229,Vvar__3__radd__26230,Vvar__4__rmul__26235,Vvar__5__rsub__26240,Vvar__6__ropp__26245,Vvar__7__rdiv__26248,Vvar__8__rinv__26253,Vvar__9__req__26256,Vvar__9__req__26256)
                       => ( cCoq_2esetoid__ring_2eField__theory_2efield__theory___24a10(Vvar__0__R__26227,Vvar__1__rO__26228,Vvar__2__rI__26229,Vvar__3__radd__26230,Vvar__4__rmul__26235,Vvar__5__rsub__26240,Vvar__6__ropp__26245,Vvar__7__rdiv__26248,Vvar__8__rinv__26253,Vvar__9__req__26256)
                         => ( cCoq_2esetoid__ring_2eRing__theory_2ering__theory___24a8(Vvar__0__R__26227,Vvar__1__rO__26228,Vvar__2__rI__26229,Vvar__3__radd__26230,Vvar__4__rmul__26235,Vvar__5__rsub__26240,Vvar__6__ropp__26245,Vvar__9__req__26256)
                            & ~ p(happ(happ(Vvar__9__req__26256,Vvar__2__rI__26229),Vvar__1__rO__26228))
                            & ! [Vvar__var__var__var__var__var__var__12__p__26299__26301__26308__26310__26312__26314__26316] :
                                ( t(Vvar__var__var__var__var__var__var__12__p__26299__26301__26308__26310__26312__26314__26316,Vvar__0__R__26227)
                               => ! [Vvar__var__var__var__var__var__var__13__q__26300__26302__26309__26311__26313__26315__26317] :
                                    ( t(Vvar__var__var__var__var__var__var__13__q__26300__26302__26309__26311__26313__26315__26317,Vvar__0__R__26227)
                                   => p(happ(happ(Vvar__9__req__26256,happ(happ(Vvar__7__rdiv__26248,Vvar__var__var__var__var__var__var__12__p__26299__26301__26308__26310__26312__26314__26316),Vvar__var__var__var__var__var__var__13__q__26300__26302__26309__26311__26313__26315__26317)),happ(happ(Vvar__4__rmul__26235,Vvar__var__var__var__var__var__var__12__p__26299__26301__26308__26310__26312__26314__26316),happ(Vvar__8__rinv__26253,Vvar__var__var__var__var__var__var__13__q__26300__26302__26309__26311__26313__26315__26317)))) ) )
                            & ! [Vvar__var__var__var__var__var__var__var__13__p__26304__26306__26318__26320__26322__26324__26326__26328] :
                                ( t(Vvar__var__var__var__var__var__var__var__13__p__26304__26306__26318__26320__26322__26324__26326__26328,Vvar__0__R__26227)
                               => ( ~ p(happ(happ(Vvar__9__req__26256,Vvar__var__var__var__var__var__var__var__13__p__26304__26306__26318__26320__26322__26324__26326__26328),Vvar__1__rO__26228))
                                 => p(happ(happ(Vvar__9__req__26256,happ(happ(Vvar__4__rmul__26235,happ(Vvar__8__rinv__26253,Vvar__var__var__var__var__var__var__var__13__p__26304__26306__26318__26320__26322__26324__26326__26328)),Vvar__var__var__var__var__var__var__var__13__p__26304__26306__26318__26320__26322__26324__26326__26328)),Vvar__2__rI__26229)) ) )
                            & p(c_24True) ) ) ) ) ) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.setoid_ring.Field_theory.linear',axiom,
    ! [Vvar__0__C__3944,VX3945] :
      ( cType___24t(Vvar__0__C__3944)
     => ( cCoq_2esetoid__ring_2eField__theory_2elinear___24t(Vvar__0__C__3944,VX3945)
       => ? [Vvar__1__num__3947] :
            ( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__3944,Vvar__1__num__3947)
            & ? [Vvar__2__denum__3948] :
                ( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__3944,Vvar__2__denum__3948)
                & ? [Vvar__3__condition__3949] :
                    ( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(Vvar__0__C__3944),Vvar__3__condition__3949)
                    & VX3945 = cCoq_2esetoid__ring_2eField__theory_2emk__linear___24a4(Vvar__0__C__3944,Vvar__1__num__3947,Vvar__2__denum__3948,Vvar__3__condition__3949) ) ) ) ) ) ).

fof('$_inversion_Coq.setoid_ring.Field_theory.rsplit',axiom,
    ! [Vvar__0__C__4222,VX4223] :
      ( cType___24t(Vvar__0__C__4222)
     => ( cCoq_2esetoid__ring_2eField__theory_2ersplit___24t(Vvar__0__C__4222,VX4223)
       => ? [Vvar__1__rsplit__left__4225] :
            ( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__4222,Vvar__1__rsplit__left__4225)
            & ? [Vvar__2__rsplit__common__4226] :
                ( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__4222,Vvar__2__rsplit__common__4226)
                & ? [Vvar__3__rsplit__right__4227] :
                    ( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__4222,Vvar__3__rsplit__right__4227)
                    & VX4223 = cCoq_2esetoid__ring_2eField__theory_2emk__rsplit___24a4(Vvar__0__C__4222,Vvar__1__rsplit__left__4225,Vvar__2__rsplit__common__4226,Vvar__3__rsplit__right__4227) ) ) ) ) ) ).

fof('$_inversion_Coq.setoid_ring.Field_theory.semi_field_theory',axiom,
    ! [Vvar__0__R__14122,Vvar__1__rO__14123,Vvar__2__rI__14124,Vvar__3__radd__14125,Vvar__4__rmul__14130,Vvar__5__rdiv__14135,Vvar__6__rinv__14140,Vvar__7__req__14143] :
      ( cType___24t(Vvar__0__R__14122)
     => ( t(Vvar__1__rO__14123,Vvar__0__R__14122)
       => ( t(Vvar__2__rI__14124,Vvar__0__R__14122)
         => ( c_24__type__14270___24t(Vvar__0__R__14122,Vvar__1__rO__14123,Vvar__2__rI__14124,Vvar__3__radd__14125,Vvar__4__rmul__14130,Vvar__5__rdiv__14135,Vvar__6__rinv__14140,Vvar__7__req__14143,Vvar__3__radd__14125)
           => ( c_24__type__14333___24t(Vvar__0__R__14122,Vvar__1__rO__14123,Vvar__2__rI__14124,Vvar__3__radd__14125,Vvar__4__rmul__14130,Vvar__5__rdiv__14135,Vvar__6__rinv__14140,Vvar__7__req__14143,Vvar__4__rmul__14130)
             => ( c_24__type__14396___24t(Vvar__0__R__14122,Vvar__1__rO__14123,Vvar__2__rI__14124,Vvar__3__radd__14125,Vvar__4__rmul__14130,Vvar__5__rdiv__14135,Vvar__6__rinv__14140,Vvar__7__req__14143,Vvar__5__rdiv__14135)
               => ( c_24__type__14450___24t(Vvar__0__R__14122,Vvar__1__rO__14123,Vvar__2__rI__14124,Vvar__3__radd__14125,Vvar__4__rmul__14130,Vvar__5__rdiv__14135,Vvar__6__rinv__14140,Vvar__7__req__14143,Vvar__6__rinv__14140)
                 => ( c_24__type__14513___24t(Vvar__0__R__14122,Vvar__1__rO__14123,Vvar__2__rI__14124,Vvar__3__radd__14125,Vvar__4__rmul__14130,Vvar__5__rdiv__14135,Vvar__6__rinv__14140,Vvar__7__req__14143,Vvar__7__req__14143)
                   => ( cCoq_2esetoid__ring_2eField__theory_2esemi__field__theory___24a8(Vvar__0__R__14122,Vvar__1__rO__14123,Vvar__2__rI__14124,Vvar__3__radd__14125,Vvar__4__rmul__14130,Vvar__5__rdiv__14135,Vvar__6__rinv__14140,Vvar__7__req__14143)
                     => ( cCoq_2esetoid__ring_2eRing__theory_2esemi__ring__theory___24a6(Vvar__0__R__14122,Vvar__1__rO__14123,Vvar__2__rI__14124,Vvar__3__radd__14125,Vvar__4__rmul__14130,Vvar__7__req__14143)
                        & ~ p(happ(happ(Vvar__7__req__14143,Vvar__2__rI__14124),Vvar__1__rO__14123))
                        & ! [Vvar__var__var__var__var__var__var__10__p__14178__14180__14187__14189__14191__14193__14195] :
                            ( t(Vvar__var__var__var__var__var__var__10__p__14178__14180__14187__14189__14191__14193__14195,Vvar__0__R__14122)
                           => ! [Vvar__var__var__var__var__var__var__11__q__14179__14181__14188__14190__14192__14194__14196] :
                                ( t(Vvar__var__var__var__var__var__var__11__q__14179__14181__14188__14190__14192__14194__14196,Vvar__0__R__14122)
                               => p(happ(happ(Vvar__7__req__14143,happ(happ(Vvar__5__rdiv__14135,Vvar__var__var__var__var__var__var__10__p__14178__14180__14187__14189__14191__14193__14195),Vvar__var__var__var__var__var__var__11__q__14179__14181__14188__14190__14192__14194__14196)),happ(happ(Vvar__4__rmul__14130,Vvar__var__var__var__var__var__var__10__p__14178__14180__14187__14189__14191__14193__14195),happ(Vvar__6__rinv__14140,Vvar__var__var__var__var__var__var__11__q__14179__14181__14188__14190__14192__14194__14196)))) ) )
                        & ! [Vvar__var__var__var__var__var__var__var__11__p__14183__14185__14197__14199__14201__14203__14205__14207] :
                            ( t(Vvar__var__var__var__var__var__var__var__11__p__14183__14185__14197__14199__14201__14203__14205__14207,Vvar__0__R__14122)
                           => ( ~ p(happ(happ(Vvar__7__req__14143,Vvar__var__var__var__var__var__var__var__11__p__14183__14185__14197__14199__14201__14203__14205__14207),Vvar__1__rO__14123))
                             => p(happ(happ(Vvar__7__req__14143,happ(happ(Vvar__4__rmul__14130,happ(Vvar__6__rinv__14140,Vvar__var__var__var__var__var__var__var__11__p__14183__14185__14197__14199__14201__14203__14205__14207)),Vvar__var__var__var__var__var__var__var__11__p__14183__14185__14197__14199__14201__14203__14205__14207)),Vvar__2__rI__14124)) ) )
                        & p(c_24True) ) ) ) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.setoid_ring.InitialRing.hypo',axiom,
    ! [VX27031] :
      ( cCoq_2esetoid__ring_2eInitialRing_2ehypo___24t(VX27031)
     => ? [Vvar__0__hypo__type__27032] :
          ( cType___24t(Vvar__0__hypo__type__27032)
          & ? [Vvar__1__hypo__proof__27033] :
              ( t(Vvar__1__hypo__proof__27033,Vvar__0__hypo__type__27032)
              & VX27031 = cCoq_2esetoid__ring_2eInitialRing_2emkhypo___24a2(Vvar__0__hypo__type__27032,Vvar__1__hypo__proof__27033) ) ) ) ).

fof('$_inversion_Coq.setoid_ring.Ring_polynom.Mon',axiom,
    ! [VX4832] :
      ( cCoq_2esetoid__ring_2eRing__polynom_2eMon___24t(VX4832)
     => ( VX4832 = cCoq_2esetoid__ring_2eRing__polynom_2emon0
        | ? [Vvar__0___24Anonymous__4833] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__4833)
            & ? [Vvar__1___24Anonymous__4834] :
                ( cCoq_2esetoid__ring_2eRing__polynom_2eMon___24t(Vvar__1___24Anonymous__4834)
                & VX4832 = cCoq_2esetoid__ring_2eRing__polynom_2ezmon___24a2(Vvar__0___24Anonymous__4833,Vvar__1___24Anonymous__4834) ) )
        | ? [Vvar__0___24Anonymous__4835] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__4835)
            & ? [Vvar__1___24Anonymous__4836] :
                ( cCoq_2esetoid__ring_2eRing__polynom_2eMon___24t(Vvar__1___24Anonymous__4836)
                & VX4832 = cCoq_2esetoid__ring_2eRing__polynom_2evmon___24a2(Vvar__0___24Anonymous__4835,Vvar__1___24Anonymous__4836) ) ) ) ) ).

fof('$_inversion_Coq.setoid_ring.Ring_polynom.PExpr',axiom,
    ! [Vvar__0__C__4853,VX4854] :
      ( cType___24t(Vvar__0__C__4853)
     => ( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__4853,VX4854)
       => ( VX4854 = cCoq_2esetoid__ring_2eRing__polynom_2ePEO___24a1(Vvar__0__C__4853)
          | VX4854 = cCoq_2esetoid__ring_2eRing__polynom_2ePEI___24a1(Vvar__0__C__4853)
          | ? [Vvar__1___24Anonymous__4858] :
              ( t(Vvar__1___24Anonymous__4858,Vvar__0__C__4853)
              & VX4854 = cCoq_2esetoid__ring_2eRing__polynom_2ePEc___24a2(Vvar__0__C__4853,Vvar__1___24Anonymous__4858) )
          | ? [Vvar__1___24Anonymous__4860] :
              ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__4860)
              & VX4854 = cCoq_2esetoid__ring_2eRing__polynom_2ePEX___24a2(Vvar__0__C__4853,Vvar__1___24Anonymous__4860) )
          | ? [Vvar__1___24Anonymous__4862] :
              ( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__4853,Vvar__1___24Anonymous__4862)
              & ? [Vvar__2___24Anonymous__4863] :
                  ( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__4853,Vvar__2___24Anonymous__4863)
                  & VX4854 = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(Vvar__0__C__4853,Vvar__1___24Anonymous__4862,Vvar__2___24Anonymous__4863) ) )
          | ? [Vvar__1___24Anonymous__4865] :
              ( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__4853,Vvar__1___24Anonymous__4865)
              & ? [Vvar__2___24Anonymous__4866] :
                  ( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__4853,Vvar__2___24Anonymous__4866)
                  & VX4854 = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(Vvar__0__C__4853,Vvar__1___24Anonymous__4865,Vvar__2___24Anonymous__4866) ) )
          | ? [Vvar__1___24Anonymous__4868] :
              ( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__4853,Vvar__1___24Anonymous__4868)
              & ? [Vvar__2___24Anonymous__4869] :
                  ( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__4853,Vvar__2___24Anonymous__4869)
                  & VX4854 = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(Vvar__0__C__4853,Vvar__1___24Anonymous__4868,Vvar__2___24Anonymous__4869) ) )
          | ? [Vvar__1___24Anonymous__4871] :
              ( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__4853,Vvar__1___24Anonymous__4871)
              & VX4854 = cCoq_2esetoid__ring_2eRing__polynom_2ePEopp___24a2(Vvar__0__C__4853,Vvar__1___24Anonymous__4871) )
          | ? [Vvar__1___24Anonymous__4873] :
              ( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__4853,Vvar__1___24Anonymous__4873)
              & ? [Vvar__2___24Anonymous__4874] :
                  ( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__2___24Anonymous__4874)
                  & VX4854 = cCoq_2esetoid__ring_2eRing__polynom_2ePEpow___24a3(Vvar__0__C__4853,Vvar__1___24Anonymous__4873,Vvar__2___24Anonymous__4874) ) ) ) ) ) ).

fof('$_inversion_Coq.setoid_ring.Ring_polynom.Pol',axiom,
    ! [Vvar__0__C__4769,VX4770] :
      ( cType___24t(Vvar__0__C__4769)
     => ( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vvar__0__C__4769,VX4770)
       => ( ? [Vvar__1___24Anonymous__4772] :
              ( t(Vvar__1___24Anonymous__4772,Vvar__0__C__4769)
              & VX4770 = cCoq_2esetoid__ring_2eRing__polynom_2ePc___24a2(Vvar__0__C__4769,Vvar__1___24Anonymous__4772) )
          | ? [Vvar__1___24Anonymous__4774] :
              ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__4774)
              & ? [Vvar__2___24Anonymous__4775] :
                  ( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vvar__0__C__4769,Vvar__2___24Anonymous__4775)
                  & VX4770 = cCoq_2esetoid__ring_2eRing__polynom_2ePinj___24a3(Vvar__0__C__4769,Vvar__1___24Anonymous__4774,Vvar__2___24Anonymous__4775) ) )
          | ? [Vvar__1___24Anonymous__4777] :
              ( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vvar__0__C__4769,Vvar__1___24Anonymous__4777)
              & ? [Vvar__2___24Anonymous__4778] :
                  ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2___24Anonymous__4778)
                  & ? [Vvar__3___24Anonymous__4779] :
                      ( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vvar__0__C__4769,Vvar__3___24Anonymous__4779)
                      & VX4770 = cCoq_2esetoid__ring_2eRing__polynom_2ePX___24a4(Vvar__0__C__4769,Vvar__1___24Anonymous__4777,Vvar__2___24Anonymous__4778,Vvar__3___24Anonymous__4779) ) ) ) ) ) ) ).

fof('$_inversion_Coq.setoid_ring.Ring_theory.almost_ring_theory',axiom,
    ! [Vvar__0__R__6461,Vvar__1__rO__6462,Vvar__2__rI__6463,Vvar__3__radd__6464,Vvar__4__rmul__6469,Vvar__5__rsub__6474,Vvar__6__ropp__6479,Vvar__7__req__6482] :
      ( cType___24t(Vvar__0__R__6461)
     => ( t(Vvar__1__rO__6462,Vvar__0__R__6461)
       => ( t(Vvar__2__rI__6463,Vvar__0__R__6461)
         => ( c_24__type__6710___24t(Vvar__0__R__6461,Vvar__1__rO__6462,Vvar__2__rI__6463,Vvar__3__radd__6464,Vvar__4__rmul__6469,Vvar__5__rsub__6474,Vvar__6__ropp__6479,Vvar__7__req__6482,Vvar__3__radd__6464)
           => ( c_24__type__6773___24t(Vvar__0__R__6461,Vvar__1__rO__6462,Vvar__2__rI__6463,Vvar__3__radd__6464,Vvar__4__rmul__6469,Vvar__5__rsub__6474,Vvar__6__ropp__6479,Vvar__7__req__6482,Vvar__4__rmul__6469)
             => ( c_24__type__6836___24t(Vvar__0__R__6461,Vvar__1__rO__6462,Vvar__2__rI__6463,Vvar__3__radd__6464,Vvar__4__rmul__6469,Vvar__5__rsub__6474,Vvar__6__ropp__6479,Vvar__7__req__6482,Vvar__5__rsub__6474)
               => ( c_24__type__6890___24t(Vvar__0__R__6461,Vvar__1__rO__6462,Vvar__2__rI__6463,Vvar__3__radd__6464,Vvar__4__rmul__6469,Vvar__5__rsub__6474,Vvar__6__ropp__6479,Vvar__7__req__6482,Vvar__6__ropp__6479)
                 => ( c_24__type__6953___24t(Vvar__0__R__6461,Vvar__1__rO__6462,Vvar__2__rI__6463,Vvar__3__radd__6464,Vvar__4__rmul__6469,Vvar__5__rsub__6474,Vvar__6__ropp__6479,Vvar__7__req__6482,Vvar__7__req__6482)
                   => ( cCoq_2esetoid__ring_2eRing__theory_2ealmost__ring__theory___24a8(Vvar__0__R__6461,Vvar__1__rO__6462,Vvar__2__rI__6463,Vvar__3__radd__6464,Vvar__4__rmul__6469,Vvar__5__rsub__6474,Vvar__6__ropp__6479,Vvar__7__req__6482)
                     => ( ! [Vvar__var__var__var__var__var__8__x__6515__6516__6569__6570__6571__6572] :
                            ( t(Vvar__var__var__var__var__var__8__x__6515__6516__6569__6570__6571__6572,Vvar__0__R__6461)
                           => p(happ(happ(Vvar__7__req__6482,happ(happ(Vvar__3__radd__6464,Vvar__1__rO__6462),Vvar__var__var__var__var__var__8__x__6515__6516__6569__6570__6571__6572)),Vvar__var__var__var__var__var__8__x__6515__6516__6569__6570__6571__6572)) )
                        & ! [Vvar__var__var__var__var__9__x__6518__6520__6573__6575__6577] :
                            ( t(Vvar__var__var__var__var__9__x__6518__6520__6573__6575__6577,Vvar__0__R__6461)
                           => ! [Vvar__var__var__var__var__10__y__6519__6521__6574__6576__6578] :
                                ( t(Vvar__var__var__var__var__10__y__6519__6521__6574__6576__6578,Vvar__0__R__6461)
                               => p(happ(happ(Vvar__7__req__6482,happ(happ(Vvar__3__radd__6464,Vvar__var__var__var__var__9__x__6518__6520__6573__6575__6577),Vvar__var__var__var__var__10__y__6519__6521__6574__6576__6578)),happ(happ(Vvar__3__radd__6464,Vvar__var__var__var__var__10__y__6519__6521__6574__6576__6578),Vvar__var__var__var__var__9__x__6518__6520__6573__6575__6577))) ) )
                        & ! [Vvar__var__var__var__var__10__x__6523__6526__6579__6582__6585] :
                            ( t(Vvar__var__var__var__var__10__x__6523__6526__6579__6582__6585,Vvar__0__R__6461)
                           => ! [Vvar__var__var__var__var__11__y__6524__6527__6580__6583__6586] :
                                ( t(Vvar__var__var__var__var__11__y__6524__6527__6580__6583__6586,Vvar__0__R__6461)
                               => ! [Vvar__var__var__var__var__12__z__6525__6528__6581__6584__6587] :
                                    ( t(Vvar__var__var__var__var__12__z__6525__6528__6581__6584__6587,Vvar__0__R__6461)
                                   => p(happ(happ(Vvar__7__req__6482,happ(happ(Vvar__3__radd__6464,Vvar__var__var__var__var__10__x__6523__6526__6579__6582__6585),happ(happ(Vvar__3__radd__6464,Vvar__var__var__var__var__11__y__6524__6527__6580__6583__6586),Vvar__var__var__var__var__12__z__6525__6528__6581__6584__6587))),happ(happ(Vvar__3__radd__6464,happ(happ(Vvar__3__radd__6464,Vvar__var__var__var__var__10__x__6523__6526__6579__6582__6585),Vvar__var__var__var__var__11__y__6524__6527__6580__6583__6586)),Vvar__var__var__var__var__12__z__6525__6528__6581__6584__6587))) ) ) )
                        & ! [Vvar__var__var__var__var__var__11__x__6530__6531__6588__6589__6590__6591] :
                            ( t(Vvar__var__var__var__var__var__11__x__6530__6531__6588__6589__6590__6591,Vvar__0__R__6461)
                           => p(happ(happ(Vvar__7__req__6482,happ(happ(Vvar__4__rmul__6469,Vvar__2__rI__6463),Vvar__var__var__var__var__var__11__x__6530__6531__6588__6589__6590__6591)),Vvar__var__var__var__var__var__11__x__6530__6531__6588__6589__6590__6591)) )
                        & ! [Vvar__var__var__var__var__var__12__x__6533__6534__6592__6593__6594__6595] :
                            ( t(Vvar__var__var__var__var__var__12__x__6533__6534__6592__6593__6594__6595,Vvar__0__R__6461)
                           => p(happ(happ(Vvar__7__req__6482,happ(happ(Vvar__4__rmul__6469,Vvar__1__rO__6462),Vvar__var__var__var__var__var__12__x__6533__6534__6592__6593__6594__6595)),Vvar__1__rO__6462)) )
                        & ! [Vvar__var__var__var__var__13__x__6536__6538__6596__6598__6600] :
                            ( t(Vvar__var__var__var__var__13__x__6536__6538__6596__6598__6600,Vvar__0__R__6461)
                           => ! [Vvar__var__var__var__var__14__y__6537__6539__6597__6599__6601] :
                                ( t(Vvar__var__var__var__var__14__y__6537__6539__6597__6599__6601,Vvar__0__R__6461)
                               => p(happ(happ(Vvar__7__req__6482,happ(happ(Vvar__4__rmul__6469,Vvar__var__var__var__var__13__x__6536__6538__6596__6598__6600),Vvar__var__var__var__var__14__y__6537__6539__6597__6599__6601)),happ(happ(Vvar__4__rmul__6469,Vvar__var__var__var__var__14__y__6537__6539__6597__6599__6601),Vvar__var__var__var__var__13__x__6536__6538__6596__6598__6600))) ) )
                        & ! [Vvar__var__var__var__var__14__x__6541__6544__6602__6605__6608] :
                            ( t(Vvar__var__var__var__var__14__x__6541__6544__6602__6605__6608,Vvar__0__R__6461)
                           => ! [Vvar__var__var__var__var__15__y__6542__6545__6603__6606__6609] :
                                ( t(Vvar__var__var__var__var__15__y__6542__6545__6603__6606__6609,Vvar__0__R__6461)
                               => ! [Vvar__var__var__var__var__16__z__6543__6546__6604__6607__6610] :
                                    ( t(Vvar__var__var__var__var__16__z__6543__6546__6604__6607__6610,Vvar__0__R__6461)
                                   => p(happ(happ(Vvar__7__req__6482,happ(happ(Vvar__4__rmul__6469,Vvar__var__var__var__var__14__x__6541__6544__6602__6605__6608),happ(happ(Vvar__4__rmul__6469,Vvar__var__var__var__var__15__y__6542__6545__6603__6606__6609),Vvar__var__var__var__var__16__z__6543__6546__6604__6607__6610))),happ(happ(Vvar__4__rmul__6469,happ(happ(Vvar__4__rmul__6469,Vvar__var__var__var__var__14__x__6541__6544__6602__6605__6608),Vvar__var__var__var__var__15__y__6542__6545__6603__6606__6609)),Vvar__var__var__var__var__16__z__6543__6546__6604__6607__6610))) ) ) )
                        & ! [Vvar__var__var__var__var__var__15__x__6548__6551__6611__6614__6617__6620] :
                            ( t(Vvar__var__var__var__var__var__15__x__6548__6551__6611__6614__6617__6620,Vvar__0__R__6461)
                           => ! [Vvar__var__var__var__var__var__16__y__6549__6552__6612__6615__6618__6621] :
                                ( t(Vvar__var__var__var__var__var__16__y__6549__6552__6612__6615__6618__6621,Vvar__0__R__6461)
                               => ! [Vvar__var__var__var__var__var__17__z__6550__6553__6613__6616__6619__6622] :
                                    ( t(Vvar__var__var__var__var__var__17__z__6550__6553__6613__6616__6619__6622,Vvar__0__R__6461)
                                   => p(happ(happ(Vvar__7__req__6482,happ(happ(Vvar__4__rmul__6469,happ(happ(Vvar__3__radd__6464,Vvar__var__var__var__var__var__15__x__6548__6551__6611__6614__6617__6620),Vvar__var__var__var__var__var__16__y__6549__6552__6612__6615__6618__6621)),Vvar__var__var__var__var__var__17__z__6550__6553__6613__6616__6619__6622)),happ(happ(Vvar__3__radd__6464,happ(happ(Vvar__4__rmul__6469,Vvar__var__var__var__var__var__15__x__6548__6551__6611__6614__6617__6620),Vvar__var__var__var__var__var__17__z__6550__6553__6613__6616__6619__6622)),happ(happ(Vvar__4__rmul__6469,Vvar__var__var__var__var__var__16__y__6549__6552__6612__6615__6618__6621),Vvar__var__var__var__var__var__17__z__6550__6553__6613__6616__6619__6622)))) ) ) )
                        & ! [Vvar__var__var__var__var__var__16__x__6555__6557__6623__6625__6627__6629] :
                            ( t(Vvar__var__var__var__var__var__16__x__6555__6557__6623__6625__6627__6629,Vvar__0__R__6461)
                           => ! [Vvar__var__var__var__var__var__17__y__6556__6558__6624__6626__6628__6630] :
                                ( t(Vvar__var__var__var__var__var__17__y__6556__6558__6624__6626__6628__6630,Vvar__0__R__6461)
                               => p(happ(happ(Vvar__7__req__6482,happ(Vvar__6__ropp__6479,happ(happ(Vvar__4__rmul__6469,Vvar__var__var__var__var__var__16__x__6555__6557__6623__6625__6627__6629),Vvar__var__var__var__var__var__17__y__6556__6558__6624__6626__6628__6630))),happ(happ(Vvar__4__rmul__6469,happ(Vvar__6__ropp__6479,Vvar__var__var__var__var__var__16__x__6555__6557__6623__6625__6627__6629)),Vvar__var__var__var__var__var__17__y__6556__6558__6624__6626__6628__6630))) ) )
                        & ! [Vvar__var__var__var__var__var__17__x__6560__6562__6631__6633__6635__6637] :
                            ( t(Vvar__var__var__var__var__var__17__x__6560__6562__6631__6633__6635__6637,Vvar__0__R__6461)
                           => ! [Vvar__var__var__var__var__var__18__y__6561__6563__6632__6634__6636__6638] :
                                ( t(Vvar__var__var__var__var__var__18__y__6561__6563__6632__6634__6636__6638,Vvar__0__R__6461)
                               => p(happ(happ(Vvar__7__req__6482,happ(Vvar__6__ropp__6479,happ(happ(Vvar__3__radd__6464,Vvar__var__var__var__var__var__17__x__6560__6562__6631__6633__6635__6637),Vvar__var__var__var__var__var__18__y__6561__6563__6632__6634__6636__6638))),happ(happ(Vvar__3__radd__6464,happ(Vvar__6__ropp__6479,Vvar__var__var__var__var__var__17__x__6560__6562__6631__6633__6635__6637)),happ(Vvar__6__ropp__6479,Vvar__var__var__var__var__var__18__y__6561__6563__6632__6634__6636__6638)))) ) )
                        & ! [Vvar__var__var__var__var__var__var__18__x__6565__6567__6639__6641__6643__6645__6647] :
                            ( t(Vvar__var__var__var__var__var__var__18__x__6565__6567__6639__6641__6643__6645__6647,Vvar__0__R__6461)
                           => ! [Vvar__var__var__var__var__var__var__19__y__6566__6568__6640__6642__6644__6646__6648] :
                                ( t(Vvar__var__var__var__var__var__var__19__y__6566__6568__6640__6642__6644__6646__6648,Vvar__0__R__6461)
                               => p(happ(happ(Vvar__7__req__6482,happ(happ(Vvar__5__rsub__6474,Vvar__var__var__var__var__var__var__18__x__6565__6567__6639__6641__6643__6645__6647),Vvar__var__var__var__var__var__var__19__y__6566__6568__6640__6642__6644__6646__6648)),happ(happ(Vvar__3__radd__6464,Vvar__var__var__var__var__var__var__18__x__6565__6567__6639__6641__6643__6645__6647),happ(Vvar__6__ropp__6479,Vvar__var__var__var__var__var__var__19__y__6566__6568__6640__6642__6644__6646__6648)))) ) )
                        & p(c_24True) ) ) ) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.setoid_ring.Ring_theory.div_theory',axiom,
    ! [Vvar__0__R__10037,Vvar__1__req__10038,Vvar__2__C__10043,Vvar__3__cadd__10044,Vvar__4__cmul__10049,Vvar__5__phi__10054,Vvar__6__cdiv__10057] :
      ( cType___24t(Vvar__0__R__10037)
     => ( c_24__type__10177___24t(Vvar__0__R__10037,Vvar__1__req__10038,Vvar__2__C__10043,Vvar__3__cadd__10044,Vvar__4__cmul__10049,Vvar__5__phi__10054,Vvar__6__cdiv__10057,Vvar__1__req__10038)
       => ( cType___24t(Vvar__2__C__10043)
         => ( c_24__type__10227___24t(Vvar__0__R__10037,Vvar__1__req__10038,Vvar__2__C__10043,Vvar__3__cadd__10044,Vvar__4__cmul__10049,Vvar__5__phi__10054,Vvar__6__cdiv__10057,Vvar__3__cadd__10044)
           => ( c_24__type__10277___24t(Vvar__0__R__10037,Vvar__1__req__10038,Vvar__2__C__10043,Vvar__3__cadd__10044,Vvar__4__cmul__10049,Vvar__5__phi__10054,Vvar__6__cdiv__10057,Vvar__4__cmul__10049)
             => ( c_24__type__10319___24t(Vvar__0__R__10037,Vvar__1__req__10038,Vvar__2__C__10043,Vvar__3__cadd__10044,Vvar__4__cmul__10049,Vvar__5__phi__10054,Vvar__6__cdiv__10057,Vvar__5__phi__10054)
               => ( c_24__type__10369___24t(Vvar__0__R__10037,Vvar__1__req__10038,Vvar__2__C__10043,Vvar__3__cadd__10044,Vvar__4__cmul__10049,Vvar__5__phi__10054,Vvar__6__cdiv__10057,Vvar__6__cdiv__10057)
                 => ( cCoq_2esetoid__ring_2eRing__theory_2ediv__theory___24a7(Vvar__0__R__10037,Vvar__1__req__10038,Vvar__2__C__10043,Vvar__3__cadd__10044,Vvar__4__cmul__10049,Vvar__5__phi__10054,Vvar__6__cdiv__10057)
                   => ( ! [Vvar__var__var__var__var__var__var__var__7__a__10089__10094__10099__10104__10109__10114__10119__10124] :
                          ( t(Vvar__var__var__var__var__var__var__var__7__a__10089__10094__10099__10104__10109__10114__10119__10124,Vvar__2__C__10043)
                         => ! [Vvar__var__var__var__var__var__var__var__8__b__10090__10095__10100__10105__10110__10115__10120__10125] :
                              ( t(Vvar__var__var__var__var__var__var__var__8__b__10090__10095__10100__10105__10110__10115__10120__10125,Vvar__2__C__10043)
                             => c_24__case__Coq_2eInit_2eDatatypes_2eprod_2410432___24a9(Vvar__0__R__10037,Vvar__1__req__10038,Vvar__2__C__10043,Vvar__3__cadd__10044,Vvar__4__cmul__10049,Vvar__5__phi__10054,Vvar__6__cdiv__10057,Vvar__var__var__var__var__var__var__var__7__a__10089__10094__10099__10104__10109__10114__10119__10124,Vvar__var__var__var__var__var__var__var__8__b__10090__10095__10100__10105__10110__10115__10120__10125) ) )
                      & p(c_24True) ) ) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.setoid_ring.Ring_theory.power_theory',axiom,
    ! [Vvar__0__R__10455,Vvar__1__rI__10456,Vvar__2__rmul__10457,Vvar__3__req__10462,Vvar__4__Cpow__10467,Vvar__5__Cp__phi__10468,Vvar__6__rpow__10471] :
      ( cType___24t(Vvar__0__R__10455)
     => ( t(Vvar__1__rI__10456,Vvar__0__R__10455)
       => ( c_24__type__10557___24t(Vvar__0__R__10455,Vvar__1__rI__10456,Vvar__2__rmul__10457,Vvar__3__req__10462,Vvar__4__Cpow__10467,Vvar__5__Cp__phi__10468,Vvar__6__rpow__10471,Vvar__2__rmul__10457)
         => ( c_24__type__10601___24t(Vvar__0__R__10455,Vvar__1__rI__10456,Vvar__2__rmul__10457,Vvar__3__req__10462,Vvar__4__Cpow__10467,Vvar__5__Cp__phi__10468,Vvar__6__rpow__10471,Vvar__3__req__10462)
           => ( cType___24t(Vvar__4__Cpow__10467)
             => ( c_24__type__10637___24t(Vvar__0__R__10455,Vvar__1__rI__10456,Vvar__2__rmul__10457,Vvar__3__req__10462,Vvar__4__Cpow__10467,Vvar__5__Cp__phi__10468,Vvar__6__rpow__10471,Vvar__5__Cp__phi__10468)
               => ( c_24__type__10681___24t(Vvar__0__R__10455,Vvar__1__rI__10456,Vvar__2__rmul__10457,Vvar__3__req__10462,Vvar__4__Cpow__10467,Vvar__5__Cp__phi__10468,Vvar__6__rpow__10471,Vvar__6__rpow__10471)
                 => ( cCoq_2esetoid__ring_2eRing__theory_2epower__theory___24a7(Vvar__0__R__10455,Vvar__1__rI__10456,Vvar__2__rmul__10457,Vvar__3__req__10462,Vvar__4__Cpow__10467,Vvar__5__Cp__phi__10468,Vvar__6__rpow__10471)
                   => ( ! [Vvar__var__var__var__var__var__var__var__7__r__10499__10501__10503__10505__10507__10509__10511__10513] :
                          ( t(Vvar__var__var__var__var__var__var__var__7__r__10499__10501__10503__10505__10507__10509__10511__10513,Vvar__0__R__10455)
                         => ! [Vvar__var__var__var__var__var__var__var__8__n__10500__10502__10504__10506__10508__10510__10512__10514] :
                              ( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__var__var__var__var__var__var__var__8__n__10500__10502__10504__10506__10508__10510__10512__10514)
                             => p(happ(happ(Vvar__3__req__10462,happ(happ(Vvar__6__rpow__10471,Vvar__var__var__var__var__var__var__var__7__r__10499__10501__10503__10505__10507__10509__10511__10513),happ(Vvar__5__Cp__phi__10468,Vvar__var__var__var__var__var__var__var__8__n__10500__10502__10504__10506__10508__10510__10512__10514))),cCoq_2esetoid__ring_2eRing__theory_2epow__N___24a5(Vvar__0__R__10455,Vvar__1__rI__10456,Vvar__2__rmul__10457,Vvar__var__var__var__var__var__var__var__7__r__10499__10501__10503__10505__10507__10509__10511__10513,Vvar__var__var__var__var__var__var__var__8__n__10500__10502__10504__10506__10508__10510__10512__10514))) ) )
                      & p(c_24True) ) ) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.setoid_ring.Ring_theory.ring_eq_ext',axiom,
    ! [Vvar__0__R__7055,Vvar__1__radd__7056,Vvar__2__rmul__7061,Vvar__3__ropp__7066,Vvar__4__req__7069] :
      ( cType___24t(Vvar__0__R__7055)
     => ( c_24__type__7160___24t(Vvar__0__R__7055,Vvar__1__radd__7056,Vvar__2__rmul__7061,Vvar__3__ropp__7066,Vvar__4__req__7069,Vvar__1__radd__7056)
       => ( c_24__type__7190___24t(Vvar__0__R__7055,Vvar__1__radd__7056,Vvar__2__rmul__7061,Vvar__3__ropp__7066,Vvar__4__req__7069,Vvar__2__rmul__7061)
         => ( c_24__type__7214___24t(Vvar__0__R__7055,Vvar__1__radd__7056,Vvar__2__rmul__7061,Vvar__3__ropp__7066,Vvar__4__req__7069,Vvar__3__ropp__7066)
           => ( c_24__type__7244___24t(Vvar__0__R__7055,Vvar__1__radd__7056,Vvar__2__rmul__7061,Vvar__3__ropp__7066,Vvar__4__req__7069,Vvar__4__req__7069)
             => ( cCoq_2esetoid__ring_2eRing__theory_2ering__eq__ext___24a5(Vvar__0__R__7055,Vvar__1__radd__7056,Vvar__2__rmul__7061,Vvar__3__ropp__7066,Vvar__4__req__7069)
               => ( cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__7274___24a5(Vvar__0__R__7055,Vvar__1__radd__7056,Vvar__2__rmul__7061,Vvar__3__ropp__7066,Vvar__4__req__7069),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(Vvar__0__R__7055,c_24__type__7298___24a5(Vvar__0__R__7055,Vvar__1__radd__7056,Vvar__2__rmul__7061,Vvar__3__ropp__7066,Vvar__4__req__7069),Vvar__4__req__7069,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(Vvar__0__R__7055,Vvar__0__R__7055,Vvar__4__req__7069,Vvar__4__req__7069)),Vvar__1__radd__7056)
                  & cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__7331___24a5(Vvar__0__R__7055,Vvar__1__radd__7056,Vvar__2__rmul__7061,Vvar__3__ropp__7066,Vvar__4__req__7069),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(Vvar__0__R__7055,c_24__type__7355___24a5(Vvar__0__R__7055,Vvar__1__radd__7056,Vvar__2__rmul__7061,Vvar__3__ropp__7066,Vvar__4__req__7069),Vvar__4__req__7069,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(Vvar__0__R__7055,Vvar__0__R__7055,Vvar__4__req__7069,Vvar__4__req__7069)),Vvar__2__rmul__7061)
                  & cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__7382___24a5(Vvar__0__R__7055,Vvar__1__radd__7056,Vvar__2__rmul__7061,Vvar__3__ropp__7066,Vvar__4__req__7069),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(Vvar__0__R__7055,Vvar__0__R__7055,Vvar__4__req__7069,Vvar__4__req__7069),Vvar__3__ropp__7066)
                  & p(c_24True) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.setoid_ring.Ring_theory.ring_kind',axiom,
    ! [VX28380] :
      ( cCoq_2esetoid__ring_2eRing__theory_2ering__kind___24t(VX28380)
     => ( VX28380 = cCoq_2esetoid__ring_2eRing__theory_2eAbstract
        | ? [Vvar__0__R__28381] :
            ( cType___24t(Vvar__0__R__28381)
            & ? [Vvar__1__req__28382] :
                ( c_24__type__117___24t(Vvar__0__R__28381,Vvar__1__req__28382)
                & ? [Vvar__2__reqb__28387] :
                    ( c_24__type__4310___24t(Vvar__0__R__28381,Vvar__2__reqb__28387)
                    & ! [Vvar__var__3__x__28393__28396] :
                        ( t(Vvar__var__3__x__28393__28396,Vvar__0__R__28381)
                       => ! [Vvar__var__4__y__28394__28397] :
                            ( t(Vvar__var__4__y__28394__28397,Vvar__0__R__28381)
                           => ( happ(happ(Vvar__2__reqb__28387,Vvar__var__3__x__28393__28396),Vvar__var__4__y__28394__28397) = cCoq_2eInit_2eDatatypes_2etrue
                             => p(happ(happ(Vvar__1__req__28382,Vvar__var__3__x__28393__28396),Vvar__var__4__y__28394__28397)) ) ) )
                    & VX28380 = cCoq_2esetoid__ring_2eRing__theory_2eComputational___24a3(Vvar__0__R__28381,Vvar__1__req__28382,Vvar__2__reqb__28387) ) ) )
        | ? [Vvar__0__R__28399] :
            ( cType___24t(Vvar__0__R__28399)
            & ? [Vvar__1__rO__28400] :
                ( t(Vvar__1__rO__28400,Vvar__0__R__28399)
                & ? [Vvar__2__rI__28401] :
                    ( t(Vvar__2__rI__28401,Vvar__0__R__28399)
                    & ? [Vvar__3__radd__28402] :
                        ( c_24__type__3267___24t(Vvar__0__R__28399,Vvar__3__radd__28402)
                        & ? [Vvar__4__rmul__28407] :
                            ( c_24__type__3267___24t(Vvar__0__R__28399,Vvar__4__rmul__28407)
                            & ? [Vvar__5__rsub__28412] :
                                ( c_24__type__3267___24t(Vvar__0__R__28399,Vvar__5__rsub__28412)
                                & ? [Vvar__6__ropp__28417] :
                                    ( c_24__type__3276___24t(Vvar__0__R__28399,Vvar__6__ropp__28417)
                                    & ? [Vvar__7__req__28420] :
                                        ( c_24__type__117___24t(Vvar__0__R__28399,Vvar__7__req__28420)
                                        & ? [Vvar__8__C__28425] :
                                            ( cType___24t(Vvar__8__C__28425)
                                            & ? [Vvar__9__cO__28426] :
                                                ( t(Vvar__9__cO__28426,Vvar__8__C__28425)
                                                & ? [Vvar__10__cI__28427] :
                                                    ( t(Vvar__10__cI__28427,Vvar__8__C__28425)
                                                    & ? [Vvar__11__cadd__28428] :
                                                        ( c_24__type__4334___24t(Vvar__0__R__28399,Vvar__8__C__28425,Vvar__11__cadd__28428)
                                                        & ? [Vvar__12__cmul__28433] :
                                                            ( c_24__type__4334___24t(Vvar__0__R__28399,Vvar__8__C__28425,Vvar__12__cmul__28433)
                                                            & ? [Vvar__13__csub__28438] :
                                                                ( c_24__type__4334___24t(Vvar__0__R__28399,Vvar__8__C__28425,Vvar__13__csub__28438)
                                                                & ? [Vvar__14__copp__28443] :
                                                                    ( c_24__type__4348___24t(Vvar__0__R__28399,Vvar__8__C__28425,Vvar__14__copp__28443)
                                                                    & ? [Vvar__15__ceqb__28446] :
                                                                        ( c_24__type__4355___24t(Vvar__0__R__28399,Vvar__8__C__28425,Vvar__15__ceqb__28446)
                                                                        & ? [Vvar__16__phi__28451] :
                                                                            ( c_24__type__3928___24t(Vvar__0__R__28399,Vvar__8__C__28425,Vvar__16__phi__28451)
                                                                            & cCoq_2esetoid__ring_2eRing__theory_2ering__morph___24a17(Vvar__0__R__28399,Vvar__1__rO__28400,Vvar__2__rI__28401,Vvar__3__radd__28402,Vvar__4__rmul__28407,Vvar__5__rsub__28412,Vvar__6__ropp__28417,Vvar__7__req__28420,Vvar__8__C__28425,Vvar__9__cO__28426,Vvar__10__cI__28427,Vvar__11__cadd__28428,Vvar__12__cmul__28433,Vvar__13__csub__28438,Vvar__14__copp__28443,Vvar__15__ceqb__28446,Vvar__16__phi__28451)
                                                                            & VX28380 = cCoq_2esetoid__ring_2eRing__theory_2eMorphism___24a17(Vvar__0__R__28399,Vvar__1__rO__28400,Vvar__2__rI__28401,Vvar__3__radd__28402,Vvar__4__rmul__28407,Vvar__5__rsub__28412,Vvar__6__ropp__28417,Vvar__7__req__28420,Vvar__8__C__28425,Vvar__9__cO__28426,Vvar__10__cI__28427,Vvar__11__cadd__28428,Vvar__12__cmul__28433,Vvar__13__csub__28438,Vvar__14__copp__28443,Vvar__15__ceqb__28446,Vvar__16__phi__28451) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.setoid_ring.Ring_theory.ring_morph',axiom,
    ! [Vvar__0__R__7385,Vvar__1__rO__7386,Vvar__2__rI__7387,Vvar__3__radd__7388,Vvar__4__rmul__7393,Vvar__5__rsub__7398,Vvar__6__ropp__7403,Vvar__7__req__7406,Vvar__8__C__7411,Vvar__9__cO__7412,Vvar__10__cI__7413,Vvar__11__cadd__7414,Vvar__12__cmul__7419,Vvar__13__csub__7424,Vvar__14__copp__7429,Vvar__15__ceqb__7432,Vvar__16__phi__7437] :
      ( cType___24t(Vvar__0__R__7385)
     => ( t(Vvar__1__rO__7386,Vvar__0__R__7385)
       => ( t(Vvar__2__rI__7387,Vvar__0__R__7385)
         => ( c_24__type__7781___24t(Vvar__0__R__7385,Vvar__1__rO__7386,Vvar__2__rI__7387,Vvar__3__radd__7388,Vvar__4__rmul__7393,Vvar__5__rsub__7398,Vvar__6__ropp__7403,Vvar__7__req__7406,Vvar__8__C__7411,Vvar__9__cO__7412,Vvar__10__cI__7413,Vvar__11__cadd__7414,Vvar__12__cmul__7419,Vvar__13__csub__7424,Vvar__14__copp__7429,Vvar__15__ceqb__7432,Vvar__16__phi__7437,Vvar__3__radd__7388)
           => ( c_24__type__7994___24t(Vvar__0__R__7385,Vvar__1__rO__7386,Vvar__2__rI__7387,Vvar__3__radd__7388,Vvar__4__rmul__7393,Vvar__5__rsub__7398,Vvar__6__ropp__7403,Vvar__7__req__7406,Vvar__8__C__7411,Vvar__9__cO__7412,Vvar__10__cI__7413,Vvar__11__cadd__7414,Vvar__12__cmul__7419,Vvar__13__csub__7424,Vvar__14__copp__7429,Vvar__15__ceqb__7432,Vvar__16__phi__7437,Vvar__4__rmul__7393)
             => ( c_24__type__8207___24t(Vvar__0__R__7385,Vvar__1__rO__7386,Vvar__2__rI__7387,Vvar__3__radd__7388,Vvar__4__rmul__7393,Vvar__5__rsub__7398,Vvar__6__ropp__7403,Vvar__7__req__7406,Vvar__8__C__7411,Vvar__9__cO__7412,Vvar__10__cI__7413,Vvar__11__cadd__7414,Vvar__12__cmul__7419,Vvar__13__csub__7424,Vvar__14__copp__7429,Vvar__15__ceqb__7432,Vvar__16__phi__7437,Vvar__5__rsub__7398)
               => ( c_24__type__8402___24t(Vvar__0__R__7385,Vvar__1__rO__7386,Vvar__2__rI__7387,Vvar__3__radd__7388,Vvar__4__rmul__7393,Vvar__5__rsub__7398,Vvar__6__ropp__7403,Vvar__7__req__7406,Vvar__8__C__7411,Vvar__9__cO__7412,Vvar__10__cI__7413,Vvar__11__cadd__7414,Vvar__12__cmul__7419,Vvar__13__csub__7424,Vvar__14__copp__7429,Vvar__15__ceqb__7432,Vvar__16__phi__7437,Vvar__6__ropp__7403)
                 => ( c_24__type__8615___24t(Vvar__0__R__7385,Vvar__1__rO__7386,Vvar__2__rI__7387,Vvar__3__radd__7388,Vvar__4__rmul__7393,Vvar__5__rsub__7398,Vvar__6__ropp__7403,Vvar__7__req__7406,Vvar__8__C__7411,Vvar__9__cO__7412,Vvar__10__cI__7413,Vvar__11__cadd__7414,Vvar__12__cmul__7419,Vvar__13__csub__7424,Vvar__14__copp__7429,Vvar__15__ceqb__7432,Vvar__16__phi__7437,Vvar__7__req__7406)
                   => ( cType___24t(Vvar__8__C__7411)
                     => ( t(Vvar__9__cO__7412,Vvar__8__C__7411)
                       => ( t(Vvar__10__cI__7413,Vvar__8__C__7411)
                         => ( c_24__type__8828___24t(Vvar__0__R__7385,Vvar__1__rO__7386,Vvar__2__rI__7387,Vvar__3__radd__7388,Vvar__4__rmul__7393,Vvar__5__rsub__7398,Vvar__6__ropp__7403,Vvar__7__req__7406,Vvar__8__C__7411,Vvar__9__cO__7412,Vvar__10__cI__7413,Vvar__11__cadd__7414,Vvar__12__cmul__7419,Vvar__13__csub__7424,Vvar__14__copp__7429,Vvar__15__ceqb__7432,Vvar__16__phi__7437,Vvar__11__cadd__7414)
                           => ( c_24__type__9041___24t(Vvar__0__R__7385,Vvar__1__rO__7386,Vvar__2__rI__7387,Vvar__3__radd__7388,Vvar__4__rmul__7393,Vvar__5__rsub__7398,Vvar__6__ropp__7403,Vvar__7__req__7406,Vvar__8__C__7411,Vvar__9__cO__7412,Vvar__10__cI__7413,Vvar__11__cadd__7414,Vvar__12__cmul__7419,Vvar__13__csub__7424,Vvar__14__copp__7429,Vvar__15__ceqb__7432,Vvar__16__phi__7437,Vvar__12__cmul__7419)
                             => ( c_24__type__9254___24t(Vvar__0__R__7385,Vvar__1__rO__7386,Vvar__2__rI__7387,Vvar__3__radd__7388,Vvar__4__rmul__7393,Vvar__5__rsub__7398,Vvar__6__ropp__7403,Vvar__7__req__7406,Vvar__8__C__7411,Vvar__9__cO__7412,Vvar__10__cI__7413,Vvar__11__cadd__7414,Vvar__12__cmul__7419,Vvar__13__csub__7424,Vvar__14__copp__7429,Vvar__15__ceqb__7432,Vvar__16__phi__7437,Vvar__13__csub__7424)
                               => ( c_24__type__9449___24t(Vvar__0__R__7385,Vvar__1__rO__7386,Vvar__2__rI__7387,Vvar__3__radd__7388,Vvar__4__rmul__7393,Vvar__5__rsub__7398,Vvar__6__ropp__7403,Vvar__7__req__7406,Vvar__8__C__7411,Vvar__9__cO__7412,Vvar__10__cI__7413,Vvar__11__cadd__7414,Vvar__12__cmul__7419,Vvar__13__csub__7424,Vvar__14__copp__7429,Vvar__15__ceqb__7432,Vvar__16__phi__7437,Vvar__14__copp__7429)
                                 => ( c_24__type__9662___24t(Vvar__0__R__7385,Vvar__1__rO__7386,Vvar__2__rI__7387,Vvar__3__radd__7388,Vvar__4__rmul__7393,Vvar__5__rsub__7398,Vvar__6__ropp__7403,Vvar__7__req__7406,Vvar__8__C__7411,Vvar__9__cO__7412,Vvar__10__cI__7413,Vvar__11__cadd__7414,Vvar__12__cmul__7419,Vvar__13__csub__7424,Vvar__14__copp__7429,Vvar__15__ceqb__7432,Vvar__16__phi__7437,Vvar__15__ceqb__7432)
                                   => ( c_24__type__9857___24t(Vvar__0__R__7385,Vvar__1__rO__7386,Vvar__2__rI__7387,Vvar__3__radd__7388,Vvar__4__rmul__7393,Vvar__5__rsub__7398,Vvar__6__ropp__7403,Vvar__7__req__7406,Vvar__8__C__7411,Vvar__9__cO__7412,Vvar__10__cI__7413,Vvar__11__cadd__7414,Vvar__12__cmul__7419,Vvar__13__csub__7424,Vvar__14__copp__7429,Vvar__15__ceqb__7432,Vvar__16__phi__7437,Vvar__16__phi__7437)
                                     => ( cCoq_2esetoid__ring_2eRing__theory_2ering__morph___24a17(Vvar__0__R__7385,Vvar__1__rO__7386,Vvar__2__rI__7387,Vvar__3__radd__7388,Vvar__4__rmul__7393,Vvar__5__rsub__7398,Vvar__6__ropp__7403,Vvar__7__req__7406,Vvar__8__C__7411,Vvar__9__cO__7412,Vvar__10__cI__7413,Vvar__11__cadd__7414,Vvar__12__cmul__7419,Vvar__13__csub__7424,Vvar__14__copp__7429,Vvar__15__ceqb__7432,Vvar__16__phi__7437)
                                       => ( p(happ(happ(Vvar__7__req__7406,happ(Vvar__16__phi__7437,Vvar__9__cO__7412)),Vvar__1__rO__7386))
                                          & p(happ(happ(Vvar__7__req__7406,happ(Vvar__16__phi__7437,Vvar__10__cI__7413)),Vvar__2__rI__7387))
                                          & ! [Vvar__var__var__var__var__var__var__19__x__7499__7501__7523__7525__7527__7529__7531] :
                                              ( t(Vvar__var__var__var__var__var__var__19__x__7499__7501__7523__7525__7527__7529__7531,Vvar__8__C__7411)
                                             => ! [Vvar__var__var__var__var__var__var__20__y__7500__7502__7524__7526__7528__7530__7532] :
                                                  ( t(Vvar__var__var__var__var__var__var__20__y__7500__7502__7524__7526__7528__7530__7532,Vvar__8__C__7411)
                                                 => p(happ(happ(Vvar__7__req__7406,happ(Vvar__16__phi__7437,happ(happ(Vvar__11__cadd__7414,Vvar__var__var__var__var__var__var__19__x__7499__7501__7523__7525__7527__7529__7531),Vvar__var__var__var__var__var__var__20__y__7500__7502__7524__7526__7528__7530__7532))),happ(happ(Vvar__3__radd__7388,happ(Vvar__16__phi__7437,Vvar__var__var__var__var__var__var__19__x__7499__7501__7523__7525__7527__7529__7531)),happ(Vvar__16__phi__7437,Vvar__var__var__var__var__var__var__20__y__7500__7502__7524__7526__7528__7530__7532)))) ) )
                                          & ! [Vvar__var__var__var__var__var__var__20__x__7504__7506__7533__7535__7537__7539__7541] :
                                              ( t(Vvar__var__var__var__var__var__var__20__x__7504__7506__7533__7535__7537__7539__7541,Vvar__8__C__7411)
                                             => ! [Vvar__var__var__var__var__var__var__21__y__7505__7507__7534__7536__7538__7540__7542] :
                                                  ( t(Vvar__var__var__var__var__var__var__21__y__7505__7507__7534__7536__7538__7540__7542,Vvar__8__C__7411)
                                                 => p(happ(happ(Vvar__7__req__7406,happ(Vvar__16__phi__7437,happ(happ(Vvar__13__csub__7424,Vvar__var__var__var__var__var__var__20__x__7504__7506__7533__7535__7537__7539__7541),Vvar__var__var__var__var__var__var__21__y__7505__7507__7534__7536__7538__7540__7542))),happ(happ(Vvar__5__rsub__7398,happ(Vvar__16__phi__7437,Vvar__var__var__var__var__var__var__20__x__7504__7506__7533__7535__7537__7539__7541)),happ(Vvar__16__phi__7437,Vvar__var__var__var__var__var__var__21__y__7505__7507__7534__7536__7538__7540__7542)))) ) )
                                          & ! [Vvar__var__var__var__var__var__var__21__x__7509__7511__7543__7545__7547__7549__7551] :
                                              ( t(Vvar__var__var__var__var__var__var__21__x__7509__7511__7543__7545__7547__7549__7551,Vvar__8__C__7411)
                                             => ! [Vvar__var__var__var__var__var__var__22__y__7510__7512__7544__7546__7548__7550__7552] :
                                                  ( t(Vvar__var__var__var__var__var__var__22__y__7510__7512__7544__7546__7548__7550__7552,Vvar__8__C__7411)
                                                 => p(happ(happ(Vvar__7__req__7406,happ(Vvar__16__phi__7437,happ(happ(Vvar__12__cmul__7419,Vvar__var__var__var__var__var__var__21__x__7509__7511__7543__7545__7547__7549__7551),Vvar__var__var__var__var__var__var__22__y__7510__7512__7544__7546__7548__7550__7552))),happ(happ(Vvar__4__rmul__7393,happ(Vvar__16__phi__7437,Vvar__var__var__var__var__var__var__21__x__7509__7511__7543__7545__7547__7549__7551)),happ(Vvar__16__phi__7437,Vvar__var__var__var__var__var__var__22__y__7510__7512__7544__7546__7548__7550__7552)))) ) )
                                          & ! [Vvar__var__var__var__var__var__var__22__x__7514__7515__7553__7554__7555__7556__7557] :
                                              ( t(Vvar__var__var__var__var__var__var__22__x__7514__7515__7553__7554__7555__7556__7557,Vvar__8__C__7411)
                                             => p(happ(happ(Vvar__7__req__7406,happ(Vvar__16__phi__7437,happ(Vvar__14__copp__7429,Vvar__var__var__var__var__var__var__22__x__7514__7515__7553__7554__7555__7556__7557))),happ(Vvar__6__ropp__7403,happ(Vvar__16__phi__7437,Vvar__var__var__var__var__var__var__22__x__7514__7515__7553__7554__7555__7556__7557)))) )
                                          & ! [Vvar__var__var__var__var__var__23__x__7517__7520__7558__7561__7564__7567] :
                                              ( t(Vvar__var__var__var__var__var__23__x__7517__7520__7558__7561__7564__7567,Vvar__8__C__7411)
                                             => ! [Vvar__var__var__var__var__var__24__y__7518__7521__7559__7562__7565__7568] :
                                                  ( t(Vvar__var__var__var__var__var__24__y__7518__7521__7559__7562__7565__7568,Vvar__8__C__7411)
                                                 => ( happ(happ(Vvar__15__ceqb__7432,Vvar__var__var__var__var__var__23__x__7517__7520__7558__7561__7564__7567),Vvar__var__var__var__var__var__24__y__7518__7521__7559__7562__7565__7568) = cCoq_2eInit_2eDatatypes_2etrue
                                                   => p(happ(happ(Vvar__7__req__7406,happ(Vvar__16__phi__7437,Vvar__var__var__var__var__var__23__x__7517__7520__7558__7561__7564__7567)),happ(Vvar__16__phi__7437,Vvar__var__var__var__var__var__24__y__7518__7521__7559__7562__7565__7568))) ) ) )
                                          & p(c_24True) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.setoid_ring.Ring_theory.ring_theory',axiom,
    ! [Vvar__0__R__25486,Vvar__1__rO__25487,Vvar__2__rI__25488,Vvar__3__radd__25489,Vvar__4__rmul__25494,Vvar__5__rsub__25499,Vvar__6__ropp__25504,Vvar__7__req__25507] :
      ( cType___24t(Vvar__0__R__25486)
     => ( t(Vvar__1__rO__25487,Vvar__0__R__25486)
       => ( t(Vvar__2__rI__25488,Vvar__0__R__25486)
         => ( c_24__type__25710___24t(Vvar__0__R__25486,Vvar__1__rO__25487,Vvar__2__rI__25488,Vvar__3__radd__25489,Vvar__4__rmul__25494,Vvar__5__rsub__25499,Vvar__6__ropp__25504,Vvar__7__req__25507,Vvar__3__radd__25489)
           => ( c_24__type__25773___24t(Vvar__0__R__25486,Vvar__1__rO__25487,Vvar__2__rI__25488,Vvar__3__radd__25489,Vvar__4__rmul__25494,Vvar__5__rsub__25499,Vvar__6__ropp__25504,Vvar__7__req__25507,Vvar__4__rmul__25494)
             => ( c_24__type__25836___24t(Vvar__0__R__25486,Vvar__1__rO__25487,Vvar__2__rI__25488,Vvar__3__radd__25489,Vvar__4__rmul__25494,Vvar__5__rsub__25499,Vvar__6__ropp__25504,Vvar__7__req__25507,Vvar__5__rsub__25499)
               => ( c_24__type__25890___24t(Vvar__0__R__25486,Vvar__1__rO__25487,Vvar__2__rI__25488,Vvar__3__radd__25489,Vvar__4__rmul__25494,Vvar__5__rsub__25499,Vvar__6__ropp__25504,Vvar__7__req__25507,Vvar__6__ropp__25504)
                 => ( c_24__type__25953___24t(Vvar__0__R__25486,Vvar__1__rO__25487,Vvar__2__rI__25488,Vvar__3__radd__25489,Vvar__4__rmul__25494,Vvar__5__rsub__25499,Vvar__6__ropp__25504,Vvar__7__req__25507,Vvar__7__req__25507)
                   => ( cCoq_2esetoid__ring_2eRing__theory_2ering__theory___24a8(Vvar__0__R__25486,Vvar__1__rO__25487,Vvar__2__rI__25488,Vvar__3__radd__25489,Vvar__4__rmul__25494,Vvar__5__rsub__25499,Vvar__6__ropp__25504,Vvar__7__req__25507)
                     => ( ! [Vvar__var__var__var__var__var__8__x__25540__25541__25584__25585__25586__25587] :
                            ( t(Vvar__var__var__var__var__var__8__x__25540__25541__25584__25585__25586__25587,Vvar__0__R__25486)
                           => p(happ(happ(Vvar__7__req__25507,happ(happ(Vvar__3__radd__25489,Vvar__1__rO__25487),Vvar__var__var__var__var__var__8__x__25540__25541__25584__25585__25586__25587)),Vvar__var__var__var__var__var__8__x__25540__25541__25584__25585__25586__25587)) )
                        & ! [Vvar__var__var__var__var__9__x__25543__25545__25588__25590__25592] :
                            ( t(Vvar__var__var__var__var__9__x__25543__25545__25588__25590__25592,Vvar__0__R__25486)
                           => ! [Vvar__var__var__var__var__10__y__25544__25546__25589__25591__25593] :
                                ( t(Vvar__var__var__var__var__10__y__25544__25546__25589__25591__25593,Vvar__0__R__25486)
                               => p(happ(happ(Vvar__7__req__25507,happ(happ(Vvar__3__radd__25489,Vvar__var__var__var__var__9__x__25543__25545__25588__25590__25592),Vvar__var__var__var__var__10__y__25544__25546__25589__25591__25593)),happ(happ(Vvar__3__radd__25489,Vvar__var__var__var__var__10__y__25544__25546__25589__25591__25593),Vvar__var__var__var__var__9__x__25543__25545__25588__25590__25592))) ) )
                        & ! [Vvar__var__var__var__var__10__x__25548__25551__25594__25597__25600] :
                            ( t(Vvar__var__var__var__var__10__x__25548__25551__25594__25597__25600,Vvar__0__R__25486)
                           => ! [Vvar__var__var__var__var__11__y__25549__25552__25595__25598__25601] :
                                ( t(Vvar__var__var__var__var__11__y__25549__25552__25595__25598__25601,Vvar__0__R__25486)
                               => ! [Vvar__var__var__var__var__12__z__25550__25553__25596__25599__25602] :
                                    ( t(Vvar__var__var__var__var__12__z__25550__25553__25596__25599__25602,Vvar__0__R__25486)
                                   => p(happ(happ(Vvar__7__req__25507,happ(happ(Vvar__3__radd__25489,Vvar__var__var__var__var__10__x__25548__25551__25594__25597__25600),happ(happ(Vvar__3__radd__25489,Vvar__var__var__var__var__11__y__25549__25552__25595__25598__25601),Vvar__var__var__var__var__12__z__25550__25553__25596__25599__25602))),happ(happ(Vvar__3__radd__25489,happ(happ(Vvar__3__radd__25489,Vvar__var__var__var__var__10__x__25548__25551__25594__25597__25600),Vvar__var__var__var__var__11__y__25549__25552__25595__25598__25601)),Vvar__var__var__var__var__12__z__25550__25553__25596__25599__25602))) ) ) )
                        & ! [Vvar__var__var__var__var__var__11__x__25555__25556__25603__25604__25605__25606] :
                            ( t(Vvar__var__var__var__var__var__11__x__25555__25556__25603__25604__25605__25606,Vvar__0__R__25486)
                           => p(happ(happ(Vvar__7__req__25507,happ(happ(Vvar__4__rmul__25494,Vvar__2__rI__25488),Vvar__var__var__var__var__var__11__x__25555__25556__25603__25604__25605__25606)),Vvar__var__var__var__var__var__11__x__25555__25556__25603__25604__25605__25606)) )
                        & ! [Vvar__var__var__var__var__12__x__25558__25560__25607__25609__25611] :
                            ( t(Vvar__var__var__var__var__12__x__25558__25560__25607__25609__25611,Vvar__0__R__25486)
                           => ! [Vvar__var__var__var__var__13__y__25559__25561__25608__25610__25612] :
                                ( t(Vvar__var__var__var__var__13__y__25559__25561__25608__25610__25612,Vvar__0__R__25486)
                               => p(happ(happ(Vvar__7__req__25507,happ(happ(Vvar__4__rmul__25494,Vvar__var__var__var__var__12__x__25558__25560__25607__25609__25611),Vvar__var__var__var__var__13__y__25559__25561__25608__25610__25612)),happ(happ(Vvar__4__rmul__25494,Vvar__var__var__var__var__13__y__25559__25561__25608__25610__25612),Vvar__var__var__var__var__12__x__25558__25560__25607__25609__25611))) ) )
                        & ! [Vvar__var__var__var__var__13__x__25563__25566__25613__25616__25619] :
                            ( t(Vvar__var__var__var__var__13__x__25563__25566__25613__25616__25619,Vvar__0__R__25486)
                           => ! [Vvar__var__var__var__var__14__y__25564__25567__25614__25617__25620] :
                                ( t(Vvar__var__var__var__var__14__y__25564__25567__25614__25617__25620,Vvar__0__R__25486)
                               => ! [Vvar__var__var__var__var__15__z__25565__25568__25615__25618__25621] :
                                    ( t(Vvar__var__var__var__var__15__z__25565__25568__25615__25618__25621,Vvar__0__R__25486)
                                   => p(happ(happ(Vvar__7__req__25507,happ(happ(Vvar__4__rmul__25494,Vvar__var__var__var__var__13__x__25563__25566__25613__25616__25619),happ(happ(Vvar__4__rmul__25494,Vvar__var__var__var__var__14__y__25564__25567__25614__25617__25620),Vvar__var__var__var__var__15__z__25565__25568__25615__25618__25621))),happ(happ(Vvar__4__rmul__25494,happ(happ(Vvar__4__rmul__25494,Vvar__var__var__var__var__13__x__25563__25566__25613__25616__25619),Vvar__var__var__var__var__14__y__25564__25567__25614__25617__25620)),Vvar__var__var__var__var__15__z__25565__25568__25615__25618__25621))) ) ) )
                        & ! [Vvar__var__var__var__var__var__14__x__25570__25573__25622__25625__25628__25631] :
                            ( t(Vvar__var__var__var__var__var__14__x__25570__25573__25622__25625__25628__25631,Vvar__0__R__25486)
                           => ! [Vvar__var__var__var__var__var__15__y__25571__25574__25623__25626__25629__25632] :
                                ( t(Vvar__var__var__var__var__var__15__y__25571__25574__25623__25626__25629__25632,Vvar__0__R__25486)
                               => ! [Vvar__var__var__var__var__var__16__z__25572__25575__25624__25627__25630__25633] :
                                    ( t(Vvar__var__var__var__var__var__16__z__25572__25575__25624__25627__25630__25633,Vvar__0__R__25486)
                                   => p(happ(happ(Vvar__7__req__25507,happ(happ(Vvar__4__rmul__25494,happ(happ(Vvar__3__radd__25489,Vvar__var__var__var__var__var__14__x__25570__25573__25622__25625__25628__25631),Vvar__var__var__var__var__var__15__y__25571__25574__25623__25626__25629__25632)),Vvar__var__var__var__var__var__16__z__25572__25575__25624__25627__25630__25633)),happ(happ(Vvar__3__radd__25489,happ(happ(Vvar__4__rmul__25494,Vvar__var__var__var__var__var__14__x__25570__25573__25622__25625__25628__25631),Vvar__var__var__var__var__var__16__z__25572__25575__25624__25627__25630__25633)),happ(happ(Vvar__4__rmul__25494,Vvar__var__var__var__var__var__15__y__25571__25574__25623__25626__25629__25632),Vvar__var__var__var__var__var__16__z__25572__25575__25624__25627__25630__25633)))) ) ) )
                        & ! [Vvar__var__var__var__var__var__var__15__x__25577__25579__25634__25636__25638__25640__25642] :
                            ( t(Vvar__var__var__var__var__var__var__15__x__25577__25579__25634__25636__25638__25640__25642,Vvar__0__R__25486)
                           => ! [Vvar__var__var__var__var__var__var__16__y__25578__25580__25635__25637__25639__25641__25643] :
                                ( t(Vvar__var__var__var__var__var__var__16__y__25578__25580__25635__25637__25639__25641__25643,Vvar__0__R__25486)
                               => p(happ(happ(Vvar__7__req__25507,happ(happ(Vvar__5__rsub__25499,Vvar__var__var__var__var__var__var__15__x__25577__25579__25634__25636__25638__25640__25642),Vvar__var__var__var__var__var__var__16__y__25578__25580__25635__25637__25639__25641__25643)),happ(happ(Vvar__3__radd__25489,Vvar__var__var__var__var__var__var__15__x__25577__25579__25634__25636__25638__25640__25642),happ(Vvar__6__ropp__25504,Vvar__var__var__var__var__var__var__16__y__25578__25580__25635__25637__25639__25641__25643)))) ) )
                        & ! [Vvar__var__var__var__var__var__var__16__x__25582__25583__25644__25645__25646__25647__25648] :
                            ( t(Vvar__var__var__var__var__var__var__16__x__25582__25583__25644__25645__25646__25647__25648,Vvar__0__R__25486)
                           => p(happ(happ(Vvar__7__req__25507,happ(happ(Vvar__3__radd__25489,Vvar__var__var__var__var__var__var__16__x__25582__25583__25644__25645__25646__25647__25648),happ(Vvar__6__ropp__25504,Vvar__var__var__var__var__var__var__16__x__25582__25583__25644__25645__25646__25647__25648))),Vvar__1__rO__25487)) )
                        & p(c_24True) ) ) ) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.setoid_ring.Ring_theory.semi_morph',axiom,
    ! [Vvar__0__R__27382,Vvar__1__rO__27383,Vvar__2__rI__27384,Vvar__3__radd__27385,Vvar__4__rmul__27390,Vvar__5__req__27395,Vvar__6__C__27400,Vvar__7__cO__27401,Vvar__8__cI__27402,Vvar__9__cadd__27403,Vvar__10__cmul__27408,Vvar__11__ceqb__27413,Vvar__12__phi__27418] :
      ( cType___24t(Vvar__0__R__27382)
     => ( t(Vvar__1__rO__27383,Vvar__0__R__27382)
       => ( t(Vvar__2__rI__27384,Vvar__0__R__27382)
         => ( c_24__type__27635___24t(Vvar__0__R__27382,Vvar__1__rO__27383,Vvar__2__rI__27384,Vvar__3__radd__27385,Vvar__4__rmul__27390,Vvar__5__req__27395,Vvar__6__C__27400,Vvar__7__cO__27401,Vvar__8__cI__27402,Vvar__9__cadd__27403,Vvar__10__cmul__27408,Vvar__11__ceqb__27413,Vvar__12__phi__27418,Vvar__3__radd__27385)
           => ( c_24__type__27760___24t(Vvar__0__R__27382,Vvar__1__rO__27383,Vvar__2__rI__27384,Vvar__3__radd__27385,Vvar__4__rmul__27390,Vvar__5__req__27395,Vvar__6__C__27400,Vvar__7__cO__27401,Vvar__8__cI__27402,Vvar__9__cadd__27403,Vvar__10__cmul__27408,Vvar__11__ceqb__27413,Vvar__12__phi__27418,Vvar__4__rmul__27390)
             => ( c_24__type__27885___24t(Vvar__0__R__27382,Vvar__1__rO__27383,Vvar__2__rI__27384,Vvar__3__radd__27385,Vvar__4__rmul__27390,Vvar__5__req__27395,Vvar__6__C__27400,Vvar__7__cO__27401,Vvar__8__cI__27402,Vvar__9__cadd__27403,Vvar__10__cmul__27408,Vvar__11__ceqb__27413,Vvar__12__phi__27418,Vvar__5__req__27395)
               => ( cType___24t(Vvar__6__C__27400)
                 => ( t(Vvar__7__cO__27401,Vvar__6__C__27400)
                   => ( t(Vvar__8__cI__27402,Vvar__6__C__27400)
                     => ( c_24__type__28010___24t(Vvar__0__R__27382,Vvar__1__rO__27383,Vvar__2__rI__27384,Vvar__3__radd__27385,Vvar__4__rmul__27390,Vvar__5__req__27395,Vvar__6__C__27400,Vvar__7__cO__27401,Vvar__8__cI__27402,Vvar__9__cadd__27403,Vvar__10__cmul__27408,Vvar__11__ceqb__27413,Vvar__12__phi__27418,Vvar__9__cadd__27403)
                       => ( c_24__type__28135___24t(Vvar__0__R__27382,Vvar__1__rO__27383,Vvar__2__rI__27384,Vvar__3__radd__27385,Vvar__4__rmul__27390,Vvar__5__req__27395,Vvar__6__C__27400,Vvar__7__cO__27401,Vvar__8__cI__27402,Vvar__9__cadd__27403,Vvar__10__cmul__27408,Vvar__11__ceqb__27413,Vvar__12__phi__27418,Vvar__10__cmul__27408)
                         => ( c_24__type__28260___24t(Vvar__0__R__27382,Vvar__1__rO__27383,Vvar__2__rI__27384,Vvar__3__radd__27385,Vvar__4__rmul__27390,Vvar__5__req__27395,Vvar__6__C__27400,Vvar__7__cO__27401,Vvar__8__cI__27402,Vvar__9__cadd__27403,Vvar__10__cmul__27408,Vvar__11__ceqb__27413,Vvar__12__phi__27418,Vvar__11__ceqb__27413)
                           => ( c_24__type__28371___24t(Vvar__0__R__27382,Vvar__1__rO__27383,Vvar__2__rI__27384,Vvar__3__radd__27385,Vvar__4__rmul__27390,Vvar__5__req__27395,Vvar__6__C__27400,Vvar__7__cO__27401,Vvar__8__cI__27402,Vvar__9__cadd__27403,Vvar__10__cmul__27408,Vvar__11__ceqb__27413,Vvar__12__phi__27418,Vvar__12__phi__27418)
                             => ( cCoq_2esetoid__ring_2eRing__theory_2esemi__morph___24a13(Vvar__0__R__27382,Vvar__1__rO__27383,Vvar__2__rI__27384,Vvar__3__radd__27385,Vvar__4__rmul__27390,Vvar__5__req__27395,Vvar__6__C__27400,Vvar__7__cO__27401,Vvar__8__cI__27402,Vvar__9__cadd__27403,Vvar__10__cmul__27408,Vvar__11__ceqb__27413,Vvar__12__phi__27418)
                               => ( p(happ(happ(Vvar__5__req__27395,happ(Vvar__12__phi__27418,Vvar__7__cO__27401)),Vvar__1__rO__27383))
                                  & p(happ(happ(Vvar__5__req__27395,happ(Vvar__12__phi__27418,Vvar__8__cI__27402)),Vvar__2__rI__27384))
                                  & ! [Vvar__var__var__var__var__var__var__15__x__27464__27466__27480__27482__27484__27486__27488] :
                                      ( t(Vvar__var__var__var__var__var__var__15__x__27464__27466__27480__27482__27484__27486__27488,Vvar__6__C__27400)
                                     => ! [Vvar__var__var__var__var__var__var__16__y__27465__27467__27481__27483__27485__27487__27489] :
                                          ( t(Vvar__var__var__var__var__var__var__16__y__27465__27467__27481__27483__27485__27487__27489,Vvar__6__C__27400)
                                         => p(happ(happ(Vvar__5__req__27395,happ(Vvar__12__phi__27418,happ(happ(Vvar__9__cadd__27403,Vvar__var__var__var__var__var__var__15__x__27464__27466__27480__27482__27484__27486__27488),Vvar__var__var__var__var__var__var__16__y__27465__27467__27481__27483__27485__27487__27489))),happ(happ(Vvar__3__radd__27385,happ(Vvar__12__phi__27418,Vvar__var__var__var__var__var__var__15__x__27464__27466__27480__27482__27484__27486__27488)),happ(Vvar__12__phi__27418,Vvar__var__var__var__var__var__var__16__y__27465__27467__27481__27483__27485__27487__27489)))) ) )
                                  & ! [Vvar__var__var__var__var__var__var__16__x__27469__27471__27490__27492__27494__27496__27498] :
                                      ( t(Vvar__var__var__var__var__var__var__16__x__27469__27471__27490__27492__27494__27496__27498,Vvar__6__C__27400)
                                     => ! [Vvar__var__var__var__var__var__var__17__y__27470__27472__27491__27493__27495__27497__27499] :
                                          ( t(Vvar__var__var__var__var__var__var__17__y__27470__27472__27491__27493__27495__27497__27499,Vvar__6__C__27400)
                                         => p(happ(happ(Vvar__5__req__27395,happ(Vvar__12__phi__27418,happ(happ(Vvar__10__cmul__27408,Vvar__var__var__var__var__var__var__16__x__27469__27471__27490__27492__27494__27496__27498),Vvar__var__var__var__var__var__var__17__y__27470__27472__27491__27493__27495__27497__27499))),happ(happ(Vvar__4__rmul__27390,happ(Vvar__12__phi__27418,Vvar__var__var__var__var__var__var__16__x__27469__27471__27490__27492__27494__27496__27498)),happ(Vvar__12__phi__27418,Vvar__var__var__var__var__var__var__17__y__27470__27472__27491__27493__27495__27497__27499)))) ) )
                                  & ! [Vvar__var__var__var__var__var__17__x__27474__27477__27500__27503__27506__27509] :
                                      ( t(Vvar__var__var__var__var__var__17__x__27474__27477__27500__27503__27506__27509,Vvar__6__C__27400)
                                     => ! [Vvar__var__var__var__var__var__18__y__27475__27478__27501__27504__27507__27510] :
                                          ( t(Vvar__var__var__var__var__var__18__y__27475__27478__27501__27504__27507__27510,Vvar__6__C__27400)
                                         => ( happ(happ(Vvar__11__ceqb__27413,Vvar__var__var__var__var__var__17__x__27474__27477__27500__27503__27506__27509),Vvar__var__var__var__var__var__18__y__27475__27478__27501__27504__27507__27510) = cCoq_2eInit_2eDatatypes_2etrue
                                           => p(happ(happ(Vvar__5__req__27395,happ(Vvar__12__phi__27418,Vvar__var__var__var__var__var__17__x__27474__27477__27500__27503__27506__27509)),happ(Vvar__12__phi__27418,Vvar__var__var__var__var__var__18__y__27475__27478__27501__27504__27507__27510))) ) ) )
                                  & p(c_24True) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.setoid_ring.Ring_theory.semi_ring_theory',axiom,
    ! [Vvar__0__R__27118,Vvar__1__rO__27119,Vvar__2__rI__27120,Vvar__3__radd__27121,Vvar__4__rmul__27126,Vvar__5__req__27131] :
      ( cType___24t(Vvar__0__R__27118)
     => ( t(Vvar__1__rO__27119,Vvar__0__R__27118)
       => ( t(Vvar__2__rI__27120,Vvar__0__R__27118)
         => ( c_24__type__27286___24t(Vvar__0__R__27118,Vvar__1__rO__27119,Vvar__2__rI__27120,Vvar__3__radd__27121,Vvar__4__rmul__27126,Vvar__5__req__27131,Vvar__3__radd__27121)
           => ( c_24__type__27325___24t(Vvar__0__R__27118,Vvar__1__rO__27119,Vvar__2__rI__27120,Vvar__3__radd__27121,Vvar__4__rmul__27126,Vvar__5__req__27131,Vvar__4__rmul__27126)
             => ( c_24__type__27364___24t(Vvar__0__R__27118,Vvar__1__rO__27119,Vvar__2__rI__27120,Vvar__3__radd__27121,Vvar__4__rmul__27126,Vvar__5__req__27131,Vvar__5__req__27131)
               => ( cCoq_2esetoid__ring_2eRing__theory_2esemi__ring__theory___24a6(Vvar__0__R__27118,Vvar__1__rO__27119,Vvar__2__rI__27120,Vvar__3__radd__27121,Vvar__4__rmul__27126,Vvar__5__req__27131)
                 => ( ! [Vvar__var__var__var__var__var__6__n__27156__27157__27195__27196__27197__27198] :
                        ( t(Vvar__var__var__var__var__var__6__n__27156__27157__27195__27196__27197__27198,Vvar__0__R__27118)
                       => p(happ(happ(Vvar__5__req__27131,happ(happ(Vvar__3__radd__27121,Vvar__1__rO__27119),Vvar__var__var__var__var__var__6__n__27156__27157__27195__27196__27197__27198)),Vvar__var__var__var__var__var__6__n__27156__27157__27195__27196__27197__27198)) )
                    & ! [Vvar__var__var__var__var__7__n__27159__27161__27199__27201__27203] :
                        ( t(Vvar__var__var__var__var__7__n__27159__27161__27199__27201__27203,Vvar__0__R__27118)
                       => ! [Vvar__var__var__var__var__8__m__27160__27162__27200__27202__27204] :
                            ( t(Vvar__var__var__var__var__8__m__27160__27162__27200__27202__27204,Vvar__0__R__27118)
                           => p(happ(happ(Vvar__5__req__27131,happ(happ(Vvar__3__radd__27121,Vvar__var__var__var__var__7__n__27159__27161__27199__27201__27203),Vvar__var__var__var__var__8__m__27160__27162__27200__27202__27204)),happ(happ(Vvar__3__radd__27121,Vvar__var__var__var__var__8__m__27160__27162__27200__27202__27204),Vvar__var__var__var__var__7__n__27159__27161__27199__27201__27203))) ) )
                    & ! [Vvar__var__var__var__var__8__n__27164__27167__27205__27208__27211] :
                        ( t(Vvar__var__var__var__var__8__n__27164__27167__27205__27208__27211,Vvar__0__R__27118)
                       => ! [Vvar__var__var__var__var__9__m__27165__27168__27206__27209__27212] :
                            ( t(Vvar__var__var__var__var__9__m__27165__27168__27206__27209__27212,Vvar__0__R__27118)
                           => ! [Vvar__var__var__var__var__10__p__27166__27169__27207__27210__27213] :
                                ( t(Vvar__var__var__var__var__10__p__27166__27169__27207__27210__27213,Vvar__0__R__27118)
                               => p(happ(happ(Vvar__5__req__27131,happ(happ(Vvar__3__radd__27121,Vvar__var__var__var__var__8__n__27164__27167__27205__27208__27211),happ(happ(Vvar__3__radd__27121,Vvar__var__var__var__var__9__m__27165__27168__27206__27209__27212),Vvar__var__var__var__var__10__p__27166__27169__27207__27210__27213))),happ(happ(Vvar__3__radd__27121,happ(happ(Vvar__3__radd__27121,Vvar__var__var__var__var__8__n__27164__27167__27205__27208__27211),Vvar__var__var__var__var__9__m__27165__27168__27206__27209__27212)),Vvar__var__var__var__var__10__p__27166__27169__27207__27210__27213))) ) ) )
                    & ! [Vvar__var__var__var__var__var__9__n__27171__27172__27214__27215__27216__27217] :
                        ( t(Vvar__var__var__var__var__var__9__n__27171__27172__27214__27215__27216__27217,Vvar__0__R__27118)
                       => p(happ(happ(Vvar__5__req__27131,happ(happ(Vvar__4__rmul__27126,Vvar__2__rI__27120),Vvar__var__var__var__var__var__9__n__27171__27172__27214__27215__27216__27217)),Vvar__var__var__var__var__var__9__n__27171__27172__27214__27215__27216__27217)) )
                    & ! [Vvar__var__var__var__var__var__10__n__27174__27175__27218__27219__27220__27221] :
                        ( t(Vvar__var__var__var__var__var__10__n__27174__27175__27218__27219__27220__27221,Vvar__0__R__27118)
                       => p(happ(happ(Vvar__5__req__27131,happ(happ(Vvar__4__rmul__27126,Vvar__1__rO__27119),Vvar__var__var__var__var__var__10__n__27174__27175__27218__27219__27220__27221)),Vvar__1__rO__27119)) )
                    & ! [Vvar__var__var__var__var__11__n__27177__27179__27222__27224__27226] :
                        ( t(Vvar__var__var__var__var__11__n__27177__27179__27222__27224__27226,Vvar__0__R__27118)
                       => ! [Vvar__var__var__var__var__12__m__27178__27180__27223__27225__27227] :
                            ( t(Vvar__var__var__var__var__12__m__27178__27180__27223__27225__27227,Vvar__0__R__27118)
                           => p(happ(happ(Vvar__5__req__27131,happ(happ(Vvar__4__rmul__27126,Vvar__var__var__var__var__11__n__27177__27179__27222__27224__27226),Vvar__var__var__var__var__12__m__27178__27180__27223__27225__27227)),happ(happ(Vvar__4__rmul__27126,Vvar__var__var__var__var__12__m__27178__27180__27223__27225__27227),Vvar__var__var__var__var__11__n__27177__27179__27222__27224__27226))) ) )
                    & ! [Vvar__var__var__var__var__12__n__27182__27185__27228__27231__27234] :
                        ( t(Vvar__var__var__var__var__12__n__27182__27185__27228__27231__27234,Vvar__0__R__27118)
                       => ! [Vvar__var__var__var__var__13__m__27183__27186__27229__27232__27235] :
                            ( t(Vvar__var__var__var__var__13__m__27183__27186__27229__27232__27235,Vvar__0__R__27118)
                           => ! [Vvar__var__var__var__var__14__p__27184__27187__27230__27233__27236] :
                                ( t(Vvar__var__var__var__var__14__p__27184__27187__27230__27233__27236,Vvar__0__R__27118)
                               => p(happ(happ(Vvar__5__req__27131,happ(happ(Vvar__4__rmul__27126,Vvar__var__var__var__var__12__n__27182__27185__27228__27231__27234),happ(happ(Vvar__4__rmul__27126,Vvar__var__var__var__var__13__m__27183__27186__27229__27232__27235),Vvar__var__var__var__var__14__p__27184__27187__27230__27233__27236))),happ(happ(Vvar__4__rmul__27126,happ(happ(Vvar__4__rmul__27126,Vvar__var__var__var__var__12__n__27182__27185__27228__27231__27234),Vvar__var__var__var__var__13__m__27183__27186__27229__27232__27235)),Vvar__var__var__var__var__14__p__27184__27187__27230__27233__27236))) ) ) )
                    & ! [Vvar__var__var__var__var__var__13__n__27189__27192__27237__27240__27243__27246] :
                        ( t(Vvar__var__var__var__var__var__13__n__27189__27192__27237__27240__27243__27246,Vvar__0__R__27118)
                       => ! [Vvar__var__var__var__var__var__14__m__27190__27193__27238__27241__27244__27247] :
                            ( t(Vvar__var__var__var__var__var__14__m__27190__27193__27238__27241__27244__27247,Vvar__0__R__27118)
                           => ! [Vvar__var__var__var__var__var__15__p__27191__27194__27239__27242__27245__27248] :
                                ( t(Vvar__var__var__var__var__var__15__p__27191__27194__27239__27242__27245__27248,Vvar__0__R__27118)
                               => p(happ(happ(Vvar__5__req__27131,happ(happ(Vvar__4__rmul__27126,happ(happ(Vvar__3__radd__27121,Vvar__var__var__var__var__var__13__n__27189__27192__27237__27240__27243__27246),Vvar__var__var__var__var__var__14__m__27190__27193__27238__27241__27244__27247)),Vvar__var__var__var__var__var__15__p__27191__27194__27239__27242__27245__27248)),happ(happ(Vvar__3__radd__27121,happ(happ(Vvar__4__rmul__27126,Vvar__var__var__var__var__var__13__n__27189__27192__27237__27240__27243__27246),Vvar__var__var__var__var__var__15__p__27191__27194__27239__27242__27245__27248)),happ(happ(Vvar__4__rmul__27126,Vvar__var__var__var__var__var__14__m__27190__27193__27238__27241__27244__27247),Vvar__var__var__var__var__var__15__p__27191__27194__27239__27242__27245__27248)))) ) ) )
                    & p(c_24True) ) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.setoid_ring.Ring_theory.sign_theory',axiom,
    ! [Vvar__0__C__9943,Vvar__1__copp__9944,Vvar__2__ceqb__9947,Vvar__3__get__sign__9952] :
      ( cType___24t(Vvar__0__C__9943)
     => ( c_24__type__9999___24t(Vvar__0__C__9943,Vvar__1__copp__9944,Vvar__2__ceqb__9947,Vvar__3__get__sign__9952,Vvar__1__copp__9944)
       => ( c_24__type__10018___24t(Vvar__0__C__9943,Vvar__1__copp__9944,Vvar__2__ceqb__9947,Vvar__3__get__sign__9952,Vvar__2__ceqb__9947)
         => ( c_24__type__10032___24t(Vvar__0__C__9943,Vvar__1__copp__9944,Vvar__2__ceqb__9947,Vvar__3__get__sign__9952,Vvar__3__get__sign__9952)
           => ( cCoq_2esetoid__ring_2eRing__theory_2esign__theory___24a4(Vvar__0__C__9943,Vvar__1__copp__9944,Vvar__2__ceqb__9947,Vvar__3__get__sign__9952)
             => ( ! [Vvar__var__var__var__var__var__4__c__9969__9972__9975__9978__9981__9984] :
                    ( t(Vvar__var__var__var__var__var__4__c__9969__9972__9975__9978__9981__9984,Vvar__0__C__9943)
                   => ! [Vvar__var__var__var__var__var__5__c_27__9970__9973__9976__9979__9982__9985] :
                        ( t(Vvar__var__var__var__var__var__5__c_27__9970__9973__9976__9979__9982__9985,Vvar__0__C__9943)
                       => ( happ(Vvar__3__get__sign__9952,Vvar__var__var__var__var__var__4__c__9969__9972__9975__9978__9981__9984) = cCoq_2eInit_2eDatatypes_2eSome___24a2(Vvar__0__C__9943,Vvar__var__var__var__var__var__5__c_27__9970__9973__9976__9979__9982__9985)
                         => happ(happ(Vvar__2__ceqb__9947,Vvar__var__var__var__var__var__4__c__9969__9972__9975__9978__9981__9984),happ(Vvar__1__copp__9944,Vvar__var__var__var__var__var__5__c_27__9970__9973__9976__9979__9982__9985)) = cCoq_2eInit_2eDatatypes_2etrue ) ) )
                & p(c_24True) ) ) ) ) ) ) ).

fof('$_inversion_Coq.setoid_ring.Ring_theory.sring_eq_ext',axiom,
    ! [Vvar__0__R__23215,Vvar__1__radd__23216,Vvar__2__rmul__23221,Vvar__3__req__23226] :
      ( cType___24t(Vvar__0__R__23215)
     => ( c_24__type__23301___24t(Vvar__0__R__23215,Vvar__1__radd__23216,Vvar__2__rmul__23221,Vvar__3__req__23226,Vvar__1__radd__23216)
       => ( c_24__type__23324___24t(Vvar__0__R__23215,Vvar__1__radd__23216,Vvar__2__rmul__23221,Vvar__3__req__23226,Vvar__2__rmul__23221)
         => ( c_24__type__23347___24t(Vvar__0__R__23215,Vvar__1__radd__23216,Vvar__2__rmul__23221,Vvar__3__req__23226,Vvar__3__req__23226)
           => ( cCoq_2esetoid__ring_2eRing__theory_2esring__eq__ext___24a4(Vvar__0__R__23215,Vvar__1__radd__23216,Vvar__2__rmul__23221,Vvar__3__req__23226)
             => ( cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__23370___24a4(Vvar__0__R__23215,Vvar__1__radd__23216,Vvar__2__rmul__23221,Vvar__3__req__23226),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(Vvar__0__R__23215,c_24__type__23388___24a4(Vvar__0__R__23215,Vvar__1__radd__23216,Vvar__2__rmul__23221,Vvar__3__req__23226),Vvar__3__req__23226,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(Vvar__0__R__23215,Vvar__0__R__23215,Vvar__3__req__23226,Vvar__3__req__23226)),Vvar__1__radd__23216)
                & cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__23414___24a4(Vvar__0__R__23215,Vvar__1__radd__23216,Vvar__2__rmul__23221,Vvar__3__req__23226),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(Vvar__0__R__23215,c_24__type__23432___24a4(Vvar__0__R__23215,Vvar__1__radd__23216,Vvar__2__rmul__23221,Vvar__3__req__23226),Vvar__3__req__23226,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(Vvar__0__R__23215,Vvar__0__R__23215,Vvar__3__req__23226,Vvar__3__req__23226)),Vvar__2__rmul__23221)
                & p(c_24True) ) ) ) ) ) ) ).

fof('$_inversion_Hammer.Tactics.Reconstr.ReconstrT',axiom,
    ! [VX27070] :
      ( cHammer_2eTactics_2eReconstr_2eReconstrT___24t(VX27070)
     => ( VX27070 = cHammer_2eTactics_2eReconstr_2eEmpty
        | VX27070 = cHammer_2eTactics_2eReconstr_2eAllHyps ) ) ).

fof('$_lam_1023',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] : c_24__lam__1023___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) = cCoq_2eInit_2eWf_2eFix__F__2___24a8(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__7,Vv__CANONICAL__8,cCoq_2eInit_2eWf_2eAcc__inv___24a4(cCoq_2eInit_2eDatatypes_2eprod___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1),Vv__CANONICAL__2,cCoq_2eInit_2eDatatypes_2epair___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__5,Vv__CANONICAL__6),cCoq_2eInit_2eDatatypes_2epair___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__7,Vv__CANONICAL__8))) ).

fof('$_lam_2486',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] :
      ( c_24__lam__2486___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3)
    <=> p(happ(happ(Vv__CANONICAL__1,Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ).

fof('$_lam_2501',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] :
      ( c_24__lam__2501___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3)
    <=> ! [Vv__CANONICAL__4] :
          ( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__4)
         => ( p(happ(happ(Vv__CANONICAL__1,Vv__CANONICAL__2),Vv__CANONICAL__4))
           => cCoq_2eInit_2ePeano_2elt___24a2(Vv__CANONICAL__3,Vv__CANONICAL__4) ) ) ) ).

fof('$_lam_2687',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] :
      ( c_24__lam__2687___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_2692',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] :
      ( c_24__lam__2692___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
    <=> ( cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(Vv__CANONICAL__2,Vv__CANONICAL__1)
        & cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(Vv__CANONICAL__1,Vv__CANONICAL__0) ) ) ).

fof('$_lam_2733',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] :
      ( c_24__lam__2733___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_2738',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] :
      ( c_24__lam__2738___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
    <=> ( cCoq_2eInit_2ePeano_2elt___24a2(Vv__CANONICAL__2,Vv__CANONICAL__1)
        & cCoq_2eInit_2ePeano_2ele___24a2(Vv__CANONICAL__1,Vv__CANONICAL__0) ) ) ).

fof('$_lam_31829',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] :
      ( c_24__lam__31829___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_31837',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] :
      ( c_24__lam__31837___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_31845',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] :
      ( c_24__lam__31845___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_31853',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] :
      ( c_24__lam__31853___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_31926',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] :
      ( c_24__lam__31926___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3)
    <=> ~ p(happ(happ(Vv__CANONICAL__1,Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ).

fof('$_lam_31934',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] :
      ( c_24__lam__31934___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3)
    <=> p(happ(happ(Vv__CANONICAL__1,Vv__CANONICAL__3),Vv__CANONICAL__2)) ) ).

fof('$_lam_31942',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] :
      ( c_24__lam__31942___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3)
    <=> p(happ(happ(Vv__CANONICAL__1,Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ).

fof('$_lam_31950',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] :
      ( c_24__lam__31950___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3)
    <=> p(happ(happ(Vv__CANONICAL__1,Vv__CANONICAL__3),Vv__CANONICAL__2)) ) ).

fof('$_lam_3207',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] :
      ( c_24__lam__3207___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
    <=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1))
        & p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(Vv__CANONICAL__1,Vv__CANONICAL__2)) ) ) ).

fof('$_lam_3212',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] :
      ( c_24__lam__3212___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
    <=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(Vv__CANONICAL__2,Vv__CANONICAL__1))
        & p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(Vv__CANONICAL__1,Vv__CANONICAL__0)) ) ) ).

fof('$_lam_32918',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1] : c_24__lam__32918___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = Vv__CANONICAL__0 ).

fof('$_lam_32940',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1] : c_24__lam__32940___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = Vv__CANONICAL__0 ).

fof('$_lam_33027',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__33027___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = cCoq_2eInit_2eDatatypes_2etrue )
        | ? [Vvar__0___24Anonymous__33028] :
            ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__33028)
            & Vv__CANONICAL__1 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__33028)
            & c_24__lam__33027___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = cCoq_2ePArith_2eBinPosDef_2ePos_2etestbit__nat___24a2(Vv__CANONICAL__0,Vvar__0___24Anonymous__33028) ) ) ) ).

fof('$_lam_33034',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__33034___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = cCoq_2eInit_2eDatatypes_2efalse )
        | ? [Vvar__0___24Anonymous__33035] :
            ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__33035)
            & Vv__CANONICAL__1 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__33035)
            & c_24__lam__33034___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = cCoq_2ePArith_2eBinPosDef_2ePos_2etestbit__nat___24a2(Vv__CANONICAL__0,Vvar__0___24Anonymous__33035) ) ) ) ).

fof('$_lam_33038',axiom,
    ! [Vv__CANONICAL__0] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
     => ( ( Vv__CANONICAL__0 = cCoq_2eInit_2eDatatypes_2eO
          & c_24__lam__33038___24a1(Vv__CANONICAL__0) = cCoq_2eInit_2eDatatypes_2etrue )
        | ? [Vvar__0___24Anonymous__33039] :
            ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__33039)
            & Vv__CANONICAL__0 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__33039)
            & c_24__lam__33038___24a1(Vv__CANONICAL__0) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ).

fof('$_lam_33136',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1] : c_24__lam__33136___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = cCoq_2eInit_2eWf_2eFix___24a6(cA,cR,cRwf,cP,cF,Vv__CANONICAL__1) ).

fof('$_lam_389',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__6] : c_24__lam__389___24a6(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__6) = happ(happ(Vv__CANONICAL__3,Vv__CANONICAL__4),Vv__CANONICAL__6) ).

fof('$_lam_555',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5] : c_24__lam__555___24a6(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5) = cCoq_2eInit_2eWf_2eFix__F___24a6(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__5,cCoq_2eInit_2eWf_2eAcc__inv___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__4,Vv__CANONICAL__5)) ).

fof('$_lam_728',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5] : c_24__lam__728___24a6(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5) = cCoq_2eInit_2eWf_2eFix__F___24a6(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__5,cCoq_2eInit_2eWf_2eAcc__inv___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__4,Vv__CANONICAL__5)) ).

fof('$_lam_963',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5] : c_24__lam__963___24a6(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5) = cCoq_2eInit_2eWf_2eFix___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__5) ).

fof('$_prop_10918',axiom,
    ! [V0__n,V1__m] :
      ( p(c_24__prop__10918___24a2(V0__n,V1__m))
    <=> V0__n = V1__m ) ).

fof('$_prop_29558',axiom,
    ! [Vvar__0___24Anonymous__29534,Vvar__0__S__29536,Vvar__1__x__29537,Vvar__2__y__29538] :
      ( p(c_24__prop__29558___24a4(Vvar__0___24Anonymous__29534,Vvar__0__S__29536,Vvar__1__x__29537,Vvar__2__y__29538))
    <=> Vvar__1__x__29537 = Vvar__2__y__29538 ) ).

fof('$_prop_29559',axiom,
    ! [Vvar__0___24Anonymous__29534,Vvar__0__x__29539,Vvar__1__y__29540] :
      ( p(c_24__prop__29559___24a3(Vvar__0___24Anonymous__29534,Vvar__0__x__29539,Vvar__1__y__29540))
    <=> Vvar__0__x__29539 = Vvar__1__y__29540 ) ).

fof('$_prop_29560',axiom,
    ! [Vvar__0___24Anonymous__29534,Vvar__0__x__29541,Vvar__1__s__29542] :
      ( p(c_24__prop__29560___24a3(Vvar__0___24Anonymous__29534,Vvar__0__x__29541,Vvar__1__s__29542))
    <=> cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2emem___24a2(Vvar__0__x__29541,Vvar__1__s__29542) = cCoq_2eInit_2eDatatypes_2etrue ) ).

fof('$_prop_29561',axiom,
    ! [Vvar__0___24Anonymous__29534,Vvar__0__P__29543,Vvar__1__Q__29544] :
      ( p(c_24__prop__29561___24a3(Vvar__0___24Anonymous__29534,Vvar__0__P__29543,Vvar__1__Q__29544))
    <=> ( p(Vvar__0__P__29543)
        & p(Vvar__1__Q__29544) ) ) ).

fof('$_prop_29562',axiom,
    ! [Vvar__0___24Anonymous__29534,Vvar__0__P__29547,Vvar__1__Q__29548] :
      ( p(c_24__prop__29562___24a3(Vvar__0___24Anonymous__29534,Vvar__0__P__29547,Vvar__1__Q__29548))
    <=> ( p(Vvar__0__P__29547)
        | p(Vvar__1__Q__29548) ) ) ).

fof('$_prop_29563',axiom,
    ! [Vvar__0___24Anonymous__29534,Vvar__0__P__29551,Vvar__1__Q__29552] :
      ( p(c_24__prop__29563___24a3(Vvar__0___24Anonymous__29534,Vvar__0__P__29551,Vvar__1__Q__29552))
    <=> ( p(Vvar__0__P__29551)
       => p(Vvar__1__Q__29552) ) ) ).

fof('$_prop_29564',axiom,
    ! [Vvar__0___24Anonymous__29534,Vvar__0__P__29556] :
      ( p(c_24__prop__29564___24a2(Vvar__0___24Anonymous__29534,Vvar__0__P__29556))
    <=> ~ p(Vvar__0__P__29556) ) ).

fof('$_prop_29578',axiom,
    ! [Vvar__0___24Anonymous__29565,Vvar__0__s__29569] :
      ( p(c_24__prop__29578___24a2(Vvar__0___24Anonymous__29565,Vvar__0__s__29569))
    <=> ! [Vvar__1__a__29570] :
          ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(Vvar__1__a__29570)
         => ~ cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eIn___24a2(Vvar__1__a__29570,Vvar__0__s__29569) ) ) ).

fof('$_prop_29579',axiom,
    ! [Vvar__0___24Anonymous__29565,Vvar__0__s1__29571,Vvar__1__s2__29572] :
      ( p(c_24__prop__29579___24a3(Vvar__0___24Anonymous__29565,Vvar__0__s1__29571,Vvar__1__s2__29572))
    <=> ! [Vvar__2__a__29573] :
          ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(Vvar__2__a__29573)
         => ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eIn___24a2(Vvar__2__a__29573,Vvar__0__s1__29571)
           => cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eIn___24a2(Vvar__2__a__29573,Vvar__1__s2__29572) ) ) ) ).

fof('$_prop_29580',axiom,
    ! [Vvar__0___24Anonymous__29565,Vvar__0__s1__29575,Vvar__1__s2__29576] :
      ( p(c_24__prop__29580___24a3(Vvar__0___24Anonymous__29565,Vvar__0__s1__29575,Vvar__1__s2__29576))
    <=> ! [Vvar__2__a__29577] :
          ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(Vvar__2__a__29577)
         => ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eIn___24a2(Vvar__2__a__29577,Vvar__0__s1__29575)
          <=> cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eIn___24a2(Vvar__2__a__29577,Vvar__1__s2__29576) ) ) ) ).

fof('$_type_10018',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__10019] :
      ( c_24__type__10018___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__10019)
    <=> ! [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__10019,Vv__CANONICAL__4),Vv__CANONICAL__5)) ) ) ) ).

fof('$_type_10032',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__10033] :
      ( c_24__type__10032___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__10033)
    <=> ! [Vv__CANONICAL__4] :
          ( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
         => cCoq_2eInit_2eDatatypes_2eoption___24t(Vv__CANONICAL__0,happ(Vvar__10033,Vv__CANONICAL__4)) ) ) ).

fof('$_type_10177',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__10178] :
      ( c_24__type__10177___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__10178)
    <=> ! [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__10178,Vv__CANONICAL__7),Vv__CANONICAL__8)) ) ) ) ).

fof('$_type_10227',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__10228] :
      ( c_24__type__10227___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__10228)
    <=> ! [Vv__CANONICAL__7] :
          ( t(Vv__CANONICAL__7,Vv__CANONICAL__2)
         => ! [Vv__CANONICAL__8] :
              ( t(Vv__CANONICAL__8,Vv__CANONICAL__2)
             => t(happ(happ(Vvar__10228,Vv__CANONICAL__7),Vv__CANONICAL__8),Vv__CANONICAL__2) ) ) ) ).

fof('$_type_10277',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__10278] :
      ( c_24__type__10277___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__10278)
    <=> ! [Vv__CANONICAL__7] :
          ( t(Vv__CANONICAL__7,Vv__CANONICAL__2)
         => ! [Vv__CANONICAL__8] :
              ( t(Vv__CANONICAL__8,Vv__CANONICAL__2)
             => t(happ(happ(Vvar__10278,Vv__CANONICAL__7),Vv__CANONICAL__8),Vv__CANONICAL__2) ) ) ) ).

fof('$_type_10319',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__10320] :
      ( c_24__type__10319___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__10320)
    <=> ! [Vv__CANONICAL__7] :
          ( t(Vv__CANONICAL__7,Vv__CANONICAL__2)
         => t(happ(Vvar__10320,Vv__CANONICAL__7),Vv__CANONICAL__0) ) ) ).

fof('$_type_10369',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__10370] :
      ( c_24__type__10369___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__10370)
    <=> ! [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__10370,Vv__CANONICAL__7),Vv__CANONICAL__8)) ) ) ) ).

fof('$_type_10445',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__10446] :
      ( c_24__type__10445___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__10446)
    <=> ! [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__10446,Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ).

fof('$_type_10453',axiom,
    ! [Vvar__10454] :
      ( c_24__type__10453___24t(Vvar__10454)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
             => t(happ(happ(Vvar__10454,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_10557',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__10558] :
      ( c_24__type__10557___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__10558)
    <=> ! [Vv__CANONICAL__7] :
          ( t(Vv__CANONICAL__7,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__8] :
              ( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
             => t(happ(happ(Vvar__10558,Vv__CANONICAL__7),Vv__CANONICAL__8),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_10601',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__10602] :
      ( c_24__type__10601___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__10602)
    <=> ! [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__10602,Vv__CANONICAL__7),Vv__CANONICAL__8)) ) ) ) ).

fof('$_type_10637',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__10638] :
      ( c_24__type__10637___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__10638)
    <=> ! [Vv__CANONICAL__7] :
          ( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__7)
         => t(happ(Vvar__10638,Vv__CANONICAL__7),Vv__CANONICAL__4) ) ) ).

fof('$_type_10681',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__10682] :
      ( c_24__type__10681___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__10682)
    <=> ! [Vv__CANONICAL__7] :
          ( t(Vv__CANONICAL__7,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__8] :
              ( t(Vv__CANONICAL__8,Vv__CANONICAL__4)
             => t(happ(happ(Vvar__10682,Vv__CANONICAL__7),Vv__CANONICAL__8),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_10700',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__10701] :
      ( c_24__type__10700___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__10701)
    <=> ! [Vv__CANONICAL__2] :
          ( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__3] :
              ( t(Vv__CANONICAL__3,Vv__CANONICAL__1)
             => t(happ(happ(Vvar__10701,Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_10755',axiom,
    ! [Vvar__10756] :
      ( c_24__type__10755___24t(Vvar__10756)
    <=> ! [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__10756,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_10817',axiom,
    ! [Vvar__10818] :
      ( c_24__type__10817___24t(Vvar__10818)
    <=> ! [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__10818,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_10839',axiom,
    ! [Vvar__10840] :
      ( c_24__type__10839___24t(Vvar__10840)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__0)
         => cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(Vvar__10840,Vv__CANONICAL__0)) ) ) ).

fof('$_type_10940',axiom,
    ! [Vvar__10941] :
      ( c_24__type__10940___24t(Vvar__10941)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__0)
         => cCoq_2eNumbers_2eBinNums_2eN___24t(happ(Vvar__10941,Vv__CANONICAL__0)) ) ) ).

fof('$_type_10943',axiom,
    ! [Vvar__10944] :
      ( c_24__type__10943___24t(Vvar__10944)
    <=> ! [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__10944,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_10953',axiom,
    ! [Vvar__10954] :
      ( c_24__type__10953___24t(Vvar__10954)
    <=> ! [Vv__CANONICAL__0] :
          ( cProp___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__1)
             => cType___24t(happ(happ(Vvar__10954,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_110',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__111] :
      ( c_24__type__110___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__111)
    <=> ! [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__111,Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ).

fof('$_type_1100',axiom,
    ! [Vvar__1101] :
      ( c_24__type__1100___24t(Vvar__1101)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cType___24t(Vv__CANONICAL__1)
             => ! [Vv__CANONICAL__2] :
                  ( c_24__type__1107___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
                 => ! [Vv__CANONICAL__3] :
                      ( c_24__type__1114___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__3)
                     => ! [Vv__CANONICAL__4] :
                          ( c_24__type__1162___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4)
                         => ! [Vv__CANONICAL__5] :
                              ( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
                             => ! [Vv__CANONICAL__6] :
                                  ( t(Vv__CANONICAL__6,Vv__CANONICAL__1)
                                 => ( cCoq_2eInit_2eWf_2eAcc___24a3(cCoq_2eInit_2eDatatypes_2eprod___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1),Vv__CANONICAL__2,cCoq_2eInit_2eDatatypes_2epair___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__5,Vv__CANONICAL__6))
                                   => t(happ(happ(happ(happ(happ(happ(happ(Vvar__1101,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__6),happ(happ(Vv__CANONICAL__3,Vv__CANONICAL__5),Vv__CANONICAL__6)) ) ) ) ) ) ) ) ) ) ).

fof('$_type_1107',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__1108] :
      ( c_24__type__1107___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__1108)
    <=> ! [Vv__CANONICAL__2] :
          ( cCoq_2eInit_2eDatatypes_2eprod___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
         => ! [Vv__CANONICAL__3] :
              ( cCoq_2eInit_2eDatatypes_2eprod___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__3)
             => cProp___24t(happ(happ(Vvar__1108,Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ).

fof('$_type_1114',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__1115] :
      ( c_24__type__1114___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__1115)
    <=> ! [Vv__CANONICAL__2] :
          ( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__3] :
              ( t(Vv__CANONICAL__3,Vv__CANONICAL__1)
             => cType___24t(happ(happ(Vvar__1115,Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ).

fof('$_type_1162',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__1163] :
      ( c_24__type__1162___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__1163)
    <=> ! [Vv__CANONICAL__4] :
          ( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__5] :
              ( t(Vv__CANONICAL__5,Vv__CANONICAL__1)
             => ! [Vv__CANONICAL__6] :
                  ( c_24__type__1195___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6)
                 => t(happ(happ(happ(Vvar__1163,Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__6),happ(happ(Vv__CANONICAL__3,Vv__CANONICAL__4),Vv__CANONICAL__5)) ) ) ) ) ).

fof('$_type_117',axiom,
    ! [Vv__CANONICAL__0,Vvar__118] :
      ( c_24__type__117___24t(Vv__CANONICAL__0,Vvar__118)
    <=> ! [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__118,Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ).

fof('$_type_11775',axiom,
    ! [Vvar__11776] :
      ( c_24__type__11775___24t(Vvar__11776)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__0)
         => cCoq_2eInit_2eDatatypes_2ebool___24t(happ(Vvar__11776,Vv__CANONICAL__0)) ) ) ).

fof('$_type_11779',axiom,
    ! [Vvar__11780] :
      ( c_24__type__11779___24t(Vvar__11780)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__0)
         => cProp___24t(happ(Vvar__11780,Vv__CANONICAL__0)) ) ) ).

fof('$_type_11784',axiom,
    ! [Vv__CANONICAL__0,Vvar__11785] :
      ( c_24__type__11784___24t(Vv__CANONICAL__0,Vvar__11785)
    <=> ! [Vv__CANONICAL__1] :
          ( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
         => cType___24t(happ(Vvar__11785,Vv__CANONICAL__1)) ) ) ).

fof('$_type_11797',axiom,
    ! [Vvar__11798] :
      ( c_24__type__11797___24t(Vvar__11798)
    <=> ! [Vv__CANONICAL__0] :
          ( c_24__type__11799___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__11804___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
                 => ! [Vv__CANONICAL__3] :
                      ( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__3)
                     => t(happ(happ(happ(happ(Vvar__11798,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),happ(Vv__CANONICAL__0,Vv__CANONICAL__3)) ) ) ) ) ) ).

fof('$_type_11799',axiom,
    ! [Vvar__11800] :
      ( c_24__type__11799___24t(Vvar__11800)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
         => cType___24t(happ(Vvar__11800,Vv__CANONICAL__0)) ) ) ).

fof('$_type_11804',axiom,
    ! [Vv__CANONICAL__0,Vvar__11805] :
      ( c_24__type__11804___24t(Vv__CANONICAL__0,Vvar__11805)
    <=> ! [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__11805,Vv__CANONICAL__1),Vv__CANONICAL__2),happ(Vv__CANONICAL__0,cCoq_2eInit_2eDatatypes_2eS___24a1(Vv__CANONICAL__1))) ) ) ) ).

fof('$_type_11821',axiom,
    ! [Vvar__11822] :
      ( c_24__type__11821___24t(Vvar__11822)
    <=> ! [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__11822,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_11823',axiom,
    ! [Vvar__11824] :
      ( c_24__type__11823___24t(Vvar__11824)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => cCoq_2eInit_2eDatatypes_2eoption___24t(Vv__CANONICAL__0,happ(Vvar__11824,Vv__CANONICAL__0)) ) ) ).

fof('$_type_11863',axiom,
    ! [Vvar__11864] :
      ( c_24__type__11863___24t(Vvar__11864)
    <=> ! [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__11864,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__0) ) ) ) ) ).

fof('$_type_11918',axiom,
    ! [Vv__CANONICAL__0,Vvar__11919] :
      ( c_24__type__11918___24t(Vv__CANONICAL__0,Vvar__11919)
    <=> ! [Vv__CANONICAL__1] :
          ( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
         => cProp___24t(happ(Vvar__11919,Vv__CANONICAL__1)) ) ) ).

fof('$_type_11931',axiom,
    ! [Vvar__11932] :
      ( c_24__type__11931___24t(Vvar__11932)
    <=> ! [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__11932,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_11943',axiom,
    ! [Vvar__11944] :
      ( c_24__type__11943___24t(Vvar__11944)
    <=> ! [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__11944,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).

fof('$_type_11945',axiom,
    ! [Vvar__11946] :
      ( c_24__type__11945___24t(Vvar__11946)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eInit_2eDatatypes_2ecomparison___24t(Vv__CANONICAL__0)
         => cCoq_2eInit_2eDatatypes_2ecomparison___24t(happ(Vvar__11946,Vv__CANONICAL__0)) ) ) ).

fof('$_type_1195',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__1196] :
      ( c_24__type__1195___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__1196)
    <=> ! [Vv__CANONICAL__6] :
          ( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__7] :
              ( t(Vv__CANONICAL__7,Vv__CANONICAL__1)
             => ( p(happ(happ(Vv__CANONICAL__2,cCoq_2eInit_2eDatatypes_2epair___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__6,Vv__CANONICAL__7)),cCoq_2eInit_2eDatatypes_2epair___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__4,Vv__CANONICAL__5)))
               => t(happ(happ(Vvar__1196,Vv__CANONICAL__6),Vv__CANONICAL__7),happ(happ(Vv__CANONICAL__3,Vv__CANONICAL__6),Vv__CANONICAL__7)) ) ) ) ) ).

fof('$_type_11987',axiom,
    ! [Vvar__11988] :
      ( c_24__type__11987___24t(Vvar__11988)
    <=> ! [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__11988,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).

fof('$_type_12132',axiom,
    ! [Vvar__12133] :
      ( c_24__type__12132___24t(Vvar__12133)
    <=> ! [Vv__CANONICAL__0] :
          ( cProp___24t(Vv__CANONICAL__0)
         => cProp___24t(happ(Vvar__12133,Vv__CANONICAL__0)) ) ) ).

fof('$_type_12265',axiom,
    ! [Vvar__12266] :
      ( c_24__type__12265___24t(Vvar__12266)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eInit_2eDecimal_2euint___24t(Vv__CANONICAL__0)
         => cCoq_2eInit_2eDecimal_2euint___24t(happ(Vvar__12266,Vv__CANONICAL__0)) ) ) ).

fof('$_type_12276',axiom,
    ! [Vvar__12277] :
      ( c_24__type__12276___24t(Vvar__12277)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eInit_2eDecimal_2euint___24t(Vv__CANONICAL__0)
         => cCoq_2eInit_2eDecimal_2eint___24t(happ(Vvar__12277,Vv__CANONICAL__0)) ) ) ).

fof('$_type_12622',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__12623] :
      ( c_24__type__12622___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__12623)
    <=> ! [Vv__CANONICAL__10] :
          ( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__11] :
              ( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
             => t(happ(happ(Vvar__12623,Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_12715',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__12716] :
      ( c_24__type__12715___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__12716)
    <=> ! [Vv__CANONICAL__10] :
          ( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__11] :
              ( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
             => t(happ(happ(Vvar__12716,Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_1279',axiom,
    ! [Vvar__1280] :
      ( c_24__type__1279___24t(Vvar__1280)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cType___24t(Vv__CANONICAL__1)
             => ! [Vv__CANONICAL__2] :
                  ( c_24__type__1107___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
                 => ! [Vv__CANONICAL__3] :
                      ( c_24__type__1114___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__3)
                     => ( cCoq_2eInit_2eWf_2ewell__founded___24a2(cCoq_2eInit_2eDatatypes_2eprod___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1),Vv__CANONICAL__2)
                       => ! [Vv__CANONICAL__5] :
                            ( c_24__type__1337___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__5)
                           => ! [Vv__CANONICAL__6] :
                                ( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
                               => ! [Vv__CANONICAL__7] :
                                    ( t(Vv__CANONICAL__7,Vv__CANONICAL__1)
                                   => t(happ(happ(happ(happ(happ(happ(happ(Vvar__1280,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__5),Vv__CANONICAL__6),Vv__CANONICAL__7),happ(happ(Vv__CANONICAL__3,Vv__CANONICAL__6),Vv__CANONICAL__7)) ) ) ) ) ) ) ) ) ) ).

fof('$_type_12808',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__12809] :
      ( c_24__type__12808___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__12809)
    <=> ! [Vv__CANONICAL__10] :
          ( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__11] :
              ( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
             => t(happ(happ(Vvar__12809,Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_12890',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__12891] :
      ( c_24__type__12890___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__12891)
    <=> ! [Vv__CANONICAL__10] :
          ( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
         => t(happ(Vvar__12891,Vv__CANONICAL__10),Vv__CANONICAL__0) ) ) ).

fof('$_type_12983',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__12984] :
      ( c_24__type__12983___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__12984)
    <=> ! [Vv__CANONICAL__10] :
          ( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__11] :
              ( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
             => t(happ(happ(Vvar__12984,Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_13065',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__13066] :
      ( c_24__type__13065___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__13066)
    <=> ! [Vv__CANONICAL__10] :
          ( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
         => t(happ(Vvar__13066,Vv__CANONICAL__10),Vv__CANONICAL__0) ) ) ).

fof('$_type_13158',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__13159] :
      ( c_24__type__13158___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__13159)
    <=> ! [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__13159,Vv__CANONICAL__10),Vv__CANONICAL__11)) ) ) ) ).

fof('$_type_1337',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__1338] :
      ( c_24__type__1337___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__1338)
    <=> ! [Vv__CANONICAL__4] :
          ( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__5] :
              ( t(Vv__CANONICAL__5,Vv__CANONICAL__1)
             => ! [Vv__CANONICAL__6] :
                  ( c_24__type__1370___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6)
                 => t(happ(happ(happ(Vvar__1338,Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__6),happ(happ(Vv__CANONICAL__3,Vv__CANONICAL__4),Vv__CANONICAL__5)) ) ) ) ) ).

fof('$_type_1370',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__1371] :
      ( c_24__type__1370___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__1371)
    <=> ! [Vv__CANONICAL__6] :
          ( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__7] :
              ( t(Vv__CANONICAL__7,Vv__CANONICAL__1)
             => ( p(happ(happ(Vv__CANONICAL__2,cCoq_2eInit_2eDatatypes_2epair___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__6,Vv__CANONICAL__7)),cCoq_2eInit_2eDatatypes_2epair___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__4,Vv__CANONICAL__5)))
               => t(happ(happ(Vvar__1371,Vv__CANONICAL__6),Vv__CANONICAL__7),happ(happ(Vv__CANONICAL__3,Vv__CANONICAL__6),Vv__CANONICAL__7)) ) ) ) ) ).

fof('$_type_1376',axiom,
    ! [Vv__CANONICAL__0,Vvar__1377] :
      ( c_24__type__1376___24t(Vv__CANONICAL__0,Vvar__1377)
    <=> ! [Vv__CANONICAL__1] :
          ( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
         => cCoq_2eInit_2eDatatypes_2enat___24t(happ(Vvar__1377,Vv__CANONICAL__1)) ) ) ).

fof('$_type_13929',axiom,
    ! [Vvar__13930] :
      ( c_24__type__13929___24t(Vvar__13930)
    <=> ! [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__13930,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_13932',axiom,
    ! [Vvar__13933] :
      ( c_24__type__13932___24t(Vvar__13933)
    <=> ! [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__13933,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_13937',axiom,
    ! [Vvar__13938] :
      ( c_24__type__13937___24t(Vvar__13938)
    <=> ! [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__13938,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).

fof('$_type_13940',axiom,
    ! [Vvar__13941] :
      ( c_24__type__13940___24t(Vvar__13941)
    <=> ! [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__13941,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_14',axiom,
    ! [Vvar__15] :
      ( c_24__type__14___24t(Vvar__15)
    <=> ! [Vv__CANONICAL__0] :
          ( cA___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cP___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
             => ! [Vv__CANONICAL__2] :
                  ( cP___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
                 => cProp___24t(happ(happ(happ(Vvar__15,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).

fof('$_type_1425',axiom,
    ! [Vvar__1426] :
      ( c_24__type__1425___24t(Vvar__1426)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__0)
         => cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(Vvar__1426,Vv__CANONICAL__0)) ) ) ).

fof('$_type_1427',axiom,
    ! [Vvar__1428] :
      ( c_24__type__1427___24t(Vvar__1428)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
         => cCoq_2eInit_2eDatatypes_2enat___24t(happ(Vvar__1428,Vv__CANONICAL__0)) ) ) ).

fof('$_type_14270',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__14271] :
      ( c_24__type__14270___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__14271)
    <=> ! [Vv__CANONICAL__8] :
          ( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__9] :
              ( t(Vv__CANONICAL__9,Vv__CANONICAL__0)
             => t(happ(happ(Vvar__14271,Vv__CANONICAL__8),Vv__CANONICAL__9),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_14333',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__14334] :
      ( c_24__type__14333___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__14334)
    <=> ! [Vv__CANONICAL__8] :
          ( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__9] :
              ( t(Vv__CANONICAL__9,Vv__CANONICAL__0)
             => t(happ(happ(Vvar__14334,Vv__CANONICAL__8),Vv__CANONICAL__9),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_14396',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__14397] :
      ( c_24__type__14396___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__14397)
    <=> ! [Vv__CANONICAL__8] :
          ( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__9] :
              ( t(Vv__CANONICAL__9,Vv__CANONICAL__0)
             => t(happ(happ(Vvar__14397,Vv__CANONICAL__8),Vv__CANONICAL__9),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_14450',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__14451] :
      ( c_24__type__14450___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__14451)
    <=> ! [Vv__CANONICAL__8] :
          ( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
         => t(happ(Vvar__14451,Vv__CANONICAL__8),Vv__CANONICAL__0) ) ) ).

fof('$_type_14513',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__14514] :
      ( c_24__type__14513___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__14514)
    <=> ! [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__14514,Vv__CANONICAL__8),Vv__CANONICAL__9)) ) ) ) ).

fof('$_type_14645',axiom,
    ! [Vvar__14646] :
      ( c_24__type__14645___24t(Vvar__14646)
    <=> ! [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__3] :
                      ( c_24__type__3267___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
                     => ! [Vv__CANONICAL__4] :
                          ( c_24__type__3267___24t(Vv__CANONICAL__0,Vv__CANONICAL__4)
                         => ! [Vv__CANONICAL__5] :
                              ( c_24__type__3276___24t(Vv__CANONICAL__0,Vv__CANONICAL__5)
                             => ! [Vv__CANONICAL__6] :
                                  ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__6)
                                 => t(happ(happ(happ(happ(happ(happ(happ(Vvar__14646,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_14708',axiom,
    ! [Vvar__14709] :
      ( c_24__type__14708___24t(Vvar__14709)
    <=> ! [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__3] :
                      ( c_24__type__3267___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
                     => ! [Vv__CANONICAL__4] :
                          ( c_24__type__3267___24t(Vv__CANONICAL__0,Vv__CANONICAL__4)
                         => ! [Vv__CANONICAL__5] :
                              ( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__5)
                             => t(happ(happ(happ(happ(happ(happ(Vvar__14709,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__0) ) ) ) ) ) ) ) ).

fof('$_type_14839',axiom,
    ! [Vvar__14840] :
      ( c_24__type__14839___24t(Vvar__14840)
    <=> ! [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__14840,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).

fof('$_type_14864',axiom,
    ! [Vvar__14865] :
      ( c_24__type__14864___24t(Vvar__14865)
    <=> ! [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__14865,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__0) ) ) ) ) ) ).

fof('$_type_15031',axiom,
    ! [Vvar__15032] :
      ( c_24__type__15031___24t(Vvar__15032)
    <=> ! [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__15032,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_15470',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__15471] :
      ( c_24__type__15470___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__15471)
    <=> ! [Vv__CANONICAL__10] :
          ( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__11] :
              ( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
             => t(happ(happ(Vvar__15471,Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_15571',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__15572] :
      ( c_24__type__15571___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__15572)
    <=> ! [Vv__CANONICAL__10] :
          ( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__11] :
              ( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
             => t(happ(happ(Vvar__15572,Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_15672',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__15673] :
      ( c_24__type__15672___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__15673)
    <=> ! [Vv__CANONICAL__10] :
          ( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__11] :
              ( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
             => t(happ(happ(Vvar__15673,Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_15762',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__15763] :
      ( c_24__type__15762___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__15763)
    <=> ! [Vv__CANONICAL__10] :
          ( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
         => t(happ(Vvar__15763,Vv__CANONICAL__10),Vv__CANONICAL__0) ) ) ).

fof('$_type_15863',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__15864] :
      ( c_24__type__15863___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__15864)
    <=> ! [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__15864,Vv__CANONICAL__10),Vv__CANONICAL__11)) ) ) ) ).

fof('$_type_15964',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__15965] :
      ( c_24__type__15964___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__15965)
    <=> ! [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__15965,Vv__CANONICAL__10),Vv__CANONICAL__11)) ) ) ) ).

fof('$_type_16065',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__16066] :
      ( c_24__type__16065___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__16066)
    <=> ! [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__16066,Vv__CANONICAL__10),Vv__CANONICAL__11)) ) ) ) ).

fof('$_type_16307',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__16308] :
      ( c_24__type__16307___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__16308)
    <=> ! [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__16308,Vv__CANONICAL__5),Vv__CANONICAL__6)) ) ) ) ).

fof('$_type_16326',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__16327] :
      ( c_24__type__16326___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__16327)
    <=> ! [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__16327,Vv__CANONICAL__5),Vv__CANONICAL__6)) ) ) ) ).

fof('$_type_16346',axiom,
    ! [Vvar__16347] :
      ( c_24__type__16346___24t(Vvar__16347)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( c_24__type__117___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
             => ! [Vv__CANONICAL__2] :
                  ( c_24__type__117___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__16347,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ) ) ) ).

fof('$_type_16470',axiom,
    ! [Vvar__16471] :
      ( c_24__type__16470___24t(Vvar__16471)
    <=> ! [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__16471,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_16475',axiom,
    ! [Vvar__16476] :
      ( c_24__type__16475___24t(Vvar__16476)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eQArith_2eQArith__base_2eQ___24t(Vv__CANONICAL__0)
         => cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(Vvar__16476,Vv__CANONICAL__0)) ) ) ).

fof('$_type_16480',axiom,
    ! [Vvar__16481] :
      ( c_24__type__16480___24t(Vvar__16481)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eQArith_2eQArith__base_2eQ___24t(Vv__CANONICAL__0)
         => cCoq_2eNumbers_2eBinNums_2epositive___24t(happ(Vvar__16481,Vv__CANONICAL__0)) ) ) ).

fof('$_type_16525',axiom,
    ! [Vvar__16526] :
      ( c_24__type__16525___24t(Vvar__16526)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__0)
         => cCoq_2eReals_2eRdefinitions_2eR___24t(happ(Vvar__16526,Vv__CANONICAL__0)) ) ) ).

fof('$_type_16686',axiom,
    ! [Vvar__16687] :
      ( c_24__type__16686___24t(Vvar__16687)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eQArith_2eQArith__base_2eQ___24t(Vv__CANONICAL__0)
         => cCoq_2emicromega_2eRMicromega_2eRcst___24t(happ(Vvar__16687,Vv__CANONICAL__0)) ) ) ).

fof('$_type_16688',axiom,
    ! [Vvar__16689] :
      ( c_24__type__16688___24t(Vvar__16689)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
         => cCoq_2emicromega_2eRMicromega_2eRcst___24t(happ(Vvar__16689,Vv__CANONICAL__0)) ) ) ).

fof('$_type_16691',axiom,
    ! [Vvar__16692] :
      ( c_24__type__16691___24t(Vvar__16692)
    <=> ! [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__16692,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_16698',axiom,
    ! [Vvar__16699] :
      ( c_24__type__16698___24t(Vvar__16699)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2emicromega_2eRMicromega_2eRcst___24t(Vv__CANONICAL__0)
         => cCoq_2emicromega_2eRMicromega_2eRcst___24t(happ(Vvar__16699,Vv__CANONICAL__0)) ) ) ).

fof('$_type_16746',axiom,
    ! [Vvar__16747] :
      ( c_24__type__16746___24t(Vvar__16747)
    <=> ! [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__16747,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_16759',axiom,
    ! [Vvar__16760] :
      ( c_24__type__16759___24t(Vvar__16760)
    <=> ! [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__16760,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_16767',axiom,
    ! [Vvar__16768] :
      ( c_24__type__16767___24t(Vvar__16768)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
         => cCoq_2eReals_2eRdefinitions_2eR___24t(happ(Vvar__16768,Vv__CANONICAL__0)) ) ) ).

fof('$_type_16792',axiom,
    ! [Vvar__16793] :
      ( c_24__type__16792___24t(Vvar__16793)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( c_24__type__242___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__16793,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).

fof('$_type_16818',axiom,
    ! [Vvar__16819] :
      ( c_24__type__16818___24t(Vvar__16819)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( c_24__type__242___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__16819,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).

fof('$_type_16935',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__16936] :
      ( c_24__type__16935___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__16936)
    <=> ! [Vv__CANONICAL__6] :
          ( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
         => cType___24t(happ(Vvar__16936,Vv__CANONICAL__6)) ) ) ).

fof('$_type_16964',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__16965] :
      ( c_24__type__16964___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__16965)
    <=> ! [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__16965,Vv__CANONICAL__6),Vv__CANONICAL__7)) ) ) ) ).

fof('$_type_17001',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__17002] :
      ( c_24__type__17001___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__17002)
    <=> ! [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__17002,Vv__CANONICAL__6),Vv__CANONICAL__7),Vv__CANONICAL__8)) ) ) ) ) ).

fof('$_type_17097',axiom,
    ! [Vvar__17098] :
      ( c_24__type__17097___24t(Vvar__17098)
    <=> ! [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__17098,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_175',axiom,
    ! [Vvar__176] :
      ( c_24__type__175___24t(Vvar__176)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( c_24__type__117___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
             => ! [Vv__CANONICAL__2] :
                  ( c_24__type__181___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
                 => ! [Vv__CANONICAL__3] :
                      ( c_24__type__219___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3)
                     => ! [Vv__CANONICAL__4] :
                          ( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
                         => ( cCoq_2eInit_2eWf_2eAcc___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__4)
                           => t(happ(happ(happ(happ(happ(Vvar__176,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),happ(Vv__CANONICAL__2,Vv__CANONICAL__4)) ) ) ) ) ) ) ) ).

fof('$_type_17676',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__17677] :
      ( c_24__type__17676___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__17677)
    <=> ! [Vv__CANONICAL__22] :
          ( t(Vv__CANONICAL__22,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__23] :
              ( t(Vv__CANONICAL__23,Vv__CANONICAL__0)
             => t(happ(happ(Vvar__17677,Vv__CANONICAL__22),Vv__CANONICAL__23),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_18022',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__18023] :
      ( c_24__type__18022___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__18023)
    <=> ! [Vv__CANONICAL__22] :
          ( t(Vv__CANONICAL__22,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__23] :
              ( t(Vv__CANONICAL__23,Vv__CANONICAL__0)
             => t(happ(happ(Vvar__18023,Vv__CANONICAL__22),Vv__CANONICAL__23),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_181',axiom,
    ! [Vv__CANONICAL__0,Vvar__182] :
      ( c_24__type__181___24t(Vv__CANONICAL__0,Vvar__182)
    <=> ! [Vv__CANONICAL__1] :
          ( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
         => cType___24t(happ(Vvar__182,Vv__CANONICAL__1)) ) ) ).

fof('$_type_18368',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__18369] :
      ( c_24__type__18368___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__18369)
    <=> ! [Vv__CANONICAL__22] :
          ( t(Vv__CANONICAL__22,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__23] :
              ( t(Vv__CANONICAL__23,Vv__CANONICAL__0)
             => t(happ(happ(Vvar__18369,Vv__CANONICAL__22),Vv__CANONICAL__23),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_18691',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__18692] :
      ( c_24__type__18691___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__18692)
    <=> ! [Vv__CANONICAL__22] :
          ( t(Vv__CANONICAL__22,Vv__CANONICAL__0)
         => t(happ(Vvar__18692,Vv__CANONICAL__22),Vv__CANONICAL__0) ) ) ).

fof('$_type_19037',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__19038] :
      ( c_24__type__19037___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__19038)
    <=> ! [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__19038,Vv__CANONICAL__22),Vv__CANONICAL__23)) ) ) ) ).

fof('$_type_19383',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__19384] :
      ( c_24__type__19383___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__19384)
    <=> ! [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__19384,Vv__CANONICAL__22),Vv__CANONICAL__23)) ) ) ) ).

fof('$_type_19729',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__19730] :
      ( c_24__type__19729___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__19730)
    <=> ! [Vv__CANONICAL__22] :
          ( t(Vv__CANONICAL__22,Vv__CANONICAL__9)
         => ! [Vv__CANONICAL__23] :
              ( t(Vv__CANONICAL__23,Vv__CANONICAL__9)
             => t(happ(happ(Vvar__19730,Vv__CANONICAL__22),Vv__CANONICAL__23),Vv__CANONICAL__9) ) ) ) ).

fof('$_type_20',axiom,
    ! [Vvar__21] :
      ( c_24__type__20___24t(Vvar__21)
    <=> ! [Vv__CANONICAL__0] :
          ( cA___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( c_24__type__4___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
             => cP___24t(Vv__CANONICAL__0,happ(happ(Vvar__21,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_20075',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__20076] :
      ( c_24__type__20075___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__20076)
    <=> ! [Vv__CANONICAL__22] :
          ( t(Vv__CANONICAL__22,Vv__CANONICAL__9)
         => ! [Vv__CANONICAL__23] :
              ( t(Vv__CANONICAL__23,Vv__CANONICAL__9)
             => t(happ(happ(Vvar__20076,Vv__CANONICAL__22),Vv__CANONICAL__23),Vv__CANONICAL__9) ) ) ) ).

fof('$_type_20421',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__20422] :
      ( c_24__type__20421___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__20422)
    <=> ! [Vv__CANONICAL__22] :
          ( t(Vv__CANONICAL__22,Vv__CANONICAL__9)
         => ! [Vv__CANONICAL__23] :
              ( t(Vv__CANONICAL__23,Vv__CANONICAL__9)
             => t(happ(happ(Vvar__20422,Vv__CANONICAL__22),Vv__CANONICAL__23),Vv__CANONICAL__9) ) ) ) ).

fof('$_type_20744',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__20745] :
      ( c_24__type__20744___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__20745)
    <=> ! [Vv__CANONICAL__22] :
          ( t(Vv__CANONICAL__22,Vv__CANONICAL__9)
         => t(happ(Vvar__20745,Vv__CANONICAL__22),Vv__CANONICAL__9) ) ) ).

fof('$_type_21090',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__21091] :
      ( c_24__type__21090___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__21091)
    <=> ! [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__21091,Vv__CANONICAL__22),Vv__CANONICAL__23)) ) ) ) ).

fof('$_type_21436',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__21437] :
      ( c_24__type__21436___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__21437)
    <=> ! [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__21437,Vv__CANONICAL__22),Vv__CANONICAL__23)) ) ) ) ).

fof('$_type_21759',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__21760] :
      ( c_24__type__21759___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__21760)
    <=> ! [Vv__CANONICAL__22] :
          ( t(Vv__CANONICAL__22,Vv__CANONICAL__9)
         => t(happ(Vvar__21760,Vv__CANONICAL__22),Vv__CANONICAL__0) ) ) ).

fof('$_type_219',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__220] :
      ( c_24__type__219___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__220)
    <=> ! [Vv__CANONICAL__3] :
          ( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
         => ( ! [Vv__CANONICAL__4] :
                ( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
               => ( p(happ(happ(Vv__CANONICAL__1,Vv__CANONICAL__4),Vv__CANONICAL__3))
                 => cCoq_2eInit_2eWf_2eAcc___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__4) ) )
           => ! [Vv__CANONICAL__5] :
                ( c_24__type__236___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__5)
               => t(happ(happ(Vvar__220,Vv__CANONICAL__3),Vv__CANONICAL__5),happ(Vv__CANONICAL__2,Vv__CANONICAL__3)) ) ) ) ) ).

fof('$_type_22082',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__22083] :
      ( c_24__type__22082___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__22083)
    <=> ! [Vv__CANONICAL__22] :
          ( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__22)
         => t(happ(Vvar__22083,Vv__CANONICAL__22),Vv__CANONICAL__19) ) ) ).

fof('$_type_22428',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__22429] :
      ( c_24__type__22428___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__22429)
    <=> ! [Vv__CANONICAL__22] :
          ( t(Vv__CANONICAL__22,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__23] :
              ( t(Vv__CANONICAL__23,Vv__CANONICAL__19)
             => t(happ(happ(Vvar__22429,Vv__CANONICAL__22),Vv__CANONICAL__23),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_23204',axiom,
    ! [Vvar__23205] :
      ( c_24__type__23204___24t(Vvar__23205)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( c_24__type__4310___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__23205,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).

fof('$_type_23213',axiom,
    ! [Vvar__23214] :
      ( c_24__type__23213___24t(Vvar__23214)
    <=> ! [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__23214,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_23301',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__23302] :
      ( c_24__type__23301___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__23302)
    <=> ! [Vv__CANONICAL__4] :
          ( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__5] :
              ( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
             => t(happ(happ(Vvar__23302,Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_23324',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__23325] :
      ( c_24__type__23324___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__23325)
    <=> ! [Vv__CANONICAL__4] :
          ( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__5] :
              ( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
             => t(happ(happ(Vvar__23325,Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_23347',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__23348] :
      ( c_24__type__23347___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__23348)
    <=> ! [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__23348,Vv__CANONICAL__4),Vv__CANONICAL__5)) ) ) ) ).

fof('$_type_23370',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__23371] :
      ( c_24__type__23370___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__23371)
    <=> ! [Vv__CANONICAL__4] :
          ( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__5] :
              ( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
             => t(happ(happ(Vvar__23371,Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_23388',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__23389] :
      ( c_24__type__23388___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__23389)
    <=> ! [Vv__CANONICAL__4] :
          ( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
         => t(happ(Vvar__23389,Vv__CANONICAL__4),Vv__CANONICAL__0) ) ) ).

fof('$_type_23414',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__23415] :
      ( c_24__type__23414___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__23415)
    <=> ! [Vv__CANONICAL__4] :
          ( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__5] :
              ( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
             => t(happ(happ(Vvar__23415,Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_23432',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__23433] :
      ( c_24__type__23432___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__23433)
    <=> ! [Vv__CANONICAL__4] :
          ( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
         => t(happ(Vvar__23433,Vv__CANONICAL__4),Vv__CANONICAL__0) ) ) ).

fof('$_type_23483',axiom,
    ! [Vvar__23484] :
      ( c_24__type__23483___24t(Vvar__23484)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( c_24__type__3267___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__23484,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__0) ) ) ) ) ) ).

fof('$_type_23538',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__23539] :
      ( c_24__type__23538___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__23539)
    <=> ! [Vv__CANONICAL__2] :
          ( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
         => cProp___24t(happ(Vvar__23539,Vv__CANONICAL__2)) ) ) ).

fof('$_type_23542',axiom,
    ! [Vvar__23543] :
      ( c_24__type__23542___24t(Vvar__23543)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( c_24__type__242___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
             => cType___24t(happ(happ(Vvar__23543,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_23560',axiom,
    ! [Vvar__23561] :
      ( c_24__type__23560___24t(Vvar__23561)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( c_24__type__242___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__23561,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ) ).

fof('$_type_23577',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__23578] :
      ( c_24__type__23577___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__23578)
    <=> ! [Vv__CANONICAL__2] :
          ( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
         => cType___24t(happ(Vvar__23578,Vv__CANONICAL__2)) ) ) ).

fof('$_type_23581',axiom,
    ! [Vvar__23582] :
      ( c_24__type__23581___24t(Vvar__23582)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( c_24__type__181___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
             => cType___24t(happ(happ(Vvar__23582,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_23599',axiom,
    ! [Vvar__23600] :
      ( c_24__type__23599___24t(Vvar__23600)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( c_24__type__181___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__23600,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).

fof('$_type_236',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__237] :
      ( c_24__type__236___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__237)
    <=> ! [Vv__CANONICAL__4] :
          ( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
         => ( p(happ(happ(Vv__CANONICAL__1,Vv__CANONICAL__4),Vv__CANONICAL__3))
           => t(happ(Vvar__237,Vv__CANONICAL__4),happ(Vv__CANONICAL__2,Vv__CANONICAL__4)) ) ) ) ).

fof('$_type_23605',axiom,
    ! [Vvar__23606] :
      ( c_24__type__23605___24t(Vvar__23606)
    <=> ! [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__23606,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ) ).

fof('$_type_23610',axiom,
    ! [Vvar__23611] :
      ( c_24__type__23610___24t(Vvar__23611)
    <=> ! [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__23611,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ) ).

fof('$_type_23994',axiom,
    ! [Vvar__23995] :
      ( c_24__type__23994___24t(Vvar__23995)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
             => cType___24t(happ(happ(Vvar__23995,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_24011',axiom,
    ! [Vvar__24012] :
      ( c_24__type__24011___24t(Vvar__24012)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => cCoq_2eVectors_2eVectorDef_2et___24t(Vv__CANONICAL__0,cCoq_2eInit_2eDatatypes_2eO,happ(Vvar__24012,Vv__CANONICAL__0)) ) ) ).

fof('$_type_24046',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__24047] :
      ( c_24__type__24046___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__24047)
    <=> ! [Vv__CANONICAL__4] :
          ( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
         => cProp___24t(happ(Vvar__24047,Vv__CANONICAL__4)) ) ) ).

fof('$_type_24090',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__24091] :
      ( c_24__type__24090___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__24091)
    <=> ! [Vv__CANONICAL__4] :
          ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__4)
         => cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(Vvar__24091,Vv__CANONICAL__4)) ) ) ).

fof('$_type_24099',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__24100] :
      ( c_24__type__24099___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__24100)
    <=> ! [Vv__CANONICAL__4] :
          ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__4)
         => cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(Vvar__24100,Vv__CANONICAL__4)) ) ) ).

fof('$_type_24121',axiom,
    ! [Vvar__24122] :
      ( c_24__type__24121___24t(Vvar__24122)
    <=> ! [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__24122,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_242',axiom,
    ! [Vv__CANONICAL__0,Vvar__243] :
      ( c_24__type__242___24t(Vv__CANONICAL__0,Vvar__243)
    <=> ! [Vv__CANONICAL__1] :
          ( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
         => cProp___24t(happ(Vvar__243,Vv__CANONICAL__1)) ) ) ).

fof('$_type_24473',axiom,
    ! [Vvar__24474] :
      ( c_24__type__24473___24t(Vvar__24474)
    <=> ! [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_2ecomparison___24t(happ(happ(Vvar__24474,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_24482',axiom,
    ! [Vvar__24483] :
      ( c_24__type__24482___24t(Vvar__24483)
    <=> ! [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__24483,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_24498',axiom,
    ! [Vvar__24499] :
      ( c_24__type__24498___24t(Vvar__24499)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__0)
         => cCoq_2eInit_2eDatatypes_2ebool___24t(happ(Vvar__24499,Vv__CANONICAL__0)) ) ) ).

fof('$_type_24537',axiom,
    ! [Vvar__24538] :
      ( c_24__type__24537___24t(Vvar__24538)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__0)
         => cCoq_2eInit_2eDatatypes_2enat___24t(happ(Vvar__24538,Vv__CANONICAL__0)) ) ) ).

fof('$_type_24659',axiom,
    ! [Vvar__24660] :
      ( c_24__type__24659___24t(Vvar__24660)
    <=> ! [Vv__CANONICAL__0] :
          ( c_24__type__24498___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( c_24__type__24498___24t(Vv__CANONICAL__1)
             => cProp___24t(happ(happ(Vvar__24660,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_2471',axiom,
    ! [Vvar__2472] :
      ( c_24__type__2471___24t(Vvar__2472)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( c_24__type__1376___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__2472,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).

fof('$_type_24723',axiom,
    ! [Vvar__24724] :
      ( c_24__type__24723___24t(Vvar__24724)
    <=> ! [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__24724,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_24730',axiom,
    ! [Vvar__24731] :
      ( c_24__type__24730___24t(Vvar__24731)
    <=> ! [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__24731,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_24732',axiom,
    ! [Vvar__24733] :
      ( c_24__type__24732___24t(Vvar__24733)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__0)
         => cCoq_2eInit_2eDatatypes_2enat___24t(happ(Vvar__24733,Vv__CANONICAL__0)) ) ) ).

fof('$_type_24755',axiom,
    ! [Vvar__24756] :
      ( c_24__type__24755___24t(Vvar__24756)
    <=> ! [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__24756,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_24925',axiom,
    ! [Vvar__24926] :
      ( c_24__type__24925___24t(Vvar__24926)
    <=> ! [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__24926,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_24928',axiom,
    ! [Vvar__24929] :
      ( c_24__type__24928___24t(Vvar__24929)
    <=> ! [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__24929,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_25',axiom,
    ! [Vvar__26] :
      ( c_24__type__25___24t(Vvar__26)
    <=> ! [Vv__CANONICAL__0] :
          ( cA___24t(Vv__CANONICAL__0)
         => cType___24t(happ(Vvar__26,Vv__CANONICAL__0)) ) ) ).

fof('$_type_2511',axiom,
    ! [Vvar__2512] :
      ( c_24__type__2511___24t(Vvar__2512)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( c_24__type__2516___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__2512,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).

fof('$_type_2516',axiom,
    ! [Vv__CANONICAL__0,Vvar__2517] :
      ( c_24__type__2516___24t(Vv__CANONICAL__0,Vvar__2517)
    <=> ! [Vv__CANONICAL__1] :
          ( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__2] :
              ( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__2)
             => cProp___24t(happ(happ(Vvar__2517,Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ).

fof('$_type_25160',axiom,
    ! [Vvar__25161] :
      ( c_24__type__25160___24t(Vvar__25161)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
         => cCoq_2eNumbers_2eBinNums_2eN___24t(happ(Vvar__25161,Vv__CANONICAL__0)) ) ) ).

fof('$_type_25163',axiom,
    ! [Vvar__25164] :
      ( c_24__type__25163___24t(Vvar__25164)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
         => cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(Vvar__25164,Vv__CANONICAL__0)) ) ) ).

fof('$_type_25167',axiom,
    ! [Vvar__25168] :
      ( c_24__type__25167___24t(Vvar__25168)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
         => cCoq_2eNumbers_2eBinNums_2epositive___24t(happ(Vvar__25168,Vv__CANONICAL__0)) ) ) ).

fof('$_type_25191',axiom,
    ! [Vvar__25192] :
      ( c_24__type__25191___24t(Vvar__25192)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
         => cCoq_2eInit_2eDatatypes_2ebool___24t(happ(Vvar__25192,Vv__CANONICAL__0)) ) ) ).

fof('$_type_25245',axiom,
    ! [Vvar__25246] :
      ( c_24__type__25245___24t(Vvar__25246)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__0)
         => cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(Vvar__25246,Vv__CANONICAL__0)) ) ) ).

fof('$_type_2555',axiom,
    ! [Vvar__2556] :
      ( c_24__type__2555___24t(Vvar__2556)
    <=> ! [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__2556,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_2559',axiom,
    ! [Vvar__2560] :
      ( c_24__type__2559___24t(Vvar__2560)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
         => cCoq_2eInit_2eDatatypes_2enat___24t(happ(Vvar__2560,Vv__CANONICAL__0)) ) ) ).

fof('$_type_2562',axiom,
    ! [Vvar__2563] :
      ( c_24__type__2562___24t(Vvar__2563)
    <=> ! [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__2563,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_25710',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__25711] :
      ( c_24__type__25710___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__25711)
    <=> ! [Vv__CANONICAL__8] :
          ( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__9] :
              ( t(Vv__CANONICAL__9,Vv__CANONICAL__0)
             => t(happ(happ(Vvar__25711,Vv__CANONICAL__8),Vv__CANONICAL__9),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_25773',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__25774] :
      ( c_24__type__25773___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__25774)
    <=> ! [Vv__CANONICAL__8] :
          ( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__9] :
              ( t(Vv__CANONICAL__9,Vv__CANONICAL__0)
             => t(happ(happ(Vvar__25774,Vv__CANONICAL__8),Vv__CANONICAL__9),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_25836',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__25837] :
      ( c_24__type__25836___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__25837)
    <=> ! [Vv__CANONICAL__8] :
          ( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__9] :
              ( t(Vv__CANONICAL__9,Vv__CANONICAL__0)
             => t(happ(happ(Vvar__25837,Vv__CANONICAL__8),Vv__CANONICAL__9),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_25890',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__25891] :
      ( c_24__type__25890___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__25891)
    <=> ! [Vv__CANONICAL__8] :
          ( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
         => t(happ(Vvar__25891,Vv__CANONICAL__8),Vv__CANONICAL__0) ) ) ).

fof('$_type_2591',axiom,
    ! [Vvar__2592] :
      ( c_24__type__2591___24t(Vvar__2592)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => cType___24t(happ(Vvar__2592,Vv__CANONICAL__0)) ) ) ).

fof('$_type_25953',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__25954] :
      ( c_24__type__25953___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__25954)
    <=> ! [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__25954,Vv__CANONICAL__8),Vv__CANONICAL__9)) ) ) ) ).

fof('$_type_2603',axiom,
    ! [Vvar__2604] :
      ( c_24__type__2603___24t(Vvar__2604)
    <=> ! [Vv__CANONICAL__0] :
          ( cProp___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cProp___24t(Vv__CANONICAL__1)
             => cType___24t(happ(happ(Vvar__2604,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_26034',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__26035] :
      ( c_24__type__26034___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__26035)
    <=> ! [Vv__CANONICAL__3] :
          ( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__3)
         => cProp___24t(happ(Vvar__26035,Vv__CANONICAL__3)) ) ) ).

fof('$_type_26055',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__26056] :
      ( c_24__type__26055___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__26056)
    <=> ! [Vv__CANONICAL__3] :
          ( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__3)
         => cProp___24t(happ(Vvar__26056,Vv__CANONICAL__3)) ) ) ).

fof('$_type_26090',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__26091] :
      ( c_24__type__26090___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__26091)
    <=> ! [Vv__CANONICAL__5] :
          ( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__5)
         => cProp___24t(happ(Vvar__26091,Vv__CANONICAL__5)) ) ) ).

fof('$_type_26098',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__26099] :
      ( c_24__type__26098___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__26099)
    <=> ! [Vv__CANONICAL__5] :
          ( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__5)
         => cProp___24t(happ(Vvar__26099,Vv__CANONICAL__5)) ) ) ).

fof('$_type_26145',axiom,
    ! [Vv__CANONICAL__0,Vvar__26146] :
      ( c_24__type__26145___24t(Vv__CANONICAL__0,Vvar__26146)
    <=> ! [Vv__CANONICAL__1] :
          ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__1)
         => t(happ(Vvar__26146,Vv__CANONICAL__1),Vv__CANONICAL__0) ) ) ).

fof('$_type_26197',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__26198] :
      ( c_24__type__26197___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__26198)
    <=> ! [Vv__CANONICAL__6] :
          ( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
         => cType___24t(happ(Vvar__26198,Vv__CANONICAL__6)) ) ) ).

fof('$_type_26225',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__26226] :
      ( c_24__type__26225___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__26226)
    <=> ! [Vv__CANONICAL__6] :
          ( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
         => cType___24t(happ(Vvar__26226,Vv__CANONICAL__6)) ) ) ).

fof('$_type_2636',axiom,
    ! [Vvar__2637] :
      ( c_24__type__2636___24t(Vvar__2637)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__0)
         => cCoq_2eNumbers_2eBinNums_2eN___24t(happ(Vvar__2637,Vv__CANONICAL__0)) ) ) ).

fof('$_type_26421',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__26422] :
      ( c_24__type__26421___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__26422)
    <=> ! [Vv__CANONICAL__10] :
          ( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__11] :
              ( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
             => t(happ(happ(Vvar__26422,Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_2643',axiom,
    ! [Vvar__2644] :
      ( c_24__type__2643___24t(Vvar__2644)
    <=> ! [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__2644,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_2647',axiom,
    ! [Vvar__2648] :
      ( c_24__type__2647___24t(Vvar__2648)
    <=> ! [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__2648,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_26514',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__26515] :
      ( c_24__type__26514___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__26515)
    <=> ! [Vv__CANONICAL__10] :
          ( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__11] :
              ( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
             => t(happ(happ(Vvar__26515,Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_26607',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__26608] :
      ( c_24__type__26607___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__26608)
    <=> ! [Vv__CANONICAL__10] :
          ( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__11] :
              ( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
             => t(happ(happ(Vvar__26608,Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_26689',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__26690] :
      ( c_24__type__26689___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__26690)
    <=> ! [Vv__CANONICAL__10] :
          ( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
         => t(happ(Vvar__26690,Vv__CANONICAL__10),Vv__CANONICAL__0) ) ) ).

fof('$_type_26782',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__26783] :
      ( c_24__type__26782___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__26783)
    <=> ! [Vv__CANONICAL__10] :
          ( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__11] :
              ( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
             => t(happ(happ(Vvar__26783,Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_26864',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__26865] :
      ( c_24__type__26864___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__26865)
    <=> ! [Vv__CANONICAL__10] :
          ( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
         => t(happ(Vvar__26865,Vv__CANONICAL__10),Vv__CANONICAL__0) ) ) ).

fof('$_type_26957',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__26958] :
      ( c_24__type__26957___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__26958)
    <=> ! [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__26958,Vv__CANONICAL__10),Vv__CANONICAL__11)) ) ) ) ).

fof('$_type_26988',axiom,
    ! [Vvar__26989] :
      ( c_24__type__26988___24t(Vvar__26989)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
             => ! [Vv__CANONICAL__2] :
                  ( c_24__type__3267___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
                 => ! [Vv__CANONICAL__3] :
                      ( c_24__type__3267___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__26989,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__0) ) ) ) ) ) ) ).

fof('$_type_27038',axiom,
    ! [Vvar__27039] :
      ( c_24__type__27038___24t(Vvar__27039)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => cProp___24t(happ(Vvar__27039,Vv__CANONICAL__0)) ) ) ).

fof('$_type_27072',axiom,
    ! [Vvar__27073] :
      ( c_24__type__27072___24t(Vvar__27073)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
             => cProp___24t(happ(happ(Vvar__27073,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_27092',axiom,
    ! [Vvar__27093] :
      ( c_24__type__27092___24t(Vvar__27093)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( c_24__type__3267___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__27093,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__0) ) ) ) ) ) ) ).

fof('$_type_27113',axiom,
    ! [Vvar__27114] :
      ( c_24__type__27113___24t(Vvar__27114)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( c_24__type__3267___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__27114,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__0) ) ) ) ) ) ).

fof('$_type_27286',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__27287] :
      ( c_24__type__27286___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__27287)
    <=> ! [Vv__CANONICAL__6] :
          ( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__7] :
              ( t(Vv__CANONICAL__7,Vv__CANONICAL__0)
             => t(happ(happ(Vvar__27287,Vv__CANONICAL__6),Vv__CANONICAL__7),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_27325',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__27326] :
      ( c_24__type__27325___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__27326)
    <=> ! [Vv__CANONICAL__6] :
          ( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__7] :
              ( t(Vv__CANONICAL__7,Vv__CANONICAL__0)
             => t(happ(happ(Vvar__27326,Vv__CANONICAL__6),Vv__CANONICAL__7),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_27364',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__27365] :
      ( c_24__type__27364___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__27365)
    <=> ! [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__27365,Vv__CANONICAL__6),Vv__CANONICAL__7)) ) ) ) ).

fof('$_type_2745',axiom,
    ! [Vvar__2746] :
      ( c_24__type__2745___24t(Vvar__2746)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
         => cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(Vvar__2746,Vv__CANONICAL__0)) ) ) ).

fof('$_type_27635',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__27636] :
      ( c_24__type__27635___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__27636)
    <=> ! [Vv__CANONICAL__13] :
          ( t(Vv__CANONICAL__13,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__14] :
              ( t(Vv__CANONICAL__14,Vv__CANONICAL__0)
             => t(happ(happ(Vvar__27636,Vv__CANONICAL__13),Vv__CANONICAL__14),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_27760',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__27761] :
      ( c_24__type__27760___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__27761)
    <=> ! [Vv__CANONICAL__13] :
          ( t(Vv__CANONICAL__13,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__14] :
              ( t(Vv__CANONICAL__14,Vv__CANONICAL__0)
             => t(happ(happ(Vvar__27761,Vv__CANONICAL__13),Vv__CANONICAL__14),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_27885',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__27886] :
      ( c_24__type__27885___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__27886)
    <=> ! [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__27886,Vv__CANONICAL__13),Vv__CANONICAL__14)) ) ) ) ).

fof('$_type_28',axiom,
    ! [Vvar__29] :
      ( c_24__type__28___24t(Vvar__29)
    <=> ! [Vv__CANONICAL__0] :
          ( cA___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cA___24t(Vv__CANONICAL__1)
             => cProp___24t(happ(happ(Vvar__29,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_28010',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__28011] :
      ( c_24__type__28010___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__28011)
    <=> ! [Vv__CANONICAL__13] :
          ( t(Vv__CANONICAL__13,Vv__CANONICAL__6)
         => ! [Vv__CANONICAL__14] :
              ( t(Vv__CANONICAL__14,Vv__CANONICAL__6)
             => t(happ(happ(Vvar__28011,Vv__CANONICAL__13),Vv__CANONICAL__14),Vv__CANONICAL__6) ) ) ) ).

fof('$_type_28135',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__28136] :
      ( c_24__type__28135___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__28136)
    <=> ! [Vv__CANONICAL__13] :
          ( t(Vv__CANONICAL__13,Vv__CANONICAL__6)
         => ! [Vv__CANONICAL__14] :
              ( t(Vv__CANONICAL__14,Vv__CANONICAL__6)
             => t(happ(happ(Vvar__28136,Vv__CANONICAL__13),Vv__CANONICAL__14),Vv__CANONICAL__6) ) ) ) ).

fof('$_type_28260',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__28261] :
      ( c_24__type__28260___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__28261)
    <=> ! [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__28261,Vv__CANONICAL__13),Vv__CANONICAL__14)) ) ) ) ).

fof('$_type_28371',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__28372] :
      ( c_24__type__28371___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__28372)
    <=> ! [Vv__CANONICAL__13] :
          ( t(Vv__CANONICAL__13,Vv__CANONICAL__6)
         => t(happ(Vvar__28372,Vv__CANONICAL__13),Vv__CANONICAL__0) ) ) ).

fof('$_type_28629',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__28630] :
      ( c_24__type__28629___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__28630)
    <=> ! [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__28630,Vv__CANONICAL__4),Vv__CANONICAL__5)) ) ) ) ).

fof('$_type_28649',axiom,
    ! [Vvar__28650] :
      ( c_24__type__28649___24t(Vvar__28650)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cType___24t(Vv__CANONICAL__1)
             => ! [Vv__CANONICAL__2] :
                  ( c_24__type__117___24t(Vv__CANONICAL__1,Vv__CANONICAL__2)
                 => ! [Vv__CANONICAL__3] :
                      ( c_24__type__28659___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__3)
                     => cProp___24t(happ(happ(happ(happ(Vvar__28650,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).

fof('$_type_28659',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__28660] :
      ( c_24__type__28659___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__28660)
    <=> ! [Vv__CANONICAL__2] :
          ( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__3] :
              ( t(Vv__CANONICAL__3,Vv__CANONICAL__1)
             => t(happ(happ(Vvar__28660,Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__1) ) ) ) ).

fof('$_type_28692',axiom,
    ! [Vvar__28693] :
      ( c_24__type__28692___24t(Vvar__28693)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cType___24t(Vv__CANONICAL__1)
             => ! [Vv__CANONICAL__2] :
                  ( c_24__type__117___24t(Vv__CANONICAL__1,Vv__CANONICAL__2)
                 => ! [Vv__CANONICAL__3] :
                      ( c_24__type__28702___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__3)
                     => ! [Vv__CANONICAL__4] :
                          ( c_24__type__28659___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__4)
                         => cProp___24t(happ(happ(happ(happ(happ(Vvar__28693,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ) ) ) ).

fof('$_type_28702',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__28703] :
      ( c_24__type__28702___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__28703)
    <=> ! [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__28703,Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ).

fof('$_type_28782',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__28783] :
      ( c_24__type__28782___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__28783)
    <=> ! [Vv__CANONICAL__3] :
          ( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
         => cProp___24t(happ(Vvar__28783,Vv__CANONICAL__3)) ) ) ).

fof('$_type_28790',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__28791] :
      ( c_24__type__28790___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__28791)
    <=> ! [Vv__CANONICAL__3] :
          ( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
         => cProp___24t(happ(Vvar__28791,Vv__CANONICAL__3)) ) ) ).

fof('$_type_28798',axiom,
    ! [Vvar__28799] :
      ( c_24__type__28798___24t(Vvar__28799)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( c_24__type__242___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
             => ! [Vv__CANONICAL__2] :
                  ( c_24__type__242___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
                 => cType___24t(happ(happ(happ(Vvar__28799,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).

fof('$_type_28838',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__28839] :
      ( c_24__type__28838___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__28839)
    <=> ! [Vv__CANONICAL__3] :
          ( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
         => cType___24t(happ(Vvar__28839,Vv__CANONICAL__3)) ) ) ).

fof('$_type_28846',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__28847] :
      ( c_24__type__28846___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__28847)
    <=> ! [Vv__CANONICAL__3] :
          ( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
         => cType___24t(happ(Vvar__28847,Vv__CANONICAL__3)) ) ) ).

fof('$_type_28854',axiom,
    ! [Vvar__28855] :
      ( c_24__type__28854___24t(Vvar__28855)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( c_24__type__181___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
             => ! [Vv__CANONICAL__2] :
                  ( c_24__type__181___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
                 => cType___24t(happ(happ(happ(Vvar__28855,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).

fof('$_type_28880',axiom,
    ! [Vvar__28881] :
      ( c_24__type__28880___24t(Vvar__28881)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cProp___24t(Vv__CANONICAL__1)
             => cType___24t(happ(happ(Vvar__28881,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_28901',axiom,
    ! [Vvar__28902] :
      ( c_24__type__28901___24t(Vvar__28902)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ( p(c_24False)
           => t(happ(Vvar__28902,Vv__CANONICAL__0),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_28958',axiom,
    ! [Vvar__28959] :
      ( c_24__type__28958___24t(Vvar__28959)
    <=> ! [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__28959,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).

fof('$_type_29442',axiom,
    ! [Vvar__29443] :
      ( c_24__type__29442___24t(Vvar__29443)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__0)
         => cProp___24t(happ(Vvar__29443,Vv__CANONICAL__0)) ) ) ).

fof('$_type_29501',axiom,
    ! [Vvar__29502] :
      ( c_24__type__29501___24t(Vvar__29502)
    <=> ! [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__29502,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_29595',axiom,
    ! [Vvar__29596] :
      ( c_24__type__29595___24t(Vvar__29596)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( c_24__type__3276___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__29596,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__0) ) ) ) ) ) ).

fof('$_type_29610',axiom,
    ! [Vvar__29611] :
      ( c_24__type__29610___24t(Vvar__29611)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( c_24__type__3267___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__29611,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__0) ) ) ) ) ) ).

fof('$_type_29672',axiom,
    ! [Vvar__29673] :
      ( c_24__type__29672___24t(Vvar__29673)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__0)
         => cType___24t(happ(Vvar__29673,Vv__CANONICAL__0)) ) ) ).

fof('$_type_29736',axiom,
    ! [Vvar__29737] :
      ( c_24__type__29736___24t(Vvar__29737)
    <=> ! [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__29737,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_29741',axiom,
    ! [Vvar__29742] :
      ( c_24__type__29741___24t(Vvar__29742)
    <=> ! [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)
                 => cProp___24t(happ(happ(happ(Vvar__29742,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).

fof('$_type_29746',axiom,
    ! [Vvar__29747] :
      ( c_24__type__29746___24t(Vvar__29747)
    <=> ! [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__29747,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).

fof('$_type_29748',axiom,
    ! [Vvar__29749] :
      ( c_24__type__29748___24t(Vvar__29749)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eInit_2eByte_2ebyte___24t(Vv__CANONICAL__0)
         => cCoq_2eInit_2eByte_2ebyte___24t(happ(Vvar__29749,Vv__CANONICAL__0)) ) ) ).

fof('$_type_29751',axiom,
    ! [Vvar__29752] :
      ( c_24__type__29751___24t(Vvar__29752)
    <=> ! [Vv__CANONICAL__0] :
          ( c_24__type__29753___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cCoq_2eInit_2eDatatypes_2eEmpty__set___24t(Vv__CANONICAL__1)
             => t(happ(happ(Vvar__29752,Vv__CANONICAL__0),Vv__CANONICAL__1),happ(Vv__CANONICAL__0,Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_29753',axiom,
    ! [Vvar__29754] :
      ( c_24__type__29753___24t(Vvar__29754)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eInit_2eDatatypes_2eEmpty__set___24t(Vv__CANONICAL__0)
         => cType___24t(happ(Vvar__29754,Vv__CANONICAL__0)) ) ) ).

fof('$_type_29755',axiom,
    ! [Vvar__29756] :
      ( c_24__type__29755___24t(Vvar__29756)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eInit_2eDatatypes_2eEmpty__set___24t(Vv__CANONICAL__0)
         => cProp___24t(happ(Vvar__29756,Vv__CANONICAL__0)) ) ) ).

fof('$_type_29761',axiom,
    ! [Vvar__29762] :
      ( c_24__type__29761___24t(Vvar__29762)
    <=> ! [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__29762,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).

fof('$_type_29766',axiom,
    ! [Vvar__29767] :
      ( c_24__type__29766___24t(Vvar__29767)
    <=> ! [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__29767,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).

fof('$_type_29778',axiom,
    ! [Vvar__29779] :
      ( c_24__type__29778___24t(Vvar__29779)
    <=> ! [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__29779,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__1) ) ) ) ) ).

fof('$_type_29791',axiom,
    ! [Vvar__29792] :
      ( c_24__type__29791___24t(Vvar__29792)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eInit_2eDecimal_2eint___24t(Vv__CANONICAL__0)
         => cCoq_2eInit_2eDecimal_2eint___24t(happ(Vvar__29792,Vv__CANONICAL__0)) ) ) ).

fof('$_type_29794',axiom,
    ! [Vvar__29795] :
      ( c_24__type__29794___24t(Vvar__29795)
    <=> ! [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__29795,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_29797',axiom,
    ! [Vvar__29798] :
      ( c_24__type__29797___24t(Vvar__29798)
    <=> ! [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__29798,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_29800',axiom,
    ! [Vvar__29801] :
      ( c_24__type__29800___24t(Vvar__29801)
    <=> ! [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__29801,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_29805',axiom,
    ! [Vvar__29806] :
      ( c_24__type__29805___24t(Vvar__29806)
    <=> ! [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__29806,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).

fof('$_type_29813',axiom,
    ! [Vvar__29814] :
      ( c_24__type__29813___24t(Vvar__29814)
    <=> ! [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__29814,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).

fof('$_type_29816',axiom,
    ! [Vvar__29817] :
      ( c_24__type__29816___24t(Vvar__29817)
    <=> ! [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__29817,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_29827',axiom,
    ! [Vvar__29828] :
      ( c_24__type__29827___24t(Vvar__29828)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( c_24__type__181___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
             => ! [Vv__CANONICAL__2] :
                  ( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
                 => ! [Vv__CANONICAL__3] :
                      ( t(Vv__CANONICAL__3,happ(Vv__CANONICAL__1,Vv__CANONICAL__2))
                     => cProp___24t(happ(happ(happ(happ(Vvar__29828,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).

fof('$_type_29836',axiom,
    ! [Vvar__29837] :
      ( c_24__type__29836___24t(Vvar__29837)
    <=> ! [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__29837,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ) ).

fof('$_type_29838',axiom,
    ! [Vvar__29839] :
      ( c_24__type__29838___24t(Vvar__29839)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vv__CANONICAL__0,happ(Vvar__29839,Vv__CANONICAL__0)) ) ) ).

fof('$_type_29843',axiom,
    ! [Vv__CANONICAL__0,Vvar__29844] :
      ( c_24__type__29843___24t(Vv__CANONICAL__0,Vvar__29844)
    <=> ! [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__29844,Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ).

fof('$_type_29854',axiom,
    ! [Vvar__29855] :
      ( c_24__type__29854___24t(Vvar__29855)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( c_24__type__29843___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__29855,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__0) ) ) ) ) ) ).

fof('$_type_29872',axiom,
    ! [Vvar__29873] :
      ( c_24__type__29872___24t(Vvar__29873)
    <=> ! [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__29873,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_29877',axiom,
    ! [Vvar__29878] :
      ( c_24__type__29877___24t(Vvar__29878)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2esetoid__ring_2eInitialRing_2ehypo___24t(Vv__CANONICAL__0)
         => cType___24t(happ(Vvar__29878,Vv__CANONICAL__0)) ) ) ).

fof('$_type_29888',axiom,
    ! [Vvar__29889] :
      ( c_24__type__29888___24t(Vvar__29889)
    <=> ! [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__29889,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__0) ) ) ) ) ).

fof('$_type_29897',axiom,
    ! [Vvar__29898] :
      ( c_24__type__29897___24t(Vvar__29898)
    <=> ! [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_2elist___24t(Vv__CANONICAL__0,happ(happ(Vvar__29898,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_29921',axiom,
    ! [Vvar__29922] :
      ( c_24__type__29921___24t(Vvar__29922)
    <=> ! [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__29922,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__0) ) ) ) ) ).

fof('$_type_29945',axiom,
    ! [Vvar__29946] :
      ( c_24__type__29945___24t(Vvar__29946)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cType___24t(Vv__CANONICAL__1)
             => ! [Vv__CANONICAL__2] :
                  ( c_24__type__10700___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__29946,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__0) ) ) ) ) ) ) ).

fof('$_type_29974',axiom,
    ! [Vvar__29975] :
      ( c_24__type__29974___24t(Vvar__29975)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cType___24t(Vv__CANONICAL__1)
             => ! [Vv__CANONICAL__2] :
                  ( c_24__type__29981___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__29975,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__0) ) ) ) ) ) ) ).

fof('$_type_29981',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__29982] :
      ( c_24__type__29981___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__29982)
    <=> ! [Vv__CANONICAL__2] :
          ( t(Vv__CANONICAL__2,Vv__CANONICAL__1)
         => ! [Vv__CANONICAL__3] :
              ( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
             => t(happ(happ(Vvar__29982,Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_30021',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__30022] :
      ( c_24__type__30021___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__30022)
    <=> ! [Vv__CANONICAL__3] :
          ( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
         => cProp___24t(happ(Vvar__30022,Vv__CANONICAL__3)) ) ) ).

fof('$_type_30045',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__30046] :
      ( c_24__type__30045___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__30046)
    <=> ! [Vv__CANONICAL__3] :
          ( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
         => cProp___24t(happ(Vvar__30046,Vv__CANONICAL__3)) ) ) ).

fof('$_type_30092',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__30093] :
      ( c_24__type__30092___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__30093)
    <=> ! [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__30093,Vv__CANONICAL__5),Vv__CANONICAL__6)) ) ) ) ).

fof('$_type_30127',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__30128] :
      ( c_24__type__30127___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__30128)
    <=> ! [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__30128,Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ).

fof('$_type_30143',axiom,
    ! [Vvar__30144] :
      ( c_24__type__30143___24t(Vvar__30144)
    <=> ! [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__30144,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_30162',axiom,
    ! [Vvar__30163] :
      ( c_24__type__30162___24t(Vvar__30163)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
         => cCoq_2eInit_2eDatatypes_2ebool___24t(happ(Vvar__30163,Vv__CANONICAL__0)) ) ) ).

fof('$_type_30184',axiom,
    ! [Vvar__30185] :
      ( c_24__type__30184___24t(Vvar__30185)
    <=> ! [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__30185,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).

fof('$_type_30202',axiom,
    ! [Vvar__30203] :
      ( c_24__type__30202___24t(Vvar__30203)
    <=> ! [Vv__CANONICAL__0] :
          ( c_24__type__30162___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( c_24__type__30162___24t(Vv__CANONICAL__1)
             => cProp___24t(happ(happ(Vvar__30203,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_30784',axiom,
    ! [Vvar__30785] :
      ( c_24__type__30784___24t(Vvar__30785)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__0)
         => cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(Vvar__30785,Vv__CANONICAL__0)) ) ) ).

fof('$_type_30788',axiom,
    ! [Vvar__30789] :
      ( c_24__type__30788___24t(Vvar__30789)
    <=> ! [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__30789,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_31041',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__31042] :
      ( c_24__type__31041___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__31042)
    <=> ! [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__31042,Vv__CANONICAL__6),Vv__CANONICAL__7)) ) ) ) ).

fof('$_type_31066',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__31067] :
      ( c_24__type__31066___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__31067)
    <=> ! [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__31067,Vv__CANONICAL__6),Vv__CANONICAL__7)) ) ) ) ).

fof('$_type_31138',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__31139] :
      ( c_24__type__31138___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__31139)
    <=> ! [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__31139,Vv__CANONICAL__6),Vv__CANONICAL__7)) ) ) ) ).

fof('$_type_31163',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__31164] :
      ( c_24__type__31163___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__31164)
    <=> ! [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__31164,Vv__CANONICAL__6),Vv__CANONICAL__7)) ) ) ) ).

fof('$_type_31205',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__31206] :
      ( c_24__type__31205___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__31206)
    <=> ! [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__31206,Vv__CANONICAL__4),Vv__CANONICAL__5)) ) ) ) ).

fof('$_type_31256',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__31257] :
      ( c_24__type__31256___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__31257)
    <=> ! [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__31257,Vv__CANONICAL__4),Vv__CANONICAL__5)) ) ) ) ).

fof('$_type_31354',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__31355] :
      ( c_24__type__31354___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__31355)
    <=> ! [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__31355,Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ).

fof('$_type_3174',axiom,
    ! [Vvar__3175] :
      ( c_24__type__3174___24t(Vvar__3175)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
         => cProp___24t(happ(Vvar__3175,Vv__CANONICAL__0)) ) ) ).

fof('$_type_31817',axiom,
    ! [Vvar__31818] :
      ( c_24__type__31817___24t(Vvar__31818)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( c_24__type__4310___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)
                     => cCoq_2eInit_2eDatatypes_2ebool___24t(happ(happ(happ(happ(Vvar__31818,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).

fof('$_type_31896',axiom,
    ! [Vvar__31897] :
      ( c_24__type__31896___24t(Vvar__31897)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
             => ! [Vv__CANONICAL__2] :
                  ( c_24__type__117___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
                 => ! [Vv__CANONICAL__3] :
                      ( c_24__type__117___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
                     => ! [Vv__CANONICAL__4] :
                          ( c_24__type__117___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__31897,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__6)) ) ) ) ) ) ) ) ) ).

fof('$_type_31908',axiom,
    ! [Vvar__31909] :
      ( c_24__type__31908___24t(Vvar__31909)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
             => cCoq_2emicromega_2eRingMicromega_2ePsatz___24t(Vv__CANONICAL__0,happ(happ(Vvar__31909,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_31910',axiom,
    ! [Vvar__31911] :
      ( c_24__type__31910___24t(Vvar__31911)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => cCoq_2emicromega_2eRingMicromega_2ePsatz___24t(Vv__CANONICAL__0,happ(Vvar__31911,Vv__CANONICAL__0)) ) ) ).

fof('$_type_31987',axiom,
    ! [Vvar__31988] :
      ( c_24__type__31987___24t(Vvar__31988)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( c_24__type__117___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
             => ! [Vv__CANONICAL__2] :
                  ( c_24__type__117___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
                 => ! [Vv__CANONICAL__3] :
                      ( c_24__type__117___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
                     => ! [Vv__CANONICAL__4] :
                          ( cCoq_2emicromega_2eRingMicromega_2eOp2___24t(Vv__CANONICAL__4)
                         => ! [Vv__CANONICAL__5] :
                              ( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
                             => ! [Vv__CANONICAL__6] :
                                  ( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
                                 => cProp___24t(happ(happ(happ(happ(happ(happ(happ(Vvar__31988,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__6)) ) ) ) ) ) ) ) ) ).

fof('$_type_31999',axiom,
    ! [Vvar__32000] :
      ( c_24__type__31999___24t(Vvar__32000)
    <=> ! [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__32000,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_32002',axiom,
    ! [Vvar__32003] :
      ( c_24__type__32002___24t(Vvar__32003)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vv__CANONICAL__0,happ(Vvar__32003,Vv__CANONICAL__0)) ) ) ).

fof('$_type_32007',axiom,
    ! [Vvar__32008] :
      ( c_24__type__32007___24t(Vvar__32008)
    <=> ! [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_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__2)
                 => cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vv__CANONICAL__0,happ(happ(happ(Vvar__32008,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).

fof('$_type_32212',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__32213] :
      ( c_24__type__32212___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__32213)
    <=> ! [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__32213,Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ).

fof('$_type_32252',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__32253] :
      ( c_24__type__32252___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__32253)
    <=> ! [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__32253,Vv__CANONICAL__4),Vv__CANONICAL__5)) ) ) ) ).

fof('$_type_32292',axiom,
    ! [Vvar__32293] :
      ( c_24__type__32292___24t(Vvar__32293)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cType___24t(Vv__CANONICAL__1)
             => ! [Vv__CANONICAL__2] :
                  ( c_24__type__117___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
                 => ! [Vv__CANONICAL__3] :
                      ( c_24__type__32302___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__3)
                     => ! [Vv__CANONICAL__4] :
                          ( c_24__type__28659___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__4)
                         => cProp___24t(happ(happ(happ(happ(happ(Vvar__32293,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ) ) ) ).

fof('$_type_32302',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__32303] :
      ( c_24__type__32302___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__32303)
    <=> ! [Vv__CANONICAL__2] :
          ( t(Vv__CANONICAL__2,Vv__CANONICAL__1)
         => ! [Vv__CANONICAL__3] :
              ( t(Vv__CANONICAL__3,Vv__CANONICAL__1)
             => cProp___24t(happ(happ(Vvar__32303,Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ).

fof('$_type_32350',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__32351] :
      ( c_24__type__32350___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__32351)
    <=> ! [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__32351,Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ).

fof('$_type_3236',axiom,
    ! [Vvar__3237] :
      ( c_24__type__3236___24t(Vvar__3237)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__0)
         => cCoq_2eNumbers_2eBinNums_2epositive___24t(happ(Vvar__3237,Vv__CANONICAL__0)) ) ) ).

fof('$_type_32389',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__32390] :
      ( c_24__type__32389___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__32390)
    <=> ! [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__32390,Vv__CANONICAL__4),Vv__CANONICAL__5)) ) ) ) ).

fof('$_type_32424',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__32425] :
      ( c_24__type__32424___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__32425)
    <=> ! [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__32425,Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ).

fof('$_type_32459',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__32460] :
      ( c_24__type__32459___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__32460)
    <=> ! [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__32460,Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ).

fof('$_type_32479',axiom,
    ! [Vvar__32480] :
      ( c_24__type__32479___24t(Vvar__32480)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( c_24__type__242___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
             => ! [Vv__CANONICAL__2] :
                  ( c_24__type__242___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
                 => ! [Vv__CANONICAL__3] :
                      ( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
                     => ( p(happ(Vv__CANONICAL__1,Vv__CANONICAL__3))
                       => ( p(happ(Vv__CANONICAL__2,Vv__CANONICAL__3))
                         => cCoq_2eInit_2eSpecif_2esig2___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,happ(happ(happ(happ(Vvar__32480,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ) ) ).

fof('$_type_32501',axiom,
    ! [Vvar__32502] :
      ( c_24__type__32501___24t(Vvar__32502)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( c_24__type__181___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
             => ! [Vv__CANONICAL__2] :
                  ( c_24__type__181___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
                 => ! [Vv__CANONICAL__3] :
                      ( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
                     => ! [Vv__CANONICAL__4] :
                          ( t(Vv__CANONICAL__4,happ(Vv__CANONICAL__1,Vv__CANONICAL__3))
                         => ! [Vv__CANONICAL__5] :
                              ( t(Vv__CANONICAL__5,happ(Vv__CANONICAL__2,Vv__CANONICAL__3))
                             => cCoq_2eInit_2eSpecif_2esigT2___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,happ(happ(happ(happ(happ(happ(Vvar__32502,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5)) ) ) ) ) ) ) ) ).

fof('$_type_32519',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__32520] :
      ( c_24__type__32519___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__32520)
    <=> ! [Vv__CANONICAL__2] :
          ( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
         => cProp___24t(happ(Vvar__32520,Vv__CANONICAL__2)) ) ) ).

fof('$_type_32525',axiom,
    ! [Vvar__32526] :
      ( c_24__type__32525___24t(Vvar__32526)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( c_24__type__242___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__32526,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__0) ) ) ) ) ).

fof('$_type_32542',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__32543] :
      ( c_24__type__32542___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__32543)
    <=> ! [Vv__CANONICAL__2] :
          ( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
         => cType___24t(happ(Vvar__32543,Vv__CANONICAL__2)) ) ) ).

fof('$_type_32548',axiom,
    ! [Vvar__32549] :
      ( c_24__type__32548___24t(Vvar__32549)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( c_24__type__181___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__32549,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__0) ) ) ) ) ).

fof('$_type_32554',axiom,
    ! [Vvar__32555] :
      ( c_24__type__32554___24t(Vvar__32555)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cProp___24t(Vv__CANONICAL__1)
             => ! [Vv__CANONICAL__2] :
                  ( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
                 => cCoq_2eInit_2eSpecif_2esumor___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,happ(happ(happ(Vvar__32555,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).

fof('$_type_32559',axiom,
    ! [Vvar__32560] :
      ( c_24__type__32559___24t(Vvar__32560)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cProp___24t(Vv__CANONICAL__1)
             => ( p(Vv__CANONICAL__1)
               => cCoq_2eInit_2eSpecif_2esumor___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,happ(happ(Vvar__32560,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ) ).

fof('$_type_3256',axiom,
    ! [Vvar__3257] :
      ( c_24__type__3256___24t(Vvar__3257)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,happ(Vvar__3257,Vv__CANONICAL__0)) ) ) ).

fof('$_type_32562',axiom,
    ! [Vvar__32563] :
      ( c_24__type__32562___24t(Vvar__32563)
    <=> ! [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__32563,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_32570',axiom,
    ! [Vvar__32571] :
      ( c_24__type__32570___24t(Vvar__32571)
    <=> ! [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__32571,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).

fof('$_type_32588',axiom,
    ! [Vvar__32589] :
      ( c_24__type__32588___24t(Vvar__32589)
    <=> ! [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__32589,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ) ) ) ).

fof('$_type_32605',axiom,
    ! [Vvar__32606] :
      ( c_24__type__32605___24t(Vvar__32606)
    <=> ! [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__32606,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5)) ) ) ) ) ) ) ) ).

fof('$_type_3261',axiom,
    ! [Vvar__3262] :
      ( c_24__type__3261___24t(Vvar__3262)
    <=> ! [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__3262,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).

fof('$_type_32641',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__32642] :
      ( c_24__type__32641___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__32642)
    <=> ! [Vv__CANONICAL__4] :
          ( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
         => cProp___24t(happ(Vvar__32642,Vv__CANONICAL__4)) ) ) ).

fof('$_type_3267',axiom,
    ! [Vv__CANONICAL__0,Vvar__3268] :
      ( c_24__type__3267___24t(Vv__CANONICAL__0,Vvar__3268)
    <=> ! [Vv__CANONICAL__1] :
          ( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__2] :
              ( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
             => t(happ(happ(Vvar__3268,Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_32707',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__32708] :
      ( c_24__type__32707___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__32708)
    <=> ! [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__32708,Vv__CANONICAL__6),Vv__CANONICAL__7)) ) ) ) ).

fof('$_type_3276',axiom,
    ! [Vv__CANONICAL__0,Vvar__3277] :
      ( c_24__type__3276___24t(Vv__CANONICAL__0,Vvar__3277)
    <=> ! [Vv__CANONICAL__1] :
          ( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
         => t(happ(Vvar__3277,Vv__CANONICAL__1),Vv__CANONICAL__0) ) ) ).

fof('$_type_32763',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__32764] :
      ( c_24__type__32763___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__32764)
    <=> ! [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__32764,Vv__CANONICAL__6),Vv__CANONICAL__7)) ) ) ) ).

fof('$_type_329',axiom,
    ! [Vvar__330] :
      ( c_24__type__329___24t(Vvar__330)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( c_24__type__117___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
             => cProp___24t(happ(happ(Vvar__330,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_32911',axiom,
    ! [Vvar__32912] :
      ( c_24__type__32911___24t(Vvar__32912)
    <=> ! [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__32912,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).

fof('$_type_32914',axiom,
    ! [Vvar__32915] :
      ( c_24__type__32914___24t(Vvar__32915)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__0)
         => cCoq_2eNumbers_2eBinNums_2epositive___24t(happ(Vvar__32915,Vv__CANONICAL__0)) ) ) ).

fof('$_type_32930',axiom,
    ! [Vvar__32931] :
      ( c_24__type__32930___24t(Vvar__32931)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
             => ! [Vv__CANONICAL__2] :
                  ( c_24__type__32935___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
                 => ! [Vv__CANONICAL__3] :
                      ( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__3)
                     => t(happ(happ(happ(happ(Vvar__32931,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__0) ) ) ) ) ) ).

fof('$_type_32935',axiom,
    ! [Vv__CANONICAL__0,Vvar__32936] :
      ( c_24__type__32935___24t(Vv__CANONICAL__0,Vvar__32936)
    <=> ! [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__32936,Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_32952',axiom,
    ! [Vvar__32953] :
      ( c_24__type__32952___24t(Vvar__32953)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
             => ! [Vv__CANONICAL__2] :
                  ( c_24__type__32957___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
                 => ! [Vv__CANONICAL__3] :
                      ( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__3)
                     => t(happ(happ(happ(happ(Vvar__32953,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__0) ) ) ) ) ) ).

fof('$_type_32957',axiom,
    ! [Vv__CANONICAL__0,Vvar__32958] :
      ( c_24__type__32957___24t(Vv__CANONICAL__0,Vvar__32958)
    <=> ! [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__32958,Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_32970',axiom,
    ! [Vvar__32971] :
      ( c_24__type__32970___24t(Vvar__32971)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__0)
         => cCoq_2eInit_2eDatatypes_2enat___24t(happ(Vvar__32971,Vv__CANONICAL__0)) ) ) ).

fof('$_type_32979',axiom,
    ! [Vvar__32980] :
      ( c_24__type__32979___24t(Vvar__32980)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__0)
         => cCoq_2ePArith_2eBinPosDef_2ePos_2emask___24t(happ(Vvar__32980,Vv__CANONICAL__0)) ) ) ).

fof('$_type_33011',axiom,
    ! [Vvar__33012] :
      ( c_24__type__33011___24t(Vvar__33012)
    <=> ! [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__33012,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_33041',axiom,
    ! [Vvar__33042] :
      ( c_24__type__33041___24t(Vvar__33042)
    <=> ! [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__33042,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_33048',axiom,
    ! [Vvar__33049] :
      ( c_24__type__33048___24t(Vvar__33049)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
         => cCoq_2eNumbers_2eBinNums_2epositive___24t(happ(Vvar__33049,Vv__CANONICAL__0)) ) ) ).

fof('$_type_33074',axiom,
    ! [Vvar__33075] :
      ( c_24__type__33074___24t(Vvar__33075)
    <=> ! [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__33075,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_33079',axiom,
    ! [Vvar__33080] :
      ( c_24__type__33079___24t(Vvar__33080)
    <=> ! [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__33080,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).

fof('$_type_33101',axiom,
    ! [Vvar__33102] :
      ( c_24__type__33101___24t(Vvar__33102)
    <=> ! [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__33102,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_33129',axiom,
    ! [Vvar__33130] :
      ( c_24__type__33129___24t(Vvar__33130)
    <=> ! [Vv__CANONICAL__0] :
          ( c_24__type__25191___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( c_24__type__25191___24t(Vv__CANONICAL__1)
             => cProp___24t(happ(happ(Vvar__33130,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_35',axiom,
    ! [Vvar__36] :
      ( c_24__type__35___24t(Vvar__36)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
         => cProp___24t(happ(Vvar__36,Vv__CANONICAL__0)) ) ) ).

fof('$_type_3928',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__3929] :
      ( c_24__type__3928___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__3929)
    <=> ! [Vv__CANONICAL__2] :
          ( t(Vv__CANONICAL__2,Vv__CANONICAL__1)
         => t(happ(Vvar__3929,Vv__CANONICAL__2),Vv__CANONICAL__0) ) ) ).

fof('$_type_4',axiom,
    ! [Vv__CANONICAL__0,Vvar__5] :
      ( c_24__type__4___24t(Vv__CANONICAL__0,Vvar__5)
    <=> ! [Vv__CANONICAL__1] :
          ( cA___24t(Vv__CANONICAL__1)
         => ( cR___24a2(Vv__CANONICAL__1,Vv__CANONICAL__0)
           => cP___24t(Vv__CANONICAL__1,happ(Vvar__5,Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_4310',axiom,
    ! [Vv__CANONICAL__0,Vvar__4311] :
      ( c_24__type__4310___24t(Vv__CANONICAL__0,Vvar__4311)
    <=> ! [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__4311,Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ).

fof('$_type_433',axiom,
    ! [Vvar__434] :
      ( c_24__type__433___24t(Vvar__434)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( c_24__type__117___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
             => ( cCoq_2eInit_2eWf_2ewell__founded___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1)
               => ! [Vv__CANONICAL__3] :
                    ( c_24__type__181___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
                   => ! [Vv__CANONICAL__4] :
                        ( c_24__type__459___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__3,Vv__CANONICAL__4)
                       => ! [Vv__CANONICAL__5] :
                            ( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
                           => t(happ(happ(happ(happ(happ(Vvar__434,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5),happ(Vv__CANONICAL__3,Vv__CANONICAL__5)) ) ) ) ) ) ) ) ).

fof('$_type_4334',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__4335] :
      ( c_24__type__4334___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__4335)
    <=> ! [Vv__CANONICAL__2] :
          ( t(Vv__CANONICAL__2,Vv__CANONICAL__1)
         => ! [Vv__CANONICAL__3] :
              ( t(Vv__CANONICAL__3,Vv__CANONICAL__1)
             => t(happ(happ(Vvar__4335,Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__1) ) ) ) ).

fof('$_type_4348',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__4349] :
      ( c_24__type__4348___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__4349)
    <=> ! [Vv__CANONICAL__2] :
          ( t(Vv__CANONICAL__2,Vv__CANONICAL__1)
         => t(happ(Vvar__4349,Vv__CANONICAL__2),Vv__CANONICAL__1) ) ) ).

fof('$_type_4355',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__4356] :
      ( c_24__type__4355___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__4356)
    <=> ! [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__4356,Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ).

fof('$_type_459',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__460] :
      ( c_24__type__459___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__460)
    <=> ! [Vv__CANONICAL__3] :
          ( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__4] :
              ( c_24__type__474___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4)
             => t(happ(happ(Vvar__460,Vv__CANONICAL__3),Vv__CANONICAL__4),happ(Vv__CANONICAL__2,Vv__CANONICAL__3)) ) ) ) ).

fof('$_type_47',axiom,
    ! [Vvar__48] :
      ( c_24__type__47___24t(Vvar__48)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cType___24t(Vv__CANONICAL__1)
             => cType___24t(happ(happ(Vvar__48,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_474',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__475] :
      ( c_24__type__474___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__475)
    <=> ! [Vv__CANONICAL__4] :
          ( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
         => ( p(happ(happ(Vv__CANONICAL__1,Vv__CANONICAL__4),Vv__CANONICAL__3))
           => t(happ(Vvar__475,Vv__CANONICAL__4),happ(Vv__CANONICAL__2,Vv__CANONICAL__4)) ) ) ) ).

fof('$_type_4767',axiom,
    ! [Vvar__4768] :
      ( c_24__type__4767___24t(Vvar__4768)
    <=> ! [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__4768,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_4817',axiom,
    ! [Vvar__4818] :
      ( c_24__type__4817___24t(Vvar__4818)
    <=> ! [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__4818,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_4822',axiom,
    ! [Vvar__4823] :
      ( c_24__type__4822___24t(Vvar__4823)
    <=> ! [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__4823,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).

fof('$_type_4830',axiom,
    ! [Vvar__4831] :
      ( c_24__type__4830___24t(Vvar__4831)
    <=> ! [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__4831,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).

fof('$_type_5076',axiom,
    ! [Vvar__5077] :
      ( c_24__type__5076___24t(Vvar__5077)
    <=> ! [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__5077,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_5079',axiom,
    ! [Vvar__5080] :
      ( c_24__type__5079___24t(Vvar__5080)
    <=> ! [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__5080,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_5084',axiom,
    ! [Vvar__5085] :
      ( c_24__type__5084___24t(Vvar__5085)
    <=> ! [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__5085,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).

fof('$_type_592',axiom,
    ! [Vvar__593] :
      ( c_24__type__592___24t(Vvar__593)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( c_24__type__117___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
             => ! [Vv__CANONICAL__2] :
                  ( c_24__type__181___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
                 => ! [Vv__CANONICAL__3] :
                      ( c_24__type__618___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3)
                     => ! [Vv__CANONICAL__4] :
                          ( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
                         => ( cCoq_2eInit_2eWf_2eAcc___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__4)
                           => t(happ(happ(happ(happ(happ(Vvar__593,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),happ(Vv__CANONICAL__2,Vv__CANONICAL__4)) ) ) ) ) ) ) ) ).

fof('$_type_618',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__619] :
      ( c_24__type__618___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__619)
    <=> ! [Vv__CANONICAL__3] :
          ( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__4] :
              ( c_24__type__633___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4)
             => t(happ(happ(Vvar__619,Vv__CANONICAL__3),Vv__CANONICAL__4),happ(Vv__CANONICAL__2,Vv__CANONICAL__3)) ) ) ) ).

fof('$_type_63',axiom,
    ! [Vvar__64] :
      ( c_24__type__63___24t(Vvar__64)
    <=> ! [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__64,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).

fof('$_type_633',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__634] :
      ( c_24__type__633___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__634)
    <=> ! [Vv__CANONICAL__4] :
          ( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
         => ( p(happ(happ(Vv__CANONICAL__1,Vv__CANONICAL__4),Vv__CANONICAL__3))
           => t(happ(Vvar__634,Vv__CANONICAL__4),happ(Vv__CANONICAL__2,Vv__CANONICAL__4)) ) ) ) ).

fof('$_type_6456',axiom,
    ! [Vvar__6457] :
      ( c_24__type__6456___24t(Vvar__6457)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
             => ! [Vv__CANONICAL__2] :
                  ( c_24__type__3267___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__6457,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__0) ) ) ) ) ) ) ).

fof('$_type_6710',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__6711] :
      ( c_24__type__6710___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__6711)
    <=> ! [Vv__CANONICAL__8] :
          ( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__9] :
              ( t(Vv__CANONICAL__9,Vv__CANONICAL__0)
             => t(happ(happ(Vvar__6711,Vv__CANONICAL__8),Vv__CANONICAL__9),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_6773',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__6774] :
      ( c_24__type__6773___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__6774)
    <=> ! [Vv__CANONICAL__8] :
          ( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__9] :
              ( t(Vv__CANONICAL__9,Vv__CANONICAL__0)
             => t(happ(happ(Vvar__6774,Vv__CANONICAL__8),Vv__CANONICAL__9),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_6836',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__6837] :
      ( c_24__type__6836___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__6837)
    <=> ! [Vv__CANONICAL__8] :
          ( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__9] :
              ( t(Vv__CANONICAL__9,Vv__CANONICAL__0)
             => t(happ(happ(Vvar__6837,Vv__CANONICAL__8),Vv__CANONICAL__9),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_684',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__685] :
      ( c_24__type__684___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__685)
    <=> ! [Vv__CANONICAL__3] :
          ( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__4] :
              ( c_24__type__699___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4)
             => t(happ(happ(Vvar__685,Vv__CANONICAL__3),Vv__CANONICAL__4),happ(Vv__CANONICAL__2,Vv__CANONICAL__3)) ) ) ) ).

fof('$_type_6890',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__6891] :
      ( c_24__type__6890___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__6891)
    <=> ! [Vv__CANONICAL__8] :
          ( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
         => t(happ(Vvar__6891,Vv__CANONICAL__8),Vv__CANONICAL__0) ) ) ).

fof('$_type_6953',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__6954] :
      ( c_24__type__6953___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__6954)
    <=> ! [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__6954,Vv__CANONICAL__8),Vv__CANONICAL__9)) ) ) ) ).

fof('$_type_699',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__700] :
      ( c_24__type__699___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__700)
    <=> ! [Vv__CANONICAL__4] :
          ( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
         => ( p(happ(happ(Vv__CANONICAL__1,Vv__CANONICAL__4),Vv__CANONICAL__3))
           => t(happ(Vvar__700,Vv__CANONICAL__4),happ(Vv__CANONICAL__2,Vv__CANONICAL__4)) ) ) ) ).

fof('$_type_7160',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__7161] :
      ( c_24__type__7160___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__7161)
    <=> ! [Vv__CANONICAL__5] :
          ( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__6] :
              ( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
             => t(happ(happ(Vvar__7161,Vv__CANONICAL__5),Vv__CANONICAL__6),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_7190',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__7191] :
      ( c_24__type__7190___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__7191)
    <=> ! [Vv__CANONICAL__5] :
          ( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__6] :
              ( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
             => t(happ(happ(Vvar__7191,Vv__CANONICAL__5),Vv__CANONICAL__6),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_7214',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__7215] :
      ( c_24__type__7214___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__7215)
    <=> ! [Vv__CANONICAL__5] :
          ( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
         => t(happ(Vvar__7215,Vv__CANONICAL__5),Vv__CANONICAL__0) ) ) ).

fof('$_type_7244',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__7245] :
      ( c_24__type__7244___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__7245)
    <=> ! [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__7245,Vv__CANONICAL__5),Vv__CANONICAL__6)) ) ) ) ).

fof('$_type_7274',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__7275] :
      ( c_24__type__7274___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__7275)
    <=> ! [Vv__CANONICAL__5] :
          ( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__6] :
              ( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
             => t(happ(happ(Vvar__7275,Vv__CANONICAL__5),Vv__CANONICAL__6),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_7298',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__7299] :
      ( c_24__type__7298___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__7299)
    <=> ! [Vv__CANONICAL__5] :
          ( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
         => t(happ(Vvar__7299,Vv__CANONICAL__5),Vv__CANONICAL__0) ) ) ).

fof('$_type_73',axiom,
    ! [Vvar__74] :
      ( c_24__type__73___24t(Vvar__74)
    <=> ! [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__74,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_7331',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__7332] :
      ( c_24__type__7331___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__7332)
    <=> ! [Vv__CANONICAL__5] :
          ( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__6] :
              ( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
             => t(happ(happ(Vvar__7332,Vv__CANONICAL__5),Vv__CANONICAL__6),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_7355',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__7356] :
      ( c_24__type__7355___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__7356)
    <=> ! [Vv__CANONICAL__5] :
          ( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
         => t(happ(Vvar__7356,Vv__CANONICAL__5),Vv__CANONICAL__0) ) ) ).

fof('$_type_7382',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__7383] :
      ( c_24__type__7382___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__7383)
    <=> ! [Vv__CANONICAL__5] :
          ( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
         => t(happ(Vvar__7383,Vv__CANONICAL__5),Vv__CANONICAL__0) ) ) ).

fof('$_type_7781',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__7782] :
      ( c_24__type__7781___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__7782)
    <=> ! [Vv__CANONICAL__17] :
          ( t(Vv__CANONICAL__17,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__18] :
              ( t(Vv__CANONICAL__18,Vv__CANONICAL__0)
             => t(happ(happ(Vvar__7782,Vv__CANONICAL__17),Vv__CANONICAL__18),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_794',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__795] :
      ( c_24__type__794___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__795)
    <=> ! [Vv__CANONICAL__3] :
          ( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__4] :
              ( c_24__type__809___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4)
             => t(happ(happ(Vvar__795,Vv__CANONICAL__3),Vv__CANONICAL__4),happ(Vv__CANONICAL__2,Vv__CANONICAL__3)) ) ) ) ).

fof('$_type_7994',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__7995] :
      ( c_24__type__7994___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__7995)
    <=> ! [Vv__CANONICAL__17] :
          ( t(Vv__CANONICAL__17,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__18] :
              ( t(Vv__CANONICAL__18,Vv__CANONICAL__0)
             => t(happ(happ(Vvar__7995,Vv__CANONICAL__17),Vv__CANONICAL__18),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_809',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__810] :
      ( c_24__type__809___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__810)
    <=> ! [Vv__CANONICAL__4] :
          ( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
         => ( p(happ(happ(Vv__CANONICAL__1,Vv__CANONICAL__4),Vv__CANONICAL__3))
           => t(happ(Vvar__810,Vv__CANONICAL__4),happ(Vv__CANONICAL__2,Vv__CANONICAL__4)) ) ) ) ).

fof('$_type_8207',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__8208] :
      ( c_24__type__8207___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__8208)
    <=> ! [Vv__CANONICAL__17] :
          ( t(Vv__CANONICAL__17,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__18] :
              ( t(Vv__CANONICAL__18,Vv__CANONICAL__0)
             => t(happ(happ(Vvar__8208,Vv__CANONICAL__17),Vv__CANONICAL__18),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_824',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__825] :
      ( c_24__type__824___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__825)
    <=> ! [Vv__CANONICAL__4] :
          ( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
         => ( p(happ(happ(Vv__CANONICAL__1,Vv__CANONICAL__4),Vv__CANONICAL__3))
           => t(happ(Vvar__825,Vv__CANONICAL__4),happ(Vv__CANONICAL__2,Vv__CANONICAL__4)) ) ) ) ).

fof('$_type_839',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__840] :
      ( c_24__type__839___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__840)
    <=> ! [Vv__CANONICAL__4] :
          ( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
         => ( p(happ(happ(Vv__CANONICAL__1,Vv__CANONICAL__4),Vv__CANONICAL__3))
           => t(happ(Vvar__840,Vv__CANONICAL__4),happ(Vv__CANONICAL__2,Vv__CANONICAL__4)) ) ) ) ).

fof('$_type_8402',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__8403] :
      ( c_24__type__8402___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__8403)
    <=> ! [Vv__CANONICAL__17] :
          ( t(Vv__CANONICAL__17,Vv__CANONICAL__0)
         => t(happ(Vvar__8403,Vv__CANONICAL__17),Vv__CANONICAL__0) ) ) ).

fof('$_type_8615',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__8616] :
      ( c_24__type__8615___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__8616)
    <=> ! [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__8616,Vv__CANONICAL__17),Vv__CANONICAL__18)) ) ) ) ).

fof('$_type_877',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__878] :
      ( c_24__type__877___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__878)
    <=> ! [Vv__CANONICAL__3] :
          ( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__4] :
              ( c_24__type__892___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4)
             => t(happ(happ(Vvar__878,Vv__CANONICAL__3),Vv__CANONICAL__4),happ(Vv__CANONICAL__2,Vv__CANONICAL__3)) ) ) ) ).

fof('$_type_8828',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__8829] :
      ( c_24__type__8828___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__8829)
    <=> ! [Vv__CANONICAL__17] :
          ( t(Vv__CANONICAL__17,Vv__CANONICAL__8)
         => ! [Vv__CANONICAL__18] :
              ( t(Vv__CANONICAL__18,Vv__CANONICAL__8)
             => t(happ(happ(Vvar__8829,Vv__CANONICAL__17),Vv__CANONICAL__18),Vv__CANONICAL__8) ) ) ) ).

fof('$_type_892',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__893] :
      ( c_24__type__892___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__893)
    <=> ! [Vv__CANONICAL__4] :
          ( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
         => ( p(happ(happ(Vv__CANONICAL__1,Vv__CANONICAL__4),Vv__CANONICAL__3))
           => t(happ(Vvar__893,Vv__CANONICAL__4),happ(Vv__CANONICAL__2,Vv__CANONICAL__4)) ) ) ) ).

fof('$_type_9041',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__9042] :
      ( c_24__type__9041___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__9042)
    <=> ! [Vv__CANONICAL__17] :
          ( t(Vv__CANONICAL__17,Vv__CANONICAL__8)
         => ! [Vv__CANONICAL__18] :
              ( t(Vv__CANONICAL__18,Vv__CANONICAL__8)
             => t(happ(happ(Vvar__9042,Vv__CANONICAL__17),Vv__CANONICAL__18),Vv__CANONICAL__8) ) ) ) ).

fof('$_type_907',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__908] :
      ( c_24__type__907___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__908)
    <=> ! [Vv__CANONICAL__4] :
          ( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
         => ( p(happ(happ(Vv__CANONICAL__1,Vv__CANONICAL__4),Vv__CANONICAL__3))
           => t(happ(Vvar__908,Vv__CANONICAL__4),happ(Vv__CANONICAL__2,Vv__CANONICAL__4)) ) ) ) ).

fof('$_type_922',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__923] :
      ( c_24__type__922___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__923)
    <=> ! [Vv__CANONICAL__4] :
          ( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
         => ( p(happ(happ(Vv__CANONICAL__1,Vv__CANONICAL__4),Vv__CANONICAL__3))
           => t(happ(Vvar__923,Vv__CANONICAL__4),happ(Vv__CANONICAL__2,Vv__CANONICAL__4)) ) ) ) ).

fof('$_type_9254',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__9255] :
      ( c_24__type__9254___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__9255)
    <=> ! [Vv__CANONICAL__17] :
          ( t(Vv__CANONICAL__17,Vv__CANONICAL__8)
         => ! [Vv__CANONICAL__18] :
              ( t(Vv__CANONICAL__18,Vv__CANONICAL__8)
             => t(happ(happ(Vvar__9255,Vv__CANONICAL__17),Vv__CANONICAL__18),Vv__CANONICAL__8) ) ) ) ).

fof('$_type_9449',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__9450] :
      ( c_24__type__9449___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__9450)
    <=> ! [Vv__CANONICAL__17] :
          ( t(Vv__CANONICAL__17,Vv__CANONICAL__8)
         => t(happ(Vvar__9450,Vv__CANONICAL__17),Vv__CANONICAL__8) ) ) ).

fof('$_type_9662',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__9663] :
      ( c_24__type__9662___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__9663)
    <=> ! [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__9663,Vv__CANONICAL__17),Vv__CANONICAL__18)) ) ) ) ).

fof('$_type_9857',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__9858] :
      ( c_24__type__9857___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__9858)
    <=> ! [Vv__CANONICAL__17] :
          ( t(Vv__CANONICAL__17,Vv__CANONICAL__8)
         => t(happ(Vvar__9858,Vv__CANONICAL__17),Vv__CANONICAL__0) ) ) ).

fof('$_type_9999',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__10000] :
      ( c_24__type__9999___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__10000)
    <=> ! [Vv__CANONICAL__4] :
          ( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
         => t(happ(Vvar__10000,Vv__CANONICAL__4),Vv__CANONICAL__0) ) ) ).

fof('$_typeof_A',axiom,
    cType___24t(cA) ).

fof('$_typeof_Coq.Arith.Between.in_int',axiom,
    c_24__type__29741___24t(cCoq_2eArith_2eBetween_2ein__int) ).

fof('$_typeof_Coq.Arith.EqNat.eq_nat',axiom,
    c_24__type__73___24t(cCoq_2eArith_2eEqNat_2eeq__nat) ).

fof('$_typeof_Coq.Arith.PeanoNat.Nat.b2n',axiom,
    c_24__type__32970___24t(cCoq_2eArith_2ePeanoNat_2eNat_2eb2n) ).

fof('$_typeof_Coq.Arith.PeanoNat.Nat.divide',axiom,
    c_24__type__73___24t(cCoq_2eArith_2ePeanoNat_2eNat_2edivide) ).

fof('$_typeof_Coq.Arith.PeanoNat.Nat.eq',axiom,
    c_24__type__73___24t(cCoq_2eArith_2ePeanoNat_2eNat_2eeq) ).

fof('$_typeof_Coq.Arith.PeanoNat.Nat.eqf',axiom,
    c_24__type__30202___24t(cCoq_2eArith_2ePeanoNat_2eNat_2eeqf) ).

fof('$_typeof_Coq.Arith.PeanoNat.Nat.le',axiom,
    c_24__type__73___24t(cCoq_2eArith_2ePeanoNat_2eNat_2ele) ).

fof('$_typeof_Coq.Arith.PeanoNat.Nat.lt',axiom,
    c_24__type__73___24t(cCoq_2eArith_2ePeanoNat_2eNat_2elt) ).

fof('$_typeof_Coq.Arith.PeanoNat.Nat.recursion',axiom,
    c_24__type__32952___24t(cCoq_2eArith_2ePeanoNat_2eNat_2erecursion) ).

fof('$_typeof_Coq.Arith.Plus.tail_plus',axiom,
    c_24__type__4767___24t(cCoq_2eArith_2ePlus_2etail__plus) ).

fof('$_typeof_Coq.Arith.Wf_nat.gtof',axiom,
    c_24__type__2471___24t(cCoq_2eArith_2eWf__nat_2egtof) ).

fof('$_typeof_Coq.Arith.Wf_nat.inv_lt_rel',axiom,
    c_24__type__2511___24t(cCoq_2eArith_2eWf__nat_2einv__lt__rel) ).

fof('$_typeof_Coq.Arith.Wf_nat.ltof',axiom,
    c_24__type__2471___24t(cCoq_2eArith_2eWf__nat_2eltof) ).

fof('$_typeof_Coq.Bool.Bool.Is_true',axiom,
    c_24__type__11779___24t(cCoq_2eBool_2eBool_2eIs__true) ).

fof('$_typeof_Coq.Bool.Bool.eqb',axiom,
    c_24__type__10943___24t(cCoq_2eBool_2eBool_2eeqb) ).

fof('$_typeof_Coq.Bool.Bool.ifb',axiom,
    c_24__type__29746___24t(cCoq_2eBool_2eBool_2eifb) ).

fof('$_typeof_Coq.Bool.Bool.reflect',axiom,
    c_24__type__10953___24t(cCoq_2eBool_2eBool_2ereflect) ).

fof('$_typeof_Coq.Bool.Bvector.Bvector',axiom,
    c_24__type__11799___24t(cCoq_2eBool_2eBvector_2eBvector) ).

fof('$_typeof_Coq.Bool.Zerob.zerob',axiom,
    c_24__type__30162___24t(cCoq_2eBool_2eZerob_2ezerob) ).

fof('$_typeof_Coq.FSets.FSetPositive.PositiveSet.Equal',axiom,
    c_24__type__24928___24t(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eEqual) ).

fof('$_typeof_Coq.FSets.FSetPositive.PositiveSet.In',axiom,
    c_24__type__24925___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__33079___24t(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eNode) ).

fof('$_typeof_Coq.FSets.FSetPositive.PositiveSet.Subset',axiom,
    c_24__type__24928___24t(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eSubset) ).

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__24928___24t(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eeq) ).

fof('$_typeof_Coq.FSets.FSetPositive.PositiveSet.mem',axiom,
    c_24__type__24755___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.Init.Byte.byte',axiom,
    cType___24t(cCoq_2eInit_2eByte_2ebyte) ).

fof('$_typeof_Coq.Init.Byte.byte_of_byte',axiom,
    c_24__type__29748___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__11945___24t(cCoq_2eInit_2eDatatypes_2eCompOpp) ).

fof('$_typeof_Coq.Init.Datatypes.CompareSpecT',axiom,
    c_24__type__11987___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.Empty_set_rect',axiom,
    c_24__type__29751___24t(cCoq_2eInit_2eDatatypes_2eEmpty__set__rect) ).

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__11823___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__1427___24t(cCoq_2eInit_2eDatatypes_2eS) ).

fof('$_typeof_Coq.Init.Datatypes.Some',axiom,
    c_24__type__11821___24t(cCoq_2eInit_2eDatatypes_2eSome) ).

fof('$_typeof_Coq.Init.Datatypes.andb',axiom,
    c_24__type__10943___24t(cCoq_2eInit_2eDatatypes_2eandb) ).

fof('$_typeof_Coq.Init.Datatypes.app',axiom,
    c_24__type__11943___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__3261___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__11863___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__10943___24t(cCoq_2eInit_2eDatatypes_2eimplb) ).

fof('$_typeof_Coq.Init.Datatypes.inl',axiom,
    c_24__type__29761___24t(cCoq_2eInit_2eDatatypes_2einl) ).

fof('$_typeof_Coq.Init.Datatypes.inr',axiom,
    c_24__type__29766___24t(cCoq_2eInit_2eDatatypes_2einr) ).

fof('$_typeof_Coq.Init.Datatypes.length',axiom,
    c_24__type__11931___24t(cCoq_2eInit_2eDatatypes_2elength) ).

fof('$_typeof_Coq.Init.Datatypes.list',axiom,
    c_24__type__2591___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__11797___24t(cCoq_2eInit_2eDatatypes_2enat__rect) ).

fof('$_typeof_Coq.Init.Datatypes.negb',axiom,
    c_24__type__11775___24t(cCoq_2eInit_2eDatatypes_2enegb) ).

fof('$_typeof_Coq.Init.Datatypes.nil',axiom,
    c_24__type__3256___24t(cCoq_2eInit_2eDatatypes_2enil) ).

fof('$_typeof_Coq.Init.Datatypes.option',axiom,
    c_24__type__2591___24t(cCoq_2eInit_2eDatatypes_2eoption) ).

fof('$_typeof_Coq.Init.Datatypes.orb',axiom,
    c_24__type__10943___24t(cCoq_2eInit_2eDatatypes_2eorb) ).

fof('$_typeof_Coq.Init.Datatypes.pair',axiom,
    c_24__type__63___24t(cCoq_2eInit_2eDatatypes_2epair) ).

fof('$_typeof_Coq.Init.Datatypes.prod',axiom,
    c_24__type__47___24t(cCoq_2eInit_2eDatatypes_2eprod) ).

fof('$_typeof_Coq.Init.Datatypes.snd',axiom,
    c_24__type__29778___24t(cCoq_2eInit_2eDatatypes_2esnd) ).

fof('$_typeof_Coq.Init.Datatypes.sum',axiom,
    c_24__type__47___24t(cCoq_2eInit_2eDatatypes_2esum) ).

fof('$_typeof_Coq.Init.Datatypes.true',axiom,
    cCoq_2eInit_2eDatatypes_2ebool___24t(cCoq_2eInit_2eDatatypes_2etrue) ).

fof('$_typeof_Coq.Init.Datatypes.tt',axiom,
    cCoq_2eInit_2eDatatypes_2eunit___24t(cCoq_2eInit_2eDatatypes_2ett) ).

fof('$_typeof_Coq.Init.Datatypes.unit',axiom,
    cType___24t(cCoq_2eInit_2eDatatypes_2eunit) ).

fof('$_typeof_Coq.Init.Datatypes.xorb',axiom,
    c_24__type__10943___24t(cCoq_2eInit_2eDatatypes_2exorb) ).

fof('$_typeof_Coq.Init.Decimal.D0',axiom,
    c_24__type__12265___24t(cCoq_2eInit_2eDecimal_2eD0) ).

fof('$_typeof_Coq.Init.Decimal.D1',axiom,
    c_24__type__12265___24t(cCoq_2eInit_2eDecimal_2eD1) ).

fof('$_typeof_Coq.Init.Decimal.D2',axiom,
    c_24__type__12265___24t(cCoq_2eInit_2eDecimal_2eD2) ).

fof('$_typeof_Coq.Init.Decimal.D3',axiom,
    c_24__type__12265___24t(cCoq_2eInit_2eDecimal_2eD3) ).

fof('$_typeof_Coq.Init.Decimal.D4',axiom,
    c_24__type__12265___24t(cCoq_2eInit_2eDecimal_2eD4) ).

fof('$_typeof_Coq.Init.Decimal.D5',axiom,
    c_24__type__12265___24t(cCoq_2eInit_2eDecimal_2eD5) ).

fof('$_typeof_Coq.Init.Decimal.D6',axiom,
    c_24__type__12265___24t(cCoq_2eInit_2eDecimal_2eD6) ).

fof('$_typeof_Coq.Init.Decimal.D7',axiom,
    c_24__type__12265___24t(cCoq_2eInit_2eDecimal_2eD7) ).

fof('$_typeof_Coq.Init.Decimal.D8',axiom,
    c_24__type__12265___24t(cCoq_2eInit_2eDecimal_2eD8) ).

fof('$_typeof_Coq.Init.Decimal.D9',axiom,
    c_24__type__12265___24t(cCoq_2eInit_2eDecimal_2eD9) ).

fof('$_typeof_Coq.Init.Decimal.Neg',axiom,
    c_24__type__12276___24t(cCoq_2eInit_2eDecimal_2eNeg) ).

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__12276___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__29791___24t(cCoq_2eInit_2eDecimal_2eint__of__int) ).

fof('$_typeof_Coq.Init.Decimal.nzhead',axiom,
    c_24__type__12265___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__12265___24t(cCoq_2eInit_2eDecimal_2euint__of__uint) ).

fof('$_typeof_Coq.Init.Logic_Type.notT',axiom,
    c_24__type__27038___24t(cCoq_2eInit_2eLogic__Type_2enotT) ).

fof('$_typeof_Coq.Init.Nat.add',axiom,
    c_24__type__4767___24t(cCoq_2eInit_2eNat_2eadd) ).

fof('$_typeof_Coq.Init.Nat.compare',axiom,
    c_24__type__30143___24t(cCoq_2eInit_2eNat_2ecompare) ).

fof('$_typeof_Coq.Init.Nat.div2',axiom,
    c_24__type__1427___24t(cCoq_2eInit_2eNat_2ediv2) ).

fof('$_typeof_Coq.Init.Nat.double',axiom,
    c_24__type__1427___24t(cCoq_2eInit_2eNat_2edouble) ).

fof('$_typeof_Coq.Init.Nat.eqb',axiom,
    c_24__type__15031___24t(cCoq_2eInit_2eNat_2eeqb) ).

fof('$_typeof_Coq.Init.Nat.even',axiom,
    c_24__type__30162___24t(cCoq_2eInit_2eNat_2eeven) ).

fof('$_typeof_Coq.Init.Nat.gcd',axiom,
    c_24__type__4767___24t(cCoq_2eInit_2eNat_2egcd) ).

fof('$_typeof_Coq.Init.Nat.leb',axiom,
    c_24__type__15031___24t(cCoq_2eInit_2eNat_2eleb) ).

fof('$_typeof_Coq.Init.Nat.log2_iter',axiom,
    c_24__type__30184___24t(cCoq_2eInit_2eNat_2elog2__iter) ).

fof('$_typeof_Coq.Init.Nat.max',axiom,
    c_24__type__4767___24t(cCoq_2eInit_2eNat_2emax) ).

fof('$_typeof_Coq.Init.Nat.min',axiom,
    c_24__type__4767___24t(cCoq_2eInit_2eNat_2emin) ).

fof('$_typeof_Coq.Init.Nat.mul',axiom,
    c_24__type__4767___24t(cCoq_2eInit_2eNat_2emul) ).

fof('$_typeof_Coq.Init.Nat.one',axiom,
    cCoq_2eInit_2eDatatypes_2enat___24t(cCoq_2eInit_2eNat_2eone) ).

fof('$_typeof_Coq.Init.Nat.pow',axiom,
    c_24__type__4767___24t(cCoq_2eInit_2eNat_2epow) ).

fof('$_typeof_Coq.Init.Nat.pred',axiom,
    c_24__type__1427___24t(cCoq_2eInit_2eNat_2epred) ).

fof('$_typeof_Coq.Init.Nat.sqrt_iter',axiom,
    c_24__type__30184___24t(cCoq_2eInit_2eNat_2esqrt__iter) ).

fof('$_typeof_Coq.Init.Nat.square',axiom,
    c_24__type__1427___24t(cCoq_2eInit_2eNat_2esquare) ).

fof('$_typeof_Coq.Init.Nat.sub',axiom,
    c_24__type__4767___24t(cCoq_2eInit_2eNat_2esub) ).

fof('$_typeof_Coq.Init.Nat.succ',axiom,
    c_24__type__1427___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__4767___24t(cCoq_2eInit_2eNat_2etail__add) ).

fof('$_typeof_Coq.Init.Nat.testbit',axiom,
    c_24__type__15031___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__35___24t(cCoq_2eInit_2ePeano_2eIsSucc) ).

fof('$_typeof_Coq.Init.Peano.ge',axiom,
    c_24__type__73___24t(cCoq_2eInit_2ePeano_2ege) ).

fof('$_typeof_Coq.Init.Peano.gt',axiom,
    c_24__type__73___24t(cCoq_2eInit_2ePeano_2egt) ).

fof('$_typeof_Coq.Init.Peano.lt',axiom,
    c_24__type__73___24t(cCoq_2eInit_2ePeano_2elt) ).

fof('$_typeof_Coq.Init.Specif.Exc',axiom,
    c_24__type__2591___24t(cCoq_2eInit_2eSpecif_2eExc) ).

fof('$_typeof_Coq.Init.Specif.except',axiom,
    c_24__type__28901___24t(cCoq_2eInit_2eSpecif_2eexcept) ).

fof('$_typeof_Coq.Init.Specif.exist',axiom,
    c_24__type__23560___24t(cCoq_2eInit_2eSpecif_2eexist) ).

fof('$_typeof_Coq.Init.Specif.exist2',axiom,
    c_24__type__32479___24t(cCoq_2eInit_2eSpecif_2eexist2) ).

fof('$_typeof_Coq.Init.Specif.existT',axiom,
    c_24__type__23599___24t(cCoq_2eInit_2eSpecif_2eexistT) ).

fof('$_typeof_Coq.Init.Specif.existT2',axiom,
    c_24__type__32501___24t(cCoq_2eInit_2eSpecif_2eexistT2) ).

fof('$_typeof_Coq.Init.Specif.inleft',axiom,
    c_24__type__32554___24t(cCoq_2eInit_2eSpecif_2einleft) ).

fof('$_typeof_Coq.Init.Specif.inright',axiom,
    c_24__type__32559___24t(cCoq_2eInit_2eSpecif_2einright) ).

fof('$_typeof_Coq.Init.Specif.left',axiom,
    c_24__type__23605___24t(cCoq_2eInit_2eSpecif_2eleft) ).

fof('$_typeof_Coq.Init.Specif.proj1_sig',axiom,
    c_24__type__32525___24t(cCoq_2eInit_2eSpecif_2eproj1__sig) ).

fof('$_typeof_Coq.Init.Specif.projT1',axiom,
    c_24__type__32548___24t(cCoq_2eInit_2eSpecif_2eprojT1) ).

fof('$_typeof_Coq.Init.Specif.right',axiom,
    c_24__type__23610___24t(cCoq_2eInit_2eSpecif_2eright) ).

fof('$_typeof_Coq.Init.Specif.sig',axiom,
    c_24__type__23542___24t(cCoq_2eInit_2eSpecif_2esig) ).

fof('$_typeof_Coq.Init.Specif.sig2',axiom,
    c_24__type__28798___24t(cCoq_2eInit_2eSpecif_2esig2) ).

fof('$_typeof_Coq.Init.Specif.sigT',axiom,
    c_24__type__23581___24t(cCoq_2eInit_2eSpecif_2esigT) ).

fof('$_typeof_Coq.Init.Specif.sigT2',axiom,
    c_24__type__28854___24t(cCoq_2eInit_2eSpecif_2esigT2) ).

fof('$_typeof_Coq.Init.Specif.sumbool',axiom,
    c_24__type__2603___24t(cCoq_2eInit_2eSpecif_2esumbool) ).

fof('$_typeof_Coq.Init.Specif.sumor',axiom,
    c_24__type__28880___24t(cCoq_2eInit_2eSpecif_2esumor) ).

fof('$_typeof_Coq.Init.Wf.Acc_rect',axiom,
    c_24__type__175___24t(cCoq_2eInit_2eWf_2eAcc__rect) ).

fof('$_typeof_Coq.Init.Wf.Fix',axiom,
    c_24__type__433___24t(cCoq_2eInit_2eWf_2eFix) ).

fof('$_typeof_Coq.Init.Wf.Fix_F',axiom,
    c_24__type__592___24t(cCoq_2eInit_2eWf_2eFix__F) ).

fof('$_typeof_Coq.Init.Wf.Fix_F_2',axiom,
    c_24__type__1100___24t(cCoq_2eInit_2eWf_2eFix__F__2) ).

fof('$_typeof_Coq.Init.Wf.well_founded',axiom,
    c_24__type__329___24t(cCoq_2eInit_2eWf_2ewell__founded) ).

fof('$_typeof_Coq.Init.Wf.well_founded_induction',axiom,
    c_24__type__433___24t(cCoq_2eInit_2eWf_2ewell__founded__induction) ).

fof('$_typeof_Coq.Init.Wf.well_founded_induction_type',axiom,
    c_24__type__433___24t(cCoq_2eInit_2eWf_2ewell__founded__induction__type) ).

fof('$_typeof_Coq.Init.Wf.well_founded_induction_type_2',axiom,
    c_24__type__1279___24t(cCoq_2eInit_2eWf_2ewell__founded__induction__type__2) ).

fof('$_typeof_Coq.Lists.List.In',axiom,
    c_24__type__14839___24t(cCoq_2eLists_2eList_2eIn) ).

fof('$_typeof_Coq.Lists.List.fold_left',axiom,
    c_24__type__29945___24t(cCoq_2eLists_2eList_2efold__left) ).

fof('$_typeof_Coq.Lists.List.fold_right',axiom,
    c_24__type__29974___24t(cCoq_2eLists_2eList_2efold__right) ).

fof('$_typeof_Coq.Lists.List.hd',axiom,
    c_24__type__29888___24t(cCoq_2eLists_2eList_2ehd) ).

fof('$_typeof_Coq.Lists.List.last',axiom,
    c_24__type__29921___24t(cCoq_2eLists_2eList_2elast) ).

fof('$_typeof_Coq.Lists.List.nth',axiom,
    c_24__type__14864___24t(cCoq_2eLists_2eList_2enth) ).

fof('$_typeof_Coq.Lists.List.tl',axiom,
    c_24__type__29897___24t(cCoq_2eLists_2eList_2etl) ).

fof('$_typeof_Coq.Lists.SetoidList.compat_op',axiom,
    c_24__type__32292___24t(cCoq_2eLists_2eSetoidList_2ecompat__op) ).

fof('$_typeof_Coq.Lists.SetoidList.transpose',axiom,
    c_24__type__28649___24t(cCoq_2eLists_2eSetoidList_2etranspose) ).

fof('$_typeof_Coq.Lists.SetoidList.transpose2',axiom,
    c_24__type__28649___24t(cCoq_2eLists_2eSetoidList_2etranspose2) ).

fof('$_typeof_Coq.Lists.SetoidList.transpose_restr',axiom,
    c_24__type__28692___24t(cCoq_2eLists_2eSetoidList_2etranspose__restr) ).

fof('$_typeof_Coq.Lists.SetoidList.transpose_restr2',axiom,
    c_24__type__28692___24t(cCoq_2eLists_2eSetoidList_2etranspose__restr2) ).

fof('$_typeof_Coq.Logic.Decidable.decidable',axiom,
    c_24__type__12132___24t(cCoq_2eLogic_2eDecidable_2edecidable) ).

fof('$_typeof_Coq.Logic.EqdepFacts.Eq_dep_eq_on',axiom,
    c_24__type__29827___24t(cCoq_2eLogic_2eEqdepFacts_2eEq__dep__eq__on) ).

fof('$_typeof_Coq.Logic.EqdepFacts.UIP_on_',axiom,
    c_24__type__29836___24t(cCoq_2eLogic_2eEqdepFacts_2eUIP__on__) ).

fof('$_typeof_Coq.NArith.BinNat.N.divide',axiom,
    c_24__type__2647___24t(cCoq_2eNArith_2eBinNat_2eN_2edivide) ).

fof('$_typeof_Coq.NArith.BinNat.N.eq',axiom,
    c_24__type__2647___24t(cCoq_2eNArith_2eBinNat_2eN_2eeq) ).

fof('$_typeof_Coq.NArith.BinNat.N.eqf',axiom,
    c_24__type__24659___24t(cCoq_2eNArith_2eBinNat_2eN_2eeqf) ).

fof('$_typeof_Coq.NArith.BinNat.N.le',axiom,
    c_24__type__2647___24t(cCoq_2eNArith_2eBinNat_2eN_2ele) ).

fof('$_typeof_Coq.NArith.BinNat.N.lt',axiom,
    c_24__type__2647___24t(cCoq_2eNArith_2eBinNat_2eN_2elt) ).

fof('$_typeof_Coq.NArith.BinNat.N.recursion',axiom,
    c_24__type__32930___24t(cCoq_2eNArith_2eBinNat_2eN_2erecursion) ).

fof('$_typeof_Coq.NArith.BinNatDef.N.add',axiom,
    c_24__type__2643___24t(cCoq_2eNArith_2eBinNatDef_2eN_2eadd) ).

fof('$_typeof_Coq.NArith.BinNatDef.N.compare',axiom,
    c_24__type__24473___24t(cCoq_2eNArith_2eBinNatDef_2eN_2ecompare) ).

fof('$_typeof_Coq.NArith.BinNatDef.N.div2',axiom,
    c_24__type__2636___24t(cCoq_2eNArith_2eBinNatDef_2eN_2ediv2) ).

fof('$_typeof_Coq.NArith.BinNatDef.N.double',axiom,
    c_24__type__2636___24t(cCoq_2eNArith_2eBinNatDef_2eN_2edouble) ).

fof('$_typeof_Coq.NArith.BinNatDef.N.eqb',axiom,
    c_24__type__24482___24t(cCoq_2eNArith_2eBinNatDef_2eN_2eeqb) ).

fof('$_typeof_Coq.NArith.BinNatDef.N.even',axiom,
    c_24__type__24498___24t(cCoq_2eNArith_2eBinNatDef_2eN_2eeven) ).

fof('$_typeof_Coq.NArith.BinNatDef.N.land',axiom,
    c_24__type__2643___24t(cCoq_2eNArith_2eBinNatDef_2eN_2eland) ).

fof('$_typeof_Coq.NArith.BinNatDef.N.lxor',axiom,
    c_24__type__2643___24t(cCoq_2eNArith_2eBinNatDef_2eN_2elxor) ).

fof('$_typeof_Coq.NArith.BinNatDef.N.max',axiom,
    c_24__type__2643___24t(cCoq_2eNArith_2eBinNatDef_2eN_2emax) ).

fof('$_typeof_Coq.NArith.BinNatDef.N.min',axiom,
    c_24__type__2643___24t(cCoq_2eNArith_2eBinNatDef_2eN_2emin) ).

fof('$_typeof_Coq.NArith.BinNatDef.N.mul',axiom,
    c_24__type__2643___24t(cCoq_2eNArith_2eBinNatDef_2eN_2emul) ).

fof('$_typeof_Coq.NArith.BinNatDef.N.pred',axiom,
    c_24__type__2636___24t(cCoq_2eNArith_2eBinNatDef_2eN_2epred) ).

fof('$_typeof_Coq.NArith.BinNatDef.N.succ',axiom,
    c_24__type__2636___24t(cCoq_2eNArith_2eBinNatDef_2eN_2esucc) ).

fof('$_typeof_Coq.NArith.BinNatDef.N.succ_pos',axiom,
    c_24__type__32914___24t(cCoq_2eNArith_2eBinNatDef_2eN_2esucc__pos) ).

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__24482___24t(cCoq_2eNArith_2eBinNatDef_2eN_2etestbit) ).

fof('$_typeof_Coq.NArith.BinNatDef.N.to_nat',axiom,
    c_24__type__24537___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__30202___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__10940___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__1425___24t(cCoq_2eNumbers_2eBinNums_2eZneg) ).

fof('$_typeof_Coq.Numbers.BinNums.Zpos',axiom,
    c_24__type__1425___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__3236___24t(cCoq_2eNumbers_2eBinNums_2exI) ).

fof('$_typeof_Coq.Numbers.BinNums.xO',axiom,
    c_24__type__3236___24t(cCoq_2eNumbers_2eBinNums_2exO) ).

fof('$_typeof_Coq.PArith.BinPos.Pos.PeanoView',axiom,
    c_24__type__29672___24t(cCoq_2ePArith_2eBinPos_2ePos_2ePeanoView) ).

fof('$_typeof_Coq.PArith.BinPos.Pos.eq',axiom,
    c_24__type__24121___24t(cCoq_2ePArith_2eBinPos_2ePos_2eeq) ).

fof('$_typeof_Coq.PArith.BinPos.Pos.lt',axiom,
    c_24__type__24121___24t(cCoq_2ePArith_2eBinPos_2ePos_2elt) ).

fof('$_typeof_Coq.PArith.BinPos.Pos.switch_Eq',axiom,
    c_24__type__33074___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__32979___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2eIsPos) ).

fof('$_typeof_Coq.PArith.BinPosDef.Pos.compare',axiom,
    c_24__type__24730___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare) ).

fof('$_typeof_Coq.PArith.BinPosDef.Pos.div2',axiom,
    c_24__type__3236___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2ediv2) ).

fof('$_typeof_Coq.PArith.BinPosDef.Pos.div2_up',axiom,
    c_24__type__3236___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2ediv2__up) ).

fof('$_typeof_Coq.PArith.BinPosDef.Pos.eqb',axiom,
    c_24__type__33011___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2eeqb) ).

fof('$_typeof_Coq.PArith.BinPosDef.Pos.iter',axiom,
    c_24__type__29595___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2eiter) ).

fof('$_typeof_Coq.PArith.BinPosDef.Pos.iter_op',axiom,
    c_24__type__29610___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__24723___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2emax) ).

fof('$_typeof_Coq.PArith.BinPosDef.Pos.min',axiom,
    c_24__type__24723___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2emin) ).

fof('$_typeof_Coq.PArith.BinPosDef.Pos.mul',axiom,
    c_24__type__24723___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2emul) ).

fof('$_typeof_Coq.PArith.BinPosDef.Pos.of_nat',axiom,
    c_24__type__33048___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2eof__nat) ).

fof('$_typeof_Coq.PArith.BinPosDef.Pos.of_succ_nat',axiom,
    c_24__type__33048___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2eof__succ__nat) ).

fof('$_typeof_Coq.PArith.BinPosDef.Pos.size',axiom,
    c_24__type__3236___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2esize) ).

fof('$_typeof_Coq.PArith.BinPosDef.Pos.size_nat',axiom,
    c_24__type__24732___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2esize__nat) ).

fof('$_typeof_Coq.PArith.BinPosDef.Pos.sub',axiom,
    c_24__type__24723___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2esub) ).

fof('$_typeof_Coq.PArith.BinPosDef.Pos.succ',axiom,
    c_24__type__3236___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__33041___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__16480___24t(cCoq_2eQArith_2eQArith__base_2eQden) ).

fof('$_typeof_Coq.QArith.QArith_base.Qmake',axiom,
    c_24__type__16470___24t(cCoq_2eQArith_2eQArith__base_2eQmake) ).

fof('$_typeof_Coq.QArith.QArith_base.Qnum',axiom,
    c_24__type__16475___24t(cCoq_2eQArith_2eQArith__base_2eQnum) ).

fof('$_typeof_Coq.Reals.RIneq.Rsqr',axiom,
    c_24__type__16525___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__16767___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__16759___24t(cCoq_2eReals_2eRdefinitions_2eRge) ).

fof('$_typeof_Coq.Reals.Rdefinitions.Rgt',axiom,
    c_24__type__16759___24t(cCoq_2eReals_2eRdefinitions_2eRgt) ).

fof('$_typeof_Coq.Reals.Rdefinitions.Rinv',axiom,
    c_24__type__16525___24t(cCoq_2eReals_2eRdefinitions_2eRinv) ).

fof('$_typeof_Coq.Reals.Rdefinitions.Rle',axiom,
    c_24__type__16759___24t(cCoq_2eReals_2eRdefinitions_2eRle) ).

fof('$_typeof_Coq.Reals.Rdefinitions.Rlt',axiom,
    c_24__type__16759___24t(cCoq_2eReals_2eRdefinitions_2eRlt) ).

fof('$_typeof_Coq.Reals.Rdefinitions.Rmult',axiom,
    c_24__type__16746___24t(cCoq_2eReals_2eRdefinitions_2eRmult) ).

fof('$_typeof_Coq.Reals.Rdefinitions.Ropp',axiom,
    c_24__type__16525___24t(cCoq_2eReals_2eRdefinitions_2eRopp) ).

fof('$_typeof_Coq.Reals.Rdefinitions.Rplus',axiom,
    c_24__type__16746___24t(cCoq_2eReals_2eRdefinitions_2eRplus) ).

fof('$_typeof_Coq.Reals.Rdefinitions.up',axiom,
    c_24__type__30784___24t(cCoq_2eReals_2eRdefinitions_2eup) ).

fof('$_typeof_Coq.Reals.Rfunctions.Z_spec',axiom,
    c_24__type__17097___24t(cCoq_2eReals_2eRfunctions_2eZ__spec) ).

fof('$_typeof_Coq.Relations.Relation_Definitions.reflexive',axiom,
    c_24__type__30788___24t(cCoq_2eRelations_2eRelation__Definitions_2ereflexive) ).

fof('$_typeof_Coq.Relations.Relation_Definitions.relation',axiom,
    c_24__type__2591___24t(cCoq_2eRelations_2eRelation__Definitions_2erelation) ).

fof('$_typeof_Coq.Relations.Relation_Definitions.symmetric',axiom,
    c_24__type__30788___24t(cCoq_2eRelations_2eRelation__Definitions_2esymmetric) ).

fof('$_typeof_Coq.Relations.Relation_Definitions.transitive',axiom,
    c_24__type__30788___24t(cCoq_2eRelations_2eRelation__Definitions_2etransitive) ).

fof('$_typeof_Coq.Setoids.Setoid.Setoid_Theory',axiom,
    c_24__type__30788___24t(cCoq_2eSetoids_2eSetoid_2eSetoid__Theory) ).

fof('$_typeof_Coq.Sets.Relations_1.Relation',axiom,
    c_24__type__2591___24t(cCoq_2eSets_2eRelations__1_2eRelation) ).

fof('$_typeof_Coq.Strings.Ascii.Ascii',axiom,
    c_24__type__29736___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__32562___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__29854___24t(cCoq_2eStructures_2eGenericMinMax_2egmax) ).

fof('$_typeof_Coq.Structures.GenericMinMax.gmin',axiom,
    c_24__type__29854___24t(cCoq_2eStructures_2eGenericMinMax_2egmin) ).

fof('$_typeof_Coq.Structures.OrderedType.Compare',axiom,
    c_24__type__16346___24t(cCoq_2eStructures_2eOrderedType_2eCompare) ).

fof('$_typeof_Coq.Structures.OrderedTypeEx.N_as_OT.eq',axiom,
    c_24__type__2647___24t(cCoq_2eStructures_2eOrderedTypeEx_2eN__as__OT_2eeq) ).

fof('$_typeof_Coq.Structures.OrderedTypeEx.N_as_OT.lt',axiom,
    c_24__type__2647___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__73___24t(cCoq_2eStructures_2eOrderedTypeEx_2eNat__as__OT_2eeq) ).

fof('$_typeof_Coq.Structures.OrderedTypeEx.Nat_as_OT.lt',axiom,
    c_24__type__73___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__24121___24t(cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2ebits__lt) ).

fof('$_typeof_Coq.Structures.OrderedTypeEx.PositiveOrderedTypeBits.eq',axiom,
    c_24__type__24121___24t(cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2eeq) ).

fof('$_typeof_Coq.Structures.OrderedTypeEx.PositiveOrderedTypeBits.lt',axiom,
    c_24__type__24121___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__24121___24t(cCoq_2eStructures_2eOrderedTypeEx_2ePositive__as__OT_2eeq) ).

fof('$_typeof_Coq.Structures.OrderedTypeEx.Positive_as_OT.lt',axiom,
    c_24__type__24121___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__33101___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__2562___24t(cCoq_2eStructures_2eOrderedTypeEx_2eZ__as__OT_2eeq) ).

fof('$_typeof_Coq.Structures.OrderedTypeEx.Z_as_OT.lt',axiom,
    c_24__type__2562___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__11799___24t(cCoq_2eVectors_2eFin_2et) ).

fof('$_typeof_Coq.Vectors.VectorDef.nil',axiom,
    c_24__type__24011___24t(cCoq_2eVectors_2eVectorDef_2enil) ).

fof('$_typeof_Coq.Vectors.VectorDef.t',axiom,
    c_24__type__23994___24t(cCoq_2eVectors_2eVectorDef_2et) ).

fof('$_typeof_Coq.ZArith.BinInt.Z.Private_Div.Quot2Div.div',axiom,
    c_24__type__10817___24t(cCoq_2eZArith_2eBinInt_2eZ_2ePrivate__Div_2eQuot2Div_2ediv) ).

fof('$_typeof_Coq.ZArith.BinInt.Z.Private_Div.Quot2Div.modulo',axiom,
    c_24__type__10817___24t(cCoq_2eZArith_2eBinInt_2eZ_2ePrivate__Div_2eQuot2Div_2emodulo) ).

fof('$_typeof_Coq.ZArith.BinInt.Z.b2z',axiom,
    c_24__type__25245___24t(cCoq_2eZArith_2eBinInt_2eZ_2eb2z) ).

fof('$_typeof_Coq.ZArith.BinInt.Z.divide',axiom,
    c_24__type__2562___24t(cCoq_2eZArith_2eBinInt_2eZ_2edivide) ).

fof('$_typeof_Coq.ZArith.BinInt.Z.eq',axiom,
    c_24__type__2562___24t(cCoq_2eZArith_2eBinInt_2eZ_2eeq) ).

fof('$_typeof_Coq.ZArith.BinInt.Z.eqf',axiom,
    c_24__type__33129___24t(cCoq_2eZArith_2eBinInt_2eZ_2eeqf) ).

fof('$_typeof_Coq.ZArith.BinInt.Z.gt',axiom,
    c_24__type__2562___24t(cCoq_2eZArith_2eBinInt_2eZ_2egt) ).

fof('$_typeof_Coq.ZArith.BinInt.Z.le',axiom,
    c_24__type__2562___24t(cCoq_2eZArith_2eBinInt_2eZ_2ele) ).

fof('$_typeof_Coq.ZArith.BinInt.Z.lt',axiom,
    c_24__type__2562___24t(cCoq_2eZArith_2eBinInt_2eZ_2elt) ).

fof('$_typeof_Coq.ZArith.BinInt.Zne',axiom,
    c_24__type__2562___24t(cCoq_2eZArith_2eBinInt_2eZne) ).

fof('$_typeof_Coq.ZArith.BinIntDef.Z.abs',axiom,
    c_24__type__2745___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2eabs) ).

fof('$_typeof_Coq.ZArith.BinIntDef.Z.abs_N',axiom,
    c_24__type__25160___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2eabs__N) ).

fof('$_typeof_Coq.ZArith.BinIntDef.Z.abs_nat',axiom,
    c_24__type__2559___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2eabs__nat) ).

fof('$_typeof_Coq.ZArith.BinIntDef.Z.add',axiom,
    c_24__type__10817___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2eadd) ).

fof('$_typeof_Coq.ZArith.BinIntDef.Z.compare',axiom,
    c_24__type__2555___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare) ).

fof('$_typeof_Coq.ZArith.BinIntDef.Z.div',axiom,
    c_24__type__10817___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2ediv) ).

fof('$_typeof_Coq.ZArith.BinIntDef.Z.even',axiom,
    c_24__type__25191___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2eeven) ).

fof('$_typeof_Coq.ZArith.BinIntDef.Z.leb',axiom,
    c_24__type__10755___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2eleb) ).

fof('$_typeof_Coq.ZArith.BinIntDef.Z.max',axiom,
    c_24__type__10817___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2emax) ).

fof('$_typeof_Coq.ZArith.BinIntDef.Z.min',axiom,
    c_24__type__10817___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2emin) ).

fof('$_typeof_Coq.ZArith.BinIntDef.Z.modulo',axiom,
    c_24__type__10817___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2emodulo) ).

fof('$_typeof_Coq.ZArith.BinIntDef.Z.mul',axiom,
    c_24__type__10817___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2emul) ).

fof('$_typeof_Coq.ZArith.BinIntDef.Z.odd',axiom,
    c_24__type__25191___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2eodd) ).

fof('$_typeof_Coq.ZArith.BinIntDef.Z.of_N',axiom,
    c_24__type__10839___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2eof__N) ).

fof('$_typeof_Coq.ZArith.BinIntDef.Z.of_nat',axiom,
    c_24__type__25163___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat) ).

fof('$_typeof_Coq.ZArith.BinIntDef.Z.one',axiom,
    cCoq_2eNumbers_2eBinNums_2eZ___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2eone) ).

fof('$_typeof_Coq.ZArith.BinIntDef.Z.opp',axiom,
    c_24__type__2745___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2eopp) ).

fof('$_typeof_Coq.ZArith.BinIntDef.Z.pow',axiom,
    c_24__type__10817___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2epow) ).

fof('$_typeof_Coq.ZArith.BinIntDef.Z.pred',axiom,
    c_24__type__2745___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2epred) ).

fof('$_typeof_Coq.ZArith.BinIntDef.Z.sub',axiom,
    c_24__type__10817___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2esub) ).

fof('$_typeof_Coq.ZArith.BinIntDef.Z.succ',axiom,
    c_24__type__2745___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__25160___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2eto__N) ).

fof('$_typeof_Coq.ZArith.BinIntDef.Z.to_nat',axiom,
    c_24__type__2559___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2eto__nat) ).

fof('$_typeof_Coq.ZArith.BinIntDef.Z.to_pos',axiom,
    c_24__type__25167___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__10755___24t(cCoq_2eZArith_2eZbool_2eZeq__bool) ).

fof('$_typeof_Coq.ZArith.Zcomplements.floor_pos',axiom,
    c_24__type__3236___24t(cCoq_2eZArith_2eZcomplements_2efloor__pos) ).

fof('$_typeof_Coq.ZArith.Zeven.Zeven',axiom,
    c_24__type__3174___24t(cCoq_2eZArith_2eZeven_2eZeven) ).

fof('$_typeof_Coq.ZArith.Zeven.Zodd',axiom,
    c_24__type__3174___24t(cCoq_2eZArith_2eZeven_2eZodd) ).

fof('$_typeof_Coq.ZArith.Zlogarithm.Is_power',axiom,
    c_24__type__29442___24t(cCoq_2eZArith_2eZlogarithm_2eIs__power) ).

fof('$_typeof_Coq.ZArith.Zlogarithm.log_inf',axiom,
    c_24__type__1425___24t(cCoq_2eZArith_2eZlogarithm_2elog__inf) ).

fof('$_typeof_Coq.ZArith.Znat.neq',axiom,
    c_24__type__73___24t(cCoq_2eZArith_2eZnat_2eneq) ).

fof('$_typeof_Coq.ZArith.Znumtheory.Euclid',axiom,
    c_24__type__17097___24t(cCoq_2eZArith_2eZnumtheory_2eEuclid) ).

fof('$_typeof_Coq.ZArith.Zpower.Zdiv_rest_proofs',axiom,
    c_24__type__29501___24t(cCoq_2eZArith_2eZpower_2eZdiv__rest__proofs) ).

fof('$_typeof_Coq.micromega.Env.Env',axiom,
    c_24__type__2591___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__29797___24t(cCoq_2emicromega_2eEnvRing_2ePEX) ).

fof('$_typeof_Coq.micromega.EnvRing.PEc',axiom,
    c_24__type__29794___24t(cCoq_2emicromega_2eEnvRing_2ePEc) ).

fof('$_typeof_Coq.micromega.EnvRing.PExpr',axiom,
    c_24__type__2591___24t(cCoq_2emicromega_2eEnvRing_2ePExpr) ).

fof('$_typeof_Coq.micromega.EnvRing.PX',axiom,
    c_24__type__29813___24t(cCoq_2emicromega_2eEnvRing_2ePX) ).

fof('$_typeof_Coq.micromega.EnvRing.Pc',axiom,
    c_24__type__29800___24t(cCoq_2emicromega_2eEnvRing_2ePc) ).

fof('$_typeof_Coq.micromega.EnvRing.Pinj',axiom,
    c_24__type__29805___24t(cCoq_2emicromega_2eEnvRing_2ePinj) ).

fof('$_typeof_Coq.micromega.EnvRing.Pol',axiom,
    c_24__type__2591___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__29816___24t(cCoq_2emicromega_2eEnvRing_2evmon) ).

fof('$_typeof_Coq.micromega.EnvRing.zmon',axiom,
    c_24__type__29816___24t(cCoq_2emicromega_2eEnvRing_2ezmon) ).

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__16698___24t(cCoq_2emicromega_2eRMicromega_2eCInv) ).

fof('$_typeof_Coq.micromega.RMicromega.CMinus',axiom,
    c_24__type__16691___24t(cCoq_2emicromega_2eRMicromega_2eCMinus) ).

fof('$_typeof_Coq.micromega.RMicromega.CMult',axiom,
    c_24__type__16691___24t(cCoq_2emicromega_2eRMicromega_2eCMult) ).

fof('$_typeof_Coq.micromega.RMicromega.COpp',axiom,
    c_24__type__16698___24t(cCoq_2emicromega_2eRMicromega_2eCOpp) ).

fof('$_typeof_Coq.micromega.RMicromega.CPlus',axiom,
    c_24__type__16691___24t(cCoq_2emicromega_2eRMicromega_2eCPlus) ).

fof('$_typeof_Coq.micromega.RMicromega.CQ',axiom,
    c_24__type__16686___24t(cCoq_2emicromega_2eRMicromega_2eCQ) ).

fof('$_typeof_Coq.micromega.RMicromega.CZ',axiom,
    c_24__type__16688___24t(cCoq_2emicromega_2eRMicromega_2eCZ) ).

fof('$_typeof_Coq.micromega.RMicromega.Rcst',axiom,
    cType___24t(cCoq_2emicromega_2eRMicromega_2eRcst) ).

fof('$_typeof_Coq.micromega.Refl.make_conj',axiom,
    c_24__type__16818___24t(cCoq_2emicromega_2eRefl_2emake__conj) ).

fof('$_typeof_Coq.micromega.Refl.make_impl',axiom,
    c_24__type__16792___24t(cCoq_2emicromega_2eRefl_2emake__impl) ).

fof('$_typeof_Coq.micromega.RingMicromega.Equal',axiom,
    cCoq_2emicromega_2eRingMicromega_2eOp1___24t(cCoq_2emicromega_2eRingMicromega_2eEqual) ).

fof('$_typeof_Coq.micromega.RingMicromega.Formula',axiom,
    c_24__type__2591___24t(cCoq_2emicromega_2eRingMicromega_2eFormula) ).

fof('$_typeof_Coq.micromega.RingMicromega.NonEqual',axiom,
    cCoq_2emicromega_2eRingMicromega_2eOp1___24t(cCoq_2emicromega_2eRingMicromega_2eNonEqual) ).

fof('$_typeof_Coq.micromega.RingMicromega.NonStrict',axiom,
    cCoq_2emicromega_2eRingMicromega_2eOp1___24t(cCoq_2emicromega_2eRingMicromega_2eNonStrict) ).

fof('$_typeof_Coq.micromega.RingMicromega.Op1',axiom,
    cType___24t(cCoq_2emicromega_2eRingMicromega_2eOp1) ).

fof('$_typeof_Coq.micromega.RingMicromega.Op2',axiom,
    cType___24t(cCoq_2emicromega_2eRingMicromega_2eOp2) ).

fof('$_typeof_Coq.micromega.RingMicromega.OpEq',axiom,
    cCoq_2emicromega_2eRingMicromega_2eOp2___24t(cCoq_2emicromega_2eRingMicromega_2eOpEq) ).

fof('$_typeof_Coq.micromega.RingMicromega.OpGe',axiom,
    cCoq_2emicromega_2eRingMicromega_2eOp2___24t(cCoq_2emicromega_2eRingMicromega_2eOpGe) ).

fof('$_typeof_Coq.micromega.RingMicromega.OpGt',axiom,
    cCoq_2emicromega_2eRingMicromega_2eOp2___24t(cCoq_2emicromega_2eRingMicromega_2eOpGt) ).

fof('$_typeof_Coq.micromega.RingMicromega.OpLe',axiom,
    cCoq_2emicromega_2eRingMicromega_2eOp2___24t(cCoq_2emicromega_2eRingMicromega_2eOpLe) ).

fof('$_typeof_Coq.micromega.RingMicromega.OpLt',axiom,
    cCoq_2emicromega_2eRingMicromega_2eOp2___24t(cCoq_2emicromega_2eRingMicromega_2eOpLt) ).

fof('$_typeof_Coq.micromega.RingMicromega.OpNEq',axiom,
    cCoq_2emicromega_2eRingMicromega_2eOp2___24t(cCoq_2emicromega_2eRingMicromega_2eOpNEq) ).

fof('$_typeof_Coq.micromega.RingMicromega.PolC',axiom,
    c_24__type__2591___24t(cCoq_2emicromega_2eRingMicromega_2ePolC) ).

fof('$_typeof_Coq.micromega.RingMicromega.PolEnv',axiom,
    c_24__type__2591___24t(cCoq_2emicromega_2eRingMicromega_2ePolEnv) ).

fof('$_typeof_Coq.micromega.RingMicromega.Psatz',axiom,
    c_24__type__2591___24t(cCoq_2emicromega_2eRingMicromega_2ePsatz) ).

fof('$_typeof_Coq.micromega.RingMicromega.PsatzC',axiom,
    c_24__type__31908___24t(cCoq_2emicromega_2eRingMicromega_2ePsatzC) ).

fof('$_typeof_Coq.micromega.RingMicromega.PsatzZ',axiom,
    c_24__type__31910___24t(cCoq_2emicromega_2eRingMicromega_2ePsatzZ) ).

fof('$_typeof_Coq.micromega.RingMicromega.Strict',axiom,
    cCoq_2emicromega_2eRingMicromega_2eOp1___24t(cCoq_2emicromega_2eRingMicromega_2eStrict) ).

fof('$_typeof_Coq.micromega.RingMicromega.cneqb',axiom,
    c_24__type__31817___24t(cCoq_2emicromega_2eRingMicromega_2ecneqb) ).

fof('$_typeof_Coq.micromega.RingMicromega.eval_op1',axiom,
    c_24__type__31896___24t(cCoq_2emicromega_2eRingMicromega_2eeval__op1) ).

fof('$_typeof_Coq.micromega.RingMicromega.eval_op2',axiom,
    c_24__type__31987___24t(cCoq_2emicromega_2eRingMicromega_2eeval__op2) ).

fof('$_typeof_Coq.micromega.RingMicromega.ge_bool',axiom,
    c_24__type__15031___24t(cCoq_2emicromega_2eRingMicromega_2ege__bool) ).

fof('$_typeof_Coq.micromega.Tauto.A',axiom,
    c_24__type__32605___24t(cCoq_2emicromega_2eTauto_2eA) ).

fof('$_typeof_Coq.micromega.Tauto.FF',axiom,
    c_24__type__32570___24t(cCoq_2emicromega_2eTauto_2eFF) ).

fof('$_typeof_Coq.micromega.Tauto.GFormula',axiom,
    c_24__type__28958___24t(cCoq_2emicromega_2eTauto_2eGFormula) ).

fof('$_typeof_Coq.micromega.Tauto.TFormula',axiom,
    c_24__type__28958___24t(cCoq_2emicromega_2eTauto_2eTFormula) ).

fof('$_typeof_Coq.micromega.Tauto.TT',axiom,
    c_24__type__32570___24t(cCoq_2emicromega_2eTauto_2eTT) ).

fof('$_typeof_Coq.micromega.Tauto.X',axiom,
    c_24__type__32588___24t(cCoq_2emicromega_2eTauto_2eX) ).

fof('$_typeof_Coq.micromega.Tauto.clause',axiom,
    c_24__type__47___24t(cCoq_2emicromega_2eTauto_2eclause) ).

fof('$_typeof_Coq.micromega.VarMap.t',axiom,
    c_24__type__2591___24t(cCoq_2emicromega_2eVarMap_2et) ).

fof('$_typeof_Coq.micromega.ZCoeff.gen_order_phi_Z',axiom,
    c_24__type__14645___24t(cCoq_2emicromega_2eZCoeff_2egen__order__phi__Z) ).

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__32911___24t(cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eAdd) ).

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.coneMember',axiom,
    cType___24t(cCoq_2emicromega_2eZMicromega_2econeMember) ).

fof('$_typeof_Coq.micromega.ZMicromega.isZ0',axiom,
    c_24__type__25191___24t(cCoq_2emicromega_2eZMicromega_2eisZ0) ).

fof('$_typeof_Coq.omega.PreOmega.Z_of_N\'',axiom,
    c_24__type__10839___24t(cCoq_2eomega_2ePreOmega_2eZ__of__N_27) ).

fof('$_typeof_Coq.omega.PreOmega.Z_of_nat\'',axiom,
    c_24__type__25163___24t(cCoq_2eomega_2ePreOmega_2eZ__of__nat_27) ).

fof('$_typeof_Coq.omega.PreOmega.Zneg\'',axiom,
    c_24__type__1425___24t(cCoq_2eomega_2ePreOmega_2eZneg_27) ).

fof('$_typeof_Coq.omega.PreOmega.Zpos\'',axiom,
    c_24__type__1425___24t(cCoq_2eomega_2ePreOmega_2eZpos_27) ).

fof('$_typeof_Coq.setoid_ring.ArithRing.protected_to_nat',axiom,
    c_24__type__24537___24t(cCoq_2esetoid__ring_2eArithRing_2eprotected__to__nat) ).

fof('$_typeof_Coq.setoid_ring.Field_theory.FEI',axiom,
    c_24__type__29838___24t(cCoq_2esetoid__ring_2eField__theory_2eFEI) ).

fof('$_typeof_Coq.setoid_ring.Field_theory.FEO',axiom,
    c_24__type__29838___24t(cCoq_2esetoid__ring_2eField__theory_2eFEO) ).

fof('$_typeof_Coq.setoid_ring.Field_theory.FEX',axiom,
    c_24__type__13932___24t(cCoq_2esetoid__ring_2eField__theory_2eFEX) ).

fof('$_typeof_Coq.setoid_ring.Field_theory.FEc',axiom,
    c_24__type__13929___24t(cCoq_2esetoid__ring_2eField__theory_2eFEc) ).

fof('$_typeof_Coq.setoid_ring.Field_theory.FEinv',axiom,
    c_24__type__13940___24t(cCoq_2esetoid__ring_2eField__theory_2eFEinv) ).

fof('$_typeof_Coq.setoid_ring.Field_theory.FEmul',axiom,
    c_24__type__13937___24t(cCoq_2esetoid__ring_2eField__theory_2eFEmul) ).

fof('$_typeof_Coq.setoid_ring.Field_theory.FExpr',axiom,
    c_24__type__2591___24t(cCoq_2esetoid__ring_2eField__theory_2eFExpr) ).

fof('$_typeof_Coq.setoid_ring.Field_theory.linear',axiom,
    c_24__type__2591___24t(cCoq_2esetoid__ring_2eField__theory_2elinear) ).

fof('$_typeof_Coq.setoid_ring.Field_theory.rsplit',axiom,
    c_24__type__2591___24t(cCoq_2esetoid__ring_2eField__theory_2ersplit) ).

fof('$_typeof_Coq.setoid_ring.InitialRing.Nopp',axiom,
    c_24__type__2636___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_phiN',axiom,
    c_24__type__14708___24t(cCoq_2esetoid__ring_2eInitialRing_2egen__phiN) ).

fof('$_typeof_Coq.setoid_ring.InitialRing.gen_phiPOS',axiom,
    c_24__type__26988___24t(cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS) ).

fof('$_typeof_Coq.setoid_ring.InitialRing.gen_phiPOS1',axiom,
    c_24__type__26988___24t(cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS1) ).

fof('$_typeof_Coq.setoid_ring.InitialRing.gen_phiZ',axiom,
    c_24__type__14645___24t(cCoq_2esetoid__ring_2eInitialRing_2egen__phiZ) ).

fof('$_typeof_Coq.setoid_ring.InitialRing.hypo',axiom,
    cType___24t(cCoq_2esetoid__ring_2eInitialRing_2ehypo) ).

fof('$_typeof_Coq.setoid_ring.InitialRing.hypo_type',axiom,
    c_24__type__29877___24t(cCoq_2esetoid__ring_2eInitialRing_2ehypo__type) ).

fof('$_typeof_Coq.setoid_ring.InitialRing.mkhypo',axiom,
    c_24__type__29872___24t(cCoq_2esetoid__ring_2eInitialRing_2emkhypo) ).

fof('$_typeof_Coq.setoid_ring.Ring.bool_eq',axiom,
    c_24__type__10943___24t(cCoq_2esetoid__ring_2eRing_2ebool__eq) ).

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__32002___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePEI) ).

fof('$_typeof_Coq.setoid_ring.Ring_polynom.PEO',axiom,
    c_24__type__32002___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePEO) ).

fof('$_typeof_Coq.setoid_ring.Ring_polynom.PEX',axiom,
    c_24__type__5079___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePEX) ).

fof('$_typeof_Coq.setoid_ring.Ring_polynom.PEadd',axiom,
    c_24__type__5084___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePEadd) ).

fof('$_typeof_Coq.setoid_ring.Ring_polynom.PEc',axiom,
    c_24__type__5076___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePEc) ).

fof('$_typeof_Coq.setoid_ring.Ring_polynom.PEmul',axiom,
    c_24__type__5084___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePEmul) ).

fof('$_typeof_Coq.setoid_ring.Ring_polynom.PEopp',axiom,
    c_24__type__23213___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePEopp) ).

fof('$_typeof_Coq.setoid_ring.Ring_polynom.PEpow',axiom,
    c_24__type__32007___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePEpow) ).

fof('$_typeof_Coq.setoid_ring.Ring_polynom.PEsub',axiom,
    c_24__type__5084___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePEsub) ).

fof('$_typeof_Coq.setoid_ring.Ring_polynom.PExpr',axiom,
    c_24__type__2591___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr) ).

fof('$_typeof_Coq.setoid_ring.Ring_polynom.PX',axiom,
    c_24__type__4830___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePX) ).

fof('$_typeof_Coq.setoid_ring.Ring_polynom.Pc',axiom,
    c_24__type__4817___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePc) ).

fof('$_typeof_Coq.setoid_ring.Ring_polynom.Peq',axiom,
    c_24__type__23204___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePeq) ).

fof('$_typeof_Coq.setoid_ring.Ring_polynom.Pinj',axiom,
    c_24__type__4822___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePinj) ).

fof('$_typeof_Coq.setoid_ring.Ring_polynom.Pol',axiom,
    c_24__type__2591___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePol) ).

fof('$_typeof_Coq.setoid_ring.Ring_polynom.mkmult_pow',axiom,
    c_24__type__27092___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__31999___24t(cCoq_2esetoid__ring_2eRing__polynom_2evmon) ).

fof('$_typeof_Coq.setoid_ring.Ring_polynom.zmon',axiom,
    c_24__type__31999___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__10453___24t(cCoq_2esetoid__ring_2eRing__theory_2eIDphi) ).

fof('$_typeof_Coq.setoid_ring.Ring_theory.SRopp',axiom,
    c_24__type__10453___24t(cCoq_2esetoid__ring_2eRing__theory_2eSRopp) ).

fof('$_typeof_Coq.setoid_ring.Ring_theory.SRsub',axiom,
    c_24__type__23483___24t(cCoq_2esetoid__ring_2eRing__theory_2eSRsub) ).

fof('$_typeof_Coq.setoid_ring.Ring_theory.id_phi_N',axiom,
    c_24__type__2636___24t(cCoq_2esetoid__ring_2eRing__theory_2eid__phi__N) ).

fof('$_typeof_Coq.setoid_ring.Ring_theory.pow_N',axiom,
    c_24__type__6456___24t(cCoq_2esetoid__ring_2eRing__theory_2epow__N) ).

fof('$_typeof_Coq.setoid_ring.Ring_theory.pow_pos',axiom,
    c_24__type__27113___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_F',axiom,
    c_24__type__20___24t(cF) ).

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__27072___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__27072___24t(cHammer_2eTactics_2eTactics_2erdone) ).

fof('$_typeof_P',axiom,
    c_24__type__25___24t(cP) ).

fof('$_typeof_R',axiom,
    c_24__type__28___24t(cR) ).

fof('$_typeof_r',axiom,
    c_24__type__14___24t(cr) ).

fof('Coq.Arith.Lt.lt_n_Sm_le',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,cCoq_2eInit_2eDatatypes_2eS___24a1(V1__m))
           => cCoq_2eInit_2ePeano_2ele___24a2(V0__n,V1__m) ) ) ) ).

fof('Coq.Arith.PeanoNat.Nat.A\'A_left',axiom,
    ! [V0__A] :
      ( c_24__type__35___24t(V0__A)
     => ! [V1__z] :
          ( cCoq_2eInit_2eDatatypes_2enat___24t(V1__z)
         => ( ! [V2__n] :
                ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__n)
               => ! [Vvar__4__m__32962] :
                    ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__4__m__32962)
                   => ( cCoq_2eInit_2ePeano_2ele___24a2(Vvar__4__m__32962,V1__z)
                     => ( cCoq_2eInit_2ePeano_2ele___24a2(V2__n,Vvar__4__m__32962)
                       => p(happ(V0__A,Vvar__4__m__32962)) ) ) ) )
           => ! [V3__n] :
                ( cCoq_2eInit_2eDatatypes_2enat___24t(V3__n)
               => ( cCoq_2eInit_2ePeano_2ele___24a2(V3__n,V1__z)
                 => p(happ(V0__A,V3__n)) ) ) ) ) ) ).

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_antisym',axiom,
    ! [V0__x] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)
     => ! [V1__y] :
          ( cCoq_2eInit_2eDatatypes_2enat___24t(V1__y)
         => ( cCoq_2eInit_2ePeano_2ele___24a2(V0__x,V1__y)
           => ( cCoq_2eInit_2ePeano_2ele___24a2(V1__y,V0__x)
             => V0__x = V1__y ) ) ) ) ).

fof('Coq.Arith.PeanoNat.Nat.Private_Tac.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.eq_stepl',axiom,
    ! [V0__x] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)
     => ! [V1__y] :
          ( cCoq_2eInit_2eDatatypes_2enat___24t(V1__y)
         => ! [V2__z] :
              ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__z)
             => ( V0__x = V1__y
               => ( V0__x = V2__z
                 => V2__z = V1__y ) ) ) ) ) ).

fof('Coq.Arith.PeanoNat.Nat.gt_wf',axiom,
    ! [V0__z] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(V0__z)
     => cCoq_2eInit_2eWf_2ewell__founded___24a2(cCoq_2eInit_2eDatatypes_2enat,c_24__lam__2738___24a1(V0__z)) ) ).

fof('Coq.Arith.PeanoNat.Nat.le_0_l',axiom,
    ! [V0__n] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
     => cCoq_2eInit_2ePeano_2ele___24a2(cCoq_2eInit_2eDatatypes_2eO,V0__n) ) ).

fof('Coq.Arith.PeanoNat.Nat.le_antisymm',axiom,
    ! [V0__n] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
     => ! [V1__m] :
          ( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
         => ( cCoq_2eInit_2ePeano_2ele___24a2(V0__n,V1__m)
           => ( cCoq_2eInit_2ePeano_2ele___24a2(V1__m,V0__n)
             => V0__n = V1__m ) ) ) ) ).

fof('Coq.Arith.PeanoNat.Nat.le_ge_cases',axiom,
    ! [V0__n] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
     => ! [V1__m] :
          ( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
         => ( cCoq_2eInit_2ePeano_2ele___24a2(V0__n,V1__m)
            | cCoq_2eInit_2ePeano_2ele___24a2(V1__m,V0__n) ) ) ) ).

fof('Coq.Arith.PeanoNat.Nat.le_gt_cases',axiom,
    ! [V0__n] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
     => ! [V1__m] :
          ( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
         => ( cCoq_2eInit_2ePeano_2ele___24a2(V0__n,V1__m)
            | cCoq_2eInit_2ePeano_2elt___24a2(V1__m,V0__n) ) ) ) ).

fof('Coq.Arith.PeanoNat.Nat.le_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_2ele___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.le_refl',axiom,
    ! [V0__n] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
     => cCoq_2eInit_2ePeano_2ele___24a2(V0__n,V0__n) ) ).

fof('Coq.Arith.PeanoNat.Nat.le_succ_l',axiom,
    ! [V0__n] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
     => ! [V1__m] :
          ( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
         => ( cCoq_2eInit_2ePeano_2ele___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(V0__n),V1__m)
          <=> cCoq_2eInit_2ePeano_2elt___24a2(V0__n,V1__m) ) ) ) ).

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_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_2elt___24a2(V0__n,V1__m)
               => ( cCoq_2eInit_2ePeano_2ele___24a2(V1__m,V2__p)
                 => cCoq_2eInit_2ePeano_2elt___24a2(V0__n,V2__p) ) ) ) ) ) ).

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__2733___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.nle_gt',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.nlt_0_r',axiom,
    ! [V0__n] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
     => ~ cCoq_2eInit_2ePeano_2elt___24a2(V0__n,cCoq_2eInit_2eDatatypes_2eO) ) ).

fof('Coq.Arith.PeanoNat.Nat.one_succ',axiom,
    cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO) = cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO) ).

fof('Coq.Arith.Wf_nat.acc_lt_rel',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__R] :
          ( c_24__type__117___24t(V0__A,V1__R)
         => ! [V2__F] :
              ( c_24__type__2516___24t(V0__A,V2__F)
             => ( ! [V3__x] :
                    ( t(V3__x,V0__A)
                   => ! [V4__y] :
                        ( t(V4__y,V0__A)
                       => ( p(happ(happ(V1__R,V3__x),V4__y))
                         => cCoq_2eArith_2eWf__nat_2einv__lt__rel___24a4(V0__A,V2__F,V3__x,V4__y) ) ) )
               => ! [V4__x] :
                    ( t(V4__x,V0__A)
                   => ( ? [V5__n] :
                          ( cCoq_2eInit_2eDatatypes_2enat___24t(V5__n)
                          & p(happ(happ(V2__F,V4__x),V5__n)) )
                     => cCoq_2eInit_2eWf_2eAcc___24a3(V0__A,V1__R,V4__x) ) ) ) ) ) ) ).

fof('Coq.Arith.Wf_nat.lt_wf',axiom,
    cCoq_2eInit_2eWf_2ewell__founded___24a2(cCoq_2eInit_2eDatatypes_2enat,cCoq_2eInit_2ePeano_2elt) ).

fof('Coq.Arith.Wf_nat.lt_wf_double_ind',axiom,
    ! [V0__P] :
      ( c_24__type__73___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__35___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.Arith.Wf_nat.well_founded_gtof',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__f] :
          ( c_24__type__1376___24t(V0__A,V1__f)
         => cCoq_2eInit_2eWf_2ewell__founded___24a2(V0__A,cCoq_2eArith_2eWf__nat_2egtof___24a2(V0__A,V1__f)) ) ) ).

fof('Coq.Arith.Wf_nat.well_founded_inv_lt_rel_compat',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__R] :
          ( c_24__type__117___24t(V0__A,V1__R)
         => ! [V2__F] :
              ( c_24__type__2516___24t(V0__A,V2__F)
             => ( ! [V3__x] :
                    ( t(V3__x,V0__A)
                   => ! [V4__y] :
                        ( t(V4__y,V0__A)
                       => ( p(happ(happ(V1__R,V3__x),V4__y))
                         => cCoq_2eArith_2eWf__nat_2einv__lt__rel___24a4(V0__A,V2__F,V3__x,V4__y) ) ) )
               => cCoq_2eInit_2eWf_2ewell__founded___24a2(V0__A,V1__R) ) ) ) ) ).

fof('Coq.Arith.Wf_nat.well_founded_inv_rel_inv_lt_rel',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__F] :
          ( c_24__type__2516___24t(V0__A,V1__F)
         => cCoq_2eInit_2eWf_2ewell__founded___24a2(V0__A,cCoq_2eArith_2eWf__nat_2einv__lt__rel___24a2(V0__A,V1__F)) ) ) ).

fof('Coq.Bool.Bool.absurd_eq_bool',axiom,
    ! [V0__b] :
      ( cCoq_2eInit_2eDatatypes_2ebool___24t(V0__b)
     => ! [V1__b_27] :
          ( cCoq_2eInit_2eDatatypes_2ebool___24t(V1__b_27)
         => ( p(c_24False)
           => V0__b = V1__b_27 ) ) ) ).

fof('Coq.Bool.Bool.absurd_eq_true',axiom,
    ! [V0__b] :
      ( cCoq_2eInit_2eDatatypes_2ebool___24t(V0__b)
     => ( p(c_24False)
       => V0__b = cCoq_2eInit_2eDatatypes_2etrue ) ) ).

fof('Coq.Bool.Bool.trans_eq_bool',axiom,
    ! [V0__x] :
      ( cCoq_2eInit_2eDatatypes_2ebool___24t(V0__x)
     => ! [V1__y] :
          ( cCoq_2eInit_2eDatatypes_2ebool___24t(V1__y)
         => ! [V2__z] :
              ( cCoq_2eInit_2eDatatypes_2ebool___24t(V2__z)
             => ( V0__x = V1__y
               => ( V1__y = V2__z
                 => V0__x = V2__z ) ) ) ) ) ).

fof('Coq.Init.Datatypes.Empty_set_ind',axiom,
    ! [V0__P] :
      ( c_24__type__29755___24t(V0__P)
     => ! [V1__e] :
          ( cCoq_2eInit_2eDatatypes_2eEmpty__set___24t(V1__e)
         => p(happ(V0__P,V1__e)) ) ) ).

fof('Coq.Init.Datatypes.Empty_set_sind',axiom,
    ! [V0__P] :
      ( c_24__type__29755___24t(V0__P)
     => ! [V1__e] :
          ( cCoq_2eInit_2eDatatypes_2eEmpty__set___24t(V1__e)
         => p(happ(V0__P,V1__e)) ) ) ).

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__11918___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__35___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.Peano.le_n',axiom,
    ! [V0__n] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
     => cCoq_2eInit_2ePeano_2ele___24a2(V0__n,V0__n) ) ).

fof('Coq.Init.Peano.nat_double_ind',axiom,
    ! [V0__R] :
      ( c_24__type__73___24t(V0__R)
     => ( ! [V1__n] :
            ( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
           => p(happ(happ(V0__R,cCoq_2eInit_2eDatatypes_2eO),V1__n)) )
       => ( ! [V2__n] :
              ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__n)
             => p(happ(happ(V0__R,cCoq_2eInit_2eDatatypes_2eS___24a1(V2__n)),cCoq_2eInit_2eDatatypes_2eO)) )
         => ( ! [V3__n] :
                ( cCoq_2eInit_2eDatatypes_2enat___24t(V3__n)
               => ! [V4__m] :
                    ( cCoq_2eInit_2eDatatypes_2enat___24t(V4__m)
                   => ( p(happ(happ(V0__R,V3__n),V4__m))
                     => p(happ(happ(V0__R,cCoq_2eInit_2eDatatypes_2eS___24a1(V3__n)),cCoq_2eInit_2eDatatypes_2eS___24a1(V4__m))) ) ) )
           => ! [V4__n] :
                ( cCoq_2eInit_2eDatatypes_2enat___24t(V4__n)
               => ! [V5__m] :
                    ( cCoq_2eInit_2eDatatypes_2enat___24t(V5__m)
                   => p(happ(happ(V0__R,V4__n),V5__m)) ) ) ) ) ) ) ).

fof('Coq.Init.Wf.Acc_ind',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__R] :
          ( c_24__type__117___24t(V0__A,V1__R)
         => ! [V2__P] :
              ( c_24__type__242___24t(V0__A,V2__P)
             => ( ! [V3__x] :
                    ( t(V3__x,V0__A)
                   => ( ! [V4__y] :
                          ( t(V4__y,V0__A)
                         => ( p(happ(happ(V1__R,V4__y),V3__x))
                           => cCoq_2eInit_2eWf_2eAcc___24a3(V0__A,V1__R,V4__y) ) )
                     => ( ! [V5__y] :
                            ( t(V5__y,V0__A)
                           => ( p(happ(happ(V1__R,V5__y),V3__x))
                             => p(happ(V2__P,V5__y)) ) )
                       => p(happ(V2__P,V3__x)) ) ) )
               => ! [V4__x] :
                    ( t(V4__x,V0__A)
                   => ( cCoq_2eInit_2eWf_2eAcc___24a3(V0__A,V1__R,V4__x)
                     => p(happ(V2__P,V4__x)) ) ) ) ) ) ) ).

fof('Coq.Init.Wf.Acc_intro',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__R] :
          ( c_24__type__117___24t(V0__A,V1__R)
         => ! [V2__x] :
              ( t(V2__x,V0__A)
             => ( ! [V3__y] :
                    ( t(V3__y,V0__A)
                   => ( p(happ(happ(V1__R,V3__y),V2__x))
                     => cCoq_2eInit_2eWf_2eAcc___24a3(V0__A,V1__R,V3__y) ) )
               => cCoq_2eInit_2eWf_2eAcc___24a3(V0__A,V1__R,V2__x) ) ) ) ) ).

fof('Coq.Init.Wf.Acc_intro_generator',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__R] :
          ( c_24__type__117___24t(V0__A,V1__R)
         => ! [V2__n] :
              ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__n)
             => ( cCoq_2eInit_2eWf_2ewell__founded___24a2(V0__A,V1__R)
               => cCoq_2eInit_2eWf_2ewell__founded___24a2(V0__A,V1__R) ) ) ) ) ).

fof('Coq.Init.Wf.Acc_inv',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__R] :
          ( c_24__type__117___24t(V0__A,V1__R)
         => ! [V2__x] :
              ( t(V2__x,V0__A)
             => ( cCoq_2eInit_2eWf_2eAcc___24a3(V0__A,V1__R,V2__x)
               => ! [V4__y] :
                    ( t(V4__y,V0__A)
                   => ( p(happ(happ(V1__R,V4__y),V2__x))
                     => cCoq_2eInit_2eWf_2eAcc___24a3(V0__A,V1__R,V4__y) ) ) ) ) ) ) ).

fof('Coq.Init.Wf.Fix_F_eq',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__R] :
          ( c_24__type__117___24t(V0__A,V1__R)
         => ! [V2__P] :
              ( c_24__type__181___24t(V0__A,V2__P)
             => ! [V3__F] :
                  ( c_24__type__684___24t(V0__A,V1__R,V2__P,V3__F)
                 => ! [V4__x] :
                      ( t(V4__x,V0__A)
                     => ( cCoq_2eInit_2eWf_2eAcc___24a3(V0__A,V1__R,V4__x)
                       => happ(happ(V3__F,V4__x),c_24__lam__728___24a5(V0__A,V1__R,V2__P,V3__F,V4__x)) = cCoq_2eInit_2eWf_2eFix__F___24a5(V0__A,V1__R,V2__P,V3__F,V4__x) ) ) ) ) ) ) ).

fof('Coq.Init.Wf.Fix_F_inv',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__R] :
          ( c_24__type__117___24t(V0__A,V1__R)
         => ( cCoq_2eInit_2eWf_2ewell__founded___24a2(V0__A,V1__R)
           => ! [V3__P] :
                ( c_24__type__181___24t(V0__A,V3__P)
               => ! [V4__F] :
                    ( c_24__type__794___24t(V0__A,V1__R,V3__P,V4__F)
                   => ( ! [V5__x] :
                          ( t(V5__x,V0__A)
                         => ! [V6__f] :
                              ( c_24__type__824___24t(V0__A,V1__R,V3__P,V5__x,V6__f)
                             => ! [V7__g] :
                                  ( c_24__type__839___24t(V0__A,V1__R,V3__P,V5__x,V7__g)
                                 => ( ! [V8__y] :
                                        ( t(V8__y,V0__A)
                                       => ( p(happ(happ(V1__R,V8__y),V5__x))
                                         => happ(V6__f,V8__y) = happ(V7__g,V8__y) ) )
                                   => happ(happ(V4__F,V5__x),V6__f) = happ(happ(V4__F,V5__x),V7__g) ) ) ) )
                     => ! [V6__x] :
                          ( t(V6__x,V0__A)
                         => ( cCoq_2eInit_2eWf_2eAcc___24a3(V0__A,V1__R,V6__x)
                           => ( cCoq_2eInit_2eWf_2eAcc___24a3(V0__A,V1__R,V6__x)
                             => cCoq_2eInit_2eWf_2eFix__F___24a5(V0__A,V1__R,V3__P,V4__F,V6__x) = cCoq_2eInit_2eWf_2eFix__F___24a5(V0__A,V1__R,V3__P,V4__F,V6__x) ) ) ) ) ) ) ) ) ) ).

fof('Coq.Init.Wf.Fix_eq',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__R] :
          ( c_24__type__117___24t(V0__A,V1__R)
         => ( cCoq_2eInit_2eWf_2ewell__founded___24a2(V0__A,V1__R)
           => ! [V3__P] :
                ( c_24__type__181___24t(V0__A,V3__P)
               => ! [V4__F] :
                    ( c_24__type__877___24t(V0__A,V1__R,V3__P,V4__F)
                   => ( ! [V5__x] :
                          ( t(V5__x,V0__A)
                         => ! [V6__f] :
                              ( c_24__type__907___24t(V0__A,V1__R,V3__P,V5__x,V6__f)
                             => ! [V7__g] :
                                  ( c_24__type__922___24t(V0__A,V1__R,V3__P,V5__x,V7__g)
                                 => ( ! [V8__y] :
                                        ( t(V8__y,V0__A)
                                       => ( p(happ(happ(V1__R,V8__y),V5__x))
                                         => happ(V6__f,V8__y) = happ(V7__g,V8__y) ) )
                                   => happ(happ(V4__F,V5__x),V6__f) = happ(happ(V4__F,V5__x),V7__g) ) ) ) )
                     => ! [V6__x] :
                          ( t(V6__x,V0__A)
                         => cCoq_2eInit_2eWf_2eFix___24a5(V0__A,V1__R,V3__P,V4__F,V6__x) = happ(happ(V4__F,V6__x),c_24__lam__963___24a5(V0__A,V1__R,V3__P,V4__F,V6__x)) ) ) ) ) ) ) ) ).

fof('Coq.Init.Wf.well_founded_ind',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__R] :
          ( c_24__type__117___24t(V0__A,V1__R)
         => ( cCoq_2eInit_2eWf_2ewell__founded___24a2(V0__A,V1__R)
           => ! [V3__P] :
                ( c_24__type__242___24t(V0__A,V3__P)
               => ( ! [V4__x] :
                      ( t(V4__x,V0__A)
                     => ( ! [V5__y] :
                            ( t(V5__y,V0__A)
                           => ( p(happ(happ(V1__R,V5__y),V4__x))
                             => p(happ(V3__P,V5__y)) ) )
                       => p(happ(V3__P,V4__x)) ) )
                 => ! [V5__a] :
                      ( t(V5__a,V0__A)
                     => p(happ(V3__P,V5__a)) ) ) ) ) ) ) ).

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',axiom,
    ! [V0__A] :
      ( cProp___24t(V0__A)
     => ! [V1__B] :
          ( cProp___24t(V1__B)
         => ( ~ ( p(V0__A)
                | p(V1__B) )
           => ( ~ p(V0__A)
              & ~ p(V1__B) ) ) ) ) ).

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.Logic.EqdepFacts.eq_dep_intro',axiom,
    ! [V0__U] :
      ( cType___24t(V0__U)
     => ! [V1__P] :
          ( c_24__type__181___24t(V0__U,V1__P)
         => ! [V2__p] :
              ( t(V2__p,V0__U)
             => ! [V3__x] :
                  ( t(V3__x,happ(V1__P,V2__p))
                 => cCoq_2eLogic_2eEqdepFacts_2eeq__dep___24a6(V0__U,V1__P,V2__p,V3__x,V2__p,V3__x) ) ) ) ) ).

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_ge_lt',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(V1__y,V0__x)
           => cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V0__x,V1__y) ) ) ) ).

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.add_comm',axiom,
    ! [V0__n] :
      ( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
     => ! [V1__m] :
          ( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
         => cCoq_2eNArith_2eBinNatDef_2eN_2eadd___24a2(V0__n,V1__m) = cCoq_2eNArith_2eBinNatDef_2eN_2eadd___24a2(V1__m,V0__n) ) ) ).

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.eq_le_incl',axiom,
    ! [V0__n] :
      ( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
     => ! [V1__m] :
          ( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
         => ( V0__n = V1__m
           => cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(V0__n,V1__m) ) ) ) ).

fof('Coq.NArith.BinNat.N.eq_stepl',axiom,
    ! [V0__x] :
      ( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__x)
     => ! [V1__y] :
          ( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__y)
         => ! [V2__z] :
              ( cCoq_2eNumbers_2eBinNums_2eN___24t(V2__z)
             => ( V0__x = V1__y
               => ( V0__x = V2__z
                 => V2__z = V1__y ) ) ) ) ) ).

fof('Coq.NArith.BinNat.N.gt_wf',axiom,
    ! [V0__z] :
      ( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__z)
     => cCoq_2eInit_2eWf_2ewell__founded___24a2(cCoq_2eNumbers_2eBinNums_2eN,c_24__lam__2692___24a1(V0__z)) ) ).

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_lt_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_2elt___24a2(V1__m,V2__p)
                 => cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V0__n,V2__p) ) ) ) ) ) ).

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_succ_l',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(cCoq_2eNArith_2eBinNatDef_2eN_2esucc___24a1(V0__n),V1__m)
          <=> cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V0__n,V1__m) ) ) ) ).

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_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_2elt___24a2(V0__n,V1__m)
               => ( cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V1__m,V2__p)
                 => cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V0__n,V2__p) ) ) ) ) ) ).

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__2687___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.BinNat.N.nle_gt',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.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.add_comm',axiom,
    ! [V0__p] :
      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V0__p)
     => ! [V1__q] :
          ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__q)
         => cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(V0__p,V1__q) = cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(V1__q,V0__p) ) ) ).

fof('Coq.PArith.BinPos.Pos.iter_invariant',axiom,
    ! [V0__p] :
      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V0__p)
     => ! [V1__A] :
          ( cType___24t(V1__A)
         => ! [V2__f] :
              ( c_24__type__3276___24t(V1__A,V2__f)
             => ! [V3__Inv] :
                  ( c_24__type__242___24t(V1__A,V3__Inv)
                 => ( ! [V4__x] :
                        ( t(V4__x,V1__A)
                       => ( p(happ(V3__Inv,V4__x))
                         => p(happ(V3__Inv,happ(V2__f,V4__x))) ) )
                   => ! [V5__x] :
                        ( t(V5__x,V1__A)
                       => ( p(happ(V3__Inv,V5__x))
                         => p(happ(V3__Inv,cCoq_2ePArith_2eBinPosDef_2ePos_2eiter___24a4(V1__A,V2__f,V5__x,V0__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.QArith.QArith_base.Qeq_refl',axiom,
    ! [V0__x] :
      ( cCoq_2eQArith_2eQArith__base_2eQ___24t(V0__x)
     => cCoq_2eQArith_2eQArith__base_2eQeq___24a2(V0__x,V0__x) ) ).

fof('Coq.Reals.RIneq.Rge_refl',axiom,
    ! [V0__r] :
      ( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r)
     => cCoq_2eReals_2eRdefinitions_2eRle___24a2(V0__r,V0__r) ) ).

fof('Coq.Reals.RIneq.Rle_refl',axiom,
    ! [V0__r] :
      ( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r)
     => cCoq_2eReals_2eRdefinitions_2eRle___24a2(V0__r,V0__r) ) ).

fof('Coq.Reals.RIneq.Rle_trans',axiom,
    ! [V0__r1] :
      ( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
     => ! [V1__r2] :
          ( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
         => ! [V2__r3] :
              ( cCoq_2eReals_2eRdefinitions_2eR___24t(V2__r3)
             => ( cCoq_2eReals_2eRdefinitions_2eRle___24a2(V0__r1,V1__r2)
               => ( cCoq_2eReals_2eRdefinitions_2eRle___24a2(V1__r2,V2__r3)
                 => cCoq_2eReals_2eRdefinitions_2eRle___24a2(V0__r1,V2__r3) ) ) ) ) ) ).

fof('Coq.Reals.RIneq.Rlt_le',axiom,
    ! [V0__r1] :
      ( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
     => ! [V1__r2] :
          ( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
         => ( cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V0__r1,V1__r2)
           => cCoq_2eReals_2eRdefinitions_2eRle___24a2(V0__r1,V1__r2) ) ) ) ).

fof('Coq.Reals.Raxioms.Rlt_trans',axiom,
    ! [V0__r1] :
      ( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
     => ! [V1__r2] :
          ( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
         => ! [V2__r3] :
              ( cCoq_2eReals_2eRdefinitions_2eR___24t(V2__r3)
             => ( cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V0__r1,V1__r2)
               => ( cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V1__r2,V2__r3)
                 => cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V0__r1,V2__r3) ) ) ) ) ) ).

fof('Coq.Structures.OrderedTypeEx.Z_as_OT.lt_trans',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)
             => ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__x,V1__y))
               => ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V1__y,V2__z))
                 => p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__x,V2__z)) ) ) ) ) ) ).

fof('Coq.ZArith.BinInt.Z.A\'A_left',axiom,
    ! [V0__A] :
      ( c_24__type__3174___24t(V0__A)
     => ! [V1__z] :
          ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__z)
         => ( ! [V2__n] :
                ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__n)
               => ! [Vvar__4__m__33120] :
                    ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__4__m__33120)
                   => ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(Vvar__4__m__33120,V1__z))
                     => ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V2__n,Vvar__4__m__33120))
                       => p(happ(V0__A,Vvar__4__m__33120)) ) ) ) )
           => ! [V3__n] :
                ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V3__n)
               => ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V3__n,V1__z))
                 => p(happ(V0__A,V3__n)) ) ) ) ) ) ).

fof('Coq.ZArith.BinInt.Z.Private_OrderTac.Tac.eq_neq',axiom,
    ! [V0__x] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
     => ! [V1__y] :
          ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
         => ! [V2__z] :
              ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__z)
             => ( V0__x = V1__y
               => ( V1__y != V2__z
                 => V0__x != V2__z ) ) ) ) ) ).

fof('Coq.ZArith.BinInt.Z.Private_OrderTac.Tac.eq_refl',axiom,
    ! [V0__x] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
     => V0__x = V0__x ) ).

fof('Coq.ZArith.BinInt.Z.Private_OrderTac.Tac.eq_sym',axiom,
    ! [V0__x] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
     => ! [V1__y] :
          ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
         => ( V0__x = V1__y
           => V1__y = V0__x ) ) ) ).

fof('Coq.ZArith.BinInt.Z.Private_OrderTac.Tac.le_antisym',axiom,
    ! [V0__x] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
     => ! [V1__y] :
          ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
         => ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__x,V1__y))
           => ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V1__y,V0__x))
             => V0__x = V1__y ) ) ) ) ).

fof('Coq.ZArith.BinInt.Z.Private_OrderTac.Tac.le_lt_trans',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)
             => ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__x,V1__y))
               => ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V1__y,V2__z))
                 => p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__x,V2__z)) ) ) ) ) ) ).

fof('Coq.ZArith.BinInt.Z.Private_OrderTac.Tac.le_refl',axiom,
    ! [V0__x] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
     => p(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.lt_trans',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)
             => ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__x,V1__y))
               => ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V1__y,V2__z))
                 => p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__x,V2__z)) ) ) ) ) ) ).

fof('Coq.ZArith.BinInt.Z.Private_OrderTac.Tac.neq_eq',axiom,
    ! [V0__x] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
     => ! [V1__y] :
          ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
         => ! [V2__z] :
              ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__z)
             => ( V0__x != V1__y
               => ( V1__y = V2__z
                 => V0__x != V2__z ) ) ) ) ) ).

fof('Coq.ZArith.BinInt.Z.Private_OrderTac.Tac.not_ge_lt',axiom,
    ! [V0__x] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
     => ! [V1__y] :
          ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
         => ( ~ p(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))
           => p(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_antisym',axiom,
    ! [V0__x] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
     => ! [V1__y] :
          ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
         => ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__x,V1__y))
           => ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V1__y,V0__x))
             => V0__x = V1__y ) ) ) ) ).

fof('Coq.ZArith.BinInt.Z.Private_Tac.le_refl',axiom,
    ! [V0__x] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
     => p(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.Private_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))
           => p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__x,V1__y)) ) ) ) ).

fof('Coq.ZArith.BinInt.Z.add_0_l',axiom,
    ! [V0__n] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
     => cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V0__n) = V0__n ) ).

fof('Coq.ZArith.BinInt.Z.add_0_r',axiom,
    ! [V0__n] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
     => cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__n,cCoq_2eNumbers_2eBinNums_2eZ0) = V0__n ) ).

fof('Coq.ZArith.BinInt.Z.add_assoc',axiom,
    ! [V0__n] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
     => ! [V1__m] :
          ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
         => ! [V2__p] :
              ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__p)
             => cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__n,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V1__m,V2__p)) = cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__n,V1__m),V2__p) ) ) ) ).

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_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__10918___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_le_incl',axiom,
    ! [V0__n] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
     => ! [V1__m] :
          ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
         => ( V0__n = V1__m
           => p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__n,V1__m)) ) ) ) ).

fof('Coq.ZArith.BinInt.Z.eq_stepl',axiom,
    ! [V0__x] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
     => ! [V1__y] :
          ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
         => ! [V2__z] :
              ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__z)
             => ( V0__x = V1__y
               => ( V0__x = V2__z
                 => V2__z = V1__y ) ) ) ) ) ).

fof('Coq.ZArith.BinInt.Z.eq_sym_iff',axiom,
    ! [V0__x] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
     => ! [V1__y] :
          ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
         => ( V0__x = V1__y
          <=> V1__y = V0__x ) ) ) ).

fof('Coq.ZArith.BinInt.Z.gt_wf',axiom,
    ! [V0__z] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__z)
     => cCoq_2eInit_2eWf_2ewell__founded___24a2(cCoq_2eNumbers_2eBinNums_2eZ,c_24__lam__3212___24a1(V0__z)) ) ).

fof('Coq.ZArith.BinInt.Z.le_antisymm',axiom,
    ! [V0__n] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
     => ! [V1__m] :
          ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
         => ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__n,V1__m))
           => ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V1__m,V0__n))
             => V0__n = V1__m ) ) ) ) ).

fof('Coq.ZArith.BinInt.Z.le_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_2ele___24a2(V0__n,V1__m)) ) ) ).

fof('Coq.ZArith.BinInt.Z.le_ge_cases',axiom,
    ! [V0__n] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
     => ! [V1__m] :
          ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
         => ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__n,V1__m))
            | p(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)
         => ( p(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_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_2ele___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.le_refl',axiom,
    ! [V0__n] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
     => p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__n,V0__n)) ) ).

fof('Coq.ZArith.BinInt.Z.le_succ_l',axiom,
    ! [V0__n] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
     => ! [V1__m] :
          ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
         => ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2esucc___24a1(V0__n),V1__m))
          <=> p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__n,V1__m)) ) ) ) ).

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)
             => ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__n,V1__m))
               => ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V1__m,V2__p))
                 => p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__n,V2__p)) ) ) ) ) ) ).

fof('Coq.ZArith.BinInt.Z.le_wd',axiom,
    cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__2562,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eNumbers_2eBinNums_2eZ,c_24__type__3174,c_3d___24a1(cCoq_2eNumbers_2eBinNums_2eZ),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eNumbers_2eBinNums_2eZ,cProp,c_3d___24a1(cCoq_2eNumbers_2eBinNums_2eZ),c_3c_3d_3e)),cCoq_2eZArith_2eBinInt_2eZ_2ele) ).

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_1_2',axiom,
    p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH),cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exO___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))
            | p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V1__m,V0__n)) ) ) ) ).

fof('Coq.ZArith.BinInt.Z.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.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))
           => p(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))
               => ( p(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_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.lt_wf',axiom,
    ! [V0__z] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__z)
     => cCoq_2eInit_2eWf_2ewell__founded___24a2(cCoq_2eNumbers_2eBinNums_2eZ,c_24__lam__3207___24a1(V0__z)) ) ).

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.ZArith.BinInt.Z.nle_gt',axiom,
    ! [V0__n] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
     => ! [V1__m] :
          ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
         => ( ~ p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__n,V1__m))
          <=> p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V1__m,V0__n)) ) ) ) ).

fof('Coq.ZArith.Znat.Z2Nat.inj_lt',axiom,
    ! [V0__n] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
     => ! [V1__m] :
          ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
         => ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V0__n))
           => ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V1__m))
             => ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__n,V1__m))
              <=> cCoq_2eInit_2ePeano_2elt___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eto__nat___24a1(V0__n),cCoq_2eZArith_2eBinIntDef_2eZ_2eto__nat___24a1(V1__m)) ) ) ) ) ) ).

fof('Coq.micromega.DeclConstant.Build_DeclaredConstant',axiom,
    ! [V0__T] :
      ( cType___24t(V0__T)
     => ! [V1__F] :
          ( t(V1__F,V0__T)
         => cCoq_2emicromega_2eDeclConstant_2eDeclaredConstant___24a2(V0__T,V1__F) ) ) ).

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__3267___24t(V0__R,V3__rplus)
                 => ! [V4__rtimes] :
                      ( c_24__type__3267___24t(V0__R,V4__rtimes)
                     => ! [V5__rminus] :
                          ( c_24__type__3267___24t(V0__R,V5__rminus)
                         => ! [V6__ropp] :
                              ( c_24__type__3276___24t(V0__R,V6__ropp)
                             => ! [V7__req] :
                                  ( c_24__type__117___24t(V0__R,V7__req)
                                 => ! [V8__rle] :
                                      ( c_24__type__117___24t(V0__R,V8__rle)
                                     => ! [V9__rlt] :
                                          ( c_24__type__117___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__3267___24t(V0__R,V3__rplus)
                 => ! [V4__rtimes] :
                      ( c_24__type__3267___24t(V0__R,V4__rtimes)
                     => ! [V5__rminus] :
                          ( c_24__type__3267___24t(V0__R,V5__rminus)
                         => ! [V6__ropp] :
                              ( c_24__type__3276___24t(V0__R,V6__ropp)
                             => ! [V7__req] :
                                  ( c_24__type__117___24t(V0__R,V7__req)
                                 => ! [V8__rle] :
                                      ( c_24__type__117___24t(V0__R,V8__rle)
                                     => ! [V9__rlt] :
                                          ( c_24__type__117___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__3267___24t(V0__R,V3__rplus)
                 => ! [V4__rtimes] :
                      ( c_24__type__3267___24t(V0__R,V4__rtimes)
                     => ! [V5__rminus] :
                          ( c_24__type__3267___24t(V0__R,V5__rminus)
                         => ! [V6__ropp] :
                              ( c_24__type__3276___24t(V0__R,V6__ropp)
                             => ! [V7__req] :
                                  ( c_24__type__117___24t(V0__R,V7__req)
                                 => ! [V8__rle] :
                                      ( c_24__type__117___24t(V0__R,V8__rle)
                                     => ! [V9__rlt] :
                                          ( c_24__type__117___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__3267___24t(V0__R,V3__rplus)
                 => ! [V4__rtimes] :
                      ( c_24__type__3267___24t(V0__R,V4__rtimes)
                     => ! [V5__rminus] :
                          ( c_24__type__3267___24t(V0__R,V5__rminus)
                         => ! [V6__ropp] :
                              ( c_24__type__3276___24t(V0__R,V6__ropp)
                             => ! [V7__req] :
                                  ( c_24__type__117___24t(V0__R,V7__req)
                                 => ! [V8__rle] :
                                      ( c_24__type__117___24t(V0__R,V8__rle)
                                     => ! [V9__rlt] :
                                          ( c_24__type__117___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__3267___24t(V0__R,V3__rplus)
                 => ! [V4__rtimes] :
                      ( c_24__type__3267___24t(V0__R,V4__rtimes)
                     => ! [V5__rminus] :
                          ( c_24__type__3267___24t(V0__R,V5__rminus)
                         => ! [V6__ropp] :
                              ( c_24__type__3276___24t(V0__R,V6__ropp)
                             => ! [V7__req] :
                                  ( c_24__type__117___24t(V0__R,V7__req)
                                 => ! [V8__rle] :
                                      ( c_24__type__117___24t(V0__R,V8__rle)
                                     => ! [V9__rlt] :
                                          ( c_24__type__117___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__3267___24t(V0__R,V3__rplus)
                 => ! [V4__rtimes] :
                      ( c_24__type__3267___24t(V0__R,V4__rtimes)
                     => ! [V5__rminus] :
                          ( c_24__type__3267___24t(V0__R,V5__rminus)
                         => ! [V6__ropp] :
                              ( c_24__type__3276___24t(V0__R,V6__ropp)
                             => ! [V7__req] :
                                  ( c_24__type__117___24t(V0__R,V7__req)
                                 => ! [V8__rle] :
                                      ( c_24__type__117___24t(V0__R,V8__rle)
                                     => ! [V9__rlt] :
                                          ( c_24__type__117___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__3267___24t(V0__R,V3__rplus)
                 => ! [V4__rtimes] :
                      ( c_24__type__3267___24t(V0__R,V4__rtimes)
                     => ! [V5__rminus] :
                          ( c_24__type__3267___24t(V0__R,V5__rminus)
                         => ! [V6__ropp] :
                              ( c_24__type__3276___24t(V0__R,V6__ropp)
                             => ! [V7__req] :
                                  ( c_24__type__117___24t(V0__R,V7__req)
                                 => ! [V8__rle] :
                                      ( c_24__type__117___24t(V0__R,V8__rle)
                                     => ! [V9__rlt] :
                                          ( c_24__type__117___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__3267___24t(V0__R,V3__rplus)
                 => ! [V4__rtimes] :
                      ( c_24__type__3267___24t(V0__R,V4__rtimes)
                     => ! [V5__rminus] :
                          ( c_24__type__3267___24t(V0__R,V5__rminus)
                         => ! [V6__ropp] :
                              ( c_24__type__3276___24t(V0__R,V6__ropp)
                             => ! [V7__req] :
                                  ( c_24__type__117___24t(V0__R,V7__req)
                                 => ! [V8__rle] :
                                      ( c_24__type__117___24t(V0__R,V8__rle)
                                     => ! [V9__rlt] :
                                          ( c_24__type__117___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__3267___24t(V0__R,V3__rplus)
                 => ! [V4__rtimes] :
                      ( c_24__type__3267___24t(V0__R,V4__rtimes)
                     => ! [V5__rminus] :
                          ( c_24__type__3267___24t(V0__R,V5__rminus)
                         => ! [V6__ropp] :
                              ( c_24__type__3276___24t(V0__R,V6__ropp)
                             => ! [V7__req] :
                                  ( c_24__type__117___24t(V0__R,V7__req)
                                 => ! [V8__rle] :
                                      ( c_24__type__117___24t(V0__R,V8__rle)
                                     => ! [V9__rlt] :
                                          ( c_24__type__117___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__3267___24t(V0__R,V3__rplus)
                 => ! [V4__rtimes] :
                      ( c_24__type__3267___24t(V0__R,V4__rtimes)
                     => ! [V5__rminus] :
                          ( c_24__type__3267___24t(V0__R,V5__rminus)
                         => ! [V6__ropp] :
                              ( c_24__type__3276___24t(V0__R,V6__ropp)
                             => ! [V7__req] :
                                  ( c_24__type__117___24t(V0__R,V7__req)
                                 => ! [V8__rle] :
                                      ( c_24__type__117___24t(V0__R,V8__rle)
                                     => ! [V9__rlt] :
                                          ( c_24__type__117___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__3267___24t(V0__R,V3__rplus)
                 => ! [V4__rtimes] :
                      ( c_24__type__3267___24t(V0__R,V4__rtimes)
                     => ! [V5__rminus] :
                          ( c_24__type__3267___24t(V0__R,V5__rminus)
                         => ! [V6__ropp] :
                              ( c_24__type__3276___24t(V0__R,V6__ropp)
                             => ! [V7__req] :
                                  ( c_24__type__117___24t(V0__R,V7__req)
                                 => ! [V8__rle] :
                                      ( c_24__type__117___24t(V0__R,V8__rle)
                                     => ! [V9__rlt] :
                                          ( c_24__type__117___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__3267___24t(V0__R,V3__rplus)
                 => ! [V4__rtimes] :
                      ( c_24__type__3267___24t(V0__R,V4__rtimes)
                     => ! [V5__rminus] :
                          ( c_24__type__3267___24t(V0__R,V5__rminus)
                         => ! [V6__ropp] :
                              ( c_24__type__3276___24t(V0__R,V6__ropp)
                             => ! [V7__req] :
                                  ( c_24__type__117___24t(V0__R,V7__req)
                                 => ! [V8__rle] :
                                      ( c_24__type__117___24t(V0__R,V8__rle)
                                     => ! [V9__rlt] :
                                          ( c_24__type__117___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__3267___24t(V0__R,V3__rplus)
                 => ! [V4__rtimes] :
                      ( c_24__type__3267___24t(V0__R,V4__rtimes)
                     => ! [V5__rminus] :
                          ( c_24__type__3267___24t(V0__R,V5__rminus)
                         => ! [V6__ropp] :
                              ( c_24__type__3276___24t(V0__R,V6__ropp)
                             => ! [V7__req] :
                                  ( c_24__type__117___24t(V0__R,V7__req)
                                 => ! [V8__rle] :
                                      ( c_24__type__117___24t(V0__R,V8__rle)
                                     => ! [V9__rlt] :
                                          ( c_24__type__117___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__3267___24t(V0__R,V3__rplus)
                 => ! [V4__rtimes] :
                      ( c_24__type__3267___24t(V0__R,V4__rtimes)
                     => ! [V5__rminus] :
                          ( c_24__type__3267___24t(V0__R,V5__rminus)
                         => ! [V6__ropp] :
                              ( c_24__type__3276___24t(V0__R,V6__ropp)
                             => ! [V7__req] :
                                  ( c_24__type__117___24t(V0__R,V7__req)
                                 => ! [V8__rle] :
                                      ( c_24__type__117___24t(V0__R,V8__rle)
                                     => ! [V9__rlt] :
                                          ( c_24__type__117___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__3267___24t(V0__R,V3__rplus)
                 => ! [V4__rtimes] :
                      ( c_24__type__3267___24t(V0__R,V4__rtimes)
                     => ! [V5__rminus] :
                          ( c_24__type__3267___24t(V0__R,V5__rminus)
                         => ! [V6__ropp] :
                              ( c_24__type__3276___24t(V0__R,V6__ropp)
                             => ! [V7__req] :
                                  ( c_24__type__117___24t(V0__R,V7__req)
                                 => ! [V8__rle] :
                                      ( c_24__type__117___24t(V0__R,V8__rle)
                                     => ! [V9__rlt] :
                                          ( c_24__type__117___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__3267___24t(V0__R,V3__rplus)
                 => ! [V4__rtimes] :
                      ( c_24__type__3267___24t(V0__R,V4__rtimes)
                     => ! [V5__rminus] :
                          ( c_24__type__3267___24t(V0__R,V5__rminus)
                         => ! [V6__ropp] :
                              ( c_24__type__3276___24t(V0__R,V6__ropp)
                             => ! [V7__req] :
                                  ( c_24__type__117___24t(V0__R,V7__req)
                                 => ! [V8__rle] :
                                      ( c_24__type__117___24t(V0__R,V8__rle)
                                     => ! [V9__rlt] :
                                          ( c_24__type__117___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__3267___24t(V0__R,V3__rplus)
                 => ! [V4__rtimes] :
                      ( c_24__type__3267___24t(V0__R,V4__rtimes)
                     => ! [V5__rminus] :
                          ( c_24__type__3267___24t(V0__R,V5__rminus)
                         => ! [V6__ropp] :
                              ( c_24__type__3276___24t(V0__R,V6__ropp)
                             => ! [V7__req] :
                                  ( c_24__type__117___24t(V0__R,V7__req)
                                 => ! [V8__rle] :
                                      ( c_24__type__117___24t(V0__R,V8__rle)
                                     => ! [V9__rlt] :
                                          ( c_24__type__117___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__3267___24t(V0__R,V3__rplus)
                 => ! [V4__rtimes] :
                      ( c_24__type__3267___24t(V0__R,V4__rtimes)
                     => ! [V5__rminus] :
                          ( c_24__type__3267___24t(V0__R,V5__rminus)
                         => ! [V6__ropp] :
                              ( c_24__type__3276___24t(V0__R,V6__ropp)
                             => ! [V7__req] :
                                  ( c_24__type__117___24t(V0__R,V7__req)
                                 => ! [V8__rle] :
                                      ( c_24__type__117___24t(V0__R,V8__rle)
                                     => ! [V9__rlt] :
                                          ( c_24__type__117___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__3267___24t(V0__R,V3__rplus)
                 => ! [V4__rtimes] :
                      ( c_24__type__3267___24t(V0__R,V4__rtimes)
                     => ! [V5__rminus] :
                          ( c_24__type__3267___24t(V0__R,V5__rminus)
                         => ! [V6__ropp] :
                              ( c_24__type__3276___24t(V0__R,V6__ropp)
                             => ! [V7__req] :
                                  ( c_24__type__117___24t(V0__R,V7__req)
                                 => ! [V8__rle] :
                                      ( c_24__type__117___24t(V0__R,V8__rle)
                                     => ! [V9__rlt] :
                                          ( c_24__type__117___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__3267___24t(V0__R,V3__rplus)
                 => ! [V4__rtimes] :
                      ( c_24__type__3267___24t(V0__R,V4__rtimes)
                     => ! [V5__rminus] :
                          ( c_24__type__3267___24t(V0__R,V5__rminus)
                         => ! [V6__ropp] :
                              ( c_24__type__3276___24t(V0__R,V6__ropp)
                             => ! [V7__req] :
                                  ( c_24__type__117___24t(V0__R,V7__req)
                                 => ! [V8__rle] :
                                      ( c_24__type__117___24t(V0__R,V8__rle)
                                     => ! [V9__rlt] :
                                          ( c_24__type__117___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__3267___24t(V0__R,V3__rplus)
                 => ! [V4__rtimes] :
                      ( c_24__type__3267___24t(V0__R,V4__rtimes)
                     => ! [V5__rminus] :
                          ( c_24__type__3267___24t(V0__R,V5__rminus)
                         => ! [V6__ropp] :
                              ( c_24__type__3276___24t(V0__R,V6__ropp)
                             => ! [V7__req] :
                                  ( c_24__type__117___24t(V0__R,V7__req)
                                 => ! [V8__rle] :
                                      ( c_24__type__117___24t(V0__R,V8__rle)
                                     => ! [V9__rlt] :
                                          ( c_24__type__117___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__3267___24t(V0__R,V3__rplus)
                 => ! [V4__rtimes] :
                      ( c_24__type__3267___24t(V0__R,V4__rtimes)
                     => ! [V5__rminus] :
                          ( c_24__type__3267___24t(V0__R,V5__rminus)
                         => ! [V6__ropp] :
                              ( c_24__type__3276___24t(V0__R,V6__ropp)
                             => ! [V7__req] :
                                  ( c_24__type__117___24t(V0__R,V7__req)
                                 => ! [V8__rle] :
                                      ( c_24__type__117___24t(V0__R,V8__rle)
                                     => ! [V9__rlt] :
                                          ( c_24__type__117___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__3267___24t(V0__R,V3__rplus)
                 => ! [V4__rtimes] :
                      ( c_24__type__3267___24t(V0__R,V4__rtimes)
                     => ! [V5__rminus] :
                          ( c_24__type__3267___24t(V0__R,V5__rminus)
                         => ! [V6__ropp] :
                              ( c_24__type__3276___24t(V0__R,V6__ropp)
                             => ! [V7__req] :
                                  ( c_24__type__117___24t(V0__R,V7__req)
                                 => ! [V8__rle] :
                                      ( c_24__type__117___24t(V0__R,V8__rle)
                                     => ! [V9__rlt] :
                                          ( c_24__type__117___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__3267___24t(V0__R,V3__rplus)
                 => ! [V4__rtimes] :
                      ( c_24__type__3267___24t(V0__R,V4__rtimes)
                     => ! [V5__rminus] :
                          ( c_24__type__3267___24t(V0__R,V5__rminus)
                         => ! [V6__ropp] :
                              ( c_24__type__3276___24t(V0__R,V6__ropp)
                             => ! [V7__req] :
                                  ( c_24__type__117___24t(V0__R,V7__req)
                                 => ! [V8__rle] :
                                      ( c_24__type__117___24t(V0__R,V8__rle)
                                     => ! [V9__rlt] :
                                          ( c_24__type__117___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__3267___24t(V0__R,V3__rplus)
                 => ! [V4__rtimes] :
                      ( c_24__type__3267___24t(V0__R,V4__rtimes)
                     => ! [V5__rminus] :
                          ( c_24__type__3267___24t(V0__R,V5__rminus)
                         => ! [V6__ropp] :
                              ( c_24__type__3276___24t(V0__R,V6__ropp)
                             => ! [V7__req] :
                                  ( c_24__type__117___24t(V0__R,V7__req)
                                 => ! [V8__rle] :
                                      ( c_24__type__117___24t(V0__R,V8__rle)
                                     => ! [V9__rlt] :
                                          ( c_24__type__117___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__3267___24t(V0__R,V3__rplus)
                 => ! [V4__rtimes] :
                      ( c_24__type__3267___24t(V0__R,V4__rtimes)
                     => ! [V5__rminus] :
                          ( c_24__type__3267___24t(V0__R,V5__rminus)
                         => ! [V6__ropp] :
                              ( c_24__type__3276___24t(V0__R,V6__ropp)
                             => ! [V7__req] :
                                  ( c_24__type__117___24t(V0__R,V7__req)
                                 => ! [V8__rle] :
                                      ( c_24__type__117___24t(V0__R,V8__rle)
                                     => ! [V9__rlt] :
                                          ( c_24__type__117___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__3267___24t(V0__R,V3__rplus)
                 => ! [V4__rtimes] :
                      ( c_24__type__3267___24t(V0__R,V4__rtimes)
                     => ! [V5__rminus] :
                          ( c_24__type__3267___24t(V0__R,V5__rminus)
                         => ! [V6__ropp] :
                              ( c_24__type__3276___24t(V0__R,V6__ropp)
                             => ! [V7__req] :
                                  ( c_24__type__117___24t(V0__R,V7__req)
                                 => ! [V8__rle] :
                                      ( c_24__type__117___24t(V0__R,V8__rle)
                                     => ! [V9__rlt] :
                                          ( c_24__type__117___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__3267___24t(V0__R,V3__rplus)
                 => ! [V4__rtimes] :
                      ( c_24__type__3267___24t(V0__R,V4__rtimes)
                     => ! [V5__rminus] :
                          ( c_24__type__3267___24t(V0__R,V5__rminus)
                         => ! [V6__ropp] :
                              ( c_24__type__3276___24t(V0__R,V6__ropp)
                             => ! [V7__req] :
                                  ( c_24__type__117___24t(V0__R,V7__req)
                                 => ! [V8__rle] :
                                      ( c_24__type__117___24t(V0__R,V8__rle)
                                     => ! [V9__rlt] :
                                          ( c_24__type__117___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__3267___24t(V0__R,V3__rplus)
                 => ! [V4__rtimes] :
                      ( c_24__type__3267___24t(V0__R,V4__rtimes)
                     => ! [V5__rminus] :
                          ( c_24__type__3267___24t(V0__R,V5__rminus)
                         => ! [V6__ropp] :
                              ( c_24__type__3276___24t(V0__R,V6__ropp)
                             => ! [V7__req] :
                                  ( c_24__type__117___24t(V0__R,V7__req)
                                 => ! [V8__rle] :
                                      ( c_24__type__117___24t(V0__R,V8__rle)
                                     => ! [V9__rlt] :
                                          ( c_24__type__117___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__3267___24t(V0__R,V3__rplus)
                 => ! [V4__rtimes] :
                      ( c_24__type__3267___24t(V0__R,V4__rtimes)
                     => ! [V5__rminus] :
                          ( c_24__type__3267___24t(V0__R,V5__rminus)
                         => ! [V6__ropp] :
                              ( c_24__type__3276___24t(V0__R,V6__ropp)
                             => ! [V7__req] :
                                  ( c_24__type__117___24t(V0__R,V7__req)
                                 => ! [V8__rle] :
                                      ( c_24__type__117___24t(V0__R,V8__rle)
                                     => ! [V9__rlt] :
                                          ( c_24__type__117___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.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__3267___24t(V0__R,V3__rplus)
                 => ! [V4__rtimes] :
                      ( c_24__type__3267___24t(V0__R,V4__rtimes)
                     => ! [V5__rminus] :
                          ( c_24__type__3267___24t(V0__R,V5__rminus)
                         => ! [V6__ropp] :
                              ( c_24__type__3276___24t(V0__R,V6__ropp)
                             => ! [V7__req] :
                                  ( c_24__type__117___24t(V0__R,V7__req)
                                 => ! [V8__rle] :
                                      ( c_24__type__117___24t(V0__R,V8__rle)
                                     => ! [V9__rlt] :
                                          ( c_24__type__117___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__3267___24t(V0__R,V3__rplus)
                 => ! [V4__rtimes] :
                      ( c_24__type__3267___24t(V0__R,V4__rtimes)
                     => ! [V5__rminus] :
                          ( c_24__type__3267___24t(V0__R,V5__rminus)
                         => ! [V6__ropp] :
                              ( c_24__type__3276___24t(V0__R,V6__ropp)
                             => ! [V7__req] :
                                  ( c_24__type__117___24t(V0__R,V7__req)
                                 => ! [V8__rle] :
                                      ( c_24__type__117___24t(V0__R,V8__rle)
                                     => ! [V9__rlt] :
                                          ( c_24__type__117___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__3267___24t(V0__R,V3__rplus)
                 => ! [V4__rtimes] :
                      ( c_24__type__3267___24t(V0__R,V4__rtimes)
                     => ! [V5__rminus] :
                          ( c_24__type__3267___24t(V0__R,V5__rminus)
                         => ! [V6__ropp] :
                              ( c_24__type__3276___24t(V0__R,V6__ropp)
                             => ! [V7__req] :
                                  ( c_24__type__117___24t(V0__R,V7__req)
                                 => ! [V8__rle] :
                                      ( c_24__type__117___24t(V0__R,V8__rle)
                                     => ! [V9__rlt] :
                                          ( c_24__type__117___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.Facts.MP.equal_refl',axiom,
    ! [V0__s] :
      ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(V0__s)
     => cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eEqual___24a2(V0__s,V0__s) ) ).

fof('Coq.omega.OmegaLemmas.OMEGA2',axiom,
    ! [V0__x] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
     => ! [V1__y] :
          ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
         => ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V0__x))
           => ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V1__y))
             => p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__x,V1__y))) ) ) ) ) ).

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__3267___24t(V0__R,V3__radd)
                 => ! [V4__rmul] :
                      ( c_24__type__3267___24t(V0__R,V4__rmul)
                     => ! [V5__rsub] :
                          ( c_24__type__3267___24t(V0__R,V5__rsub)
                         => ! [V6__ropp] :
                              ( c_24__type__3276___24t(V0__R,V6__ropp)
                             => ! [V7__req] :
                                  ( c_24__type__117___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_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__3267___24t(V0__R,V3__radd)
                 => ! [V4__rmul] :
                      ( c_24__type__3267___24t(V0__R,V4__rmul)
                     => ! [V5__rsub] :
                          ( c_24__type__3267___24t(V0__R,V5__rsub)
                         => ! [V6__ropp] :
                              ( c_24__type__3276___24t(V0__R,V6__ropp)
                             => ! [V7__req] :
                                  ( c_24__type__117___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(V3__radd,V10__x),V1__rO)),V10__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__3267___24t(V0__R,V3__radd)
                 => ! [V4__rmul] :
                      ( c_24__type__3267___24t(V0__R,V4__rmul)
                     => ! [V5__rsub] :
                          ( c_24__type__3267___24t(V0__R,V5__rsub)
                         => ! [V6__ropp] :
                              ( c_24__type__3276___24t(V0__R,V6__ropp)
                             => ! [V7__req] :
                                  ( c_24__type__117___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.ARadd_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__3267___24t(V0__R,V3__radd)
                 => ! [V4__rmul] :
                      ( c_24__type__3267___24t(V0__R,V4__rmul)
                     => ! [V5__rsub] :
                          ( c_24__type__3267___24t(V0__R,V5__rsub)
                         => ! [V6__ropp] :
                              ( c_24__type__3276___24t(V0__R,V6__ropp)
                             => ! [V7__req] :
                                  ( c_24__type__117___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(V3__radd,V9__x),V10__y)),happ(happ(V3__radd,V10__y),V9__x))) ) ) ) ) ) ) ) ) ) ) ) ).

fof('Coq.setoid_ring.Ring_theory.ARdistr_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__3267___24t(V0__R,V3__radd)
                 => ! [V4__rmul] :
                      ( c_24__type__3267___24t(V0__R,V4__rmul)
                     => ! [V5__rsub] :
                          ( c_24__type__3267___24t(V0__R,V5__rsub)
                         => ! [V6__ropp] :
                              ( c_24__type__3276___24t(V0__R,V6__ropp)
                             => ! [V7__req] :
                                  ( c_24__type__117___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,happ(happ(V3__radd,V9__x),V10__y)),V11__z)),happ(happ(V3__radd,happ(happ(V4__rmul,V9__x),V11__z)),happ(happ(V4__rmul,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__3267___24t(V0__R,V3__radd)
                 => ! [V4__rmul] :
                      ( c_24__type__3267___24t(V0__R,V4__rmul)
                     => ! [V5__rsub] :
                          ( c_24__type__3267___24t(V0__R,V5__rsub)
                         => ! [V6__ropp] :
                              ( c_24__type__3276___24t(V0__R,V6__ropp)
                             => ! [V7__req] :
                                  ( c_24__type__117___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__3267___24t(V0__R,V3__radd)
                 => ! [V4__rmul] :
                      ( c_24__type__3267___24t(V0__R,V4__rmul)
                     => ! [V5__rsub] :
                          ( c_24__type__3267___24t(V0__R,V5__rsub)
                         => ! [V6__ropp] :
                              ( c_24__type__3276___24t(V0__R,V6__ropp)
                             => ! [V7__req] :
                                  ( c_24__type__117___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__3267___24t(V0__R,V3__radd)
                 => ! [V4__rmul] :
                      ( c_24__type__3267___24t(V0__R,V4__rmul)
                     => ! [V5__rsub] :
                          ( c_24__type__3267___24t(V0__R,V5__rsub)
                         => ! [V6__ropp] :
                              ( c_24__type__3276___24t(V0__R,V6__ropp)
                             => ! [V7__req] :
                                  ( c_24__type__117___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_1_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__3267___24t(V0__R,V3__radd)
                 => ! [V4__rmul] :
                      ( c_24__type__3267___24t(V0__R,V4__rmul)
                     => ! [V5__rsub] :
                          ( c_24__type__3267___24t(V0__R,V5__rsub)
                         => ! [V6__ropp] :
                              ( c_24__type__3276___24t(V0__R,V6__ropp)
                             => ! [V7__req] :
                                  ( c_24__type__117___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),V2__rI)),V10__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__3267___24t(V0__R,V3__radd)
                 => ! [V4__rmul] :
                      ( c_24__type__3267___24t(V0__R,V4__rmul)
                     => ! [V5__rsub] :
                          ( c_24__type__3267___24t(V0__R,V5__rsub)
                         => ! [V6__ropp] :
                              ( c_24__type__3276___24t(V0__R,V6__ropp)
                             => ! [V7__req] :
                                  ( c_24__type__117___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__3267___24t(V0__R,V3__radd)
                 => ! [V4__rmul] :
                      ( c_24__type__3267___24t(V0__R,V4__rmul)
                     => ! [V5__rsub] :
                          ( c_24__type__3267___24t(V0__R,V5__rsub)
                         => ! [V6__ropp] :
                              ( c_24__type__3276___24t(V0__R,V6__ropp)
                             => ! [V7__req] :
                                  ( c_24__type__117___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_add',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__3267___24t(V0__R,V3__radd)
                 => ! [V4__rmul] :
                      ( c_24__type__3267___24t(V0__R,V4__rmul)
                     => ! [V5__rsub] :
                          ( c_24__type__3267___24t(V0__R,V5__rsub)
                         => ! [V6__ropp] :
                              ( c_24__type__3276___24t(V0__R,V6__ropp)
                             => ! [V7__req] :
                                  ( c_24__type__117___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(V3__radd,V9__x),V10__y))),happ(happ(V3__radd,happ(V6__ropp,V9__x)),happ(V6__ropp,V10__y)))) ) ) ) ) ) ) ) ) ) ) ) ).

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__3267___24t(V0__R,V3__radd)
                 => ! [V4__rmul] :
                      ( c_24__type__3267___24t(V0__R,V4__rmul)
                     => ! [V5__rsub] :
                          ( c_24__type__3267___24t(V0__R,V5__rsub)
                         => ! [V6__ropp] :
                              ( c_24__type__3276___24t(V0__R,V6__ropp)
                             => ! [V7__req] :
                                  ( c_24__type__117___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__3267___24t(V0__R,V3__radd)
                 => ! [V4__rmul] :
                      ( c_24__type__3267___24t(V0__R,V4__rmul)
                     => ! [V5__rsub] :
                          ( c_24__type__3267___24t(V0__R,V5__rsub)
                         => ! [V6__ropp] :
                              ( c_24__type__3276___24t(V0__R,V6__ropp)
                             => ! [V7__req] :
                                  ( c_24__type__117___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.Eqsth',axiom,
    ! [V0__R] :
      ( cType___24t(V0__R)
     => cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(V0__R,c_3d___24a1(V0__R)) ) ).

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__3267___24t(V0__R,V3__radd)
                 => ! [V4__rmul] :
                      ( c_24__type__3267___24t(V0__R,V4__rmul)
                     => ! [V5__rsub] :
                          ( c_24__type__3267___24t(V0__R,V5__rsub)
                         => ! [V6__ropp] :
                              ( c_24__type__3276___24t(V0__R,V6__ropp)
                             => ! [V7__req] :
                                  ( c_24__type__117___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__3267___24t(V0__R,V3__radd)
                 => ! [V4__rmul] :
                      ( c_24__type__3267___24t(V0__R,V4__rmul)
                     => ! [V5__rsub] :
                          ( c_24__type__3267___24t(V0__R,V5__rsub)
                         => ! [V6__ropp] :
                              ( c_24__type__3276___24t(V0__R,V6__ropp)
                             => ! [V7__req] :
                                  ( c_24__type__117___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('Coq.setoid_ring.Ring_theory.mk_srt',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__3267___24t(V0__R,V3__radd)
                 => ! [V4__rmul] :
                      ( c_24__type__3267___24t(V0__R,V4__rmul)
                     => ! [V5__req] :
                          ( c_24__type__117___24t(V0__R,V5__req)
                         => ( ! [V6__n] :
                                ( t(V6__n,V0__R)
                               => p(happ(happ(V5__req,happ(happ(V3__radd,V1__rO),V6__n)),V6__n)) )
                           => ( ! [V7__n] :
                                  ( t(V7__n,V0__R)
                                 => ! [V8__m] :
                                      ( t(V8__m,V0__R)
                                     => p(happ(happ(V5__req,happ(happ(V3__radd,V7__n),V8__m)),happ(happ(V3__radd,V8__m),V7__n))) ) )
                             => ( ! [V8__n] :
                                    ( t(V8__n,V0__R)
                                   => ! [V9__m] :
                                        ( t(V9__m,V0__R)
                                       => ! [V10__p] :
                                            ( t(V10__p,V0__R)
                                           => p(happ(happ(V5__req,happ(happ(V3__radd,V8__n),happ(happ(V3__radd,V9__m),V10__p))),happ(happ(V3__radd,happ(happ(V3__radd,V8__n),V9__m)),V10__p))) ) ) )
                               => ( ! [V9__n] :
                                      ( t(V9__n,V0__R)
                                     => p(happ(happ(V5__req,happ(happ(V4__rmul,V2__rI),V9__n)),V9__n)) )
                                 => ( ! [V10__n] :
                                        ( t(V10__n,V0__R)
                                       => p(happ(happ(V5__req,happ(happ(V4__rmul,V1__rO),V10__n)),V1__rO)) )
                                   => ( ! [V11__n] :
                                          ( t(V11__n,V0__R)
                                         => ! [V12__m] :
                                              ( t(V12__m,V0__R)
                                             => p(happ(happ(V5__req,happ(happ(V4__rmul,V11__n),V12__m)),happ(happ(V4__rmul,V12__m),V11__n))) ) )
                                     => ( ! [V12__n] :
                                            ( t(V12__n,V0__R)
                                           => ! [V13__m] :
                                                ( t(V13__m,V0__R)
                                               => ! [V14__p] :
                                                    ( t(V14__p,V0__R)
                                                   => p(happ(happ(V5__req,happ(happ(V4__rmul,V12__n),happ(happ(V4__rmul,V13__m),V14__p))),happ(happ(V4__rmul,happ(happ(V4__rmul,V12__n),V13__m)),V14__p))) ) ) )
                                       => ( ! [V13__n] :
                                              ( t(V13__n,V0__R)
                                             => ! [V14__m] :
                                                  ( t(V14__m,V0__R)
                                                 => ! [V15__p] :
                                                      ( t(V15__p,V0__R)
                                                     => p(happ(happ(V5__req,happ(happ(V4__rmul,happ(happ(V3__radd,V13__n),V14__m)),V15__p)),happ(happ(V3__radd,happ(happ(V4__rmul,V13__n),V15__p)),happ(happ(V4__rmul,V14__m),V15__p)))) ) ) )
                                         => cCoq_2esetoid__ring_2eRing__theory_2esemi__ring__theory___24a6(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__req) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).

fof('GenRec.setoid_fix.Fix_F_equiv_inv',axiom,
    ! [V0__x] :
      ( cA___24t(V0__x)
     => ( cCoq_2eInit_2eWf_2eAcc___24a3(cA,cR,V0__x)
       => ( cCoq_2eInit_2eWf_2eAcc___24a3(cA,cR,V0__x)
         => cr___24a3(V0__x,cCoq_2eInit_2eWf_2eFix__F___24a5(cA,cR,cP,cF,V0__x),cCoq_2eInit_2eWf_2eFix__F___24a5(cA,cR,cP,cF,V0__x)) ) ) ) ).

fof('Hstep',axiom,
    ! [V0__x] :
      ( cA___24t(V0__x)
     => ! [V1__f] :
          ( c_24__type__4___24t(V0__x,V1__f)
         => ! [V2__g] :
              ( c_24__type__4___24t(V0__x,V2__g)
             => ( ! [V3__y] :
                    ( cA___24t(V3__y)
                   => ( cR___24a2(V3__y,V0__x)
                     => cr___24a3(V3__y,happ(V1__f,V3__y),happ(V2__g,V3__y)) ) )
               => cr___24a3(V0__x,cF___24a2(V0__x,V1__f),cF___24a2(V0__x,V2__g)) ) ) ) ) ).

fof('Rwf',axiom,
    cCoq_2eInit_2eWf_2ewell__founded___24a2(cA,cR) ).

fof('$adef_Coq.NArith.BinNatDef.N.land_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2eNArith_2eBinNatDef_2eN_2eland,V_24X1),V_24X2) = cCoq_2eNArith_2eBinNatDef_2eN_2eland___24a2(V_24X1,V_24X2) ).

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('$adef_Coq.micromega.ZMicromega.CutProof_$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('$adef_Coq.Arith.PeanoNat.Nat.eqf_$a2',axiom,
    ! [V_24X1,V_24X2] :
      ( p(happ(happ(cCoq_2eArith_2ePeanoNat_2eNat_2eeqf,V_24X1),V_24X2))
    <=> cCoq_2eArith_2ePeanoNat_2eNat_2eeqf___24a2(V_24X1,V_24X2) ) ).

fof('$adef_Coq.Init.Nat.mul_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eNat_2emul,V_24X1),V_24X2) = cCoq_2eInit_2eNat_2emul___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.Init.Decimal.D7_$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('$adef_Coq.Init.Peano.le_$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('$adef_$_case_Coq.Init.Datatypes.list$31552_$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_2431552,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = c_24__case__Coq_2eInit_2eDatatypes_2elist_2431552___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).

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('$adef_$_lam_31837_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] :
      ( p(happ(happ(happ(happ(c_24__lam__31837,V_24X1),V_24X2),V_24X3),V_24X4))
    <=> c_24__lam__31837___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).

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('$adef_Coq.Classes.RelationClasses.Equivalence_$a2',axiom,
    ! [V_24X1,V_24X2] :
      ( p(happ(happ(cCoq_2eClasses_2eRelationClasses_2eEquivalence,V_24X1),V_24X2))
    <=> cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(V_24X1,V_24X2) ) ).

fof('$adef_Coq.Arith.Even.even_$a1',axiom,
    ! [V_24X1] :
      ( p(happ(cCoq_2eArith_2eEven_2eeven,V_24X1))
    <=> cCoq_2eArith_2eEven_2eeven___24a1(V_24X1) ) ).

fof('$adef_Coq.micromega.Tauto.TT_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2emicromega_2eTauto_2eTT,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2emicromega_2eTauto_2eTT___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).

fof('$adef_Coq.PArith.BinPos.Pos.PeanoSucc_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2ePArith_2eBinPos_2ePos_2ePeanoSucc,V_24X1),V_24X2) = cCoq_2ePArith_2eBinPos_2ePos_2ePeanoSucc___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.setoid_ring.Ring_theory.SRopp_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2esetoid__ring_2eRing__theory_2eSRopp,V_24X1) = cCoq_2esetoid__ring_2eRing__theory_2eSRopp___24a1(V_24X1) ).

fof('$adef_Coq.Logic.Decidable.decidable_$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('$adef_Coq.Reals.Rdefinitions.IZR_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eReals_2eRdefinitions_2eIZR,V_24X1) = cCoq_2eReals_2eRdefinitions_2eIZR___24a1(V_24X1) ).

fof('$adef_$_lam_33034_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(c_24__lam__33034,V_24X1),V_24X2) = c_24__lam__33034___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.Relations.Relation_Operators.le_AsB_$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_2ele__AsB,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6))
    <=> cCoq_2eRelations_2eRelation__Operators_2ele__AsB___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ) ).

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('$adef_Coq.ZArith.BinInt.Z.eqf_$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('$adef_Coq.Relations.Relation_Definitions.preorder_$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('$adef_Coq.PArith.BinPos.Pos.lt_$a2',axiom,
    ! [V_24X1,V_24X2] :
      ( p(happ(happ(cCoq_2ePArith_2eBinPos_2ePos_2elt,V_24X1),V_24X2))
    <=> cCoq_2ePArith_2eBinPos_2ePos_2elt___24a2(V_24X1,V_24X2) ) ).

fof('$adef_Coq.NArith.BinNat.N.lt_$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('$adef_Coq.NArith.BinNatDef.N.testbit_$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('$adef_Coq.Vectors.VectorDef.cons_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2eVectors_2eVectorDef_2econs,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2eVectors_2eVectorDef_2econs___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).

fof('$adef_Coq.ZArith.BinIntDef.Z.of_N_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eZArith_2eBinIntDef_2eZ_2eof__N,V_24X1) = cCoq_2eZArith_2eBinIntDef_2eZ_2eof__N___24a1(V_24X1) ).

fof('$adef_Coq.PArith.BinPosDef.Pos.to_nat_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2ePArith_2eBinPosDef_2ePos_2eto__nat,V_24X1) = cCoq_2ePArith_2eBinPosDef_2ePos_2eto__nat___24a1(V_24X1) ).

fof('$adef_Coq.Init.Decimal.D0_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eInit_2eDecimal_2eD0,V_24X1) = cCoq_2eInit_2eDecimal_2eD0___24a1(V_24X1) ).

fof('$adef_$_lam_555_$a6',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(c_24__lam__555,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = c_24__lam__555___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).

fof('$adef_Coq.Relations.Relation_Operators.clos_refl_sym_trans_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] :
      ( p(happ(happ(happ(happ(cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans,V_24X1),V_24X2),V_24X3),V_24X4))
    <=> cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).

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('$adef_Coq.ZArith.BinIntDef.Z.modulo_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eBinIntDef_2eZ_2emodulo,V_24X1),V_24X2) = cCoq_2eZArith_2eBinIntDef_2eZ_2emodulo___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.Init.Datatypes.BoolSpec_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] :
      ( p(happ(happ(happ(cCoq_2eInit_2eDatatypes_2eBoolSpec,V_24X1),V_24X2),V_24X3))
    <=> cCoq_2eInit_2eDatatypes_2eBoolSpec___24a3(V_24X1,V_24X2,V_24X3) ) ).

fof('$adef_Coq.ZArith.BinIntDef.Z.abs_N_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eZArith_2eBinIntDef_2eZ_2eabs__N,V_24X1) = cCoq_2eZArith_2eBinIntDef_2eZ_2eabs__N___24a1(V_24X1) ).

fof('$adef_Coq.setoid_ring.Ring_theory.SRopp_$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('$adef_$_lam_31837_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__31837,V_24X1),V_24X2),V_24X3) = c_24__lam__31837___24a3(V_24X1,V_24X2,V_24X3) ).

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('$adef_Coq.micromega.VarMap.t_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2emicromega_2eVarMap_2et,V_24X1) = cCoq_2emicromega_2eVarMap_2et___24a1(V_24X1) ).

fof('$adef_Coq.Lists.List.nth_$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('$adef_$_case_Coq.Init.Datatypes.nat$17068_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__case__Coq_2eInit_2eDatatypes_2enat_2417068,V_24X1),V_24X2),V_24X3) = c_24__case__Coq_2eInit_2eDatatypes_2enat_2417068___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_Coq.Lists.SetoidList.transpose_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] :
      ( p(happ(happ(happ(happ(cCoq_2eLists_2eSetoidList_2etranspose,V_24X1),V_24X2),V_24X3),V_24X4))
    <=> cCoq_2eLists_2eSetoidList_2etranspose___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).

fof('$adef_Coq.PArith.BinPosDef.Pos.of_nat_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2ePArith_2eBinPosDef_2ePos_2eof__nat,V_24X1) = cCoq_2ePArith_2eBinPosDef_2ePos_2eof__nat___24a1(V_24X1) ).

fof('$adef_Coq.Init.Datatypes.nat_rect_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eInit_2eDatatypes_2enat__rect,V_24X1) = cCoq_2eInit_2eDatatypes_2enat__rect___24a1(V_24X1) ).

fof('$adef_Coq.Init.Decimal.nzhead_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eInit_2eDecimal_2enzhead,V_24X1) = cCoq_2eInit_2eDecimal_2enzhead___24a1(V_24X1) ).

fof('$adef_Coq.ZArith.Znumtheory.prime_$a1',axiom,
    ! [V_24X1] :
      ( p(happ(cCoq_2eZArith_2eZnumtheory_2eprime,V_24X1))
    <=> cCoq_2eZArith_2eZnumtheory_2eprime___24a1(V_24X1) ) ).

fof('$adef_Coq.Lists.List.Exists_$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('$adef_Coq.NArith.BinNatDef.N.succ_pos_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eNArith_2eBinNatDef_2eN_2esucc__pos,V_24X1) = cCoq_2eNArith_2eBinNatDef_2eN_2esucc__pos___24a1(V_24X1) ).

fof('$adef_$_lam_389_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__lam__389,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__lam__389___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).

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('$adef_Coq.Init.Datatypes.inr_$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('$adef_Coq.micromega.RingMicromega.eval_op2_$a5',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2emicromega_2eRingMicromega_2eeval__op2,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2emicromega_2eRingMicromega_2eeval__op2___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).

fof('$adef_Coq.Init.Wf.well_founded_induction_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eInit_2eWf_2ewell__founded__induction,V_24X1),V_24X2),V_24X3) = cCoq_2eInit_2eWf_2ewell__founded__induction___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('$adef_Coq.setoid_ring.Ring_theory.sring_eq_ext_$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('$adef_Coq.Reals.RIneq.mkposreal_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eReals_2eRIneq_2emkposreal,V_24X1) = cCoq_2eReals_2eRIneq_2emkposreal___24a1(V_24X1) ).

fof('$adef_Coq.setoid_ring.Ring_polynom.PEc_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2ePEc,V_24X1),V_24X2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEc___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.Vectors.Fin.F1_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eVectors_2eFin_2eF1,V_24X1) = cCoq_2eVectors_2eFin_2eF1___24a1(V_24X1) ).

fof('$adef_Coq.Vectors.VectorDef.Forall_$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('$adef_Coq.QArith.QArith_base.Qnum_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eQArith_2eQArith__base_2eQnum,V_24X1) = cCoq_2eQArith_2eQArith__base_2eQnum___24a1(V_24X1) ).

fof('$adef_F_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cF,V_24X1),V_24X2) = cF___24a2(V_24X1,V_24X2) ).

fof('$adef_$_lam_963_$a5',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(c_24__lam__963,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = c_24__lam__963___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('$adef_Coq.Init.Logic.ex2_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] :
      ( p(happ(happ(happ(cCoq_2eInit_2eLogic_2eex2,V_24X1),V_24X2),V_24X3))
    <=> cCoq_2eInit_2eLogic_2eex2___24a3(V_24X1,V_24X2,V_24X3) ) ).

fof('$adef_Coq.micromega.ZCoeff.gen_order_phi_Z_$a6',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(cCoq_2emicromega_2eZCoeff_2egen__order__phi__Z,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = cCoq_2emicromega_2eZCoeff_2egen__order__phi__Z___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).

fof('$adef_Coq.micromega.EnvRing.Pol_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2emicromega_2eEnvRing_2ePol,V_24X1) = cCoq_2emicromega_2eEnvRing_2ePol___24a1(V_24X1) ).

fof('$adef_Coq.micromega.Tauto.Cj_$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('$adef_$_lam_31934_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] :
      ( p(happ(happ(happ(happ(c_24__lam__31934,V_24X1),V_24X2),V_24X3),V_24X4))
    <=> c_24__lam__31934___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).

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('$adef_Coq.Structures.OrderedTypeEx.PositiveOrderedTypeBits.bits_lt_$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('$adef_Coq.micromega.RMicromega.CMult_$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('$adef_$_lam_33027_$a1',axiom,
    ! [V_24X1] : happ(c_24__lam__33027,V_24X1) = c_24__lam__33027___24a1(V_24X1) ).

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('$adef_Coq.setoid_ring.InitialRing.gen_phiZ_$a6',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eInitialRing_2egen__phiZ,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = cCoq_2esetoid__ring_2eInitialRing_2egen__phiZ___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).

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('$adef_Coq.PArith.BinPosDef.Pos.succ_$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('$adef_$_lam_33034_$a1',axiom,
    ! [V_24X1] : happ(c_24__lam__33034,V_24X1) = c_24__lam__33034___24a1(V_24X1) ).

fof('$adef_Coq.Sets.Relations_1.Symmetric_$a2',axiom,
    ! [V_24X1,V_24X2] :
      ( p(happ(happ(cCoq_2eSets_2eRelations__1_2eSymmetric,V_24X1),V_24X2))
    <=> cCoq_2eSets_2eRelations__1_2eSymmetric___24a2(V_24X1,V_24X2) ) ).

fof('$adef_Coq.Init.Decimal.Pos_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eInit_2eDecimal_2ePos,V_24X1) = cCoq_2eInit_2eDecimal_2ePos___24a1(V_24X1) ).

fof('$adef_Coq.setoid_ring.Ring_polynom.Pol_$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('$adef_Coq.micromega.Tauto.D_$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('$adef_Coq.Init.Wf.well_founded_induction_type_$a5',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2eInit_2eWf_2ewell__founded__induction__type,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2eInit_2eWf_2ewell__founded__induction__type___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).

fof('$adef_$_lam_2733_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] :
      ( p(happ(happ(happ(c_24__lam__2733,V_24X1),V_24X2),V_24X3))
    <=> c_24__lam__2733___24a3(V_24X1,V_24X2,V_24X3) ) ).

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('$adef_Coq.Init.Datatypes.prod_$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('$adef_$_lam_2486_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] :
      ( p(happ(happ(happ(happ(c_24__lam__2486,V_24X1),V_24X2),V_24X3),V_24X4))
    <=> c_24__lam__2486___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).

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('$adef_Coq.Reals.Rdefinitions.IPR_$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('$adef_Coq.Init.Specif.Exc_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eInit_2eSpecif_2eExc,V_24X1) = cCoq_2eInit_2eSpecif_2eExc___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('$adef_$_lam_1023_$a9',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9] : happ(happ(happ(happ(happ(happ(happ(happ(happ(c_24__lam__1023,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9) = c_24__lam__1023___24a9(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9) ).

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('$adef_Coq.Vectors.VectorDef.Forall2_$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('$adef_Coq.setoid_ring.Field_theory.FEdiv_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2esetoid__ring_2eField__theory_2eFEdiv,V_24X1),V_24X2),V_24X3) = cCoq_2esetoid__ring_2eField__theory_2eFEdiv___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_Coq.ZArith.BinIntDef.Z.compare_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare,V_24X1),V_24X2) = cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.Init.Nat.compare_$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('$adef_Coq.setoid_ring.Ring_theory.ring_theory_$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('$adef_Coq.Arith.Wf_nat.inv_lt_rel_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2eArith_2eWf__nat_2einv__lt__rel,V_24X1),V_24X2) = cCoq_2eArith_2eWf__nat_2einv__lt__rel___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('$adef_Coq.QArith.QArith_base.Qden_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eQArith_2eQArith__base_2eQden,V_24X1) = cCoq_2eQArith_2eQArith__base_2eQden___24a1(V_24X1) ).

fof('$adef_$_lam_963_$a6',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(c_24__lam__963,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = c_24__lam__963___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).

fof('$adef_Coq.setoid_ring.InitialRing.gen_phiPOS_$a5',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).

fof('$adef_Coq.Init.Peano.IsSucc_$a1',axiom,
    ! [V_24X1] :
      ( p(happ(cCoq_2eInit_2ePeano_2eIsSucc,V_24X1))
    <=> cCoq_2eInit_2ePeano_2eIsSucc___24a1(V_24X1) ) ).

fof('$adef_Coq.Init.Datatypes.app_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eInit_2eDatatypes_2eapp,V_24X1),V_24X2),V_24X3) = cCoq_2eInit_2eDatatypes_2eapp___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_Coq.NArith.BinNatDef.N.div2_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eNArith_2eBinNatDef_2eN_2ediv2,V_24X1) = cCoq_2eNArith_2eBinNatDef_2eN_2ediv2___24a1(V_24X1) ).

fof('$adef_Coq.Init.Datatypes.eq_true_$a1',axiom,
    ! [V_24X1] :
      ( p(happ(cCoq_2eInit_2eDatatypes_2eeq__true,V_24X1))
    <=> cCoq_2eInit_2eDatatypes_2eeq__true___24a1(V_24X1) ) ).

fof('$adef_Coq.setoid_ring.InitialRing.gen_phiZ_$a7',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7] : happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eInitialRing_2egen__phiZ,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7) = cCoq_2esetoid__ring_2eInitialRing_2egen__phiZ___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7) ).

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('$adef_Coq.micromega.VarMap.Elt_$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('$adef_Coq.Init.Specif.sig_$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('$adef_$_case_Coq.Init.Datatypes.list$31639_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__case__Coq_2eInit_2eDatatypes_2elist_2431639,V_24X1),V_24X2),V_24X3) = c_24__case__Coq_2eInit_2eDatatypes_2elist_2431639___24a3(V_24X1,V_24X2,V_24X3) ).

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('$adef_Coq.ZArith.BinIntDef.Z.leb_$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('$adef_$_case_Coq.Init.Datatypes.prod$10432_$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_2410432,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_2410432___24a9(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9) ) ).

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('$adef_Coq.NArith.BinNat.N.peano_rect_$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('$adef_Coq.ZArith.BinIntDef.Z.mul_$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('$adef_Coq.micromega.ZMicromega.EnumProof_$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('$adef_$_lam_33136_$a1',axiom,
    ! [V_24X1] : happ(c_24__lam__33136,V_24X1) = c_24__lam__33136___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('$adef_Coq.Relations.Relation_Operators.symprod_$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('$adef_Coq.micromega.RMicromega.CZ_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2emicromega_2eRMicromega_2eCZ,V_24X1) = cCoq_2emicromega_2eRMicromega_2eCZ___24a1(V_24X1) ).

fof('$adef_$_case_Coq.Numbers.BinNums.positive$29653_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(c_24__case__Coq_2eNumbers_2eBinNums_2epositive_2429653,V_24X1),V_24X2) = c_24__case__Coq_2eNumbers_2eBinNums_2epositive_2429653___24a2(V_24X1,V_24X2) ).

fof('$adef_P_$a1',axiom,
    ! [V_24X1] : happ(cP,V_24X1) = cP___24a1(V_24X1) ).

fof('$adef_Coq.Lists.SetoidList.compat_op_$a5',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] :
      ( p(happ(happ(happ(happ(happ(cCoq_2eLists_2eSetoidList_2ecompat__op,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5))
    <=> cCoq_2eLists_2eSetoidList_2ecompat__op___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ) ).

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('$adef_Coq.Init.Decimal.D4_$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('$adef_Coq.setoid_ring.Field_theory.linear_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2esetoid__ring_2eField__theory_2elinear,V_24X1) = cCoq_2esetoid__ring_2eField__theory_2elinear___24a1(V_24X1) ).

fof('$adef_Coq.micromega.RingMicromega.Build_Formula_$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('$adef_Coq.Init.Nat.gcd_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eNat_2egcd,V_24X1),V_24X2) = cCoq_2eInit_2eNat_2egcd___24a2(V_24X1,V_24X2) ).

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('$adef_Coq.micromega.ZMicromega.isZ0_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2emicromega_2eZMicromega_2eisZ0,V_24X1) = cCoq_2emicromega_2eZMicromega_2eisZ0___24a1(V_24X1) ).

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('$adef_Coq.Init.Specif.sumbool_$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('$adef_Coq.Arith.PeanoNat.Nat.recursion_$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('$adef_Coq.setoid_ring.Field_theory.mk_rsplit_$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('$adef_$_fix_29669_v_CANONICAL_0_$a1',axiom,
    ! [V_24X1] : happ(c_24__fix__29669__v__CANONICAL__0,V_24X1) = c_24__fix__29669__v__CANONICAL__0___24a1(V_24X1) ).

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('$adef_$_lam_33136_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(c_24__lam__33136,V_24X1),V_24X2) = c_24__lam__33136___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('$adef_Coq.Numbers.BinNums.Zneg_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eNumbers_2eBinNums_2eZneg,V_24X1) = cCoq_2eNumbers_2eBinNums_2eZneg___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('$adef_Coq.micromega.RingMicromega.ge_bool_$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('$adef_Coq.Lists.SetoidList.transpose_restr2_$a5',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] :
      ( p(happ(happ(happ(happ(happ(cCoq_2eLists_2eSetoidList_2etranspose__restr2,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5))
    <=> cCoq_2eLists_2eSetoidList_2etranspose__restr2___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ) ).

fof('$adef_$_lam_2486_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__2486,V_24X1),V_24X2),V_24X3) = c_24__lam__2486___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_Coq.ZArith.Zeven.Zeven_$a1',axiom,
    ! [V_24X1] :
      ( p(happ(cCoq_2eZArith_2eZeven_2eZeven,V_24X1))
    <=> cCoq_2eZArith_2eZeven_2eZeven___24a1(V_24X1) ) ).

fof('$adef_Coq.Init.Wf.well_founded_induction_type_2_$a7',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7] : happ(happ(happ(happ(happ(happ(happ(cCoq_2eInit_2eWf_2ewell__founded__induction__type__2,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7) = cCoq_2eInit_2eWf_2ewell__founded__induction__type__2___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7) ).

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('$adef_Coq.Vectors.VectorDef.Exists_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] :
      ( p(happ(happ(happ(happ(cCoq_2eVectors_2eVectorDef_2eExists,V_24X1),V_24X2),V_24X3),V_24X4))
    <=> cCoq_2eVectors_2eVectorDef_2eExists___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).

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('$adef_Coq.Sets.Relations_1.Transitive_$a2',axiom,
    ! [V_24X1,V_24X2] :
      ( p(happ(happ(cCoq_2eSets_2eRelations__1_2eTransitive,V_24X1),V_24X2))
    <=> cCoq_2eSets_2eRelations__1_2eTransitive___24a2(V_24X1,V_24X2) ) ).

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('$adef_$_prop_29563_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__prop__29563,V_24X1),V_24X2),V_24X3) = c_24__prop__29563___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_$_prop_29558_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__prop__29558,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__prop__29558___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).

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('$adef_Coq.setoid_ring.Ring_polynom.PX_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2ePX,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2esetoid__ring_2eRing__polynom_2ePX___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).

fof('$adef_Coq.Init.Nat.max_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eNat_2emax,V_24X1),V_24X2) = cCoq_2eInit_2eNat_2emax___24a2(V_24X1,V_24X2) ).

fof('$adef_$_lam_2738_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] :
      ( p(happ(happ(happ(c_24__lam__2738,V_24X1),V_24X2),V_24X3))
    <=> c_24__lam__2738___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_32918_$a1',axiom,
    ! [V_24X1] : happ(c_24__lam__32918,V_24X1) = c_24__lam__32918___24a1(V_24X1) ).

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('$adef_Coq.Arith.Between.between_$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('$adef_r_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] :
      ( p(happ(happ(happ(cr,V_24X1),V_24X2),V_24X3))
    <=> cr___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('$adef_$_lam_31950_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] :
      ( p(happ(happ(happ(happ(c_24__lam__31950,V_24X1),V_24X2),V_24X3),V_24X4))
    <=> c_24__lam__31950___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).

fof('$adef_Coq.Init.Wf.Fix_F_2_$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_2eInit_2eWf_2eFix__F__2,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8) = cCoq_2eInit_2eWf_2eFix__F__2___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8) ).

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('$adef_Coq.PArith.BinPosDef.Pos.sub_mask_$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('$adef_Coq.setoid_ring.Ring_polynom.Peq_$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('$adef_$_let_var_6_p_27101_27103_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__let__var__6__p__27101__27103,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__let__var__6__p__27101__27103___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_31926_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] :
      ( p(happ(happ(happ(happ(c_24__lam__31926,V_24X1),V_24X2),V_24X3),V_24X4))
    <=> c_24__lam__31926___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).

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('$adef_Coq.setoid_ring.Ring_polynom.PEadd_$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('$adef_$_lam_31950_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(c_24__lam__31950,V_24X1),V_24X2) = c_24__lam__31950___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('$adef_Coq.Arith.Wf_nat.gtof_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2eArith_2eWf__nat_2egtof,V_24X1),V_24X2) = cCoq_2eArith_2eWf__nat_2egtof___24a2(V_24X1,V_24X2) ).

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('$adef_Coq.micromega.RingMicromega.cneqb_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2emicromega_2eRingMicromega_2ecneqb,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2emicromega_2eRingMicromega_2ecneqb___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).

fof('$adef_Coq.micromega.EnvRing.PEopp_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2emicromega_2eEnvRing_2ePEopp,V_24X1),V_24X2) = cCoq_2emicromega_2eEnvRing_2ePEopp___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.Init.Specif.exist2_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2eInit_2eSpecif_2eexist2,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2eInit_2eSpecif_2eexist2___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).

fof('$adef_Coq.Sets.Relations_1.Equivalence_$a2',axiom,
    ! [V_24X1,V_24X2] :
      ( p(happ(happ(cCoq_2eSets_2eRelations__1_2eEquivalence,V_24X1),V_24X2))
    <=> cCoq_2eSets_2eRelations__1_2eEquivalence___24a2(V_24X1,V_24X2) ) ).

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('$adef_Coq.micromega.RingMicromega.SORaddon_$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('$adef_Coq.Strings.String.String_$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('$adef_Coq.Init.Nat.square_$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('$adef_Coq.micromega.RingMicromega.PsatzMulE_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2emicromega_2eRingMicromega_2ePsatzMulE,V_24X1),V_24X2),V_24X3) = cCoq_2emicromega_2eRingMicromega_2ePsatzMulE___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_Coq.Classes.Morphisms.respectful_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2eClasses_2eMorphisms_2erespectful,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).

fof('$adef_Coq.micromega.RingMicromega.PolEnv_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2emicromega_2eRingMicromega_2ePolEnv,V_24X1) = cCoq_2emicromega_2eRingMicromega_2ePolEnv___24a1(V_24X1) ).

fof('$adef_$_lam_31829_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__31829,V_24X1),V_24X2),V_24X3) = c_24__lam__31829___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('$adef_Coq.Init.Wf.Fix_$a5',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2eInit_2eWf_2eFix,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2eInit_2eWf_2eFix___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).

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('$adef_Coq.FSets.FSetPositive.PositiveSet.In_$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('$adef_Coq.Sets.Relations_1.Preorder_$a2',axiom,
    ! [V_24X1,V_24X2] :
      ( p(happ(happ(cCoq_2eSets_2eRelations__1_2ePreorder,V_24X1),V_24X2))
    <=> cCoq_2eSets_2eRelations__1_2ePreorder___24a2(V_24X1,V_24X2) ) ).

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('$adef_Coq.Init.Nat.leb_$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('$adef_Coq.Init.Datatypes.id_$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('$adef_$_lam_3212_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] :
      ( p(happ(happ(happ(c_24__lam__3212,V_24X1),V_24X2),V_24X3))
    <=> c_24__lam__3212___24a3(V_24X1,V_24X2,V_24X3) ) ).

fof('$adef_Coq.NArith.BinNatDef.N.succ_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eNArith_2eBinNatDef_2eN_2esucc,V_24X1) = cCoq_2eNArith_2eBinNatDef_2eN_2esucc___24a1(V_24X1) ).

fof('$adef_Coq.Structures.OrderedType.GT_$a5',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2eStructures_2eOrderedType_2eGT,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2eStructures_2eOrderedType_2eGT___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).

fof('$adef_Coq.Relations.Relation_Definitions.transitive_$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('$adef_Coq.Reals.Rdefinitions.Rle_$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('$adef_Hammer.Tactics.Tactics.rdone_$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('$adef_Coq.Relations.Relation_Definitions.order_$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('$adef_Coq.micromega.Tauto.TFormula_$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('$adef_Coq.setoid_ring.Ring_theory.id_phi_N_$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('$adef_Coq.micromega.EnvRing.zmon_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2emicromega_2eEnvRing_2ezmon,V_24X1),V_24X2) = cCoq_2emicromega_2eEnvRing_2ezmon___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.Vectors.Fin.FS_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2eVectors_2eFin_2eFS,V_24X1),V_24X2) = cCoq_2eVectors_2eFin_2eFS___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.Bool.Zerob.zerob_$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('$adef_$_prop_29560_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__prop__29560,V_24X1),V_24X2),V_24X3) = c_24__prop__29560___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_Coq.Arith.Between.in_int_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] :
      ( p(happ(happ(happ(cCoq_2eArith_2eBetween_2ein__int,V_24X1),V_24X2),V_24X3))
    <=> cCoq_2eArith_2eBetween_2ein__int___24a3(V_24X1,V_24X2,V_24X3) ) ).

fof('$adef_Coq.micromega.EnvRing.PExpr_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2emicromega_2eEnvRing_2ePExpr,V_24X1) = cCoq_2emicromega_2eEnvRing_2ePExpr___24a1(V_24X1) ).

fof('$adef_Coq.Init.Nat.eqb_$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('$adef_$_lam_31853_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__31853,V_24X1),V_24X2),V_24X3) = c_24__lam__31853___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_$_lam_31853_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] :
      ( p(happ(happ(happ(happ(c_24__lam__31853,V_24X1),V_24X2),V_24X3),V_24X4))
    <=> c_24__lam__31853___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).

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('$adef_Coq.Sorting.Sorted.HdRel_$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('$adef_Coq.Init.Peano.ge_$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('$adef_Hammer.Tactics.Reconstr.rdone_$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('$adef_Coq.Relations.Relation_Operators.clos_refl_trans_1n_$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('$adef_Coq.NArith.BinNat.N.divide_$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('$adef_$_case_Coq.Numbers.BinNums.Z$17085_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__case__Coq_2eNumbers_2eBinNums_2eZ_2417085,V_24X1),V_24X2),V_24X3) = c_24__case__Coq_2eNumbers_2eBinNums_2eZ_2417085___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_Coq.Vectors.VectorDef.In_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] :
      ( p(happ(happ(happ(happ(cCoq_2eVectors_2eVectorDef_2eIn,V_24X1),V_24X2),V_24X3),V_24X4))
    <=> cCoq_2eVectors_2eVectorDef_2eIn___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).

fof('$adef_$_lam_2687_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] :
      ( p(happ(happ(happ(c_24__lam__2687,V_24X1),V_24X2),V_24X3))
    <=> c_24__lam__2687___24a3(V_24X1,V_24X2,V_24X3) ) ).

fof('$adef_Coq.Lists.SetoidList.transpose2_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] :
      ( p(happ(happ(happ(happ(cCoq_2eLists_2eSetoidList_2etranspose2,V_24X1),V_24X2),V_24X3),V_24X4))
    <=> cCoq_2eLists_2eSetoidList_2etranspose2___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).

fof('$adef_Coq.Lists.SetoidList.NoDupA_$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('$adef_Coq.PArith.BinPosDef.Pos.testbit_nat_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2ePArith_2eBinPosDef_2ePos_2etestbit__nat,V_24X1) = cCoq_2ePArith_2eBinPosDef_2ePos_2etestbit__nat___24a1(V_24X1) ).

fof('$adef_$_lam_3212_$a1',axiom,
    ! [V_24X1] : happ(c_24__lam__3212,V_24X1) = c_24__lam__3212___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('$adef_Coq.micromega.RingMicromega.eval_op1_$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('$adef_Coq.Logic.EqdepFacts.Eq_dep_eq_on_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] :
      ( p(happ(happ(happ(happ(cCoq_2eLogic_2eEqdepFacts_2eEq__dep__eq__on,V_24X1),V_24X2),V_24X3),V_24X4))
    <=> cCoq_2eLogic_2eEqdepFacts_2eEq__dep__eq__on___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).

fof('$adef_Coq.Init.Decimal.D9_$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('$adef_Coq.FSets.FSetPositive.PositiveSet.Subset_$a2',axiom,
    ! [V_24X1,V_24X2] :
      ( p(happ(happ(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eSubset,V_24X1),V_24X2))
    <=> cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eSubset___24a2(V_24X1,V_24X2) ) ).

fof('$adef_Coq.setoid_ring.Ring.bool_eq_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2esetoid__ring_2eRing_2ebool__eq,V_24X1),V_24X2) = cCoq_2esetoid__ring_2eRing_2ebool__eq___24a2(V_24X1,V_24X2) ).

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('$adef_R_$a2',axiom,
    ! [V_24X1,V_24X2] :
      ( p(happ(happ(cR,V_24X1),V_24X2))
    <=> cR___24a2(V_24X1,V_24X2) ) ).

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('$adef_Coq.Arith.EqNat.eq_nat_$a2',axiom,
    ! [V_24X1,V_24X2] :
      ( p(happ(happ(cCoq_2eArith_2eEqNat_2eeq__nat,V_24X1),V_24X2))
    <=> cCoq_2eArith_2eEqNat_2eeq__nat___24a2(V_24X1,V_24X2) ) ).

fof('$adef_Coq.ZArith.BinInt.Z.b2z_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eZArith_2eBinInt_2eZ_2eb2z,V_24X1) = cCoq_2eZArith_2eBinInt_2eZ_2eb2z___24a1(V_24X1) ).

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('$adef_Coq.Lists.List.Forall2_$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('$adef_Coq.micromega.Tauto.A_$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('$adef_Coq.micromega.ZMicromega.Zdivide_pol_$a2',axiom,
    ! [V_24X1,V_24X2] :
      ( p(happ(happ(cCoq_2emicromega_2eZMicromega_2eZdivide__pol,V_24X1),V_24X2))
    <=> cCoq_2emicromega_2eZMicromega_2eZdivide__pol___24a2(V_24X1,V_24X2) ) ).

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('$adef_Coq.Relations.Relation_Definitions.reflexive_$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('$adef_$_lam_3207_$a1',axiom,
    ! [V_24X1] : happ(c_24__lam__3207,V_24X1) = c_24__lam__3207___24a1(V_24X1) ).

fof('$adef_$_lam_728_$a6',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(c_24__lam__728,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = c_24__lam__728___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).

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('$adef_Coq.Logic.EqdepFacts.eq_dep1_$a6',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] :
      ( p(happ(happ(happ(happ(happ(happ(cCoq_2eLogic_2eEqdepFacts_2eeq__dep1,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6))
    <=> cCoq_2eLogic_2eEqdepFacts_2eeq__dep1___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ) ).

fof('$adef_Coq.setoid_ring.Field_theory.almost_field_theory_$a10',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10] :
      ( p(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eField__theory_2ealmost__field__theory,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9),V_24X10))
    <=> cCoq_2esetoid__ring_2eField__theory_2ealmost__field__theory___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10) ) ).

fof('$adef_Coq.Arith.Wf_nat.ltof_$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('$adef_$_lam_728_$a5',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(c_24__lam__728,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = c_24__lam__728___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).

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('$adef_Coq.NArith.BinNatDef.N.max_$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('$adef_$_lam_2692_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] :
      ( p(happ(happ(happ(c_24__lam__2692,V_24X1),V_24X2),V_24X3))
    <=> c_24__lam__2692___24a3(V_24X1,V_24X2,V_24X3) ) ).

fof('$adef_Coq.Init.Wf.Acc_inv_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2eInit_2eWf_2eAcc__inv,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2eInit_2eWf_2eAcc__inv___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).

fof('$adef_Coq.Sets.Relations_1.Reflexive_$a2',axiom,
    ! [V_24X1,V_24X2] :
      ( p(happ(happ(cCoq_2eSets_2eRelations__1_2eReflexive,V_24X1),V_24X2))
    <=> cCoq_2eSets_2eRelations__1_2eReflexive___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('$adef_Coq.Reals.Rdefinitions.Rge_$a2',axiom,
    ! [V_24X1,V_24X2] :
      ( p(happ(happ(cCoq_2eReals_2eRdefinitions_2eRge,V_24X1),V_24X2))
    <=> cCoq_2eReals_2eRdefinitions_2eRge___24a2(V_24X1,V_24X2) ) ).

fof('$adef_Coq.PArith.BinPosDef.Pos.mul_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2ePArith_2eBinPosDef_2ePos_2emul,V_24X1),V_24X2) = cCoq_2ePArith_2eBinPosDef_2ePos_2emul___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.Init.Datatypes.CompGtT_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eInit_2eDatatypes_2eCompGtT,V_24X1),V_24X2),V_24X3) = cCoq_2eInit_2eDatatypes_2eCompGtT___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_$_prop_29561_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__prop__29561,V_24X1),V_24X2),V_24X3) = c_24__prop__29561___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_Coq.PArith.BinPosDef.Pos.testbit_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2ePArith_2eBinPosDef_2ePos_2etestbit,V_24X1),V_24X2) = cCoq_2ePArith_2eBinPosDef_2ePos_2etestbit___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.Reals.Rdefinitions.Rmult_$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('$adef_Coq.ZArith.Znumtheory.rel_prime_$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('$adef_$_lam_31942_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] :
      ( p(happ(happ(happ(happ(c_24__lam__31942,V_24X1),V_24X2),V_24X3),V_24X4))
    <=> c_24__lam__31942___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).

fof('$adef_Coq.ZArith.Znumtheory.Bezout_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] :
      ( p(happ(happ(happ(cCoq_2eZArith_2eZnumtheory_2eBezout,V_24X1),V_24X2),V_24X3))
    <=> cCoq_2eZArith_2eZnumtheory_2eBezout___24a3(V_24X1,V_24X2,V_24X3) ) ).

fof('$adef_Coq.micromega.Tauto.GFormula_$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('$adef_Coq.setoid_ring.Ring_theory.Morphism_$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('$adef_Coq.Init.Specif.exist_$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] : happ(happ(cCoq_2eZArith_2eBinInt_2eZ_2ele,V_24X1),V_24X2) = cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V_24X1,V_24X2) ).

fof('$adef_$_lam_555_$a5',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(c_24__lam__555,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = c_24__lam__555___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).

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('$adef_Coq.ZArith.Zcomplements.floor_pos_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eZArith_2eZcomplements_2efloor__pos,V_24X1) = cCoq_2eZArith_2eZcomplements_2efloor__pos___24a1(V_24X1) ).

fof('$adef_$_lam_31942_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(c_24__lam__31942,V_24X1),V_24X2) = c_24__lam__31942___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('$adef_Coq.Sets.Relations_1.Antisymmetric_$a2',axiom,
    ! [V_24X1,V_24X2] :
      ( p(happ(happ(cCoq_2eSets_2eRelations__1_2eAntisymmetric,V_24X1),V_24X2))
    <=> cCoq_2eSets_2eRelations__1_2eAntisymmetric___24a2(V_24X1,V_24X2) ) ).

fof('$adef_Coq.PArith.BinPosDef.Pos.compare_cont_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare__cont,V_24X1) = cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare__cont___24a1(V_24X1) ).

fof('$adef_Coq.ZArith.Zeven.Zodd_$a1',axiom,
    ! [V_24X1] :
      ( p(happ(cCoq_2eZArith_2eZeven_2eZodd,V_24X1))
    <=> cCoq_2eZArith_2eZeven_2eZodd___24a1(V_24X1) ) ).

fof('$adef_Coq.Init.Specif.inleft_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eInit_2eSpecif_2einleft,V_24X1),V_24X2),V_24X3) = cCoq_2eInit_2eSpecif_2einleft___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_Coq.micromega.EnvRing.Pinj_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2emicromega_2eEnvRing_2ePinj,V_24X1),V_24X2),V_24X3) = cCoq_2emicromega_2eEnvRing_2ePinj___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_Coq.Structures.GenericMinMax.gmax_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2eStructures_2eGenericMinMax_2egmax,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2eStructures_2eGenericMinMax_2egmax___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).

fof('$adef_Coq.Init.Wf.well_founded_$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('$adef_Coq.Arith.Wf_nat.gtof_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] :
      ( p(happ(happ(happ(happ(cCoq_2eArith_2eWf__nat_2egtof,V_24X1),V_24X2),V_24X3),V_24X4))
    <=> cCoq_2eArith_2eWf__nat_2egtof___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).

fof('$adef_$_lam_2738_$a1',axiom,
    ! [V_24X1] : happ(c_24__lam__2738,V_24X1) = c_24__lam__2738___24a1(V_24X1) ).

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('$adef_Coq.Init.Datatypes.cons_$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('$adef_$_lam_389_$a6',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(c_24__lam__389,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = c_24__lam__389___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).

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('$adef_Coq.Init.Decimal.D1_$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('$adef_Coq.ZArith.BinIntDef.Z.of_nat_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat,V_24X1) = cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat___24a1(V_24X1) ).

fof('$adef_Coq.Init.Nat.div2_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eInit_2eNat_2ediv2,V_24X1) = cCoq_2eInit_2eNat_2ediv2___24a1(V_24X1) ).

fof('$adef_Coq.Init.Datatypes.pair_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2eInit_2eDatatypes_2epair,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2eInit_2eDatatypes_2epair___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).

fof('$adef_$_lam_2501_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] :
      ( p(happ(happ(happ(happ(c_24__lam__2501,V_24X1),V_24X2),V_24X3),V_24X4))
    <=> c_24__lam__2501___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('$adef_Coq.Init.Datatypes.negb_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eInit_2eDatatypes_2enegb,V_24X1) = cCoq_2eInit_2eDatatypes_2enegb___24a1(V_24X1) ).

fof('$adef_Coq.micromega.RMicromega.COpp_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2emicromega_2eRMicromega_2eCOpp,V_24X1) = cCoq_2emicromega_2eRMicromega_2eCOpp___24a1(V_24X1) ).

fof('$adef_Coq.Init.Nat.testbit_$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('$adef_$_lam_2501_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__2501,V_24X1),V_24X2),V_24X3) = c_24__lam__2501___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_Coq.PArith.BinPosDef.Pos.IsPos_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2ePArith_2eBinPosDef_2ePos_2eIsPos,V_24X1) = cCoq_2ePArith_2eBinPosDef_2ePos_2eIsPos___24a1(V_24X1) ).

fof('$adef_Coq.PArith.BinPosDef.Pos.div2_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2ePArith_2eBinPosDef_2ePos_2ediv2,V_24X1) = cCoq_2ePArith_2eBinPosDef_2ePos_2ediv2___24a1(V_24X1) ).

fof('$adef_$_lam_31845_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] :
      ( p(happ(happ(happ(happ(c_24__lam__31845,V_24X1),V_24X2),V_24X3),V_24X4))
    <=> c_24__lam__31845___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).

fof('$adef_Coq.Reals.Rdefinitions.Ropp_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eReals_2eRdefinitions_2eRopp,V_24X1) = cCoq_2eReals_2eRdefinitions_2eRopp___24a1(V_24X1) ).

fof('$adef_Coq.Init.Nat.sqrt_iter_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2eInit_2eNat_2esqrt__iter,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2eInit_2eNat_2esqrt__iter___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).

fof('$adef_$_lam_32940_$a1',axiom,
    ! [V_24X1] : happ(c_24__lam__32940,V_24X1) = c_24__lam__32940___24a1(V_24X1) ).

fof('$adef_Coq.PArith.BinPosDef.Pos.max_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2ePArith_2eBinPosDef_2ePos_2emax,V_24X1),V_24X2) = cCoq_2ePArith_2eBinPosDef_2ePos_2emax___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.Vectors.VectorDef.Exists2_$a6',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] :
      ( p(happ(happ(happ(happ(happ(happ(cCoq_2eVectors_2eVectorDef_2eExists2,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6))
    <=> cCoq_2eVectors_2eVectorDef_2eExists2___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ) ).

fof('$adef_$_prop_29578_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(c_24__prop__29578,V_24X1),V_24X2) = c_24__prop__29578___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('$adef_Coq.Init.Datatypes.Some_$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('$adef_$_lam_3207_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] :
      ( p(happ(happ(happ(c_24__lam__3207,V_24X1),V_24X2),V_24X3))
    <=> c_24__lam__3207___24a3(V_24X1,V_24X2,V_24X3) ) ).

fof('$adef_$_prop_29562_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__prop__29562,V_24X1),V_24X2),V_24X3) = c_24__prop__29562___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_Coq.Structures.OrderedType.EQ_$a5',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2eStructures_2eOrderedType_2eEQ,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2eStructures_2eOrderedType_2eEQ___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).

fof('$adef_$_lam_2733_$a1',axiom,
    ! [V_24X1] : happ(c_24__lam__2733,V_24X1) = c_24__lam__2733___24a1(V_24X1) ).

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('$adef_$_lam_2687_$a1',axiom,
    ! [V_24X1] : happ(c_24__lam__2687,V_24X1) = c_24__lam__2687___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('$adef_$_lam_2692_$a1',axiom,
    ! [V_24X1] : happ(c_24__lam__2692,V_24X1) = c_24__lam__2692___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('$adef_Coq.NArith.BinNatDef.N.double_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eNArith_2eBinNatDef_2eN_2edouble,V_24X1) = cCoq_2eNArith_2eBinNatDef_2eN_2edouble___24a1(V_24X1) ).

fof('$adef_Coq.Init.Logic_Type.notT_$a1',axiom,
    ! [V_24X1] :
      ( p(happ(cCoq_2eInit_2eLogic__Type_2enotT,V_24X1))
    <=> cCoq_2eInit_2eLogic__Type_2enotT___24a1(V_24X1) ) ).

fof('$adef_Coq.Init.Datatypes.list_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eInit_2eDatatypes_2elist,V_24X1) = cCoq_2eInit_2eDatatypes_2elist___24a1(V_24X1) ).

fof('$adef_Coq.Init.Nat.add_$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('$adef_$_lam_32918_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(c_24__lam__32918,V_24X1),V_24X2) = c_24__lam__32918___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.Init.Specif.sigT2_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eInit_2eSpecif_2esigT2,V_24X1),V_24X2),V_24X3) = cCoq_2eInit_2eSpecif_2esigT2___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_Coq.Init.Nat.sub_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eNat_2esub,V_24X1),V_24X2) = cCoq_2eInit_2eNat_2esub___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.Structures.OrderedType.Compare_$a5',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2eStructures_2eOrderedType_2eCompare,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2eStructures_2eOrderedType_2eCompare___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).

fof('$adef_Coq.PArith.BinPos.Pos.SubMaskSpec_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] :
      ( p(happ(happ(happ(cCoq_2ePArith_2eBinPos_2ePos_2eSubMaskSpec,V_24X1),V_24X2),V_24X3))
    <=> cCoq_2ePArith_2eBinPos_2ePos_2eSubMaskSpec___24a3(V_24X1,V_24X2,V_24X3) ) ).

fof('$adef_Coq.micromega.Tauto.clause_$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('$adef_Coq.setoid_ring.Field_theory.FEc_$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('$adef_Coq.Bool.Bool.ReflectF_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eBool_2eBool_2eReflectF,V_24X1) = cCoq_2eBool_2eBool_2eReflectF___24a1(V_24X1) ).

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('$adef_Coq.micromega.ZMicromega.Vars.Facts.MP.Dec.FSetDecideAuxiliary.FSet_Prop_$a1',axiom,
    ! [V_24X1] :
      ( p(happ(cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__Prop,V_24X1))
    <=> cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__Prop___24a1(V_24X1) ) ).

fof('$adef_Coq.Reals.Rfunctions.ZintNull_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eReals_2eRfunctions_2eZintNull,V_24X1) = cCoq_2eReals_2eRfunctions_2eZintNull___24a1(V_24X1) ).

fof('$adef_Coq.setoid_ring.Field_theory.FEI_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2esetoid__ring_2eField__theory_2eFEI,V_24X1) = cCoq_2esetoid__ring_2eField__theory_2eFEI___24a1(V_24X1) ).

fof('$adef_Coq.micromega.EnvRing.PEX_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2emicromega_2eEnvRing_2ePEX,V_24X1),V_24X2) = cCoq_2emicromega_2eEnvRing_2ePEX___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.ZArith.BinIntDef.Z.pos_sub_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eBinIntDef_2eZ_2epos__sub,V_24X1),V_24X2) = cCoq_2eZArith_2eBinIntDef_2eZ_2epos__sub___24a2(V_24X1,V_24X2) ).

fof('$adef_$_lam_31829_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] :
      ( p(happ(happ(happ(happ(c_24__lam__31829,V_24X1),V_24X2),V_24X3),V_24X4))
    <=> c_24__lam__31829___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).

fof('$adef_Coq.Bool.Bool.ReflectT_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eBool_2eBool_2eReflectT,V_24X1) = cCoq_2eBool_2eBool_2eReflectT___24a1(V_24X1) ).

fof('$adef_Coq.ZArith.Znumtheory.Euclid_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eZnumtheory_2eEuclid,V_24X1),V_24X2) = cCoq_2eZArith_2eZnumtheory_2eEuclid___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.Init.Specif.right_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eSpecif_2eright,V_24X1),V_24X2) = cCoq_2eInit_2eSpecif_2eright___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.setoid_ring.Ring_theory.power_theory_$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('$adef_$_lam_31845_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__31845,V_24X1),V_24X2),V_24X3) = c_24__lam__31845___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('$adef_Coq.setoid_ring.Ring_polynom.Pinj_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2ePinj,V_24X1),V_24X2),V_24X3) = cCoq_2esetoid__ring_2eRing__polynom_2ePinj___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_Coq.Sorting.Sorted.StronglySorted_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] :
      ( p(happ(happ(happ(cCoq_2eSorting_2eSorted_2eStronglySorted,V_24X1),V_24X2),V_24X3))
    <=> cCoq_2eSorting_2eSorted_2eStronglySorted___24a3(V_24X1,V_24X2,V_24X3) ) ).

fof('$adef_Coq.NArith.BinNatDef.N.lxor_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2eNArith_2eBinNatDef_2eN_2elxor,V_24X1),V_24X2) = cCoq_2eNArith_2eBinNatDef_2eN_2elxor___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.ZArith.BinIntDef.Z.div_eucl_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eBinIntDef_2eZ_2ediv__eucl,V_24X1),V_24X2) = cCoq_2eZArith_2eBinIntDef_2eZ_2ediv__eucl___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.Lists.List.Add_$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('$adef_Coq.ZArith.Zlogarithm.log_inf_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eZArith_2eZlogarithm_2elog__inf,V_24X1) = cCoq_2eZArith_2eZlogarithm_2elog__inf___24a1(V_24X1) ).

fof('$adef_Coq.Bool.Bool.ifb_$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('$adef_Coq.PArith.BinPosDef.Pos.div2_up_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2ePArith_2eBinPosDef_2ePos_2ediv2__up,V_24X1) = cCoq_2ePArith_2eBinPosDef_2ePos_2ediv2__up___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('$adef_Coq.setoid_ring.Field_theory.FEadd_$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('$adef_Coq.Init.Decimal.uint_of_uint_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eInit_2eDecimal_2euint__of__uint,V_24X1) = cCoq_2eInit_2eDecimal_2euint__of__uint___24a1(V_24X1) ).

fof('$adef_Coq.ZArith.BinIntDef.Z.odd_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eZArith_2eBinIntDef_2eZ_2eodd,V_24X1) = cCoq_2eZArith_2eBinIntDef_2eZ_2eodd___24a1(V_24X1) ).

fof('$adef_Coq.PArith.BinPosDef.Pos.lxor_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2ePArith_2eBinPosDef_2ePos_2elxor,V_24X1),V_24X2) = cCoq_2ePArith_2eBinPosDef_2ePos_2elxor___24a2(V_24X1,V_24X2) ).

fof('$adef_$_lam_1023_$a7',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7] : happ(happ(happ(happ(happ(happ(happ(c_24__lam__1023,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7) = c_24__lam__1023___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7) ).

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('$adef_Coq.Init.Datatypes.S_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eInit_2eDatatypes_2eS,V_24X1) = cCoq_2eInit_2eDatatypes_2eS___24a1(V_24X1) ).

fof('$adef_Coq.Strings.Ascii.Ascii_$a8',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8] : happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2eStrings_2eAscii_2eAscii,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8) = cCoq_2eStrings_2eAscii_2eAscii___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8) ).

fof('$adef_Coq.micromega.EnvRing.PEpow_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2emicromega_2eEnvRing_2ePEpow,V_24X1),V_24X2),V_24X3) = cCoq_2emicromega_2eEnvRing_2ePEpow___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_Coq.setoid_ring.Ring_polynom.zmon_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2ezmon,V_24X1),V_24X2) = cCoq_2esetoid__ring_2eRing__polynom_2ezmon___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.setoid_ring.Ring_theory.semi_morph_$a13',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13] :
      ( p(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__theory_2esemi__morph,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9),V_24X10),V_24X11),V_24X12),V_24X13))
    <=> cCoq_2esetoid__ring_2eRing__theory_2esemi__morph___24a13(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13) ) ).

fof('$adef_Coq.micromega.VarMap.Empty_$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('$adef_Coq.ZArith.BinIntDef.Z.add_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eBinIntDef_2eZ_2eadd,V_24X1),V_24X2) = cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.Init.Decimal.DecimalExp_$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('$adef_$_prop_29579_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__prop__29579,V_24X1),V_24X2),V_24X3) = c_24__prop__29579___24a3(V_24X1,V_24X2,V_24X3) ).

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('$adef_Coq.Init.Wf.Fix_F_2_$a7',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7] : happ(happ(happ(happ(happ(happ(happ(cCoq_2eInit_2eWf_2eFix__F__2,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7) = cCoq_2eInit_2eWf_2eFix__F__2___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7) ).

fof('$adef_Coq.ZArith.Znat.neq_$a2',axiom,
    ! [V_24X1,V_24X2] :
      ( p(happ(happ(cCoq_2eZArith_2eZnat_2eneq,V_24X1),V_24X2))
    <=> cCoq_2eZArith_2eZnat_2eneq___24a2(V_24X1,V_24X2) ) ).

fof('$adef_Coq.micromega.RingMicromega.Formula_$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('$adef_$_lam_31926_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(c_24__lam__31926,V_24X1),V_24X2) = c_24__lam__31926___24a2(V_24X1,V_24X2) ).

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('$adef_Coq.setoid_ring.InitialRing.gen_phiN_$a6',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eInitialRing_2egen__phiN,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = cCoq_2esetoid__ring_2eInitialRing_2egen__phiN___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).

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('$adef_Coq.Init.Nat.min_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eNat_2emin,V_24X1),V_24X2) = cCoq_2eInit_2eNat_2emin___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.Init.Specif.existT2_$a6',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(cCoq_2eInit_2eSpecif_2eexistT2,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = cCoq_2eInit_2eSpecif_2eexistT2___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).

fof('$adef_$_lam_32940_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(c_24__lam__32940,V_24X1),V_24X2) = c_24__lam__32940___24a2(V_24X1,V_24X2) ).

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('$adef_Coq.Lists.SetoidList.InA_$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('$adef_Coq.setoid_ring.InitialRing.mkhypo_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2esetoid__ring_2eInitialRing_2emkhypo,V_24X1),V_24X2) = cCoq_2esetoid__ring_2eInitialRing_2emkhypo___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.Reals.Rdefinitions.Rlt_$a2',axiom,
    ! [V_24X1,V_24X2] :
      ( p(happ(happ(cCoq_2eReals_2eRdefinitions_2eRlt,V_24X1),V_24X2))
    <=> cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V_24X1,V_24X2) ) ).

fof('$adef_Coq.Reals.RIneq.mknonzeroreal_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eReals_2eRIneq_2emknonzeroreal,V_24X1) = cCoq_2eReals_2eRIneq_2emknonzeroreal___24a1(V_24X1) ).

fof('$adef_Coq.ZArith.BinIntDef.Z.sub_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eBinIntDef_2eZ_2esub,V_24X1),V_24X2) = cCoq_2eZArith_2eBinIntDef_2eZ_2esub___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.ZArith.BinIntDef.Z.div_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eBinIntDef_2eZ_2ediv,V_24X1),V_24X2) = cCoq_2eZArith_2eBinIntDef_2eZ_2ediv___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.setoid_ring.Ring_polynom.PEopp_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2ePEopp,V_24X1),V_24X2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEopp___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.micromega.RingMicromega.PsatzZ_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2emicromega_2eRingMicromega_2ePsatzZ,V_24X1) = cCoq_2emicromega_2eRingMicromega_2ePsatzZ___24a1(V_24X1) ).

fof('$adef_Coq.Bool.Bool.Is_true_$a1',axiom,
    ! [V_24X1] :
      ( p(happ(cCoq_2eBool_2eBool_2eIs__true,V_24X1))
    <=> cCoq_2eBool_2eBool_2eIs__true___24a1(V_24X1) ) ).

fof('$adef_Coq.Init.Nat.modulo_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eNat_2emodulo,V_24X1),V_24X2) = cCoq_2eInit_2eNat_2emodulo___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('$adef_$_let_var_6_p_27099_27102_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__let__var__6__p__27099__27102,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__let__var__6__p__27099__27102___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).

fof('$adef_Coq.Lists.List.fold_right_$a5',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2eLists_2eList_2efold__right,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2eLists_2eList_2efold__right___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).

fof('$adef_Coq.setoid_ring.Ring_theory.pow_pos_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__theory_2epow__pos,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2esetoid__ring_2eRing__theory_2epow__pos___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).

fof('$adef_Coq.Init.Wf.Fix_$a6',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(cCoq_2eInit_2eWf_2eFix,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = cCoq_2eInit_2eWf_2eFix___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).

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('$adef_Coq.Init.Wf.Fix_F_$a5',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2eInit_2eWf_2eFix__F,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2eInit_2eWf_2eFix__F___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).

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('$adef_Coq.Init.Nat.odd_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eInit_2eNat_2eodd,V_24X1) = cCoq_2eInit_2eNat_2eodd___24a1(V_24X1) ).

fof('$adef_Coq.ZArith.BinIntDef.Z.even_$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('$adef_Coq.Lists.List.tl_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2eLists_2eList_2etl,V_24X1),V_24X2) = cCoq_2eLists_2eList_2etl___24a2(V_24X1,V_24X2) ).

fof('$adef_$_prop_29559_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__prop__29559,V_24X1),V_24X2),V_24X3) = c_24__prop__29559___24a3(V_24X1,V_24X2,V_24X3) ).

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('$adef_Coq.setoid_ring.Ring_theory.sign_theory_$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('$adef_Coq.PArith.BinPosDef.Pos.land_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2ePArith_2eBinPosDef_2ePos_2eland,V_24X1),V_24X2) = cCoq_2ePArith_2eBinPosDef_2ePos_2eland___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.Numbers.BinNums.xO_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eNumbers_2eBinNums_2exO,V_24X1) = cCoq_2eNumbers_2eBinNums_2exO___24a1(V_24X1) ).

fof('$adef_Coq.NArith.BinNatDef.N.even_$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('$adef_Coq.Lists.List.NoDup_$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('$adef_Coq.Lists.SetoidList.transpose_restr_$a5',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] :
      ( p(happ(happ(happ(happ(happ(cCoq_2eLists_2eSetoidList_2etranspose__restr,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5))
    <=> cCoq_2eLists_2eSetoidList_2etranspose__restr___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ) ).

fof('$adef_Coq.Init.Wf.Fix_F_$a6',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(cCoq_2eInit_2eWf_2eFix__F,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = cCoq_2eInit_2eWf_2eFix__F___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).

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('$adef_Coq.Init.Wf.Acc_rect_$a5',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2eInit_2eWf_2eAcc__rect,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2eInit_2eWf_2eAcc__rect___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).

fof('$adef_Coq.setoid_ring.Field_theory.FEinv_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2esetoid__ring_2eField__theory_2eFEinv,V_24X1),V_24X2) = cCoq_2esetoid__ring_2eField__theory_2eFEinv___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.ZArith.Zpower.Zdiv_rest_proof_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2eZArith_2eZpower_2eZdiv__rest__proof,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2eZArith_2eZpower_2eZdiv__rest__proof___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).

fof('$adef_Coq.Init.Wf.Acc_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] :
      ( p(happ(happ(happ(cCoq_2eInit_2eWf_2eAcc,V_24X1),V_24X2),V_24X3))
    <=> cCoq_2eInit_2eWf_2eAcc___24a3(V_24X1,V_24X2,V_24X3) ) ).

fof('$adef_Coq.setoid_ring.Ring_theory.pow_N_$a5',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__theory_2epow__N,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2esetoid__ring_2eRing__theory_2epow__N___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).

fof('$adef_Coq.Init.Specif.sigT_$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('$adef_Coq.setoid_ring.Field_theory.semi_field_theory_$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('$adef_Coq.Init.Decimal.D3_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eInit_2eDecimal_2eD3,V_24X1) = cCoq_2eInit_2eDecimal_2eD3___24a1(V_24X1) ).

fof('$adef_$_prop_29580_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__prop__29580,V_24X1),V_24X2),V_24X3) = c_24__prop__29580___24a3(V_24X1,V_24X2,V_24X3) ).

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('$adef_Coq.Sets.Relations_1.Order_$a2',axiom,
    ! [V_24X1,V_24X2] :
      ( p(happ(happ(cCoq_2eSets_2eRelations__1_2eOrder,V_24X1),V_24X2))
    <=> cCoq_2eSets_2eRelations__1_2eOrder___24a2(V_24X1,V_24X2) ) ).

fof('$adef_Coq.QArith.QArith_base.Qeq_$a2',axiom,
    ! [V_24X1,V_24X2] :
      ( p(happ(happ(cCoq_2eQArith_2eQArith__base_2eQeq,V_24X1),V_24X2))
    <=> cCoq_2eQArith_2eQArith__base_2eQeq___24a2(V_24X1,V_24X2) ) ).

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('$adef_Coq.ZArith.BinIntDef.Z.pow_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eBinIntDef_2eZ_2epow,V_24X1),V_24X2) = cCoq_2eZArith_2eBinIntDef_2eZ_2epow___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.QArith.QArith_base.Qmake_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2eQArith_2eQArith__base_2eQmake,V_24X1),V_24X2) = cCoq_2eQArith_2eQArith__base_2eQmake___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.Relations.Relation_Operators.clos_refl_trans_n1_$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('$adef_Coq.Arith.Wf_nat.inv_lt_rel_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] :
      ( p(happ(happ(happ(happ(cCoq_2eArith_2eWf__nat_2einv__lt__rel,V_24X1),V_24X2),V_24X3),V_24X4))
    <=> cCoq_2eArith_2eWf__nat_2einv__lt__rel___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).

fof('$adef_$_case_Coq.Init.Datatypes.nat$17090_$a1',axiom,
    ! [V_24X1] : happ(c_24__case__Coq_2eInit_2eDatatypes_2enat_2417090,V_24X1) = c_24__case__Coq_2eInit_2eDatatypes_2enat_2417090___24a1(V_24X1) ).

fof('$adef_Coq.setoid_ring.Ring_polynom.PEX_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2ePEX,V_24X1),V_24X2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEX___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.micromega.EnvRing.PEc_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2emicromega_2eEnvRing_2ePEc,V_24X1),V_24X2) = cCoq_2emicromega_2eEnvRing_2ePEc___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.NArith.BinNatDef.N.pred_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eNArith_2eBinNatDef_2eN_2epred,V_24X1) = cCoq_2eNArith_2eBinNatDef_2eN_2epred___24a1(V_24X1) ).

fof('$adef_$_prop_10918_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(c_24__prop__10918,V_24X1),V_24X2) = c_24__prop__10918___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.micromega.OrderedRing.SOR_$a10',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10] :
      ( p(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2emicromega_2eOrderedRing_2eSOR,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9),V_24X10))
    <=> cCoq_2emicromega_2eOrderedRing_2eSOR___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10) ) ).

fof('$adef_Coq.Relations.Relation_Operators.clos_refl_trans_$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('$adef_Coq.Sets.Relations_1.PER_$a2',axiom,
    ! [V_24X1,V_24X2] :
      ( p(happ(happ(cCoq_2eSets_2eRelations__1_2ePER,V_24X1),V_24X2))
    <=> cCoq_2eSets_2eRelations__1_2ePER___24a2(V_24X1,V_24X2) ) ).

fof('$adef_Coq.micromega.EnvRing.PX_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2emicromega_2eEnvRing_2ePX,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2emicromega_2eEnvRing_2ePX___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).

fof('$adef_Coq.Init.Datatypes.sum_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eDatatypes_2esum,V_24X1),V_24X2) = cCoq_2eInit_2eDatatypes_2esum___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.micromega.EnvRing.PEadd_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2emicromega_2eEnvRing_2ePEadd,V_24X1),V_24X2),V_24X3) = cCoq_2emicromega_2eEnvRing_2ePEadd___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_Coq.Init.Wf.well_founded_induction_type_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eInit_2eWf_2ewell__founded__induction__type,V_24X1),V_24X2),V_24X3) = cCoq_2eInit_2eWf_2ewell__founded__induction__type___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_Coq.NArith.BinNatDef.N.min_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2eNArith_2eBinNatDef_2eN_2emin,V_24X1),V_24X2) = cCoq_2eNArith_2eBinNatDef_2eN_2emin___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.setoid_ring.InitialRing.hypo_type_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2esetoid__ring_2eInitialRing_2ehypo__type,V_24X1) = cCoq_2esetoid__ring_2eInitialRing_2ehypo__type___24a1(V_24X1) ).

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('$adef_Coq.PArith.BinPosDef.Pos.size_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2ePArith_2eBinPosDef_2ePos_2esize,V_24X1) = cCoq_2ePArith_2eBinPosDef_2ePos_2esize___24a1(V_24X1) ).

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('$adef_$_lam_33038_$a1',axiom,
    ! [V_24X1] : happ(c_24__lam__33038,V_24X1) = c_24__lam__33038___24a1(V_24X1) ).

fof('$adef_$_lam_33027_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(c_24__lam__33027,V_24X1),V_24X2) = c_24__lam__33027___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.Init.Specif.sig2_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eInit_2eSpecif_2esig2,V_24X1),V_24X2),V_24X3) = cCoq_2eInit_2eSpecif_2esig2___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_Coq.setoid_ring.Field_theory.FEpow_$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('$adef_$_fix_31684_v_CANONICAL_1_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__fix__31684__v__CANONICAL__1,V_24X1),V_24X2),V_24X3) = c_24__fix__31684__v__CANONICAL__1___24a3(V_24X1,V_24X2,V_24X3) ).

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('$adef_$_prop_29564_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(c_24__prop__29564,V_24X1),V_24X2) = c_24__prop__29564___24a2(V_24X1,V_24X2) ).

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('$adef_$_lam_31934_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(c_24__lam__31934,V_24X1),V_24X2) = c_24__lam__31934___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.micromega.ZMicromega.is_diff_env_elt_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] :
      ( p(happ(happ(happ(happ(cCoq_2emicromega_2eZMicromega_2eis__diff__env__elt,V_24X1),V_24X2),V_24X3),V_24X4))
    <=> cCoq_2emicromega_2eZMicromega_2eis__diff__env__elt___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).

fof('$adef_Coq.Vectors.Fin.t_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eVectors_2eFin_2et,V_24X1) = cCoq_2eVectors_2eFin_2et___24a1(V_24X1) ).

fof('$adef_Coq.NArith.BinNat.N.le_$a2',axiom,
    ! [V_24X1,V_24X2] :
      ( p(happ(happ(cCoq_2eNArith_2eBinNat_2eN_2ele,V_24X1),V_24X2))
    <=> cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(V_24X1,V_24X2) ) ).

fof('$adef_Coq.setoid_ring.Field_theory.FEO_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2esetoid__ring_2eField__theory_2eFEO,V_24X1) = cCoq_2esetoid__ring_2eField__theory_2eFEO___24a1(V_24X1) ).

fof('$adef_Coq.PArith.BinPosDef.Pos.testbit_nat_$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('$adef_Coq.Lists.List.In_$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('$adef_Coq.ZArith.Zpower.Zdiv_rest_proofs_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eZpower_2eZdiv__rest__proofs,V_24X1),V_24X2) = cCoq_2eZArith_2eZpower_2eZdiv__rest__proofs___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.PArith.BinPosDef.Pos.of_succ_nat_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2ePArith_2eBinPosDef_2ePos_2eof__succ__nat,V_24X1) = cCoq_2ePArith_2eBinPosDef_2ePos_2eof__succ__nat___24a1(V_24X1) ).

fof('$adef_Coq.micromega.EnvRing.PEsub_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2emicromega_2eEnvRing_2ePEsub,V_24X1),V_24X2),V_24X3) = cCoq_2emicromega_2eEnvRing_2ePEsub___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_Coq.PArith.BinPosDef.Pos.add_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2ePArith_2eBinPosDef_2ePos_2eadd,V_24X1),V_24X2) = cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.Init.Nat.double_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eInit_2eNat_2edouble,V_24X1) = cCoq_2eInit_2eNat_2edouble___24a1(V_24X1) ).

fof('$adef_Coq.Init.Datatypes.andb_$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('$adef_Coq.Init.Peano.gt_$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('$adef_Coq.Init.Peano.lt_$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('$tdef_$_type_29813',axiom,
    ! [V_24Y] :
      ( c_24__type__29813___24t(V_24Y)
    <=> t(V_24Y,c_24__type__29813) ) ).

fof('$tdef_$_type_10817',axiom,
    ! [V_24Y] :
      ( c_24__type__10817___24t(V_24Y)
    <=> t(V_24Y,c_24__type__10817) ) ).

fof('$tdef_$_type_32350',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24Y] :
      ( c_24__type__32350___24t(V_24X1,V_24X2,V_24X3,V_24Y)
    <=> t(V_24Y,c_24__type__32350___24a3(V_24X1,V_24X2,V_24X3)) ) ).

fof('$tdef_$_type_24498',axiom,
    ! [V_24Y] :
      ( c_24__type__24498___24t(V_24Y)
    <=> t(V_24Y,c_24__type__24498) ) ).

fof('$tdef_$_type_24090',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
      ( c_24__type__24090___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
    <=> t(V_24Y,c_24__type__24090___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).

fof('$tdef_$_type_2562',axiom,
    ! [V_24Y] :
      ( c_24__type__2562___24t(V_24Y)
    <=> t(V_24Y,c_24__type__2562) ) ).

fof('$tdef_$_type_1370',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y] :
      ( c_24__type__1370___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y)
    <=> t(V_24Y,c_24__type__1370___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6)) ) ).

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_29897',axiom,
    ! [V_24Y] :
      ( c_24__type__29897___24t(V_24Y)
    <=> t(V_24Y,c_24__type__29897) ) ).

fof('$tdef_$_type_29791',axiom,
    ! [V_24Y] :
      ( c_24__type__29791___24t(V_24Y)
    <=> t(V_24Y,c_24__type__29791) ) ).

fof('$tdef_$_type_10177',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y] :
      ( c_24__type__10177___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y)
    <=> t(V_24Y,c_24__type__10177___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7)) ) ).

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_7355',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
      ( c_24__type__7355___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
    <=> t(V_24Y,c_24__type__7355___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).

fof('$tdef_$_type_3276',axiom,
    ! [V_24X1,V_24Y] :
      ( c_24__type__3276___24t(V_24X1,V_24Y)
    <=> t(V_24Y,c_24__type__3276___24a1(V_24X1)) ) ).

fof('$tdef_$_type_15672',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__15672___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__15672___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).

fof('$tdef_$_type_30045',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24Y] :
      ( c_24__type__30045___24t(V_24X1,V_24X2,V_24X3,V_24Y)
    <=> t(V_24Y,c_24__type__30045___24a3(V_24X1,V_24X2,V_24X3)) ) ).

fof('$tdef_$_type_5084',axiom,
    ! [V_24Y] :
      ( c_24__type__5084___24t(V_24Y)
    <=> t(V_24Y,c_24__type__5084) ) ).

fof('$tdef_$_type_3236',axiom,
    ! [V_24Y] :
      ( c_24__type__3236___24t(V_24Y)
    <=> t(V_24Y,c_24__type__3236) ) ).

fof('$tdef_$_type_12808',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__12808___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__12808___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).

fof('$tdef_$_type_32002',axiom,
    ! [V_24Y] :
      ( c_24__type__32002___24t(V_24Y)
    <=> t(V_24Y,c_24__type__32002) ) ).

fof('$tdef_$_type_16346',axiom,
    ! [V_24Y] :
      ( c_24__type__16346___24t(V_24Y)
    <=> t(V_24Y,c_24__type__16346) ) ).

fof('$tdef_$_type_6890',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
      ( c_24__type__6890___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__6890___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).

fof('$tdef_$_type_28371',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__28371___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__28371___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_23581',axiom,
    ! [V_24Y] :
      ( c_24__type__23581___24t(V_24Y)
    <=> t(V_24Y,c_24__type__23581) ) ).

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_30021',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24Y] :
      ( c_24__type__30021___24t(V_24X1,V_24X2,V_24X3,V_24Y)
    <=> t(V_24Y,c_24__type__30021___24a3(V_24X1,V_24X2,V_24X3)) ) ).

fof('$tdef_$_type_32970',axiom,
    ! [V_24Y] :
      ( c_24__type__32970___24t(V_24Y)
    <=> t(V_24Y,c_24__type__32970) ) ).

fof('$tdef_$_type_29672',axiom,
    ! [V_24Y] :
      ( c_24__type__29672___24t(V_24Y)
    <=> t(V_24Y,c_24__type__29672) ) ).

fof('$tdef_$_type_12276',axiom,
    ! [V_24Y] :
      ( c_24__type__12276___24t(V_24Y)
    <=> t(V_24Y,c_24__type__12276) ) ).

fof('$tdef_$_type_16065',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__16065___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__16065___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.VarMap.t',axiom,
    ! [V_24X1,V_24Y] :
      ( cCoq_2emicromega_2eVarMap_2et___24t(V_24X1,V_24Y)
    <=> t(V_24Y,cCoq_2emicromega_2eVarMap_2et___24a1(V_24X1)) ) ).

fof('$tdef_Coq.Reals.RIneq.nonposreal',axiom,
    ! [V_24Y] :
      ( cCoq_2eReals_2eRIneq_2enonposreal___24t(V_24Y)
    <=> t(V_24Y,cCoq_2eReals_2eRIneq_2enonposreal) ) ).

fof('$tdef_$_type_329',axiom,
    ! [V_24Y] :
      ( c_24__type__329___24t(V_24Y)
    <=> t(V_24Y,c_24__type__329) ) ).

fof('$tdef_$_type_23610',axiom,
    ! [V_24Y] :
      ( c_24__type__23610___24t(V_24Y)
    <=> t(V_24Y,c_24__type__23610) ) ).

fof('$tdef_$_type_31910',axiom,
    ! [V_24Y] :
      ( c_24__type__31910___24t(V_24Y)
    <=> t(V_24Y,c_24__type__31910) ) ).

fof('$tdef_$_type_10700',axiom,
    ! [V_24X1,V_24X2,V_24Y] :
      ( c_24__type__10700___24t(V_24X1,V_24X2,V_24Y)
    <=> t(V_24Y,c_24__type__10700___24a2(V_24X1,V_24X2)) ) ).

fof('$tdef_$_type_10018',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
      ( c_24__type__10018___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
    <=> t(V_24Y,c_24__type__10018___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).

fof('$tdef_$_type_3928',axiom,
    ! [V_24X1,V_24X2,V_24Y] :
      ( c_24__type__3928___24t(V_24X1,V_24X2,V_24Y)
    <=> t(V_24Y,c_24__type__3928___24a2(V_24X1,V_24X2)) ) ).

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_27760',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__27760___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__27760___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_27072',axiom,
    ! [V_24Y] :
      ( c_24__type__27072___24t(V_24Y)
    <=> t(V_24Y,c_24__type__27072) ) ).

fof('$tdef_$_type_14645',axiom,
    ! [V_24Y] :
      ( c_24__type__14645___24t(V_24Y)
    <=> t(V_24Y,c_24__type__14645) ) ).

fof('$tdef_$_type_30202',axiom,
    ! [V_24Y] :
      ( c_24__type__30202___24t(V_24Y)
    <=> t(V_24Y,c_24__type__30202) ) ).

fof('$tdef_$_type_30143',axiom,
    ! [V_24Y] :
      ( c_24__type__30143___24t(V_24Y)
    <=> t(V_24Y,c_24__type__30143) ) ).

fof('$tdef_$_type_23542',axiom,
    ! [V_24Y] :
      ( c_24__type__23542___24t(V_24Y)
    <=> t(V_24Y,c_24__type__23542) ) ).

fof('$tdef_$_type_11918',axiom,
    ! [V_24X1,V_24Y] :
      ( c_24__type__11918___24t(V_24X1,V_24Y)
    <=> t(V_24Y,c_24__type__11918___24a1(V_24X1)) ) ).

fof('$tdef_$_type_19383',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__19383___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__19383___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_7331',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
      ( c_24__type__7331___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
    <=> t(V_24Y,c_24__type__7331___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).

fof('$tdef_$_type_16525',axiom,
    ! [V_24Y] :
      ( c_24__type__16525___24t(V_24Y)
    <=> t(V_24Y,c_24__type__16525) ) ).

fof('$tdef_$_type_1100',axiom,
    ! [V_24Y] :
      ( c_24__type__1100___24t(V_24Y)
    <=> t(V_24Y,c_24__type__1100) ) ).

fof('$tdef_$_type_24046',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
      ( c_24__type__24046___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
    <=> t(V_24Y,c_24__type__24046___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).

fof('$tdef_$_type_14513',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
      ( c_24__type__14513___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__14513___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).

fof('$tdef_$_type_26607',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__26607___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__26607___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).

fof('$tdef_$_type_11784',axiom,
    ! [V_24X1,V_24Y] :
      ( c_24__type__11784___24t(V_24X1,V_24Y)
    <=> t(V_24Y,c_24__type__11784___24a1(V_24X1)) ) ).

fof('$tdef_$_type_33041',axiom,
    ! [V_24Y] :
      ( c_24__type__33041___24t(V_24Y)
    <=> t(V_24Y,c_24__type__33041) ) ).

fof('$tdef_$_type_32763',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y] :
      ( c_24__type__32763___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y)
    <=> t(V_24Y,c_24__type__32763___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6)) ) ).

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_30092',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
      ( c_24__type__30092___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
    <=> t(V_24Y,c_24__type__30092___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).

fof('$tdef_$_type_4310',axiom,
    ! [V_24X1,V_24Y] :
      ( c_24__type__4310___24t(V_24X1,V_24Y)
    <=> t(V_24Y,c_24__type__4310___24a1(V_24X1)) ) ).

fof('$tdef_$_type_29761',axiom,
    ! [V_24Y] :
      ( c_24__type__29761___24t(V_24Y)
    <=> t(V_24Y,c_24__type__29761) ) ).

fof('$tdef_$_type_29442',axiom,
    ! [V_24Y] :
      ( c_24__type__29442___24t(V_24Y)
    <=> t(V_24Y,c_24__type__29442) ) ).

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_6953',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
      ( c_24__type__6953___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__6953___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).

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_32302',axiom,
    ! [V_24X1,V_24X2,V_24Y] :
      ( c_24__type__32302___24t(V_24X1,V_24X2,V_24Y)
    <=> t(V_24Y,c_24__type__32302___24a2(V_24X1,V_24X2)) ) ).

fof('$tdef_$_type_27113',axiom,
    ! [V_24Y] :
      ( c_24__type__27113___24t(V_24Y)
    <=> t(V_24Y,c_24__type__27113) ) ).

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_14270',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
      ( c_24__type__14270___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__14270___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).

fof('$tdef_$_type_26957',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__26957___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__26957___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).

fof('$tdef_Coq.Structures.OrdersTac.ord',axiom,
    ! [V_24Y] :
      ( cCoq_2eStructures_2eOrdersTac_2eord___24t(V_24Y)
    <=> t(V_24Y,cCoq_2eStructures_2eOrdersTac_2eord) ) ).

fof('$tdef_Coq.micromega.EnvRing.PExpr',axiom,
    ! [V_24X1,V_24Y] :
      ( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(V_24X1,V_24Y)
    <=> t(V_24Y,cCoq_2emicromega_2eEnvRing_2ePExpr___24a1(V_24X1)) ) ).

fof('$tdef_Coq.Init.Datatypes.option',axiom,
    ! [V_24X1,V_24Y] :
      ( cCoq_2eInit_2eDatatypes_2eoption___24t(V_24X1,V_24Y)
    <=> t(V_24Y,cCoq_2eInit_2eDatatypes_2eoption___24a1(V_24X1)) ) ).

fof('$tdef_$_type_28901',axiom,
    ! [V_24Y] :
      ( c_24__type__28901___24t(V_24Y)
    <=> t(V_24Y,c_24__type__28901) ) ).

fof('$tdef_$_type_1376',axiom,
    ! [V_24X1,V_24Y] :
      ( c_24__type__1376___24t(V_24X1,V_24Y)
    <=> t(V_24Y,c_24__type__1376___24a1(V_24X1)) ) ).

fof('$tdef_$_type_26055',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24Y] :
      ( c_24__type__26055___24t(V_24X1,V_24X2,V_24X3,V_24Y)
    <=> t(V_24Y,c_24__type__26055___24a3(V_24X1,V_24X2,V_24X3)) ) ).

fof('$tdef_$_type_5079',axiom,
    ! [V_24Y] :
      ( c_24__type__5079___24t(V_24Y)
    <=> t(V_24Y,c_24__type__5079) ) ).

fof('$tdef_$_type_29805',axiom,
    ! [V_24Y] :
      ( c_24__type__29805___24t(V_24Y)
    <=> t(V_24Y,c_24__type__29805) ) ).

fof('$tdef_$_type_14708',axiom,
    ! [V_24Y] :
      ( c_24__type__14708___24t(V_24Y)
    <=> t(V_24Y,c_24__type__14708) ) ).

fof('$tdef_$_type_10319',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y] :
      ( c_24__type__10319___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y)
    <=> t(V_24Y,c_24__type__10319___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7)) ) ).

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_32559',axiom,
    ! [V_24Y] :
      ( c_24__type__32559___24t(V_24Y)
    <=> t(V_24Y,c_24__type__32559) ) ).

fof('$tdef_$_type_23388',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
      ( c_24__type__23388___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
    <=> t(V_24Y,c_24__type__23388___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).

fof('$tdef_$_type_32212',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24Y] :
      ( c_24__type__32212___24t(V_24X1,V_24X2,V_24X3,V_24Y)
    <=> t(V_24Y,c_24__type__32212___24a3(V_24X1,V_24X2,V_24X3)) ) ).

fof('$tdef_$_type_4830',axiom,
    ! [V_24Y] :
      ( c_24__type__4830___24t(V_24Y)
    <=> t(V_24Y,c_24__type__4830) ) ).

fof('$tdef_$_type_29610',axiom,
    ! [V_24Y] :
      ( c_24__type__29610___24t(V_24Y)
    <=> t(V_24Y,c_24__type__29610) ) ).

fof('$tdef_$_type_29981',axiom,
    ! [V_24X1,V_24X2,V_24Y] :
      ( c_24__type__29981___24t(V_24X1,V_24X2,V_24Y)
    <=> t(V_24Y,c_24__type__29981___24a2(V_24X1,V_24X2)) ) ).

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_29827',axiom,
    ! [V_24Y] :
      ( c_24__type__29827___24t(V_24Y)
    <=> t(V_24Y,c_24__type__29827) ) ).

fof('$tdef_$_type_18022',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__18022___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__18022___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_8615',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__8615___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__8615___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_31066',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y] :
      ( c_24__type__31066___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y)
    <=> t(V_24Y,c_24__type__31066___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6)) ) ).

fof('$tdef_$_type_24730',axiom,
    ! [V_24Y] :
      ( c_24__type__24730___24t(V_24Y)
    <=> t(V_24Y,c_24__type__24730) ) ).

fof('$tdef_$_type_4',axiom,
    ! [V_24X1,V_24Y] :
      ( c_24__type__4___24t(V_24X1,V_24Y)
    <=> t(V_24Y,c_24__type__4___24a1(V_24X1)) ) ).

fof('$tdef_$_type_21436',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__21436___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__21436___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_809',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
      ( c_24__type__809___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
    <=> t(V_24Y,c_24__type__809___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).

fof('$tdef_$_type_8828',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__8828___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__8828___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.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_25191',axiom,
    ! [V_24Y] :
      ( c_24__type__25191___24t(V_24Y)
    <=> t(V_24Y,c_24__type__25191) ) ).

fof('$tdef_$_type_2516',axiom,
    ! [V_24X1,V_24Y] :
      ( c_24__type__2516___24t(V_24X1,V_24Y)
    <=> t(V_24Y,c_24__type__2516___24a1(V_24X1)) ) ).

fof('$tdef_$_type_26782',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__26782___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__26782___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).

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_25163',axiom,
    ! [V_24Y] :
      ( c_24__type__25163___24t(V_24Y)
    <=> t(V_24Y,c_24__type__25163) ) ).

fof('$tdef_$_type_23483',axiom,
    ! [V_24Y] :
      ( c_24__type__23483___24t(V_24Y)
    <=> t(V_24Y,c_24__type__23483) ) ).

fof('$tdef_$_type_9449',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__9449___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__9449___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_18691',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__18691___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__18691___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_2745',axiom,
    ! [V_24Y] :
      ( c_24__type__2745___24t(V_24Y)
    <=> t(V_24Y,c_24__type__2745) ) ).

fof('$tdef_$_type_17097',axiom,
    ! [V_24Y] :
      ( c_24__type__17097___24t(V_24Y)
    <=> t(V_24Y,c_24__type__17097) ) ).

fof('$tdef_$_type_23301',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
      ( c_24__type__23301___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
    <=> t(V_24Y,c_24__type__23301___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).

fof('$tdef_$_type_21090',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__21090___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__21090___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_17001',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y] :
      ( c_24__type__17001___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y)
    <=> t(V_24Y,c_24__type__17001___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6)) ) ).

fof('$tdef_$_type_29736',axiom,
    ! [V_24Y] :
      ( c_24__type__29736___24t(V_24Y)
    <=> t(V_24Y,c_24__type__29736) ) ).

fof('$tdef_$_type_1107',axiom,
    ! [V_24X1,V_24X2,V_24Y] :
      ( c_24__type__1107___24t(V_24X1,V_24X2,V_24Y)
    <=> t(V_24Y,c_24__type__1107___24a2(V_24X1,V_24X2)) ) ).

fof('$tdef_$_type_31138',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y] :
      ( c_24__type__31138___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y)
    <=> t(V_24Y,c_24__type__31138___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6)) ) ).

fof('$tdef_$_type_28135',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__28135___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__28135___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_32641',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
      ( c_24__type__32641___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
    <=> t(V_24Y,c_24__type__32641___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).

fof('$tdef_$_type_32519',axiom,
    ! [V_24X1,V_24X2,V_24Y] :
      ( c_24__type__32519___24t(V_24X1,V_24X2,V_24Y)
    <=> t(V_24Y,c_24__type__32519___24a2(V_24X1,V_24X2)) ) ).

fof('$tdef_$_type_29854',axiom,
    ! [V_24Y] :
      ( c_24__type__29854___24t(V_24Y)
    <=> t(V_24Y,c_24__type__29854) ) ).

fof('$tdef_$_type_32389',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
      ( c_24__type__32389___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
    <=> t(V_24Y,c_24__type__32389___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).

fof('$tdef_$_type_25167',axiom,
    ! [V_24Y] :
      ( c_24__type__25167___24t(V_24Y)
    <=> t(V_24Y,c_24__type__25167) ) ).

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_28649',axiom,
    ! [V_24Y] :
      ( c_24__type__28649___24t(V_24Y)
    <=> t(V_24Y,c_24__type__28649) ) ).

fof('$tdef_$_type_8207',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__8207___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__8207___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_33101',axiom,
    ! [V_24Y] :
      ( c_24__type__33101___24t(V_24Y)
    <=> t(V_24Y,c_24__type__33101) ) ).

fof('$tdef_$_type_16470',axiom,
    ! [V_24Y] :
      ( c_24__type__16470___24t(V_24Y)
    <=> t(V_24Y,c_24__type__16470) ) ).

fof('$tdef_$_type_12890',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__12890___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__12890___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).

fof('$tdef_$_type_16326',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
      ( c_24__type__16326___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
    <=> t(V_24Y,c_24__type__16326___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).

fof('$tdef_$_type_14333',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
      ( c_24__type__14333___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__14333___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_32424',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24Y] :
      ( c_24__type__32424___24t(V_24X1,V_24X2,V_24X3,V_24Y)
    <=> t(V_24Y,c_24__type__32424___24a3(V_24X1,V_24X2,V_24X3)) ) ).

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_23560',axiom,
    ! [V_24Y] :
      ( c_24__type__23560___24t(V_24Y)
    <=> t(V_24Y,c_24__type__23560) ) ).

fof('$tdef_$_type_31256',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
      ( c_24__type__31256___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
    <=> t(V_24Y,c_24__type__31256___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).

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_3174',axiom,
    ! [V_24Y] :
      ( c_24__type__3174___24t(V_24Y)
    <=> t(V_24Y,c_24__type__3174) ) ).

fof('$tdef_$_type_27364',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y] :
      ( c_24__type__27364___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y)
    <=> t(V_24Y,c_24__type__27364___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6)) ) ).

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_31908',axiom,
    ! [V_24Y] :
      ( c_24__type__31908___24t(V_24Y)
    <=> t(V_24Y,c_24__type__31908) ) ).

fof('$tdef_$_type_26421',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__26421___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__26421___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).

fof('$tdef_$_type_11821',axiom,
    ! [V_24Y] :
      ( c_24__type__11821___24t(V_24Y)
    <=> t(V_24Y,c_24__type__11821) ) ).

fof('$tdef_$_type_10839',axiom,
    ! [V_24Y] :
      ( c_24__type__10839___24t(V_24Y)
    <=> t(V_24Y,c_24__type__10839) ) ).

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_28838',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24Y] :
      ( c_24__type__28838___24t(V_24X1,V_24X2,V_24X3,V_24Y)
    <=> t(V_24Y,c_24__type__28838___24a3(V_24X1,V_24X2,V_24X3)) ) ).

fof('$tdef_$_type_16480',axiom,
    ! [V_24Y] :
      ( c_24__type__16480___24t(V_24Y)
    <=> t(V_24Y,c_24__type__16480) ) ).

fof('$tdef_Coq.Reals.Rdefinitions.R',axiom,
    ! [V_24Y] :
      ( cCoq_2eReals_2eRdefinitions_2eR___24t(V_24Y)
    <=> t(V_24Y,cCoq_2eReals_2eRdefinitions_2eR) ) ).

fof('$tdef_$_type_117',axiom,
    ! [V_24X1,V_24Y] :
      ( c_24__type__117___24t(V_24X1,V_24Y)
    <=> t(V_24Y,c_24__type__117___24a1(V_24X1)) ) ).

fof('$tdef_$_type_31205',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
      ( c_24__type__31205___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
    <=> t(V_24Y,c_24__type__31205___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).

fof('$tdef_$_type_14',axiom,
    ! [V_24Y] :
      ( c_24__type__14___24t(V_24Y)
    <=> t(V_24Y,c_24__type__14) ) ).

fof('$tdef_$_type_23538',axiom,
    ! [V_24X1,V_24X2,V_24Y] :
      ( c_24__type__23538___24t(V_24X1,V_24X2,V_24Y)
    <=> t(V_24Y,c_24__type__23538___24a2(V_24X1,V_24X2)) ) ).

fof('$tdef_$_type_2471',axiom,
    ! [V_24Y] :
      ( c_24__type__2471___24t(V_24Y)
    <=> t(V_24Y,c_24__type__2471) ) ).

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_29836',axiom,
    ! [V_24Y] :
      ( c_24__type__29836___24t(V_24Y)
    <=> t(V_24Y,c_24__type__29836) ) ).

fof('$tdef_$_type_2643',axiom,
    ! [V_24Y] :
      ( c_24__type__2643___24t(V_24Y)
    <=> t(V_24Y,c_24__type__2643) ) ).

fof('$tdef_$_type_32979',axiom,
    ! [V_24Y] :
      ( c_24__type__32979___24t(V_24Y)
    <=> t(V_24Y,c_24__type__32979) ) ).

fof('$tdef_$_type_28958',axiom,
    ! [V_24Y] :
      ( c_24__type__28958___24t(V_24Y)
    <=> t(V_24Y,c_24__type__28958) ) ).

fof('$tdef_$_type_31817',axiom,
    ! [V_24Y] :
      ( c_24__type__31817___24t(V_24Y)
    <=> t(V_24Y,c_24__type__31817) ) ).

fof('$tdef_$_type_7190',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
      ( c_24__type__7190___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
    <=> t(V_24Y,c_24__type__7190___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).

fof('$tdef_$_type_33074',axiom,
    ! [V_24Y] :
      ( c_24__type__33074___24t(V_24Y)
    <=> t(V_24Y,c_24__type__33074) ) ).

fof('$tdef_$_type_24011',axiom,
    ! [V_24Y] :
      ( c_24__type__24011___24t(V_24Y)
    <=> t(V_24Y,c_24__type__24011) ) ).

fof('$tdef_$_type_23414',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
      ( c_24__type__23414___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
    <=> t(V_24Y,c_24__type__23414___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).

fof('$tdef_$_type_21759',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__21759___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__21759___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_459',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24Y] :
      ( c_24__type__459___24t(V_24X1,V_24X2,V_24X3,V_24Y)
    <=> t(V_24Y,c_24__type__459___24a3(V_24X1,V_24X2,V_24X3)) ) ).

fof('$tdef_$_type_13929',axiom,
    ! [V_24Y] :
      ( c_24__type__13929___24t(V_24Y)
    <=> t(V_24Y,c_24__type__13929) ) ).

fof('$tdef_$_type_11943',axiom,
    ! [V_24Y] :
      ( c_24__type__11943___24t(V_24Y)
    <=> t(V_24Y,c_24__type__11943) ) ).

fof('$tdef_$_type_26098',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
      ( c_24__type__26098___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
    <=> t(V_24Y,c_24__type__26098___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).

fof('$tdef_$_type_699',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
      ( c_24__type__699___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
    <=> t(V_24Y,c_24__type__699___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).

fof('$tdef_$_type_32914',axiom,
    ! [V_24Y] :
      ( c_24__type__32914___24t(V_24Y)
    <=> t(V_24Y,c_24__type__32914) ) ).

fof('$tdef_$_type_25160',axiom,
    ! [V_24Y] :
      ( c_24__type__25160___24t(V_24Y)
    <=> t(V_24Y,c_24__type__25160) ) ).

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_618',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24Y] :
      ( c_24__type__618___24t(V_24X1,V_24X2,V_24X3,V_24Y)
    <=> t(V_24Y,c_24__type__618___24a3(V_24X1,V_24X2,V_24X3)) ) ).

fof('$tdef_$_type_29797',axiom,
    ! [V_24Y] :
      ( c_24__type__29797___24t(V_24Y)
    <=> t(V_24Y,c_24__type__29797) ) ).

fof('$tdef_$_type_16759',axiom,
    ! [V_24Y] :
      ( c_24__type__16759___24t(V_24Y)
    <=> t(V_24Y,c_24__type__16759) ) ).

fof('$tdef_$_type_16792',axiom,
    ! [V_24Y] :
      ( c_24__type__16792___24t(V_24Y)
    <=> t(V_24Y,c_24__type__16792) ) ).

fof('$tdef_Coq.setoid_ring.Field_theory.FExpr',axiom,
    ! [V_24X1,V_24Y] :
      ( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(V_24X1,V_24Y)
    <=> t(V_24Y,cCoq_2esetoid__ring_2eField__theory_2eFExpr___24a1(V_24X1)) ) ).

fof('$tdef_Coq.Reals.RIneq.nonnegreal',axiom,
    ! [V_24Y] :
      ( cCoq_2eReals_2eRIneq_2enonnegreal___24t(V_24Y)
    <=> t(V_24Y,cCoq_2eReals_2eRIneq_2enonnegreal) ) ).

fof('$tdef_$_type_16688',axiom,
    ! [V_24Y] :
      ( c_24__type__16688___24t(V_24Y)
    <=> t(V_24Y,c_24__type__16688) ) ).

fof('$tdef_$_type_28010',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__28010___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__28010___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_20421',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__20421___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__20421___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.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_29778',axiom,
    ! [V_24Y] :
      ( c_24__type__29778___24t(V_24Y)
    <=> t(V_24Y,c_24__type__29778) ) ).

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.Init.Datatypes.unit',axiom,
    ! [V_24Y] :
      ( cCoq_2eInit_2eDatatypes_2eunit___24t(V_24Y)
    <=> t(V_24Y,cCoq_2eInit_2eDatatypes_2eunit) ) ).

fof('$tdef_$_type_32007',axiom,
    ! [V_24Y] :
      ( c_24__type__32007___24t(V_24Y)
    <=> t(V_24Y,c_24__type__32007) ) ).

fof('$tdef_$_type_175',axiom,
    ! [V_24Y] :
      ( c_24__type__175___24t(V_24Y)
    <=> t(V_24Y,c_24__type__175) ) ).

fof('$tdef_$_type_7781',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__7781___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__7781___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_27635',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__27635___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__27635___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_33011',axiom,
    ! [V_24Y] :
      ( c_24__type__33011___24t(V_24Y)
    <=> t(V_24Y,c_24__type__33011) ) ).

fof('$tdef_$_type_592',axiom,
    ! [V_24Y] :
      ( c_24__type__592___24t(V_24Y)
    <=> t(V_24Y,c_24__type__592) ) ).

fof('$tdef_$_type_32930',axiom,
    ! [V_24Y] :
      ( c_24__type__32930___24t(V_24Y)
    <=> t(V_24Y,c_24__type__32930) ) ).

fof('$tdef_$_type_25773',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
      ( c_24__type__25773___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__25773___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).

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_7274',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
      ( c_24__type__7274___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
    <=> t(V_24Y,c_24__type__7274___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).

fof('$tdef_$_type_24723',axiom,
    ! [V_24Y] :
      ( c_24__type__24723___24t(V_24Y)
    <=> t(V_24Y,c_24__type__24723) ) ).

fof('$tdef_$_type_32570',axiom,
    ! [V_24Y] :
      ( c_24__type__32570___24t(V_24Y)
    <=> t(V_24Y,c_24__type__32570) ) ).

fof('$tdef_$_type_29945',axiom,
    ! [V_24Y] :
      ( c_24__type__29945___24t(V_24Y)
    <=> t(V_24Y,c_24__type__29945) ) ).

fof('$tdef_$_type_23213',axiom,
    ! [V_24Y] :
      ( c_24__type__23213___24t(V_24Y)
    <=> t(V_24Y,c_24__type__23213) ) ).

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_33048',axiom,
    ! [V_24Y] :
      ( c_24__type__33048___24t(V_24Y)
    <=> t(V_24Y,c_24__type__33048) ) ).

fof('$tdef_$_type_13932',axiom,
    ! [V_24Y] :
      ( c_24__type__13932___24t(V_24Y)
    <=> t(V_24Y,c_24__type__13932) ) ).

fof('$tdef_$_type_29877',axiom,
    ! [V_24Y] :
      ( c_24__type__29877___24t(V_24Y)
    <=> t(V_24Y,c_24__type__29877) ) ).

fof('$tdef_$_type_7244',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
      ( c_24__type__7244___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
    <=> t(V_24Y,c_24__type__7244___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).

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_236',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
      ( c_24__type__236___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
    <=> t(V_24Y,c_24__type__236___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).

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_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_24732',axiom,
    ! [V_24Y] :
      ( c_24__type__24732___24t(V_24Y)
    <=> t(V_24Y,c_24__type__24732) ) ).

fof('$tdef_$_type_25953',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
      ( c_24__type__25953___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__25953___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).

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_16767',axiom,
    ! [V_24Y] :
      ( c_24__type__16767___24t(V_24Y)
    <=> t(V_24Y,c_24__type__16767) ) ).

fof('$tdef_$_type_30162',axiom,
    ! [V_24Y] :
      ( c_24__type__30162___24t(V_24Y)
    <=> t(V_24Y,c_24__type__30162) ) ).

fof('$tdef_$_type_23370',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
      ( c_24__type__23370___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
    <=> t(V_24Y,c_24__type__23370___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).

fof('$tdef_$_type_29501',axiom,
    ! [V_24Y] :
      ( c_24__type__29501___24t(V_24Y)
    <=> t(V_24Y,c_24__type__29501) ) ).

fof('$tdef_$_type_219',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24Y] :
      ( c_24__type__219___24t(V_24X1,V_24X2,V_24X3,V_24Y)
    <=> t(V_24Y,c_24__type__219___24a3(V_24X1,V_24X2,V_24X3)) ) ).

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_4817',axiom,
    ! [V_24Y] :
      ( c_24__type__4817___24t(V_24Y)
    <=> t(V_24Y,c_24__type__4817) ) ).

fof('$tdef_$_type_11797',axiom,
    ! [V_24Y] :
      ( c_24__type__11797___24t(V_24Y)
    <=> t(V_24Y,c_24__type__11797) ) ).

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_31354',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24Y] :
      ( c_24__type__31354___24t(V_24X1,V_24X2,V_24X3,V_24Y)
    <=> t(V_24Y,c_24__type__31354___24a3(V_24X1,V_24X2,V_24X3)) ) ).

fof('$tdef_$_type_877',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24Y] :
      ( c_24__type__877___24t(V_24X1,V_24X2,V_24X3,V_24Y)
    <=> t(V_24Y,c_24__type__877___24a3(V_24X1,V_24X2,V_24X3)) ) ).

fof('$tdef_$_type_18368',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__18368___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__18368___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_633',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
      ( c_24__type__633___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
    <=> t(V_24Y,c_24__type__633___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).

fof('$tdef_$_type_25710',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
      ( c_24__type__25710___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__25710___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).

fof('$tdef_$_type_20744',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__20744___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__20744___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_29753',axiom,
    ! [V_24Y] :
      ( c_24__type__29753___24t(V_24Y)
    <=> t(V_24Y,c_24__type__29753) ) ).

fof('$tdef_$_type_16935',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y] :
      ( c_24__type__16935___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y)
    <=> t(V_24Y,c_24__type__16935___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6)) ) ).

fof('$tdef_Coq.setoid_ring.InitialRing.hypo',axiom,
    ! [V_24Y] :
      ( cCoq_2esetoid__ring_2eInitialRing_2ehypo___24t(V_24Y)
    <=> t(V_24Y,cCoq_2esetoid__ring_2eInitialRing_2ehypo) ) ).

fof('$tdef_$_type_16475',axiom,
    ! [V_24Y] :
      ( c_24__type__16475___24t(V_24Y)
    <=> t(V_24Y,c_24__type__16475) ) ).

fof('$tdef_$_type_12132',axiom,
    ! [V_24Y] :
      ( c_24__type__12132___24t(V_24Y)
    <=> t(V_24Y,c_24__type__12132) ) ).

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_32542',axiom,
    ! [V_24X1,V_24X2,V_24Y] :
      ( c_24__type__32542___24t(V_24X1,V_24X2,V_24Y)
    <=> t(V_24Y,c_24__type__32542___24a2(V_24X1,V_24X2)) ) ).

fof('$tdef_$_type_26864',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__26864___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__26864___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).

fof('$tdef_$_type_26090',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
      ( c_24__type__26090___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
    <=> t(V_24Y,c_24__type__26090___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).

fof('$tdef_$_type_32292',axiom,
    ! [V_24Y] :
      ( c_24__type__32292___24t(V_24Y)
    <=> t(V_24Y,c_24__type__32292) ) ).

fof('$tdef_$_type_27038',axiom,
    ! [V_24Y] :
      ( c_24__type__27038___24t(V_24Y)
    <=> t(V_24Y,c_24__type__27038) ) ).

fof('$tdef_$_type_242',axiom,
    ! [V_24X1,V_24Y] :
      ( c_24__type__242___24t(V_24X1,V_24Y)
    <=> t(V_24Y,c_24__type__242___24a1(V_24X1)) ) ).

fof('$tdef_$_type_25245',axiom,
    ! [V_24Y] :
      ( c_24__type__25245___24t(V_24Y)
    <=> t(V_24Y,c_24__type__25245) ) ).

fof('$tdef_$_type_10557',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y] :
      ( c_24__type__10557___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y)
    <=> t(V_24Y,c_24__type__10557___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7)) ) ).

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_10369',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y] :
      ( c_24__type__10369___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y)
    <=> t(V_24Y,c_24__type__10369___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7)) ) ).

fof('$tdef_$_type_28260',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__28260___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__28260___24a13(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13)) ) ).

fof('$tdef_Coq.Reals.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_Coq.Init.Decimal.int',axiom,
    ! [V_24Y] :
      ( cCoq_2eInit_2eDecimal_2eint___24t(V_24Y)
    <=> t(V_24Y,cCoq_2eInit_2eDecimal_2eint) ) ).

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_28854',axiom,
    ! [V_24Y] :
      ( c_24__type__28854___24t(V_24Y)
    <=> t(V_24Y,c_24__type__28854) ) ).

fof('$tdef_$_type_10940',axiom,
    ! [V_24Y] :
      ( c_24__type__10940___24t(V_24Y)
    <=> t(V_24Y,c_24__type__10940) ) ).

fof('$tdef_$_type_23347',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
      ( c_24__type__23347___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
    <=> t(V_24Y,c_24__type__23347___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).

fof('$tdef_$_type_7160',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
      ( c_24__type__7160___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
    <=> t(V_24Y,c_24__type__7160___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).

fof('$tdef_$_type_31999',axiom,
    ! [V_24Y] :
      ( c_24__type__31999___24t(V_24Y)
    <=> t(V_24Y,c_24__type__31999) ) ).

fof('$tdef_$_type_10227',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y] :
      ( c_24__type__10227___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y)
    <=> t(V_24Y,c_24__type__10227___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7)) ) ).

fof('$tdef_$_type_684',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24Y] :
      ( c_24__type__684___24t(V_24X1,V_24X2,V_24X3,V_24Y)
    <=> t(V_24Y,c_24__type__684___24a3(V_24X1,V_24X2,V_24X3)) ) ).

fof('$tdef_$_type_29921',axiom,
    ! [V_24Y] :
      ( c_24__type__29921___24t(V_24Y)
    <=> t(V_24Y,c_24__type__29921) ) ).

fof('$tdef_$_type_15762',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__15762___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__15762___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).

fof('$tdef_$_type_3256',axiom,
    ! [V_24Y] :
      ( c_24__type__3256___24t(V_24Y)
    <=> t(V_24Y,c_24__type__3256) ) ).

fof('$tdef_$_type_181',axiom,
    ! [V_24X1,V_24Y] :
      ( c_24__type__181___24t(V_24X1,V_24Y)
    <=> t(V_24Y,c_24__type__181___24a1(V_24X1)) ) ).

fof('$tdef_$_type_28702',axiom,
    ! [V_24X1,V_24X2,V_24Y] :
      ( c_24__type__28702___24t(V_24X1,V_24X2,V_24Y)
    <=> t(V_24Y,c_24__type__28702___24a2(V_24X1,V_24X2)) ) ).

fof('$tdef_$_type_29974',axiom,
    ! [V_24Y] :
      ( c_24__type__29974___24t(V_24Y)
    <=> t(V_24Y,c_24__type__29974) ) ).

fof('$tdef_$_type_26197',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y] :
      ( c_24__type__26197___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y)
    <=> t(V_24Y,c_24__type__26197___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6)) ) ).

fof('$tdef_$_type_28629',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
      ( c_24__type__28629___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
    <=> t(V_24Y,c_24__type__28629___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).

fof('$tdef_$_type_32252',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
      ( c_24__type__32252___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
    <=> t(V_24Y,c_24__type__32252___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).

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_11931',axiom,
    ! [V_24Y] :
      ( c_24__type__11931___24t(V_24Y)
    <=> t(V_24Y,c_24__type__11931) ) ).

fof('$tdef_$_type_22082',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__22082___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__22082___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.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_5076',axiom,
    ! [V_24Y] :
      ( c_24__type__5076___24t(V_24Y)
    <=> t(V_24Y,c_24__type__5076) ) ).

fof('$tdef_$_type_29595',axiom,
    ! [V_24Y] :
      ( c_24__type__29595___24t(V_24Y)
    <=> t(V_24Y,c_24__type__29595) ) ).

fof('$tdef_$_type_24099',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
      ( c_24__type__24099___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
    <=> t(V_24Y,c_24__type__24099___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).

fof('$tdef_$_type_7298',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
      ( c_24__type__7298___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
    <=> t(V_24Y,c_24__type__7298___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).

fof('$tdef_A',axiom,
    ! [V_24Y] :
      ( cA___24t(V_24Y)
    <=> t(V_24Y,cA) ) ).

fof('$tdef_$_type_32911',axiom,
    ! [V_24Y] :
      ( c_24__type__32911___24t(V_24Y)
    <=> t(V_24Y,c_24__type__32911) ) ).

fof('$tdef_$_type_24659',axiom,
    ! [V_24Y] :
      ( c_24__type__24659___24t(V_24Y)
    <=> t(V_24Y,c_24__type__24659) ) ).

fof('$tdef_$_type_3267',axiom,
    ! [V_24X1,V_24Y] :
      ( c_24__type__3267___24t(V_24X1,V_24Y)
    <=> t(V_24Y,c_24__type__3267___24a1(V_24X1)) ) ).

fof('$tdef_$_type_13940',axiom,
    ! [V_24Y] :
      ( c_24__type__13940___24t(V_24Y)
    <=> t(V_24Y,c_24__type__13940) ) ).

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_23577',axiom,
    ! [V_24X1,V_24X2,V_24Y] :
      ( c_24__type__23577___24t(V_24X1,V_24X2,V_24Y)
    <=> t(V_24Y,c_24__type__23577___24a2(V_24X1,V_24X2)) ) ).

fof('$tdef_$_type_23599',axiom,
    ! [V_24Y] :
      ( c_24__type__23599___24t(V_24Y)
    <=> t(V_24Y,c_24__type__23599) ) ).

fof('$tdef_$_type_31041',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y] :
      ( c_24__type__31041___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y)
    <=> t(V_24Y,c_24__type__31041___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6)) ) ).

fof('$tdef_$_type_16691',axiom,
    ! [V_24Y] :
      ( c_24__type__16691___24t(V_24Y)
    <=> t(V_24Y,c_24__type__16691) ) ).

fof('$tdef_$_type_16964',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y] :
      ( c_24__type__16964___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y)
    <=> t(V_24Y,c_24__type__16964___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6)) ) ).

fof('$tdef_$_type_110',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24Y] :
      ( c_24__type__110___24t(V_24X1,V_24X2,V_24X3,V_24Y)
    <=> t(V_24Y,c_24__type__110___24a3(V_24X1,V_24X2,V_24X3)) ) ).

fof('$tdef_$_type_10445',axiom,
    ! [V_24X1,V_24X2,V_24Y] :
      ( c_24__type__10445___24t(V_24X1,V_24X2,V_24Y)
    <=> t(V_24Y,c_24__type__10445___24a2(V_24X1,V_24X2)) ) ).

fof('$tdef_$_type_7994',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__7994___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__7994___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.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_26145',axiom,
    ! [V_24X1,V_24Y] :
      ( c_24__type__26145___24t(V_24X1,V_24Y)
    <=> t(V_24Y,c_24__type__26145___24a1(V_24X1)) ) ).

fof('$tdef_$_type_12983',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__12983___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__12983___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).

fof('$tdef_$_type_31896',axiom,
    ! [V_24Y] :
      ( c_24__type__31896___24t(V_24Y)
    <=> t(V_24Y,c_24__type__31896) ) ).

fof('$tdef_$_type_29746',axiom,
    ! [V_24Y] :
      ( c_24__type__29746___24t(V_24Y)
    <=> t(V_24Y,c_24__type__29746) ) ).

fof('$tdef_$_type_32459',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24Y] :
      ( c_24__type__32459___24t(V_24X1,V_24X2,V_24X3,V_24Y)
    <=> t(V_24Y,c_24__type__32459___24a3(V_24X1,V_24X2,V_24X3)) ) ).

fof('$tdef_$_type_907',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
      ( c_24__type__907___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
    <=> t(V_24Y,c_24__type__907___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).

fof('$tdef_$_type_28692',axiom,
    ! [V_24Y] :
      ( c_24__type__28692___24t(V_24Y)
    <=> t(V_24Y,c_24__type__28692) ) ).

fof('$tdef_$_type_922',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
      ( c_24__type__922___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
    <=> t(V_24Y,c_24__type__922___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).

fof('$tdef_$_type_29741',axiom,
    ! [V_24Y] :
      ( c_24__type__29741___24t(V_24Y)
    <=> t(V_24Y,c_24__type__29741) ) ).

fof('$tdef_$_type_28846',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24Y] :
      ( c_24__type__28846___24t(V_24X1,V_24X2,V_24X3,V_24Y)
    <=> t(V_24Y,c_24__type__28846___24a3(V_24X1,V_24X2,V_24X3)) ) ).

fof('$tdef_$_type_7382',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
      ( c_24__type__7382___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
    <=> t(V_24Y,c_24__type__7382___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).

fof('$tdef_$_type_19729',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__19729___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__19729___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_824',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
      ( c_24__type__824___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
    <=> t(V_24Y,c_24__type__824___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).

fof('$tdef_$_type_16818',axiom,
    ! [V_24Y] :
      ( c_24__type__16818___24t(V_24Y)
    <=> t(V_24Y,c_24__type__16818) ) ).

fof('$tdef_$_type_14864',axiom,
    ! [V_24Y] :
      ( c_24__type__14864___24t(V_24Y)
    <=> t(V_24Y,c_24__type__14864) ) ).

fof('$tdef_$_type_10953',axiom,
    ! [V_24Y] :
      ( c_24__type__10953___24t(V_24Y)
    <=> t(V_24Y,c_24__type__10953) ) ).

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_4767',axiom,
    ! [V_24Y] :
      ( c_24__type__4767___24t(V_24Y)
    <=> t(V_24Y,c_24__type__4767) ) ).

fof('$tdef_$_type_27092',axiom,
    ! [V_24Y] :
      ( c_24__type__27092___24t(V_24Y)
    <=> t(V_24Y,c_24__type__27092) ) ).

fof('$tdef_$_type_20',axiom,
    ! [V_24Y] :
      ( c_24__type__20___24t(V_24Y)
    <=> t(V_24Y,c_24__type__20) ) ).

fof('$tdef_$_type_16746',axiom,
    ! [V_24Y] :
      ( c_24__type__16746___24t(V_24Y)
    <=> t(V_24Y,c_24__type__16746) ) ).

fof('$tdef_$_type_11823',axiom,
    ! [V_24Y] :
      ( c_24__type__11823___24t(V_24Y)
    <=> t(V_24Y,c_24__type__11823) ) ).

fof('$tdef_$_type_6456',axiom,
    ! [V_24Y] :
      ( c_24__type__6456___24t(V_24Y)
    <=> t(V_24Y,c_24__type__6456) ) ).

fof('$tdef_$_type_11804',axiom,
    ! [V_24X1,V_24Y] :
      ( c_24__type__11804___24t(V_24X1,V_24Y)
    <=> t(V_24Y,c_24__type__11804___24a1(V_24X1)) ) ).

fof('$tdef_$_type_1337',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
      ( c_24__type__1337___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
    <=> t(V_24Y,c_24__type__1337___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).

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_2555',axiom,
    ! [V_24Y] :
      ( c_24__type__2555___24t(V_24Y)
    <=> t(V_24Y,c_24__type__2555) ) ).

fof('$tdef_$_type_11863',axiom,
    ! [V_24Y] :
      ( c_24__type__11863___24t(V_24Y)
    <=> t(V_24Y,c_24__type__11863) ) ).

fof('$tdef_$_type_32525',axiom,
    ! [V_24Y] :
      ( c_24__type__32525___24t(V_24Y)
    <=> t(V_24Y,c_24__type__32525) ) ).

fof('$tdef_$_type_26514',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__26514___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__26514___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).

fof('$tdef_$_type_29755',axiom,
    ! [V_24Y] :
      ( c_24__type__29755___24t(V_24Y)
    <=> t(V_24Y,c_24__type__29755) ) ).

fof('$tdef_$_type_29751',axiom,
    ! [V_24Y] :
      ( c_24__type__29751___24t(V_24Y)
    <=> t(V_24Y,c_24__type__29751) ) ).

fof('$tdef_$_type_10032',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
      ( c_24__type__10032___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
    <=> t(V_24Y,c_24__type__10032___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).

fof('$tdef_$_type_27885',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__27885___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__27885___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_1195',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y] :
      ( c_24__type__1195___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y)
    <=> t(V_24Y,c_24__type__1195___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6)) ) ).

fof('$tdef_$_type_31987',axiom,
    ! [V_24Y] :
      ( c_24__type__31987___24t(V_24Y)
    <=> t(V_24Y,c_24__type__31987) ) ).

fof('$tdef_$_type_30784',axiom,
    ! [V_24Y] :
      ( c_24__type__30784___24t(V_24Y)
    <=> t(V_24Y,c_24__type__30784) ) ).

fof('$tdef_$_type_7214',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
      ( c_24__type__7214___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
    <=> t(V_24Y,c_24__type__7214___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).

fof('$tdef_Coq.Bool.Bool.reflect',axiom,
    ! [V_24X1,V_24X2,V_24Y] :
      ( cCoq_2eBool_2eBool_2ereflect___24t(V_24X1,V_24X2,V_24Y)
    <=> t(V_24Y,cCoq_2eBool_2eBool_2ereflect___24a2(V_24X1,V_24X2)) ) ).

fof('$tdef_$_type_32707',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y] :
      ( c_24__type__32707___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y)
    <=> t(V_24Y,c_24__type__32707___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6)) ) ).

fof('$tdef_$_type_32562',axiom,
    ! [V_24Y] :
      ( c_24__type__32562___24t(V_24Y)
    <=> t(V_24Y,c_24__type__32562) ) ).

fof('$tdef_$_type_32554',axiom,
    ! [V_24Y] :
      ( c_24__type__32554___24t(V_24Y)
    <=> t(V_24Y,c_24__type__32554) ) ).

fof('$tdef_$_type_12265',axiom,
    ! [V_24Y] :
      ( c_24__type__12265___24t(V_24Y)
    <=> t(V_24Y,c_24__type__12265) ) ).

fof('$tdef_$_type_26689',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__26689___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__26689___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.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_25890',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
      ( c_24__type__25890___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__25890___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).

fof('$tdef_$_type_2603',axiom,
    ! [V_24Y] :
      ( c_24__type__2603___24t(V_24Y)
    <=> t(V_24Y,c_24__type__2603) ) ).

fof('$tdef_$_type_32588',axiom,
    ! [V_24Y] :
      ( c_24__type__32588___24t(V_24Y)
    <=> t(V_24Y,c_24__type__32588) ) ).

fof('$tdef_$_type_30788',axiom,
    ! [V_24Y] :
      ( c_24__type__30788___24t(V_24Y)
    <=> t(V_24Y,c_24__type__30788) ) ).

fof('$tdef_$_type_9857',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__9857___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__9857___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_433',axiom,
    ! [V_24Y] :
      ( c_24__type__433___24t(V_24Y)
    <=> t(V_24Y,c_24__type__433) ) ).

fof('$tdef_$_type_10637',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y] :
      ( c_24__type__10637___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y)
    <=> t(V_24Y,c_24__type__10637___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7)) ) ).

fof('$tdef_$_type_892',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
      ( c_24__type__892___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
    <=> t(V_24Y,c_24__type__892___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).

fof('$tdef_$_type_15031',axiom,
    ! [V_24Y] :
      ( c_24__type__15031___24t(V_24Y)
    <=> t(V_24Y,c_24__type__15031) ) ).

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_3261',axiom,
    ! [V_24Y] :
      ( c_24__type__3261___24t(V_24Y)
    <=> t(V_24Y,c_24__type__3261) ) ).

fof('$tdef_$_type_28659',axiom,
    ! [V_24X1,V_24X2,V_24Y] :
      ( c_24__type__28659___24t(V_24X1,V_24X2,V_24Y)
    <=> t(V_24Y,c_24__type__28659___24a2(V_24X1,V_24X2)) ) ).

fof('$tdef_$_type_23324',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
      ( c_24__type__23324___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
    <=> t(V_24Y,c_24__type__23324___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).

fof('$tdef_$_type_19037',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__19037___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__19037___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_30127',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24Y] :
      ( c_24__type__30127___24t(V_24X1,V_24X2,V_24X3,V_24Y)
    <=> t(V_24Y,c_24__type__30127___24a3(V_24X1,V_24X2,V_24X3)) ) ).

fof('$tdef_$_type_24537',axiom,
    ! [V_24Y] :
      ( c_24__type__24537___24t(V_24Y)
    <=> t(V_24Y,c_24__type__24537) ) ).

fof('$tdef_$_type_16686',axiom,
    ! [V_24Y] :
      ( c_24__type__16686___24t(V_24Y)
    <=> t(V_24Y,c_24__type__16686) ) ).

fof('$tdef_$_type_8402',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__8402___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__8402___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.QArith.QArith_base.Q',axiom,
    ! [V_24Y] :
      ( cCoq_2eQArith_2eQArith__base_2eQ___24t(V_24Y)
    <=> t(V_24Y,cCoq_2eQArith_2eQArith__base_2eQ) ) ).

fof('$tdef_Coq.PArith.BinPos.Pos.PeanoView',axiom,
    ! [V_24X1,V_24Y] :
      ( cCoq_2ePArith_2eBinPos_2ePos_2ePeanoView___24t(V_24X1,V_24Y)
    <=> t(V_24Y,cCoq_2ePArith_2eBinPos_2ePos_2ePeanoView___24a1(V_24X1)) ) ).

fof('$tdef_Coq.Numbers.BinNums.positive',axiom,
    ! [V_24Y] :
      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V_24Y)
    <=> t(V_24Y,cCoq_2eNumbers_2eBinNums_2epositive) ) ).

fof('$tdef_$_type_10943',axiom,
    ! [V_24Y] :
      ( c_24__type__10943___24t(V_24Y)
    <=> t(V_24Y,c_24__type__10943) ) ).

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_16698',axiom,
    ! [V_24Y] :
      ( c_24__type__16698___24t(V_24Y)
    <=> t(V_24Y,c_24__type__16698) ) ).

fof('$tdef_$_type_13158',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__13158___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__13158___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).

fof('$tdef_$_type_32605',axiom,
    ! [V_24Y] :
      ( c_24__type__32605___24t(V_24Y)
    <=> t(V_24Y,c_24__type__32605) ) ).

fof('$tdef_$_type_9662',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__9662___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__9662___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_73',axiom,
    ! [V_24Y] :
      ( c_24__type__73___24t(V_24Y)
    <=> t(V_24Y,c_24__type__73) ) ).

fof('$tdef_$_type_26988',axiom,
    ! [V_24Y] :
      ( c_24__type__26988___24t(V_24Y)
    <=> t(V_24Y,c_24__type__26988) ) ).

fof('$tdef_$_type_15571',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__15571___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__15571___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).

fof('$tdef_Coq.Structures.OrderedTypeEx.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_32952',axiom,
    ! [V_24Y] :
      ( c_24__type__32952___24t(V_24Y)
    <=> t(V_24Y,c_24__type__32952) ) ).

fof('$tdef_$_type_26225',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y] :
      ( c_24__type__26225___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y)
    <=> t(V_24Y,c_24__type__26225___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6)) ) ).

fof('$tdef_$_type_28798',axiom,
    ! [V_24Y] :
      ( c_24__type__28798___24t(V_24Y)
    <=> t(V_24Y,c_24__type__28798) ) ).

fof('$tdef_$_type_4334',axiom,
    ! [V_24X1,V_24X2,V_24Y] :
      ( c_24__type__4334___24t(V_24X1,V_24X2,V_24Y)
    <=> t(V_24Y,c_24__type__4334___24a2(V_24X1,V_24X2)) ) ).

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_32935',axiom,
    ! [V_24X1,V_24Y] :
      ( c_24__type__32935___24t(V_24X1,V_24Y)
    <=> t(V_24Y,c_24__type__32935___24a1(V_24X1)) ) ).

fof('$tdef_$_type_23204',axiom,
    ! [V_24Y] :
      ( c_24__type__23204___24t(V_24Y)
    <=> t(V_24Y,c_24__type__23204) ) ).

fof('$tdef_$_type_14396',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
      ( c_24__type__14396___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__14396___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).

fof('$tdef_$_type_24121',axiom,
    ! [V_24Y] :
      ( c_24__type__24121___24t(V_24Y)
    <=> t(V_24Y,c_24__type__24121) ) ).

fof('$tdef_$_type_35',axiom,
    ! [V_24Y] :
      ( c_24__type__35___24t(V_24Y)
    <=> t(V_24Y,c_24__type__35) ) ).

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_23432',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
      ( c_24__type__23432___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
    <=> t(V_24Y,c_24__type__23432___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).

fof('$tdef_$_type_1279',axiom,
    ! [V_24Y] :
      ( c_24__type__1279___24t(V_24Y)
    <=> t(V_24Y,c_24__type__1279) ) ).

fof('$tdef_$_type_1162',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
      ( c_24__type__1162___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
    <=> t(V_24Y,c_24__type__1162___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).

fof('$tdef_$_type_15863',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__15863___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__15863___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).

fof('$tdef_$_type_63',axiom,
    ! [V_24Y] :
      ( c_24__type__63___24t(V_24Y)
    <=> t(V_24Y,c_24__type__63) ) ).

fof('$tdef_P',axiom,
    ! [V_24X1,V_24Y] :
      ( cP___24t(V_24X1,V_24Y)
    <=> t(V_24Y,cP___24a1(V_24X1)) ) ).

fof('$tdef_Coq.setoid_ring.Ring_polynom.PExpr',axiom,
    ! [V_24X1,V_24Y] :
      ( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V_24X1,V_24Y)
    <=> t(V_24Y,cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V_24X1)) ) ).

fof('$tdef_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_47',axiom,
    ! [V_24Y] :
      ( c_24__type__47___24t(V_24Y)
    <=> t(V_24Y,c_24__type__47) ) ).

fof('$tdef_$_type_29800',axiom,
    ! [V_24Y] :
      ( c_24__type__29800___24t(V_24Y)
    <=> t(V_24Y,c_24__type__29800) ) ).

fof('$tdef_$_type_23605',axiom,
    ! [V_24Y] :
      ( c_24__type__23605___24t(V_24Y)
    <=> t(V_24Y,c_24__type__23605) ) ).

fof('$tdef_$_type_6773',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
      ( c_24__type__6773___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__6773___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).

fof('$tdef_$_type_794',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24Y] :
      ( c_24__type__794___24t(V_24X1,V_24X2,V_24X3,V_24Y)
    <=> t(V_24Y,c_24__type__794___24a3(V_24X1,V_24X2,V_24X3)) ) ).

fof('$tdef_Coq.NArith.BinNatDef.N.t',axiom,
    ! [V_24Y] :
      ( cCoq_2eNArith_2eBinNatDef_2eN_2et___24t(V_24Y)
    <=> t(V_24Y,cCoq_2eNArith_2eBinNatDef_2eN_2et) ) ).

fof('$tdef_Coq.Init.Datatypes.ID',axiom,
    ! [V_24Y] :
      ( cCoq_2eInit_2eDatatypes_2eID___24t(V_24Y)
    <=> t(V_24Y,cCoq_2eInit_2eDatatypes_2eID) ) ).

fof('$tdef_$_type_2511',axiom,
    ! [V_24Y] :
      ( c_24__type__2511___24t(V_24Y)
    <=> t(V_24Y,c_24__type__2511) ) ).

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_28782',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24Y] :
      ( c_24__type__28782___24t(V_24X1,V_24X2,V_24X3,V_24Y)
    <=> t(V_24Y,c_24__type__28782___24a3(V_24X1,V_24X2,V_24X3)) ) ).

fof('$tdef_$_type_9999',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
      ( c_24__type__9999___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
    <=> t(V_24Y,c_24__type__9999___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).

fof('$tdef_$_type_24473',axiom,
    ! [V_24Y] :
      ( c_24__type__24473___24t(V_24Y)
    <=> t(V_24Y,c_24__type__24473) ) ).

fof('$tdef_$_type_30184',axiom,
    ! [V_24Y] :
      ( c_24__type__30184___24t(V_24Y)
    <=> t(V_24Y,c_24__type__30184) ) ).

fof('$tdef_$_type_29794',axiom,
    ! [V_24Y] :
      ( c_24__type__29794___24t(V_24Y)
    <=> t(V_24Y,c_24__type__29794) ) ).

fof('$tdef_$_type_2591',axiom,
    ! [V_24Y] :
      ( c_24__type__2591___24t(V_24Y)
    <=> t(V_24Y,c_24__type__2591) ) ).

fof('$tdef_$_type_26034',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24Y] :
      ( c_24__type__26034___24t(V_24X1,V_24X2,V_24X3,V_24Y)
    <=> t(V_24Y,c_24__type__26034___24a3(V_24X1,V_24X2,V_24X3)) ) ).

fof('$tdef_$_type_29766',axiom,
    ! [V_24Y] :
      ( c_24__type__29766___24t(V_24Y)
    <=> t(V_24Y,c_24__type__29766) ) ).

fof('$tdef_$_type_11799',axiom,
    ! [V_24Y] :
      ( c_24__type__11799___24t(V_24Y)
    <=> t(V_24Y,c_24__type__11799) ) ).

fof('$tdef_$_type_9254',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__9254___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__9254___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.Ring_theory.ring_kind',axiom,
    ! [V_24Y] :
      ( cCoq_2esetoid__ring_2eRing__theory_2ering__kind___24t(V_24Y)
    <=> t(V_24Y,cCoq_2esetoid__ring_2eRing__theory_2ering__kind) ) ).

fof('$tdef_$_type_12715',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__12715___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__12715___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).

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_28790',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24Y] :
      ( c_24__type__28790___24t(V_24X1,V_24X2,V_24X3,V_24Y)
    <=> t(V_24Y,c_24__type__28790___24a3(V_24X1,V_24X2,V_24X3)) ) ).

fof('$tdef_$_type_10601',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y] :
      ( c_24__type__10601___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y)
    <=> t(V_24Y,c_24__type__10601___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7)) ) ).

fof('$tdef_Coq.Sets.Relations_1.Relation',axiom,
    ! [V_24X1,V_24Y] :
      ( cCoq_2eSets_2eRelations__1_2eRelation___24t(V_24X1,V_24Y)
    <=> t(V_24Y,cCoq_2eSets_2eRelations__1_2eRelation___24a1(V_24X1)) ) ).

fof('$tdef_$_type_22428',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__22428___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__22428___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_28',axiom,
    ! [V_24Y] :
      ( c_24__type__28___24t(V_24Y)
    <=> t(V_24Y,c_24__type__28) ) ).

fof('$tdef_$_type_6836',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
      ( c_24__type__6836___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__6836___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).

fof('$tdef_$_type_15964',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__15964___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__15964___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).

fof('$tdef_$_type_29843',axiom,
    ! [V_24X1,V_24Y] :
      ( c_24__type__29843___24t(V_24X1,V_24Y)
    <=> t(V_24Y,c_24__type__29843___24a1(V_24X1)) ) ).

fof('$tdef_$_type_4822',axiom,
    ! [V_24Y] :
      ( c_24__type__4822___24t(V_24Y)
    <=> t(V_24Y,c_24__type__4822) ) ).

fof('$tdef_$_type_29816',axiom,
    ! [V_24Y] :
      ( c_24__type__29816___24t(V_24Y)
    <=> t(V_24Y,c_24__type__29816) ) ).

fof('$tdef_$_type_29838',axiom,
    ! [V_24Y] :
      ( c_24__type__29838___24t(V_24Y)
    <=> t(V_24Y,c_24__type__29838) ) ).

fof('$tdef_$_type_474',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
      ( c_24__type__474___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
    <=> t(V_24Y,c_24__type__474___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).

fof('$tdef_$_type_2647',axiom,
    ! [V_24Y] :
      ( c_24__type__2647___24t(V_24Y)
    <=> t(V_24Y,c_24__type__2647) ) ).

fof('$tdef_$_type_31163',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y] :
      ( c_24__type__31163___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y)
    <=> t(V_24Y,c_24__type__31163___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6)) ) ).

fof('$tdef_$_type_24925',axiom,
    ! [V_24Y] :
      ( c_24__type__24925___24t(V_24Y)
    <=> t(V_24Y,c_24__type__24925) ) ).

fof('$tdef_Type',axiom,
    ! [V_24Y] :
      ( cType___24t(V_24Y)
    <=> t(V_24Y,cType) ) ).

fof('$tdef_$_type_2636',axiom,
    ! [V_24Y] :
      ( c_24__type__2636___24t(V_24Y)
    <=> t(V_24Y,c_24__type__2636) ) ).

fof('$tdef_$_type_23994',axiom,
    ! [V_24Y] :
      ( c_24__type__23994___24t(V_24Y)
    <=> t(V_24Y,c_24__type__23994) ) ).

fof('$tdef_$_type_13065',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__13065___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__13065___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).

fof('$tdef_Coq.PArith.BinPosDef.Pos.mask',axiom,
    ! [V_24Y] :
      ( cCoq_2ePArith_2eBinPosDef_2ePos_2emask___24t(V_24Y)
    <=> t(V_24Y,cCoq_2ePArith_2eBinPosDef_2ePos_2emask) ) ).

fof('$tdef_$_type_33129',axiom,
    ! [V_24Y] :
      ( c_24__type__33129___24t(V_24Y)
    <=> t(V_24Y,c_24__type__33129) ) ).

fof('$tdef_$_type_13937',axiom,
    ! [V_24Y] :
      ( c_24__type__13937___24t(V_24Y)
    <=> t(V_24Y,c_24__type__13937) ) ).

fof('$tdef_$_type_11987',axiom,
    ! [V_24Y] :
      ( c_24__type__11987___24t(V_24Y)
    <=> t(V_24Y,c_24__type__11987) ) ).

fof('$tdef_$_type_27286',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y] :
      ( c_24__type__27286___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y)
    <=> t(V_24Y,c_24__type__27286___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6)) ) ).

fof('$tdef_$_type_17676',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__17676___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__17676___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_11775',axiom,
    ! [V_24Y] :
      ( c_24__type__11775___24t(V_24Y)
    <=> t(V_24Y,c_24__type__11775) ) ).

fof('$tdef_$_type_839',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
      ( c_24__type__839___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
    <=> t(V_24Y,c_24__type__839___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).

fof('$tdef_$_type_25836',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
      ( c_24__type__25836___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__25836___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).

fof('$tdef_$_type_9041',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__9041___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__9041___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_15470',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__15470___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__15470___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).

fof('$tdef_$_type_24755',axiom,
    ! [V_24Y] :
      ( c_24__type__24755___24t(V_24Y)
    <=> t(V_24Y,c_24__type__24755) ) ).

fof('$tdef_$_type_1427',axiom,
    ! [V_24Y] :
      ( c_24__type__1427___24t(V_24Y)
    <=> t(V_24Y,c_24__type__1427) ) ).

fof('$tdef_$_type_33079',axiom,
    ! [V_24Y] :
      ( c_24__type__33079___24t(V_24Y)
    <=> t(V_24Y,c_24__type__33079) ) ).

fof('$tdef_$_type_10755',axiom,
    ! [V_24Y] :
      ( c_24__type__10755___24t(V_24Y)
    <=> t(V_24Y,c_24__type__10755) ) ).

fof('$tdef_Coq.Vectors.Fin.t',axiom,
    ! [V_24X1,V_24Y] :
      ( cCoq_2eVectors_2eFin_2et___24t(V_24X1,V_24Y)
    <=> t(V_24Y,cCoq_2eVectors_2eFin_2et___24a1(V_24X1)) ) ).

fof('$tdef_Coq.Reals.RIneq.nonzeroreal',axiom,
    ! [V_24Y] :
      ( cCoq_2eReals_2eRIneq_2enonzeroreal___24t(V_24Y)
    <=> t(V_24Y,cCoq_2eReals_2eRIneq_2enonzeroreal) ) ).

fof('$tdef_$_type_32957',axiom,
    ! [V_24X1,V_24Y] :
      ( c_24__type__32957___24t(V_24X1,V_24Y)
    <=> t(V_24Y,c_24__type__32957___24a1(V_24X1)) ) ).

fof('$tdef_$_type_28880',axiom,
    ! [V_24Y] :
      ( c_24__type__28880___24t(V_24Y)
    <=> t(V_24Y,c_24__type__28880) ) ).

fof('$tdef_$_type_11779',axiom,
    ! [V_24Y] :
      ( c_24__type__11779___24t(V_24Y)
    <=> t(V_24Y,c_24__type__11779) ) ).

fof('$tdef_$_type_1114',axiom,
    ! [V_24X1,V_24X2,V_24Y] :
      ( c_24__type__1114___24t(V_24X1,V_24X2,V_24Y)
    <=> t(V_24Y,c_24__type__1114___24a2(V_24X1,V_24X2)) ) ).

fof('$tdef_$_type_25',axiom,
    ! [V_24Y] :
      ( c_24__type__25___24t(V_24Y)
    <=> t(V_24Y,c_24__type__25) ) ).

fof('$tdef_$_type_14839',axiom,
    ! [V_24Y] :
      ( c_24__type__14839___24t(V_24Y)
    <=> t(V_24Y,c_24__type__14839) ) ).

fof('$tdef_$_type_11945',axiom,
    ! [V_24Y] :
      ( c_24__type__11945___24t(V_24Y)
    <=> t(V_24Y,c_24__type__11945) ) ).

fof('$tdef_$_type_6710',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
      ( c_24__type__6710___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__6710___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).

fof('$tdef_$_type_12622',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__12622___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__12622___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).

fof('$tdef_$_type_4348',axiom,
    ! [V_24X1,V_24X2,V_24Y] :
      ( c_24__type__4348___24t(V_24X1,V_24X2,V_24Y)
    <=> t(V_24Y,c_24__type__4348___24a2(V_24X1,V_24X2)) ) ).

fof('$tdef_$_type_10681',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y] :
      ( c_24__type__10681___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y)
    <=> t(V_24Y,c_24__type__10681___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7)) ) ).

fof('$tdef_$_type_16307',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
      ( c_24__type__16307___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
    <=> t(V_24Y,c_24__type__16307___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).

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('$tdef_$_type_32548',axiom,
    ! [V_24Y] :
      ( c_24__type__32548___24t(V_24Y)
    <=> t(V_24Y,c_24__type__32548) ) ).

fof('$tdef_$_type_2559',axiom,
    ! [V_24Y] :
      ( c_24__type__2559___24t(V_24Y)
    <=> t(V_24Y,c_24__type__2559) ) ).

fof('$tdef_$_type_24482',axiom,
    ! [V_24Y] :
      ( c_24__type__24482___24t(V_24Y)
    <=> t(V_24Y,c_24__type__24482) ) ).

fof('$tdef_$_type_1425',axiom,
    ! [V_24Y] :
      ( c_24__type__1425___24t(V_24Y)
    <=> t(V_24Y,c_24__type__1425) ) ).

fof('$tdef_$_type_27325',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y] :
      ( c_24__type__27325___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y)
    <=> t(V_24Y,c_24__type__27325___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6)) ) ).

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_24928',axiom,
    ! [V_24Y] :
      ( c_24__type__24928___24t(V_24Y)
    <=> t(V_24Y,c_24__type__24928) ) ).

fof('$tdef_$_type_14450',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
      ( c_24__type__14450___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__14450___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).

fof('$tdef_$_type_29888',axiom,
    ! [V_24Y] :
      ( c_24__type__29888___24t(V_24Y)
    <=> t(V_24Y,c_24__type__29888) ) ).

fof('$tdef_Coq.Init.Datatypes.Empty_set',axiom,
    ! [V_24Y] :
      ( cCoq_2eInit_2eDatatypes_2eEmpty__set___24t(V_24Y)
    <=> t(V_24Y,cCoq_2eInit_2eDatatypes_2eEmpty__set) ) ).

fof('$tdef_$_type_10277',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y] :
      ( c_24__type__10277___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y)
    <=> t(V_24Y,c_24__type__10277___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7)) ) ).

fof('$tdef_$_type_32479',axiom,
    ! [V_24Y] :
      ( c_24__type__32479___24t(V_24Y)
    <=> t(V_24Y,c_24__type__32479) ) ).

fof('$tdef_$_type_29872',axiom,
    ! [V_24Y] :
      ( c_24__type__29872___24t(V_24Y)
    <=> t(V_24Y,c_24__type__29872) ) ).

fof('$tdef_$_type_29748',axiom,
    ! [V_24Y] :
      ( c_24__type__29748___24t(V_24Y)
    <=> t(V_24Y,c_24__type__29748) ) ).

fof('$tdef_$_type_10453',axiom,
    ! [V_24Y] :
      ( c_24__type__10453___24t(V_24Y)
    <=> t(V_24Y,c_24__type__10453) ) ).

fof('$tdef_$_type_4355',axiom,
    ! [V_24X1,V_24X2,V_24Y] :
      ( c_24__type__4355___24t(V_24X1,V_24X2,V_24Y)
    <=> t(V_24Y,c_24__type__4355___24a2(V_24X1,V_24X2)) ) ).

fof('$tdef_$_type_32501',axiom,
    ! [V_24Y] :
      ( c_24__type__32501___24t(V_24Y)
    <=> t(V_24Y,c_24__type__32501) ) ).

fof('$tdef_$_type_20075',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__20075___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__20075___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('_HAMMER_GOAL',conjecture,
    ! [V0__x] :
      ( cA___24t(V0__x)
     => cr___24a3(V0__x,cCoq_2eInit_2eWf_2eFix___24a6(cA,cR,cRwf,cP,cF,V0__x),cF___24a2(V0__x,c_24__lam__33136___24a1(V0__x))) ) ).

%------------------------------------------------------------------------------