TPTP Problem File: SEV633+1.p

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%------------------------------------------------------------------------------
% File     : SEV633+1 : TPTP v9.3.1. Released v9.3.0.
% Domain   : Set theory
% Problem  : CoqHammer - Hoare2 dec while correct
% 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    : Hoare2.dec.while.correct.p [Kal26]

% Status   : Unknown
% Rating   : 1.00 v9.3.0
% Syntax   : Number of formulae    : 3135 (1370 unt;   0 def)
%            Number of atoms       : 10458 (3164 equ)
%            Maximal formula atoms :  257 (   3 avg)
%            Number of connectives : 7418 (  95   ~; 869   |;2280   &)
%                                         (1141 <=>;3033  =>;   0  <=;   0 <~>)
%            Maximal formula depth :  258 (   6 avg)
%            Maximal term depth    :   23 (   1 avg)
%            Number of predicates  :  638 ( 637 usr;   0 prp; 1-23 aty)
%            Number of functors    : 1875 (1875 usr;1237 con; 0-22 aty)
%            Number of variables   : 10152 (9148   !;1004   ?)
% 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$148400',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_24148487___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_24148400___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__148404] :
                ( t(Vvar__1___24Anonymous__148404,Vv__CANONICAL__0)
                & ? [Vvar__2___24Anonymous__148405] :
                    ( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vvar__2___24Anonymous__148405)
                    & c_24__case__Coq_2eInit_2eDatatypes_2elist_24148487___24a3(Vv__CANONICAL__0,Vv__CANONICAL__4,Vv__CANONICAL__5) = cCoq_2eInit_2eDatatypes_2econs___24a3(Vv__CANONICAL__0,Vvar__1___24Anonymous__148404,Vvar__2___24Anonymous__148405)
                    & c_24__case__Coq_2eInit_2eDatatypes_2elist_24148400___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__148404,c_24__fix__148532__v__CANONICAL__1___24a3(Vv__CANONICAL__0,Vvar__2___24Anonymous__148405,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$148487',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_24148487___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__148491] :
              ( t(Vvar__1___24Anonymous__148491,Vv__CANONICAL__0)
              & ? [Vvar__2___24Anonymous__148492] :
                  ( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vvar__2___24Anonymous__148492)
                  & Vv__CANONICAL__2 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vv__CANONICAL__0,Vvar__1___24Anonymous__148491,Vvar__2___24Anonymous__148492)
                  & c_24__case__Coq_2eInit_2eDatatypes_2elist_24148487___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = cCoq_2eInit_2eDatatypes_2econs___24a3(Vv__CANONICAL__0,Vvar__1___24Anonymous__148491,c_24__fix__148532__v__CANONICAL__1___24a3(Vv__CANONICAL__0,Vvar__2___24Anonymous__148492,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$126273',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_24126273___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = cCoq_2eNumbers_2eBinNums_2eZ0 )
        | ? [Vvar__0___24Anonymous__126274] :
            ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__126274)
            & Vv__CANONICAL__2 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__126274)
            & c_24__case__Coq_2eInit_2eDatatypes_2enat_24126273___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__126274)) ) ) ) ).

fof('$_case_Coq.Init.Datatypes.nat$126295',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_24126295___24a1(Vv__CANONICAL__0) = cCoq_2eNumbers_2eBinNums_2eZ0 )
        | ? [Vvar__0___24Anonymous__126296] :
            ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__126296)
            & Vv__CANONICAL__0 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__126296)
            & c_24__case__Coq_2eInit_2eDatatypes_2enat_24126295___24a1(Vv__CANONICAL__0) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eof__succ__nat___24a1(Vvar__0___24Anonymous__126296)) ) ) ) ).

fof('$_case_Coq.Init.Datatypes.nat$4629',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__2)
     => ( ( Vv__CANONICAL__2 = cCoq_2eInit_2eDatatypes_2eO
          & c_24__case__Coq_2eInit_2eDatatypes_2enat_244629___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = Vv__CANONICAL__3 )
        | ? [Vvar__0___24Anonymous__4630] :
            ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__4630)
            & Vv__CANONICAL__2 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__4630)
            & c_24__case__Coq_2eInit_2eDatatypes_2enat_244629___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = cCoq_2eInit_2eDatatypes_2eS___24a1(c_24__fix__4648__v__CANONICAL__0___24a2(Vvar__0___24Anonymous__4630,Vv__CANONICAL__3)) ) ) ) ).

fof('$_case_Coq.Init.Datatypes.nat$4740',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__2)
     => ( ( Vv__CANONICAL__2 = cCoq_2eInit_2eDatatypes_2eO
          & c_24__case__Coq_2eInit_2eDatatypes_2enat_244740___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = Vv__CANONICAL__2 )
        | ? [Vvar__0___24Anonymous__4741] :
            ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__4741)
            & ( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__3)
             => ( Vv__CANONICAL__2 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__4741)
                & ( ( Vv__CANONICAL__3 = cCoq_2eInit_2eDatatypes_2eO
                    & c_24__case__Coq_2eInit_2eDatatypes_2enat_244740___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = Vv__CANONICAL__2 )
                  | ? [Vvar__0___24Anonymous__4753] :
                      ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__4753)
                      & Vv__CANONICAL__3 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__4753)
                      & c_24__case__Coq_2eInit_2eDatatypes_2enat_244740___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = c_24__fix__4781__v__CANONICAL__0___24a2(Vvar__0___24Anonymous__4741,Vvar__0___24Anonymous__4753) ) ) ) ) ) ) ) ).

fof('$_case_Coq.Init.Datatypes.nat$4839',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__2)
     => ( ( Vv__CANONICAL__2 = cCoq_2eInit_2eDatatypes_2eO
          & c_24__case__Coq_2eInit_2eDatatypes_2enat_244839___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = cCoq_2eInit_2eDatatypes_2eO )
        | ? [Vvar__0___24Anonymous__4840] :
            ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__4840)
            & Vv__CANONICAL__2 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__4840)
            & c_24__case__Coq_2eInit_2eDatatypes_2enat_244839___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = cCoq_2eInit_2eNat_2eadd___24a2(Vv__CANONICAL__3,c_24__fix__4858__v__CANONICAL__0___24a2(Vvar__0___24Anonymous__4840,Vv__CANONICAL__3)) ) ) ) ).

fof('$_case_Coq.Init.Datatypes.nat$82845',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__2)
     => ( ( Vv__CANONICAL__2 = cCoq_2eInit_2eDatatypes_2eO
          & c_24__case__Coq_2eInit_2eDatatypes_2enat_2482845___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = Vv__CANONICAL__3 )
        | ? [Vvar__0___24Anonymous__82846] :
            ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__82846)
            & Vv__CANONICAL__2 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__82846)
            & c_24__case__Coq_2eInit_2eDatatypes_2enat_2482845___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = cCoq_2eInit_2eDatatypes_2eS___24a1(c_24__fix__4648__v__CANONICAL__0___24a2(Vvar__0___24Anonymous__82846,Vv__CANONICAL__3)) ) ) ) ).

fof('$_case_Coq.Init.Datatypes.nat$82954',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__2)
     => ( ( Vv__CANONICAL__2 = cCoq_2eInit_2eDatatypes_2eO
          & c_24__case__Coq_2eInit_2eDatatypes_2enat_2482954___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = Vv__CANONICAL__2 )
        | ? [Vvar__0___24Anonymous__82955] :
            ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__82955)
            & ( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__3)
             => ( Vv__CANONICAL__2 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__82955)
                & ( ( Vv__CANONICAL__3 = cCoq_2eInit_2eDatatypes_2eO
                    & c_24__case__Coq_2eInit_2eDatatypes_2enat_2482954___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = Vv__CANONICAL__2 )
                  | ? [Vvar__0___24Anonymous__82967] :
                      ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__82967)
                      & Vv__CANONICAL__3 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__82967)
                      & c_24__case__Coq_2eInit_2eDatatypes_2enat_2482954___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = c_24__fix__4781__v__CANONICAL__0___24a2(Vvar__0___24Anonymous__82955,Vvar__0___24Anonymous__82967) ) ) ) ) ) ) ) ).

fof('$_case_Coq.Init.Datatypes.nat$83048',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__2)
     => ( ( Vv__CANONICAL__2 = cCoq_2eInit_2eDatatypes_2eO
          & c_24__case__Coq_2eInit_2eDatatypes_2enat_2483048___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = cCoq_2eInit_2eDatatypes_2eO )
        | ? [Vvar__0___24Anonymous__83049] :
            ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__83049)
            & Vv__CANONICAL__2 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__83049)
            & c_24__case__Coq_2eInit_2eDatatypes_2enat_2483048___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = cCoq_2eInit_2eNat_2eadd___24a2(Vv__CANONICAL__3,c_24__fix__4858__v__CANONICAL__0___24a2(Vvar__0___24Anonymous__83049,Vv__CANONICAL__3)) ) ) ) ).

fof('$_case_Coq.Init.Datatypes.nat$83724',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__2)
     => ( ( Vv__CANONICAL__2 = cCoq_2eInit_2eDatatypes_2eO
          & c_24__case__Coq_2eInit_2eDatatypes_2enat_2483724___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = Vv__CANONICAL__3 )
        | ? [Vvar__0___24Anonymous__83725] :
            ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__83725)
            & Vv__CANONICAL__2 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__83725)
            & c_24__case__Coq_2eInit_2eDatatypes_2enat_2483724___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = cCoq_2eInit_2eDatatypes_2eS___24a1(c_24__fix__4648__v__CANONICAL__0___24a2(Vvar__0___24Anonymous__83725,Vv__CANONICAL__3)) ) ) ) ).

fof('$_case_Coq.Init.Datatypes.nat$83833',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__2)
     => ( ( Vv__CANONICAL__2 = cCoq_2eInit_2eDatatypes_2eO
          & c_24__case__Coq_2eInit_2eDatatypes_2enat_2483833___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = Vv__CANONICAL__2 )
        | ? [Vvar__0___24Anonymous__83834] :
            ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__83834)
            & ( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__3)
             => ( Vv__CANONICAL__2 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__83834)
                & ( ( Vv__CANONICAL__3 = cCoq_2eInit_2eDatatypes_2eO
                    & c_24__case__Coq_2eInit_2eDatatypes_2enat_2483833___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = Vv__CANONICAL__2 )
                  | ? [Vvar__0___24Anonymous__83846] :
                      ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__83846)
                      & Vv__CANONICAL__3 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__83846)
                      & c_24__case__Coq_2eInit_2eDatatypes_2enat_2483833___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = c_24__fix__4781__v__CANONICAL__0___24a2(Vvar__0___24Anonymous__83834,Vvar__0___24Anonymous__83846) ) ) ) ) ) ) ) ).

fof('$_case_Coq.Init.Datatypes.nat$83927',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__2)
     => ( ( Vv__CANONICAL__2 = cCoq_2eInit_2eDatatypes_2eO
          & c_24__case__Coq_2eInit_2eDatatypes_2enat_2483927___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = cCoq_2eInit_2eDatatypes_2eO )
        | ? [Vvar__0___24Anonymous__83928] :
            ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__83928)
            & Vv__CANONICAL__2 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__83928)
            & c_24__case__Coq_2eInit_2eDatatypes_2enat_2483927___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = cCoq_2eInit_2eNat_2eadd___24a2(Vv__CANONICAL__3,c_24__fix__4858__v__CANONICAL__0___24a2(Vvar__0___24Anonymous__83928,Vv__CANONICAL__3)) ) ) ) ).

fof('$_case_Coq.Init.Datatypes.prod$139550',axiom,
    ! [Vv__CANONICAL__0,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__139563___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__139555] :
                  ( t(Vvar__2___24Anonymous__139555,Vv__CANONICAL__2)
                  & ? [Vvar__3___24Anonymous__139556] :
                      ( t(Vvar__3___24Anonymous__139556,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__139555,Vvar__3___24Anonymous__139556)
                      & ( c_24__case__Coq_2eInit_2eDatatypes_2eprod_24139550___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__139555)),Vvar__3___24Anonymous__139556)))) ) ) ) ) ) ) ) ) ).

fof('$_case_Coq.Numbers.BinNums.Z$126290',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_24126295___24a1(Vv__CANONICAL__2) = cCoq_2eNumbers_2eBinNums_2eZ0
          & c_24__case__Coq_2eNumbers_2eBinNums_2eZ_24126290___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = cCoq_2eNumbers_2eBinNums_2eZ0 )
        | ? [Vvar__0___24Anonymous__126291] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__126291)
            & c_24__case__Coq_2eInit_2eDatatypes_2enat_24126295___24a1(Vv__CANONICAL__2) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__126291)
            & c_24__case__Coq_2eNumbers_2eBinNums_2eZ_24126290___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__126291) )
        | ? [Vvar__0___24Anonymous__126292] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__126292)
            & c_24__case__Coq_2eInit_2eDatatypes_2enat_24126295___24a1(Vv__CANONICAL__2) = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__126292)
            & c_24__case__Coq_2eNumbers_2eBinNums_2eZ_24126290___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__126292) ) ) ) ).

fof('$_case_Coq.Numbers.BinNums.positive$145139',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1] :
      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__1)
     => ( ? [Vvar__0___24Anonymous__145140] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__145140)
            & Vv__CANONICAL__1 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__145140)
            & c_24__case__Coq_2eNumbers_2eBinNums_2epositive_24145139___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = cCoq_2eNumbers_2eBinNums_2exO___24a1(c_24__fix__145155__v__CANONICAL__0___24a1(Vvar__0___24Anonymous__145140)) )
        | ? [Vvar__0___24Anonymous__145147] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__145147)
            & Vv__CANONICAL__1 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__145147)
            & c_24__case__Coq_2eNumbers_2eBinNums_2epositive_24145139___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__145147) )
        | ( Vv__CANONICAL__1 = cCoq_2eNumbers_2eBinNums_2exH
          & c_24__case__Coq_2eNumbers_2eBinNums_2epositive_24145139___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2eNumbers_2eBinNums_2exH) ) ) ) ).

fof('$_def_$_let_var_6_p_131809_131812',axiom,
    ! [V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__131808] : c_24__let__var__6__p__131809__131812___24a4(V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__131808) = cCoq_2esetoid__ring_2eRing__theory_2epow__pos___24a4(V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__131808) ).

fof('$_def_$_let_var_6_p_131811_131813',axiom,
    ! [V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__131810] : c_24__let__var__6__p__131811__131813___24a4(V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__131810) = cCoq_2esetoid__ring_2eRing__theory_2epow__pos___24a4(V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__131810) ).

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__5028] :
                  ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__5028)
                  & V2__m = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__5028)
                  & ( cCoq_2eArith_2eEqNat_2eeq__nat___24a2(V1__n,V2__m)
                  <=> p(c_24False) ) ) ) ) )
        | ? [Vvar__0___24Anonymous__5029] :
            ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__5029)
            & ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__m)
             => ( V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__5029)
                & ( ( V2__m = cCoq_2eInit_2eDatatypes_2eO
                    & ( cCoq_2eArith_2eEqNat_2eeq__nat___24a2(V1__n,V2__m)
                    <=> p(c_24False) ) )
                  | ? [Vvar__0___24Anonymous__5032] :
                      ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__5032)
                      & V2__m = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__5032)
                      & ( cCoq_2eArith_2eEqNat_2eeq__nat___24a2(V1__n,V2__m)
                      <=> cCoq_2eArith_2eEqNat_2eeq__nat___24a2(Vvar__0___24Anonymous__5029,Vvar__0___24Anonymous__5032) ) ) ) ) ) ) ) ) ).

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__7029___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__126229] :
            ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__126229)
            & V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__126229)
            & cCoq_2eArith_2ePlus_2etail__plus___24a2(V1__n,V2__m) = cCoq_2eArith_2ePlus_2etail__plus___24a2(Vvar__0___24Anonymous__126229,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.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__4089] :
            ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__4089)
            & V0__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__4089)
            & 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__4402] :
      ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(Vvar__4402)
    <=> cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__4402) ) ).

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__7106] :
            ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree___24t(Vvar__0___24Anonymous__7106)
            & ? [Vvar__1___24Anonymous__7107] :
                ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__1___24Anonymous__7107)
                & ? [Vvar__2___24Anonymous__7108] :
                    ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree___24t(Vvar__2___24Anonymous__7108)
                    & ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(V1__i)
                     => ( V2__m = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eNode___24a3(Vvar__0___24Anonymous__7106,Vvar__1___24Anonymous__7107,Vvar__2___24Anonymous__7108)
                        & ( ? [Vvar__0___24Anonymous__7121] :
                              ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__7121)
                              & V1__i = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__7121)
                              & cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2emem___24a2(V1__i,V2__m) = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2emem___24a2(Vvar__0___24Anonymous__7121,Vvar__2___24Anonymous__7108) )
                          | ? [Vvar__0___24Anonymous__7122] :
                              ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__7122)
                              & V1__i = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__7122)
                              & cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2emem___24a2(V1__i,V2__m) = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2emem___24a2(Vvar__0___24Anonymous__7122,Vvar__0___24Anonymous__7106) )
                          | ( V1__i = cCoq_2eNumbers_2eBinNums_2exH
                            & cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2emem___24a2(V1__i,V2__m) = Vvar__1___24Anonymous__7107 ) ) ) ) ) ) ) ) ) ).

fof('$_def_Coq.FSets.FSetPositive.PositiveSet.t',axiom,
    ! [Vvar__4403] :
      ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(Vvar__4403)
    <=> cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree___24t(Vvar__4403) ) ).

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__145730] :
      ( cCoq_2eInit_2eDatatypes_2eID___24t(Vvar__145730)
    <=> ! [V0__A] :
          ( cType___24t(V0__A)
         => ! [V1___24Anonymous] :
              ( t(V1___24Anonymous,V0__A)
             => t(happ(happ(Vvar__145730,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__5019] :
              ( t(Vvar__1___24Anonymous__5019,V0__A)
              & ? [Vvar__2___24Anonymous__5020] :
                  ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__5020)
                  & V2__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__5019,Vvar__2___24Anonymous__5020)
                  & cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V2__l,V3__m) = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__5019,cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,Vvar__2___24Anonymous__5020,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__1910] :
              ( t(Vvar__2___24Anonymous__1910,V0__A)
              & ? [Vvar__3___24Anonymous__1911] :
                  ( t(Vvar__3___24Anonymous__1911,V1__B)
                  & V2__p = cCoq_2eInit_2eDatatypes_2epair___24a4(V0__A,V1__B,Vvar__2___24Anonymous__1910,Vvar__3___24Anonymous__1911)
                  & cCoq_2eInit_2eDatatypes_2efst___24a3(V0__A,V1__B,V2__p) = Vvar__2___24Anonymous__1910 ) ) ) ) ) ).

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__1940] :
              ( t(Vvar__1___24Anonymous__1940,V0__A)
              & ? [Vvar__2___24Anonymous__1941] :
                  ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__1941)
                  & V2__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__1940,Vvar__2___24Anonymous__1941)
                  & cCoq_2eInit_2eDatatypes_2elength___24a2(V0__A,V2__l) = cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2elength___24a2(V0__A,Vvar__2___24Anonymous__1941)) ) ) ) ) ) ).

fof('$_def_Coq.Init.Datatypes.nat_rect',axiom,
    ! [V0__P,V1__f,V2__f,V4__n] :
      ( c_24__type__4983___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__4981] :
              ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__4981)
              & V4__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__4981)
              & cCoq_2eInit_2eDatatypes_2enat__rect___24a4(V0__P,V1__f,V2__f,V4__n) = happ(happ(V2__f,Vvar__0___24Anonymous__4981),cCoq_2eInit_2eDatatypes_2enat__rect___24a4(V0__P,V1__f,V2__f,Vvar__0___24Anonymous__4981)) ) ) ) ) ).

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__1922] :
              ( t(Vvar__2___24Anonymous__1922,V0__A)
              & ? [Vvar__3___24Anonymous__1923] :
                  ( t(Vvar__3___24Anonymous__1923,V1__B)
                  & V2__p = cCoq_2eInit_2eDatatypes_2epair___24a4(V0__A,V1__B,Vvar__2___24Anonymous__1922,Vvar__3___24Anonymous__1923)
                  & cCoq_2eInit_2eDatatypes_2esnd___24a3(V0__A,V1__B,V2__p) = Vvar__3___24Anonymous__1923 ) ) ) ) ) ).

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__145732] :
            ( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0___24Anonymous__145732)
            & V1__d = cCoq_2eInit_2eDecimal_2eD0___24a1(Vvar__0___24Anonymous__145732)
            & cCoq_2eInit_2eDecimal_2enzhead___24a1(V1__d) = cCoq_2eInit_2eDecimal_2enzhead___24a1(Vvar__0___24Anonymous__145732) )
        | ? [Vvar__0___24Anonymous__145733] :
            ( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0___24Anonymous__145733)
            & V1__d = cCoq_2eInit_2eDecimal_2eD1___24a1(Vvar__0___24Anonymous__145733)
            & cCoq_2eInit_2eDecimal_2enzhead___24a1(V1__d) = V1__d )
        | ? [Vvar__0___24Anonymous__145734] :
            ( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0___24Anonymous__145734)
            & V1__d = cCoq_2eInit_2eDecimal_2eD2___24a1(Vvar__0___24Anonymous__145734)
            & cCoq_2eInit_2eDecimal_2enzhead___24a1(V1__d) = V1__d )
        | ? [Vvar__0___24Anonymous__145735] :
            ( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0___24Anonymous__145735)
            & V1__d = cCoq_2eInit_2eDecimal_2eD3___24a1(Vvar__0___24Anonymous__145735)
            & cCoq_2eInit_2eDecimal_2enzhead___24a1(V1__d) = V1__d )
        | ? [Vvar__0___24Anonymous__145736] :
            ( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0___24Anonymous__145736)
            & V1__d = cCoq_2eInit_2eDecimal_2eD4___24a1(Vvar__0___24Anonymous__145736)
            & cCoq_2eInit_2eDecimal_2enzhead___24a1(V1__d) = V1__d )
        | ? [Vvar__0___24Anonymous__145737] :
            ( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0___24Anonymous__145737)
            & V1__d = cCoq_2eInit_2eDecimal_2eD5___24a1(Vvar__0___24Anonymous__145737)
            & cCoq_2eInit_2eDecimal_2enzhead___24a1(V1__d) = V1__d )
        | ? [Vvar__0___24Anonymous__145738] :
            ( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0___24Anonymous__145738)
            & V1__d = cCoq_2eInit_2eDecimal_2eD6___24a1(Vvar__0___24Anonymous__145738)
            & cCoq_2eInit_2eDecimal_2enzhead___24a1(V1__d) = V1__d )
        | ? [Vvar__0___24Anonymous__145739] :
            ( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0___24Anonymous__145739)
            & V1__d = cCoq_2eInit_2eDecimal_2eD7___24a1(Vvar__0___24Anonymous__145739)
            & cCoq_2eInit_2eDecimal_2enzhead___24a1(V1__d) = V1__d )
        | ? [Vvar__0___24Anonymous__145740] :
            ( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0___24Anonymous__145740)
            & V1__d = cCoq_2eInit_2eDecimal_2eD8___24a1(Vvar__0___24Anonymous__145740)
            & cCoq_2eInit_2eDecimal_2enzhead___24a1(V1__d) = V1__d )
        | ? [Vvar__0___24Anonymous__145741] :
            ( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0___24Anonymous__145741)
            & V1__d = cCoq_2eInit_2eDecimal_2eD9___24a1(Vvar__0___24Anonymous__145741)
            & 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__327] :
            ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__327)
            & V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__327)
            & cCoq_2eInit_2eNat_2eadd___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eNat_2eadd___24a2(Vvar__0___24Anonymous__327,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__2665] :
                  ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__2665)
                  & V2__m = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__2665)
                  & cCoq_2eInit_2eNat_2ecompare___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2eLt ) ) ) )
        | ? [Vvar__0___24Anonymous__2666] :
            ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__2666)
            & ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__m)
             => ( V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__2666)
                & ( ( V2__m = cCoq_2eInit_2eDatatypes_2eO
                    & cCoq_2eInit_2eNat_2ecompare___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2eGt )
                  | ? [Vvar__0___24Anonymous__2669] :
                      ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__2669)
                      & V2__m = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__2669)
                      & cCoq_2eInit_2eNat_2ecompare___24a2(V1__n,V2__m) = cCoq_2eInit_2eNat_2ecompare___24a2(Vvar__0___24Anonymous__2666,Vvar__0___24Anonymous__2669) ) ) ) ) ) ) ) ).

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__2714] :
            ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__2714)
            & ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__2714)
             => ( V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__2714)
                & ( ( Vvar__0___24Anonymous__2714 = cCoq_2eInit_2eDatatypes_2eO
                    & cCoq_2eInit_2eNat_2ediv2___24a1(V1__n) = cCoq_2eInit_2eDatatypes_2eO )
                  | ? [Vvar__0___24Anonymous__2717] :
                      ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__2717)
                      & Vvar__0___24Anonymous__2714 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__2717)
                      & cCoq_2eInit_2eNat_2ediv2___24a1(V1__n) = cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eNat_2ediv2___24a1(Vvar__0___24Anonymous__2717)) ) ) ) ) ) ) ) ).

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__521] :
                  ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__521)
                  & V2__m = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__521)
                  & cCoq_2eInit_2eNat_2eeqb___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) )
        | ? [Vvar__0___24Anonymous__522] :
            ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__522)
            & ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__m)
             => ( V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__522)
                & ( ( V2__m = cCoq_2eInit_2eDatatypes_2eO
                    & cCoq_2eInit_2eNat_2eeqb___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2efalse )
                  | ? [Vvar__0___24Anonymous__525] :
                      ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__525)
                      & V2__m = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__525)
                      & cCoq_2eInit_2eNat_2eeqb___24a2(V1__n,V2__m) = cCoq_2eInit_2eNat_2eeqb___24a2(Vvar__0___24Anonymous__522,Vvar__0___24Anonymous__525) ) ) ) ) ) ) ) ).

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__2686] :
            ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__2686)
            & ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__2686)
             => ( V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__2686)
                & ( ( Vvar__0___24Anonymous__2686 = cCoq_2eInit_2eDatatypes_2eO
                    & cCoq_2eInit_2eNat_2eeven___24a1(V1__n) = cCoq_2eInit_2eDatatypes_2efalse )
                  | ? [Vvar__0___24Anonymous__2689] :
                      ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__2689)
                      & Vvar__0___24Anonymous__2686 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__2689)
                      & cCoq_2eInit_2eNat_2eeven___24a1(V1__n) = cCoq_2eInit_2eNat_2eeven___24a1(Vvar__0___24Anonymous__2689) ) ) ) ) ) ) ) ).

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__332] :
            ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__332)
            & ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__m)
             => ( V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__332)
                & ( ( V2__m = cCoq_2eInit_2eDatatypes_2eO
                    & cCoq_2eInit_2eNat_2eleb___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2efalse )
                  | ? [Vvar__0___24Anonymous__335] :
                      ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__335)
                      & V2__m = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__335)
                      & cCoq_2eInit_2eNat_2eleb___24a2(V1__n,V2__m) = cCoq_2eInit_2eNat_2eleb___24a2(Vvar__0___24Anonymous__332,Vvar__0___24Anonymous__335) ) ) ) ) ) ) ) ).

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__14685] :
            ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__14685)
            & ( cCoq_2eInit_2eDatatypes_2enat___24t(V4__r)
             => ( V1__k = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__14685)
                & ( ( 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__14685,cCoq_2eInit_2eDatatypes_2eS___24a1(V2__p),cCoq_2eInit_2eDatatypes_2eS___24a1(V3__q),V3__q) )
                  | ? [Vvar__0___24Anonymous__14688] :
                      ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__14688)
                      & V4__r = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__14688)
                      & cCoq_2eInit_2eNat_2elog2__iter___24a4(V1__k,V2__p,V3__q,V4__r) = cCoq_2eInit_2eNat_2elog2__iter___24a4(Vvar__0___24Anonymous__14685,V2__p,cCoq_2eInit_2eDatatypes_2eS___24a1(V3__q),Vvar__0___24Anonymous__14688) ) ) ) ) ) ) ) ).

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__2674] :
            ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__2674)
            & ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__m)
             => ( V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__2674)
                & ( ( V2__m = cCoq_2eInit_2eDatatypes_2eO
                    & cCoq_2eInit_2eNat_2emax___24a2(V1__n,V2__m) = V1__n )
                  | ? [Vvar__0___24Anonymous__2677] :
                      ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__2677)
                      & V2__m = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__2677)
                      & cCoq_2eInit_2eNat_2emax___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eNat_2emax___24a2(Vvar__0___24Anonymous__2674,Vvar__0___24Anonymous__2677)) ) ) ) ) ) ) ) ).

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__2680] :
            ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__2680)
            & ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__m)
             => ( V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__2680)
                & ( ( V2__m = cCoq_2eInit_2eDatatypes_2eO
                    & cCoq_2eInit_2eNat_2emin___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2eO )
                  | ? [Vvar__0___24Anonymous__2683] :
                      ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__2683)
                      & V2__m = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__2683)
                      & cCoq_2eInit_2eNat_2emin___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eNat_2emin___24a2(Vvar__0___24Anonymous__2680,Vvar__0___24Anonymous__2683)) ) ) ) ) ) ) ) ).

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__680] :
            ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__680)
            & V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__680)
            & cCoq_2eInit_2eNat_2emul___24a2(V1__n,V2__m) = cCoq_2eInit_2eNat_2eadd___24a2(V2__m,cCoq_2eInit_2eNat_2emul___24a2(Vvar__0___24Anonymous__680,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__2691] :
            ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__2691)
            & V2__m = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__2691)
            & 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__2691)) ) ) ) ).

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__2663] :
            ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__2663)
            & V0__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__2663)
            & cCoq_2eInit_2eNat_2epred___24a1(V0__n) = Vvar__0___24Anonymous__2663 ) ) ) ).

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__80951] :
            ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__80951)
            & ( cCoq_2eInit_2eDatatypes_2enat___24t(V4__r)
             => ( V1__k = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__80951)
                & ( ( 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__80951,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__80954] :
                      ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__80954)
                      & V4__r = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__80954)
                      & cCoq_2eInit_2eNat_2esqrt__iter___24a4(V1__k,V2__p,V3__q,V4__r) = cCoq_2eInit_2eNat_2esqrt__iter___24a4(Vvar__0___24Anonymous__80951,V2__p,V3__q,Vvar__0___24Anonymous__80954) ) ) ) ) ) ) ) ).

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__683] :
            ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__683)
            & ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__m)
             => ( V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__683)
                & ( ( V2__m = cCoq_2eInit_2eDatatypes_2eO
                    & cCoq_2eInit_2eNat_2esub___24a2(V1__n,V2__m) = V1__n )
                  | ? [Vvar__0___24Anonymous__686] :
                      ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__686)
                      & V2__m = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__686)
                      & cCoq_2eInit_2eNat_2esub___24a2(V1__n,V2__m) = cCoq_2eInit_2eNat_2esub___24a2(Vvar__0___24Anonymous__683,Vvar__0___24Anonymous__686) ) ) ) ) ) ) ) ).

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

fof('$_def_Coq.Init.Nat.t',axiom,
    ! [Vvar__125127] :
      ( cCoq_2eInit_2eNat_2et___24t(Vvar__125127)
    <=> cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__125127) ) ).

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__125129] :
            ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__125129)
            & V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__125129)
            & cCoq_2eInit_2eNat_2etail__add___24a2(V1__n,V2__m) = cCoq_2eInit_2eNat_2etail__add___24a2(Vvar__0___24Anonymous__125129,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__2719] :
            ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__2719)
            & V2__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__2719)
            & cCoq_2eInit_2eNat_2etestbit___24a2(V1__a,V2__n) = cCoq_2eInit_2eNat_2etestbit___24a2(cCoq_2eInit_2eNat_2ediv2___24a1(V1__a),Vvar__0___24Anonymous__2719) ) ) ) ).

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__126227] :
            ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__126227)
            & V0__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__126227)
            & ( 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__6855___24t(V0__A,V1__P,V1__P)
       => ( cCoq_2eInit_2eSpecif_2esig___24t(V0__A,V1__P,V2__e)
         => ? [Vvar__2__x__6849] :
              ( t(Vvar__2__x__6849,V0__A)
              & p(happ(V1__P,Vvar__2__x__6849))
              & V2__e = cCoq_2eInit_2eSpecif_2eexist___24a3(V0__A,V1__P,Vvar__2__x__6849)
              & cCoq_2eInit_2eSpecif_2eproj1__sig___24a3(V0__A,V1__P,V2__e) = Vvar__2__x__6849 ) ) ) ) ).

fof('$_def_Coq.Init.Specif.projT1',axiom,
    ! [V0__A,V1__P,V2__x] :
      ( cType___24t(V0__A)
     => ( c_24__type__139754___24t(V0__A,V1__P,V1__P)
       => ( cCoq_2eInit_2eSpecif_2esigT___24t(V0__A,V1__P,V2__x)
         => ? [Vvar__2__x__139748] :
              ( t(Vvar__2__x__139748,V0__A)
              & ? [Vvar__3___24Anonymous__139749] :
                  ( t(Vvar__3___24Anonymous__139749,happ(V1__P,Vvar__2__x__139748))
                  & V2__x = cCoq_2eInit_2eSpecif_2eexistT___24a4(V0__A,V1__P,Vvar__2__x__139748,Vvar__3___24Anonymous__139749)
                  & cCoq_2eInit_2eSpecif_2eprojT1___24a3(V0__A,V1__P,V2__x) = Vvar__2__x__139748 ) ) ) ) ) ).

fof('$_def_Coq.Init.Wf.well_founded',axiom,
    ! [V0__A,V1__R] :
      ( cCoq_2eInit_2eWf_2ewell__founded___24a2(V0__A,V1__R)
    <=> ! [V2__a] :
          ( t(V2__a,V0__A)
         => cCoq_2eInit_2eWf_2eAcc___24a3(V0__A,V1__R,V2__a) ) ) ).

fof('$_def_Coq.Lists.List.In',axiom,
    ! [V0__A,V2__a,V3__l] :
      ( cType___24t(V0__A)
     => ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l)
       => ( ( V3__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)
            & ( cCoq_2eLists_2eList_2eIn___24a3(V0__A,V2__a,V3__l)
            <=> p(c_24False) ) )
          | ? [Vvar__1___24Anonymous__2570] :
              ( t(Vvar__1___24Anonymous__2570,V0__A)
              & ? [Vvar__2___24Anonymous__2571] :
                  ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__2571)
                  & V3__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__2570,Vvar__2___24Anonymous__2571)
                  & ( cCoq_2eLists_2eList_2eIn___24a3(V0__A,V2__a,V3__l)
                  <=> ( Vvar__1___24Anonymous__2570 = V2__a
                      | cCoq_2eLists_2eList_2eIn___24a3(V0__A,V2__a,Vvar__2___24Anonymous__2571) ) ) ) ) ) ) ) ).

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__5063] :
                ( t(Vvar__1___24Anonymous__5063,V1__B)
                & ? [Vvar__2___24Anonymous__5064] :
                    ( cCoq_2eInit_2eDatatypes_2elist___24t(V1__B,Vvar__2___24Anonymous__5064)
                    & V4__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V1__B,Vvar__1___24Anonymous__5063,Vvar__2___24Anonymous__5064)
                    & 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__5064,happ(happ(V2__f,V5__a0),Vvar__1___24Anonymous__5063)) ) ) ) ) ) ) ).

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__125055] :
                ( t(Vvar__1___24Anonymous__125055,V1__B)
                & ? [Vvar__2___24Anonymous__125056] :
                    ( cCoq_2eInit_2eDatatypes_2elist___24t(V1__B,Vvar__2___24Anonymous__125056)
                    & V5__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V1__B,Vvar__1___24Anonymous__125055,Vvar__2___24Anonymous__125056)
                    & cCoq_2eLists_2eList_2efold__right___24a5(V0__A,V1__B,V2__f,V3__a0,V5__l) = happ(happ(V2__f,Vvar__1___24Anonymous__125055),cCoq_2eLists_2eList_2efold__right___24a5(V0__A,V1__B,V2__f,V3__a0,Vvar__2___24Anonymous__125056)) ) ) ) ) ) ) ).

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__147109] :
              ( t(Vvar__1___24Anonymous__147109,V0__A)
              & ? [Vvar__2___24Anonymous__147110] :
                  ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__147110)
                  & V2__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__147109,Vvar__2___24Anonymous__147110)
                  & cCoq_2eLists_2eList_2ehd___24a3(V0__A,V1__default,V2__l) = Vvar__1___24Anonymous__147109 ) ) ) ) ) ).

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__152537] :
              ( t(Vvar__1___24Anonymous__152537,V0__A)
              & ? [Vvar__2___24Anonymous__152538] :
                  ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__152538)
                  & ( cType___24t(V0__A)
                   => ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__152538)
                     => ( V2__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__152537,Vvar__2___24Anonymous__152538)
                        & ( ( Vvar__2___24Anonymous__152538 = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)
                            & cCoq_2eLists_2eList_2elast___24a3(V0__A,V2__l,V3__d) = Vvar__1___24Anonymous__152537 )
                          | ? [Vvar__1___24Anonymous__152549] :
                              ( t(Vvar__1___24Anonymous__152549,V0__A)
                              & ? [Vvar__2___24Anonymous__152550] :
                                  ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__152550)
                                  & Vvar__2___24Anonymous__152538 = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__152549,Vvar__2___24Anonymous__152550)
                                  & cCoq_2eLists_2eList_2elast___24a3(V0__A,V2__l,V3__d) = cCoq_2eLists_2eList_2elast___24a3(V0__A,Vvar__2___24Anonymous__152538,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__5038] :
                      ( t(Vvar__1___24Anonymous__5038,V0__A)
                      & ? [Vvar__2___24Anonymous__5039] :
                          ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__5039)
                          & V3__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__5038,Vvar__2___24Anonymous__5039)
                          & cCoq_2eLists_2eList_2enth___24a4(V0__A,V2__n,V3__l,V4__default) = Vvar__1___24Anonymous__5038 ) ) ) ) ) )
          | ? [Vvar__0___24Anonymous__5041] :
              ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__5041)
              & ( cType___24t(V0__A)
               => ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l)
                 => ( V2__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__5041)
                    & ( ( 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__5048] :
                          ( t(Vvar__1___24Anonymous__5048,V0__A)
                          & ? [Vvar__2___24Anonymous__5049] :
                              ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__5049)
                              & V3__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__5048,Vvar__2___24Anonymous__5049)
                              & cCoq_2eLists_2eList_2enth___24a4(V0__A,V2__n,V3__l,V4__default) = cCoq_2eLists_2eList_2enth___24a4(V0__A,Vvar__0___24Anonymous__5041,Vvar__2___24Anonymous__5049,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__155067] :
              ( t(Vvar__1___24Anonymous__155067,V0__A)
              & ? [Vvar__2___24Anonymous__155068] :
                  ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__155068)
                  & V1__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__155067,Vvar__2___24Anonymous__155068)
                  & cCoq_2eLists_2eList_2etl___24a2(V0__A,V1__l) = Vvar__2___24Anonymous__155068 ) ) ) ) ) ).

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

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

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

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

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

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

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

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

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

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

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

fof('$_def_Coq.NArith.BinNat.N.recursion',axiom,
    ! [V0__A] : cCoq_2eNArith_2eBinNat_2eN_2erecursion___24a1(V0__A) = cCoq_2eNArith_2eBinNat_2eN_2epeano__rect___24a1(c_24__lam__152854___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__4120] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__4120)
            & ( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
             => ( V0__n = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__4120)
                & ( ( V1__m = cCoq_2eNumbers_2eBinNums_2eN0
                    & cCoq_2eNArith_2eBinNatDef_2eN_2eadd___24a2(V0__n,V1__m) = V0__n )
                  | ? [Vvar__0___24Anonymous__4123] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__4123)
                      & V1__m = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__4123)
                      & cCoq_2eNArith_2eBinNatDef_2eN_2eadd___24a2(V0__n,V1__m) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(Vvar__0___24Anonymous__4120,Vvar__0___24Anonymous__4123)) ) ) ) ) ) ) ) ).

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__135995] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__135995)
            & ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__135995)
             => ( V0__n = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__135995)
                & ( ? [Vvar__0___24Anonymous__135999] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__135999)
                      & Vvar__0___24Anonymous__135995 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__135999)
                      & cCoq_2eNArith_2eBinNatDef_2eN_2ediv2___24a1(V0__n) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__135999) )
                  | ? [Vvar__0___24Anonymous__136000] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__136000)
                      & Vvar__0___24Anonymous__135995 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__136000)
                      & cCoq_2eNArith_2eBinNatDef_2eN_2ediv2___24a1(V0__n) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__136000) )
                  | ( Vvar__0___24Anonymous__135995 = 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__7010] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__7010)
            & V0__n = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__7010)
            & cCoq_2eNArith_2eBinNatDef_2eN_2edouble___24a1(V0__n) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__7010)) ) ) ) ).

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__4133] :
                  ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__4133)
                  & V2__m = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__4133)
                  & cCoq_2eNArith_2eBinNatDef_2eN_2eeqb___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) )
        | ? [Vvar__0___24Anonymous__4134] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__4134)
            & ( cCoq_2eNumbers_2eBinNums_2eN___24t(V2__m)
             => ( V1__n = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__4134)
                & ( ( V2__m = cCoq_2eNumbers_2eBinNums_2eN0
                    & cCoq_2eNArith_2eBinNatDef_2eN_2eeqb___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2efalse )
                  | ? [Vvar__0___24Anonymous__4137] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__4137)
                      & V2__m = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__4137)
                      & cCoq_2eNArith_2eBinNatDef_2eN_2eeqb___24a2(V1__n,V2__m) = cCoq_2ePArith_2eBinPosDef_2ePos_2eeqb___24a2(Vvar__0___24Anonymous__4134,Vvar__0___24Anonymous__4137) ) ) ) ) ) ) ) ).

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__149945] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__149945)
            & ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__149945)
             => ( V0__n = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__149945)
                & ( ? [Vvar__0___24Anonymous__149949] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__149949)
                      & Vvar__0___24Anonymous__149945 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__149949)
                      & cCoq_2eNArith_2eBinNatDef_2eN_2eeven___24a1(V0__n) = cCoq_2eInit_2eDatatypes_2efalse )
                  | ? [Vvar__0___24Anonymous__149950] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__149950)
                      & Vvar__0___24Anonymous__149945 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__149950)
                      & cCoq_2eNArith_2eBinNatDef_2eN_2eeven___24a1(V0__n) = cCoq_2eInit_2eDatatypes_2etrue )
                  | ( Vvar__0___24Anonymous__149945 = cCoq_2eNumbers_2eBinNums_2exH
                    & cCoq_2eNArith_2eBinNatDef_2eN_2eeven___24a1(V0__n) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ) ) ) ).

fof('$_def_Coq.NArith.BinNatDef.N.lxor',axiom,
    ! [V0__n,V1__m] :
      ( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
     => ( ( V0__n = cCoq_2eNumbers_2eBinNums_2eN0
          & cCoq_2eNArith_2eBinNatDef_2eN_2elxor___24a2(V0__n,V1__m) = V1__m )
        | ? [Vvar__0___24Anonymous__145051] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__145051)
            & ( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
             => ( V0__n = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__145051)
                & ( ( V1__m = cCoq_2eNumbers_2eBinNums_2eN0
                    & cCoq_2eNArith_2eBinNatDef_2eN_2elxor___24a2(V0__n,V1__m) = V0__n )
                  | ? [Vvar__0___24Anonymous__145054] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__145054)
                      & V1__m = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__145054)
                      & cCoq_2eNArith_2eBinNatDef_2eN_2elxor___24a2(V0__n,V1__m) = cCoq_2ePArith_2eBinPosDef_2ePos_2elxor___24a2(Vvar__0___24Anonymous__145051,Vvar__0___24Anonymous__145054) ) ) ) ) ) ) ) ).

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__4127] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__4127)
            & ( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
             => ( V0__n = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__4127)
                & ( ( V1__m = cCoq_2eNumbers_2eBinNums_2eN0
                    & cCoq_2eNArith_2eBinNatDef_2eN_2emul___24a2(V0__n,V1__m) = cCoq_2eNumbers_2eBinNums_2eN0 )
                  | ? [Vvar__0___24Anonymous__4130] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__4130)
                      & V1__m = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__4130)
                      & cCoq_2eNArith_2eBinNatDef_2eN_2emul___24a2(V0__n,V1__m) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2emul___24a2(Vvar__0___24Anonymous__4127,Vvar__0___24Anonymous__4130)) ) ) ) ) ) ) ) ).

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__7012] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__7012)
            & V0__n = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__7012)
            & cCoq_2eNArith_2eBinNatDef_2eN_2epred___24a1(V0__n) = cCoq_2ePArith_2eBinPosDef_2ePos_2epred__N___24a1(Vvar__0___24Anonymous__7012) ) ) ) ).

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__7011] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__7011)
            & V0__n = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__7011)
            & cCoq_2eNArith_2eBinNatDef_2eN_2esucc___24a1(V0__n) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2esucc___24a1(Vvar__0___24Anonymous__7011)) ) ) ) ).

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__155452] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__155452)
            & V0__n = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__155452)
            & cCoq_2eNArith_2eBinNatDef_2eN_2esucc__pos___24a1(V0__n) = cCoq_2ePArith_2eBinPosDef_2ePos_2esucc___24a1(Vvar__0___24Anonymous__155452) ) ) ) ).

fof('$_def_Coq.NArith.BinNatDef.N.t',axiom,
    ! [Vvar__149944] :
      ( cCoq_2eNArith_2eBinNatDef_2eN_2et___24t(Vvar__149944)
    <=> cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__149944) ) ).

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__145056] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__145056)
            & V0__a = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__145056)
            & cCoq_2eNArith_2eBinNatDef_2eN_2etestbit___24a2(V0__a,V1__n) = cCoq_2ePArith_2eBinPosDef_2ePos_2etestbit___24a2(Vvar__0___24Anonymous__145056,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__7024] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__7024)
            & V0__a = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__7024)
            & cCoq_2eNArith_2eBinNatDef_2eN_2eto__nat___24a1(V0__a) = cCoq_2ePArith_2eBinPosDef_2ePos_2eto__nat___24a1(Vvar__0___24Anonymous__7024) ) ) ) ).

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__136019] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__136019)
            & V0__p = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__136019)
            & cCoq_2ePArith_2eBinPosDef_2ePos_2ediv2___24a1(V0__p) = Vvar__0___24Anonymous__136019 )
        | ? [Vvar__0___24Anonymous__136020] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__136020)
            & V0__p = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__136020)
            & cCoq_2ePArith_2eBinPosDef_2ePos_2ediv2___24a1(V0__p) = Vvar__0___24Anonymous__136020 )
        | ( V0__p = cCoq_2eNumbers_2eBinNums_2exH
          & cCoq_2ePArith_2eBinPosDef_2ePos_2ediv2___24a1(V0__p) = cCoq_2eNumbers_2eBinNums_2exH ) ) ) ).

fof('$_def_Coq.PArith.BinPosDef.Pos.eqb',axiom,
    ! [V1__p,V2__q] :
      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__p)
     => ( ? [Vvar__0___24Anonymous__145181] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__145181)
            & ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V2__q)
             => ( V1__p = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__145181)
                & ( ? [Vvar__0___24Anonymous__145185] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__145185)
                      & V2__q = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__145185)
                      & cCoq_2ePArith_2eBinPosDef_2ePos_2eeqb___24a2(V1__p,V2__q) = cCoq_2ePArith_2eBinPosDef_2ePos_2eeqb___24a2(Vvar__0___24Anonymous__145181,Vvar__0___24Anonymous__145185) )
                  | ? [Vvar__0___24Anonymous__145186] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__145186)
                      & V2__q = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__145186)
                      & 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__145187] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__145187)
            & ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V2__q)
             => ( V1__p = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__145187)
                & ( ? [Vvar__0___24Anonymous__145191] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__145191)
                      & V2__q = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__145191)
                      & cCoq_2ePArith_2eBinPosDef_2ePos_2eeqb___24a2(V1__p,V2__q) = cCoq_2eInit_2eDatatypes_2efalse )
                  | ? [Vvar__0___24Anonymous__145192] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__145192)
                      & V2__q = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__145192)
                      & cCoq_2ePArith_2eBinPosDef_2ePos_2eeqb___24a2(V1__p,V2__q) = cCoq_2ePArith_2eBinPosDef_2ePos_2eeqb___24a2(Vvar__0___24Anonymous__145187,Vvar__0___24Anonymous__145192) )
                  | ( 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__145193] :
                  ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__145193)
                  & V2__q = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__145193)
                  & cCoq_2ePArith_2eBinPosDef_2ePos_2eeqb___24a2(V1__p,V2__q) = cCoq_2eInit_2eDatatypes_2efalse )
              | ? [Vvar__0___24Anonymous__145194] :
                  ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__145194)
                  & V2__q = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__145194)
                  & 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__136007] :
              ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__136007)
              & V4__n = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__136007)
              & 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__136007),Vvar__0___24Anonymous__136007)) )
          | ? [Vvar__0___24Anonymous__136008] :
              ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__136008)
              & V4__n = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__136008)
              & 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__136008),Vvar__0___24Anonymous__136008) )
          | ( 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__7072] :
              ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__7072)
              & V3__p = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__7072)
              & 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__7072,happ(happ(V1__op,V4__a),V4__a))) )
          | ? [Vvar__0___24Anonymous__7073] :
              ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__7073)
              & V3__p = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__7073)
              & 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__7073,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__4385] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__4385)
            & V1__x = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__4385)
            & 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__4385,V2__y))) )
        | ? [Vvar__0___24Anonymous__4386] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__4386)
            & V1__x = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__4386)
            & cCoq_2ePArith_2eBinPosDef_2ePos_2emul___24a2(V1__x,V2__y) = cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2emul___24a2(Vvar__0___24Anonymous__4386,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__4394] :
            ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__4394)
            & ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__4394)
             => ( V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__4394)
                & ( ( Vvar__0___24Anonymous__4394 = cCoq_2eInit_2eDatatypes_2eO
                    & cCoq_2ePArith_2eBinPosDef_2ePos_2eof__nat___24a1(V1__n) = cCoq_2eNumbers_2eBinNums_2exH )
                  | ? [Vvar__0___24Anonymous__4397] :
                      ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__4397)
                      & Vvar__0___24Anonymous__4394 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__4397)
                      & 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__4394)) ) ) ) ) ) ) ) ).

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__4401] :
            ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__4401)
            & V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__4401)
            & 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__4401)) ) ) ) ).

fof('$_def_Coq.PArith.BinPosDef.Pos.size',axiom,
    ! [V1__p] :
      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__p)
     => ( ? [Vvar__0___24Anonymous__155385] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__155385)
            & V1__p = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__155385)
            & cCoq_2ePArith_2eBinPosDef_2ePos_2esize___24a1(V1__p) = cCoq_2ePArith_2eBinPosDef_2ePos_2esucc___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2esize___24a1(Vvar__0___24Anonymous__155385)) )
        | ? [Vvar__0___24Anonymous__155386] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__155386)
            & V1__p = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__155386)
            & cCoq_2ePArith_2eBinPosDef_2ePos_2esize___24a1(V1__p) = cCoq_2ePArith_2eBinPosDef_2ePos_2esucc___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2esize___24a1(Vvar__0___24Anonymous__155386)) )
        | ( 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__7069] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__7069)
            & V1__p = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__7069)
            & cCoq_2ePArith_2eBinPosDef_2ePos_2esize__nat___24a1(V1__p) = cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2esize__nat___24a1(Vvar__0___24Anonymous__7069)) )
        | ? [Vvar__0___24Anonymous__7070] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__7070)
            & V1__p = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__7070)
            & cCoq_2ePArith_2eBinPosDef_2ePos_2esize__nat___24a1(V1__p) = cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2esize__nat___24a1(Vvar__0___24Anonymous__7070)) )
        | ( 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__4382] :
              ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__4382)
              & cCoq_2ePArith_2eBinPosDef_2ePos_2esub__mask___24a2(V0__x,V1__y) = cCoq_2ePArith_2eBinPosDef_2ePos_2eIsPos___24a1(Vvar__0___24Anonymous__4382)
              & cCoq_2ePArith_2eBinPosDef_2ePos_2esub___24a2(V0__x,V1__y) = Vvar__0___24Anonymous__4382 )
          | ( 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__4348] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__4348)
            & V1__x = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__4348)
            & cCoq_2ePArith_2eBinPosDef_2ePos_2esucc___24a1(V1__x) = cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2esucc___24a1(Vvar__0___24Anonymous__4348)) )
        | ? [Vvar__0___24Anonymous__4349] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__4349)
            & V1__x = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__4349)
            & cCoq_2ePArith_2eBinPosDef_2ePos_2esucc___24a1(V1__x) = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__4349) )
        | ( 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__150038] :
      ( cCoq_2ePArith_2eBinPosDef_2ePos_2et___24t(Vvar__150038)
    <=> cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__150038) ) ).

fof('$_def_Coq.PArith.BinPosDef.Pos.testbit_nat',axiom,
    ! [V1__p] :
      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__p)
     => ( ? [Vvar__0___24Anonymous__83177] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__83177)
            & V1__p = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__83177)
            & cCoq_2ePArith_2eBinPosDef_2ePos_2etestbit__nat___24a1(V1__p) = c_24__lam__83190___24a1(Vvar__0___24Anonymous__83177) )
        | ? [Vvar__0___24Anonymous__83181] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__83181)
            & V1__p = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__83181)
            & cCoq_2ePArith_2eBinPosDef_2ePos_2etestbit__nat___24a1(V1__p) = c_24__lam__83197___24a1(Vvar__0___24Anonymous__83181) )
        | ( V1__p = cCoq_2eNumbers_2eBinNums_2exH
          & cCoq_2ePArith_2eBinPosDef_2ePos_2etestbit__nat___24a1(V1__p) = c_24__lam__83201 ) ) ) ).

fof('$_def_Coq.QArith.QArith_base.Qden',axiom,
    ! [V0__q] :
      ( cCoq_2eQArith_2eQArith__base_2eQ___24t(V0__q)
     => ? [Vvar__0__Qnum__126239] :
          ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__0__Qnum__126239)
          & ? [Vvar__1__Qden__126240] :
              ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1__Qden__126240)
              & V0__q = cCoq_2eQArith_2eQArith__base_2eQmake___24a2(Vvar__0__Qnum__126239,Vvar__1__Qden__126240)
              & cCoq_2eQArith_2eQArith__base_2eQden___24a1(V0__q) = Vvar__1__Qden__126240 ) ) ) ).

fof('$_def_Coq.QArith.QArith_base.Qnum',axiom,
    ! [V0__q] :
      ( cCoq_2eQArith_2eQArith__base_2eQ___24t(V0__q)
     => ? [Vvar__0__Qnum__126234] :
          ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__0__Qnum__126234)
          & ? [Vvar__1__Qden__126235] :
              ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1__Qden__126235)
              & V0__q = cCoq_2eQArith_2eQArith__base_2eQmake___24a2(Vvar__0__Qnum__126234,Vvar__1__Qden__126235)
              & cCoq_2eQArith_2eQArith__base_2eQnum___24a1(V0__q) = Vvar__0__Qnum__126234 ) ) ) ).

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__2856] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__2856)
            & V0__z = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__2856)
            & cCoq_2eReals_2eRdefinitions_2eIZR___24a1(V0__z) = cCoq_2eReals_2eRdefinitions_2eIPR___24a1(Vvar__0___24Anonymous__2856) )
        | ? [Vvar__0___24Anonymous__2857] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__2857)
            & V0__z = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__2857)
            & cCoq_2eReals_2eRdefinitions_2eIZR___24a1(V0__z) = cCoq_2eReals_2eRdefinitions_2eRopp___24a1(cCoq_2eReals_2eRdefinitions_2eIPR___24a1(Vvar__0___24Anonymous__2857)) ) ) ) ).

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

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

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

fof('$_def_Coq.Relations.Relation_Definitions.relation',axiom,
    ! [V0__A] : cCoq_2eRelations_2eRelation__Definitions_2erelation___24a1(V0__A) = c_24__type__2863___24a1(V0__A) ).

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

fof('$_def_Coq.Sets.Relations_1.Relation',axiom,
    ! [V0__U] : cCoq_2eSets_2eRelations__1_2eRelation___24a1(V0__U) = c_24__type__2863___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__146997___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__146997___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__149954] :
      ( cCoq_2eStructures_2eOrderedTypeEx_2eN__as__OT_2et___24t(Vvar__149954)
    <=> cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__149954) ) ).

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__123931] :
      ( cCoq_2eStructures_2eOrderedTypeEx_2eNat__as__OT_2et___24t(Vvar__123931)
    <=> cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__123931) ) ).

fof('$_def_Coq.Structures.OrderedTypeEx.PositiveOrderedTypeBits.bits_lt',axiom,
    ! [V1__p,V2__q] :
      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__p)
     => ( ? [Vvar__0___24Anonymous__150041] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__150041)
            & ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V2__q)
             => ( V1__p = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__150041)
                & ( ? [Vvar__0___24Anonymous__150045] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__150045)
                      & V2__q = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__150045)
                      & ( cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2ebits__lt___24a2(V1__p,V2__q)
                      <=> cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2ebits__lt___24a2(Vvar__0___24Anonymous__150041,Vvar__0___24Anonymous__150045) ) )
                  | ? [Vvar__0___24Anonymous__150046] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__150046)
                      & V2__q = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__150046)
                      & ( 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__150047] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__150047)
            & ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V2__q)
             => ( V1__p = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__150047)
                & ( ? [Vvar__0___24Anonymous__150051] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__150051)
                      & V2__q = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__150051)
                      & ( cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2ebits__lt___24a2(V1__p,V2__q)
                      <=> p(c_24True) ) )
                  | ? [Vvar__0___24Anonymous__150052] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__150052)
                      & V2__q = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__150052)
                      & ( cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2ebits__lt___24a2(V1__p,V2__q)
                      <=> cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2ebits__lt___24a2(Vvar__0___24Anonymous__150047,Vvar__0___24Anonymous__150052) ) )
                  | ( 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__150053] :
                  ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__150053)
                  & V2__q = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__150053)
                  & ( cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2ebits__lt___24a2(V1__p,V2__q)
                  <=> p(c_24True) ) )
              | ? [Vvar__0___24Anonymous__150054] :
                  ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__150054)
                  & V2__q = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__150054)
                  & ( 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__150039] :
      ( cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2et___24t(Vvar__150039)
    <=> cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__150039) ) ).

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__150060] :
      ( cCoq_2eStructures_2eOrderedTypeEx_2ePositive__as__OT_2et___24t(Vvar__150060)
    <=> cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__150060) ) ).

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__123994] :
      ( cCoq_2eStructures_2eOrderedTypeEx_2eString__as__OT_2et___24t(Vvar__123994)
    <=> cCoq_2eStrings_2eString_2estring___24t(Vvar__123994) ) ).

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__150117] :
      ( cCoq_2eStructures_2eOrderedTypeEx_2eZ__as__OT_2et___24t(Vvar__150117)
    <=> cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__150117) ) ).

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__7204] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__7204)
            & V0__z = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__7204)
            & cCoq_2eZArith_2eBinIntDef_2eZ_2eabs___24a1(V0__z) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__7204) )
        | ? [Vvar__0___24Anonymous__7205] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__7205)
            & V0__z = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__7205)
            & cCoq_2eZArith_2eBinIntDef_2eZ_2eabs___24a1(V0__z) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__7205) ) ) ) ).

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__83514] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__83514)
            & V0__z = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__83514)
            & cCoq_2eZArith_2eBinIntDef_2eZ_2eabs__N___24a1(V0__z) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__83514) )
        | ? [Vvar__0___24Anonymous__83515] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__83515)
            & V0__z = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__83515)
            & cCoq_2eZArith_2eBinIntDef_2eZ_2eabs__N___24a1(V0__z) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__83515) ) ) ) ).

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__4443] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__4443)
            & V0__z = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__4443)
            & cCoq_2eZArith_2eBinIntDef_2eZ_2eabs__nat___24a1(V0__z) = cCoq_2ePArith_2eBinPosDef_2ePos_2eto__nat___24a1(Vvar__0___24Anonymous__4443) )
        | ? [Vvar__0___24Anonymous__4444] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__4444)
            & V0__z = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__4444)
            & cCoq_2eZArith_2eBinIntDef_2eZ_2eabs__nat___24a1(V0__z) = cCoq_2ePArith_2eBinPosDef_2ePos_2eto__nat___24a1(Vvar__0___24Anonymous__4444) ) ) ) ).

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__533] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__533)
            & ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
             => ( V0__x = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__533)
                & ( ( V1__y = cCoq_2eNumbers_2eBinNums_2eZ0
                    & cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__x,V1__y) = V0__x )
                  | ? [Vvar__0___24Anonymous__537] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__537)
                      & V1__y = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__537)
                      & cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(Vvar__0___24Anonymous__533,Vvar__0___24Anonymous__537)) )
                  | ? [Vvar__0___24Anonymous__538] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__538)
                      & V1__y = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__538)
                      & cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__x,V1__y) = cCoq_2eZArith_2eBinIntDef_2eZ_2epos__sub___24a2(Vvar__0___24Anonymous__533,Vvar__0___24Anonymous__538) ) ) ) ) )
        | ? [Vvar__0___24Anonymous__539] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__539)
            & ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
             => ( V0__x = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__539)
                & ( ( V1__y = cCoq_2eNumbers_2eBinNums_2eZ0
                    & cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__x,V1__y) = V0__x )
                  | ? [Vvar__0___24Anonymous__543] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__543)
                      & V1__y = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__543)
                      & cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__x,V1__y) = cCoq_2eZArith_2eBinIntDef_2eZ_2epos__sub___24a2(Vvar__0___24Anonymous__543,Vvar__0___24Anonymous__539) )
                  | ? [Vvar__0___24Anonymous__544] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__544)
                      & V1__y = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__544)
                      & cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(Vvar__0___24Anonymous__539,Vvar__0___24Anonymous__544)) ) ) ) ) ) ) ) ).

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__565] :
                  ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__565)
                  & V1__y = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__565)
                  & cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eLt )
              | ? [Vvar__0___24Anonymous__566] :
                  ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__566)
                  & V1__y = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__566)
                  & cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eGt ) ) ) )
        | ? [Vvar__0___24Anonymous__567] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__567)
            & ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
             => ( V0__x = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__567)
                & ( ( V1__y = cCoq_2eNumbers_2eBinNums_2eZ0
                    & cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eGt )
                  | ? [Vvar__0___24Anonymous__571] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__571)
                      & V1__y = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__571)
                      & cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare___24a2(Vvar__0___24Anonymous__567,Vvar__0___24Anonymous__571) )
                  | ? [Vvar__0___24Anonymous__572] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__572)
                      & V1__y = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__572)
                      & cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eGt ) ) ) ) )
        | ? [Vvar__0___24Anonymous__573] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__573)
            & ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
             => ( V0__x = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__573)
                & ( ( V1__y = cCoq_2eNumbers_2eBinNums_2eZ0
                    & cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eLt )
                  | ? [Vvar__0___24Anonymous__577] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__577)
                      & V1__y = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__577)
                      & cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eLt )
                  | ? [Vvar__0___24Anonymous__578] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__578)
                      & V1__y = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__578)
                      & cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eCompOpp___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare___24a2(Vvar__0___24Anonymous__573,Vvar__0___24Anonymous__578)) ) ) ) ) ) ) ) ).

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__4453] :
            ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__2___24Anonymous__4453)
            & ? [Vvar__3___24Anonymous__4454] :
                ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__3___24Anonymous__4454)
                & 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__4453,Vvar__3___24Anonymous__4454)
                & cCoq_2eZArith_2eBinIntDef_2eZ_2ediv___24a2(V0__a,V1__b) = Vvar__2___24Anonymous__4453 ) ) ) ) ).

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__150102] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__150102)
            & ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__150102)
             => ( V0__z = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__150102)
                & ( ? [Vvar__0___24Anonymous__150106] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__150106)
                      & Vvar__0___24Anonymous__150102 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__150106)
                      & cCoq_2eZArith_2eBinIntDef_2eZ_2eeven___24a1(V0__z) = cCoq_2eInit_2eDatatypes_2efalse )
                  | ? [Vvar__0___24Anonymous__150107] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__150107)
                      & Vvar__0___24Anonymous__150102 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__150107)
                      & cCoq_2eZArith_2eBinIntDef_2eZ_2eeven___24a1(V0__z) = cCoq_2eInit_2eDatatypes_2etrue )
                  | ( Vvar__0___24Anonymous__150102 = cCoq_2eNumbers_2eBinNums_2exH
                    & cCoq_2eZArith_2eBinIntDef_2eZ_2eeven___24a1(V0__z) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) )
        | ? [Vvar__0___24Anonymous__150108] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__150108)
            & ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__150108)
             => ( V0__z = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__150108)
                & ( ? [Vvar__0___24Anonymous__150112] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__150112)
                      & Vvar__0___24Anonymous__150108 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__150112)
                      & cCoq_2eZArith_2eBinIntDef_2eZ_2eeven___24a1(V0__z) = cCoq_2eInit_2eDatatypes_2efalse )
                  | ? [Vvar__0___24Anonymous__150113] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__150113)
                      & Vvar__0___24Anonymous__150108 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__150113)
                      & cCoq_2eZArith_2eBinIntDef_2eZ_2eeven___24a1(V0__z) = cCoq_2eInit_2eDatatypes_2etrue )
                  | ( Vvar__0___24Anonymous__150108 = 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__4461] :
            ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__2___24Anonymous__4461)
            & ? [Vvar__3___24Anonymous__4462] :
                ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__3___24Anonymous__4462)
                & 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__4461,Vvar__3___24Anonymous__4462)
                & cCoq_2eZArith_2eBinIntDef_2eZ_2emodulo___24a2(V0__a,V1__b) = Vvar__3___24Anonymous__4462 ) ) ) ) ).

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__552] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__552)
            & ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
             => ( V0__x = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__552)
                & ( ( V1__y = cCoq_2eNumbers_2eBinNums_2eZ0
                    & cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZ0 )
                  | ? [Vvar__0___24Anonymous__556] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__556)
                      & V1__y = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__556)
                      & cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2emul___24a2(Vvar__0___24Anonymous__552,Vvar__0___24Anonymous__556)) )
                  | ? [Vvar__0___24Anonymous__557] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__557)
                      & V1__y = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__557)
                      & cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2emul___24a2(Vvar__0___24Anonymous__552,Vvar__0___24Anonymous__557)) ) ) ) ) )
        | ? [Vvar__0___24Anonymous__558] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__558)
            & ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
             => ( V0__x = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__558)
                & ( ( V1__y = cCoq_2eNumbers_2eBinNums_2eZ0
                    & cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZ0 )
                  | ? [Vvar__0___24Anonymous__562] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__562)
                      & V1__y = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__562)
                      & cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2emul___24a2(Vvar__0___24Anonymous__558,Vvar__0___24Anonymous__562)) )
                  | ? [Vvar__0___24Anonymous__563] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__563)
                      & V1__y = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__563)
                      & cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2emul___24a2(Vvar__0___24Anonymous__558,Vvar__0___24Anonymous__563)) ) ) ) ) ) ) ) ).

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__145669] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__145669)
            & ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__145669)
             => ( V0__z = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__145669)
                & ( ? [Vvar__0___24Anonymous__145673] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__145673)
                      & Vvar__0___24Anonymous__145669 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__145673)
                      & cCoq_2eZArith_2eBinIntDef_2eZ_2eodd___24a1(V0__z) = cCoq_2eInit_2eDatatypes_2etrue )
                  | ? [Vvar__0___24Anonymous__145674] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__145674)
                      & Vvar__0___24Anonymous__145669 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__145674)
                      & cCoq_2eZArith_2eBinIntDef_2eZ_2eodd___24a1(V0__z) = cCoq_2eInit_2eDatatypes_2efalse )
                  | ( Vvar__0___24Anonymous__145669 = cCoq_2eNumbers_2eBinNums_2exH
                    & cCoq_2eZArith_2eBinIntDef_2eZ_2eodd___24a1(V0__z) = cCoq_2eInit_2eDatatypes_2etrue ) ) ) ) )
        | ? [Vvar__0___24Anonymous__145675] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__145675)
            & ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__145675)
             => ( V0__z = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__145675)
                & ( ? [Vvar__0___24Anonymous__145679] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__145679)
                      & Vvar__0___24Anonymous__145675 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__145679)
                      & cCoq_2eZArith_2eBinIntDef_2eZ_2eodd___24a1(V0__z) = cCoq_2eInit_2eDatatypes_2etrue )
                  | ? [Vvar__0___24Anonymous__145680] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__145680)
                      & Vvar__0___24Anonymous__145675 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__145680)
                      & cCoq_2eZArith_2eBinIntDef_2eZ_2eodd___24a1(V0__z) = cCoq_2eInit_2eDatatypes_2efalse )
                  | ( Vvar__0___24Anonymous__145675 = 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__7210] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__7210)
            & V0__n = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__7210)
            & cCoq_2eZArith_2eBinIntDef_2eZ_2eof__N___24a1(V0__n) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__7210) ) ) ) ).

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__582] :
            ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__582)
            & V0__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__582)
            & 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__582)) ) ) ) ).

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__548] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__548)
            & V0__x = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__548)
            & cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V0__x) = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__548) )
        | ? [Vvar__0___24Anonymous__549] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__549)
            & V0__x = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__549)
            & cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V0__x) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__549) ) ) ) ).

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__152259] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__152259)
            & V1__y = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__152259)
            & cCoq_2eZArith_2eBinIntDef_2eZ_2epow___24a2(V0__x,V1__y) = cCoq_2eZArith_2eBinIntDef_2eZ_2epow__pos___24a2(V0__x,Vvar__0___24Anonymous__152259) )
        | ? [Vvar__0___24Anonymous__152260] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__152260)
            & V1__y = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__152260)
            & 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__150099] :
      ( cCoq_2eZArith_2eBinIntDef_2eZ_2et___24t(Vvar__150099)
    <=> cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__150099) ) ).

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__7206] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__7206)
            & V0__z = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__7206)
            & cCoq_2eZArith_2eBinIntDef_2eZ_2eto__N___24a1(V0__z) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__7206) )
        | ? [Vvar__0___24Anonymous__7207] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__7207)
            & V0__z = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__7207)
            & 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__4447] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__4447)
            & V0__z = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__4447)
            & cCoq_2eZArith_2eBinIntDef_2eZ_2eto__nat___24a1(V0__z) = cCoq_2ePArith_2eBinPosDef_2ePos_2eto__nat___24a1(Vvar__0___24Anonymous__4447) )
        | ? [Vvar__0___24Anonymous__4448] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__4448)
            & V0__z = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__4448)
            & 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__150100] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__150100)
            & V0__z = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__150100)
            & cCoq_2eZArith_2eBinIntDef_2eZ_2eto__pos___24a1(V0__z) = Vvar__0___24Anonymous__150100 )
        | ? [Vvar__0___24Anonymous__150101] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__150101)
            & V0__z = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__150101)
            & cCoq_2eZArith_2eBinIntDef_2eZ_2eto__pos___24a1(V0__z) = cCoq_2eNumbers_2eBinNums_2exH ) ) ) ).

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

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

fof('$_def_Coq.ZArith.Zeven.Zeven',axiom,
    ! [V0__z] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__z)
     => ( ( V0__z = cCoq_2eNumbers_2eBinNums_2eZ0
          & ( cCoq_2eZArith_2eZeven_2eZeven___24a1(V0__z)
          <=> p(c_24True) ) )
        | ? [Vvar__0___24Anonymous__149735] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__149735)
            & ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__149735)
             => ( V0__z = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__149735)
                & ( ? [Vvar__0___24Anonymous__149739] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__149739)
                      & Vvar__0___24Anonymous__149735 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__149739)
                      & ( cCoq_2eZArith_2eZeven_2eZeven___24a1(V0__z)
                      <=> p(c_24False) ) )
                  | ? [Vvar__0___24Anonymous__149740] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__149740)
                      & Vvar__0___24Anonymous__149735 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__149740)
                      & ( cCoq_2eZArith_2eZeven_2eZeven___24a1(V0__z)
                      <=> p(c_24True) ) )
                  | ( Vvar__0___24Anonymous__149735 = cCoq_2eNumbers_2eBinNums_2exH
                    & ( cCoq_2eZArith_2eZeven_2eZeven___24a1(V0__z)
                    <=> p(c_24False) ) ) ) ) ) )
        | ? [Vvar__0___24Anonymous__149741] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__149741)
            & ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__149741)
             => ( V0__z = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__149741)
                & ( ? [Vvar__0___24Anonymous__149745] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__149745)
                      & Vvar__0___24Anonymous__149741 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__149745)
                      & ( cCoq_2eZArith_2eZeven_2eZeven___24a1(V0__z)
                      <=> p(c_24False) ) )
                  | ? [Vvar__0___24Anonymous__149746] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__149746)
                      & Vvar__0___24Anonymous__149741 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__149746)
                      & ( cCoq_2eZArith_2eZeven_2eZeven___24a1(V0__z)
                      <=> p(c_24True) ) )
                  | ( Vvar__0___24Anonymous__149741 = 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__143379] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__143379)
            & ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__143379)
             => ( V0__z = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__143379)
                & ( ? [Vvar__0___24Anonymous__143383] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__143383)
                      & Vvar__0___24Anonymous__143379 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__143383)
                      & ( cCoq_2eZArith_2eZeven_2eZodd___24a1(V0__z)
                      <=> p(c_24True) ) )
                  | ? [Vvar__0___24Anonymous__143384] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__143384)
                      & Vvar__0___24Anonymous__143379 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__143384)
                      & ( cCoq_2eZArith_2eZeven_2eZodd___24a1(V0__z)
                      <=> p(c_24False) ) )
                  | ( Vvar__0___24Anonymous__143379 = cCoq_2eNumbers_2eBinNums_2exH
                    & ( cCoq_2eZArith_2eZeven_2eZodd___24a1(V0__z)
                    <=> p(c_24True) ) ) ) ) ) )
        | ? [Vvar__0___24Anonymous__143385] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__143385)
            & ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__143385)
             => ( V0__z = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__143385)
                & ( ? [Vvar__0___24Anonymous__143389] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__143389)
                      & Vvar__0___24Anonymous__143385 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__143389)
                      & ( cCoq_2eZArith_2eZeven_2eZodd___24a1(V0__z)
                      <=> p(c_24True) ) )
                  | ? [Vvar__0___24Anonymous__143390] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__143390)
                      & Vvar__0___24Anonymous__143385 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__143390)
                      & ( cCoq_2eZArith_2eZeven_2eZodd___24a1(V0__z)
                      <=> p(c_24False) ) )
                  | ( Vvar__0___24Anonymous__143385 = 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__135991] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__135991)
            & V1__p = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__135991)
            & ( cCoq_2eZArith_2eZlogarithm_2eIs__power___24a1(V1__p)
            <=> p(c_24False) ) )
        | ? [Vvar__0___24Anonymous__135992] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__135992)
            & V1__p = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__135992)
            & ( cCoq_2eZArith_2eZlogarithm_2eIs__power___24a1(V1__p)
            <=> cCoq_2eZArith_2eZlogarithm_2eIs__power___24a1(Vvar__0___24Anonymous__135992) ) )
        | ( 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__152093] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__152093)
            & V1__p = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__152093)
            & cCoq_2eZArith_2eZlogarithm_2elog__inf___24a1(V1__p) = cCoq_2eZArith_2eBinIntDef_2eZ_2esucc___24a1(cCoq_2eZArith_2eZlogarithm_2elog__inf___24a1(Vvar__0___24Anonymous__152093)) )
        | ? [Vvar__0___24Anonymous__152094] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__152094)
            & V1__p = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__152094)
            & cCoq_2eZArith_2eZlogarithm_2elog__inf___24a1(V1__p) = cCoq_2eZArith_2eBinIntDef_2eZ_2esucc___24a1(cCoq_2eZArith_2eZlogarithm_2elog__inf___24a1(Vvar__0___24Anonymous__152094)) )
        | ( V1__p = cCoq_2eNumbers_2eBinNums_2exH
          & cCoq_2eZArith_2eZlogarithm_2elog__inf___24a1(V1__p) = cCoq_2eNumbers_2eBinNums_2eZ0 ) ) ) ).

fof('$_def_Coq.micromega.Env.Env',axiom,
    ! [V0__D] : cCoq_2emicromega_2eEnv_2eEnv___24a1(V0__D) = c_24__type__124053___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__138014] :
              ( t(Vvar__1___24Anonymous__138014,V1__A)
              & ? [Vvar__2___24Anonymous__138015] :
                  ( cCoq_2eInit_2eDatatypes_2elist___24t(V1__A,Vvar__2___24Anonymous__138015)
                  & ( cType___24t(V1__A)
                   => ( cCoq_2eInit_2eDatatypes_2elist___24t(V1__A,Vvar__2___24Anonymous__138015)
                     => ( V3__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V1__A,Vvar__1___24Anonymous__138014,Vvar__2___24Anonymous__138015)
                        & ( ( Vvar__2___24Anonymous__138015 = 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__138014)) ) )
                          | ? [Vvar__1___24Anonymous__138026] :
                              ( t(Vvar__1___24Anonymous__138026,V1__A)
                              & ? [Vvar__2___24Anonymous__138027] :
                                  ( cCoq_2eInit_2eDatatypes_2elist___24t(V1__A,Vvar__2___24Anonymous__138027)
                                  & Vvar__2___24Anonymous__138015 = cCoq_2eInit_2eDatatypes_2econs___24a3(V1__A,Vvar__1___24Anonymous__138026,Vvar__2___24Anonymous__138027)
                                  & ( cCoq_2emicromega_2eRefl_2emake__conj___24a3(V1__A,V2__eval,V3__l)
                                  <=> ( p(happ(V2__eval,Vvar__1___24Anonymous__138014))
                                      & cCoq_2emicromega_2eRefl_2emake__conj___24a3(V1__A,V2__eval,Vvar__2___24Anonymous__138015) ) ) ) ) ) ) ) ) ) ) ) ) ) ).

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__147845] :
              ( t(Vvar__1___24Anonymous__147845,V1__A)
              & ? [Vvar__2___24Anonymous__147846] :
                  ( cCoq_2eInit_2eDatatypes_2elist___24t(V1__A,Vvar__2___24Anonymous__147846)
                  & V3__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V1__A,Vvar__1___24Anonymous__147845,Vvar__2___24Anonymous__147846)
                  & ( cCoq_2emicromega_2eRefl_2emake__impl___24a4(V1__A,V2__eval,V3__l,V4__goal)
                  <=> ( p(happ(V2__eval,Vvar__1___24Anonymous__147845))
                     => cCoq_2emicromega_2eRefl_2emake__impl___24a4(V1__A,V2__eval,Vvar__2___24Anonymous__147846,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__155201___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__155209___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__155217___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__155225___24a3(V0__R,V1__rO,V3__rle) ) ) ) ) ).

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__131787] :
                  ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__131787)
                  & V2__m = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__131787)
                  & cCoq_2emicromega_2eRingMicromega_2ege__bool___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) )
        | ? [Vvar__0___24Anonymous__131788] :
            ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__131788)
            & ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__m)
             => ( V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__131788)
                & ( ( V2__m = cCoq_2eInit_2eDatatypes_2eO
                    & cCoq_2emicromega_2eRingMicromega_2ege__bool___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2etrue )
                  | ? [Vvar__0___24Anonymous__131791] :
                      ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__131791)
                      & V2__m = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__131791)
                      & cCoq_2emicromega_2eRingMicromega_2ege__bool___24a2(V1__n,V2__m) = cCoq_2emicromega_2eRingMicromega_2ege__bool___24a2(Vvar__0___24Anonymous__131788,Vvar__0___24Anonymous__131791) ) ) ) ) ) ) ) ).

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__135945] :
      ( cCoq_2emicromega_2eZMicromega_2eZWitness___24t(Vvar__135945)
    <=> cCoq_2emicromega_2eRingMicromega_2ePsatz___24t(cCoq_2eNumbers_2eBinNums_2eZ,Vvar__135945) ) ).

fof('$_def_Coq.micromega.ZMicromega.coneMember',axiom,
    ! [Vvar__149734] :
      ( cCoq_2emicromega_2eZMicromega_2econeMember___24t(Vvar__149734)
    <=> cCoq_2emicromega_2eZMicromega_2eZWitness___24t(Vvar__149734) ) ).

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__147095] :
      ( cCoq_2esetoid__ring_2eInitialRing_2eNword___24t(Vvar__147095)
    <=> cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eNumbers_2eBinNums_2eN,Vvar__147095) ) ).

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__147061] :
              ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__147061)
              & ( cType___24t(V0__R)
               => ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__147061)
                 => ( V5__p = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__147061)
                    & ( ? [Vvar__0___24Anonymous__147065] :
                          ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__147065)
                          & Vvar__0___24Anonymous__147061 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__147065)
                          & 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__147061))) )
                      | ? [Vvar__0___24Anonymous__147066] :
                          ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__147066)
                          & Vvar__0___24Anonymous__147061 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__147066)
                          & 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__147061))) )
                      | ( Vvar__0___24Anonymous__147061 = 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__147067] :
              ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__147067)
              & ( cType___24t(V0__R)
               => ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__147067)
                 => ( V5__p = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__147067)
                    & ( ? [Vvar__0___24Anonymous__147071] :
                          ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__147071)
                          & Vvar__0___24Anonymous__147067 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__147071)
                          & 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__147067)) )
                      | ? [Vvar__0___24Anonymous__147072] :
                          ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__147072)
                          & Vvar__0___24Anonymous__147067 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__147072)
                          & 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__147067)) )
                      | ( Vvar__0___24Anonymous__147067 = 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__147028] :
              ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__147028)
              & V5__p = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__147028)
              & 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__147028))) )
          | ? [Vvar__0___24Anonymous__147029] :
              ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__147029)
              & V5__p = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__147029)
              & 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__147029)) )
          | ( 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__121728] :
              ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__121728)
              & V6__z = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__121728)
              & 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__121728) )
          | ? [Vvar__0___24Anonymous__121729] :
              ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__121729)
              & V6__z = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__121729)
              & 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__121729)) ) ) ) ) ).

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__2915] :
              ( t(Vvar__1___24Anonymous__2915,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__2915)
                    & ( ? [Vvar__1___24Anonymous__2925] :
                          ( t(Vvar__1___24Anonymous__2925,V0__C)
                          & V4__P_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePc___24a2(V0__C,Vvar__1___24Anonymous__2925)
                          & cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,V3__P,V4__P_27) = happ(happ(V1__ceqb,Vvar__1___24Anonymous__2915),Vvar__1___24Anonymous__2925) )
                      | ? [Vvar__1___24Anonymous__2927] :
                          ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__2927)
                          & ? [Vvar__2___24Anonymous__2928] :
                              ( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__2___24Anonymous__2928)
                              & V4__P_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePinj___24a3(V0__C,Vvar__1___24Anonymous__2927,Vvar__2___24Anonymous__2928)
                              & cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,V3__P,V4__P_27) = cCoq_2eInit_2eDatatypes_2efalse ) )
                      | ? [Vvar__1___24Anonymous__2931] :
                          ( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__1___24Anonymous__2931)
                          & ? [Vvar__2___24Anonymous__2932] :
                              ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2___24Anonymous__2932)
                              & ? [Vvar__3___24Anonymous__2933] :
                                  ( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__3___24Anonymous__2933)
                                  & V4__P_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePX___24a4(V0__C,Vvar__1___24Anonymous__2931,Vvar__2___24Anonymous__2932,Vvar__3___24Anonymous__2933)
                                  & cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,V3__P,V4__P_27) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ) ) ) )
          | ? [Vvar__1___24Anonymous__2938] :
              ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__2938)
              & ? [Vvar__2___24Anonymous__2939] :
                  ( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__2___24Anonymous__2939)
                  & ( 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__2938,Vvar__2___24Anonymous__2939)
                        & ( ? [Vvar__1___24Anonymous__2959] :
                              ( t(Vvar__1___24Anonymous__2959,V0__C)
                              & V4__P_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePc___24a2(V0__C,Vvar__1___24Anonymous__2959)
                              & cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,V3__P,V4__P_27) = cCoq_2eInit_2eDatatypes_2efalse )
                          | ? [Vvar__1___24Anonymous__2961] :
                              ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__2961)
                              & ? [Vvar__2___24Anonymous__2962] :
                                  ( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__2___24Anonymous__2962)
                                  & ( cType___24t(V0__C)
                                   => ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__2938)
                                     => ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__2961)
                                       => ( V4__P_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePinj___24a3(V0__C,Vvar__1___24Anonymous__2961,Vvar__2___24Anonymous__2962)
                                          & ( ( cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare___24a2(Vvar__1___24Anonymous__2938,Vvar__1___24Anonymous__2961) = 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__2939,Vvar__2___24Anonymous__2962) )
                                            | ( cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare___24a2(Vvar__1___24Anonymous__2938,Vvar__1___24Anonymous__2961) = 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__2938,Vvar__1___24Anonymous__2961) = 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__2967] :
                              ( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__1___24Anonymous__2967)
                              & ? [Vvar__2___24Anonymous__2968] :
                                  ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2___24Anonymous__2968)
                                  & ? [Vvar__3___24Anonymous__2969] :
                                      ( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__3___24Anonymous__2969)
                                      & V4__P_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePX___24a4(V0__C,Vvar__1___24Anonymous__2967,Vvar__2___24Anonymous__2968,Vvar__3___24Anonymous__2969)
                                      & cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,V3__P,V4__P_27) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ) ) ) ) )
          | ? [Vvar__1___24Anonymous__2974] :
              ( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__1___24Anonymous__2974)
              & ? [Vvar__2___24Anonymous__2975] :
                  ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2___24Anonymous__2975)
                  & ? [Vvar__3___24Anonymous__2976] :
                      ( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__3___24Anonymous__2976)
                      & ( 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__2974,Vvar__2___24Anonymous__2975,Vvar__3___24Anonymous__2976)
                            & ( ? [Vvar__1___24Anonymous__3009] :
                                  ( t(Vvar__1___24Anonymous__3009,V0__C)
                                  & V4__P_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePc___24a2(V0__C,Vvar__1___24Anonymous__3009)
                                  & cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,V3__P,V4__P_27) = cCoq_2eInit_2eDatatypes_2efalse )
                              | ? [Vvar__1___24Anonymous__3011] :
                                  ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__3011)
                                  & ? [Vvar__2___24Anonymous__3012] :
                                      ( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__2___24Anonymous__3012)
                                      & V4__P_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePinj___24a3(V0__C,Vvar__1___24Anonymous__3011,Vvar__2___24Anonymous__3012)
                                      & cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,V3__P,V4__P_27) = cCoq_2eInit_2eDatatypes_2efalse ) )
                              | ? [Vvar__1___24Anonymous__3015] :
                                  ( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__1___24Anonymous__3015)
                                  & ? [Vvar__2___24Anonymous__3016] :
                                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2___24Anonymous__3016)
                                      & ? [Vvar__3___24Anonymous__3017] :
                                          ( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__3___24Anonymous__3017)
                                          & ( cType___24t(V0__C)
                                           => ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2___24Anonymous__2975)
                                             => ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2___24Anonymous__3016)
                                               => ( V4__P_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePX___24a4(V0__C,Vvar__1___24Anonymous__3015,Vvar__2___24Anonymous__3016,Vvar__3___24Anonymous__3017)
                                                  & ( ( cType___24t(V0__C)
                                                     => ( c_24__type__3030___24t(V0__C,V1__ceqb)
                                                       => ( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__1___24Anonymous__2974)
                                                         => ( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__1___24Anonymous__3015)
                                                           => ( cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare___24a2(Vvar__2___24Anonymous__2975,Vvar__2___24Anonymous__3016) = cCoq_2eInit_2eDatatypes_2eEq
                                                              & ( ( cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,Vvar__1___24Anonymous__2974,Vvar__1___24Anonymous__3015) = 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__2976,Vvar__3___24Anonymous__3017) )
                                                                | ( cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,Vvar__1___24Anonymous__2974,Vvar__1___24Anonymous__3015) = 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__2975,Vvar__2___24Anonymous__3016) = 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__2975,Vvar__2___24Anonymous__3016) = 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__148633] :
              ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__148633)
              & V5__p = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__148633)
              & 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__148633),V4__x,Vvar__0___24Anonymous__148633) )
          | ? [Vvar__0___24Anonymous__148634] :
              ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__148634)
              & V5__p = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__148634)
              & 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__148634),V4__x,Vvar__0___24Anonymous__148634) )
          | ( 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__5391] :
              ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__5391)
              & V4__p = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__5391)
              & 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__5391) ) ) ) ) ).

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__131808] :
              ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__131808)
              & V4__i = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__131808)
              & 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__131809__131812___24a4(V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__131808)),c_24__let__var__6__p__131809__131812___24a4(V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__131808))) )
          | ? [Vvar__0___24Anonymous__131810] :
              ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__131810)
              & V4__i = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__131810)
              & 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__131811__131813___24a4(V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__131810)),c_24__let__var__6__p__131811__131813___24a4(V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__131810)) )
          | ( V4__i = cCoq_2eNumbers_2eBinNums_2exH
            & cCoq_2esetoid__ring_2eRing__theory_2epow__pos___24a4(V0__R,V1__rmul,V3__x,V4__i) = V3__x ) ) ) ) ).

fof('$_def_Hammer.Tactics.Reconstr.rdone',axiom,
    ! [V0__T,V1__x] :
      ( cHammer_2eTactics_2eReconstr_2erdone___24a2(V0__T,V1__x)
    <=> p(c_24True) ) ).

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

fof('$_def_Hoare2.dec_correct',axiom,
    ! [V0__dec] :
      ( cHoare2_2edec__correct___24a1(V0__dec)
    <=> cPLF_2eHoare_2ehoare__triple___24a3(cHoare2_2epre__dec___24a1(V0__dec),cHoare2_2eextract__dec___24a1(V0__dec),cHoare2_2epost__dec___24a1(V0__dec)) ) ).

fof('$_def_Hoare2.parity',axiom,
    ! [V1__x] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(V1__x)
     => ( ( V1__x = cCoq_2eInit_2eDatatypes_2eO
          & cHoare2_2eparity___24a1(V1__x) = cCoq_2eInit_2eDatatypes_2eO )
        | ? [Vvar__0___24Anonymous__84382] :
            ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__84382)
            & ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__84382)
             => ( V1__x = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__84382)
                & ( ( Vvar__0___24Anonymous__84382 = cCoq_2eInit_2eDatatypes_2eO
                    & cHoare2_2eparity___24a1(V1__x) = cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO) )
                  | ? [Vvar__0___24Anonymous__84385] :
                      ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__84385)
                      & Vvar__0___24Anonymous__84382 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__84385)
                      & cHoare2_2eparity___24a1(V1__x) = cHoare2_2eparity___24a1(Vvar__0___24Anonymous__84385) ) ) ) ) ) ) ) ).

fof('$_def_Hoare2.verification_conditions_dec',axiom,
    ! [V0__dec] :
      ( cHoare2_2edecorated___24t(V0__dec)
     => ? [Vvar__0___24Anonymous__152874] :
          ( cPLF_2eHoare_2eAssertion___24t(Vvar__0___24Anonymous__152874)
          & ? [Vvar__1___24Anonymous__152875] :
              ( cHoare2_2edcom___24t(Vvar__1___24Anonymous__152875)
              & V0__dec = cHoare2_2eDecorated___24a2(Vvar__0___24Anonymous__152874,Vvar__1___24Anonymous__152875)
              & ( cHoare2_2everification__conditions__dec___24a1(V0__dec)
              <=> cHoare2_2everification__conditions___24a2(Vvar__0___24Anonymous__152874,Vvar__1___24Anonymous__152875) ) ) ) ) ).

fof('$_def_PLF.Hoare.Assertion',axiom,
    ! [Vvar__351] :
      ( cPLF_2eHoare_2eAssertion___24t(Vvar__351)
    <=> ! [V0___24Anonymous] :
          ( cPLF_2eImp_2estate___24t(V0___24Anonymous)
         => cProp___24t(happ(Vvar__351,V0___24Anonymous)) ) ) ).

fof('$_def_PLF.Hoare.ExAssertions.as5',axiom,
    ! [V0__st] :
      ( cPLF_2eHoare_2eExAssertions_2eas5___24a1(V0__st)
    <=> p(c_24True) ) ).

fof('$_def_PLF.Hoare.ExAssertions.as6',axiom,
    ! [V0__st] :
      ( cPLF_2eHoare_2eExAssertions_2eas6___24a1(V0__st)
    <=> p(c_24False) ) ).

fof('$_def_PLF.Hoare.assert_implies',axiom,
    ! [V0__P,V1__Q] :
      ( cPLF_2eHoare_2eassert__implies___24a2(V0__P,V1__Q)
    <=> ! [V2__st] :
          ( cPLF_2eImp_2estate___24t(V2__st)
         => ( p(happ(V0__P,V2__st))
           => p(happ(V1__Q,V2__st)) ) ) ) ).

fof('$_def_PLF.Imp.state',axiom,
    ! [Vvar__40] :
      ( cPLF_2eImp_2estate___24t(Vvar__40)
    <=> cPLF_2eMaps_2etotal__map___24t(cCoq_2eInit_2eDatatypes_2enat,Vvar__40) ) ).

fof('$_def_PLF.Maps.total_map',axiom,
    ! [V0__A] : cPLF_2eMaps_2etotal__map___24a1(V0__A) = c_24__type__5130___24a1(V0__A) ).

fof('$_discrim_Coq.Bool.Bool.ReflectT$Coq.Bool.Bool.ReflectF',axiom,
    ! [Vvar__0__P__4955,Vvar__1___24Anonymous__4956,Vvar__0__P__4957,Vvar__1___24Anonymous__4958] : cCoq_2eBool_2eBool_2eReflectT___24a1(Vvar__0__P__4955) != cCoq_2eBool_2eBool_2eReflectF___24a1(Vvar__0__P__4957) ).

fof('$_discrim_Coq.FSets.FSetPositive.PositiveSet.Leaf$Coq.FSets.FSetPositive.PositiveSet.Node',axiom,
    ! [Vvar__0___24Anonymous__7096,Vvar__1___24Anonymous__7097,Vvar__2___24Anonymous__7098] : cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eLeaf != cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eNode___24a3(Vvar__0___24Anonymous__7096,Vvar__1___24Anonymous__7097,Vvar__2___24Anonymous__7098) ).

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__85292,Vvar__1__Plt__85293,Vvar__2__Pgt__85294,Vvar__3___24Anonymous__85295,Vvar__0__Peq__85296,Vvar__1__Plt__85297,Vvar__2__Pgt__85298,Vvar__3___24Anonymous__85299] : cCoq_2eInit_2eDatatypes_2eCompEqT___24a3(Vvar__0__Peq__85292,Vvar__1__Plt__85293,Vvar__2__Pgt__85294) != cCoq_2eInit_2eDatatypes_2eCompLtT___24a3(Vvar__0__Peq__85296,Vvar__1__Plt__85297,Vvar__2__Pgt__85298) ).

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__6] : cCoq_2eInit_2eDatatypes_2eO != cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__6) ).

fof('$_discrim_Coq.Init.Datatypes.Some$Coq.Init.Datatypes.None',axiom,
    ! [Vvar__0__A__5001,Vvar__1___24Anonymous__5002,Vvar__0__A__5003] : cCoq_2eInit_2eDatatypes_2eSome___24a2(Vvar__0__A__5001,Vvar__1___24Anonymous__5002) != cCoq_2eInit_2eDatatypes_2eNone___24a1(Vvar__0__A__5003) ).

fof('$_discrim_Coq.Init.Datatypes.inl$Coq.Init.Datatypes.inr',axiom,
    ! [Vvar__0__A__119411,Vvar__1__B__119412,Vvar__2___24Anonymous__119413,Vvar__0__A__119414,Vvar__1__B__119415,Vvar__2___24Anonymous__119416] : cCoq_2eInit_2eDatatypes_2einl___24a3(Vvar__0__A__119411,Vvar__1__B__119412,Vvar__2___24Anonymous__119413) != cCoq_2eInit_2eDatatypes_2einr___24a3(Vvar__0__A__119414,Vvar__1__B__119415,Vvar__2___24Anonymous__119416) ).

fof('$_discrim_Coq.Init.Datatypes.nil$Coq.Init.Datatypes.cons',axiom,
    ! [Vvar__0__A__603,Vvar__0__A__604,Vvar__1___24Anonymous__605,Vvar__2___24Anonymous__606] : cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__603) != cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__604,Vvar__1___24Anonymous__605,Vvar__2___24Anonymous__606) ).

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__124032,Vvar__1__f__124033,Vvar__0__i__124034,Vvar__1__f__124035,Vvar__2__e__124036] : cCoq_2eInit_2eDecimal_2eDecimal___24a2(Vvar__0__i__124032,Vvar__1__f__124033) != cCoq_2eInit_2eDecimal_2eDecimalExp___24a3(Vvar__0__i__124034,Vvar__1__f__124035,Vvar__2__e__124036) ).

fof('$_discrim_Coq.Init.Decimal.Nil$Coq.Init.Decimal.D0',axiom,
    ! [Vvar__0___24Anonymous__80636] : cCoq_2eInit_2eDecimal_2eNil != cCoq_2eInit_2eDecimal_2eD0___24a1(Vvar__0___24Anonymous__80636) ).

fof('$_discrim_Coq.Init.Decimal.Pos$Coq.Init.Decimal.Neg',axiom,
    ! [Vvar__0__d__119432,Vvar__0__d__119433] : cCoq_2eInit_2eDecimal_2ePos___24a1(Vvar__0__d__119432) != cCoq_2eInit_2eDecimal_2eNeg___24a1(Vvar__0__d__119433) ).

fof('$_discrim_Coq.Init.Specif.inleft$Coq.Init.Specif.inright',axiom,
    ! [Vvar__0__A__3807,Vvar__1__B__3808,Vvar__2___24Anonymous__3809,Vvar__0__A__3810,Vvar__1__B__3811,Vvar__2___24Anonymous__3812] : cCoq_2eInit_2eSpecif_2einleft___24a3(Vvar__0__A__3807,Vvar__1__B__3808,Vvar__2___24Anonymous__3809) != cCoq_2eInit_2eSpecif_2einright___24a2(Vvar__0__A__3810,Vvar__1__B__3811) ).

fof('$_discrim_Coq.Init.Specif.left$Coq.Init.Specif.right',axiom,
    ! [Vvar__0__A__3767,Vvar__1__B__3768,Vvar__2___24Anonymous__3769,Vvar__0__A__3770,Vvar__1__B__3771,Vvar__2___24Anonymous__3772] : cCoq_2eInit_2eSpecif_2eleft___24a2(Vvar__0__A__3767,Vvar__1__B__3768) != cCoq_2eInit_2eSpecif_2eright___24a2(Vvar__0__A__3770,Vvar__1__B__3771) ).

fof('$_discrim_Coq.Numbers.BinNums.N0$Coq.Numbers.BinNums.Npos',axiom,
    ! [Vvar__0___24Anonymous__1778] : cCoq_2eNumbers_2eBinNums_2eN0 != cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__1778) ).

fof('$_discrim_Coq.Numbers.BinNums.Z0$Coq.Numbers.BinNums.Zpos',axiom,
    ! [Vvar__0___24Anonymous__228] : cCoq_2eNumbers_2eBinNums_2eZ0 != cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__228) ).

fof('$_discrim_Coq.Numbers.BinNums.xI$Coq.Numbers.BinNums.xO',axiom,
    ! [Vvar__0___24Anonymous__214,Vvar__0___24Anonymous__215] : cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__214) != cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__215) ).

fof('$_discrim_Coq.PArith.BinPos.Pos.PeanoOne$Coq.PArith.BinPos.Pos.PeanoSucc',axiom,
    ! [Vvar__0__p__145160,Vvar__1___24Anonymous__145161] : cCoq_2ePArith_2eBinPos_2ePos_2ePeanoOne != cCoq_2ePArith_2eBinPos_2ePos_2ePeanoSucc___24a2(Vvar__0__p__145160,Vvar__1___24Anonymous__145161) ).

fof('$_discrim_Coq.PArith.BinPosDef.Pos.IsNul$Coq.PArith.BinPosDef.Pos.IsPos',axiom,
    ! [Vvar__0___24Anonymous__7065] : cCoq_2ePArith_2eBinPosDef_2ePos_2eIsNul != cCoq_2ePArith_2eBinPosDef_2ePos_2eIsPos___24a1(Vvar__0___24Anonymous__7065) ).

fof('$_discrim_Coq.Reals.Rfunctions.ZintNull$Coq.Reals.Rfunctions.ZintPos',axiom,
    ! [Vvar__0__x__126315,Vvar__1___24Anonymous__126316,Vvar__0__x__126317,Vvar__1__n__126318,Vvar__2___24Anonymous__126319] : cCoq_2eReals_2eRfunctions_2eZintNull___24a1(Vvar__0__x__126315) != cCoq_2eReals_2eRfunctions_2eZintPos___24a2(Vvar__0__x__126317,Vvar__1__n__126318) ).

fof('$_discrim_Coq.Strings.String.EmptyString$Coq.Strings.String.String',axiom,
    ! [Vvar__0___24Anonymous__203,Vvar__1___24Anonymous__204] : cCoq_2eStrings_2eString_2eEmptyString != cCoq_2eStrings_2eString_2eString___24a2(Vvar__0___24Anonymous__203,Vvar__1___24Anonymous__204) ).

fof('$_discrim_Coq.Structures.OrderedType.LT$Coq.Structures.OrderedType.EQ',axiom,
    ! [Vvar__0__X__122028,Vvar__1__lt__122029,Vvar__2__eq__122030,Vvar__3__x__122031,Vvar__4__y__122032,Vvar__5___24Anonymous__122033,Vvar__0__X__122034,Vvar__1__lt__122035,Vvar__2__eq__122036,Vvar__3__x__122037,Vvar__4__y__122038,Vvar__5___24Anonymous__122039] : cCoq_2eStructures_2eOrderedType_2eLT___24a5(Vvar__0__X__122028,Vvar__1__lt__122029,Vvar__2__eq__122030,Vvar__3__x__122031,Vvar__4__y__122032) != cCoq_2eStructures_2eOrderedType_2eEQ___24a5(Vvar__0__X__122034,Vvar__1__lt__122035,Vvar__2__eq__122036,Vvar__3__x__122037,Vvar__4__y__122038) ).

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__1980,Vvar__0__n__1981,Vvar__1___24Anonymous__1982] : cCoq_2eVectors_2eFin_2eF1___24a1(Vvar__0__n__1980) != cCoq_2eVectors_2eFin_2eFS___24a2(Vvar__0__n__1981,Vvar__1___24Anonymous__1982) ).

fof('$_discrim_Coq.Vectors.VectorDef.nil$Coq.Vectors.VectorDef.cons',axiom,
    ! [Vvar__0__A__3846,Vvar__0__A__3847,Vvar__1__h__3848,Vvar__2__n__3849,Vvar__3___24Anonymous__3850] : cCoq_2eVectors_2eVectorDef_2enil___24a1(Vvar__0__A__3846) != cCoq_2eVectors_2eVectorDef_2econs___24a4(Vvar__0__A__3847,Vvar__1__h__3848,Vvar__2__n__3849,Vvar__3___24Anonymous__3850) ).

fof('$_discrim_Coq.micromega.EnvRing.PEc$Coq.micromega.EnvRing.PEX',axiom,
    ! [Vvar__0__C__124179,Vvar__1___24Anonymous__124180,Vvar__0__C__124181,Vvar__1___24Anonymous__124182] : cCoq_2emicromega_2eEnvRing_2ePEc___24a2(Vvar__0__C__124179,Vvar__1___24Anonymous__124180) != cCoq_2emicromega_2eEnvRing_2ePEX___24a2(Vvar__0__C__124181,Vvar__1___24Anonymous__124182) ).

fof('$_discrim_Coq.micromega.EnvRing.Pc$Coq.micromega.EnvRing.Pinj',axiom,
    ! [Vvar__0__C__124243,Vvar__1___24Anonymous__124244,Vvar__0__C__124245,Vvar__1___24Anonymous__124246,Vvar__2___24Anonymous__124247] : cCoq_2emicromega_2eEnvRing_2ePc___24a2(Vvar__0__C__124243,Vvar__1___24Anonymous__124244) != cCoq_2emicromega_2eEnvRing_2ePinj___24a3(Vvar__0__C__124245,Vvar__1___24Anonymous__124246,Vvar__2___24Anonymous__124247) ).

fof('$_discrim_Coq.micromega.EnvRing.mon0$Coq.micromega.EnvRing.zmon',axiom,
    ! [Vvar__0___24Anonymous__124280,Vvar__1___24Anonymous__124281] : cCoq_2emicromega_2eEnvRing_2emon0 != cCoq_2emicromega_2eEnvRing_2ezmon___24a2(Vvar__0___24Anonymous__124280,Vvar__1___24Anonymous__124281) ).

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__131742,Vvar__1___24Anonymous__131743,Vvar__0__C__131744,Vvar__1___24Anonymous__131745] : cCoq_2emicromega_2eRingMicromega_2ePsatzIn___24a2(Vvar__0__C__131742,Vvar__1___24Anonymous__131743) != cCoq_2emicromega_2eRingMicromega_2ePsatzSquare___24a2(Vvar__0__C__131744,Vvar__1___24Anonymous__131745) ).

fof('$_discrim_Coq.micromega.Tauto.TT$Coq.micromega.Tauto.FF',axiom,
    ! [Vvar__0__TA__149520,Vvar__1__TX__149521,Vvar__2__AA__149522,Vvar__3__AF__149523,Vvar__0__TA__149524,Vvar__1__TX__149525,Vvar__2__AA__149526,Vvar__3__AF__149527] : cCoq_2emicromega_2eTauto_2eTT___24a4(Vvar__0__TA__149520,Vvar__1__TX__149521,Vvar__2__AA__149522,Vvar__3__AF__149523) != cCoq_2emicromega_2eTauto_2eFF___24a4(Vvar__0__TA__149524,Vvar__1__TX__149525,Vvar__2__AA__149526,Vvar__3__AF__149527) ).

fof('$_discrim_Coq.micromega.VarMap.Empty$Coq.micromega.VarMap.Elt',axiom,
    ! [Vvar__0__A__142732,Vvar__0__A__142733,Vvar__1___24Anonymous__142734] : cCoq_2emicromega_2eVarMap_2eEmpty___24a1(Vvar__0__A__142732) != cCoq_2emicromega_2eVarMap_2eElt___24a2(Vvar__0__A__142733,Vvar__1___24Anonymous__142734) ).

fof('$_discrim_Coq.micromega.ZMicromega.DoneProof$Coq.micromega.ZMicromega.RatProof',axiom,
    ! [Vvar__0___24Anonymous__135973,Vvar__1___24Anonymous__135974] : cCoq_2emicromega_2eZMicromega_2eDoneProof != cCoq_2emicromega_2eZMicromega_2eRatProof___24a2(Vvar__0___24Anonymous__135973,Vvar__1___24Anonymous__135974) ).

fof('$_discrim_Coq.setoid_ring.Field_theory.FEO$Coq.setoid_ring.Field_theory.FEI',axiom,
    ! [Vvar__0__C__119746,Vvar__0__C__119747] : cCoq_2esetoid__ring_2eField__theory_2eFEO___24a1(Vvar__0__C__119746) != cCoq_2esetoid__ring_2eField__theory_2eFEI___24a1(Vvar__0__C__119747) ).

fof('$_discrim_Coq.setoid_ring.Ring_polynom.PEO$Coq.setoid_ring.Ring_polynom.PEI',axiom,
    ! [Vvar__0__C__3247,Vvar__0__C__3248] : cCoq_2esetoid__ring_2eRing__polynom_2ePEO___24a1(Vvar__0__C__3247) != cCoq_2esetoid__ring_2eRing__polynom_2ePEI___24a1(Vvar__0__C__3248) ).

fof('$_discrim_Coq.setoid_ring.Ring_polynom.Pc$Coq.setoid_ring.Ring_polynom.Pinj',axiom,
    ! [Vvar__0__C__2889,Vvar__1___24Anonymous__2890,Vvar__0__C__2891,Vvar__1___24Anonymous__2892,Vvar__2___24Anonymous__2893] : cCoq_2esetoid__ring_2eRing__polynom_2ePc___24a2(Vvar__0__C__2889,Vvar__1___24Anonymous__2890) != cCoq_2esetoid__ring_2eRing__polynom_2ePinj___24a3(Vvar__0__C__2891,Vvar__1___24Anonymous__2892,Vvar__2___24Anonymous__2893) ).

fof('$_discrim_Coq.setoid_ring.Ring_polynom.mon0$Coq.setoid_ring.Ring_polynom.zmon',axiom,
    ! [Vvar__0___24Anonymous__3057,Vvar__1___24Anonymous__3058] : cCoq_2esetoid__ring_2eRing__polynom_2emon0 != cCoq_2esetoid__ring_2eRing__polynom_2ezmon___24a2(Vvar__0___24Anonymous__3057,Vvar__1___24Anonymous__3058) ).

fof('$_discrim_Coq.setoid_ring.Ring_theory.Abstract$Coq.setoid_ring.Ring_theory.Computational',axiom,
    ! [Vvar__0__R__148814,Vvar__1__req__148815,Vvar__2__reqb__148816,Vvar__3___24Anonymous__148817] : cCoq_2esetoid__ring_2eRing__theory_2eAbstract != cCoq_2esetoid__ring_2eRing__theory_2eComputational___24a3(Vvar__0__R__148814,Vvar__1__req__148815,Vvar__2__reqb__148816) ).

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

fof('$_discrim_Hoare2.DCSkip$Hoare2.DCSeq',axiom,
    ! [Vvar__0___24Anonymous__150458,Vvar__0___24Anonymous__150459,Vvar__1___24Anonymous__150460] : cHoare2_2eDCSkip___24a1(Vvar__0___24Anonymous__150458) != cHoare2_2eDCSeq___24a2(Vvar__0___24Anonymous__150459,Vvar__1___24Anonymous__150460) ).

fof('$_discrim_PLF.Hoare.Himp.CSkip$PLF.Hoare.Himp.CAsgn',axiom,
    ! [Vvar__0___24Anonymous__842,Vvar__1___24Anonymous__843] : cPLF_2eHoare_2eHimp_2eCSkip != cPLF_2eHoare_2eHimp_2eCAsgn___24a2(Vvar__0___24Anonymous__842,Vvar__1___24Anonymous__843) ).

fof('$_discrim_PLF.Hoare.HoareAssertAssume.CSkip$PLF.Hoare.HoareAssertAssume.CAss',axiom,
    ! [Vvar__0___24Anonymous__1087,Vvar__1___24Anonymous__1088] : cPLF_2eHoare_2eHoareAssertAssume_2eCSkip != cPLF_2eHoare_2eHoareAssertAssume_2eCAss___24a2(Vvar__0___24Anonymous__1087,Vvar__1___24Anonymous__1088) ).

fof('$_discrim_PLF.Hoare.HoareAssertAssume.RNormal$PLF.Hoare.HoareAssertAssume.RError',axiom,
    ! [Vvar__0___24Anonymous__1129] : cPLF_2eHoare_2eHoareAssertAssume_2eRNormal___24a1(Vvar__0___24Anonymous__1129) != cPLF_2eHoare_2eHoareAssertAssume_2eRError ).

fof('$_discrim_PLF.Hoare.If1.CSkip$PLF.Hoare.If1.CAss',axiom,
    ! [Vvar__0___24Anonymous__1390,Vvar__1___24Anonymous__1391] : cPLF_2eHoare_2eIf1_2eCSkip != cPLF_2eHoare_2eIf1_2eCAss___24a2(Vvar__0___24Anonymous__1390,Vvar__1___24Anonymous__1391) ).

fof('$_discrim_PLF.Hoare.RepeatExercise.CSkip$PLF.Hoare.RepeatExercise.CAsgn',axiom,
    ! [Vvar__0___24Anonymous__1618,Vvar__1___24Anonymous__1619] : cPLF_2eHoare_2eRepeatExercise_2eCSkip != cPLF_2eHoare_2eRepeatExercise_2eCAsgn___24a2(Vvar__0___24Anonymous__1618,Vvar__1___24Anonymous__1619) ).

fof('$_discrim_PLF.Imp.AExp.ANum$PLF.Imp.AExp.APlus',axiom,
    ! [Vvar__0__n__6966,Vvar__0__a1__6967,Vvar__1__a2__6968] : cPLF_2eImp_2eAExp_2eANum___24a1(Vvar__0__n__6966) != cPLF_2eImp_2eAExp_2eAPlus___24a2(Vvar__0__a1__6967,Vvar__1__a2__6968) ).

fof('$_discrim_PLF.Imp.AExp.BTrue$PLF.Imp.AExp.BFalse',axiom,
    cPLF_2eImp_2eAExp_2eBTrue != cPLF_2eImp_2eAExp_2eBFalse ).

fof('$_discrim_PLF.Imp.ANum$PLF.Imp.AId',axiom,
    ! [Vvar__0__n__80,Vvar__0__x__81] : cPLF_2eImp_2eANum___24a1(Vvar__0__n__80) != cPLF_2eImp_2eAId___24a1(Vvar__0__x__81) ).

fof('$_discrim_PLF.Imp.BTrue$PLF.Imp.BFalse',axiom,
    cPLF_2eImp_2eBTrue != cPLF_2eImp_2eBFalse ).

fof('$_discrim_PLF.Imp.BreakImp.CSkip$PLF.Imp.BreakImp.CBreak',axiom,
    cPLF_2eImp_2eBreakImp_2eCSkip != cPLF_2eImp_2eBreakImp_2eCBreak ).

fof('$_discrim_PLF.Imp.BreakImp.SContinue$PLF.Imp.BreakImp.SBreak',axiom,
    cPLF_2eImp_2eBreakImp_2eSContinue != cPLF_2eImp_2eBreakImp_2eSBreak ).

fof('$_discrim_PLF.Imp.CSkip$PLF.Imp.CAss',axiom,
    ! [Vvar__0__x__159,Vvar__1__a__160] : cPLF_2eImp_2eCSkip != cPLF_2eImp_2eCAss___24a2(Vvar__0__x__159,Vvar__1__a__160) ).

fof('$_discrim_PLF.Imp.SPush$PLF.Imp.SLoad',axiom,
    ! [Vvar__0__n__662,Vvar__0__x__663] : cPLF_2eImp_2eSPush___24a1(Vvar__0__n__662) != cPLF_2eImp_2eSLoad___24a1(Vvar__0__x__663) ).

fof('$_discrim_PLF.Imp.aevalR_division.ANum$PLF.Imp.aevalR_division.APlus',axiom,
    ! [Vvar__0__n__4508,Vvar__0__a1__4509,Vvar__1__a2__4510] : cPLF_2eImp_2eaevalR__division_2eANum___24a1(Vvar__0__n__4508) != cPLF_2eImp_2eaevalR__division_2eAPlus___24a2(Vvar__0__a1__4509,Vvar__1__a2__4510) ).

fof('$_discrim_PLF.Imp.aevalR_extended.AAny$PLF.Imp.aevalR_extended.ANum',axiom,
    ! [Vvar__0__n__83618] : cPLF_2eImp_2eaevalR__extended_2eAAny != cPLF_2eImp_2eaevalR__extended_2eANum___24a1(Vvar__0__n__83618) ).

fof('$_fix_145155_v_CANONICAL_0',axiom,
    ! [Vv__CANONICAL__1] :
      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__1)
     => ( ? [Vvar__0___24Anonymous__145156] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__145156)
            & Vv__CANONICAL__1 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__145156)
            & c_24__fix__145155__v__CANONICAL__0___24a1(Vv__CANONICAL__1) = cCoq_2eNumbers_2eBinNums_2exO___24a1(c_24__fix__145155__v__CANONICAL__0___24a1(Vvar__0___24Anonymous__145156)) )
        | ? [Vvar__0___24Anonymous__145157] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__145157)
            & Vv__CANONICAL__1 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__145157)
            & c_24__fix__145155__v__CANONICAL__0___24a1(Vv__CANONICAL__1) = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__145157) )
        | ( Vv__CANONICAL__1 = cCoq_2eNumbers_2eBinNums_2exH
          & c_24__fix__145155__v__CANONICAL__0___24a1(Vv__CANONICAL__1) = cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2eNumbers_2eBinNums_2exH) ) ) ) ).

fof('$_fix_148532_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__148532__v__CANONICAL__1___24a3(Vv__CANONICAL__0,Vv__CANONICAL__2,Vv__CANONICAL__3) = Vv__CANONICAL__3 )
          | ? [Vvar__1___24Anonymous__148536] :
              ( t(Vvar__1___24Anonymous__148536,Vv__CANONICAL__0)
              & ? [Vvar__2___24Anonymous__148537] :
                  ( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vvar__2___24Anonymous__148537)
                  & Vv__CANONICAL__2 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vv__CANONICAL__0,Vvar__1___24Anonymous__148536,Vvar__2___24Anonymous__148537)
                  & c_24__fix__148532__v__CANONICAL__1___24a3(Vv__CANONICAL__0,Vv__CANONICAL__2,Vv__CANONICAL__3) = cCoq_2eInit_2eDatatypes_2econs___24a3(Vv__CANONICAL__0,Vvar__1___24Anonymous__148536,c_24__fix__148532__v__CANONICAL__1___24a3(Vv__CANONICAL__0,Vvar__2___24Anonymous__148537,Vv__CANONICAL__3)) ) ) ) ) ) ).

fof('$_fix_4648_v_CANONICAL_0',axiom,
    ! [Vv__CANONICAL__1,Vv__CANONICAL__2] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
     => ( ( Vv__CANONICAL__1 = cCoq_2eInit_2eDatatypes_2eO
          & c_24__fix__4648__v__CANONICAL__0___24a2(Vv__CANONICAL__1,Vv__CANONICAL__2) = Vv__CANONICAL__2 )
        | ? [Vvar__0___24Anonymous__4649] :
            ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__4649)
            & Vv__CANONICAL__1 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__4649)
            & c_24__fix__4648__v__CANONICAL__0___24a2(Vv__CANONICAL__1,Vv__CANONICAL__2) = cCoq_2eInit_2eDatatypes_2eS___24a1(c_24__fix__4648__v__CANONICAL__0___24a2(Vvar__0___24Anonymous__4649,Vv__CANONICAL__2)) ) ) ) ).

fof('$_fix_4781_v_CANONICAL_0',axiom,
    ! [Vv__CANONICAL__1,Vv__CANONICAL__2] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
     => ( ( Vv__CANONICAL__1 = cCoq_2eInit_2eDatatypes_2eO
          & c_24__fix__4781__v__CANONICAL__0___24a2(Vv__CANONICAL__1,Vv__CANONICAL__2) = Vv__CANONICAL__1 )
        | ? [Vvar__0___24Anonymous__4782] :
            ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__4782)
            & ( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__2)
             => ( Vv__CANONICAL__1 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__4782)
                & ( ( Vv__CANONICAL__2 = cCoq_2eInit_2eDatatypes_2eO
                    & c_24__fix__4781__v__CANONICAL__0___24a2(Vv__CANONICAL__1,Vv__CANONICAL__2) = Vv__CANONICAL__1 )
                  | ? [Vvar__0___24Anonymous__4785] :
                      ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__4785)
                      & Vv__CANONICAL__2 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__4785)
                      & c_24__fix__4781__v__CANONICAL__0___24a2(Vv__CANONICAL__1,Vv__CANONICAL__2) = c_24__fix__4781__v__CANONICAL__0___24a2(Vvar__0___24Anonymous__4782,Vvar__0___24Anonymous__4785) ) ) ) ) ) ) ) ).

fof('$_fix_4858_v_CANONICAL_0',axiom,
    ! [Vv__CANONICAL__1,Vv__CANONICAL__2] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
     => ( ( Vv__CANONICAL__1 = cCoq_2eInit_2eDatatypes_2eO
          & c_24__fix__4858__v__CANONICAL__0___24a2(Vv__CANONICAL__1,Vv__CANONICAL__2) = cCoq_2eInit_2eDatatypes_2eO )
        | ? [Vvar__0___24Anonymous__4859] :
            ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__4859)
            & Vv__CANONICAL__1 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__4859)
            & c_24__fix__4858__v__CANONICAL__0___24a2(Vv__CANONICAL__1,Vv__CANONICAL__2) = cCoq_2eInit_2eNat_2eadd___24a2(Vv__CANONICAL__2,c_24__fix__4858__v__CANONICAL__0___24a2(Vvar__0___24Anonymous__4859,Vv__CANONICAL__2)) ) ) ) ).

fof('$_inj_Coq.Bool.Bool.ReflectF',axiom,
    ! [Vvar__0__P__4963,Vvar__0__P__4964,Vvar__1___24Anonymous__4965,Vvar__1___24Anonymous__4966] :
      ( cCoq_2eBool_2eBool_2eReflectF___24a1(Vvar__0__P__4963) = cCoq_2eBool_2eBool_2eReflectF___24a1(Vvar__0__P__4964)
     => ( c_24Proof = c_24Proof
        & Vvar__0__P__4963 = Vvar__0__P__4964 ) ) ).

fof('$_inj_Coq.Bool.Bool.ReflectT',axiom,
    ! [Vvar__0__P__4959,Vvar__0__P__4960,Vvar__1___24Anonymous__4961,Vvar__1___24Anonymous__4962] :
      ( cCoq_2eBool_2eBool_2eReflectT___24a1(Vvar__0__P__4959) = cCoq_2eBool_2eBool_2eReflectT___24a1(Vvar__0__P__4960)
     => ( c_24Proof = c_24Proof
        & Vvar__0__P__4959 = Vvar__0__P__4960 ) ) ).

fof('$_inj_Coq.FSets.FSetPositive.PositiveSet.Node',axiom,
    ! [Vvar__0___24Anonymous__7099,Vvar__0___24Anonymous__7100,Vvar__1___24Anonymous__7101,Vvar__1___24Anonymous__7102,Vvar__2___24Anonymous__7103,Vvar__2___24Anonymous__7104] :
      ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eNode___24a3(Vvar__0___24Anonymous__7099,Vvar__1___24Anonymous__7101,Vvar__2___24Anonymous__7103) = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eNode___24a3(Vvar__0___24Anonymous__7100,Vvar__1___24Anonymous__7102,Vvar__2___24Anonymous__7104)
     => ( Vvar__2___24Anonymous__7103 = Vvar__2___24Anonymous__7104
        & Vvar__1___24Anonymous__7101 = Vvar__1___24Anonymous__7102
        & Vvar__0___24Anonymous__7099 = Vvar__0___24Anonymous__7100 ) ) ).

fof('$_inj_Coq.Init.Datatypes.CompEqT',axiom,
    ! [Vvar__0__Peq__85300,Vvar__0__Peq__85301,Vvar__1__Plt__85302,Vvar__1__Plt__85303,Vvar__2__Pgt__85304,Vvar__2__Pgt__85305,Vvar__3___24Anonymous__85306,Vvar__3___24Anonymous__85307] :
      ( cCoq_2eInit_2eDatatypes_2eCompEqT___24a3(Vvar__0__Peq__85300,Vvar__1__Plt__85302,Vvar__2__Pgt__85304) = cCoq_2eInit_2eDatatypes_2eCompEqT___24a3(Vvar__0__Peq__85301,Vvar__1__Plt__85303,Vvar__2__Pgt__85305)
     => ( c_24Proof = c_24Proof
        & Vvar__2__Pgt__85304 = Vvar__2__Pgt__85305
        & Vvar__1__Plt__85302 = Vvar__1__Plt__85303
        & Vvar__0__Peq__85300 = Vvar__0__Peq__85301 ) ) ).

fof('$_inj_Coq.Init.Datatypes.CompGtT',axiom,
    ! [Vvar__0__Peq__85316,Vvar__0__Peq__85317,Vvar__1__Plt__85318,Vvar__1__Plt__85319,Vvar__2__Pgt__85320,Vvar__2__Pgt__85321,Vvar__3___24Anonymous__85322,Vvar__3___24Anonymous__85323] :
      ( cCoq_2eInit_2eDatatypes_2eCompGtT___24a3(Vvar__0__Peq__85316,Vvar__1__Plt__85318,Vvar__2__Pgt__85320) = cCoq_2eInit_2eDatatypes_2eCompGtT___24a3(Vvar__0__Peq__85317,Vvar__1__Plt__85319,Vvar__2__Pgt__85321)
     => ( c_24Proof = c_24Proof
        & Vvar__2__Pgt__85320 = Vvar__2__Pgt__85321
        & Vvar__1__Plt__85318 = Vvar__1__Plt__85319
        & Vvar__0__Peq__85316 = Vvar__0__Peq__85317 ) ) ).

fof('$_inj_Coq.Init.Datatypes.CompLtT',axiom,
    ! [Vvar__0__Peq__85308,Vvar__0__Peq__85309,Vvar__1__Plt__85310,Vvar__1__Plt__85311,Vvar__2__Pgt__85312,Vvar__2__Pgt__85313,Vvar__3___24Anonymous__85314,Vvar__3___24Anonymous__85315] :
      ( cCoq_2eInit_2eDatatypes_2eCompLtT___24a3(Vvar__0__Peq__85308,Vvar__1__Plt__85310,Vvar__2__Pgt__85312) = cCoq_2eInit_2eDatatypes_2eCompLtT___24a3(Vvar__0__Peq__85309,Vvar__1__Plt__85311,Vvar__2__Pgt__85313)
     => ( c_24Proof = c_24Proof
        & Vvar__2__Pgt__85312 = Vvar__2__Pgt__85313
        & Vvar__1__Plt__85310 = Vvar__1__Plt__85311
        & Vvar__0__Peq__85308 = Vvar__0__Peq__85309 ) ) ).

fof('$_inj_Coq.Init.Datatypes.None',axiom,
    ! [Vvar__0__A__5008,Vvar__0__A__5009] :
      ( cCoq_2eInit_2eDatatypes_2eNone___24a1(Vvar__0__A__5008) = cCoq_2eInit_2eDatatypes_2eNone___24a1(Vvar__0__A__5009)
     => Vvar__0__A__5008 = Vvar__0__A__5009 ) ).

fof('$_inj_Coq.Init.Datatypes.S',axiom,
    ! [Vvar__0___24Anonymous__7,Vvar__0___24Anonymous__8] :
      ( cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__7) = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__8)
     => Vvar__0___24Anonymous__7 = Vvar__0___24Anonymous__8 ) ).

fof('$_inj_Coq.Init.Datatypes.Some',axiom,
    ! [Vvar__0__A__5004,Vvar__0__A__5005,Vvar__1___24Anonymous__5006,Vvar__1___24Anonymous__5007] :
      ( cCoq_2eInit_2eDatatypes_2eSome___24a2(Vvar__0__A__5004,Vvar__1___24Anonymous__5006) = cCoq_2eInit_2eDatatypes_2eSome___24a2(Vvar__0__A__5005,Vvar__1___24Anonymous__5007)
     => ( Vvar__1___24Anonymous__5006 = Vvar__1___24Anonymous__5007
        & Vvar__0__A__5004 = Vvar__0__A__5005 ) ) ).

fof('$_inj_Coq.Init.Datatypes.cons',axiom,
    ! [Vvar__0__A__609,Vvar__0__A__610,Vvar__1___24Anonymous__611,Vvar__1___24Anonymous__612,Vvar__2___24Anonymous__613,Vvar__2___24Anonymous__614] :
      ( cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__609,Vvar__1___24Anonymous__611,Vvar__2___24Anonymous__613) = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__610,Vvar__1___24Anonymous__612,Vvar__2___24Anonymous__614)
     => ( Vvar__2___24Anonymous__613 = Vvar__2___24Anonymous__614
        & Vvar__1___24Anonymous__611 = Vvar__1___24Anonymous__612
        & Vvar__0__A__609 = Vvar__0__A__610 ) ) ).

fof('$_inj_Coq.Init.Datatypes.inl',axiom,
    ! [Vvar__0__A__119417,Vvar__0__A__119418,Vvar__1__B__119419,Vvar__1__B__119420,Vvar__2___24Anonymous__119421,Vvar__2___24Anonymous__119422] :
      ( cCoq_2eInit_2eDatatypes_2einl___24a3(Vvar__0__A__119417,Vvar__1__B__119419,Vvar__2___24Anonymous__119421) = cCoq_2eInit_2eDatatypes_2einl___24a3(Vvar__0__A__119418,Vvar__1__B__119420,Vvar__2___24Anonymous__119422)
     => ( Vvar__2___24Anonymous__119421 = Vvar__2___24Anonymous__119422
        & Vvar__1__B__119419 = Vvar__1__B__119420
        & Vvar__0__A__119417 = Vvar__0__A__119418 ) ) ).

fof('$_inj_Coq.Init.Datatypes.inr',axiom,
    ! [Vvar__0__A__119423,Vvar__0__A__119424,Vvar__1__B__119425,Vvar__1__B__119426,Vvar__2___24Anonymous__119427,Vvar__2___24Anonymous__119428] :
      ( cCoq_2eInit_2eDatatypes_2einr___24a3(Vvar__0__A__119423,Vvar__1__B__119425,Vvar__2___24Anonymous__119427) = cCoq_2eInit_2eDatatypes_2einr___24a3(Vvar__0__A__119424,Vvar__1__B__119426,Vvar__2___24Anonymous__119428)
     => ( Vvar__2___24Anonymous__119427 = Vvar__2___24Anonymous__119428
        & Vvar__1__B__119425 = Vvar__1__B__119426
        & Vvar__0__A__119423 = Vvar__0__A__119424 ) ) ).

fof('$_inj_Coq.Init.Datatypes.nil',axiom,
    ! [Vvar__0__A__607,Vvar__0__A__608] :
      ( cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__607) = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__608)
     => Vvar__0__A__607 = Vvar__0__A__608 ) ).

fof('$_inj_Coq.Init.Datatypes.pair',axiom,
    ! [Vvar__0__A__1890,Vvar__0__A__1891,Vvar__1__B__1892,Vvar__1__B__1893,Vvar__2___24Anonymous__1894,Vvar__2___24Anonymous__1895,Vvar__3___24Anonymous__1896,Vvar__3___24Anonymous__1897] :
      ( cCoq_2eInit_2eDatatypes_2epair___24a4(Vvar__0__A__1890,Vvar__1__B__1892,Vvar__2___24Anonymous__1894,Vvar__3___24Anonymous__1896) = cCoq_2eInit_2eDatatypes_2epair___24a4(Vvar__0__A__1891,Vvar__1__B__1893,Vvar__2___24Anonymous__1895,Vvar__3___24Anonymous__1897)
     => ( Vvar__3___24Anonymous__1896 = Vvar__3___24Anonymous__1897
        & Vvar__2___24Anonymous__1894 = Vvar__2___24Anonymous__1895
        & Vvar__1__B__1892 = Vvar__1__B__1893
        & Vvar__0__A__1890 = Vvar__0__A__1891 ) ) ).

fof('$_inj_Coq.Init.Decimal.D0',axiom,
    ! [Vvar__0___24Anonymous__80637,Vvar__0___24Anonymous__80638] :
      ( cCoq_2eInit_2eDecimal_2eD0___24a1(Vvar__0___24Anonymous__80637) = cCoq_2eInit_2eDecimal_2eD0___24a1(Vvar__0___24Anonymous__80638)
     => Vvar__0___24Anonymous__80637 = Vvar__0___24Anonymous__80638 ) ).

fof('$_inj_Coq.Init.Decimal.D1',axiom,
    ! [Vvar__0___24Anonymous__80639,Vvar__0___24Anonymous__80640] :
      ( cCoq_2eInit_2eDecimal_2eD1___24a1(Vvar__0___24Anonymous__80639) = cCoq_2eInit_2eDecimal_2eD1___24a1(Vvar__0___24Anonymous__80640)
     => Vvar__0___24Anonymous__80639 = Vvar__0___24Anonymous__80640 ) ).

fof('$_inj_Coq.Init.Decimal.D2',axiom,
    ! [Vvar__0___24Anonymous__80641,Vvar__0___24Anonymous__80642] :
      ( cCoq_2eInit_2eDecimal_2eD2___24a1(Vvar__0___24Anonymous__80641) = cCoq_2eInit_2eDecimal_2eD2___24a1(Vvar__0___24Anonymous__80642)
     => Vvar__0___24Anonymous__80641 = Vvar__0___24Anonymous__80642 ) ).

fof('$_inj_Coq.Init.Decimal.D3',axiom,
    ! [Vvar__0___24Anonymous__80643,Vvar__0___24Anonymous__80644] :
      ( cCoq_2eInit_2eDecimal_2eD3___24a1(Vvar__0___24Anonymous__80643) = cCoq_2eInit_2eDecimal_2eD3___24a1(Vvar__0___24Anonymous__80644)
     => Vvar__0___24Anonymous__80643 = Vvar__0___24Anonymous__80644 ) ).

fof('$_inj_Coq.Init.Decimal.D4',axiom,
    ! [Vvar__0___24Anonymous__80645,Vvar__0___24Anonymous__80646] :
      ( cCoq_2eInit_2eDecimal_2eD4___24a1(Vvar__0___24Anonymous__80645) = cCoq_2eInit_2eDecimal_2eD4___24a1(Vvar__0___24Anonymous__80646)
     => Vvar__0___24Anonymous__80645 = Vvar__0___24Anonymous__80646 ) ).

fof('$_inj_Coq.Init.Decimal.D5',axiom,
    ! [Vvar__0___24Anonymous__80647,Vvar__0___24Anonymous__80648] :
      ( cCoq_2eInit_2eDecimal_2eD5___24a1(Vvar__0___24Anonymous__80647) = cCoq_2eInit_2eDecimal_2eD5___24a1(Vvar__0___24Anonymous__80648)
     => Vvar__0___24Anonymous__80647 = Vvar__0___24Anonymous__80648 ) ).

fof('$_inj_Coq.Init.Decimal.D6',axiom,
    ! [Vvar__0___24Anonymous__80649,Vvar__0___24Anonymous__80650] :
      ( cCoq_2eInit_2eDecimal_2eD6___24a1(Vvar__0___24Anonymous__80649) = cCoq_2eInit_2eDecimal_2eD6___24a1(Vvar__0___24Anonymous__80650)
     => Vvar__0___24Anonymous__80649 = Vvar__0___24Anonymous__80650 ) ).

fof('$_inj_Coq.Init.Decimal.D7',axiom,
    ! [Vvar__0___24Anonymous__80651,Vvar__0___24Anonymous__80652] :
      ( cCoq_2eInit_2eDecimal_2eD7___24a1(Vvar__0___24Anonymous__80651) = cCoq_2eInit_2eDecimal_2eD7___24a1(Vvar__0___24Anonymous__80652)
     => Vvar__0___24Anonymous__80651 = Vvar__0___24Anonymous__80652 ) ).

fof('$_inj_Coq.Init.Decimal.D8',axiom,
    ! [Vvar__0___24Anonymous__80653,Vvar__0___24Anonymous__80654] :
      ( cCoq_2eInit_2eDecimal_2eD8___24a1(Vvar__0___24Anonymous__80653) = cCoq_2eInit_2eDecimal_2eD8___24a1(Vvar__0___24Anonymous__80654)
     => Vvar__0___24Anonymous__80653 = Vvar__0___24Anonymous__80654 ) ).

fof('$_inj_Coq.Init.Decimal.D9',axiom,
    ! [Vvar__0___24Anonymous__80655,Vvar__0___24Anonymous__80656] :
      ( cCoq_2eInit_2eDecimal_2eD9___24a1(Vvar__0___24Anonymous__80655) = cCoq_2eInit_2eDecimal_2eD9___24a1(Vvar__0___24Anonymous__80656)
     => Vvar__0___24Anonymous__80655 = Vvar__0___24Anonymous__80656 ) ).

fof('$_inj_Coq.Init.Decimal.Decimal',axiom,
    ! [Vvar__0__i__124037,Vvar__0__i__124038,Vvar__1__f__124039,Vvar__1__f__124040] :
      ( cCoq_2eInit_2eDecimal_2eDecimal___24a2(Vvar__0__i__124037,Vvar__1__f__124039) = cCoq_2eInit_2eDecimal_2eDecimal___24a2(Vvar__0__i__124038,Vvar__1__f__124040)
     => ( Vvar__1__f__124039 = Vvar__1__f__124040
        & Vvar__0__i__124037 = Vvar__0__i__124038 ) ) ).

fof('$_inj_Coq.Init.Decimal.DecimalExp',axiom,
    ! [Vvar__0__i__124041,Vvar__0__i__124042,Vvar__1__f__124043,Vvar__1__f__124044,Vvar__2__e__124045,Vvar__2__e__124046] :
      ( cCoq_2eInit_2eDecimal_2eDecimalExp___24a3(Vvar__0__i__124041,Vvar__1__f__124043,Vvar__2__e__124045) = cCoq_2eInit_2eDecimal_2eDecimalExp___24a3(Vvar__0__i__124042,Vvar__1__f__124044,Vvar__2__e__124046)
     => ( Vvar__2__e__124045 = Vvar__2__e__124046
        & Vvar__1__f__124043 = Vvar__1__f__124044
        & Vvar__0__i__124041 = Vvar__0__i__124042 ) ) ).

fof('$_inj_Coq.Init.Decimal.Neg',axiom,
    ! [Vvar__0__d__119436,Vvar__0__d__119437] :
      ( cCoq_2eInit_2eDecimal_2eNeg___24a1(Vvar__0__d__119436) = cCoq_2eInit_2eDecimal_2eNeg___24a1(Vvar__0__d__119437)
     => Vvar__0__d__119436 = Vvar__0__d__119437 ) ).

fof('$_inj_Coq.Init.Decimal.Pos',axiom,
    ! [Vvar__0__d__119434,Vvar__0__d__119435] :
      ( cCoq_2eInit_2eDecimal_2ePos___24a1(Vvar__0__d__119434) = cCoq_2eInit_2eDecimal_2ePos___24a1(Vvar__0__d__119435)
     => Vvar__0__d__119434 = Vvar__0__d__119435 ) ).

fof('$_inj_Coq.Init.Specif.exist',axiom,
    ! [Vvar__0__A__3737,Vvar__0__A__3738,Vvar__1__P__3739,Vvar__1__P__3740,Vvar__2__x__3741,Vvar__2__x__3742,Vvar__3___24Anonymous__3743,Vvar__3___24Anonymous__3744] :
      ( cCoq_2eInit_2eSpecif_2eexist___24a3(Vvar__0__A__3737,Vvar__1__P__3739,Vvar__2__x__3741) = cCoq_2eInit_2eSpecif_2eexist___24a3(Vvar__0__A__3738,Vvar__1__P__3740,Vvar__2__x__3742)
     => ( c_24Proof = c_24Proof
        & Vvar__2__x__3741 = Vvar__2__x__3742
        & Vvar__1__P__3739 = Vvar__1__P__3740
        & Vvar__0__A__3737 = Vvar__0__A__3738 ) ) ).

fof('$_inj_Coq.Init.Specif.exist2',axiom,
    ! [Vvar__0__A__149155,Vvar__0__A__149156,Vvar__1__P__149157,Vvar__1__P__149158,Vvar__2__Q__149159,Vvar__2__Q__149160,Vvar__3__x__149161,Vvar__3__x__149162,Vvar__4___24Anonymous__149163,Vvar__4___24Anonymous__149164,Vvar__5___24Anonymous__149165,Vvar__5___24Anonymous__149166] :
      ( cCoq_2eInit_2eSpecif_2eexist2___24a4(Vvar__0__A__149155,Vvar__1__P__149157,Vvar__2__Q__149159,Vvar__3__x__149161) = cCoq_2eInit_2eSpecif_2eexist2___24a4(Vvar__0__A__149156,Vvar__1__P__149158,Vvar__2__Q__149160,Vvar__3__x__149162)
     => ( c_24Proof = c_24Proof
        & c_24Proof = c_24Proof
        & Vvar__3__x__149161 = Vvar__3__x__149162
        & Vvar__2__Q__149159 = Vvar__2__Q__149160
        & Vvar__1__P__149157 = Vvar__1__P__149158
        & Vvar__0__A__149155 = Vvar__0__A__149156 ) ) ).

fof('$_inj_Coq.Init.Specif.existT',axiom,
    ! [Vvar__0__A__139666,Vvar__0__A__139667,Vvar__1__P__139668,Vvar__1__P__139669,Vvar__2__x__139670,Vvar__2__x__139671,Vvar__3___24Anonymous__139672,Vvar__3___24Anonymous__139673] :
      ( cCoq_2eInit_2eSpecif_2eexistT___24a4(Vvar__0__A__139666,Vvar__1__P__139668,Vvar__2__x__139670,Vvar__3___24Anonymous__139672) = cCoq_2eInit_2eSpecif_2eexistT___24a4(Vvar__0__A__139667,Vvar__1__P__139669,Vvar__2__x__139671,Vvar__3___24Anonymous__139673)
     => ( Vvar__3___24Anonymous__139672 = Vvar__3___24Anonymous__139673
        & Vvar__2__x__139670 = Vvar__2__x__139671
        & Vvar__1__P__139668 = Vvar__1__P__139669
        & Vvar__0__A__139666 = Vvar__0__A__139667 ) ) ).

fof('$_inj_Coq.Init.Specif.existT2',axiom,
    ! [Vvar__0__A__139728,Vvar__0__A__139729,Vvar__1__P__139730,Vvar__1__P__139731,Vvar__2__Q__139732,Vvar__2__Q__139733,Vvar__3__x__139734,Vvar__3__x__139735,Vvar__4___24Anonymous__139736,Vvar__4___24Anonymous__139737,Vvar__5___24Anonymous__139738,Vvar__5___24Anonymous__139739] :
      ( cCoq_2eInit_2eSpecif_2eexistT2___24a6(Vvar__0__A__139728,Vvar__1__P__139730,Vvar__2__Q__139732,Vvar__3__x__139734,Vvar__4___24Anonymous__139736,Vvar__5___24Anonymous__139738) = cCoq_2eInit_2eSpecif_2eexistT2___24a6(Vvar__0__A__139729,Vvar__1__P__139731,Vvar__2__Q__139733,Vvar__3__x__139735,Vvar__4___24Anonymous__139737,Vvar__5___24Anonymous__139739)
     => ( Vvar__5___24Anonymous__139738 = Vvar__5___24Anonymous__139739
        & Vvar__4___24Anonymous__139736 = Vvar__4___24Anonymous__139737
        & Vvar__3__x__139734 = Vvar__3__x__139735
        & Vvar__2__Q__139732 = Vvar__2__Q__139733
        & Vvar__1__P__139730 = Vvar__1__P__139731
        & Vvar__0__A__139728 = Vvar__0__A__139729 ) ) ).

fof('$_inj_Coq.Init.Specif.inleft',axiom,
    ! [Vvar__0__A__3813,Vvar__0__A__3814,Vvar__1__B__3815,Vvar__1__B__3816,Vvar__2___24Anonymous__3817,Vvar__2___24Anonymous__3818] :
      ( cCoq_2eInit_2eSpecif_2einleft___24a3(Vvar__0__A__3813,Vvar__1__B__3815,Vvar__2___24Anonymous__3817) = cCoq_2eInit_2eSpecif_2einleft___24a3(Vvar__0__A__3814,Vvar__1__B__3816,Vvar__2___24Anonymous__3818)
     => ( Vvar__2___24Anonymous__3817 = Vvar__2___24Anonymous__3818
        & Vvar__1__B__3815 = Vvar__1__B__3816
        & Vvar__0__A__3813 = Vvar__0__A__3814 ) ) ).

fof('$_inj_Coq.Init.Specif.inright',axiom,
    ! [Vvar__0__A__3819,Vvar__0__A__3820,Vvar__1__B__3821,Vvar__1__B__3822,Vvar__2___24Anonymous__3823,Vvar__2___24Anonymous__3824] :
      ( cCoq_2eInit_2eSpecif_2einright___24a2(Vvar__0__A__3819,Vvar__1__B__3821) = cCoq_2eInit_2eSpecif_2einright___24a2(Vvar__0__A__3820,Vvar__1__B__3822)
     => ( c_24Proof = c_24Proof
        & Vvar__1__B__3821 = Vvar__1__B__3822
        & Vvar__0__A__3819 = Vvar__0__A__3820 ) ) ).

fof('$_inj_Coq.Init.Specif.left',axiom,
    ! [Vvar__0__A__3773,Vvar__0__A__3774,Vvar__1__B__3775,Vvar__1__B__3776,Vvar__2___24Anonymous__3777,Vvar__2___24Anonymous__3778] :
      ( cCoq_2eInit_2eSpecif_2eleft___24a2(Vvar__0__A__3773,Vvar__1__B__3775) = cCoq_2eInit_2eSpecif_2eleft___24a2(Vvar__0__A__3774,Vvar__1__B__3776)
     => ( c_24Proof = c_24Proof
        & Vvar__1__B__3775 = Vvar__1__B__3776
        & Vvar__0__A__3773 = Vvar__0__A__3774 ) ) ).

fof('$_inj_Coq.Init.Specif.right',axiom,
    ! [Vvar__0__A__3779,Vvar__0__A__3780,Vvar__1__B__3781,Vvar__1__B__3782,Vvar__2___24Anonymous__3783,Vvar__2___24Anonymous__3784] :
      ( cCoq_2eInit_2eSpecif_2eright___24a2(Vvar__0__A__3779,Vvar__1__B__3781) = cCoq_2eInit_2eSpecif_2eright___24a2(Vvar__0__A__3780,Vvar__1__B__3782)
     => ( c_24Proof = c_24Proof
        & Vvar__1__B__3781 = Vvar__1__B__3782
        & Vvar__0__A__3779 = Vvar__0__A__3780 ) ) ).

fof('$_inj_Coq.Numbers.BinNums.Npos',axiom,
    ! [Vvar__0___24Anonymous__1779,Vvar__0___24Anonymous__1780] :
      ( cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__1779) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__1780)
     => Vvar__0___24Anonymous__1779 = Vvar__0___24Anonymous__1780 ) ).

fof('$_inj_Coq.Numbers.BinNums.Zneg',axiom,
    ! [Vvar__0___24Anonymous__231,Vvar__0___24Anonymous__232] :
      ( cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__231) = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__232)
     => Vvar__0___24Anonymous__231 = Vvar__0___24Anonymous__232 ) ).

fof('$_inj_Coq.Numbers.BinNums.Zpos',axiom,
    ! [Vvar__0___24Anonymous__229,Vvar__0___24Anonymous__230] :
      ( cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__229) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__230)
     => Vvar__0___24Anonymous__229 = Vvar__0___24Anonymous__230 ) ).

fof('$_inj_Coq.Numbers.BinNums.xI',axiom,
    ! [Vvar__0___24Anonymous__216,Vvar__0___24Anonymous__217] :
      ( cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__216) = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__217)
     => Vvar__0___24Anonymous__216 = Vvar__0___24Anonymous__217 ) ).

fof('$_inj_Coq.Numbers.BinNums.xO',axiom,
    ! [Vvar__0___24Anonymous__218,Vvar__0___24Anonymous__219] :
      ( cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__218) = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__219)
     => Vvar__0___24Anonymous__218 = Vvar__0___24Anonymous__219 ) ).

fof('$_inj_Coq.PArith.BinPos.Pos.PeanoSucc',axiom,
    ! [Vvar__0__p__145162,Vvar__0__p__145163,Vvar__1___24Anonymous__145164,Vvar__1___24Anonymous__145165] :
      ( cCoq_2ePArith_2eBinPos_2ePos_2ePeanoSucc___24a2(Vvar__0__p__145162,Vvar__1___24Anonymous__145164) = cCoq_2ePArith_2eBinPos_2ePos_2ePeanoSucc___24a2(Vvar__0__p__145163,Vvar__1___24Anonymous__145165)
     => ( Vvar__1___24Anonymous__145164 = Vvar__1___24Anonymous__145165
        & Vvar__0__p__145162 = Vvar__0__p__145163 ) ) ).

fof('$_inj_Coq.PArith.BinPosDef.Pos.IsPos',axiom,
    ! [Vvar__0___24Anonymous__7066,Vvar__0___24Anonymous__7067] :
      ( cCoq_2ePArith_2eBinPosDef_2ePos_2eIsPos___24a1(Vvar__0___24Anonymous__7066) = cCoq_2ePArith_2eBinPosDef_2ePos_2eIsPos___24a1(Vvar__0___24Anonymous__7067)
     => Vvar__0___24Anonymous__7066 = Vvar__0___24Anonymous__7067 ) ).

fof('$_inj_Coq.QArith.QArith_base.Qmake',axiom,
    ! [Vvar__0__Qnum__122183,Vvar__0__Qnum__122184,Vvar__1__Qden__122185,Vvar__1__Qden__122186] :
      ( cCoq_2eQArith_2eQArith__base_2eQmake___24a2(Vvar__0__Qnum__122183,Vvar__1__Qden__122185) = cCoq_2eQArith_2eQArith__base_2eQmake___24a2(Vvar__0__Qnum__122184,Vvar__1__Qden__122186)
     => ( Vvar__1__Qden__122185 = Vvar__1__Qden__122186
        & Vvar__0__Qnum__122183 = Vvar__0__Qnum__122184 ) ) ).

fof('$_inj_Coq.Reals.RIneq.mknegreal',axiom,
    ! [Vvar__0__neg__147826,Vvar__0__neg__147827,Vvar__1__cond__neg__147828,Vvar__1__cond__neg__147829] :
      ( cCoq_2eReals_2eRIneq_2emknegreal___24a1(Vvar__0__neg__147826) = cCoq_2eReals_2eRIneq_2emknegreal___24a1(Vvar__0__neg__147827)
     => ( c_24Proof = c_24Proof
        & Vvar__0__neg__147826 = Vvar__0__neg__147827 ) ) ).

fof('$_inj_Coq.Reals.RIneq.mknonnegreal',axiom,
    ! [Vvar__0__nonneg__147805,Vvar__0__nonneg__147806,Vvar__1__cond__nonneg__147807,Vvar__1__cond__nonneg__147808] :
      ( cCoq_2eReals_2eRIneq_2emknonnegreal___24a1(Vvar__0__nonneg__147805) = cCoq_2eReals_2eRIneq_2emknonnegreal___24a1(Vvar__0__nonneg__147806)
     => ( c_24Proof = c_24Proof
        & Vvar__0__nonneg__147805 = Vvar__0__nonneg__147806 ) ) ).

fof('$_inj_Coq.Reals.RIneq.mknonposreal',axiom,
    ! [Vvar__0__nonpos__147819,Vvar__0__nonpos__147820,Vvar__1__cond__nonpos__147821,Vvar__1__cond__nonpos__147822] :
      ( cCoq_2eReals_2eRIneq_2emknonposreal___24a1(Vvar__0__nonpos__147819) = cCoq_2eReals_2eRIneq_2emknonposreal___24a1(Vvar__0__nonpos__147820)
     => ( c_24Proof = c_24Proof
        & Vvar__0__nonpos__147819 = Vvar__0__nonpos__147820 ) ) ).

fof('$_inj_Coq.Reals.RIneq.mknonzeroreal',axiom,
    ! [Vvar__0__nonzero__147833,Vvar__0__nonzero__147834,Vvar__1__cond__nonzero__147835,Vvar__1__cond__nonzero__147836] :
      ( cCoq_2eReals_2eRIneq_2emknonzeroreal___24a1(Vvar__0__nonzero__147833) = cCoq_2eReals_2eRIneq_2emknonzeroreal___24a1(Vvar__0__nonzero__147834)
     => ( c_24Proof = c_24Proof
        & Vvar__0__nonzero__147833 = Vvar__0__nonzero__147834 ) ) ).

fof('$_inj_Coq.Reals.RIneq.mkposreal',axiom,
    ! [Vvar__0__pos__147812,Vvar__0__pos__147813,Vvar__1__cond__pos__147814,Vvar__1__cond__pos__147815] :
      ( cCoq_2eReals_2eRIneq_2emkposreal___24a1(Vvar__0__pos__147812) = cCoq_2eReals_2eRIneq_2emkposreal___24a1(Vvar__0__pos__147813)
     => ( c_24Proof = c_24Proof
        & Vvar__0__pos__147812 = Vvar__0__pos__147813 ) ) ).

fof('$_inj_Coq.Reals.Rfunctions.ZintNeg',axiom,
    ! [Vvar__0__x__126330,Vvar__0__x__126331,Vvar__1__n__126332,Vvar__1__n__126333,Vvar__2___24Anonymous__126334,Vvar__2___24Anonymous__126335] :
      ( cCoq_2eReals_2eRfunctions_2eZintNeg___24a2(Vvar__0__x__126330,Vvar__1__n__126332) = cCoq_2eReals_2eRfunctions_2eZintNeg___24a2(Vvar__0__x__126331,Vvar__1__n__126333)
     => ( c_24Proof = c_24Proof
        & Vvar__1__n__126332 = Vvar__1__n__126333
        & Vvar__0__x__126330 = Vvar__0__x__126331 ) ) ).

fof('$_inj_Coq.Reals.Rfunctions.ZintNull',axiom,
    ! [Vvar__0__x__126320,Vvar__0__x__126321,Vvar__1___24Anonymous__126322,Vvar__1___24Anonymous__126323] :
      ( cCoq_2eReals_2eRfunctions_2eZintNull___24a1(Vvar__0__x__126320) = cCoq_2eReals_2eRfunctions_2eZintNull___24a1(Vvar__0__x__126321)
     => ( c_24Proof = c_24Proof
        & Vvar__0__x__126320 = Vvar__0__x__126321 ) ) ).

fof('$_inj_Coq.Reals.Rfunctions.ZintPos',axiom,
    ! [Vvar__0__x__126324,Vvar__0__x__126325,Vvar__1__n__126326,Vvar__1__n__126327,Vvar__2___24Anonymous__126328,Vvar__2___24Anonymous__126329] :
      ( cCoq_2eReals_2eRfunctions_2eZintPos___24a2(Vvar__0__x__126324,Vvar__1__n__126326) = cCoq_2eReals_2eRfunctions_2eZintPos___24a2(Vvar__0__x__126325,Vvar__1__n__126327)
     => ( c_24Proof = c_24Proof
        & Vvar__1__n__126326 = Vvar__1__n__126327
        & Vvar__0__x__126324 = Vvar__0__x__126325 ) ) ).

fof('$_inj_Coq.Strings.Ascii.Ascii',axiom,
    ! [Vvar__0___24Anonymous__4908,Vvar__0___24Anonymous__4909,Vvar__1___24Anonymous__4910,Vvar__1___24Anonymous__4911,Vvar__2___24Anonymous__4912,Vvar__2___24Anonymous__4913,Vvar__3___24Anonymous__4914,Vvar__3___24Anonymous__4915,Vvar__4___24Anonymous__4916,Vvar__4___24Anonymous__4917,Vvar__5___24Anonymous__4918,Vvar__5___24Anonymous__4919,Vvar__6___24Anonymous__4920,Vvar__6___24Anonymous__4921,Vvar__7___24Anonymous__4922,Vvar__7___24Anonymous__4923] :
      ( cCoq_2eStrings_2eAscii_2eAscii___24a8(Vvar__0___24Anonymous__4908,Vvar__1___24Anonymous__4910,Vvar__2___24Anonymous__4912,Vvar__3___24Anonymous__4914,Vvar__4___24Anonymous__4916,Vvar__5___24Anonymous__4918,Vvar__6___24Anonymous__4920,Vvar__7___24Anonymous__4922) = cCoq_2eStrings_2eAscii_2eAscii___24a8(Vvar__0___24Anonymous__4909,Vvar__1___24Anonymous__4911,Vvar__2___24Anonymous__4913,Vvar__3___24Anonymous__4915,Vvar__4___24Anonymous__4917,Vvar__5___24Anonymous__4919,Vvar__6___24Anonymous__4921,Vvar__7___24Anonymous__4923)
     => ( Vvar__7___24Anonymous__4922 = Vvar__7___24Anonymous__4923
        & Vvar__6___24Anonymous__4920 = Vvar__6___24Anonymous__4921
        & Vvar__5___24Anonymous__4918 = Vvar__5___24Anonymous__4919
        & Vvar__4___24Anonymous__4916 = Vvar__4___24Anonymous__4917
        & Vvar__3___24Anonymous__4914 = Vvar__3___24Anonymous__4915
        & Vvar__2___24Anonymous__4912 = Vvar__2___24Anonymous__4913
        & Vvar__1___24Anonymous__4910 = Vvar__1___24Anonymous__4911
        & Vvar__0___24Anonymous__4908 = Vvar__0___24Anonymous__4909 ) ) ).

fof('$_inj_Coq.Strings.String.String',axiom,
    ! [Vvar__0___24Anonymous__205,Vvar__0___24Anonymous__206,Vvar__1___24Anonymous__207,Vvar__1___24Anonymous__208] :
      ( cCoq_2eStrings_2eString_2eString___24a2(Vvar__0___24Anonymous__205,Vvar__1___24Anonymous__207) = cCoq_2eStrings_2eString_2eString___24a2(Vvar__0___24Anonymous__206,Vvar__1___24Anonymous__208)
     => ( Vvar__1___24Anonymous__207 = Vvar__1___24Anonymous__208
        & Vvar__0___24Anonymous__205 = Vvar__0___24Anonymous__206 ) ) ).

fof('$_inj_Coq.Structures.OrderedType.EQ',axiom,
    ! [Vvar__0__X__122052,Vvar__0__X__122053,Vvar__1__lt__122054,Vvar__1__lt__122055,Vvar__2__eq__122056,Vvar__2__eq__122057,Vvar__3__x__122058,Vvar__3__x__122059,Vvar__4__y__122060,Vvar__4__y__122061,Vvar__5___24Anonymous__122062,Vvar__5___24Anonymous__122063] :
      ( cCoq_2eStructures_2eOrderedType_2eEQ___24a5(Vvar__0__X__122052,Vvar__1__lt__122054,Vvar__2__eq__122056,Vvar__3__x__122058,Vvar__4__y__122060) = cCoq_2eStructures_2eOrderedType_2eEQ___24a5(Vvar__0__X__122053,Vvar__1__lt__122055,Vvar__2__eq__122057,Vvar__3__x__122059,Vvar__4__y__122061)
     => ( c_24Proof = c_24Proof
        & Vvar__4__y__122060 = Vvar__4__y__122061
        & Vvar__3__x__122058 = Vvar__3__x__122059
        & Vvar__2__eq__122056 = Vvar__2__eq__122057
        & Vvar__1__lt__122054 = Vvar__1__lt__122055
        & Vvar__0__X__122052 = Vvar__0__X__122053 ) ) ).

fof('$_inj_Coq.Structures.OrderedType.GT',axiom,
    ! [Vvar__0__X__122064,Vvar__0__X__122065,Vvar__1__lt__122066,Vvar__1__lt__122067,Vvar__2__eq__122068,Vvar__2__eq__122069,Vvar__3__x__122070,Vvar__3__x__122071,Vvar__4__y__122072,Vvar__4__y__122073,Vvar__5___24Anonymous__122074,Vvar__5___24Anonymous__122075] :
      ( cCoq_2eStructures_2eOrderedType_2eGT___24a5(Vvar__0__X__122064,Vvar__1__lt__122066,Vvar__2__eq__122068,Vvar__3__x__122070,Vvar__4__y__122072) = cCoq_2eStructures_2eOrderedType_2eGT___24a5(Vvar__0__X__122065,Vvar__1__lt__122067,Vvar__2__eq__122069,Vvar__3__x__122071,Vvar__4__y__122073)
     => ( c_24Proof = c_24Proof
        & Vvar__4__y__122072 = Vvar__4__y__122073
        & Vvar__3__x__122070 = Vvar__3__x__122071
        & Vvar__2__eq__122068 = Vvar__2__eq__122069
        & Vvar__1__lt__122066 = Vvar__1__lt__122067
        & Vvar__0__X__122064 = Vvar__0__X__122065 ) ) ).

fof('$_inj_Coq.Structures.OrderedType.LT',axiom,
    ! [Vvar__0__X__122040,Vvar__0__X__122041,Vvar__1__lt__122042,Vvar__1__lt__122043,Vvar__2__eq__122044,Vvar__2__eq__122045,Vvar__3__x__122046,Vvar__3__x__122047,Vvar__4__y__122048,Vvar__4__y__122049,Vvar__5___24Anonymous__122050,Vvar__5___24Anonymous__122051] :
      ( cCoq_2eStructures_2eOrderedType_2eLT___24a5(Vvar__0__X__122040,Vvar__1__lt__122042,Vvar__2__eq__122044,Vvar__3__x__122046,Vvar__4__y__122048) = cCoq_2eStructures_2eOrderedType_2eLT___24a5(Vvar__0__X__122041,Vvar__1__lt__122043,Vvar__2__eq__122045,Vvar__3__x__122047,Vvar__4__y__122049)
     => ( c_24Proof = c_24Proof
        & Vvar__4__y__122048 = Vvar__4__y__122049
        & Vvar__3__x__122046 = Vvar__3__x__122047
        & Vvar__2__eq__122044 = Vvar__2__eq__122045
        & Vvar__1__lt__122042 = Vvar__1__lt__122043
        & Vvar__0__X__122040 = Vvar__0__X__122041 ) ) ).

fof('$_inj_Coq.Vectors.Fin.F1',axiom,
    ! [Vvar__0__n__1983,Vvar__0__n__1984] :
      ( cCoq_2eVectors_2eFin_2eF1___24a1(Vvar__0__n__1983) = cCoq_2eVectors_2eFin_2eF1___24a1(Vvar__0__n__1984)
     => Vvar__0__n__1983 = Vvar__0__n__1984 ) ).

fof('$_inj_Coq.Vectors.Fin.FS',axiom,
    ! [Vvar__0__n__1985,Vvar__0__n__1986,Vvar__1___24Anonymous__1987,Vvar__1___24Anonymous__1988] :
      ( cCoq_2eVectors_2eFin_2eFS___24a2(Vvar__0__n__1985,Vvar__1___24Anonymous__1987) = cCoq_2eVectors_2eFin_2eFS___24a2(Vvar__0__n__1986,Vvar__1___24Anonymous__1988)
     => ( Vvar__1___24Anonymous__1987 = Vvar__1___24Anonymous__1988
        & Vvar__0__n__1985 = Vvar__0__n__1986 ) ) ).

fof('$_inj_Coq.Vectors.VectorDef.cons',axiom,
    ! [Vvar__0__A__3853,Vvar__0__A__3854,Vvar__1__h__3855,Vvar__1__h__3856,Vvar__2__n__3857,Vvar__2__n__3858,Vvar__3___24Anonymous__3859,Vvar__3___24Anonymous__3860] :
      ( cCoq_2eVectors_2eVectorDef_2econs___24a4(Vvar__0__A__3853,Vvar__1__h__3855,Vvar__2__n__3857,Vvar__3___24Anonymous__3859) = cCoq_2eVectors_2eVectorDef_2econs___24a4(Vvar__0__A__3854,Vvar__1__h__3856,Vvar__2__n__3858,Vvar__3___24Anonymous__3860)
     => ( Vvar__3___24Anonymous__3859 = Vvar__3___24Anonymous__3860
        & Vvar__2__n__3857 = Vvar__2__n__3858
        & Vvar__1__h__3855 = Vvar__1__h__3856
        & Vvar__0__A__3853 = Vvar__0__A__3854 ) ) ).

fof('$_inj_Coq.Vectors.VectorDef.nil',axiom,
    ! [Vvar__0__A__3851,Vvar__0__A__3852] :
      ( cCoq_2eVectors_2eVectorDef_2enil___24a1(Vvar__0__A__3851) = cCoq_2eVectors_2eVectorDef_2enil___24a1(Vvar__0__A__3852)
     => Vvar__0__A__3851 = Vvar__0__A__3852 ) ).

fof('$_inj_Coq.ZArith.Znumtheory.Euclid_intro',axiom,
    ! [Vvar__0__a__143433,Vvar__0__a__143434,Vvar__1__b__143435,Vvar__1__b__143436,Vvar__2__u__143437,Vvar__2__u__143438,Vvar__3__v__143439,Vvar__3__v__143440,Vvar__4__d__143441,Vvar__4__d__143442,Vvar__5___24Anonymous__143443,Vvar__5___24Anonymous__143444,Vvar__6___24Anonymous__143445,Vvar__6___24Anonymous__143446] :
      ( cCoq_2eZArith_2eZnumtheory_2eEuclid__intro___24a5(Vvar__0__a__143433,Vvar__1__b__143435,Vvar__2__u__143437,Vvar__3__v__143439,Vvar__4__d__143441) = cCoq_2eZArith_2eZnumtheory_2eEuclid__intro___24a5(Vvar__0__a__143434,Vvar__1__b__143436,Vvar__2__u__143438,Vvar__3__v__143440,Vvar__4__d__143442)
     => ( c_24Proof = c_24Proof
        & c_24Proof = c_24Proof
        & Vvar__4__d__143441 = Vvar__4__d__143442
        & Vvar__3__v__143439 = Vvar__3__v__143440
        & Vvar__2__u__143437 = Vvar__2__u__143438
        & Vvar__1__b__143435 = Vvar__1__b__143436
        & Vvar__0__a__143433 = Vvar__0__a__143434 ) ) ).

fof('$_inj_Coq.ZArith.Zpower.Zdiv_rest_proof',axiom,
    ! [Vvar__0__x__149781,Vvar__0__x__149782,Vvar__1__p__149783,Vvar__1__p__149784,Vvar__2__q__149785,Vvar__2__q__149786,Vvar__3__r__149787,Vvar__3__r__149788,Vvar__4___24Anonymous__149789,Vvar__4___24Anonymous__149790,Vvar__5___24Anonymous__149791,Vvar__5___24Anonymous__149792,Vvar__6___24Anonymous__149793,Vvar__6___24Anonymous__149794] :
      ( cCoq_2eZArith_2eZpower_2eZdiv__rest__proof___24a4(Vvar__0__x__149781,Vvar__1__p__149783,Vvar__2__q__149785,Vvar__3__r__149787) = cCoq_2eZArith_2eZpower_2eZdiv__rest__proof___24a4(Vvar__0__x__149782,Vvar__1__p__149784,Vvar__2__q__149786,Vvar__3__r__149788)
     => ( c_24Proof = c_24Proof
        & c_24Proof = c_24Proof
        & c_24Proof = c_24Proof
        & Vvar__3__r__149787 = Vvar__3__r__149788
        & Vvar__2__q__149785 = Vvar__2__q__149786
        & Vvar__1__p__149783 = Vvar__1__p__149784
        & Vvar__0__x__149781 = Vvar__0__x__149782 ) ) ).

fof('$_inj_Coq.micromega.EnvRing.PEX',axiom,
    ! [Vvar__0__C__124187,Vvar__0__C__124188,Vvar__1___24Anonymous__124189,Vvar__1___24Anonymous__124190] :
      ( cCoq_2emicromega_2eEnvRing_2ePEX___24a2(Vvar__0__C__124187,Vvar__1___24Anonymous__124189) = cCoq_2emicromega_2eEnvRing_2ePEX___24a2(Vvar__0__C__124188,Vvar__1___24Anonymous__124190)
     => ( Vvar__1___24Anonymous__124189 = Vvar__1___24Anonymous__124190
        & Vvar__0__C__124187 = Vvar__0__C__124188 ) ) ).

fof('$_inj_Coq.micromega.EnvRing.PEadd',axiom,
    ! [Vvar__0__C__124191,Vvar__0__C__124192,Vvar__1___24Anonymous__124193,Vvar__1___24Anonymous__124194,Vvar__2___24Anonymous__124195,Vvar__2___24Anonymous__124196] :
      ( cCoq_2emicromega_2eEnvRing_2ePEadd___24a3(Vvar__0__C__124191,Vvar__1___24Anonymous__124193,Vvar__2___24Anonymous__124195) = cCoq_2emicromega_2eEnvRing_2ePEadd___24a3(Vvar__0__C__124192,Vvar__1___24Anonymous__124194,Vvar__2___24Anonymous__124196)
     => ( Vvar__2___24Anonymous__124195 = Vvar__2___24Anonymous__124196
        & Vvar__1___24Anonymous__124193 = Vvar__1___24Anonymous__124194
        & Vvar__0__C__124191 = Vvar__0__C__124192 ) ) ).

fof('$_inj_Coq.micromega.EnvRing.PEc',axiom,
    ! [Vvar__0__C__124183,Vvar__0__C__124184,Vvar__1___24Anonymous__124185,Vvar__1___24Anonymous__124186] :
      ( cCoq_2emicromega_2eEnvRing_2ePEc___24a2(Vvar__0__C__124183,Vvar__1___24Anonymous__124185) = cCoq_2emicromega_2eEnvRing_2ePEc___24a2(Vvar__0__C__124184,Vvar__1___24Anonymous__124186)
     => ( Vvar__1___24Anonymous__124185 = Vvar__1___24Anonymous__124186
        & Vvar__0__C__124183 = Vvar__0__C__124184 ) ) ).

fof('$_inj_Coq.micromega.EnvRing.PEmul',axiom,
    ! [Vvar__0__C__124203,Vvar__0__C__124204,Vvar__1___24Anonymous__124205,Vvar__1___24Anonymous__124206,Vvar__2___24Anonymous__124207,Vvar__2___24Anonymous__124208] :
      ( cCoq_2emicromega_2eEnvRing_2ePEmul___24a3(Vvar__0__C__124203,Vvar__1___24Anonymous__124205,Vvar__2___24Anonymous__124207) = cCoq_2emicromega_2eEnvRing_2ePEmul___24a3(Vvar__0__C__124204,Vvar__1___24Anonymous__124206,Vvar__2___24Anonymous__124208)
     => ( Vvar__2___24Anonymous__124207 = Vvar__2___24Anonymous__124208
        & Vvar__1___24Anonymous__124205 = Vvar__1___24Anonymous__124206
        & Vvar__0__C__124203 = Vvar__0__C__124204 ) ) ).

fof('$_inj_Coq.micromega.EnvRing.PEopp',axiom,
    ! [Vvar__0__C__124209,Vvar__0__C__124210,Vvar__1___24Anonymous__124211,Vvar__1___24Anonymous__124212] :
      ( cCoq_2emicromega_2eEnvRing_2ePEopp___24a2(Vvar__0__C__124209,Vvar__1___24Anonymous__124211) = cCoq_2emicromega_2eEnvRing_2ePEopp___24a2(Vvar__0__C__124210,Vvar__1___24Anonymous__124212)
     => ( Vvar__1___24Anonymous__124211 = Vvar__1___24Anonymous__124212
        & Vvar__0__C__124209 = Vvar__0__C__124210 ) ) ).

fof('$_inj_Coq.micromega.EnvRing.PEpow',axiom,
    ! [Vvar__0__C__124213,Vvar__0__C__124214,Vvar__1___24Anonymous__124215,Vvar__1___24Anonymous__124216,Vvar__2___24Anonymous__124217,Vvar__2___24Anonymous__124218] :
      ( cCoq_2emicromega_2eEnvRing_2ePEpow___24a3(Vvar__0__C__124213,Vvar__1___24Anonymous__124215,Vvar__2___24Anonymous__124217) = cCoq_2emicromega_2eEnvRing_2ePEpow___24a3(Vvar__0__C__124214,Vvar__1___24Anonymous__124216,Vvar__2___24Anonymous__124218)
     => ( Vvar__2___24Anonymous__124217 = Vvar__2___24Anonymous__124218
        & Vvar__1___24Anonymous__124215 = Vvar__1___24Anonymous__124216
        & Vvar__0__C__124213 = Vvar__0__C__124214 ) ) ).

fof('$_inj_Coq.micromega.EnvRing.PEsub',axiom,
    ! [Vvar__0__C__124197,Vvar__0__C__124198,Vvar__1___24Anonymous__124199,Vvar__1___24Anonymous__124200,Vvar__2___24Anonymous__124201,Vvar__2___24Anonymous__124202] :
      ( cCoq_2emicromega_2eEnvRing_2ePEsub___24a3(Vvar__0__C__124197,Vvar__1___24Anonymous__124199,Vvar__2___24Anonymous__124201) = cCoq_2emicromega_2eEnvRing_2ePEsub___24a3(Vvar__0__C__124198,Vvar__1___24Anonymous__124200,Vvar__2___24Anonymous__124202)
     => ( Vvar__2___24Anonymous__124201 = Vvar__2___24Anonymous__124202
        & Vvar__1___24Anonymous__124199 = Vvar__1___24Anonymous__124200
        & Vvar__0__C__124197 = Vvar__0__C__124198 ) ) ).

fof('$_inj_Coq.micromega.EnvRing.PX',axiom,
    ! [Vvar__0__C__124258,Vvar__0__C__124259,Vvar__1___24Anonymous__124260,Vvar__1___24Anonymous__124261,Vvar__2___24Anonymous__124262,Vvar__2___24Anonymous__124263,Vvar__3___24Anonymous__124264,Vvar__3___24Anonymous__124265] :
      ( cCoq_2emicromega_2eEnvRing_2ePX___24a4(Vvar__0__C__124258,Vvar__1___24Anonymous__124260,Vvar__2___24Anonymous__124262,Vvar__3___24Anonymous__124264) = cCoq_2emicromega_2eEnvRing_2ePX___24a4(Vvar__0__C__124259,Vvar__1___24Anonymous__124261,Vvar__2___24Anonymous__124263,Vvar__3___24Anonymous__124265)
     => ( Vvar__3___24Anonymous__124264 = Vvar__3___24Anonymous__124265
        & Vvar__2___24Anonymous__124262 = Vvar__2___24Anonymous__124263
        & Vvar__1___24Anonymous__124260 = Vvar__1___24Anonymous__124261
        & Vvar__0__C__124258 = Vvar__0__C__124259 ) ) ).

fof('$_inj_Coq.micromega.EnvRing.Pc',axiom,
    ! [Vvar__0__C__124248,Vvar__0__C__124249,Vvar__1___24Anonymous__124250,Vvar__1___24Anonymous__124251] :
      ( cCoq_2emicromega_2eEnvRing_2ePc___24a2(Vvar__0__C__124248,Vvar__1___24Anonymous__124250) = cCoq_2emicromega_2eEnvRing_2ePc___24a2(Vvar__0__C__124249,Vvar__1___24Anonymous__124251)
     => ( Vvar__1___24Anonymous__124250 = Vvar__1___24Anonymous__124251
        & Vvar__0__C__124248 = Vvar__0__C__124249 ) ) ).

fof('$_inj_Coq.micromega.EnvRing.Pinj',axiom,
    ! [Vvar__0__C__124252,Vvar__0__C__124253,Vvar__1___24Anonymous__124254,Vvar__1___24Anonymous__124255,Vvar__2___24Anonymous__124256,Vvar__2___24Anonymous__124257] :
      ( cCoq_2emicromega_2eEnvRing_2ePinj___24a3(Vvar__0__C__124252,Vvar__1___24Anonymous__124254,Vvar__2___24Anonymous__124256) = cCoq_2emicromega_2eEnvRing_2ePinj___24a3(Vvar__0__C__124253,Vvar__1___24Anonymous__124255,Vvar__2___24Anonymous__124257)
     => ( Vvar__2___24Anonymous__124256 = Vvar__2___24Anonymous__124257
        & Vvar__1___24Anonymous__124254 = Vvar__1___24Anonymous__124255
        & Vvar__0__C__124252 = Vvar__0__C__124253 ) ) ).

fof('$_inj_Coq.micromega.EnvRing.vmon',axiom,
    ! [Vvar__0___24Anonymous__124286,Vvar__0___24Anonymous__124287,Vvar__1___24Anonymous__124288,Vvar__1___24Anonymous__124289] :
      ( cCoq_2emicromega_2eEnvRing_2evmon___24a2(Vvar__0___24Anonymous__124286,Vvar__1___24Anonymous__124288) = cCoq_2emicromega_2eEnvRing_2evmon___24a2(Vvar__0___24Anonymous__124287,Vvar__1___24Anonymous__124289)
     => ( Vvar__1___24Anonymous__124288 = Vvar__1___24Anonymous__124289
        & Vvar__0___24Anonymous__124286 = Vvar__0___24Anonymous__124287 ) ) ).

fof('$_inj_Coq.micromega.EnvRing.zmon',axiom,
    ! [Vvar__0___24Anonymous__124282,Vvar__0___24Anonymous__124283,Vvar__1___24Anonymous__124284,Vvar__1___24Anonymous__124285] :
      ( cCoq_2emicromega_2eEnvRing_2ezmon___24a2(Vvar__0___24Anonymous__124282,Vvar__1___24Anonymous__124284) = cCoq_2emicromega_2eEnvRing_2ezmon___24a2(Vvar__0___24Anonymous__124283,Vvar__1___24Anonymous__124285)
     => ( Vvar__1___24Anonymous__124284 = Vvar__1___24Anonymous__124285
        & Vvar__0___24Anonymous__124282 = Vvar__0___24Anonymous__124283 ) ) ).

fof('$_inj_Coq.micromega.RMicromega.CInv',axiom,
    ! [Vvar__0__r__122328,Vvar__0__r__122329] :
      ( cCoq_2emicromega_2eRMicromega_2eCInv___24a1(Vvar__0__r__122328) = cCoq_2emicromega_2eRMicromega_2eCInv___24a1(Vvar__0__r__122329)
     => Vvar__0__r__122328 = Vvar__0__r__122329 ) ).

fof('$_inj_Coq.micromega.RMicromega.CMinus',axiom,
    ! [Vvar__0__r1__122316,Vvar__0__r1__122317,Vvar__1__r2__122318,Vvar__1__r2__122319] :
      ( cCoq_2emicromega_2eRMicromega_2eCMinus___24a2(Vvar__0__r1__122316,Vvar__1__r2__122318) = cCoq_2emicromega_2eRMicromega_2eCMinus___24a2(Vvar__0__r1__122317,Vvar__1__r2__122319)
     => ( Vvar__1__r2__122318 = Vvar__1__r2__122319
        & Vvar__0__r1__122316 = Vvar__0__r1__122317 ) ) ).

fof('$_inj_Coq.micromega.RMicromega.CMult',axiom,
    ! [Vvar__0__r1__122320,Vvar__0__r1__122321,Vvar__1__r2__122322,Vvar__1__r2__122323] :
      ( cCoq_2emicromega_2eRMicromega_2eCMult___24a2(Vvar__0__r1__122320,Vvar__1__r2__122322) = cCoq_2emicromega_2eRMicromega_2eCMult___24a2(Vvar__0__r1__122321,Vvar__1__r2__122323)
     => ( Vvar__1__r2__122322 = Vvar__1__r2__122323
        & Vvar__0__r1__122320 = Vvar__0__r1__122321 ) ) ).

fof('$_inj_Coq.micromega.RMicromega.COpp',axiom,
    ! [Vvar__0__r__122330,Vvar__0__r__122331] :
      ( cCoq_2emicromega_2eRMicromega_2eCOpp___24a1(Vvar__0__r__122330) = cCoq_2emicromega_2eRMicromega_2eCOpp___24a1(Vvar__0__r__122331)
     => Vvar__0__r__122330 = Vvar__0__r__122331 ) ).

fof('$_inj_Coq.micromega.RMicromega.CPlus',axiom,
    ! [Vvar__0__r1__122312,Vvar__0__r1__122313,Vvar__1__r2__122314,Vvar__1__r2__122315] :
      ( cCoq_2emicromega_2eRMicromega_2eCPlus___24a2(Vvar__0__r1__122312,Vvar__1__r2__122314) = cCoq_2emicromega_2eRMicromega_2eCPlus___24a2(Vvar__0__r1__122313,Vvar__1__r2__122315)
     => ( Vvar__1__r2__122314 = Vvar__1__r2__122315
        & Vvar__0__r1__122312 = Vvar__0__r1__122313 ) ) ).

fof('$_inj_Coq.micromega.RMicromega.CPow',axiom,
    ! [Vvar__0__r1__122324,Vvar__0__r1__122325,Vvar__1__z__122326,Vvar__1__z__122327] :
      ( cCoq_2emicromega_2eRMicromega_2eCPow___24a2(Vvar__0__r1__122324,Vvar__1__z__122326) = cCoq_2emicromega_2eRMicromega_2eCPow___24a2(Vvar__0__r1__122325,Vvar__1__z__122327)
     => ( Vvar__1__z__122326 = Vvar__1__z__122327
        & Vvar__0__r1__122324 = Vvar__0__r1__122325 ) ) ).

fof('$_inj_Coq.micromega.RMicromega.CQ',axiom,
    ! [Vvar__0__r__122308,Vvar__0__r__122309] :
      ( cCoq_2emicromega_2eRMicromega_2eCQ___24a1(Vvar__0__r__122308) = cCoq_2emicromega_2eRMicromega_2eCQ___24a1(Vvar__0__r__122309)
     => Vvar__0__r__122308 = Vvar__0__r__122309 ) ).

fof('$_inj_Coq.micromega.RMicromega.CZ',axiom,
    ! [Vvar__0__r__122310,Vvar__0__r__122311] :
      ( cCoq_2emicromega_2eRMicromega_2eCZ___24a1(Vvar__0__r__122310) = cCoq_2emicromega_2eRMicromega_2eCZ___24a1(Vvar__0__r__122311)
     => Vvar__0__r__122310 = Vvar__0__r__122311 ) ).

fof('$_inj_Coq.micromega.RingMicromega.Build_Formula',axiom,
    ! [Vvar__0__T__131799,Vvar__0__T__131800,Vvar__1__Flhs__131801,Vvar__1__Flhs__131802,Vvar__2__Fop__131803,Vvar__2__Fop__131804,Vvar__3__Frhs__131805,Vvar__3__Frhs__131806] :
      ( cCoq_2emicromega_2eRingMicromega_2eBuild__Formula___24a4(Vvar__0__T__131799,Vvar__1__Flhs__131801,Vvar__2__Fop__131803,Vvar__3__Frhs__131805) = cCoq_2emicromega_2eRingMicromega_2eBuild__Formula___24a4(Vvar__0__T__131800,Vvar__1__Flhs__131802,Vvar__2__Fop__131804,Vvar__3__Frhs__131806)
     => ( Vvar__3__Frhs__131805 = Vvar__3__Frhs__131806
        & Vvar__2__Fop__131803 = Vvar__2__Fop__131804
        & Vvar__1__Flhs__131801 = Vvar__1__Flhs__131802
        & Vvar__0__T__131799 = Vvar__0__T__131800 ) ) ).

fof('$_inj_Coq.micromega.RingMicromega.PsatzAdd',axiom,
    ! [Vvar__0__C__131766,Vvar__0__C__131767,Vvar__1___24Anonymous__131768,Vvar__1___24Anonymous__131769,Vvar__2___24Anonymous__131770,Vvar__2___24Anonymous__131771] :
      ( cCoq_2emicromega_2eRingMicromega_2ePsatzAdd___24a3(Vvar__0__C__131766,Vvar__1___24Anonymous__131768,Vvar__2___24Anonymous__131770) = cCoq_2emicromega_2eRingMicromega_2ePsatzAdd___24a3(Vvar__0__C__131767,Vvar__1___24Anonymous__131769,Vvar__2___24Anonymous__131771)
     => ( Vvar__2___24Anonymous__131770 = Vvar__2___24Anonymous__131771
        & Vvar__1___24Anonymous__131768 = Vvar__1___24Anonymous__131769
        & Vvar__0__C__131766 = Vvar__0__C__131767 ) ) ).

fof('$_inj_Coq.micromega.RingMicromega.PsatzC',axiom,
    ! [Vvar__0__C__131772,Vvar__0__C__131773,Vvar__1___24Anonymous__131774,Vvar__1___24Anonymous__131775] :
      ( cCoq_2emicromega_2eRingMicromega_2ePsatzC___24a2(Vvar__0__C__131772,Vvar__1___24Anonymous__131774) = cCoq_2emicromega_2eRingMicromega_2ePsatzC___24a2(Vvar__0__C__131773,Vvar__1___24Anonymous__131775)
     => ( Vvar__1___24Anonymous__131774 = Vvar__1___24Anonymous__131775
        & Vvar__0__C__131772 = Vvar__0__C__131773 ) ) ).

fof('$_inj_Coq.micromega.RingMicromega.PsatzIn',axiom,
    ! [Vvar__0__C__131746,Vvar__0__C__131747,Vvar__1___24Anonymous__131748,Vvar__1___24Anonymous__131749] :
      ( cCoq_2emicromega_2eRingMicromega_2ePsatzIn___24a2(Vvar__0__C__131746,Vvar__1___24Anonymous__131748) = cCoq_2emicromega_2eRingMicromega_2ePsatzIn___24a2(Vvar__0__C__131747,Vvar__1___24Anonymous__131749)
     => ( Vvar__1___24Anonymous__131748 = Vvar__1___24Anonymous__131749
        & Vvar__0__C__131746 = Vvar__0__C__131747 ) ) ).

fof('$_inj_Coq.micromega.RingMicromega.PsatzMulC',axiom,
    ! [Vvar__0__C__131754,Vvar__0__C__131755,Vvar__1___24Anonymous__131756,Vvar__1___24Anonymous__131757,Vvar__2___24Anonymous__131758,Vvar__2___24Anonymous__131759] :
      ( cCoq_2emicromega_2eRingMicromega_2ePsatzMulC___24a3(Vvar__0__C__131754,Vvar__1___24Anonymous__131756,Vvar__2___24Anonymous__131758) = cCoq_2emicromega_2eRingMicromega_2ePsatzMulC___24a3(Vvar__0__C__131755,Vvar__1___24Anonymous__131757,Vvar__2___24Anonymous__131759)
     => ( Vvar__2___24Anonymous__131758 = Vvar__2___24Anonymous__131759
        & Vvar__1___24Anonymous__131756 = Vvar__1___24Anonymous__131757
        & Vvar__0__C__131754 = Vvar__0__C__131755 ) ) ).

fof('$_inj_Coq.micromega.RingMicromega.PsatzMulE',axiom,
    ! [Vvar__0__C__131760,Vvar__0__C__131761,Vvar__1___24Anonymous__131762,Vvar__1___24Anonymous__131763,Vvar__2___24Anonymous__131764,Vvar__2___24Anonymous__131765] :
      ( cCoq_2emicromega_2eRingMicromega_2ePsatzMulE___24a3(Vvar__0__C__131760,Vvar__1___24Anonymous__131762,Vvar__2___24Anonymous__131764) = cCoq_2emicromega_2eRingMicromega_2ePsatzMulE___24a3(Vvar__0__C__131761,Vvar__1___24Anonymous__131763,Vvar__2___24Anonymous__131765)
     => ( Vvar__2___24Anonymous__131764 = Vvar__2___24Anonymous__131765
        & Vvar__1___24Anonymous__131762 = Vvar__1___24Anonymous__131763
        & Vvar__0__C__131760 = Vvar__0__C__131761 ) ) ).

fof('$_inj_Coq.micromega.RingMicromega.PsatzSquare',axiom,
    ! [Vvar__0__C__131750,Vvar__0__C__131751,Vvar__1___24Anonymous__131752,Vvar__1___24Anonymous__131753] :
      ( cCoq_2emicromega_2eRingMicromega_2ePsatzSquare___24a2(Vvar__0__C__131750,Vvar__1___24Anonymous__131752) = cCoq_2emicromega_2eRingMicromega_2ePsatzSquare___24a2(Vvar__0__C__131751,Vvar__1___24Anonymous__131753)
     => ( Vvar__1___24Anonymous__131752 = Vvar__1___24Anonymous__131753
        & Vvar__0__C__131750 = Vvar__0__C__131751 ) ) ).

fof('$_inj_Coq.micromega.RingMicromega.PsatzZ',axiom,
    ! [Vvar__0__C__131776,Vvar__0__C__131777] :
      ( cCoq_2emicromega_2eRingMicromega_2ePsatzZ___24a1(Vvar__0__C__131776) = cCoq_2emicromega_2eRingMicromega_2ePsatzZ___24a1(Vvar__0__C__131777)
     => Vvar__0__C__131776 = Vvar__0__C__131777 ) ).

fof('$_inj_Coq.micromega.Tauto.A',axiom,
    ! [Vvar__0__TA__149554,Vvar__0__TA__149555,Vvar__1__TX__149556,Vvar__1__TX__149557,Vvar__2__AA__149558,Vvar__2__AA__149559,Vvar__3__AF__149560,Vvar__3__AF__149561,Vvar__4___24Anonymous__149562,Vvar__4___24Anonymous__149563,Vvar__5___24Anonymous__149564,Vvar__5___24Anonymous__149565] :
      ( cCoq_2emicromega_2eTauto_2eA___24a6(Vvar__0__TA__149554,Vvar__1__TX__149556,Vvar__2__AA__149558,Vvar__3__AF__149560,Vvar__4___24Anonymous__149562,Vvar__5___24Anonymous__149564) = cCoq_2emicromega_2eTauto_2eA___24a6(Vvar__0__TA__149555,Vvar__1__TX__149557,Vvar__2__AA__149559,Vvar__3__AF__149561,Vvar__4___24Anonymous__149563,Vvar__5___24Anonymous__149565)
     => ( Vvar__5___24Anonymous__149564 = Vvar__5___24Anonymous__149565
        & Vvar__4___24Anonymous__149562 = Vvar__4___24Anonymous__149563
        & Vvar__3__AF__149560 = Vvar__3__AF__149561
        & Vvar__2__AA__149558 = Vvar__2__AA__149559
        & Vvar__1__TX__149556 = Vvar__1__TX__149557
        & Vvar__0__TA__149554 = Vvar__0__TA__149555 ) ) ).

fof('$_inj_Coq.micromega.Tauto.Cj',axiom,
    ! [Vvar__0__TA__149566,Vvar__0__TA__149567,Vvar__1__TX__149568,Vvar__1__TX__149569,Vvar__2__AA__149570,Vvar__2__AA__149571,Vvar__3__AF__149572,Vvar__3__AF__149573,Vvar__4___24Anonymous__149574,Vvar__4___24Anonymous__149575,Vvar__5___24Anonymous__149576,Vvar__5___24Anonymous__149577] :
      ( cCoq_2emicromega_2eTauto_2eCj___24a6(Vvar__0__TA__149566,Vvar__1__TX__149568,Vvar__2__AA__149570,Vvar__3__AF__149572,Vvar__4___24Anonymous__149574,Vvar__5___24Anonymous__149576) = cCoq_2emicromega_2eTauto_2eCj___24a6(Vvar__0__TA__149567,Vvar__1__TX__149569,Vvar__2__AA__149571,Vvar__3__AF__149573,Vvar__4___24Anonymous__149575,Vvar__5___24Anonymous__149577)
     => ( Vvar__5___24Anonymous__149576 = Vvar__5___24Anonymous__149577
        & Vvar__4___24Anonymous__149574 = Vvar__4___24Anonymous__149575
        & Vvar__3__AF__149572 = Vvar__3__AF__149573
        & Vvar__2__AA__149570 = Vvar__2__AA__149571
        & Vvar__1__TX__149568 = Vvar__1__TX__149569
        & Vvar__0__TA__149566 = Vvar__0__TA__149567 ) ) ).

fof('$_inj_Coq.micromega.Tauto.D',axiom,
    ! [Vvar__0__TA__149578,Vvar__0__TA__149579,Vvar__1__TX__149580,Vvar__1__TX__149581,Vvar__2__AA__149582,Vvar__2__AA__149583,Vvar__3__AF__149584,Vvar__3__AF__149585,Vvar__4___24Anonymous__149586,Vvar__4___24Anonymous__149587,Vvar__5___24Anonymous__149588,Vvar__5___24Anonymous__149589] :
      ( cCoq_2emicromega_2eTauto_2eD___24a6(Vvar__0__TA__149578,Vvar__1__TX__149580,Vvar__2__AA__149582,Vvar__3__AF__149584,Vvar__4___24Anonymous__149586,Vvar__5___24Anonymous__149588) = cCoq_2emicromega_2eTauto_2eD___24a6(Vvar__0__TA__149579,Vvar__1__TX__149581,Vvar__2__AA__149583,Vvar__3__AF__149585,Vvar__4___24Anonymous__149587,Vvar__5___24Anonymous__149589)
     => ( Vvar__5___24Anonymous__149588 = Vvar__5___24Anonymous__149589
        & Vvar__4___24Anonymous__149586 = Vvar__4___24Anonymous__149587
        & Vvar__3__AF__149584 = Vvar__3__AF__149585
        & Vvar__2__AA__149582 = Vvar__2__AA__149583
        & Vvar__1__TX__149580 = Vvar__1__TX__149581
        & Vvar__0__TA__149578 = Vvar__0__TA__149579 ) ) ).

fof('$_inj_Coq.micromega.Tauto.FF',axiom,
    ! [Vvar__0__TA__149536,Vvar__0__TA__149537,Vvar__1__TX__149538,Vvar__1__TX__149539,Vvar__2__AA__149540,Vvar__2__AA__149541,Vvar__3__AF__149542,Vvar__3__AF__149543] :
      ( cCoq_2emicromega_2eTauto_2eFF___24a4(Vvar__0__TA__149536,Vvar__1__TX__149538,Vvar__2__AA__149540,Vvar__3__AF__149542) = cCoq_2emicromega_2eTauto_2eFF___24a4(Vvar__0__TA__149537,Vvar__1__TX__149539,Vvar__2__AA__149541,Vvar__3__AF__149543)
     => ( Vvar__3__AF__149542 = Vvar__3__AF__149543
        & Vvar__2__AA__149540 = Vvar__2__AA__149541
        & Vvar__1__TX__149538 = Vvar__1__TX__149539
        & Vvar__0__TA__149536 = Vvar__0__TA__149537 ) ) ).

fof('$_inj_Coq.micromega.Tauto.I',axiom,
    ! [Vvar__0__TA__149600,Vvar__0__TA__149601,Vvar__1__TX__149602,Vvar__1__TX__149603,Vvar__2__AA__149604,Vvar__2__AA__149605,Vvar__3__AF__149606,Vvar__3__AF__149607,Vvar__4___24Anonymous__149608,Vvar__4___24Anonymous__149609,Vvar__5___24Anonymous__149610,Vvar__5___24Anonymous__149611,Vvar__6___24Anonymous__149612,Vvar__6___24Anonymous__149613] :
      ( cCoq_2emicromega_2eTauto_2eI___24a7(Vvar__0__TA__149600,Vvar__1__TX__149602,Vvar__2__AA__149604,Vvar__3__AF__149606,Vvar__4___24Anonymous__149608,Vvar__5___24Anonymous__149610,Vvar__6___24Anonymous__149612) = cCoq_2emicromega_2eTauto_2eI___24a7(Vvar__0__TA__149601,Vvar__1__TX__149603,Vvar__2__AA__149605,Vvar__3__AF__149607,Vvar__4___24Anonymous__149609,Vvar__5___24Anonymous__149611,Vvar__6___24Anonymous__149613)
     => ( Vvar__6___24Anonymous__149612 = Vvar__6___24Anonymous__149613
        & Vvar__5___24Anonymous__149610 = Vvar__5___24Anonymous__149611
        & Vvar__4___24Anonymous__149608 = Vvar__4___24Anonymous__149609
        & Vvar__3__AF__149606 = Vvar__3__AF__149607
        & Vvar__2__AA__149604 = Vvar__2__AA__149605
        & Vvar__1__TX__149602 = Vvar__1__TX__149603
        & Vvar__0__TA__149600 = Vvar__0__TA__149601 ) ) ).

fof('$_inj_Coq.micromega.Tauto.N',axiom,
    ! [Vvar__0__TA__149590,Vvar__0__TA__149591,Vvar__1__TX__149592,Vvar__1__TX__149593,Vvar__2__AA__149594,Vvar__2__AA__149595,Vvar__3__AF__149596,Vvar__3__AF__149597,Vvar__4___24Anonymous__149598,Vvar__4___24Anonymous__149599] :
      ( cCoq_2emicromega_2eTauto_2eN___24a5(Vvar__0__TA__149590,Vvar__1__TX__149592,Vvar__2__AA__149594,Vvar__3__AF__149596,Vvar__4___24Anonymous__149598) = cCoq_2emicromega_2eTauto_2eN___24a5(Vvar__0__TA__149591,Vvar__1__TX__149593,Vvar__2__AA__149595,Vvar__3__AF__149597,Vvar__4___24Anonymous__149599)
     => ( Vvar__4___24Anonymous__149598 = Vvar__4___24Anonymous__149599
        & Vvar__3__AF__149596 = Vvar__3__AF__149597
        & Vvar__2__AA__149594 = Vvar__2__AA__149595
        & Vvar__1__TX__149592 = Vvar__1__TX__149593
        & Vvar__0__TA__149590 = Vvar__0__TA__149591 ) ) ).

fof('$_inj_Coq.micromega.Tauto.TT',axiom,
    ! [Vvar__0__TA__149528,Vvar__0__TA__149529,Vvar__1__TX__149530,Vvar__1__TX__149531,Vvar__2__AA__149532,Vvar__2__AA__149533,Vvar__3__AF__149534,Vvar__3__AF__149535] :
      ( cCoq_2emicromega_2eTauto_2eTT___24a4(Vvar__0__TA__149528,Vvar__1__TX__149530,Vvar__2__AA__149532,Vvar__3__AF__149534) = cCoq_2emicromega_2eTauto_2eTT___24a4(Vvar__0__TA__149529,Vvar__1__TX__149531,Vvar__2__AA__149533,Vvar__3__AF__149535)
     => ( Vvar__3__AF__149534 = Vvar__3__AF__149535
        & Vvar__2__AA__149532 = Vvar__2__AA__149533
        & Vvar__1__TX__149530 = Vvar__1__TX__149531
        & Vvar__0__TA__149528 = Vvar__0__TA__149529 ) ) ).

fof('$_inj_Coq.micromega.Tauto.X',axiom,
    ! [Vvar__0__TA__149544,Vvar__0__TA__149545,Vvar__1__TX__149546,Vvar__1__TX__149547,Vvar__2__AA__149548,Vvar__2__AA__149549,Vvar__3__AF__149550,Vvar__3__AF__149551,Vvar__4___24Anonymous__149552,Vvar__4___24Anonymous__149553] :
      ( cCoq_2emicromega_2eTauto_2eX___24a5(Vvar__0__TA__149544,Vvar__1__TX__149546,Vvar__2__AA__149548,Vvar__3__AF__149550,Vvar__4___24Anonymous__149552) = cCoq_2emicromega_2eTauto_2eX___24a5(Vvar__0__TA__149545,Vvar__1__TX__149547,Vvar__2__AA__149549,Vvar__3__AF__149551,Vvar__4___24Anonymous__149553)
     => ( Vvar__4___24Anonymous__149552 = Vvar__4___24Anonymous__149553
        & Vvar__3__AF__149550 = Vvar__3__AF__149551
        & Vvar__2__AA__149548 = Vvar__2__AA__149549
        & Vvar__1__TX__149546 = Vvar__1__TX__149547
        & Vvar__0__TA__149544 = Vvar__0__TA__149545 ) ) ).

fof('$_inj_Coq.micromega.VarMap.Branch',axiom,
    ! [Vvar__0__A__142741,Vvar__0__A__142742,Vvar__1___24Anonymous__142743,Vvar__1___24Anonymous__142744,Vvar__2___24Anonymous__142745,Vvar__2___24Anonymous__142746,Vvar__3___24Anonymous__142747,Vvar__3___24Anonymous__142748] :
      ( cCoq_2emicromega_2eVarMap_2eBranch___24a4(Vvar__0__A__142741,Vvar__1___24Anonymous__142743,Vvar__2___24Anonymous__142745,Vvar__3___24Anonymous__142747) = cCoq_2emicromega_2eVarMap_2eBranch___24a4(Vvar__0__A__142742,Vvar__1___24Anonymous__142744,Vvar__2___24Anonymous__142746,Vvar__3___24Anonymous__142748)
     => ( Vvar__3___24Anonymous__142747 = Vvar__3___24Anonymous__142748
        & Vvar__2___24Anonymous__142745 = Vvar__2___24Anonymous__142746
        & Vvar__1___24Anonymous__142743 = Vvar__1___24Anonymous__142744
        & Vvar__0__A__142741 = Vvar__0__A__142742 ) ) ).

fof('$_inj_Coq.micromega.VarMap.Elt',axiom,
    ! [Vvar__0__A__142737,Vvar__0__A__142738,Vvar__1___24Anonymous__142739,Vvar__1___24Anonymous__142740] :
      ( cCoq_2emicromega_2eVarMap_2eElt___24a2(Vvar__0__A__142737,Vvar__1___24Anonymous__142739) = cCoq_2emicromega_2eVarMap_2eElt___24a2(Vvar__0__A__142738,Vvar__1___24Anonymous__142740)
     => ( Vvar__1___24Anonymous__142739 = Vvar__1___24Anonymous__142740
        & Vvar__0__A__142737 = Vvar__0__A__142738 ) ) ).

fof('$_inj_Coq.micromega.VarMap.Empty',axiom,
    ! [Vvar__0__A__142735,Vvar__0__A__142736] :
      ( cCoq_2emicromega_2eVarMap_2eEmpty___24a1(Vvar__0__A__142735) = cCoq_2emicromega_2eVarMap_2eEmpty___24a1(Vvar__0__A__142736)
     => Vvar__0__A__142735 = Vvar__0__A__142736 ) ).

fof('$_inj_Coq.micromega.ZMicromega.CutProof',axiom,
    ! [Vvar__0___24Anonymous__135979,Vvar__0___24Anonymous__135980,Vvar__1___24Anonymous__135981,Vvar__1___24Anonymous__135982] :
      ( cCoq_2emicromega_2eZMicromega_2eCutProof___24a2(Vvar__0___24Anonymous__135979,Vvar__1___24Anonymous__135981) = cCoq_2emicromega_2eZMicromega_2eCutProof___24a2(Vvar__0___24Anonymous__135980,Vvar__1___24Anonymous__135982)
     => ( Vvar__1___24Anonymous__135981 = Vvar__1___24Anonymous__135982
        & Vvar__0___24Anonymous__135979 = Vvar__0___24Anonymous__135980 ) ) ).

fof('$_inj_Coq.micromega.ZMicromega.EnumProof',axiom,
    ! [Vvar__0___24Anonymous__135983,Vvar__0___24Anonymous__135984,Vvar__1___24Anonymous__135985,Vvar__1___24Anonymous__135986,Vvar__2___24Anonymous__135987,Vvar__2___24Anonymous__135988] :
      ( cCoq_2emicromega_2eZMicromega_2eEnumProof___24a3(Vvar__0___24Anonymous__135983,Vvar__1___24Anonymous__135985,Vvar__2___24Anonymous__135987) = cCoq_2emicromega_2eZMicromega_2eEnumProof___24a3(Vvar__0___24Anonymous__135984,Vvar__1___24Anonymous__135986,Vvar__2___24Anonymous__135988)
     => ( Vvar__2___24Anonymous__135987 = Vvar__2___24Anonymous__135988
        & Vvar__1___24Anonymous__135985 = Vvar__1___24Anonymous__135986
        & Vvar__0___24Anonymous__135983 = Vvar__0___24Anonymous__135984 ) ) ).

fof('$_inj_Coq.micromega.ZMicromega.RatProof',axiom,
    ! [Vvar__0___24Anonymous__135975,Vvar__0___24Anonymous__135976,Vvar__1___24Anonymous__135977,Vvar__1___24Anonymous__135978] :
      ( cCoq_2emicromega_2eZMicromega_2eRatProof___24a2(Vvar__0___24Anonymous__135975,Vvar__1___24Anonymous__135977) = cCoq_2emicromega_2eZMicromega_2eRatProof___24a2(Vvar__0___24Anonymous__135976,Vvar__1___24Anonymous__135978)
     => ( Vvar__1___24Anonymous__135977 = Vvar__1___24Anonymous__135978
        & Vvar__0___24Anonymous__135975 = Vvar__0___24Anonymous__135976 ) ) ).

fof('$_inj_Coq.setoid_ring.Field_theory.FEI',axiom,
    ! [Vvar__0__C__119750,Vvar__0__C__119751] :
      ( cCoq_2esetoid__ring_2eField__theory_2eFEI___24a1(Vvar__0__C__119750) = cCoq_2esetoid__ring_2eField__theory_2eFEI___24a1(Vvar__0__C__119751)
     => Vvar__0__C__119750 = Vvar__0__C__119751 ) ).

fof('$_inj_Coq.setoid_ring.Field_theory.FEO',axiom,
    ! [Vvar__0__C__119748,Vvar__0__C__119749] :
      ( cCoq_2esetoid__ring_2eField__theory_2eFEO___24a1(Vvar__0__C__119748) = cCoq_2esetoid__ring_2eField__theory_2eFEO___24a1(Vvar__0__C__119749)
     => Vvar__0__C__119748 = Vvar__0__C__119749 ) ).

fof('$_inj_Coq.setoid_ring.Field_theory.FEX',axiom,
    ! [Vvar__0__C__119756,Vvar__0__C__119757,Vvar__1___24Anonymous__119758,Vvar__1___24Anonymous__119759] :
      ( cCoq_2esetoid__ring_2eField__theory_2eFEX___24a2(Vvar__0__C__119756,Vvar__1___24Anonymous__119758) = cCoq_2esetoid__ring_2eField__theory_2eFEX___24a2(Vvar__0__C__119757,Vvar__1___24Anonymous__119759)
     => ( Vvar__1___24Anonymous__119758 = Vvar__1___24Anonymous__119759
        & Vvar__0__C__119756 = Vvar__0__C__119757 ) ) ).

fof('$_inj_Coq.setoid_ring.Field_theory.FEadd',axiom,
    ! [Vvar__0__C__119760,Vvar__0__C__119761,Vvar__1___24Anonymous__119762,Vvar__1___24Anonymous__119763,Vvar__2___24Anonymous__119764,Vvar__2___24Anonymous__119765] :
      ( cCoq_2esetoid__ring_2eField__theory_2eFEadd___24a3(Vvar__0__C__119760,Vvar__1___24Anonymous__119762,Vvar__2___24Anonymous__119764) = cCoq_2esetoid__ring_2eField__theory_2eFEadd___24a3(Vvar__0__C__119761,Vvar__1___24Anonymous__119763,Vvar__2___24Anonymous__119765)
     => ( Vvar__2___24Anonymous__119764 = Vvar__2___24Anonymous__119765
        & Vvar__1___24Anonymous__119762 = Vvar__1___24Anonymous__119763
        & Vvar__0__C__119760 = Vvar__0__C__119761 ) ) ).

fof('$_inj_Coq.setoid_ring.Field_theory.FEc',axiom,
    ! [Vvar__0__C__119752,Vvar__0__C__119753,Vvar__1___24Anonymous__119754,Vvar__1___24Anonymous__119755] :
      ( cCoq_2esetoid__ring_2eField__theory_2eFEc___24a2(Vvar__0__C__119752,Vvar__1___24Anonymous__119754) = cCoq_2esetoid__ring_2eField__theory_2eFEc___24a2(Vvar__0__C__119753,Vvar__1___24Anonymous__119755)
     => ( Vvar__1___24Anonymous__119754 = Vvar__1___24Anonymous__119755
        & Vvar__0__C__119752 = Vvar__0__C__119753 ) ) ).

fof('$_inj_Coq.setoid_ring.Field_theory.FEdiv',axiom,
    ! [Vvar__0__C__119786,Vvar__0__C__119787,Vvar__1___24Anonymous__119788,Vvar__1___24Anonymous__119789,Vvar__2___24Anonymous__119790,Vvar__2___24Anonymous__119791] :
      ( cCoq_2esetoid__ring_2eField__theory_2eFEdiv___24a3(Vvar__0__C__119786,Vvar__1___24Anonymous__119788,Vvar__2___24Anonymous__119790) = cCoq_2esetoid__ring_2eField__theory_2eFEdiv___24a3(Vvar__0__C__119787,Vvar__1___24Anonymous__119789,Vvar__2___24Anonymous__119791)
     => ( Vvar__2___24Anonymous__119790 = Vvar__2___24Anonymous__119791
        & Vvar__1___24Anonymous__119788 = Vvar__1___24Anonymous__119789
        & Vvar__0__C__119786 = Vvar__0__C__119787 ) ) ).

fof('$_inj_Coq.setoid_ring.Field_theory.FEinv',axiom,
    ! [Vvar__0__C__119782,Vvar__0__C__119783,Vvar__1___24Anonymous__119784,Vvar__1___24Anonymous__119785] :
      ( cCoq_2esetoid__ring_2eField__theory_2eFEinv___24a2(Vvar__0__C__119782,Vvar__1___24Anonymous__119784) = cCoq_2esetoid__ring_2eField__theory_2eFEinv___24a2(Vvar__0__C__119783,Vvar__1___24Anonymous__119785)
     => ( Vvar__1___24Anonymous__119784 = Vvar__1___24Anonymous__119785
        & Vvar__0__C__119782 = Vvar__0__C__119783 ) ) ).

fof('$_inj_Coq.setoid_ring.Field_theory.FEmul',axiom,
    ! [Vvar__0__C__119772,Vvar__0__C__119773,Vvar__1___24Anonymous__119774,Vvar__1___24Anonymous__119775,Vvar__2___24Anonymous__119776,Vvar__2___24Anonymous__119777] :
      ( cCoq_2esetoid__ring_2eField__theory_2eFEmul___24a3(Vvar__0__C__119772,Vvar__1___24Anonymous__119774,Vvar__2___24Anonymous__119776) = cCoq_2esetoid__ring_2eField__theory_2eFEmul___24a3(Vvar__0__C__119773,Vvar__1___24Anonymous__119775,Vvar__2___24Anonymous__119777)
     => ( Vvar__2___24Anonymous__119776 = Vvar__2___24Anonymous__119777
        & Vvar__1___24Anonymous__119774 = Vvar__1___24Anonymous__119775
        & Vvar__0__C__119772 = Vvar__0__C__119773 ) ) ).

fof('$_inj_Coq.setoid_ring.Field_theory.FEopp',axiom,
    ! [Vvar__0__C__119778,Vvar__0__C__119779,Vvar__1___24Anonymous__119780,Vvar__1___24Anonymous__119781] :
      ( cCoq_2esetoid__ring_2eField__theory_2eFEopp___24a2(Vvar__0__C__119778,Vvar__1___24Anonymous__119780) = cCoq_2esetoid__ring_2eField__theory_2eFEopp___24a2(Vvar__0__C__119779,Vvar__1___24Anonymous__119781)
     => ( Vvar__1___24Anonymous__119780 = Vvar__1___24Anonymous__119781
        & Vvar__0__C__119778 = Vvar__0__C__119779 ) ) ).

fof('$_inj_Coq.setoid_ring.Field_theory.FEpow',axiom,
    ! [Vvar__0__C__119792,Vvar__0__C__119793,Vvar__1___24Anonymous__119794,Vvar__1___24Anonymous__119795,Vvar__2___24Anonymous__119796,Vvar__2___24Anonymous__119797] :
      ( cCoq_2esetoid__ring_2eField__theory_2eFEpow___24a3(Vvar__0__C__119792,Vvar__1___24Anonymous__119794,Vvar__2___24Anonymous__119796) = cCoq_2esetoid__ring_2eField__theory_2eFEpow___24a3(Vvar__0__C__119793,Vvar__1___24Anonymous__119795,Vvar__2___24Anonymous__119797)
     => ( Vvar__2___24Anonymous__119796 = Vvar__2___24Anonymous__119797
        & Vvar__1___24Anonymous__119794 = Vvar__1___24Anonymous__119795
        & Vvar__0__C__119792 = Vvar__0__C__119793 ) ) ).

fof('$_inj_Coq.setoid_ring.Field_theory.FEsub',axiom,
    ! [Vvar__0__C__119766,Vvar__0__C__119767,Vvar__1___24Anonymous__119768,Vvar__1___24Anonymous__119769,Vvar__2___24Anonymous__119770,Vvar__2___24Anonymous__119771] :
      ( cCoq_2esetoid__ring_2eField__theory_2eFEsub___24a3(Vvar__0__C__119766,Vvar__1___24Anonymous__119768,Vvar__2___24Anonymous__119770) = cCoq_2esetoid__ring_2eField__theory_2eFEsub___24a3(Vvar__0__C__119767,Vvar__1___24Anonymous__119769,Vvar__2___24Anonymous__119771)
     => ( Vvar__2___24Anonymous__119770 = Vvar__2___24Anonymous__119771
        & Vvar__1___24Anonymous__119768 = Vvar__1___24Anonymous__119769
        & Vvar__0__C__119766 = Vvar__0__C__119767 ) ) ).

fof('$_inj_Coq.setoid_ring.Field_theory.mk_linear',axiom,
    ! [Vvar__0__C__120089,Vvar__0__C__120090,Vvar__1__num__120091,Vvar__1__num__120092,Vvar__2__denum__120093,Vvar__2__denum__120094,Vvar__3__condition__120095,Vvar__3__condition__120096] :
      ( cCoq_2esetoid__ring_2eField__theory_2emk__linear___24a4(Vvar__0__C__120089,Vvar__1__num__120091,Vvar__2__denum__120093,Vvar__3__condition__120095) = cCoq_2esetoid__ring_2eField__theory_2emk__linear___24a4(Vvar__0__C__120090,Vvar__1__num__120092,Vvar__2__denum__120094,Vvar__3__condition__120096)
     => ( Vvar__3__condition__120095 = Vvar__3__condition__120096
        & Vvar__2__denum__120093 = Vvar__2__denum__120094
        & Vvar__1__num__120091 = Vvar__1__num__120092
        & Vvar__0__C__120089 = Vvar__0__C__120090 ) ) ).

fof('$_inj_Coq.setoid_ring.Field_theory.mk_rsplit',axiom,
    ! [Vvar__0__C__120378,Vvar__0__C__120379,Vvar__1__rsplit__left__120380,Vvar__1__rsplit__left__120381,Vvar__2__rsplit__common__120382,Vvar__2__rsplit__common__120383,Vvar__3__rsplit__right__120384,Vvar__3__rsplit__right__120385] :
      ( cCoq_2esetoid__ring_2eField__theory_2emk__rsplit___24a4(Vvar__0__C__120378,Vvar__1__rsplit__left__120380,Vvar__2__rsplit__common__120382,Vvar__3__rsplit__right__120384) = cCoq_2esetoid__ring_2eField__theory_2emk__rsplit___24a4(Vvar__0__C__120379,Vvar__1__rsplit__left__120381,Vvar__2__rsplit__common__120383,Vvar__3__rsplit__right__120385)
     => ( Vvar__3__rsplit__right__120384 = Vvar__3__rsplit__right__120385
        & Vvar__2__rsplit__common__120382 = Vvar__2__rsplit__common__120383
        & Vvar__1__rsplit__left__120380 = Vvar__1__rsplit__left__120381
        & Vvar__0__C__120378 = Vvar__0__C__120379 ) ) ).

fof('$_inj_Coq.setoid_ring.InitialRing.mkhypo',axiom,
    ! [Vvar__0__hypo__type__147099,Vvar__0__hypo__type__147100,Vvar__1__hypo__proof__147101,Vvar__1__hypo__proof__147102] :
      ( cCoq_2esetoid__ring_2eInitialRing_2emkhypo___24a2(Vvar__0__hypo__type__147099,Vvar__1__hypo__proof__147101) = cCoq_2esetoid__ring_2eInitialRing_2emkhypo___24a2(Vvar__0__hypo__type__147100,Vvar__1__hypo__proof__147102)
     => ( Vvar__1__hypo__proof__147101 = Vvar__1__hypo__proof__147102
        & Vvar__0__hypo__type__147099 = Vvar__0__hypo__type__147100 ) ) ).

fof('$_inj_Coq.setoid_ring.Ring_polynom.PEI',axiom,
    ! [Vvar__0__C__3251,Vvar__0__C__3252] :
      ( cCoq_2esetoid__ring_2eRing__polynom_2ePEI___24a1(Vvar__0__C__3251) = cCoq_2esetoid__ring_2eRing__polynom_2ePEI___24a1(Vvar__0__C__3252)
     => Vvar__0__C__3251 = Vvar__0__C__3252 ) ).

fof('$_inj_Coq.setoid_ring.Ring_polynom.PEO',axiom,
    ! [Vvar__0__C__3249,Vvar__0__C__3250] :
      ( cCoq_2esetoid__ring_2eRing__polynom_2ePEO___24a1(Vvar__0__C__3249) = cCoq_2esetoid__ring_2eRing__polynom_2ePEO___24a1(Vvar__0__C__3250)
     => Vvar__0__C__3249 = Vvar__0__C__3250 ) ).

fof('$_inj_Coq.setoid_ring.Ring_polynom.PEX',axiom,
    ! [Vvar__0__C__3257,Vvar__0__C__3258,Vvar__1___24Anonymous__3259,Vvar__1___24Anonymous__3260] :
      ( cCoq_2esetoid__ring_2eRing__polynom_2ePEX___24a2(Vvar__0__C__3257,Vvar__1___24Anonymous__3259) = cCoq_2esetoid__ring_2eRing__polynom_2ePEX___24a2(Vvar__0__C__3258,Vvar__1___24Anonymous__3260)
     => ( Vvar__1___24Anonymous__3259 = Vvar__1___24Anonymous__3260
        & Vvar__0__C__3257 = Vvar__0__C__3258 ) ) ).

fof('$_inj_Coq.setoid_ring.Ring_polynom.PEadd',axiom,
    ! [Vvar__0__C__3261,Vvar__0__C__3262,Vvar__1___24Anonymous__3263,Vvar__1___24Anonymous__3264,Vvar__2___24Anonymous__3265,Vvar__2___24Anonymous__3266] :
      ( cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(Vvar__0__C__3261,Vvar__1___24Anonymous__3263,Vvar__2___24Anonymous__3265) = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(Vvar__0__C__3262,Vvar__1___24Anonymous__3264,Vvar__2___24Anonymous__3266)
     => ( Vvar__2___24Anonymous__3265 = Vvar__2___24Anonymous__3266
        & Vvar__1___24Anonymous__3263 = Vvar__1___24Anonymous__3264
        & Vvar__0__C__3261 = Vvar__0__C__3262 ) ) ).

fof('$_inj_Coq.setoid_ring.Ring_polynom.PEc',axiom,
    ! [Vvar__0__C__3253,Vvar__0__C__3254,Vvar__1___24Anonymous__3255,Vvar__1___24Anonymous__3256] :
      ( cCoq_2esetoid__ring_2eRing__polynom_2ePEc___24a2(Vvar__0__C__3253,Vvar__1___24Anonymous__3255) = cCoq_2esetoid__ring_2eRing__polynom_2ePEc___24a2(Vvar__0__C__3254,Vvar__1___24Anonymous__3256)
     => ( Vvar__1___24Anonymous__3255 = Vvar__1___24Anonymous__3256
        & Vvar__0__C__3253 = Vvar__0__C__3254 ) ) ).

fof('$_inj_Coq.setoid_ring.Ring_polynom.PEmul',axiom,
    ! [Vvar__0__C__3273,Vvar__0__C__3274,Vvar__1___24Anonymous__3275,Vvar__1___24Anonymous__3276,Vvar__2___24Anonymous__3277,Vvar__2___24Anonymous__3278] :
      ( cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(Vvar__0__C__3273,Vvar__1___24Anonymous__3275,Vvar__2___24Anonymous__3277) = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(Vvar__0__C__3274,Vvar__1___24Anonymous__3276,Vvar__2___24Anonymous__3278)
     => ( Vvar__2___24Anonymous__3277 = Vvar__2___24Anonymous__3278
        & Vvar__1___24Anonymous__3275 = Vvar__1___24Anonymous__3276
        & Vvar__0__C__3273 = Vvar__0__C__3274 ) ) ).

fof('$_inj_Coq.setoid_ring.Ring_polynom.PEopp',axiom,
    ! [Vvar__0__C__3279,Vvar__0__C__3280,Vvar__1___24Anonymous__3281,Vvar__1___24Anonymous__3282] :
      ( cCoq_2esetoid__ring_2eRing__polynom_2ePEopp___24a2(Vvar__0__C__3279,Vvar__1___24Anonymous__3281) = cCoq_2esetoid__ring_2eRing__polynom_2ePEopp___24a2(Vvar__0__C__3280,Vvar__1___24Anonymous__3282)
     => ( Vvar__1___24Anonymous__3281 = Vvar__1___24Anonymous__3282
        & Vvar__0__C__3279 = Vvar__0__C__3280 ) ) ).

fof('$_inj_Coq.setoid_ring.Ring_polynom.PEpow',axiom,
    ! [Vvar__0__C__3283,Vvar__0__C__3284,Vvar__1___24Anonymous__3285,Vvar__1___24Anonymous__3286,Vvar__2___24Anonymous__3287,Vvar__2___24Anonymous__3288] :
      ( cCoq_2esetoid__ring_2eRing__polynom_2ePEpow___24a3(Vvar__0__C__3283,Vvar__1___24Anonymous__3285,Vvar__2___24Anonymous__3287) = cCoq_2esetoid__ring_2eRing__polynom_2ePEpow___24a3(Vvar__0__C__3284,Vvar__1___24Anonymous__3286,Vvar__2___24Anonymous__3288)
     => ( Vvar__2___24Anonymous__3287 = Vvar__2___24Anonymous__3288
        & Vvar__1___24Anonymous__3285 = Vvar__1___24Anonymous__3286
        & Vvar__0__C__3283 = Vvar__0__C__3284 ) ) ).

fof('$_inj_Coq.setoid_ring.Ring_polynom.PEsub',axiom,
    ! [Vvar__0__C__3267,Vvar__0__C__3268,Vvar__1___24Anonymous__3269,Vvar__1___24Anonymous__3270,Vvar__2___24Anonymous__3271,Vvar__2___24Anonymous__3272] :
      ( cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(Vvar__0__C__3267,Vvar__1___24Anonymous__3269,Vvar__2___24Anonymous__3271) = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(Vvar__0__C__3268,Vvar__1___24Anonymous__3270,Vvar__2___24Anonymous__3272)
     => ( Vvar__2___24Anonymous__3271 = Vvar__2___24Anonymous__3272
        & Vvar__1___24Anonymous__3269 = Vvar__1___24Anonymous__3270
        & Vvar__0__C__3267 = Vvar__0__C__3268 ) ) ).

fof('$_inj_Coq.setoid_ring.Ring_polynom.PX',axiom,
    ! [Vvar__0__C__2904,Vvar__0__C__2905,Vvar__1___24Anonymous__2906,Vvar__1___24Anonymous__2907,Vvar__2___24Anonymous__2908,Vvar__2___24Anonymous__2909,Vvar__3___24Anonymous__2910,Vvar__3___24Anonymous__2911] :
      ( cCoq_2esetoid__ring_2eRing__polynom_2ePX___24a4(Vvar__0__C__2904,Vvar__1___24Anonymous__2906,Vvar__2___24Anonymous__2908,Vvar__3___24Anonymous__2910) = cCoq_2esetoid__ring_2eRing__polynom_2ePX___24a4(Vvar__0__C__2905,Vvar__1___24Anonymous__2907,Vvar__2___24Anonymous__2909,Vvar__3___24Anonymous__2911)
     => ( Vvar__3___24Anonymous__2910 = Vvar__3___24Anonymous__2911
        & Vvar__2___24Anonymous__2908 = Vvar__2___24Anonymous__2909
        & Vvar__1___24Anonymous__2906 = Vvar__1___24Anonymous__2907
        & Vvar__0__C__2904 = Vvar__0__C__2905 ) ) ).

fof('$_inj_Coq.setoid_ring.Ring_polynom.Pc',axiom,
    ! [Vvar__0__C__2894,Vvar__0__C__2895,Vvar__1___24Anonymous__2896,Vvar__1___24Anonymous__2897] :
      ( cCoq_2esetoid__ring_2eRing__polynom_2ePc___24a2(Vvar__0__C__2894,Vvar__1___24Anonymous__2896) = cCoq_2esetoid__ring_2eRing__polynom_2ePc___24a2(Vvar__0__C__2895,Vvar__1___24Anonymous__2897)
     => ( Vvar__1___24Anonymous__2896 = Vvar__1___24Anonymous__2897
        & Vvar__0__C__2894 = Vvar__0__C__2895 ) ) ).

fof('$_inj_Coq.setoid_ring.Ring_polynom.Pinj',axiom,
    ! [Vvar__0__C__2898,Vvar__0__C__2899,Vvar__1___24Anonymous__2900,Vvar__1___24Anonymous__2901,Vvar__2___24Anonymous__2902,Vvar__2___24Anonymous__2903] :
      ( cCoq_2esetoid__ring_2eRing__polynom_2ePinj___24a3(Vvar__0__C__2898,Vvar__1___24Anonymous__2900,Vvar__2___24Anonymous__2902) = cCoq_2esetoid__ring_2eRing__polynom_2ePinj___24a3(Vvar__0__C__2899,Vvar__1___24Anonymous__2901,Vvar__2___24Anonymous__2903)
     => ( Vvar__2___24Anonymous__2902 = Vvar__2___24Anonymous__2903
        & Vvar__1___24Anonymous__2900 = Vvar__1___24Anonymous__2901
        & Vvar__0__C__2898 = Vvar__0__C__2899 ) ) ).

fof('$_inj_Coq.setoid_ring.Ring_polynom.vmon',axiom,
    ! [Vvar__0___24Anonymous__3063,Vvar__0___24Anonymous__3064,Vvar__1___24Anonymous__3065,Vvar__1___24Anonymous__3066] :
      ( cCoq_2esetoid__ring_2eRing__polynom_2evmon___24a2(Vvar__0___24Anonymous__3063,Vvar__1___24Anonymous__3065) = cCoq_2esetoid__ring_2eRing__polynom_2evmon___24a2(Vvar__0___24Anonymous__3064,Vvar__1___24Anonymous__3066)
     => ( Vvar__1___24Anonymous__3065 = Vvar__1___24Anonymous__3066
        & Vvar__0___24Anonymous__3063 = Vvar__0___24Anonymous__3064 ) ) ).

fof('$_inj_Coq.setoid_ring.Ring_polynom.zmon',axiom,
    ! [Vvar__0___24Anonymous__3059,Vvar__0___24Anonymous__3060,Vvar__1___24Anonymous__3061,Vvar__1___24Anonymous__3062] :
      ( cCoq_2esetoid__ring_2eRing__polynom_2ezmon___24a2(Vvar__0___24Anonymous__3059,Vvar__1___24Anonymous__3061) = cCoq_2esetoid__ring_2eRing__polynom_2ezmon___24a2(Vvar__0___24Anonymous__3060,Vvar__1___24Anonymous__3062)
     => ( Vvar__1___24Anonymous__3061 = Vvar__1___24Anonymous__3062
        & Vvar__0___24Anonymous__3059 = Vvar__0___24Anonymous__3060 ) ) ).

fof('$_inj_Coq.setoid_ring.Ring_theory.Computational',axiom,
    ! [Vvar__0__R__148818,Vvar__0__R__148819,Vvar__1__req__148820,Vvar__1__req__148821,Vvar__2__reqb__148822,Vvar__2__reqb__148823,Vvar__3___24Anonymous__148824,Vvar__3___24Anonymous__148825] :
      ( cCoq_2esetoid__ring_2eRing__theory_2eComputational___24a3(Vvar__0__R__148818,Vvar__1__req__148820,Vvar__2__reqb__148822) = cCoq_2esetoid__ring_2eRing__theory_2eComputational___24a3(Vvar__0__R__148819,Vvar__1__req__148821,Vvar__2__reqb__148823)
     => ( c_24Proof = c_24Proof
        & Vvar__2__reqb__148822 = Vvar__2__reqb__148823
        & Vvar__1__req__148820 = Vvar__1__req__148821
        & Vvar__0__R__148818 = Vvar__0__R__148819 ) ) ).

fof('$_inj_Coq.setoid_ring.Ring_theory.Morphism',axiom,
    ! [Vvar__0__R__148826,Vvar__0__R__148827,Vvar__1__rO__148828,Vvar__1__rO__148829,Vvar__2__rI__148830,Vvar__2__rI__148831,Vvar__3__radd__148832,Vvar__3__radd__148833,Vvar__4__rmul__148834,Vvar__4__rmul__148835,Vvar__5__rsub__148836,Vvar__5__rsub__148837,Vvar__6__ropp__148838,Vvar__6__ropp__148839,Vvar__7__req__148840,Vvar__7__req__148841,Vvar__8__C__148842,Vvar__8__C__148843,Vvar__9__cO__148844,Vvar__9__cO__148845,Vvar__10__cI__148846,Vvar__10__cI__148847,Vvar__11__cadd__148848,Vvar__11__cadd__148849,Vvar__12__cmul__148850,Vvar__12__cmul__148851,Vvar__13__csub__148852,Vvar__13__csub__148853,Vvar__14__copp__148854,Vvar__14__copp__148855,Vvar__15__ceqb__148856,Vvar__15__ceqb__148857,Vvar__16__phi__148858,Vvar__16__phi__148859,Vvar__17___24Anonymous__148860,Vvar__17___24Anonymous__148861] :
      ( cCoq_2esetoid__ring_2eRing__theory_2eMorphism___24a17(Vvar__0__R__148826,Vvar__1__rO__148828,Vvar__2__rI__148830,Vvar__3__radd__148832,Vvar__4__rmul__148834,Vvar__5__rsub__148836,Vvar__6__ropp__148838,Vvar__7__req__148840,Vvar__8__C__148842,Vvar__9__cO__148844,Vvar__10__cI__148846,Vvar__11__cadd__148848,Vvar__12__cmul__148850,Vvar__13__csub__148852,Vvar__14__copp__148854,Vvar__15__ceqb__148856,Vvar__16__phi__148858) = cCoq_2esetoid__ring_2eRing__theory_2eMorphism___24a17(Vvar__0__R__148827,Vvar__1__rO__148829,Vvar__2__rI__148831,Vvar__3__radd__148833,Vvar__4__rmul__148835,Vvar__5__rsub__148837,Vvar__6__ropp__148839,Vvar__7__req__148841,Vvar__8__C__148843,Vvar__9__cO__148845,Vvar__10__cI__148847,Vvar__11__cadd__148849,Vvar__12__cmul__148851,Vvar__13__csub__148853,Vvar__14__copp__148855,Vvar__15__ceqb__148857,Vvar__16__phi__148859)
     => ( c_24Proof = c_24Proof
        & Vvar__16__phi__148858 = Vvar__16__phi__148859
        & Vvar__15__ceqb__148856 = Vvar__15__ceqb__148857
        & Vvar__14__copp__148854 = Vvar__14__copp__148855
        & Vvar__13__csub__148852 = Vvar__13__csub__148853
        & Vvar__12__cmul__148850 = Vvar__12__cmul__148851
        & Vvar__11__cadd__148848 = Vvar__11__cadd__148849
        & Vvar__10__cI__148846 = Vvar__10__cI__148847
        & Vvar__9__cO__148844 = Vvar__9__cO__148845
        & Vvar__8__C__148842 = Vvar__8__C__148843
        & Vvar__7__req__148840 = Vvar__7__req__148841
        & Vvar__6__ropp__148838 = Vvar__6__ropp__148839
        & Vvar__5__rsub__148836 = Vvar__5__rsub__148837
        & Vvar__4__rmul__148834 = Vvar__4__rmul__148835
        & Vvar__3__radd__148832 = Vvar__3__radd__148833
        & Vvar__2__rI__148830 = Vvar__2__rI__148831
        & Vvar__1__rO__148828 = Vvar__1__rO__148829
        & Vvar__0__R__148826 = Vvar__0__R__148827 ) ) ).

fof('$_inj_Hoare2.DCAsgn',axiom,
    ! [Vvar__0___24Anonymous__150467,Vvar__0___24Anonymous__150468,Vvar__1___24Anonymous__150469,Vvar__1___24Anonymous__150470,Vvar__2___24Anonymous__150471,Vvar__2___24Anonymous__150472] :
      ( cHoare2_2eDCAsgn___24a3(Vvar__0___24Anonymous__150467,Vvar__1___24Anonymous__150469,Vvar__2___24Anonymous__150471) = cHoare2_2eDCAsgn___24a3(Vvar__0___24Anonymous__150468,Vvar__1___24Anonymous__150470,Vvar__2___24Anonymous__150472)
     => ( Vvar__2___24Anonymous__150471 = Vvar__2___24Anonymous__150472
        & Vvar__1___24Anonymous__150469 = Vvar__1___24Anonymous__150470
        & Vvar__0___24Anonymous__150467 = Vvar__0___24Anonymous__150468 ) ) ).

fof('$_inj_Hoare2.DCIf',axiom,
    ! [Vvar__0___24Anonymous__150473,Vvar__0___24Anonymous__150474,Vvar__1___24Anonymous__150475,Vvar__1___24Anonymous__150476,Vvar__2___24Anonymous__150477,Vvar__2___24Anonymous__150478,Vvar__3___24Anonymous__150479,Vvar__3___24Anonymous__150480,Vvar__4___24Anonymous__150481,Vvar__4___24Anonymous__150482,Vvar__5___24Anonymous__150483,Vvar__5___24Anonymous__150484] :
      ( cHoare2_2eDCIf___24a6(Vvar__0___24Anonymous__150473,Vvar__1___24Anonymous__150475,Vvar__2___24Anonymous__150477,Vvar__3___24Anonymous__150479,Vvar__4___24Anonymous__150481,Vvar__5___24Anonymous__150483) = cHoare2_2eDCIf___24a6(Vvar__0___24Anonymous__150474,Vvar__1___24Anonymous__150476,Vvar__2___24Anonymous__150478,Vvar__3___24Anonymous__150480,Vvar__4___24Anonymous__150482,Vvar__5___24Anonymous__150484)
     => ( Vvar__5___24Anonymous__150483 = Vvar__5___24Anonymous__150484
        & Vvar__4___24Anonymous__150481 = Vvar__4___24Anonymous__150482
        & Vvar__3___24Anonymous__150479 = Vvar__3___24Anonymous__150480
        & Vvar__2___24Anonymous__150477 = Vvar__2___24Anonymous__150478
        & Vvar__1___24Anonymous__150475 = Vvar__1___24Anonymous__150476
        & Vvar__0___24Anonymous__150473 = Vvar__0___24Anonymous__150474 ) ) ).

fof('$_inj_Hoare2.DCPost',axiom,
    ! [Vvar__0___24Anonymous__150497,Vvar__0___24Anonymous__150498,Vvar__1___24Anonymous__150499,Vvar__1___24Anonymous__150500] :
      ( cHoare2_2eDCPost___24a2(Vvar__0___24Anonymous__150497,Vvar__1___24Anonymous__150499) = cHoare2_2eDCPost___24a2(Vvar__0___24Anonymous__150498,Vvar__1___24Anonymous__150500)
     => ( Vvar__1___24Anonymous__150499 = Vvar__1___24Anonymous__150500
        & Vvar__0___24Anonymous__150497 = Vvar__0___24Anonymous__150498 ) ) ).

fof('$_inj_Hoare2.DCPre',axiom,
    ! [Vvar__0___24Anonymous__150493,Vvar__0___24Anonymous__150494,Vvar__1___24Anonymous__150495,Vvar__1___24Anonymous__150496] :
      ( cHoare2_2eDCPre___24a2(Vvar__0___24Anonymous__150493,Vvar__1___24Anonymous__150495) = cHoare2_2eDCPre___24a2(Vvar__0___24Anonymous__150494,Vvar__1___24Anonymous__150496)
     => ( Vvar__1___24Anonymous__150495 = Vvar__1___24Anonymous__150496
        & Vvar__0___24Anonymous__150493 = Vvar__0___24Anonymous__150494 ) ) ).

fof('$_inj_Hoare2.DCSeq',axiom,
    ! [Vvar__0___24Anonymous__150463,Vvar__0___24Anonymous__150464,Vvar__1___24Anonymous__150465,Vvar__1___24Anonymous__150466] :
      ( cHoare2_2eDCSeq___24a2(Vvar__0___24Anonymous__150463,Vvar__1___24Anonymous__150465) = cHoare2_2eDCSeq___24a2(Vvar__0___24Anonymous__150464,Vvar__1___24Anonymous__150466)
     => ( Vvar__1___24Anonymous__150465 = Vvar__1___24Anonymous__150466
        & Vvar__0___24Anonymous__150463 = Vvar__0___24Anonymous__150464 ) ) ).

fof('$_inj_Hoare2.DCSkip',axiom,
    ! [Vvar__0___24Anonymous__150461,Vvar__0___24Anonymous__150462] :
      ( cHoare2_2eDCSkip___24a1(Vvar__0___24Anonymous__150461) = cHoare2_2eDCSkip___24a1(Vvar__0___24Anonymous__150462)
     => Vvar__0___24Anonymous__150461 = Vvar__0___24Anonymous__150462 ) ).

fof('$_inj_Hoare2.DCWhile',axiom,
    ! [Vvar__0___24Anonymous__150485,Vvar__0___24Anonymous__150486,Vvar__1___24Anonymous__150487,Vvar__1___24Anonymous__150488,Vvar__2___24Anonymous__150489,Vvar__2___24Anonymous__150490,Vvar__3___24Anonymous__150491,Vvar__3___24Anonymous__150492] :
      ( cHoare2_2eDCWhile___24a4(Vvar__0___24Anonymous__150485,Vvar__1___24Anonymous__150487,Vvar__2___24Anonymous__150489,Vvar__3___24Anonymous__150491) = cHoare2_2eDCWhile___24a4(Vvar__0___24Anonymous__150486,Vvar__1___24Anonymous__150488,Vvar__2___24Anonymous__150490,Vvar__3___24Anonymous__150492)
     => ( Vvar__3___24Anonymous__150491 = Vvar__3___24Anonymous__150492
        & Vvar__2___24Anonymous__150489 = Vvar__2___24Anonymous__150490
        & Vvar__1___24Anonymous__150487 = Vvar__1___24Anonymous__150488
        & Vvar__0___24Anonymous__150485 = Vvar__0___24Anonymous__150486 ) ) ).

fof('$_inj_Hoare2.Decorated',axiom,
    ! [Vvar__0___24Anonymous__150316,Vvar__0___24Anonymous__150317,Vvar__1___24Anonymous__150318,Vvar__1___24Anonymous__150319] :
      ( cHoare2_2eDecorated___24a2(Vvar__0___24Anonymous__150316,Vvar__1___24Anonymous__150318) = cHoare2_2eDecorated___24a2(Vvar__0___24Anonymous__150317,Vvar__1___24Anonymous__150319)
     => ( Vvar__1___24Anonymous__150318 = Vvar__1___24Anonymous__150319
        & Vvar__0___24Anonymous__150316 = Vvar__0___24Anonymous__150317 ) ) ).

fof('$_inj_PLF.Hoare.Himp.CAsgn',axiom,
    ! [Vvar__0___24Anonymous__844,Vvar__0___24Anonymous__845,Vvar__1___24Anonymous__846,Vvar__1___24Anonymous__847] :
      ( cPLF_2eHoare_2eHimp_2eCAsgn___24a2(Vvar__0___24Anonymous__844,Vvar__1___24Anonymous__846) = cPLF_2eHoare_2eHimp_2eCAsgn___24a2(Vvar__0___24Anonymous__845,Vvar__1___24Anonymous__847)
     => ( Vvar__1___24Anonymous__846 = Vvar__1___24Anonymous__847
        & Vvar__0___24Anonymous__844 = Vvar__0___24Anonymous__845 ) ) ).

fof('$_inj_PLF.Hoare.Himp.CHavoc',axiom,
    ! [Vvar__0___24Anonymous__862,Vvar__0___24Anonymous__863] :
      ( cPLF_2eHoare_2eHimp_2eCHavoc___24a1(Vvar__0___24Anonymous__862) = cPLF_2eHoare_2eHimp_2eCHavoc___24a1(Vvar__0___24Anonymous__863)
     => Vvar__0___24Anonymous__862 = Vvar__0___24Anonymous__863 ) ).

fof('$_inj_PLF.Hoare.Himp.CIf',axiom,
    ! [Vvar__0___24Anonymous__852,Vvar__0___24Anonymous__853,Vvar__1___24Anonymous__854,Vvar__1___24Anonymous__855,Vvar__2___24Anonymous__856,Vvar__2___24Anonymous__857] :
      ( cPLF_2eHoare_2eHimp_2eCIf___24a3(Vvar__0___24Anonymous__852,Vvar__1___24Anonymous__854,Vvar__2___24Anonymous__856) = cPLF_2eHoare_2eHimp_2eCIf___24a3(Vvar__0___24Anonymous__853,Vvar__1___24Anonymous__855,Vvar__2___24Anonymous__857)
     => ( Vvar__2___24Anonymous__856 = Vvar__2___24Anonymous__857
        & Vvar__1___24Anonymous__854 = Vvar__1___24Anonymous__855
        & Vvar__0___24Anonymous__852 = Vvar__0___24Anonymous__853 ) ) ).

fof('$_inj_PLF.Hoare.Himp.CSeq',axiom,
    ! [Vvar__0___24Anonymous__848,Vvar__0___24Anonymous__849,Vvar__1___24Anonymous__850,Vvar__1___24Anonymous__851] :
      ( cPLF_2eHoare_2eHimp_2eCSeq___24a2(Vvar__0___24Anonymous__848,Vvar__1___24Anonymous__850) = cPLF_2eHoare_2eHimp_2eCSeq___24a2(Vvar__0___24Anonymous__849,Vvar__1___24Anonymous__851)
     => ( Vvar__1___24Anonymous__850 = Vvar__1___24Anonymous__851
        & Vvar__0___24Anonymous__848 = Vvar__0___24Anonymous__849 ) ) ).

fof('$_inj_PLF.Hoare.Himp.CWhile',axiom,
    ! [Vvar__0___24Anonymous__858,Vvar__0___24Anonymous__859,Vvar__1___24Anonymous__860,Vvar__1___24Anonymous__861] :
      ( cPLF_2eHoare_2eHimp_2eCWhile___24a2(Vvar__0___24Anonymous__858,Vvar__1___24Anonymous__860) = cPLF_2eHoare_2eHimp_2eCWhile___24a2(Vvar__0___24Anonymous__859,Vvar__1___24Anonymous__861)
     => ( Vvar__1___24Anonymous__860 = Vvar__1___24Anonymous__861
        & Vvar__0___24Anonymous__858 = Vvar__0___24Anonymous__859 ) ) ).

fof('$_inj_PLF.Hoare.HoareAssertAssume.CAss',axiom,
    ! [Vvar__0___24Anonymous__1089,Vvar__0___24Anonymous__1090,Vvar__1___24Anonymous__1091,Vvar__1___24Anonymous__1092] :
      ( cPLF_2eHoare_2eHoareAssertAssume_2eCAss___24a2(Vvar__0___24Anonymous__1089,Vvar__1___24Anonymous__1091) = cPLF_2eHoare_2eHoareAssertAssume_2eCAss___24a2(Vvar__0___24Anonymous__1090,Vvar__1___24Anonymous__1092)
     => ( Vvar__1___24Anonymous__1091 = Vvar__1___24Anonymous__1092
        & Vvar__0___24Anonymous__1089 = Vvar__0___24Anonymous__1090 ) ) ).

fof('$_inj_PLF.Hoare.HoareAssertAssume.CAssert',axiom,
    ! [Vvar__0___24Anonymous__1107,Vvar__0___24Anonymous__1108] :
      ( cPLF_2eHoare_2eHoareAssertAssume_2eCAssert___24a1(Vvar__0___24Anonymous__1107) = cPLF_2eHoare_2eHoareAssertAssume_2eCAssert___24a1(Vvar__0___24Anonymous__1108)
     => Vvar__0___24Anonymous__1107 = Vvar__0___24Anonymous__1108 ) ).

fof('$_inj_PLF.Hoare.HoareAssertAssume.CAssume',axiom,
    ! [Vvar__0___24Anonymous__1109,Vvar__0___24Anonymous__1110] :
      ( cPLF_2eHoare_2eHoareAssertAssume_2eCAssume___24a1(Vvar__0___24Anonymous__1109) = cPLF_2eHoare_2eHoareAssertAssume_2eCAssume___24a1(Vvar__0___24Anonymous__1110)
     => Vvar__0___24Anonymous__1109 = Vvar__0___24Anonymous__1110 ) ).

fof('$_inj_PLF.Hoare.HoareAssertAssume.CIf',axiom,
    ! [Vvar__0___24Anonymous__1097,Vvar__0___24Anonymous__1098,Vvar__1___24Anonymous__1099,Vvar__1___24Anonymous__1100,Vvar__2___24Anonymous__1101,Vvar__2___24Anonymous__1102] :
      ( cPLF_2eHoare_2eHoareAssertAssume_2eCIf___24a3(Vvar__0___24Anonymous__1097,Vvar__1___24Anonymous__1099,Vvar__2___24Anonymous__1101) = cPLF_2eHoare_2eHoareAssertAssume_2eCIf___24a3(Vvar__0___24Anonymous__1098,Vvar__1___24Anonymous__1100,Vvar__2___24Anonymous__1102)
     => ( Vvar__2___24Anonymous__1101 = Vvar__2___24Anonymous__1102
        & Vvar__1___24Anonymous__1099 = Vvar__1___24Anonymous__1100
        & Vvar__0___24Anonymous__1097 = Vvar__0___24Anonymous__1098 ) ) ).

fof('$_inj_PLF.Hoare.HoareAssertAssume.CSeq',axiom,
    ! [Vvar__0___24Anonymous__1093,Vvar__0___24Anonymous__1094,Vvar__1___24Anonymous__1095,Vvar__1___24Anonymous__1096] :
      ( cPLF_2eHoare_2eHoareAssertAssume_2eCSeq___24a2(Vvar__0___24Anonymous__1093,Vvar__1___24Anonymous__1095) = cPLF_2eHoare_2eHoareAssertAssume_2eCSeq___24a2(Vvar__0___24Anonymous__1094,Vvar__1___24Anonymous__1096)
     => ( Vvar__1___24Anonymous__1095 = Vvar__1___24Anonymous__1096
        & Vvar__0___24Anonymous__1093 = Vvar__0___24Anonymous__1094 ) ) ).

fof('$_inj_PLF.Hoare.HoareAssertAssume.CWhile',axiom,
    ! [Vvar__0___24Anonymous__1103,Vvar__0___24Anonymous__1104,Vvar__1___24Anonymous__1105,Vvar__1___24Anonymous__1106] :
      ( cPLF_2eHoare_2eHoareAssertAssume_2eCWhile___24a2(Vvar__0___24Anonymous__1103,Vvar__1___24Anonymous__1105) = cPLF_2eHoare_2eHoareAssertAssume_2eCWhile___24a2(Vvar__0___24Anonymous__1104,Vvar__1___24Anonymous__1106)
     => ( Vvar__1___24Anonymous__1105 = Vvar__1___24Anonymous__1106
        & Vvar__0___24Anonymous__1103 = Vvar__0___24Anonymous__1104 ) ) ).

fof('$_inj_PLF.Hoare.HoareAssertAssume.RNormal',axiom,
    ! [Vvar__0___24Anonymous__1130,Vvar__0___24Anonymous__1131] :
      ( cPLF_2eHoare_2eHoareAssertAssume_2eRNormal___24a1(Vvar__0___24Anonymous__1130) = cPLF_2eHoare_2eHoareAssertAssume_2eRNormal___24a1(Vvar__0___24Anonymous__1131)
     => Vvar__0___24Anonymous__1130 = Vvar__0___24Anonymous__1131 ) ).

fof('$_inj_PLF.Hoare.If1.CAss',axiom,
    ! [Vvar__0___24Anonymous__1392,Vvar__0___24Anonymous__1393,Vvar__1___24Anonymous__1394,Vvar__1___24Anonymous__1395] :
      ( cPLF_2eHoare_2eIf1_2eCAss___24a2(Vvar__0___24Anonymous__1392,Vvar__1___24Anonymous__1394) = cPLF_2eHoare_2eIf1_2eCAss___24a2(Vvar__0___24Anonymous__1393,Vvar__1___24Anonymous__1395)
     => ( Vvar__1___24Anonymous__1394 = Vvar__1___24Anonymous__1395
        & Vvar__0___24Anonymous__1392 = Vvar__0___24Anonymous__1393 ) ) ).

fof('$_inj_PLF.Hoare.If1.CIf',axiom,
    ! [Vvar__0___24Anonymous__1400,Vvar__0___24Anonymous__1401,Vvar__1___24Anonymous__1402,Vvar__1___24Anonymous__1403,Vvar__2___24Anonymous__1404,Vvar__2___24Anonymous__1405] :
      ( cPLF_2eHoare_2eIf1_2eCIf___24a3(Vvar__0___24Anonymous__1400,Vvar__1___24Anonymous__1402,Vvar__2___24Anonymous__1404) = cPLF_2eHoare_2eIf1_2eCIf___24a3(Vvar__0___24Anonymous__1401,Vvar__1___24Anonymous__1403,Vvar__2___24Anonymous__1405)
     => ( Vvar__2___24Anonymous__1404 = Vvar__2___24Anonymous__1405
        & Vvar__1___24Anonymous__1402 = Vvar__1___24Anonymous__1403
        & Vvar__0___24Anonymous__1400 = Vvar__0___24Anonymous__1401 ) ) ).

fof('$_inj_PLF.Hoare.If1.CIf1',axiom,
    ! [Vvar__0___24Anonymous__1410,Vvar__0___24Anonymous__1411,Vvar__1___24Anonymous__1412,Vvar__1___24Anonymous__1413] :
      ( cPLF_2eHoare_2eIf1_2eCIf1___24a2(Vvar__0___24Anonymous__1410,Vvar__1___24Anonymous__1412) = cPLF_2eHoare_2eIf1_2eCIf1___24a2(Vvar__0___24Anonymous__1411,Vvar__1___24Anonymous__1413)
     => ( Vvar__1___24Anonymous__1412 = Vvar__1___24Anonymous__1413
        & Vvar__0___24Anonymous__1410 = Vvar__0___24Anonymous__1411 ) ) ).

fof('$_inj_PLF.Hoare.If1.CSeq',axiom,
    ! [Vvar__0___24Anonymous__1396,Vvar__0___24Anonymous__1397,Vvar__1___24Anonymous__1398,Vvar__1___24Anonymous__1399] :
      ( cPLF_2eHoare_2eIf1_2eCSeq___24a2(Vvar__0___24Anonymous__1396,Vvar__1___24Anonymous__1398) = cPLF_2eHoare_2eIf1_2eCSeq___24a2(Vvar__0___24Anonymous__1397,Vvar__1___24Anonymous__1399)
     => ( Vvar__1___24Anonymous__1398 = Vvar__1___24Anonymous__1399
        & Vvar__0___24Anonymous__1396 = Vvar__0___24Anonymous__1397 ) ) ).

fof('$_inj_PLF.Hoare.If1.CWhile',axiom,
    ! [Vvar__0___24Anonymous__1406,Vvar__0___24Anonymous__1407,Vvar__1___24Anonymous__1408,Vvar__1___24Anonymous__1409] :
      ( cPLF_2eHoare_2eIf1_2eCWhile___24a2(Vvar__0___24Anonymous__1406,Vvar__1___24Anonymous__1408) = cPLF_2eHoare_2eIf1_2eCWhile___24a2(Vvar__0___24Anonymous__1407,Vvar__1___24Anonymous__1409)
     => ( Vvar__1___24Anonymous__1408 = Vvar__1___24Anonymous__1409
        & Vvar__0___24Anonymous__1406 = Vvar__0___24Anonymous__1407 ) ) ).

fof('$_inj_PLF.Hoare.RepeatExercise.CAsgn',axiom,
    ! [Vvar__0___24Anonymous__1620,Vvar__0___24Anonymous__1621,Vvar__1___24Anonymous__1622,Vvar__1___24Anonymous__1623] :
      ( cPLF_2eHoare_2eRepeatExercise_2eCAsgn___24a2(Vvar__0___24Anonymous__1620,Vvar__1___24Anonymous__1622) = cPLF_2eHoare_2eRepeatExercise_2eCAsgn___24a2(Vvar__0___24Anonymous__1621,Vvar__1___24Anonymous__1623)
     => ( Vvar__1___24Anonymous__1622 = Vvar__1___24Anonymous__1623
        & Vvar__0___24Anonymous__1620 = Vvar__0___24Anonymous__1621 ) ) ).

fof('$_inj_PLF.Hoare.RepeatExercise.CIf',axiom,
    ! [Vvar__0___24Anonymous__1628,Vvar__0___24Anonymous__1629,Vvar__1___24Anonymous__1630,Vvar__1___24Anonymous__1631,Vvar__2___24Anonymous__1632,Vvar__2___24Anonymous__1633] :
      ( cPLF_2eHoare_2eRepeatExercise_2eCIf___24a3(Vvar__0___24Anonymous__1628,Vvar__1___24Anonymous__1630,Vvar__2___24Anonymous__1632) = cPLF_2eHoare_2eRepeatExercise_2eCIf___24a3(Vvar__0___24Anonymous__1629,Vvar__1___24Anonymous__1631,Vvar__2___24Anonymous__1633)
     => ( Vvar__2___24Anonymous__1632 = Vvar__2___24Anonymous__1633
        & Vvar__1___24Anonymous__1630 = Vvar__1___24Anonymous__1631
        & Vvar__0___24Anonymous__1628 = Vvar__0___24Anonymous__1629 ) ) ).

fof('$_inj_PLF.Hoare.RepeatExercise.CRepeat',axiom,
    ! [Vvar__0___24Anonymous__1638,Vvar__0___24Anonymous__1639,Vvar__1___24Anonymous__1640,Vvar__1___24Anonymous__1641] :
      ( cPLF_2eHoare_2eRepeatExercise_2eCRepeat___24a2(Vvar__0___24Anonymous__1638,Vvar__1___24Anonymous__1640) = cPLF_2eHoare_2eRepeatExercise_2eCRepeat___24a2(Vvar__0___24Anonymous__1639,Vvar__1___24Anonymous__1641)
     => ( Vvar__1___24Anonymous__1640 = Vvar__1___24Anonymous__1641
        & Vvar__0___24Anonymous__1638 = Vvar__0___24Anonymous__1639 ) ) ).

fof('$_inj_PLF.Hoare.RepeatExercise.CSeq',axiom,
    ! [Vvar__0___24Anonymous__1624,Vvar__0___24Anonymous__1625,Vvar__1___24Anonymous__1626,Vvar__1___24Anonymous__1627] :
      ( cPLF_2eHoare_2eRepeatExercise_2eCSeq___24a2(Vvar__0___24Anonymous__1624,Vvar__1___24Anonymous__1626) = cPLF_2eHoare_2eRepeatExercise_2eCSeq___24a2(Vvar__0___24Anonymous__1625,Vvar__1___24Anonymous__1627)
     => ( Vvar__1___24Anonymous__1626 = Vvar__1___24Anonymous__1627
        & Vvar__0___24Anonymous__1624 = Vvar__0___24Anonymous__1625 ) ) ).

fof('$_inj_PLF.Hoare.RepeatExercise.CWhile',axiom,
    ! [Vvar__0___24Anonymous__1634,Vvar__0___24Anonymous__1635,Vvar__1___24Anonymous__1636,Vvar__1___24Anonymous__1637] :
      ( cPLF_2eHoare_2eRepeatExercise_2eCWhile___24a2(Vvar__0___24Anonymous__1634,Vvar__1___24Anonymous__1636) = cPLF_2eHoare_2eRepeatExercise_2eCWhile___24a2(Vvar__0___24Anonymous__1635,Vvar__1___24Anonymous__1637)
     => ( Vvar__1___24Anonymous__1636 = Vvar__1___24Anonymous__1637
        & Vvar__0___24Anonymous__1634 = Vvar__0___24Anonymous__1635 ) ) ).

fof('$_inj_PLF.Imp.AExp.AMinus',axiom,
    ! [Vvar__0__a1__6975,Vvar__0__a1__6976,Vvar__1__a2__6977,Vvar__1__a2__6978] :
      ( cPLF_2eImp_2eAExp_2eAMinus___24a2(Vvar__0__a1__6975,Vvar__1__a2__6977) = cPLF_2eImp_2eAExp_2eAMinus___24a2(Vvar__0__a1__6976,Vvar__1__a2__6978)
     => ( Vvar__1__a2__6977 = Vvar__1__a2__6978
        & Vvar__0__a1__6975 = Vvar__0__a1__6976 ) ) ).

fof('$_inj_PLF.Imp.AExp.AMult',axiom,
    ! [Vvar__0__a1__6979,Vvar__0__a1__6980,Vvar__1__a2__6981,Vvar__1__a2__6982] :
      ( cPLF_2eImp_2eAExp_2eAMult___24a2(Vvar__0__a1__6979,Vvar__1__a2__6981) = cPLF_2eImp_2eAExp_2eAMult___24a2(Vvar__0__a1__6980,Vvar__1__a2__6982)
     => ( Vvar__1__a2__6981 = Vvar__1__a2__6982
        & Vvar__0__a1__6979 = Vvar__0__a1__6980 ) ) ).

fof('$_inj_PLF.Imp.AExp.ANum',axiom,
    ! [Vvar__0__n__6969,Vvar__0__n__6970] :
      ( cPLF_2eImp_2eAExp_2eANum___24a1(Vvar__0__n__6969) = cPLF_2eImp_2eAExp_2eANum___24a1(Vvar__0__n__6970)
     => Vvar__0__n__6969 = Vvar__0__n__6970 ) ).

fof('$_inj_PLF.Imp.AExp.APlus',axiom,
    ! [Vvar__0__a1__6971,Vvar__0__a1__6972,Vvar__1__a2__6973,Vvar__1__a2__6974] :
      ( cPLF_2eImp_2eAExp_2eAPlus___24a2(Vvar__0__a1__6971,Vvar__1__a2__6973) = cPLF_2eImp_2eAExp_2eAPlus___24a2(Vvar__0__a1__6972,Vvar__1__a2__6974)
     => ( Vvar__1__a2__6973 = Vvar__1__a2__6974
        & Vvar__0__a1__6971 = Vvar__0__a1__6972 ) ) ).

fof('$_inj_PLF.Imp.AExp.BAnd',axiom,
    ! [Vvar__0__b1__149848,Vvar__0__b1__149849,Vvar__1__b2__149850,Vvar__1__b2__149851] :
      ( cPLF_2eImp_2eAExp_2eBAnd___24a2(Vvar__0__b1__149848,Vvar__1__b2__149850) = cPLF_2eImp_2eAExp_2eBAnd___24a2(Vvar__0__b1__149849,Vvar__1__b2__149851)
     => ( Vvar__1__b2__149850 = Vvar__1__b2__149851
        & Vvar__0__b1__149848 = Vvar__0__b1__149849 ) ) ).

fof('$_inj_PLF.Imp.AExp.BEq',axiom,
    ! [Vvar__0__a1__149838,Vvar__0__a1__149839,Vvar__1__a2__149840,Vvar__1__a2__149841] :
      ( cPLF_2eImp_2eAExp_2eBEq___24a2(Vvar__0__a1__149838,Vvar__1__a2__149840) = cPLF_2eImp_2eAExp_2eBEq___24a2(Vvar__0__a1__149839,Vvar__1__a2__149841)
     => ( Vvar__1__a2__149840 = Vvar__1__a2__149841
        & Vvar__0__a1__149838 = Vvar__0__a1__149839 ) ) ).

fof('$_inj_PLF.Imp.AExp.BLe',axiom,
    ! [Vvar__0__a1__149842,Vvar__0__a1__149843,Vvar__1__a2__149844,Vvar__1__a2__149845] :
      ( cPLF_2eImp_2eAExp_2eBLe___24a2(Vvar__0__a1__149842,Vvar__1__a2__149844) = cPLF_2eImp_2eAExp_2eBLe___24a2(Vvar__0__a1__149843,Vvar__1__a2__149845)
     => ( Vvar__1__a2__149844 = Vvar__1__a2__149845
        & Vvar__0__a1__149842 = Vvar__0__a1__149843 ) ) ).

fof('$_inj_PLF.Imp.AExp.BNot',axiom,
    ! [Vvar__0__b__149846,Vvar__0__b__149847] :
      ( cPLF_2eImp_2eAExp_2eBNot___24a1(Vvar__0__b__149846) = cPLF_2eImp_2eAExp_2eBNot___24a1(Vvar__0__b__149847)
     => Vvar__0__b__149846 = Vvar__0__b__149847 ) ).

fof('$_inj_PLF.Imp.AId',axiom,
    ! [Vvar__0__x__84,Vvar__0__x__85] :
      ( cPLF_2eImp_2eAId___24a1(Vvar__0__x__84) = cPLF_2eImp_2eAId___24a1(Vvar__0__x__85)
     => Vvar__0__x__84 = Vvar__0__x__85 ) ).

fof('$_inj_PLF.Imp.AMinus',axiom,
    ! [Vvar__0__a1__90,Vvar__0__a1__91,Vvar__1__a2__92,Vvar__1__a2__93] :
      ( cPLF_2eImp_2eAMinus___24a2(Vvar__0__a1__90,Vvar__1__a2__92) = cPLF_2eImp_2eAMinus___24a2(Vvar__0__a1__91,Vvar__1__a2__93)
     => ( Vvar__1__a2__92 = Vvar__1__a2__93
        & Vvar__0__a1__90 = Vvar__0__a1__91 ) ) ).

fof('$_inj_PLF.Imp.AMult',axiom,
    ! [Vvar__0__a1__94,Vvar__0__a1__95,Vvar__1__a2__96,Vvar__1__a2__97] :
      ( cPLF_2eImp_2eAMult___24a2(Vvar__0__a1__94,Vvar__1__a2__96) = cPLF_2eImp_2eAMult___24a2(Vvar__0__a1__95,Vvar__1__a2__97)
     => ( Vvar__1__a2__96 = Vvar__1__a2__97
        & Vvar__0__a1__94 = Vvar__0__a1__95 ) ) ).

fof('$_inj_PLF.Imp.ANum',axiom,
    ! [Vvar__0__n__82,Vvar__0__n__83] :
      ( cPLF_2eImp_2eANum___24a1(Vvar__0__n__82) = cPLF_2eImp_2eANum___24a1(Vvar__0__n__83)
     => Vvar__0__n__82 = Vvar__0__n__83 ) ).

fof('$_inj_PLF.Imp.APlus',axiom,
    ! [Vvar__0__a1__86,Vvar__0__a1__87,Vvar__1__a2__88,Vvar__1__a2__89] :
      ( cPLF_2eImp_2eAPlus___24a2(Vvar__0__a1__86,Vvar__1__a2__88) = cPLF_2eImp_2eAPlus___24a2(Vvar__0__a1__87,Vvar__1__a2__89)
     => ( Vvar__1__a2__88 = Vvar__1__a2__89
        & Vvar__0__a1__86 = Vvar__0__a1__87 ) ) ).

fof('$_inj_PLF.Imp.BAnd',axiom,
    ! [Vvar__0__b1__302,Vvar__0__b1__303,Vvar__1__b2__304,Vvar__1__b2__305] :
      ( cPLF_2eImp_2eBAnd___24a2(Vvar__0__b1__302,Vvar__1__b2__304) = cPLF_2eImp_2eBAnd___24a2(Vvar__0__b1__303,Vvar__1__b2__305)
     => ( Vvar__1__b2__304 = Vvar__1__b2__305
        & Vvar__0__b1__302 = Vvar__0__b1__303 ) ) ).

fof('$_inj_PLF.Imp.BEq',axiom,
    ! [Vvar__0__a1__292,Vvar__0__a1__293,Vvar__1__a2__294,Vvar__1__a2__295] :
      ( cPLF_2eImp_2eBEq___24a2(Vvar__0__a1__292,Vvar__1__a2__294) = cPLF_2eImp_2eBEq___24a2(Vvar__0__a1__293,Vvar__1__a2__295)
     => ( Vvar__1__a2__294 = Vvar__1__a2__295
        & Vvar__0__a1__292 = Vvar__0__a1__293 ) ) ).

fof('$_inj_PLF.Imp.BLe',axiom,
    ! [Vvar__0__a1__296,Vvar__0__a1__297,Vvar__1__a2__298,Vvar__1__a2__299] :
      ( cPLF_2eImp_2eBLe___24a2(Vvar__0__a1__296,Vvar__1__a2__298) = cPLF_2eImp_2eBLe___24a2(Vvar__0__a1__297,Vvar__1__a2__299)
     => ( Vvar__1__a2__298 = Vvar__1__a2__299
        & Vvar__0__a1__296 = Vvar__0__a1__297 ) ) ).

fof('$_inj_PLF.Imp.BNot',axiom,
    ! [Vvar__0__b__300,Vvar__0__b__301] :
      ( cPLF_2eImp_2eBNot___24a1(Vvar__0__b__300) = cPLF_2eImp_2eBNot___24a1(Vvar__0__b__301)
     => Vvar__0__b__300 = Vvar__0__b__301 ) ).

fof('$_inj_PLF.Imp.BreakImp.CAss',axiom,
    ! [Vvar__0__x__743,Vvar__0__x__744,Vvar__1__a__745,Vvar__1__a__746] :
      ( cPLF_2eImp_2eBreakImp_2eCAss___24a2(Vvar__0__x__743,Vvar__1__a__745) = cPLF_2eImp_2eBreakImp_2eCAss___24a2(Vvar__0__x__744,Vvar__1__a__746)
     => ( Vvar__1__a__745 = Vvar__1__a__746
        & Vvar__0__x__743 = Vvar__0__x__744 ) ) ).

fof('$_inj_PLF.Imp.BreakImp.CIf',axiom,
    ! [Vvar__0__b__751,Vvar__0__b__752,Vvar__1__c1__753,Vvar__1__c1__754,Vvar__2__c2__755,Vvar__2__c2__756] :
      ( cPLF_2eImp_2eBreakImp_2eCIf___24a3(Vvar__0__b__751,Vvar__1__c1__753,Vvar__2__c2__755) = cPLF_2eImp_2eBreakImp_2eCIf___24a3(Vvar__0__b__752,Vvar__1__c1__754,Vvar__2__c2__756)
     => ( Vvar__2__c2__755 = Vvar__2__c2__756
        & Vvar__1__c1__753 = Vvar__1__c1__754
        & Vvar__0__b__751 = Vvar__0__b__752 ) ) ).

fof('$_inj_PLF.Imp.BreakImp.CSeq',axiom,
    ! [Vvar__0__c1__747,Vvar__0__c1__748,Vvar__1__c2__749,Vvar__1__c2__750] :
      ( cPLF_2eImp_2eBreakImp_2eCSeq___24a2(Vvar__0__c1__747,Vvar__1__c2__749) = cPLF_2eImp_2eBreakImp_2eCSeq___24a2(Vvar__0__c1__748,Vvar__1__c2__750)
     => ( Vvar__1__c2__749 = Vvar__1__c2__750
        & Vvar__0__c1__747 = Vvar__0__c1__748 ) ) ).

fof('$_inj_PLF.Imp.BreakImp.CWhile',axiom,
    ! [Vvar__0__b__757,Vvar__0__b__758,Vvar__1__c__759,Vvar__1__c__760] :
      ( cPLF_2eImp_2eBreakImp_2eCWhile___24a2(Vvar__0__b__757,Vvar__1__c__759) = cPLF_2eImp_2eBreakImp_2eCWhile___24a2(Vvar__0__b__758,Vvar__1__c__760)
     => ( Vvar__1__c__759 = Vvar__1__c__760
        & Vvar__0__b__757 = Vvar__0__b__758 ) ) ).

fof('$_inj_PLF.Imp.CAss',axiom,
    ! [Vvar__0__x__161,Vvar__0__x__162,Vvar__1__a__163,Vvar__1__a__164] :
      ( cPLF_2eImp_2eCAss___24a2(Vvar__0__x__161,Vvar__1__a__163) = cPLF_2eImp_2eCAss___24a2(Vvar__0__x__162,Vvar__1__a__164)
     => ( Vvar__1__a__163 = Vvar__1__a__164
        & Vvar__0__x__161 = Vvar__0__x__162 ) ) ).

fof('$_inj_PLF.Imp.CIf',axiom,
    ! [Vvar__0__b__169,Vvar__0__b__170,Vvar__1__c1__171,Vvar__1__c1__172,Vvar__2__c2__173,Vvar__2__c2__174] :
      ( cPLF_2eImp_2eCIf___24a3(Vvar__0__b__169,Vvar__1__c1__171,Vvar__2__c2__173) = cPLF_2eImp_2eCIf___24a3(Vvar__0__b__170,Vvar__1__c1__172,Vvar__2__c2__174)
     => ( Vvar__2__c2__173 = Vvar__2__c2__174
        & Vvar__1__c1__171 = Vvar__1__c1__172
        & Vvar__0__b__169 = Vvar__0__b__170 ) ) ).

fof('$_inj_PLF.Imp.CSeq',axiom,
    ! [Vvar__0__c1__165,Vvar__0__c1__166,Vvar__1__c2__167,Vvar__1__c2__168] :
      ( cPLF_2eImp_2eCSeq___24a2(Vvar__0__c1__165,Vvar__1__c2__167) = cPLF_2eImp_2eCSeq___24a2(Vvar__0__c1__166,Vvar__1__c2__168)
     => ( Vvar__1__c2__167 = Vvar__1__c2__168
        & Vvar__0__c1__165 = Vvar__0__c1__166 ) ) ).

fof('$_inj_PLF.Imp.CWhile',axiom,
    ! [Vvar__0__b__175,Vvar__0__b__176,Vvar__1__c__177,Vvar__1__c__178] :
      ( cPLF_2eImp_2eCWhile___24a2(Vvar__0__b__175,Vvar__1__c__177) = cPLF_2eImp_2eCWhile___24a2(Vvar__0__b__176,Vvar__1__c__178)
     => ( Vvar__1__c__177 = Vvar__1__c__178
        & Vvar__0__b__175 = Vvar__0__b__176 ) ) ).

fof('$_inj_PLF.Imp.SLoad',axiom,
    ! [Vvar__0__x__666,Vvar__0__x__667] :
      ( cPLF_2eImp_2eSLoad___24a1(Vvar__0__x__666) = cPLF_2eImp_2eSLoad___24a1(Vvar__0__x__667)
     => Vvar__0__x__666 = Vvar__0__x__667 ) ).

fof('$_inj_PLF.Imp.SPush',axiom,
    ! [Vvar__0__n__664,Vvar__0__n__665] :
      ( cPLF_2eImp_2eSPush___24a1(Vvar__0__n__664) = cPLF_2eImp_2eSPush___24a1(Vvar__0__n__665)
     => Vvar__0__n__664 = Vvar__0__n__665 ) ).

fof('$_inj_PLF.Imp.aevalR_division.ADiv',axiom,
    ! [Vvar__0__a1__4525,Vvar__0__a1__4526,Vvar__1__a2__4527,Vvar__1__a2__4528] :
      ( cPLF_2eImp_2eaevalR__division_2eADiv___24a2(Vvar__0__a1__4525,Vvar__1__a2__4527) = cPLF_2eImp_2eaevalR__division_2eADiv___24a2(Vvar__0__a1__4526,Vvar__1__a2__4528)
     => ( Vvar__1__a2__4527 = Vvar__1__a2__4528
        & Vvar__0__a1__4525 = Vvar__0__a1__4526 ) ) ).

fof('$_inj_PLF.Imp.aevalR_division.AMinus',axiom,
    ! [Vvar__0__a1__4517,Vvar__0__a1__4518,Vvar__1__a2__4519,Vvar__1__a2__4520] :
      ( cPLF_2eImp_2eaevalR__division_2eAMinus___24a2(Vvar__0__a1__4517,Vvar__1__a2__4519) = cPLF_2eImp_2eaevalR__division_2eAMinus___24a2(Vvar__0__a1__4518,Vvar__1__a2__4520)
     => ( Vvar__1__a2__4519 = Vvar__1__a2__4520
        & Vvar__0__a1__4517 = Vvar__0__a1__4518 ) ) ).

fof('$_inj_PLF.Imp.aevalR_division.AMult',axiom,
    ! [Vvar__0__a1__4521,Vvar__0__a1__4522,Vvar__1__a2__4523,Vvar__1__a2__4524] :
      ( cPLF_2eImp_2eaevalR__division_2eAMult___24a2(Vvar__0__a1__4521,Vvar__1__a2__4523) = cPLF_2eImp_2eaevalR__division_2eAMult___24a2(Vvar__0__a1__4522,Vvar__1__a2__4524)
     => ( Vvar__1__a2__4523 = Vvar__1__a2__4524
        & Vvar__0__a1__4521 = Vvar__0__a1__4522 ) ) ).

fof('$_inj_PLF.Imp.aevalR_division.ANum',axiom,
    ! [Vvar__0__n__4511,Vvar__0__n__4512] :
      ( cPLF_2eImp_2eaevalR__division_2eANum___24a1(Vvar__0__n__4511) = cPLF_2eImp_2eaevalR__division_2eANum___24a1(Vvar__0__n__4512)
     => Vvar__0__n__4511 = Vvar__0__n__4512 ) ).

fof('$_inj_PLF.Imp.aevalR_division.APlus',axiom,
    ! [Vvar__0__a1__4513,Vvar__0__a1__4514,Vvar__1__a2__4515,Vvar__1__a2__4516] :
      ( cPLF_2eImp_2eaevalR__division_2eAPlus___24a2(Vvar__0__a1__4513,Vvar__1__a2__4515) = cPLF_2eImp_2eaevalR__division_2eAPlus___24a2(Vvar__0__a1__4514,Vvar__1__a2__4516)
     => ( Vvar__1__a2__4515 = Vvar__1__a2__4516
        & Vvar__0__a1__4513 = Vvar__0__a1__4514 ) ) ).

fof('$_inj_PLF.Imp.aevalR_extended.AMinus',axiom,
    ! [Vvar__0__a1__83625,Vvar__0__a1__83626,Vvar__1__a2__83627,Vvar__1__a2__83628] :
      ( cPLF_2eImp_2eaevalR__extended_2eAMinus___24a2(Vvar__0__a1__83625,Vvar__1__a2__83627) = cPLF_2eImp_2eaevalR__extended_2eAMinus___24a2(Vvar__0__a1__83626,Vvar__1__a2__83628)
     => ( Vvar__1__a2__83627 = Vvar__1__a2__83628
        & Vvar__0__a1__83625 = Vvar__0__a1__83626 ) ) ).

fof('$_inj_PLF.Imp.aevalR_extended.AMult',axiom,
    ! [Vvar__0__a1__83629,Vvar__0__a1__83630,Vvar__1__a2__83631,Vvar__1__a2__83632] :
      ( cPLF_2eImp_2eaevalR__extended_2eAMult___24a2(Vvar__0__a1__83629,Vvar__1__a2__83631) = cPLF_2eImp_2eaevalR__extended_2eAMult___24a2(Vvar__0__a1__83630,Vvar__1__a2__83632)
     => ( Vvar__1__a2__83631 = Vvar__1__a2__83632
        & Vvar__0__a1__83629 = Vvar__0__a1__83630 ) ) ).

fof('$_inj_PLF.Imp.aevalR_extended.ANum',axiom,
    ! [Vvar__0__n__83619,Vvar__0__n__83620] :
      ( cPLF_2eImp_2eaevalR__extended_2eANum___24a1(Vvar__0__n__83619) = cPLF_2eImp_2eaevalR__extended_2eANum___24a1(Vvar__0__n__83620)
     => Vvar__0__n__83619 = Vvar__0__n__83620 ) ).

fof('$_inj_PLF.Imp.aevalR_extended.APlus',axiom,
    ! [Vvar__0__a1__83621,Vvar__0__a1__83622,Vvar__1__a2__83623,Vvar__1__a2__83624] :
      ( cPLF_2eImp_2eaevalR__extended_2eAPlus___24a2(Vvar__0__a1__83621,Vvar__1__a2__83623) = cPLF_2eImp_2eaevalR__extended_2eAPlus___24a2(Vvar__0__a1__83622,Vvar__1__a2__83624)
     => ( Vvar__1__a2__83623 = Vvar__1__a2__83624
        & Vvar__0__a1__83621 = Vvar__0__a1__83622 ) ) ).

fof('$_inversion_Coq.Arith.Between.P_nth',axiom,
    ! [Vvar__0__P__84236,Vvar__1__Q__84238,Vvar__2__init__84241,Vvar__3___24Anonymous__84242,Vvar__4___24Anonymous__84243] :
      ( c_24__type__84269___24t(Vvar__0__P__84236,Vvar__1__Q__84238,Vvar__2__init__84241,Vvar__3___24Anonymous__84242,Vvar__4___24Anonymous__84243,Vvar__0__P__84236)
     => ( c_24__type__84277___24t(Vvar__0__P__84236,Vvar__1__Q__84238,Vvar__2__init__84241,Vvar__3___24Anonymous__84242,Vvar__4___24Anonymous__84243,Vvar__1__Q__84238)
       => ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__2__init__84241)
         => ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__3___24Anonymous__84242)
           => ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__4___24Anonymous__84243)
             => ( cCoq_2eArith_2eBetween_2eP__nth___24a5(Vvar__0__P__84236,Vvar__1__Q__84238,Vvar__2__init__84241,Vvar__3___24Anonymous__84242,Vvar__4___24Anonymous__84243)
               => ( ( Vvar__4___24Anonymous__84243 = cCoq_2eInit_2eDatatypes_2eO
                    & Vvar__3___24Anonymous__84242 = Vvar__2__init__84241 )
                  | ? [Vvar__3__k__84257] :
                      ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__3__k__84257)
                      & ? [Vvar__4__l__84258] :
                          ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__4__l__84258)
                          & ? [Vvar__5__n__84259] :
                              ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__5__n__84259)
                              & cCoq_2eArith_2eBetween_2eP__nth___24a5(Vvar__0__P__84236,Vvar__1__Q__84238,Vvar__2__init__84241,Vvar__3__k__84257,Vvar__5__n__84259)
                              & cCoq_2eArith_2eBetween_2ebetween___24a3(Vvar__0__P__84236,cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__3__k__84257),Vvar__4__l__84258)
                              & p(happ(Vvar__1__Q__84238,Vvar__4__l__84258))
                              & Vvar__4___24Anonymous__84243 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__5__n__84259)
                              & Vvar__3___24Anonymous__84242 = Vvar__4__l__84258 ) ) ) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.Arith.Between.between',axiom,
    ! [Vvar__0__P__4926,Vvar__1__k__4928,Vvar__2___24Anonymous__4929] :
      ( c_24__type__4943___24t(Vvar__0__P__4926,Vvar__1__k__4928,Vvar__2___24Anonymous__4929,Vvar__0__P__4926)
     => ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__1__k__4928)
       => ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__2___24Anonymous__4929)
         => ( cCoq_2eArith_2eBetween_2ebetween___24a3(Vvar__0__P__4926,Vvar__1__k__4928,Vvar__2___24Anonymous__4929)
           => ( Vvar__2___24Anonymous__4929 = Vvar__1__k__4928
              | ? [Vvar__2__l__4937] :
                  ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__2__l__4937)
                  & cCoq_2eArith_2eBetween_2ebetween___24a3(Vvar__0__P__4926,Vvar__1__k__4928,Vvar__2__l__4937)
                  & p(happ(Vvar__0__P__4926,Vvar__2__l__4937))
                  & Vvar__2___24Anonymous__4929 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__2__l__4937) ) ) ) ) ) ) ).

fof('$_inversion_Coq.Arith.Between.exists_between',axiom,
    ! [Vvar__0__Q__14812,Vvar__1__k__14814,Vvar__2___24Anonymous__14815] :
      ( c_24__type__14831___24t(Vvar__0__Q__14812,Vvar__1__k__14814,Vvar__2___24Anonymous__14815,Vvar__0__Q__14812)
     => ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__1__k__14814)
       => ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__2___24Anonymous__14815)
         => ( cCoq_2eArith_2eBetween_2eexists__between___24a3(Vvar__0__Q__14812,Vvar__1__k__14814,Vvar__2___24Anonymous__14815)
           => ( ? [Vvar__2__l__14820] :
                  ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__2__l__14820)
                  & cCoq_2eArith_2eBetween_2eexists__between___24a3(Vvar__0__Q__14812,Vvar__1__k__14814,Vvar__2__l__14820)
                  & Vvar__2___24Anonymous__14815 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__2__l__14820) )
              | ? [Vvar__2__l__14825] :
                  ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__2__l__14825)
                  & cCoq_2eInit_2ePeano_2ele___24a2(Vvar__1__k__14814,Vvar__2__l__14825)
                  & p(happ(Vvar__0__Q__14812,Vvar__2__l__14825))
                  & Vvar__2___24Anonymous__14815 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__2__l__14825) ) ) ) ) ) ) ).

fof('$_inversion_Coq.Arith.Even.even',axiom,
    ! [Vvar__0___24Anonymous__1965] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__1965)
     => ( cCoq_2eArith_2eEven_2eeven___24a1(Vvar__0___24Anonymous__1965)
       => ( Vvar__0___24Anonymous__1965 = cCoq_2eInit_2eDatatypes_2eO
          | ? [Vvar__0__n__1967] :
              ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0__n__1967)
              & cCoq_2eArith_2eEven_2eodd___24a1(Vvar__0__n__1967)
              & Vvar__0___24Anonymous__1965 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0__n__1967) ) ) ) ) ).

fof('$_inversion_Coq.Arith.Even.odd',axiom,
    ! [Vvar__0___24Anonymous__1969] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__1969)
     => ( cCoq_2eArith_2eEven_2eodd___24a1(Vvar__0___24Anonymous__1969)
       => ? [Vvar__0__n__1971] :
            ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0__n__1971)
            & cCoq_2eArith_2eEven_2eeven___24a1(Vvar__0__n__1971)
            & Vvar__0___24Anonymous__1969 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0__n__1971) ) ) ) ).

fof('$_inversion_Coq.Bool.Bool.reflect',axiom,
    ! [Vvar__0__P__4945,Vvar__1___24Anonymous__4946,VX4947] :
      ( cProp___24t(Vvar__0__P__4945)
     => ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__1___24Anonymous__4946)
       => ( cCoq_2eBool_2eBool_2ereflect___24t(Vvar__0__P__4945,Vvar__1___24Anonymous__4946,VX4947)
         => ( ( p(Vvar__0__P__4945)
              & Vvar__1___24Anonymous__4946 = cCoq_2eInit_2eDatatypes_2etrue
              & VX4947 = cCoq_2eBool_2eBool_2eReflectT___24a1(Vvar__0__P__4945) )
            | ( ~ p(Vvar__0__P__4945)
              & Vvar__1___24Anonymous__4946 = cCoq_2eInit_2eDatatypes_2efalse
              & VX4947 = cCoq_2eBool_2eBool_2eReflectF___24a1(Vvar__0__P__4945) ) ) ) ) ) ).

fof('$_inversion_Coq.FSets.FSetPositive.PositiveSet.ct',axiom,
    ! [Vvar__0___24Anonymous__145456,Vvar__1___24Anonymous__145457,Vvar__2___24Anonymous__145458] :
      ( cCoq_2eInit_2eDatatypes_2ecomparison___24t(Vvar__0___24Anonymous__145456)
     => ( cCoq_2eInit_2eDatatypes_2ecomparison___24t(Vvar__1___24Anonymous__145457)
       => ( cCoq_2eInit_2eDatatypes_2ecomparison___24t(Vvar__2___24Anonymous__145458)
         => ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2ect___24a3(Vvar__0___24Anonymous__145456,Vvar__1___24Anonymous__145457,Vvar__2___24Anonymous__145458)
           => ( ? [Vvar__0__x__145460] :
                  ( cCoq_2eInit_2eDatatypes_2ecomparison___24t(Vvar__0__x__145460)
                  & Vvar__2___24Anonymous__145458 = Vvar__0__x__145460
                  & Vvar__1___24Anonymous__145457 = Vvar__0__x__145460
                  & Vvar__0___24Anonymous__145456 = Vvar__0__x__145460 )
              | ? [Vvar__0__x__145461] :
                  ( cCoq_2eInit_2eDatatypes_2ecomparison___24t(Vvar__0__x__145461)
                  & Vvar__2___24Anonymous__145458 = Vvar__0__x__145461
                  & Vvar__1___24Anonymous__145457 = cCoq_2eInit_2eDatatypes_2eEq
                  & Vvar__0___24Anonymous__145456 = Vvar__0__x__145461 )
              | ? [Vvar__0__x__145462] :
                  ( cCoq_2eInit_2eDatatypes_2ecomparison___24t(Vvar__0__x__145462)
                  & Vvar__2___24Anonymous__145458 = Vvar__0__x__145462
                  & Vvar__1___24Anonymous__145457 = Vvar__0__x__145462
                  & Vvar__0___24Anonymous__145456 = cCoq_2eInit_2eDatatypes_2eEq )
              | ? [Vvar__0__x__145463] :
                  ( cCoq_2eInit_2eDatatypes_2ecomparison___24t(Vvar__0__x__145463)
                  & Vvar__2___24Anonymous__145458 = Vvar__0__x__145463
                  & Vvar__1___24Anonymous__145457 = cCoq_2eInit_2eDatatypes_2eLt
                  & Vvar__0___24Anonymous__145456 = cCoq_2eInit_2eDatatypes_2eGt )
              | ? [Vvar__0__x__145464] :
                  ( cCoq_2eInit_2eDatatypes_2ecomparison___24t(Vvar__0__x__145464)
                  & Vvar__2___24Anonymous__145458 = Vvar__0__x__145464
                  & Vvar__1___24Anonymous__145457 = cCoq_2eInit_2eDatatypes_2eGt
                  & Vvar__0___24Anonymous__145456 = cCoq_2eInit_2eDatatypes_2eLt ) ) ) ) ) ) ).

fof('$_inversion_Coq.FSets.FSetPositive.PositiveSet.tree',axiom,
    ! [VX7092] :
      ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree___24t(VX7092)
     => ( VX7092 = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eLeaf
        | ? [Vvar__0___24Anonymous__7093] :
            ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree___24t(Vvar__0___24Anonymous__7093)
            & ? [Vvar__1___24Anonymous__7094] :
                ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__1___24Anonymous__7094)
                & ? [Vvar__2___24Anonymous__7095] :
                    ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree___24t(Vvar__2___24Anonymous__7095)
                    & VX7092 = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eNode___24a3(Vvar__0___24Anonymous__7093,Vvar__1___24Anonymous__7094,Vvar__2___24Anonymous__7095) ) ) ) ) ) ).

fof('$_inversion_Coq.Init.Byte.byte',axiom,
    ! [VX4967] :
      ( cCoq_2eInit_2eByte_2ebyte___24t(VX4967)
     => ( VX4967 = cCoq_2eInit_2eByte_2ex00
        | VX4967 = cCoq_2eInit_2eByte_2ex01
        | VX4967 = cCoq_2eInit_2eByte_2ex02
        | VX4967 = cCoq_2eInit_2eByte_2ex03
        | VX4967 = cCoq_2eInit_2eByte_2ex04
        | VX4967 = cCoq_2eInit_2eByte_2ex05
        | VX4967 = cCoq_2eInit_2eByte_2ex06
        | VX4967 = cCoq_2eInit_2eByte_2ex07
        | VX4967 = cCoq_2eInit_2eByte_2ex08
        | VX4967 = cCoq_2eInit_2eByte_2ex09
        | VX4967 = cCoq_2eInit_2eByte_2ex0a
        | VX4967 = cCoq_2eInit_2eByte_2ex0b
        | VX4967 = cCoq_2eInit_2eByte_2ex0c
        | VX4967 = cCoq_2eInit_2eByte_2ex0d
        | VX4967 = cCoq_2eInit_2eByte_2ex0e
        | VX4967 = cCoq_2eInit_2eByte_2ex0f
        | VX4967 = cCoq_2eInit_2eByte_2ex10
        | VX4967 = cCoq_2eInit_2eByte_2ex11
        | VX4967 = cCoq_2eInit_2eByte_2ex12
        | VX4967 = cCoq_2eInit_2eByte_2ex13
        | VX4967 = cCoq_2eInit_2eByte_2ex14
        | VX4967 = cCoq_2eInit_2eByte_2ex15
        | VX4967 = cCoq_2eInit_2eByte_2ex16
        | VX4967 = cCoq_2eInit_2eByte_2ex17
        | VX4967 = cCoq_2eInit_2eByte_2ex18
        | VX4967 = cCoq_2eInit_2eByte_2ex19
        | VX4967 = cCoq_2eInit_2eByte_2ex1a
        | VX4967 = cCoq_2eInit_2eByte_2ex1b
        | VX4967 = cCoq_2eInit_2eByte_2ex1c
        | VX4967 = cCoq_2eInit_2eByte_2ex1d
        | VX4967 = cCoq_2eInit_2eByte_2ex1e
        | VX4967 = cCoq_2eInit_2eByte_2ex1f
        | VX4967 = cCoq_2eInit_2eByte_2ex20
        | VX4967 = cCoq_2eInit_2eByte_2ex21
        | VX4967 = cCoq_2eInit_2eByte_2ex22
        | VX4967 = cCoq_2eInit_2eByte_2ex23
        | VX4967 = cCoq_2eInit_2eByte_2ex24
        | VX4967 = cCoq_2eInit_2eByte_2ex25
        | VX4967 = cCoq_2eInit_2eByte_2ex26
        | VX4967 = cCoq_2eInit_2eByte_2ex27
        | VX4967 = cCoq_2eInit_2eByte_2ex28
        | VX4967 = cCoq_2eInit_2eByte_2ex29
        | VX4967 = cCoq_2eInit_2eByte_2ex2a
        | VX4967 = cCoq_2eInit_2eByte_2ex2b
        | VX4967 = cCoq_2eInit_2eByte_2ex2c
        | VX4967 = cCoq_2eInit_2eByte_2ex2d
        | VX4967 = cCoq_2eInit_2eByte_2ex2e
        | VX4967 = cCoq_2eInit_2eByte_2ex2f
        | VX4967 = cCoq_2eInit_2eByte_2ex30
        | VX4967 = cCoq_2eInit_2eByte_2ex31
        | VX4967 = cCoq_2eInit_2eByte_2ex32
        | VX4967 = cCoq_2eInit_2eByte_2ex33
        | VX4967 = cCoq_2eInit_2eByte_2ex34
        | VX4967 = cCoq_2eInit_2eByte_2ex35
        | VX4967 = cCoq_2eInit_2eByte_2ex36
        | VX4967 = cCoq_2eInit_2eByte_2ex37
        | VX4967 = cCoq_2eInit_2eByte_2ex38
        | VX4967 = cCoq_2eInit_2eByte_2ex39
        | VX4967 = cCoq_2eInit_2eByte_2ex3a
        | VX4967 = cCoq_2eInit_2eByte_2ex3b
        | VX4967 = cCoq_2eInit_2eByte_2ex3c
        | VX4967 = cCoq_2eInit_2eByte_2ex3d
        | VX4967 = cCoq_2eInit_2eByte_2ex3e
        | VX4967 = cCoq_2eInit_2eByte_2ex3f
        | VX4967 = cCoq_2eInit_2eByte_2ex40
        | VX4967 = cCoq_2eInit_2eByte_2ex41
        | VX4967 = cCoq_2eInit_2eByte_2ex42
        | VX4967 = cCoq_2eInit_2eByte_2ex43
        | VX4967 = cCoq_2eInit_2eByte_2ex44
        | VX4967 = cCoq_2eInit_2eByte_2ex45
        | VX4967 = cCoq_2eInit_2eByte_2ex46
        | VX4967 = cCoq_2eInit_2eByte_2ex47
        | VX4967 = cCoq_2eInit_2eByte_2ex48
        | VX4967 = cCoq_2eInit_2eByte_2ex49
        | VX4967 = cCoq_2eInit_2eByte_2ex4a
        | VX4967 = cCoq_2eInit_2eByte_2ex4b
        | VX4967 = cCoq_2eInit_2eByte_2ex4c
        | VX4967 = cCoq_2eInit_2eByte_2ex4d
        | VX4967 = cCoq_2eInit_2eByte_2ex4e
        | VX4967 = cCoq_2eInit_2eByte_2ex4f
        | VX4967 = cCoq_2eInit_2eByte_2ex50
        | VX4967 = cCoq_2eInit_2eByte_2ex51
        | VX4967 = cCoq_2eInit_2eByte_2ex52
        | VX4967 = cCoq_2eInit_2eByte_2ex53
        | VX4967 = cCoq_2eInit_2eByte_2ex54
        | VX4967 = cCoq_2eInit_2eByte_2ex55
        | VX4967 = cCoq_2eInit_2eByte_2ex56
        | VX4967 = cCoq_2eInit_2eByte_2ex57
        | VX4967 = cCoq_2eInit_2eByte_2ex58
        | VX4967 = cCoq_2eInit_2eByte_2ex59
        | VX4967 = cCoq_2eInit_2eByte_2ex5a
        | VX4967 = cCoq_2eInit_2eByte_2ex5b
        | VX4967 = cCoq_2eInit_2eByte_2ex5c
        | VX4967 = cCoq_2eInit_2eByte_2ex5d
        | VX4967 = cCoq_2eInit_2eByte_2ex5e
        | VX4967 = cCoq_2eInit_2eByte_2ex5f
        | VX4967 = cCoq_2eInit_2eByte_2ex60
        | VX4967 = cCoq_2eInit_2eByte_2ex61
        | VX4967 = cCoq_2eInit_2eByte_2ex62
        | VX4967 = cCoq_2eInit_2eByte_2ex63
        | VX4967 = cCoq_2eInit_2eByte_2ex64
        | VX4967 = cCoq_2eInit_2eByte_2ex65
        | VX4967 = cCoq_2eInit_2eByte_2ex66
        | VX4967 = cCoq_2eInit_2eByte_2ex67
        | VX4967 = cCoq_2eInit_2eByte_2ex68
        | VX4967 = cCoq_2eInit_2eByte_2ex69
        | VX4967 = cCoq_2eInit_2eByte_2ex6a
        | VX4967 = cCoq_2eInit_2eByte_2ex6b
        | VX4967 = cCoq_2eInit_2eByte_2ex6c
        | VX4967 = cCoq_2eInit_2eByte_2ex6d
        | VX4967 = cCoq_2eInit_2eByte_2ex6e
        | VX4967 = cCoq_2eInit_2eByte_2ex6f
        | VX4967 = cCoq_2eInit_2eByte_2ex70
        | VX4967 = cCoq_2eInit_2eByte_2ex71
        | VX4967 = cCoq_2eInit_2eByte_2ex72
        | VX4967 = cCoq_2eInit_2eByte_2ex73
        | VX4967 = cCoq_2eInit_2eByte_2ex74
        | VX4967 = cCoq_2eInit_2eByte_2ex75
        | VX4967 = cCoq_2eInit_2eByte_2ex76
        | VX4967 = cCoq_2eInit_2eByte_2ex77
        | VX4967 = cCoq_2eInit_2eByte_2ex78
        | VX4967 = cCoq_2eInit_2eByte_2ex79
        | VX4967 = cCoq_2eInit_2eByte_2ex7a
        | VX4967 = cCoq_2eInit_2eByte_2ex7b
        | VX4967 = cCoq_2eInit_2eByte_2ex7c
        | VX4967 = cCoq_2eInit_2eByte_2ex7d
        | VX4967 = cCoq_2eInit_2eByte_2ex7e
        | VX4967 = cCoq_2eInit_2eByte_2ex7f
        | VX4967 = cCoq_2eInit_2eByte_2ex80
        | VX4967 = cCoq_2eInit_2eByte_2ex81
        | VX4967 = cCoq_2eInit_2eByte_2ex82
        | VX4967 = cCoq_2eInit_2eByte_2ex83
        | VX4967 = cCoq_2eInit_2eByte_2ex84
        | VX4967 = cCoq_2eInit_2eByte_2ex85
        | VX4967 = cCoq_2eInit_2eByte_2ex86
        | VX4967 = cCoq_2eInit_2eByte_2ex87
        | VX4967 = cCoq_2eInit_2eByte_2ex88
        | VX4967 = cCoq_2eInit_2eByte_2ex89
        | VX4967 = cCoq_2eInit_2eByte_2ex8a
        | VX4967 = cCoq_2eInit_2eByte_2ex8b
        | VX4967 = cCoq_2eInit_2eByte_2ex8c
        | VX4967 = cCoq_2eInit_2eByte_2ex8d
        | VX4967 = cCoq_2eInit_2eByte_2ex8e
        | VX4967 = cCoq_2eInit_2eByte_2ex8f
        | VX4967 = cCoq_2eInit_2eByte_2ex90
        | VX4967 = cCoq_2eInit_2eByte_2ex91
        | VX4967 = cCoq_2eInit_2eByte_2ex92
        | VX4967 = cCoq_2eInit_2eByte_2ex93
        | VX4967 = cCoq_2eInit_2eByte_2ex94
        | VX4967 = cCoq_2eInit_2eByte_2ex95
        | VX4967 = cCoq_2eInit_2eByte_2ex96
        | VX4967 = cCoq_2eInit_2eByte_2ex97
        | VX4967 = cCoq_2eInit_2eByte_2ex98
        | VX4967 = cCoq_2eInit_2eByte_2ex99
        | VX4967 = cCoq_2eInit_2eByte_2ex9a
        | VX4967 = cCoq_2eInit_2eByte_2ex9b
        | VX4967 = cCoq_2eInit_2eByte_2ex9c
        | VX4967 = cCoq_2eInit_2eByte_2ex9d
        | VX4967 = cCoq_2eInit_2eByte_2ex9e
        | VX4967 = cCoq_2eInit_2eByte_2ex9f
        | VX4967 = cCoq_2eInit_2eByte_2exa0
        | VX4967 = cCoq_2eInit_2eByte_2exa1
        | VX4967 = cCoq_2eInit_2eByte_2exa2
        | VX4967 = cCoq_2eInit_2eByte_2exa3
        | VX4967 = cCoq_2eInit_2eByte_2exa4
        | VX4967 = cCoq_2eInit_2eByte_2exa5
        | VX4967 = cCoq_2eInit_2eByte_2exa6
        | VX4967 = cCoq_2eInit_2eByte_2exa7
        | VX4967 = cCoq_2eInit_2eByte_2exa8
        | VX4967 = cCoq_2eInit_2eByte_2exa9
        | VX4967 = cCoq_2eInit_2eByte_2exaa
        | VX4967 = cCoq_2eInit_2eByte_2exab
        | VX4967 = cCoq_2eInit_2eByte_2exac
        | VX4967 = cCoq_2eInit_2eByte_2exad
        | VX4967 = cCoq_2eInit_2eByte_2exae
        | VX4967 = cCoq_2eInit_2eByte_2exaf
        | VX4967 = cCoq_2eInit_2eByte_2exb0
        | VX4967 = cCoq_2eInit_2eByte_2exb1
        | VX4967 = cCoq_2eInit_2eByte_2exb2
        | VX4967 = cCoq_2eInit_2eByte_2exb3
        | VX4967 = cCoq_2eInit_2eByte_2exb4
        | VX4967 = cCoq_2eInit_2eByte_2exb5
        | VX4967 = cCoq_2eInit_2eByte_2exb6
        | VX4967 = cCoq_2eInit_2eByte_2exb7
        | VX4967 = cCoq_2eInit_2eByte_2exb8
        | VX4967 = cCoq_2eInit_2eByte_2exb9
        | VX4967 = cCoq_2eInit_2eByte_2exba
        | VX4967 = cCoq_2eInit_2eByte_2exbb
        | VX4967 = cCoq_2eInit_2eByte_2exbc
        | VX4967 = cCoq_2eInit_2eByte_2exbd
        | VX4967 = cCoq_2eInit_2eByte_2exbe
        | VX4967 = cCoq_2eInit_2eByte_2exbf
        | VX4967 = cCoq_2eInit_2eByte_2exc0
        | VX4967 = cCoq_2eInit_2eByte_2exc1
        | VX4967 = cCoq_2eInit_2eByte_2exc2
        | VX4967 = cCoq_2eInit_2eByte_2exc3
        | VX4967 = cCoq_2eInit_2eByte_2exc4
        | VX4967 = cCoq_2eInit_2eByte_2exc5
        | VX4967 = cCoq_2eInit_2eByte_2exc6
        | VX4967 = cCoq_2eInit_2eByte_2exc7
        | VX4967 = cCoq_2eInit_2eByte_2exc8
        | VX4967 = cCoq_2eInit_2eByte_2exc9
        | VX4967 = cCoq_2eInit_2eByte_2exca
        | VX4967 = cCoq_2eInit_2eByte_2excb
        | VX4967 = cCoq_2eInit_2eByte_2excc
        | VX4967 = cCoq_2eInit_2eByte_2excd
        | VX4967 = cCoq_2eInit_2eByte_2exce
        | VX4967 = cCoq_2eInit_2eByte_2excf
        | VX4967 = cCoq_2eInit_2eByte_2exd0
        | VX4967 = cCoq_2eInit_2eByte_2exd1
        | VX4967 = cCoq_2eInit_2eByte_2exd2
        | VX4967 = cCoq_2eInit_2eByte_2exd3
        | VX4967 = cCoq_2eInit_2eByte_2exd4
        | VX4967 = cCoq_2eInit_2eByte_2exd5
        | VX4967 = cCoq_2eInit_2eByte_2exd6
        | VX4967 = cCoq_2eInit_2eByte_2exd7
        | VX4967 = cCoq_2eInit_2eByte_2exd8
        | VX4967 = cCoq_2eInit_2eByte_2exd9
        | VX4967 = cCoq_2eInit_2eByte_2exda
        | VX4967 = cCoq_2eInit_2eByte_2exdb
        | VX4967 = cCoq_2eInit_2eByte_2exdc
        | VX4967 = cCoq_2eInit_2eByte_2exdd
        | VX4967 = cCoq_2eInit_2eByte_2exde
        | VX4967 = cCoq_2eInit_2eByte_2exdf
        | VX4967 = cCoq_2eInit_2eByte_2exe0
        | VX4967 = cCoq_2eInit_2eByte_2exe1
        | VX4967 = cCoq_2eInit_2eByte_2exe2
        | VX4967 = cCoq_2eInit_2eByte_2exe3
        | VX4967 = cCoq_2eInit_2eByte_2exe4
        | VX4967 = cCoq_2eInit_2eByte_2exe5
        | VX4967 = cCoq_2eInit_2eByte_2exe6
        | VX4967 = cCoq_2eInit_2eByte_2exe7
        | VX4967 = cCoq_2eInit_2eByte_2exe8
        | VX4967 = cCoq_2eInit_2eByte_2exe9
        | VX4967 = cCoq_2eInit_2eByte_2exea
        | VX4967 = cCoq_2eInit_2eByte_2exeb
        | VX4967 = cCoq_2eInit_2eByte_2exec
        | VX4967 = cCoq_2eInit_2eByte_2exed
        | VX4967 = cCoq_2eInit_2eByte_2exee
        | VX4967 = cCoq_2eInit_2eByte_2exef
        | VX4967 = cCoq_2eInit_2eByte_2exf0
        | VX4967 = cCoq_2eInit_2eByte_2exf1
        | VX4967 = cCoq_2eInit_2eByte_2exf2
        | VX4967 = cCoq_2eInit_2eByte_2exf3
        | VX4967 = cCoq_2eInit_2eByte_2exf4
        | VX4967 = cCoq_2eInit_2eByte_2exf5
        | VX4967 = cCoq_2eInit_2eByte_2exf6
        | VX4967 = cCoq_2eInit_2eByte_2exf7
        | VX4967 = cCoq_2eInit_2eByte_2exf8
        | VX4967 = cCoq_2eInit_2eByte_2exf9
        | VX4967 = cCoq_2eInit_2eByte_2exfa
        | VX4967 = cCoq_2eInit_2eByte_2exfb
        | VX4967 = cCoq_2eInit_2eByte_2exfc
        | VX4967 = cCoq_2eInit_2eByte_2exfd
        | VX4967 = cCoq_2eInit_2eByte_2exfe
        | VX4967 = cCoq_2eInit_2eByte_2exff ) ) ).

fof('$_inversion_Coq.Init.Datatypes.BoolSpec',axiom,
    ! [Vvar__0__P__4970,Vvar__1__Q__4971,Vvar__2___24Anonymous__4972] :
      ( cProp___24t(Vvar__0__P__4970)
     => ( cProp___24t(Vvar__1__Q__4971)
       => ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__2___24Anonymous__4972)
         => ( cCoq_2eInit_2eDatatypes_2eBoolSpec___24a3(Vvar__0__P__4970,Vvar__1__Q__4971,Vvar__2___24Anonymous__4972)
           => ( ( p(Vvar__0__P__4970)
                & Vvar__2___24Anonymous__4972 = cCoq_2eInit_2eDatatypes_2etrue )
              | ( p(Vvar__1__Q__4971)
                & Vvar__2___24Anonymous__4972 = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ) ) ).

fof('$_inversion_Coq.Init.Datatypes.CompareSpec',axiom,
    ! [Vvar__0__Peq__1946,Vvar__1__Plt__1947,Vvar__2__Pgt__1948,Vvar__3___24Anonymous__1949] :
      ( cProp___24t(Vvar__0__Peq__1946)
     => ( cProp___24t(Vvar__1__Plt__1947)
       => ( cProp___24t(Vvar__2__Pgt__1948)
         => ( cCoq_2eInit_2eDatatypes_2ecomparison___24t(Vvar__3___24Anonymous__1949)
           => ( cCoq_2eInit_2eDatatypes_2eCompareSpec___24a4(Vvar__0__Peq__1946,Vvar__1__Plt__1947,Vvar__2__Pgt__1948,Vvar__3___24Anonymous__1949)
             => ( ( p(Vvar__0__Peq__1946)
                  & Vvar__3___24Anonymous__1949 = cCoq_2eInit_2eDatatypes_2eEq )
                | ( p(Vvar__1__Plt__1947)
                  & Vvar__3___24Anonymous__1949 = cCoq_2eInit_2eDatatypes_2eLt )
                | ( p(Vvar__2__Pgt__1948)
                  & Vvar__3___24Anonymous__1949 = cCoq_2eInit_2eDatatypes_2eGt ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.Init.Datatypes.CompareSpecT',axiom,
    ! [Vvar__0__Peq__85251,Vvar__1__Plt__85252,Vvar__2__Pgt__85253,Vvar__3___24Anonymous__85254,VX85255] :
      ( cProp___24t(Vvar__0__Peq__85251)
     => ( cProp___24t(Vvar__1__Plt__85252)
       => ( cProp___24t(Vvar__2__Pgt__85253)
         => ( cCoq_2eInit_2eDatatypes_2ecomparison___24t(Vvar__3___24Anonymous__85254)
           => ( cCoq_2eInit_2eDatatypes_2eCompareSpecT___24t(Vvar__0__Peq__85251,Vvar__1__Plt__85252,Vvar__2__Pgt__85253,Vvar__3___24Anonymous__85254,VX85255)
             => ( ( p(Vvar__0__Peq__85251)
                  & Vvar__3___24Anonymous__85254 = cCoq_2eInit_2eDatatypes_2eEq
                  & VX85255 = cCoq_2eInit_2eDatatypes_2eCompEqT___24a3(Vvar__0__Peq__85251,Vvar__1__Plt__85252,Vvar__2__Pgt__85253) )
                | ( p(Vvar__1__Plt__85252)
                  & Vvar__3___24Anonymous__85254 = cCoq_2eInit_2eDatatypes_2eLt
                  & VX85255 = cCoq_2eInit_2eDatatypes_2eCompLtT___24a3(Vvar__0__Peq__85251,Vvar__1__Plt__85252,Vvar__2__Pgt__85253) )
                | ( p(Vvar__2__Pgt__85253)
                  & Vvar__3___24Anonymous__85254 = cCoq_2eInit_2eDatatypes_2eGt
                  & VX85255 = cCoq_2eInit_2eDatatypes_2eCompGtT___24a3(Vvar__0__Peq__85251,Vvar__1__Plt__85252,Vvar__2__Pgt__85253) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.Init.Datatypes.bool',axiom,
    ! [VX3] :
      ( cCoq_2eInit_2eDatatypes_2ebool___24t(VX3)
     => ( VX3 = cCoq_2eInit_2eDatatypes_2etrue
        | VX3 = cCoq_2eInit_2eDatatypes_2efalse ) ) ).

fof('$_inversion_Coq.Init.Datatypes.comparison',axiom,
    ! [VX11] :
      ( cCoq_2eInit_2eDatatypes_2ecomparison___24t(VX11)
     => ( VX11 = cCoq_2eInit_2eDatatypes_2eEq
        | VX11 = cCoq_2eInit_2eDatatypes_2eLt
        | VX11 = cCoq_2eInit_2eDatatypes_2eGt ) ) ).

fof('$_inversion_Coq.Init.Datatypes.eq_true',axiom,
    ! [Vvar__0___24Anonymous__145722] :
      ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__0___24Anonymous__145722)
     => ( cCoq_2eInit_2eDatatypes_2eeq__true___24a1(Vvar__0___24Anonymous__145722)
       => Vvar__0___24Anonymous__145722 = cCoq_2eInit_2eDatatypes_2etrue ) ) ).

fof('$_inversion_Coq.Init.Datatypes.identity',axiom,
    ! [Vvar__0__A__145724,Vvar__1__a__145725,Vvar__2___24Anonymous__145726] :
      ( cType___24t(Vvar__0__A__145724)
     => ( t(Vvar__1__a__145725,Vvar__0__A__145724)
       => ( t(Vvar__2___24Anonymous__145726,Vvar__0__A__145724)
         => ( cCoq_2eInit_2eDatatypes_2eidentity___24a3(Vvar__0__A__145724,Vvar__1__a__145725,Vvar__2___24Anonymous__145726)
           => Vvar__2___24Anonymous__145726 = Vvar__1__a__145725 ) ) ) ) ).

fof('$_inversion_Coq.Init.Datatypes.list',axiom,
    ! [Vvar__0__A__595,VX596] :
      ( cType___24t(Vvar__0__A__595)
     => ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__595,VX596)
       => ( VX596 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__595)
          | ? [Vvar__1___24Anonymous__599] :
              ( t(Vvar__1___24Anonymous__599,Vvar__0__A__595)
              & ? [Vvar__2___24Anonymous__600] :
                  ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__595,Vvar__2___24Anonymous__600)
                  & VX596 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__595,Vvar__1___24Anonymous__599,Vvar__2___24Anonymous__600) ) ) ) ) ) ).

fof('$_inversion_Coq.Init.Datatypes.nat',axiom,
    ! [VX4] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(VX4)
     => ( VX4 = cCoq_2eInit_2eDatatypes_2eO
        | ? [Vvar__0___24Anonymous__5] :
            ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__5)
            & VX4 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__5) ) ) ) ).

fof('$_inversion_Coq.Init.Datatypes.option',axiom,
    ! [Vvar__0__A__4996,VX4997] :
      ( cType___24t(Vvar__0__A__4996)
     => ( cCoq_2eInit_2eDatatypes_2eoption___24t(Vvar__0__A__4996,VX4997)
       => ( ? [Vvar__1___24Anonymous__4999] :
              ( t(Vvar__1___24Anonymous__4999,Vvar__0__A__4996)
              & VX4997 = cCoq_2eInit_2eDatatypes_2eSome___24a2(Vvar__0__A__4996,Vvar__1___24Anonymous__4999) )
          | VX4997 = cCoq_2eInit_2eDatatypes_2eNone___24a1(Vvar__0__A__4996) ) ) ) ).

fof('$_inversion_Coq.Init.Datatypes.prod',axiom,
    ! [Vvar__0__A__1880,Vvar__1__B__1881,VX1882] :
      ( cType___24t(Vvar__0__A__1880)
     => ( cType___24t(Vvar__1__B__1881)
       => ( cCoq_2eInit_2eDatatypes_2eprod___24t(Vvar__0__A__1880,Vvar__1__B__1881,VX1882)
         => ? [Vvar__2___24Anonymous__1885] :
              ( t(Vvar__2___24Anonymous__1885,Vvar__0__A__1880)
              & ? [Vvar__3___24Anonymous__1886] :
                  ( t(Vvar__3___24Anonymous__1886,Vvar__1__B__1881)
                  & VX1882 = cCoq_2eInit_2eDatatypes_2epair___24a4(Vvar__0__A__1880,Vvar__1__B__1881,Vvar__2___24Anonymous__1885,Vvar__3___24Anonymous__1886) ) ) ) ) ) ).

fof('$_inversion_Coq.Init.Datatypes.sum',axiom,
    ! [Vvar__0__A__119401,Vvar__1__B__119402,VX119403] :
      ( cType___24t(Vvar__0__A__119401)
     => ( cType___24t(Vvar__1__B__119402)
       => ( cCoq_2eInit_2eDatatypes_2esum___24t(Vvar__0__A__119401,Vvar__1__B__119402,VX119403)
         => ( ? [Vvar__2___24Anonymous__119406] :
                ( t(Vvar__2___24Anonymous__119406,Vvar__0__A__119401)
                & VX119403 = cCoq_2eInit_2eDatatypes_2einl___24a3(Vvar__0__A__119401,Vvar__1__B__119402,Vvar__2___24Anonymous__119406) )
            | ? [Vvar__2___24Anonymous__119409] :
                ( t(Vvar__2___24Anonymous__119409,Vvar__1__B__119402)
                & VX119403 = cCoq_2eInit_2eDatatypes_2einr___24a3(Vvar__0__A__119401,Vvar__1__B__119402,Vvar__2___24Anonymous__119409) ) ) ) ) ) ).

fof('$_inversion_Coq.Init.Datatypes.unit',axiom,
    ! [VX589] :
      ( cCoq_2eInit_2eDatatypes_2eunit___24t(VX589)
     => VX589 = cCoq_2eInit_2eDatatypes_2ett ) ).

fof('$_inversion_Coq.Init.Decimal.decimal',axiom,
    ! [VX124026] :
      ( cCoq_2eInit_2eDecimal_2edecimal___24t(VX124026)
     => ( ? [Vvar__0__i__124027] :
            ( cCoq_2eInit_2eDecimal_2eint___24t(Vvar__0__i__124027)
            & ? [Vvar__1__f__124028] :
                ( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__1__f__124028)
                & VX124026 = cCoq_2eInit_2eDecimal_2eDecimal___24a2(Vvar__0__i__124027,Vvar__1__f__124028) ) )
        | ? [Vvar__0__i__124029] :
            ( cCoq_2eInit_2eDecimal_2eint___24t(Vvar__0__i__124029)
            & ? [Vvar__1__f__124030] :
                ( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__1__f__124030)
                & ? [Vvar__2__e__124031] :
                    ( cCoq_2eInit_2eDecimal_2eint___24t(Vvar__2__e__124031)
                    & VX124026 = cCoq_2eInit_2eDecimal_2eDecimalExp___24a3(Vvar__0__i__124029,Vvar__1__f__124030,Vvar__2__e__124031) ) ) ) ) ) ).

fof('$_inversion_Coq.Init.Decimal.int',axiom,
    ! [VX119429] :
      ( cCoq_2eInit_2eDecimal_2eint___24t(VX119429)
     => ( ? [Vvar__0__d__119430] :
            ( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0__d__119430)
            & VX119429 = cCoq_2eInit_2eDecimal_2ePos___24a1(Vvar__0__d__119430) )
        | ? [Vvar__0__d__119431] :
            ( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0__d__119431)
            & VX119429 = cCoq_2eInit_2eDecimal_2eNeg___24a1(Vvar__0__d__119431) ) ) ) ).

fof('$_inversion_Coq.Init.Decimal.uint',axiom,
    ! [VX80526] :
      ( cCoq_2eInit_2eDecimal_2euint___24t(VX80526)
     => ( VX80526 = cCoq_2eInit_2eDecimal_2eNil
        | ? [Vvar__0___24Anonymous__80527] :
            ( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0___24Anonymous__80527)
            & VX80526 = cCoq_2eInit_2eDecimal_2eD0___24a1(Vvar__0___24Anonymous__80527) )
        | ? [Vvar__0___24Anonymous__80528] :
            ( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0___24Anonymous__80528)
            & VX80526 = cCoq_2eInit_2eDecimal_2eD1___24a1(Vvar__0___24Anonymous__80528) )
        | ? [Vvar__0___24Anonymous__80529] :
            ( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0___24Anonymous__80529)
            & VX80526 = cCoq_2eInit_2eDecimal_2eD2___24a1(Vvar__0___24Anonymous__80529) )
        | ? [Vvar__0___24Anonymous__80530] :
            ( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0___24Anonymous__80530)
            & VX80526 = cCoq_2eInit_2eDecimal_2eD3___24a1(Vvar__0___24Anonymous__80530) )
        | ? [Vvar__0___24Anonymous__80531] :
            ( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0___24Anonymous__80531)
            & VX80526 = cCoq_2eInit_2eDecimal_2eD4___24a1(Vvar__0___24Anonymous__80531) )
        | ? [Vvar__0___24Anonymous__80532] :
            ( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0___24Anonymous__80532)
            & VX80526 = cCoq_2eInit_2eDecimal_2eD5___24a1(Vvar__0___24Anonymous__80532) )
        | ? [Vvar__0___24Anonymous__80533] :
            ( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0___24Anonymous__80533)
            & VX80526 = cCoq_2eInit_2eDecimal_2eD6___24a1(Vvar__0___24Anonymous__80533) )
        | ? [Vvar__0___24Anonymous__80534] :
            ( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0___24Anonymous__80534)
            & VX80526 = cCoq_2eInit_2eDecimal_2eD7___24a1(Vvar__0___24Anonymous__80534) )
        | ? [Vvar__0___24Anonymous__80535] :
            ( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0___24Anonymous__80535)
            & VX80526 = cCoq_2eInit_2eDecimal_2eD8___24a1(Vvar__0___24Anonymous__80535) )
        | ? [Vvar__0___24Anonymous__80536] :
            ( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0___24Anonymous__80536)
            & VX80526 = cCoq_2eInit_2eDecimal_2eD9___24a1(Vvar__0___24Anonymous__80536) ) ) ) ).

fof('$_inversion_Coq.Init.Peano.le',axiom,
    ! [Vvar__0__n__341,Vvar__1___24Anonymous__342] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0__n__341)
     => ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__1___24Anonymous__342)
       => ( cCoq_2eInit_2ePeano_2ele___24a2(Vvar__0__n__341,Vvar__1___24Anonymous__342)
         => ( Vvar__1___24Anonymous__342 = Vvar__0__n__341
            | ? [Vvar__1__m__346] :
                ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__1__m__346)
                & cCoq_2eInit_2ePeano_2ele___24a2(Vvar__0__n__341,Vvar__1__m__346)
                & Vvar__1___24Anonymous__342 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__1__m__346) ) ) ) ) ) ).

fof('$_inversion_Coq.Init.Specif.sig',axiom,
    ! [Vvar__0__A__3714,Vvar__1__P__3715,VX3718] :
      ( cType___24t(Vvar__0__A__3714)
     => ( c_24__type__3728___24t(Vvar__0__A__3714,Vvar__1__P__3715,Vvar__1__P__3715)
       => ( cCoq_2eInit_2eSpecif_2esig___24t(Vvar__0__A__3714,Vvar__1__P__3715,VX3718)
         => ? [Vvar__2__x__3723] :
              ( t(Vvar__2__x__3723,Vvar__0__A__3714)
              & p(happ(Vvar__1__P__3715,Vvar__2__x__3723))
              & VX3718 = cCoq_2eInit_2eSpecif_2eexist___24a3(Vvar__0__A__3714,Vvar__1__P__3715,Vvar__2__x__3723) ) ) ) ) ).

fof('$_inversion_Coq.Init.Specif.sig2',axiom,
    ! [Vvar__0__A__149111,Vvar__1__P__149112,Vvar__2__Q__149115,VX149118] :
      ( cType___24t(Vvar__0__A__149111)
     => ( c_24__type__149135___24t(Vvar__0__A__149111,Vvar__1__P__149112,Vvar__2__Q__149115,Vvar__1__P__149112)
       => ( c_24__type__149143___24t(Vvar__0__A__149111,Vvar__1__P__149112,Vvar__2__Q__149115,Vvar__2__Q__149115)
         => ( cCoq_2eInit_2eSpecif_2esig2___24t(Vvar__0__A__149111,Vvar__1__P__149112,Vvar__2__Q__149115,VX149118)
           => ? [Vvar__3__x__149126] :
                ( t(Vvar__3__x__149126,Vvar__0__A__149111)
                & p(happ(Vvar__1__P__149112,Vvar__3__x__149126))
                & p(happ(Vvar__2__Q__149115,Vvar__3__x__149126))
                & VX149118 = cCoq_2eInit_2eSpecif_2eexist2___24a4(Vvar__0__A__149111,Vvar__1__P__149112,Vvar__2__Q__149115,Vvar__3__x__149126) ) ) ) ) ) ).

fof('$_inversion_Coq.Init.Specif.sigT',axiom,
    ! [Vvar__0__A__139643,Vvar__1__P__139644,VX139647] :
      ( cType___24t(Vvar__0__A__139643)
     => ( c_24__type__139657___24t(Vvar__0__A__139643,Vvar__1__P__139644,Vvar__1__P__139644)
       => ( cCoq_2eInit_2eSpecif_2esigT___24t(Vvar__0__A__139643,Vvar__1__P__139644,VX139647)
         => ? [Vvar__2__x__139652] :
              ( t(Vvar__2__x__139652,Vvar__0__A__139643)
              & ? [Vvar__3___24Anonymous__139653] :
                  ( t(Vvar__3___24Anonymous__139653,happ(Vvar__1__P__139644,Vvar__2__x__139652))
                  & VX139647 = cCoq_2eInit_2eSpecif_2eexistT___24a4(Vvar__0__A__139643,Vvar__1__P__139644,Vvar__2__x__139652,Vvar__3___24Anonymous__139653) ) ) ) ) ) ).

fof('$_inversion_Coq.Init.Specif.sigT2',axiom,
    ! [Vvar__0__A__139684,Vvar__1__P__139685,Vvar__2__Q__139688,VX139691] :
      ( cType___24t(Vvar__0__A__139684)
     => ( c_24__type__139708___24t(Vvar__0__A__139684,Vvar__1__P__139685,Vvar__2__Q__139688,Vvar__1__P__139685)
       => ( c_24__type__139716___24t(Vvar__0__A__139684,Vvar__1__P__139685,Vvar__2__Q__139688,Vvar__2__Q__139688)
         => ( cCoq_2eInit_2eSpecif_2esigT2___24t(Vvar__0__A__139684,Vvar__1__P__139685,Vvar__2__Q__139688,VX139691)
           => ? [Vvar__3__x__139699] :
                ( t(Vvar__3__x__139699,Vvar__0__A__139684)
                & ? [Vvar__4___24Anonymous__139700] :
                    ( t(Vvar__4___24Anonymous__139700,happ(Vvar__1__P__139685,Vvar__3__x__139699))
                    & ? [Vvar__5___24Anonymous__139701] :
                        ( t(Vvar__5___24Anonymous__139701,happ(Vvar__2__Q__139688,Vvar__3__x__139699))
                        & VX139691 = cCoq_2eInit_2eSpecif_2eexistT2___24a6(Vvar__0__A__139684,Vvar__1__P__139685,Vvar__2__Q__139688,Vvar__3__x__139699,Vvar__4___24Anonymous__139700,Vvar__5___24Anonymous__139701) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.Init.Specif.sumbool',axiom,
    ! [Vvar__0__A__3755,Vvar__1__B__3756,VX3757] :
      ( cProp___24t(Vvar__0__A__3755)
     => ( cProp___24t(Vvar__1__B__3756)
       => ( cCoq_2eInit_2eSpecif_2esumbool___24t(Vvar__0__A__3755,Vvar__1__B__3756,VX3757)
         => ( ( p(Vvar__0__A__3755)
              & VX3757 = cCoq_2eInit_2eSpecif_2eleft___24a2(Vvar__0__A__3755,Vvar__1__B__3756) )
            | ( p(Vvar__1__B__3756)
              & VX3757 = cCoq_2eInit_2eSpecif_2eright___24a2(Vvar__0__A__3755,Vvar__1__B__3756) ) ) ) ) ) ).

fof('$_inversion_Coq.Init.Specif.sumor',axiom,
    ! [Vvar__0__A__3795,Vvar__1__B__3796,VX3797] :
      ( cType___24t(Vvar__0__A__3795)
     => ( cProp___24t(Vvar__1__B__3796)
       => ( cCoq_2eInit_2eSpecif_2esumor___24t(Vvar__0__A__3795,Vvar__1__B__3796,VX3797)
         => ( ? [Vvar__2___24Anonymous__3800] :
                ( t(Vvar__2___24Anonymous__3800,Vvar__0__A__3795)
                & VX3797 = cCoq_2eInit_2eSpecif_2einleft___24a3(Vvar__0__A__3795,Vvar__1__B__3796,Vvar__2___24Anonymous__3800) )
            | ( p(Vvar__1__B__3796)
              & VX3797 = cCoq_2eInit_2eSpecif_2einright___24a2(Vvar__0__A__3795,Vvar__1__B__3796) ) ) ) ) ) ).

fof('$_inversion_Coq.Init.Wf.Acc',axiom,
    ! [Vvar__0__A__6900,Vvar__1__R__6901,Vvar__2__x__6906] :
      ( cType___24t(Vvar__0__A__6900)
     => ( c_24__type__6935___24t(Vvar__0__A__6900,Vvar__1__R__6901,Vvar__2__x__6906,Vvar__1__R__6901)
       => ( t(Vvar__2__x__6906,Vvar__0__A__6900)
         => ( cCoq_2eInit_2eWf_2eAcc___24a3(Vvar__0__A__6900,Vvar__1__R__6901,Vvar__2__x__6906)
           => ( ! [Vvar__var__var__var__var__3__y__6916__6918__6920__6922__6924] :
                  ( t(Vvar__var__var__var__var__3__y__6916__6918__6920__6922__6924,Vvar__0__A__6900)
                 => ( p(happ(happ(Vvar__1__R__6901,Vvar__var__var__var__var__3__y__6916__6918__6920__6922__6924),Vvar__2__x__6906))
                   => cCoq_2eInit_2eWf_2eAcc___24a3(Vvar__0__A__6900,Vvar__1__R__6901,Vvar__var__var__var__var__3__y__6916__6918__6920__6922__6924) ) )
              & p(c_24True) ) ) ) ) ) ).

fof('$_inversion_Coq.Lists.List.Add',axiom,
    ! [Vvar__0__A__125082,Vvar__1__a__125083,Vvar__2___24Anonymous__125084,Vvar__3___24Anonymous__125085] :
      ( cType___24t(Vvar__0__A__125082)
     => ( t(Vvar__1__a__125083,Vvar__0__A__125082)
       => ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__125082,Vvar__2___24Anonymous__125084)
         => ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__125082,Vvar__3___24Anonymous__125085)
           => ( cCoq_2eLists_2eList_2eAdd___24a4(Vvar__0__A__125082,Vvar__1__a__125083,Vvar__2___24Anonymous__125084,Vvar__3___24Anonymous__125085)
             => ( ? [Vvar__2__l__125089] :
                    ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__125082,Vvar__2__l__125089)
                    & Vvar__3___24Anonymous__125085 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__125082,Vvar__1__a__125083,Vvar__2__l__125089)
                    & Vvar__2___24Anonymous__125084 = Vvar__2__l__125089 )
                | ? [Vvar__2__x__125092] :
                    ( t(Vvar__2__x__125092,Vvar__0__A__125082)
                    & ? [Vvar__3__l__125093] :
                        ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__125082,Vvar__3__l__125093)
                        & ? [Vvar__4__l_27__125094] :
                            ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__125082,Vvar__4__l_27__125094)
                            & cCoq_2eLists_2eList_2eAdd___24a4(Vvar__0__A__125082,Vvar__1__a__125083,Vvar__3__l__125093,Vvar__4__l_27__125094)
                            & Vvar__3___24Anonymous__125085 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__125082,Vvar__2__x__125092,Vvar__4__l_27__125094)
                            & Vvar__2___24Anonymous__125084 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__125082,Vvar__2__x__125092,Vvar__3__l__125093) ) ) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.Lists.List.Exists',axiom,
    ! [Vvar__0__A__147117,Vvar__1__P__147118,Vvar__2___24Anonymous__147121] :
      ( cType___24t(Vvar__0__A__147117)
     => ( c_24__type__147141___24t(Vvar__0__A__147117,Vvar__1__P__147118,Vvar__2___24Anonymous__147121,Vvar__1__P__147118)
       => ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__147117,Vvar__2___24Anonymous__147121)
         => ( cCoq_2eLists_2eList_2eExists___24a3(Vvar__0__A__147117,Vvar__1__P__147118,Vvar__2___24Anonymous__147121)
           => ( ? [Vvar__2__x__147127] :
                  ( t(Vvar__2__x__147127,Vvar__0__A__147117)
                  & ? [Vvar__3__l__147128] :
                      ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__147117,Vvar__3__l__147128)
                      & p(happ(Vvar__1__P__147118,Vvar__2__x__147127))
                      & Vvar__2___24Anonymous__147121 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__147117,Vvar__2__x__147127,Vvar__3__l__147128) ) )
              | ? [Vvar__2__x__147134] :
                  ( t(Vvar__2__x__147134,Vvar__0__A__147117)
                  & ? [Vvar__3__l__147135] :
                      ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__147117,Vvar__3__l__147135)
                      & cCoq_2eLists_2eList_2eExists___24a3(Vvar__0__A__147117,Vvar__1__P__147118,Vvar__3__l__147135)
                      & Vvar__2___24Anonymous__147121 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__147117,Vvar__2__x__147134,Vvar__3__l__147135) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.Lists.List.Forall',axiom,
    ! [Vvar__0__A__147143,Vvar__1__P__147144,Vvar__2___24Anonymous__147147] :
      ( cType___24t(Vvar__0__A__147143)
     => ( c_24__type__147165___24t(Vvar__0__A__147143,Vvar__1__P__147144,Vvar__2___24Anonymous__147147,Vvar__1__P__147144)
       => ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__147143,Vvar__2___24Anonymous__147147)
         => ( cCoq_2eLists_2eList_2eForall___24a3(Vvar__0__A__147143,Vvar__1__P__147144,Vvar__2___24Anonymous__147147)
           => ( Vvar__2___24Anonymous__147147 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__147143)
              | ? [Vvar__2__x__147157] :
                  ( t(Vvar__2__x__147157,Vvar__0__A__147143)
                  & ? [Vvar__3__l__147158] :
                      ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__147143,Vvar__3__l__147158)
                      & p(happ(Vvar__1__P__147144,Vvar__2__x__147157))
                      & cCoq_2eLists_2eList_2eForall___24a3(Vvar__0__A__147143,Vvar__1__P__147144,Vvar__3__l__147158)
                      & Vvar__2___24Anonymous__147147 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__147143,Vvar__2__x__147157,Vvar__3__l__147158) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.Lists.List.Forall2',axiom,
    ! [Vvar__0__A__147167,Vvar__1__B__147168,Vvar__2__R__147169,Vvar__3___24Anonymous__147174,Vvar__4___24Anonymous__147175] :
      ( cType___24t(Vvar__0__A__147167)
     => ( cType___24t(Vvar__1__B__147168)
       => ( c_24__type__147212___24t(Vvar__0__A__147167,Vvar__1__B__147168,Vvar__2__R__147169,Vvar__3___24Anonymous__147174,Vvar__4___24Anonymous__147175,Vvar__2__R__147169)
         => ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__147167,Vvar__3___24Anonymous__147174)
           => ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__1__B__147168,Vvar__4___24Anonymous__147175)
             => ( cCoq_2eLists_2eList_2eForall2___24a5(Vvar__0__A__147167,Vvar__1__B__147168,Vvar__2__R__147169,Vvar__3___24Anonymous__147174,Vvar__4___24Anonymous__147175)
               => ( ( Vvar__4___24Anonymous__147175 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__1__B__147168)
                    & Vvar__3___24Anonymous__147174 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__147167) )
                  | ? [Vvar__3__x__147191] :
                      ( t(Vvar__3__x__147191,Vvar__0__A__147167)
                      & ? [Vvar__4__y__147192] :
                          ( t(Vvar__4__y__147192,Vvar__1__B__147168)
                          & ? [Vvar__5__l__147193] :
                              ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__147167,Vvar__5__l__147193)
                              & ? [Vvar__6__l_27__147194] :
                                  ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__1__B__147168,Vvar__6__l_27__147194)
                                  & p(happ(happ(Vvar__2__R__147169,Vvar__3__x__147191),Vvar__4__y__147192))
                                  & cCoq_2eLists_2eList_2eForall2___24a5(Vvar__0__A__147167,Vvar__1__B__147168,Vvar__2__R__147169,Vvar__5__l__147193,Vvar__6__l_27__147194)
                                  & Vvar__4___24Anonymous__147175 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__1__B__147168,Vvar__4__y__147192,Vvar__6__l_27__147194)
                                  & Vvar__3___24Anonymous__147174 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__147167,Vvar__3__x__147191,Vvar__5__l__147193) ) ) ) ) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.Lists.List.ForallOrdPairs',axiom,
    ! [Vvar__0__A__147214,Vvar__1__R__147215,Vvar__2___24Anonymous__147220] :
      ( cType___24t(Vvar__0__A__147214)
     => ( c_24__type__147247___24t(Vvar__0__A__147214,Vvar__1__R__147215,Vvar__2___24Anonymous__147220,Vvar__1__R__147215)
       => ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__147214,Vvar__2___24Anonymous__147220)
         => ( cCoq_2eLists_2eList_2eForallOrdPairs___24a3(Vvar__0__A__147214,Vvar__1__R__147215,Vvar__2___24Anonymous__147220)
           => ( Vvar__2___24Anonymous__147220 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__147214)
              | ? [Vvar__2__a__147234] :
                  ( t(Vvar__2__a__147234,Vvar__0__A__147214)
                  & ? [Vvar__3__l__147235] :
                      ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__147214,Vvar__3__l__147235)
                      & cCoq_2eLists_2eList_2eForall___24a3(Vvar__0__A__147214,happ(Vvar__1__R__147215,Vvar__2__a__147234),Vvar__3__l__147235)
                      & cCoq_2eLists_2eList_2eForallOrdPairs___24a3(Vvar__0__A__147214,Vvar__1__R__147215,Vvar__3__l__147235)
                      & Vvar__2___24Anonymous__147220 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__147214,Vvar__2__a__147234,Vvar__3__l__147235) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.Lists.List.NoDup',axiom,
    ! [Vvar__0__A__5120,Vvar__1___24Anonymous__5121] :
      ( cType___24t(Vvar__0__A__5120)
     => ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__5120,Vvar__1___24Anonymous__5121)
       => ( cCoq_2eLists_2eList_2eNoDup___24a2(Vvar__0__A__5120,Vvar__1___24Anonymous__5121)
         => ( Vvar__1___24Anonymous__5121 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__5120)
            | ? [Vvar__1__x__5125] :
                ( t(Vvar__1__x__5125,Vvar__0__A__5120)
                & ? [Vvar__2__l__5126] :
                    ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__5120,Vvar__2__l__5126)
                    & ~ cCoq_2eLists_2eList_2eIn___24a3(Vvar__0__A__5120,Vvar__1__x__5125,Vvar__2__l__5126)
                    & cCoq_2eLists_2eList_2eNoDup___24a2(Vvar__0__A__5120,Vvar__2__l__5126)
                    & Vvar__1___24Anonymous__5121 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__5120,Vvar__1__x__5125,Vvar__2__l__5126) ) ) ) ) ) ) ).

fof('$_inversion_Coq.Lists.SetoidList.InA',axiom,
    ! [Vvar__0__A__85324,Vvar__1__eqA__85325,Vvar__2__x__85330,Vvar__3___24Anonymous__85331] :
      ( cType___24t(Vvar__0__A__85324)
     => ( c_24__type__85364___24t(Vvar__0__A__85324,Vvar__1__eqA__85325,Vvar__2__x__85330,Vvar__3___24Anonymous__85331,Vvar__1__eqA__85325)
       => ( t(Vvar__2__x__85330,Vvar__0__A__85324)
         => ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__85324,Vvar__3___24Anonymous__85331)
           => ( cCoq_2eLists_2eSetoidList_2eInA___24a4(Vvar__0__A__85324,Vvar__1__eqA__85325,Vvar__2__x__85330,Vvar__3___24Anonymous__85331)
             => ( ? [Vvar__3__y__85340] :
                    ( t(Vvar__3__y__85340,Vvar__0__A__85324)
                    & ? [Vvar__4__l__85341] :
                        ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__85324,Vvar__4__l__85341)
                        & p(happ(happ(Vvar__1__eqA__85325,Vvar__2__x__85330),Vvar__3__y__85340))
                        & Vvar__3___24Anonymous__85331 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__85324,Vvar__3__y__85340,Vvar__4__l__85341) ) )
                | ? [Vvar__3__y__85350] :
                    ( t(Vvar__3__y__85350,Vvar__0__A__85324)
                    & ? [Vvar__4__l__85351] :
                        ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__85324,Vvar__4__l__85351)
                        & cCoq_2eLists_2eSetoidList_2eInA___24a4(Vvar__0__A__85324,Vvar__1__eqA__85325,Vvar__2__x__85330,Vvar__4__l__85351)
                        & Vvar__3___24Anonymous__85331 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__85324,Vvar__3__y__85350,Vvar__4__l__85351) ) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.Lists.SetoidList.NoDupA',axiom,
    ! [Vvar__0__A__135611,Vvar__1__eqA__135612,Vvar__2___24Anonymous__135617] :
      ( cType___24t(Vvar__0__A__135611)
     => ( c_24__type__135644___24t(Vvar__0__A__135611,Vvar__1__eqA__135612,Vvar__2___24Anonymous__135617,Vvar__1__eqA__135612)
       => ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__135611,Vvar__2___24Anonymous__135617)
         => ( cCoq_2eLists_2eSetoidList_2eNoDupA___24a3(Vvar__0__A__135611,Vvar__1__eqA__135612,Vvar__2___24Anonymous__135617)
           => ( Vvar__2___24Anonymous__135617 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__135611)
              | ? [Vvar__2__x__135631] :
                  ( t(Vvar__2__x__135631,Vvar__0__A__135611)
                  & ? [Vvar__3__l__135632] :
                      ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__135611,Vvar__3__l__135632)
                      & ~ cCoq_2eLists_2eSetoidList_2eInA___24a4(Vvar__0__A__135611,Vvar__1__eqA__135612,Vvar__2__x__135631,Vvar__3__l__135632)
                      & cCoq_2eLists_2eSetoidList_2eNoDupA___24a3(Vvar__0__A__135611,Vvar__1__eqA__135612,Vvar__3__l__135632)
                      & Vvar__2___24Anonymous__135617 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__135611,Vvar__2__x__135631,Vvar__3__l__135632) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.Lists.SetoidList.eqlistA',axiom,
    ! [Vvar__0__A__135646,Vvar__1__eqA__135647,Vvar__2___24Anonymous__135652,Vvar__3___24Anonymous__135653] :
      ( cType___24t(Vvar__0__A__135646)
     => ( c_24__type__135684___24t(Vvar__0__A__135646,Vvar__1__eqA__135647,Vvar__2___24Anonymous__135652,Vvar__3___24Anonymous__135653,Vvar__1__eqA__135647)
       => ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__135646,Vvar__2___24Anonymous__135652)
         => ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__135646,Vvar__3___24Anonymous__135653)
           => ( cCoq_2eLists_2eSetoidList_2eeqlistA___24a4(Vvar__0__A__135646,Vvar__1__eqA__135647,Vvar__2___24Anonymous__135652,Vvar__3___24Anonymous__135653)
             => ( ( Vvar__3___24Anonymous__135653 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__135646)
                  & Vvar__2___24Anonymous__135652 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__135646) )
                | ? [Vvar__2__x__135667] :
                    ( t(Vvar__2__x__135667,Vvar__0__A__135646)
                    & ? [Vvar__3__x_27__135668] :
                        ( t(Vvar__3__x_27__135668,Vvar__0__A__135646)
                        & ? [Vvar__4__l__135669] :
                            ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__135646,Vvar__4__l__135669)
                            & ? [Vvar__5__l_27__135670] :
                                ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__135646,Vvar__5__l_27__135670)
                                & p(happ(happ(Vvar__1__eqA__135647,Vvar__2__x__135667),Vvar__3__x_27__135668))
                                & cCoq_2eLists_2eSetoidList_2eeqlistA___24a4(Vvar__0__A__135646,Vvar__1__eqA__135647,Vvar__4__l__135669,Vvar__5__l_27__135670)
                                & Vvar__3___24Anonymous__135653 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__135646,Vvar__3__x_27__135668,Vvar__5__l_27__135670)
                                & Vvar__2___24Anonymous__135652 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__135646,Vvar__2__x__135667,Vvar__4__l__135669) ) ) ) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.Logic.EqdepFacts.eq_dep',axiom,
    ! [Vvar__0__U__145750,Vvar__1__P__145751,Vvar__2__p__145754,Vvar__3__x__145755,Vvar__4__q__145756,Vvar__5___24Anonymous__145757] :
      ( cType___24t(Vvar__0__U__145750)
     => ( c_24__type__145772___24t(Vvar__0__U__145750,Vvar__1__P__145751,Vvar__2__p__145754,Vvar__3__x__145755,Vvar__4__q__145756,Vvar__5___24Anonymous__145757,Vvar__1__P__145751)
       => ( t(Vvar__2__p__145754,Vvar__0__U__145750)
         => ( t(Vvar__3__x__145755,happ(Vvar__1__P__145751,Vvar__2__p__145754))
           => ( t(Vvar__4__q__145756,Vvar__0__U__145750)
             => ( t(Vvar__5___24Anonymous__145757,happ(Vvar__1__P__145751,Vvar__4__q__145756))
               => ( cCoq_2eLogic_2eEqdepFacts_2eeq__dep___24a6(Vvar__0__U__145750,Vvar__1__P__145751,Vvar__2__p__145754,Vvar__3__x__145755,Vvar__4__q__145756,Vvar__5___24Anonymous__145757)
                 => ( Vvar__5___24Anonymous__145757 = Vvar__3__x__145755
                    & Vvar__4__q__145756 = Vvar__2__p__145754 ) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.Logic.EqdepFacts.eq_dep1',axiom,
    ! [Vvar__0__U__145774,Vvar__1__P__145775,Vvar__2__p__145778,Vvar__3__x__145779,Vvar__4__q__145780,Vvar__5__y__145781] :
      ( cType___24t(Vvar__0__U__145774)
     => ( c_24__type__145800___24t(Vvar__0__U__145774,Vvar__1__P__145775,Vvar__2__p__145778,Vvar__3__x__145779,Vvar__4__q__145780,Vvar__5__y__145781,Vvar__1__P__145775)
       => ( t(Vvar__2__p__145778,Vvar__0__U__145774)
         => ( t(Vvar__3__x__145779,happ(Vvar__1__P__145775,Vvar__2__p__145778))
           => ( t(Vvar__4__q__145780,Vvar__0__U__145774)
             => ( t(Vvar__5__y__145781,happ(Vvar__1__P__145775,Vvar__4__q__145780))
               => ( cCoq_2eLogic_2eEqdepFacts_2eeq__dep1___24a6(Vvar__0__U__145774,Vvar__1__P__145775,Vvar__2__p__145778,Vvar__3__x__145779,Vvar__4__q__145780,Vvar__5__y__145781)
                 => ( Vvar__4__q__145780 = Vvar__2__p__145778
                    & Vvar__3__x__145779 = cCoq_2eInit_2eLogic_2eeq__rect___24a5(Vvar__0__U__145774,Vvar__4__q__145780,Vvar__1__P__145775,Vvar__5__y__145781,Vvar__2__p__145778)
                    & p(c_24True) ) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.Numbers.BinNums.N',axiom,
    ! [VX1776] :
      ( cCoq_2eNumbers_2eBinNums_2eN___24t(VX1776)
     => ( VX1776 = cCoq_2eNumbers_2eBinNums_2eN0
        | ? [Vvar__0___24Anonymous__1777] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__1777)
            & VX1776 = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__1777) ) ) ) ).

fof('$_inversion_Coq.Numbers.BinNums.Z',axiom,
    ! [VX222] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(VX222)
     => ( VX222 = cCoq_2eNumbers_2eBinNums_2eZ0
        | ? [Vvar__0___24Anonymous__223] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__223)
            & VX222 = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__223) )
        | ? [Vvar__0___24Anonymous__224] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__224)
            & VX222 = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__224) ) ) ) ).

fof('$_inversion_Coq.Numbers.BinNums.positive',axiom,
    ! [VX209] :
      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(VX209)
     => ( ? [Vvar__0___24Anonymous__210] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__210)
            & VX209 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__210) )
        | ? [Vvar__0___24Anonymous__211] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__211)
            & VX209 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__211) )
        | VX209 = cCoq_2eNumbers_2eBinNums_2exH ) ) ).

fof('$_inversion_Coq.PArith.BinPos.Pos.PeanoView',axiom,
    ! [Vvar__0___24Anonymous__145101,VX145102] :
      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__145101)
     => ( cCoq_2ePArith_2eBinPos_2ePos_2ePeanoView___24t(Vvar__0___24Anonymous__145101,VX145102)
       => ( ( Vvar__0___24Anonymous__145101 = cCoq_2eNumbers_2eBinNums_2exH
            & VX145102 = cCoq_2ePArith_2eBinPos_2ePos_2ePeanoOne )
          | ? [Vvar__0__p__145103] :
              ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0__p__145103)
              & ? [Vvar__1___24Anonymous__145104] :
                  ( cCoq_2ePArith_2eBinPos_2ePos_2ePeanoView___24t(Vvar__0__p__145103,Vvar__1___24Anonymous__145104)
                  & Vvar__0___24Anonymous__145101 = c_24__case__Coq_2eNumbers_2eBinNums_2epositive_24145139___24a2(Vvar__0___24Anonymous__145101,Vvar__0__p__145103)
                  & VX145102 = cCoq_2ePArith_2eBinPos_2ePos_2ePeanoSucc___24a2(Vvar__0__p__145103,Vvar__1___24Anonymous__145104) ) ) ) ) ) ).

fof('$_inversion_Coq.PArith.BinPos.Pos.SubMaskSpec',axiom,
    ! [Vvar__0__p__150023,Vvar__1__q__150024,Vvar__2___24Anonymous__150025] :
      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0__p__150023)
     => ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1__q__150024)
       => ( cCoq_2ePArith_2eBinPosDef_2ePos_2emask___24t(Vvar__2___24Anonymous__150025)
         => ( cCoq_2ePArith_2eBinPos_2ePos_2eSubMaskSpec___24a3(Vvar__0__p__150023,Vvar__1__q__150024,Vvar__2___24Anonymous__150025)
           => ( ( Vvar__0__p__150023 = Vvar__1__q__150024
                & Vvar__2___24Anonymous__150025 = cCoq_2ePArith_2eBinPosDef_2ePos_2eIsNul )
              | ? [Vvar__2__r__150032] :
                  ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2__r__150032)
                  & cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(Vvar__1__q__150024,Vvar__2__r__150032) = Vvar__0__p__150023
                  & Vvar__2___24Anonymous__150025 = cCoq_2ePArith_2eBinPosDef_2ePos_2eIsPos___24a1(Vvar__2__r__150032) )
              | ? [Vvar__2__r__150036] :
                  ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2__r__150036)
                  & cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(Vvar__0__p__150023,Vvar__2__r__150036) = Vvar__1__q__150024
                  & Vvar__2___24Anonymous__150025 = cCoq_2ePArith_2eBinPosDef_2ePos_2eIsNeg ) ) ) ) ) ) ).

fof('$_inversion_Coq.PArith.BinPosDef.Pos.mask',axiom,
    ! [VX7062] :
      ( cCoq_2ePArith_2eBinPosDef_2ePos_2emask___24t(VX7062)
     => ( VX7062 = cCoq_2ePArith_2eBinPosDef_2ePos_2eIsNul
        | ? [Vvar__0___24Anonymous__7063] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__7063)
            & VX7062 = cCoq_2ePArith_2eBinPosDef_2ePos_2eIsPos___24a1(Vvar__0___24Anonymous__7063) )
        | VX7062 = cCoq_2ePArith_2eBinPosDef_2ePos_2eIsNeg ) ) ).

fof('$_inversion_Coq.QArith.QArith_base.Q',axiom,
    ! [VX122180] :
      ( cCoq_2eQArith_2eQArith__base_2eQ___24t(VX122180)
     => ? [Vvar__0__Qnum__122181] :
          ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__0__Qnum__122181)
          & ? [Vvar__1__Qden__122182] :
              ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1__Qden__122182)
              & VX122180 = cCoq_2eQArith_2eQArith__base_2eQmake___24a2(Vvar__0__Qnum__122181,Vvar__1__Qden__122182) ) ) ) ).

fof('$_inversion_Coq.Reals.RIneq.negreal',axiom,
    ! [VX147823] :
      ( cCoq_2eReals_2eRIneq_2enegreal___24t(VX147823)
     => ? [Vvar__0__neg__147824] :
          ( cCoq_2eReals_2eRdefinitions_2eR___24t(Vvar__0__neg__147824)
          & cCoq_2eReals_2eRdefinitions_2eRlt___24a2(Vvar__0__neg__147824,cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0))
          & VX147823 = cCoq_2eReals_2eRIneq_2emknegreal___24a1(Vvar__0__neg__147824) ) ) ).

fof('$_inversion_Coq.Reals.RIneq.nonnegreal',axiom,
    ! [VX147802] :
      ( cCoq_2eReals_2eRIneq_2enonnegreal___24t(VX147802)
     => ? [Vvar__0__nonneg__147803] :
          ( cCoq_2eReals_2eRdefinitions_2eR___24t(Vvar__0__nonneg__147803)
          & cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),Vvar__0__nonneg__147803)
          & VX147802 = cCoq_2eReals_2eRIneq_2emknonnegreal___24a1(Vvar__0__nonneg__147803) ) ) ).

fof('$_inversion_Coq.Reals.RIneq.nonposreal',axiom,
    ! [VX147816] :
      ( cCoq_2eReals_2eRIneq_2enonposreal___24t(VX147816)
     => ? [Vvar__0__nonpos__147817] :
          ( cCoq_2eReals_2eRdefinitions_2eR___24t(Vvar__0__nonpos__147817)
          & cCoq_2eReals_2eRdefinitions_2eRle___24a2(Vvar__0__nonpos__147817,cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0))
          & VX147816 = cCoq_2eReals_2eRIneq_2emknonposreal___24a1(Vvar__0__nonpos__147817) ) ) ).

fof('$_inversion_Coq.Reals.RIneq.nonzeroreal',axiom,
    ! [VX147830] :
      ( cCoq_2eReals_2eRIneq_2enonzeroreal___24t(VX147830)
     => ? [Vvar__0__nonzero__147831] :
          ( cCoq_2eReals_2eRdefinitions_2eR___24t(Vvar__0__nonzero__147831)
          & Vvar__0__nonzero__147831 != cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)
          & VX147830 = cCoq_2eReals_2eRIneq_2emknonzeroreal___24a1(Vvar__0__nonzero__147831) ) ) ).

fof('$_inversion_Coq.Reals.RIneq.posreal',axiom,
    ! [VX147809] :
      ( cCoq_2eReals_2eRIneq_2eposreal___24t(VX147809)
     => ? [Vvar__0__pos__147810] :
          ( cCoq_2eReals_2eRdefinitions_2eR___24t(Vvar__0__pos__147810)
          & cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),Vvar__0__pos__147810)
          & VX147809 = cCoq_2eReals_2eRIneq_2emkposreal___24a1(Vvar__0__pos__147810) ) ) ).

fof('$_inversion_Coq.Reals.Rfunctions.Z_spec',axiom,
    ! [Vvar__0__x__126247,Vvar__1___24Anonymous__126248,VX126249] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__0__x__126247)
     => ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__1___24Anonymous__126248)
       => ( cCoq_2eReals_2eRfunctions_2eZ__spec___24t(Vvar__0__x__126247,Vvar__1___24Anonymous__126248,VX126249)
         => ( ( Vvar__0__x__126247 = cCoq_2eNumbers_2eBinNums_2eZ0
              & Vvar__1___24Anonymous__126248 = cCoq_2eNumbers_2eBinNums_2eZ0
              & VX126249 = cCoq_2eReals_2eRfunctions_2eZintNull___24a1(Vvar__0__x__126247) )
            | ? [Vvar__1__n__126253] :
                ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__1__n__126253)
                & Vvar__0__x__126247 = cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat___24a1(Vvar__1__n__126253)
                & Vvar__1___24Anonymous__126248 = c_24__case__Coq_2eInit_2eDatatypes_2enat_24126273___24a3(Vvar__0__x__126247,Vvar__1___24Anonymous__126248,Vvar__1__n__126253)
                & VX126249 = cCoq_2eReals_2eRfunctions_2eZintPos___24a2(Vvar__0__x__126247,Vvar__1__n__126253) )
            | ? [Vvar__1__n__126258] :
                ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__1__n__126258)
                & Vvar__0__x__126247 = cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat___24a1(Vvar__1__n__126258))
                & Vvar__1___24Anonymous__126248 = c_24__case__Coq_2eNumbers_2eBinNums_2eZ_24126290___24a3(Vvar__0__x__126247,Vvar__1___24Anonymous__126248,Vvar__1__n__126258)
                & VX126249 = cCoq_2eReals_2eRfunctions_2eZintNeg___24a2(Vvar__0__x__126247,Vvar__1__n__126258) ) ) ) ) ) ).

fof('$_inversion_Coq.Relations.Relation_Definitions.PER',axiom,
    ! [Vvar__0__A__152564,Vvar__1__R__152565] :
      ( cType___24t(Vvar__0__A__152564)
     => ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vvar__0__A__152564,Vvar__1__R__152565)
       => ( cCoq_2eRelations_2eRelation__Definitions_2ePER___24a2(Vvar__0__A__152564,Vvar__1__R__152565)
         => ( cCoq_2eRelations_2eRelation__Definitions_2esymmetric___24a2(Vvar__0__A__152564,Vvar__1__R__152565)
            & cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2(Vvar__0__A__152564,Vvar__1__R__152565)
            & p(c_24True) ) ) ) ) ).

fof('$_inversion_Coq.Relations.Relation_Definitions.equivalence',axiom,
    ! [Vvar__0__A__147860,Vvar__1__R__147861] :
      ( cType___24t(Vvar__0__A__147860)
     => ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vvar__0__A__147860,Vvar__1__R__147861)
       => ( cCoq_2eRelations_2eRelation__Definitions_2eequivalence___24a2(Vvar__0__A__147860,Vvar__1__R__147861)
         => ( cCoq_2eRelations_2eRelation__Definitions_2ereflexive___24a2(Vvar__0__A__147860,Vvar__1__R__147861)
            & cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2(Vvar__0__A__147860,Vvar__1__R__147861)
            & cCoq_2eRelations_2eRelation__Definitions_2esymmetric___24a2(Vvar__0__A__147860,Vvar__1__R__147861)
            & p(c_24True) ) ) ) ) ).

fof('$_inversion_Coq.Relations.Relation_Definitions.order',axiom,
    ! [Vvar__0__A__151947,Vvar__1__R__151948] :
      ( cType___24t(Vvar__0__A__151947)
     => ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vvar__0__A__151947,Vvar__1__R__151948)
       => ( cCoq_2eRelations_2eRelation__Definitions_2eorder___24a2(Vvar__0__A__151947,Vvar__1__R__151948)
         => ( cCoq_2eRelations_2eRelation__Definitions_2ereflexive___24a2(Vvar__0__A__151947,Vvar__1__R__151948)
            & cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2(Vvar__0__A__151947,Vvar__1__R__151948)
            & cCoq_2eRelations_2eRelation__Definitions_2eantisymmetric___24a2(Vvar__0__A__151947,Vvar__1__R__151948)
            & p(c_24True) ) ) ) ) ).

fof('$_inversion_Coq.Relations.Relation_Definitions.preorder',axiom,
    ! [Vvar__0__A__152557,Vvar__1__R__152558] :
      ( cType___24t(Vvar__0__A__152557)
     => ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vvar__0__A__152557,Vvar__1__R__152558)
       => ( cCoq_2eRelations_2eRelation__Definitions_2epreorder___24a2(Vvar__0__A__152557,Vvar__1__R__152558)
         => ( cCoq_2eRelations_2eRelation__Definitions_2ereflexive___24a2(Vvar__0__A__152557,Vvar__1__R__152558)
            & cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2(Vvar__0__A__152557,Vvar__1__R__152558)
            & p(c_24True) ) ) ) ) ).

fof('$_inversion_Coq.Relations.Relation_Operators.Desc',axiom,
    ! [Vvar__0__A__148106,Vvar__1__leA__148107,Vvar__2___24Anonymous__148112] :
      ( cType___24t(Vvar__0__A__148106)
     => ( c_24__type__148202___24t(Vvar__0__A__148106,Vvar__1__leA__148107,Vvar__2___24Anonymous__148112,Vvar__1__leA__148107)
       => ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__148106,Vvar__2___24Anonymous__148112)
         => ( cCoq_2eRelations_2eRelation__Operators_2eDesc___24a3(Vvar__0__A__148106,Vvar__1__leA__148107,Vvar__2___24Anonymous__148112)
           => ( Vvar__2___24Anonymous__148112 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__148106)
              | ? [Vvar__2__x__148126] :
                  ( t(Vvar__2__x__148126,Vvar__0__A__148106)
                  & Vvar__2___24Anonymous__148112 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__148106,Vvar__2__x__148126,cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__148106)) )
              | ? [Vvar__2__x__148133] :
                  ( t(Vvar__2__x__148133,Vvar__0__A__148106)
                  & ? [Vvar__3__y__148134] :
                      ( t(Vvar__3__y__148134,Vvar__0__A__148106)
                      & ? [Vvar__4__l__148135] :
                          ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__148106,Vvar__4__l__148135)
                          & cCoq_2eRelations_2eRelation__Operators_2eclos__refl___24a4(Vvar__0__A__148106,Vvar__1__leA__148107,Vvar__2__x__148133,Vvar__3__y__148134)
                          & cCoq_2eRelations_2eRelation__Operators_2eDesc___24a3(Vvar__0__A__148106,Vvar__1__leA__148107,cCoq_2eInit_2eDatatypes_2eapp___24a3(Vvar__0__A__148106,Vvar__4__l__148135,cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__148106,Vvar__3__y__148134,cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__148106))))
                          & Vvar__2___24Anonymous__148112 = c_24__case__Coq_2eInit_2eDatatypes_2elist_24148400___24a6(Vvar__0__A__148106,Vvar__1__leA__148107,Vvar__2___24Anonymous__148112,Vvar__2__x__148133,Vvar__3__y__148134,Vvar__4__l__148135) ) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.Relations.Relation_Operators.Ltl',axiom,
    ! [Vvar__0__A__148055,Vvar__1__leA__148056,Vvar__2___24Anonymous__148061,Vvar__3___24Anonymous__148062] :
      ( cType___24t(Vvar__0__A__148055)
     => ( c_24__type__148104___24t(Vvar__0__A__148055,Vvar__1__leA__148056,Vvar__2___24Anonymous__148061,Vvar__3___24Anonymous__148062,Vvar__1__leA__148056)
       => ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__148055,Vvar__2___24Anonymous__148061)
         => ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__148055,Vvar__3___24Anonymous__148062)
           => ( cCoq_2eRelations_2eRelation__Operators_2eLtl___24a4(Vvar__0__A__148055,Vvar__1__leA__148056,Vvar__2___24Anonymous__148061,Vvar__3___24Anonymous__148062)
             => ( ? [Vvar__2__a__148070] :
                    ( t(Vvar__2__a__148070,Vvar__0__A__148055)
                    & ? [Vvar__3__x__148071] :
                        ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__148055,Vvar__3__x__148071)
                        & Vvar__3___24Anonymous__148062 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__148055,Vvar__2__a__148070,Vvar__3__x__148071)
                        & Vvar__2___24Anonymous__148061 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__148055) ) )
                | ? [Vvar__2__a__148078] :
                    ( t(Vvar__2__a__148078,Vvar__0__A__148055)
                    & ? [Vvar__3__b__148079] :
                        ( t(Vvar__3__b__148079,Vvar__0__A__148055)
                        & p(happ(happ(Vvar__1__leA__148056,Vvar__2__a__148078),Vvar__3__b__148079))
                        & ? [Vvar__5__x__148081] :
                            ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__148055,Vvar__5__x__148081)
                            & ? [Vvar__6__y__148082] :
                                ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__148055,Vvar__6__y__148082)
                                & Vvar__3___24Anonymous__148062 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__148055,Vvar__3__b__148079,Vvar__6__y__148082)
                                & Vvar__2___24Anonymous__148061 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__148055,Vvar__2__a__148078,Vvar__5__x__148081) ) ) ) )
                | ? [Vvar__2__a__148089] :
                    ( t(Vvar__2__a__148089,Vvar__0__A__148055)
                    & ? [Vvar__3__x__148090] :
                        ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__148055,Vvar__3__x__148090)
                        & ? [Vvar__4__y__148091] :
                            ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__148055,Vvar__4__y__148091)
                            & cCoq_2eRelations_2eRelation__Operators_2eLtl___24a4(Vvar__0__A__148055,Vvar__1__leA__148056,Vvar__3__x__148090,Vvar__4__y__148091)
                            & Vvar__3___24Anonymous__148062 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__148055,Vvar__2__a__148089,Vvar__4__y__148091)
                            & Vvar__2___24Anonymous__148061 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__148055,Vvar__2__a__148089,Vvar__3__x__148090) ) ) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.Relations.Relation_Operators.clos_refl',axiom,
    ! [Vvar__0__A__147868,Vvar__1__R__147869,Vvar__2__x__147870,Vvar__3___24Anonymous__147871] :
      ( cType___24t(Vvar__0__A__147868)
     => ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vvar__0__A__147868,Vvar__1__R__147869)
       => ( t(Vvar__2__x__147870,Vvar__0__A__147868)
         => ( t(Vvar__3___24Anonymous__147871,Vvar__0__A__147868)
           => ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl___24a4(Vvar__0__A__147868,Vvar__1__R__147869,Vvar__2__x__147870,Vvar__3___24Anonymous__147871)
             => ( ? [Vvar__3__y__147876] :
                    ( t(Vvar__3__y__147876,Vvar__0__A__147868)
                    & p(happ(happ(Vvar__1__R__147869,Vvar__2__x__147870),Vvar__3__y__147876))
                    & Vvar__3___24Anonymous__147871 = Vvar__3__y__147876 )
                | Vvar__3___24Anonymous__147871 = Vvar__2__x__147870 ) ) ) ) ) ) ).

fof('$_inversion_Coq.Relations.Relation_Operators.clos_refl_sym_trans_1n',axiom,
    ! [Vvar__0__A__152603,Vvar__1__R__152604,Vvar__2__x__152605,Vvar__3___24Anonymous__152606] :
      ( cType___24t(Vvar__0__A__152603)
     => ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vvar__0__A__152603,Vvar__1__R__152604)
       => ( t(Vvar__2__x__152605,Vvar__0__A__152603)
         => ( t(Vvar__3___24Anonymous__152606,Vvar__0__A__152603)
           => ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans__1n___24a4(Vvar__0__A__152603,Vvar__1__R__152604,Vvar__2__x__152605,Vvar__3___24Anonymous__152606)
             => ( Vvar__3___24Anonymous__152606 = Vvar__2__x__152605
                | ? [Vvar__3__y__152614] :
                    ( t(Vvar__3__y__152614,Vvar__0__A__152603)
                    & ? [Vvar__4__z__152615] :
                        ( t(Vvar__4__z__152615,Vvar__0__A__152603)
                        & ( p(happ(happ(Vvar__1__R__152604,Vvar__2__x__152605),Vvar__3__y__152614))
                          | p(happ(happ(Vvar__1__R__152604,Vvar__3__y__152614),Vvar__2__x__152605)) )
                        & cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans__1n___24a4(Vvar__0__A__152603,Vvar__1__R__152604,Vvar__3__y__152614,Vvar__4__z__152615)
                        & Vvar__3___24Anonymous__152606 = Vvar__4__z__152615 ) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.Relations.Relation_Operators.clos_refl_sym_trans_n1',axiom,
    ! [Vvar__0__A__152618,Vvar__1__R__152619,Vvar__2__x__152620,Vvar__3___24Anonymous__152621] :
      ( cType___24t(Vvar__0__A__152618)
     => ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vvar__0__A__152618,Vvar__1__R__152619)
       => ( t(Vvar__2__x__152620,Vvar__0__A__152618)
         => ( t(Vvar__3___24Anonymous__152621,Vvar__0__A__152618)
           => ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans__n1___24a4(Vvar__0__A__152618,Vvar__1__R__152619,Vvar__2__x__152620,Vvar__3___24Anonymous__152621)
             => ( Vvar__3___24Anonymous__152621 = Vvar__2__x__152620
                | ? [Vvar__3__y__152629] :
                    ( t(Vvar__3__y__152629,Vvar__0__A__152618)
                    & ? [Vvar__4__z__152630] :
                        ( t(Vvar__4__z__152630,Vvar__0__A__152618)
                        & ( p(happ(happ(Vvar__1__R__152619,Vvar__3__y__152629),Vvar__4__z__152630))
                          | p(happ(happ(Vvar__1__R__152619,Vvar__4__z__152630),Vvar__3__y__152629)) )
                        & cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans__n1___24a4(Vvar__0__A__152618,Vvar__1__R__152619,Vvar__2__x__152620,Vvar__3__y__152629)
                        & Vvar__3___24Anonymous__152621 = Vvar__4__z__152630 ) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.Relations.Relation_Operators.clos_refl_trans',axiom,
    ! [Vvar__0__A__147881,Vvar__1__R__147882,Vvar__2__x__147883,Vvar__3___24Anonymous__147884] :
      ( cType___24t(Vvar__0__A__147881)
     => ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vvar__0__A__147881,Vvar__1__R__147882)
       => ( t(Vvar__2__x__147883,Vvar__0__A__147881)
         => ( t(Vvar__3___24Anonymous__147884,Vvar__0__A__147881)
           => ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a4(Vvar__0__A__147881,Vvar__1__R__147882,Vvar__2__x__147883,Vvar__3___24Anonymous__147884)
             => ( ? [Vvar__3__y__147889] :
                    ( t(Vvar__3__y__147889,Vvar__0__A__147881)
                    & p(happ(happ(Vvar__1__R__147882,Vvar__2__x__147883),Vvar__3__y__147889))
                    & Vvar__3___24Anonymous__147884 = Vvar__3__y__147889 )
                | Vvar__3___24Anonymous__147884 = Vvar__2__x__147883
                | ? [Vvar__3__y__147897] :
                    ( t(Vvar__3__y__147897,Vvar__0__A__147881)
                    & ? [Vvar__4__z__147898] :
                        ( t(Vvar__4__z__147898,Vvar__0__A__147881)
                        & cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a4(Vvar__0__A__147881,Vvar__1__R__147882,Vvar__2__x__147883,Vvar__3__y__147897)
                        & cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a4(Vvar__0__A__147881,Vvar__1__R__147882,Vvar__3__y__147897,Vvar__4__z__147898)
                        & Vvar__3___24Anonymous__147884 = Vvar__4__z__147898 ) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.Relations.Relation_Operators.clos_refl_trans_1n',axiom,
    ! [Vvar__0__A__147901,Vvar__1__R__147902,Vvar__2__x__147903,Vvar__3___24Anonymous__147904] :
      ( cType___24t(Vvar__0__A__147901)
     => ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vvar__0__A__147901,Vvar__1__R__147902)
       => ( t(Vvar__2__x__147903,Vvar__0__A__147901)
         => ( t(Vvar__3___24Anonymous__147904,Vvar__0__A__147901)
           => ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans__1n___24a4(Vvar__0__A__147901,Vvar__1__R__147902,Vvar__2__x__147903,Vvar__3___24Anonymous__147904)
             => ( Vvar__3___24Anonymous__147904 = Vvar__2__x__147903
                | ? [Vvar__3__y__147912] :
                    ( t(Vvar__3__y__147912,Vvar__0__A__147901)
                    & ? [Vvar__4__z__147913] :
                        ( t(Vvar__4__z__147913,Vvar__0__A__147901)
                        & p(happ(happ(Vvar__1__R__147902,Vvar__2__x__147903),Vvar__3__y__147912))
                        & cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans__1n___24a4(Vvar__0__A__147901,Vvar__1__R__147902,Vvar__3__y__147912,Vvar__4__z__147913)
                        & Vvar__3___24Anonymous__147904 = Vvar__4__z__147913 ) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.Relations.Relation_Operators.clos_refl_trans_n1',axiom,
    ! [Vvar__0__A__152588,Vvar__1__R__152589,Vvar__2__x__152590,Vvar__3___24Anonymous__152591] :
      ( cType___24t(Vvar__0__A__152588)
     => ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vvar__0__A__152588,Vvar__1__R__152589)
       => ( t(Vvar__2__x__152590,Vvar__0__A__152588)
         => ( t(Vvar__3___24Anonymous__152591,Vvar__0__A__152588)
           => ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans__n1___24a4(Vvar__0__A__152588,Vvar__1__R__152589,Vvar__2__x__152590,Vvar__3___24Anonymous__152591)
             => ( Vvar__3___24Anonymous__152591 = Vvar__2__x__152590
                | ? [Vvar__3__y__152599] :
                    ( t(Vvar__3__y__152599,Vvar__0__A__152588)
                    & ? [Vvar__4__z__152600] :
                        ( t(Vvar__4__z__152600,Vvar__0__A__152588)
                        & p(happ(happ(Vvar__1__R__152589,Vvar__3__y__152599),Vvar__4__z__152600))
                        & cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans__n1___24a4(Vvar__0__A__152588,Vvar__1__R__152589,Vvar__2__x__152590,Vvar__3__y__152599)
                        & Vvar__3___24Anonymous__152591 = Vvar__4__z__152600 ) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.Relations.Relation_Operators.clos_trans',axiom,
    ! [Vvar__0__A__138037,Vvar__1__R__138038,Vvar__2__x__138039,Vvar__3___24Anonymous__138040] :
      ( cType___24t(Vvar__0__A__138037)
     => ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vvar__0__A__138037,Vvar__1__R__138038)
       => ( t(Vvar__2__x__138039,Vvar__0__A__138037)
         => ( t(Vvar__3___24Anonymous__138040,Vvar__0__A__138037)
           => ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a4(Vvar__0__A__138037,Vvar__1__R__138038,Vvar__2__x__138039,Vvar__3___24Anonymous__138040)
             => ( ? [Vvar__3__y__138045] :
                    ( t(Vvar__3__y__138045,Vvar__0__A__138037)
                    & p(happ(happ(Vvar__1__R__138038,Vvar__2__x__138039),Vvar__3__y__138045))
                    & Vvar__3___24Anonymous__138040 = Vvar__3__y__138045 )
                | ? [Vvar__3__y__138050] :
                    ( t(Vvar__3__y__138050,Vvar__0__A__138037)
                    & ? [Vvar__4__z__138051] :
                        ( t(Vvar__4__z__138051,Vvar__0__A__138037)
                        & cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a4(Vvar__0__A__138037,Vvar__1__R__138038,Vvar__2__x__138039,Vvar__3__y__138050)
                        & cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a4(Vvar__0__A__138037,Vvar__1__R__138038,Vvar__3__y__138050,Vvar__4__z__138051)
                        & Vvar__3___24Anonymous__138040 = Vvar__4__z__138051 ) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.Relations.Relation_Operators.clos_trans_1n',axiom,
    ! [Vvar__0__A__152571,Vvar__1__R__152572,Vvar__2__x__152573,Vvar__3___24Anonymous__152574] :
      ( cType___24t(Vvar__0__A__152571)
     => ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vvar__0__A__152571,Vvar__1__R__152572)
       => ( t(Vvar__2__x__152573,Vvar__0__A__152571)
         => ( t(Vvar__3___24Anonymous__152574,Vvar__0__A__152571)
           => ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans__1n___24a4(Vvar__0__A__152571,Vvar__1__R__152572,Vvar__2__x__152573,Vvar__3___24Anonymous__152574)
             => ( ? [Vvar__3__y__152579] :
                    ( t(Vvar__3__y__152579,Vvar__0__A__152571)
                    & p(happ(happ(Vvar__1__R__152572,Vvar__2__x__152573),Vvar__3__y__152579))
                    & Vvar__3___24Anonymous__152574 = Vvar__3__y__152579 )
                | ? [Vvar__3__y__152584] :
                    ( t(Vvar__3__y__152584,Vvar__0__A__152571)
                    & ? [Vvar__4__z__152585] :
                        ( t(Vvar__4__z__152585,Vvar__0__A__152571)
                        & p(happ(happ(Vvar__1__R__152572,Vvar__2__x__152573),Vvar__3__y__152584))
                        & cCoq_2eRelations_2eRelation__Operators_2eclos__trans__1n___24a4(Vvar__0__A__152571,Vvar__1__R__152572,Vvar__3__y__152584,Vvar__4__z__152585)
                        & Vvar__3___24Anonymous__152574 = Vvar__4__z__152585 ) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.Relations.Relation_Operators.clos_trans_n1',axiom,
    ! [Vvar__0__A__138054,Vvar__1__R__138055,Vvar__2__x__138056,Vvar__3___24Anonymous__138057] :
      ( cType___24t(Vvar__0__A__138054)
     => ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vvar__0__A__138054,Vvar__1__R__138055)
       => ( t(Vvar__2__x__138056,Vvar__0__A__138054)
         => ( t(Vvar__3___24Anonymous__138057,Vvar__0__A__138054)
           => ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans__n1___24a4(Vvar__0__A__138054,Vvar__1__R__138055,Vvar__2__x__138056,Vvar__3___24Anonymous__138057)
             => ( ? [Vvar__3__y__138062] :
                    ( t(Vvar__3__y__138062,Vvar__0__A__138054)
                    & p(happ(happ(Vvar__1__R__138055,Vvar__2__x__138056),Vvar__3__y__138062))
                    & Vvar__3___24Anonymous__138057 = Vvar__3__y__138062 )
                | ? [Vvar__3__y__138067] :
                    ( t(Vvar__3__y__138067,Vvar__0__A__138054)
                    & ? [Vvar__4__z__138068] :
                        ( t(Vvar__4__z__138068,Vvar__0__A__138054)
                        & p(happ(happ(Vvar__1__R__138055,Vvar__3__y__138067),Vvar__4__z__138068))
                        & cCoq_2eRelations_2eRelation__Operators_2eclos__trans__n1___24a4(Vvar__0__A__138054,Vvar__1__R__138055,Vvar__2__x__138056,Vvar__3__y__138067)
                        & Vvar__3___24Anonymous__138057 = Vvar__4__z__138068 ) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.Relations.Relation_Operators.le_AsB',axiom,
    ! [Vvar__0__A__155071,Vvar__1__B__155072,Vvar__2__leA__155073,Vvar__3__leB__155078,Vvar__4___24Anonymous__155083,Vvar__5___24Anonymous__155084] :
      ( cType___24t(Vvar__0__A__155071)
     => ( cType___24t(Vvar__1__B__155072)
       => ( c_24__type__155153___24t(Vvar__0__A__155071,Vvar__1__B__155072,Vvar__2__leA__155073,Vvar__3__leB__155078,Vvar__4___24Anonymous__155083,Vvar__5___24Anonymous__155084,Vvar__2__leA__155073)
         => ( c_24__type__155178___24t(Vvar__0__A__155071,Vvar__1__B__155072,Vvar__2__leA__155073,Vvar__3__leB__155078,Vvar__4___24Anonymous__155083,Vvar__5___24Anonymous__155084,Vvar__3__leB__155078)
           => ( cCoq_2eInit_2eDatatypes_2esum___24t(Vvar__0__A__155071,Vvar__1__B__155072,Vvar__4___24Anonymous__155083)
             => ( cCoq_2eInit_2eDatatypes_2esum___24t(Vvar__0__A__155071,Vvar__1__B__155072,Vvar__5___24Anonymous__155084)
               => ( cCoq_2eRelations_2eRelation__Operators_2ele__AsB___24a6(Vvar__0__A__155071,Vvar__1__B__155072,Vvar__2__leA__155073,Vvar__3__leB__155078,Vvar__4___24Anonymous__155083,Vvar__5___24Anonymous__155084)
                 => ( ? [Vvar__4__x__155098] :
                        ( t(Vvar__4__x__155098,Vvar__0__A__155071)
                        & ? [Vvar__5__y__155099] :
                            ( t(Vvar__5__y__155099,Vvar__0__A__155071)
                            & p(happ(happ(Vvar__2__leA__155073,Vvar__4__x__155098),Vvar__5__y__155099))
                            & Vvar__5___24Anonymous__155084 = cCoq_2eInit_2eDatatypes_2einl___24a3(Vvar__0__A__155071,Vvar__1__B__155072,Vvar__5__y__155099)
                            & Vvar__4___24Anonymous__155083 = cCoq_2eInit_2eDatatypes_2einl___24a3(Vvar__0__A__155071,Vvar__1__B__155072,Vvar__4__x__155098) ) )
                    | ? [Vvar__4__x__155113] :
                        ( t(Vvar__4__x__155113,Vvar__0__A__155071)
                        & ? [Vvar__5__y__155114] :
                            ( t(Vvar__5__y__155114,Vvar__1__B__155072)
                            & Vvar__5___24Anonymous__155084 = cCoq_2eInit_2eDatatypes_2einr___24a3(Vvar__0__A__155071,Vvar__1__B__155072,Vvar__5__y__155114)
                            & Vvar__4___24Anonymous__155083 = cCoq_2eInit_2eDatatypes_2einl___24a3(Vvar__0__A__155071,Vvar__1__B__155072,Vvar__4__x__155113) ) )
                    | ? [Vvar__4__x__155127] :
                        ( t(Vvar__4__x__155127,Vvar__1__B__155072)
                        & ? [Vvar__5__y__155128] :
                            ( t(Vvar__5__y__155128,Vvar__1__B__155072)
                            & p(happ(happ(Vvar__3__leB__155078,Vvar__4__x__155127),Vvar__5__y__155128))
                            & Vvar__5___24Anonymous__155084 = cCoq_2eInit_2eDatatypes_2einr___24a3(Vvar__0__A__155071,Vvar__1__B__155072,Vvar__5__y__155128)
                            & Vvar__4___24Anonymous__155083 = cCoq_2eInit_2eDatatypes_2einr___24a3(Vvar__0__A__155071,Vvar__1__B__155072,Vvar__4__x__155127) ) ) ) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.Relations.Relation_Operators.lexprod',axiom,
    ! [Vvar__0__A__152633,Vvar__1__B__152634,Vvar__2__leA__152637,Vvar__3__leB__152642,Vvar__4___24Anonymous__152649,Vvar__5___24Anonymous__152650] :
      ( cType___24t(Vvar__0__A__152633)
     => ( c_24__type__152713___24t(Vvar__0__A__152633,Vvar__1__B__152634,Vvar__2__leA__152637,Vvar__3__leB__152642,Vvar__4___24Anonymous__152649,Vvar__5___24Anonymous__152650,Vvar__1__B__152634)
       => ( c_24__type__152742___24t(Vvar__0__A__152633,Vvar__1__B__152634,Vvar__2__leA__152637,Vvar__3__leB__152642,Vvar__4___24Anonymous__152649,Vvar__5___24Anonymous__152650,Vvar__2__leA__152637)
         => ( c_24__type__152779___24t(Vvar__0__A__152633,Vvar__1__B__152634,Vvar__2__leA__152637,Vvar__3__leB__152642,Vvar__4___24Anonymous__152649,Vvar__5___24Anonymous__152650,Vvar__3__leB__152642)
           => ( cCoq_2eInit_2eSpecif_2esigT___24t(Vvar__0__A__152633,Vvar__1__B__152634,Vvar__4___24Anonymous__152649)
             => ( cCoq_2eInit_2eSpecif_2esigT___24t(Vvar__0__A__152633,Vvar__1__B__152634,Vvar__5___24Anonymous__152650)
               => ( cCoq_2eRelations_2eRelation__Operators_2elexprod___24a6(Vvar__0__A__152633,Vvar__1__B__152634,Vvar__2__leA__152637,Vvar__3__leB__152642,Vvar__4___24Anonymous__152649,Vvar__5___24Anonymous__152650)
                 => ( ? [Vvar__4__x__152668] :
                        ( t(Vvar__4__x__152668,Vvar__0__A__152633)
                        & ? [Vvar__5__x_27__152669] :
                            ( t(Vvar__5__x_27__152669,Vvar__0__A__152633)
                            & ? [Vvar__6__y__152670] :
                                ( t(Vvar__6__y__152670,happ(Vvar__1__B__152634,Vvar__4__x__152668))
                                & ? [Vvar__7__y_27__152671] :
                                    ( t(Vvar__7__y_27__152671,happ(Vvar__1__B__152634,Vvar__5__x_27__152669))
                                    & p(happ(happ(Vvar__2__leA__152637,Vvar__4__x__152668),Vvar__5__x_27__152669))
                                    & Vvar__5___24Anonymous__152650 = cCoq_2eInit_2eSpecif_2eexistT___24a4(Vvar__0__A__152633,Vvar__1__B__152634,Vvar__5__x_27__152669,Vvar__7__y_27__152671)
                                    & Vvar__4___24Anonymous__152649 = cCoq_2eInit_2eSpecif_2eexistT___24a4(Vvar__0__A__152633,Vvar__1__B__152634,Vvar__4__x__152668,Vvar__6__y__152670) ) ) ) )
                    | ? [Vvar__4__x__152689] :
                        ( t(Vvar__4__x__152689,Vvar__0__A__152633)
                        & ? [Vvar__5__y__152690] :
                            ( t(Vvar__5__y__152690,happ(Vvar__1__B__152634,Vvar__4__x__152689))
                            & ? [Vvar__6__y_27__152691] :
                                ( t(Vvar__6__y_27__152691,happ(Vvar__1__B__152634,Vvar__4__x__152689))
                                & p(happ(happ(happ(Vvar__3__leB__152642,Vvar__4__x__152689),Vvar__5__y__152690),Vvar__6__y_27__152691))
                                & Vvar__5___24Anonymous__152650 = cCoq_2eInit_2eSpecif_2eexistT___24a4(Vvar__0__A__152633,Vvar__1__B__152634,Vvar__4__x__152689,Vvar__6__y_27__152691)
                                & Vvar__4___24Anonymous__152649 = cCoq_2eInit_2eSpecif_2eexistT___24a4(Vvar__0__A__152633,Vvar__1__B__152634,Vvar__4__x__152689,Vvar__5__y__152690) ) ) ) ) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.Relations.Relation_Operators.swapprod',axiom,
    ! [Vvar__0__A__148013,Vvar__1__R__148014,Vvar__2___24Anonymous__148019,Vvar__3___24Anonymous__148020] :
      ( cType___24t(Vvar__0__A__148013)
     => ( c_24__type__148053___24t(Vvar__0__A__148013,Vvar__1__R__148014,Vvar__2___24Anonymous__148019,Vvar__3___24Anonymous__148020,Vvar__1__R__148014)
       => ( cCoq_2eInit_2eDatatypes_2eprod___24t(Vvar__0__A__148013,Vvar__0__A__148013,Vvar__2___24Anonymous__148019)
         => ( cCoq_2eInit_2eDatatypes_2eprod___24t(Vvar__0__A__148013,Vvar__0__A__148013,Vvar__3___24Anonymous__148020)
           => ( cCoq_2eRelations_2eRelation__Operators_2eswapprod___24a4(Vvar__0__A__148013,Vvar__1__R__148014,Vvar__2___24Anonymous__148019,Vvar__3___24Anonymous__148020)
             => ( ? [Vvar__2__x__148028] :
                    ( t(Vvar__2__x__148028,Vvar__0__A__148013)
                    & ? [Vvar__3__y__148029] :
                        ( t(Vvar__3__y__148029,Vvar__0__A__148013)
                        & ? [Vvar__4__p__148030] :
                            ( cCoq_2eInit_2eDatatypes_2eprod___24t(Vvar__0__A__148013,Vvar__0__A__148013,Vvar__4__p__148030)
                            & cCoq_2eRelations_2eRelation__Operators_2esymprod___24a6(Vvar__0__A__148013,Vvar__0__A__148013,Vvar__1__R__148014,Vvar__1__R__148014,cCoq_2eInit_2eDatatypes_2epair___24a4(Vvar__0__A__148013,Vvar__0__A__148013,Vvar__2__x__148028,Vvar__3__y__148029),Vvar__4__p__148030)
                            & Vvar__3___24Anonymous__148020 = Vvar__4__p__148030
                            & Vvar__2___24Anonymous__148019 = cCoq_2eInit_2eDatatypes_2epair___24a4(Vvar__0__A__148013,Vvar__0__A__148013,Vvar__2__x__148028,Vvar__3__y__148029) ) ) )
                | ? [Vvar__2__x__148038] :
                    ( t(Vvar__2__x__148038,Vvar__0__A__148013)
                    & ? [Vvar__3__y__148039] :
                        ( t(Vvar__3__y__148039,Vvar__0__A__148013)
                        & ? [Vvar__4__p__148040] :
                            ( cCoq_2eInit_2eDatatypes_2eprod___24t(Vvar__0__A__148013,Vvar__0__A__148013,Vvar__4__p__148040)
                            & cCoq_2eRelations_2eRelation__Operators_2esymprod___24a6(Vvar__0__A__148013,Vvar__0__A__148013,Vvar__1__R__148014,Vvar__1__R__148014,cCoq_2eInit_2eDatatypes_2epair___24a4(Vvar__0__A__148013,Vvar__0__A__148013,Vvar__2__x__148038,Vvar__3__y__148039),Vvar__4__p__148040)
                            & Vvar__3___24Anonymous__148020 = Vvar__4__p__148040
                            & Vvar__2___24Anonymous__148019 = cCoq_2eInit_2eDatatypes_2epair___24a4(Vvar__0__A__148013,Vvar__0__A__148013,Vvar__3__y__148039,Vvar__2__x__148038) ) ) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.Relations.Relation_Operators.symprod',axiom,
    ! [Vvar__0__A__147916,Vvar__1__B__147917,Vvar__2__leA__147918,Vvar__3__leB__147923,Vvar__4___24Anonymous__147928,Vvar__5___24Anonymous__147929] :
      ( cType___24t(Vvar__0__A__147916)
     => ( cType___24t(Vvar__1__B__147917)
       => ( c_24__type__147986___24t(Vvar__0__A__147916,Vvar__1__B__147917,Vvar__2__leA__147918,Vvar__3__leB__147923,Vvar__4___24Anonymous__147928,Vvar__5___24Anonymous__147929,Vvar__2__leA__147918)
         => ( c_24__type__148011___24t(Vvar__0__A__147916,Vvar__1__B__147917,Vvar__2__leA__147918,Vvar__3__leB__147923,Vvar__4___24Anonymous__147928,Vvar__5___24Anonymous__147929,Vvar__3__leB__147923)
           => ( cCoq_2eInit_2eDatatypes_2eprod___24t(Vvar__0__A__147916,Vvar__1__B__147917,Vvar__4___24Anonymous__147928)
             => ( cCoq_2eInit_2eDatatypes_2eprod___24t(Vvar__0__A__147916,Vvar__1__B__147917,Vvar__5___24Anonymous__147929)
               => ( cCoq_2eRelations_2eRelation__Operators_2esymprod___24a6(Vvar__0__A__147916,Vvar__1__B__147917,Vvar__2__leA__147918,Vvar__3__leB__147923,Vvar__4___24Anonymous__147928,Vvar__5___24Anonymous__147929)
                 => ( ? [Vvar__4__x__147943] :
                        ( t(Vvar__4__x__147943,Vvar__0__A__147916)
                        & ? [Vvar__5__x_27__147944] :
                            ( t(Vvar__5__x_27__147944,Vvar__0__A__147916)
                            & p(happ(happ(Vvar__2__leA__147918,Vvar__4__x__147943),Vvar__5__x_27__147944))
                            & ? [Vvar__7__y__147946] :
                                ( t(Vvar__7__y__147946,Vvar__1__B__147917)
                                & Vvar__5___24Anonymous__147929 = cCoq_2eInit_2eDatatypes_2epair___24a4(Vvar__0__A__147916,Vvar__1__B__147917,Vvar__5__x_27__147944,Vvar__7__y__147946)
                                & Vvar__4___24Anonymous__147928 = cCoq_2eInit_2eDatatypes_2epair___24a4(Vvar__0__A__147916,Vvar__1__B__147917,Vvar__4__x__147943,Vvar__7__y__147946) ) ) )
                    | ? [Vvar__4__y__147959] :
                        ( t(Vvar__4__y__147959,Vvar__1__B__147917)
                        & ? [Vvar__5__y_27__147960] :
                            ( t(Vvar__5__y_27__147960,Vvar__1__B__147917)
                            & p(happ(happ(Vvar__3__leB__147923,Vvar__4__y__147959),Vvar__5__y_27__147960))
                            & ? [Vvar__7__x__147962] :
                                ( t(Vvar__7__x__147962,Vvar__0__A__147916)
                                & Vvar__5___24Anonymous__147929 = cCoq_2eInit_2eDatatypes_2epair___24a4(Vvar__0__A__147916,Vvar__1__B__147917,Vvar__7__x__147962,Vvar__5__y_27__147960)
                                & Vvar__4___24Anonymous__147928 = cCoq_2eInit_2eDatatypes_2epair___24a4(Vvar__0__A__147916,Vvar__1__B__147917,Vvar__7__x__147962,Vvar__4__y__147959) ) ) ) ) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.Sorting.Sorted.HdRel',axiom,
    ! [Vvar__0__A__149002,Vvar__1__R__149003,Vvar__2__a__149008,Vvar__3___24Anonymous__149009] :
      ( cType___24t(Vvar__0__A__149002)
     => ( c_24__type__149039___24t(Vvar__0__A__149002,Vvar__1__R__149003,Vvar__2__a__149008,Vvar__3___24Anonymous__149009,Vvar__1__R__149003)
       => ( t(Vvar__2__a__149008,Vvar__0__A__149002)
         => ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__149002,Vvar__3___24Anonymous__149009)
           => ( cCoq_2eSorting_2eSorted_2eHdRel___24a4(Vvar__0__A__149002,Vvar__1__R__149003,Vvar__2__a__149008,Vvar__3___24Anonymous__149009)
             => ( Vvar__3___24Anonymous__149009 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__149002)
                | ? [Vvar__3__b__149025] :
                    ( t(Vvar__3__b__149025,Vvar__0__A__149002)
                    & ? [Vvar__4__l__149026] :
                        ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__149002,Vvar__4__l__149026)
                        & p(happ(happ(Vvar__1__R__149003,Vvar__2__a__149008),Vvar__3__b__149025))
                        & Vvar__3___24Anonymous__149009 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__149002,Vvar__3__b__149025,Vvar__4__l__149026) ) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.Sorting.Sorted.LocallySorted',axiom,
    ! [Vvar__0__A__148959,Vvar__1__R__148960,Vvar__2___24Anonymous__148965] :
      ( cType___24t(Vvar__0__A__148959)
     => ( c_24__type__149000___24t(Vvar__0__A__148959,Vvar__1__R__148960,Vvar__2___24Anonymous__148965,Vvar__1__R__148960)
       => ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__148959,Vvar__2___24Anonymous__148965)
         => ( cCoq_2eSorting_2eSorted_2eLocallySorted___24a3(Vvar__0__A__148959,Vvar__1__R__148960,Vvar__2___24Anonymous__148965)
           => ( Vvar__2___24Anonymous__148965 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__148959)
              | ? [Vvar__2__a__148979] :
                  ( t(Vvar__2__a__148979,Vvar__0__A__148959)
                  & Vvar__2___24Anonymous__148965 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__148959,Vvar__2__a__148979,cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__148959)) )
              | ? [Vvar__2__a__148986] :
                  ( t(Vvar__2__a__148986,Vvar__0__A__148959)
                  & ? [Vvar__3__b__148987] :
                      ( t(Vvar__3__b__148987,Vvar__0__A__148959)
                      & ? [Vvar__4__l__148988] :
                          ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__148959,Vvar__4__l__148988)
                          & cCoq_2eSorting_2eSorted_2eLocallySorted___24a3(Vvar__0__A__148959,Vvar__1__R__148960,cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__148959,Vvar__3__b__148987,Vvar__4__l__148988))
                          & p(happ(happ(Vvar__1__R__148960,Vvar__2__a__148986),Vvar__3__b__148987))
                          & Vvar__2___24Anonymous__148965 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__148959,Vvar__2__a__148986,cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__148959,Vvar__3__b__148987,Vvar__4__l__148988)) ) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.Sorting.Sorted.Sorted',axiom,
    ! [Vvar__0__A__149041,Vvar__1__R__149042,Vvar__2___24Anonymous__149047] :
      ( cType___24t(Vvar__0__A__149041)
     => ( c_24__type__149074___24t(Vvar__0__A__149041,Vvar__1__R__149042,Vvar__2___24Anonymous__149047,Vvar__1__R__149042)
       => ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__149041,Vvar__2___24Anonymous__149047)
         => ( cCoq_2eSorting_2eSorted_2eSorted___24a3(Vvar__0__A__149041,Vvar__1__R__149042,Vvar__2___24Anonymous__149047)
           => ( Vvar__2___24Anonymous__149047 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__149041)
              | ? [Vvar__2__a__149061] :
                  ( t(Vvar__2__a__149061,Vvar__0__A__149041)
                  & ? [Vvar__3__l__149062] :
                      ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__149041,Vvar__3__l__149062)
                      & cCoq_2eSorting_2eSorted_2eSorted___24a3(Vvar__0__A__149041,Vvar__1__R__149042,Vvar__3__l__149062)
                      & cCoq_2eSorting_2eSorted_2eHdRel___24a4(Vvar__0__A__149041,Vvar__1__R__149042,Vvar__2__a__149061,Vvar__3__l__149062)
                      & Vvar__2___24Anonymous__149047 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__149041,Vvar__2__a__149061,Vvar__3__l__149062) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.Sorting.Sorted.StronglySorted',axiom,
    ! [Vvar__0__A__149076,Vvar__1__R__149077,Vvar__2___24Anonymous__149082] :
      ( cType___24t(Vvar__0__A__149076)
     => ( c_24__type__149109___24t(Vvar__0__A__149076,Vvar__1__R__149077,Vvar__2___24Anonymous__149082,Vvar__1__R__149077)
       => ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__149076,Vvar__2___24Anonymous__149082)
         => ( cCoq_2eSorting_2eSorted_2eStronglySorted___24a3(Vvar__0__A__149076,Vvar__1__R__149077,Vvar__2___24Anonymous__149082)
           => ( Vvar__2___24Anonymous__149082 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__149076)
              | ? [Vvar__2__a__149096] :
                  ( t(Vvar__2__a__149096,Vvar__0__A__149076)
                  & ? [Vvar__3__l__149097] :
                      ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__149076,Vvar__3__l__149097)
                      & cCoq_2eSorting_2eSorted_2eStronglySorted___24a3(Vvar__0__A__149076,Vvar__1__R__149077,Vvar__3__l__149097)
                      & cCoq_2eLists_2eList_2eForall___24a3(Vvar__0__A__149076,happ(Vvar__1__R__149077,Vvar__2__a__149096),Vvar__3__l__149097)
                      & Vvar__2___24Anonymous__149082 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__149076,Vvar__2__a__149096,Vvar__3__l__149097) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.Strings.Ascii.ascii',axiom,
    ! [VX4899] :
      ( cCoq_2eStrings_2eAscii_2eascii___24t(VX4899)
     => ? [Vvar__0___24Anonymous__4900] :
          ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__0___24Anonymous__4900)
          & ? [Vvar__1___24Anonymous__4901] :
              ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__1___24Anonymous__4901)
              & ? [Vvar__2___24Anonymous__4902] :
                  ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__2___24Anonymous__4902)
                  & ? [Vvar__3___24Anonymous__4903] :
                      ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__3___24Anonymous__4903)
                      & ? [Vvar__4___24Anonymous__4904] :
                          ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__4___24Anonymous__4904)
                          & ? [Vvar__5___24Anonymous__4905] :
                              ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__5___24Anonymous__4905)
                              & ? [Vvar__6___24Anonymous__4906] :
                                  ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__6___24Anonymous__4906)
                                  & ? [Vvar__7___24Anonymous__4907] :
                                      ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__7___24Anonymous__4907)
                                      & VX4899 = cCoq_2eStrings_2eAscii_2eAscii___24a8(Vvar__0___24Anonymous__4900,Vvar__1___24Anonymous__4901,Vvar__2___24Anonymous__4902,Vvar__3___24Anonymous__4903,Vvar__4___24Anonymous__4904,Vvar__5___24Anonymous__4905,Vvar__6___24Anonymous__4906,Vvar__7___24Anonymous__4907) ) ) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.Strings.String.string',axiom,
    ! [VX200] :
      ( cCoq_2eStrings_2eString_2estring___24t(VX200)
     => ( VX200 = cCoq_2eStrings_2eString_2eEmptyString
        | ? [Vvar__0___24Anonymous__201] :
            ( cCoq_2eStrings_2eAscii_2eascii___24t(Vvar__0___24Anonymous__201)
            & ? [Vvar__1___24Anonymous__202] :
                ( cCoq_2eStrings_2eString_2estring___24t(Vvar__1___24Anonymous__202)
                & VX200 = cCoq_2eStrings_2eString_2eString___24a2(Vvar__0___24Anonymous__201,Vvar__1___24Anonymous__202) ) ) ) ) ).

fof('$_inversion_Coq.Structures.OrderedType.Compare',axiom,
    ! [Vvar__0__X__121884,Vvar__1__lt__121885,Vvar__2__eq__121890,Vvar__3__x__121895,Vvar__4__y__121896,VX121897] :
      ( cType___24t(Vvar__0__X__121884)
     => ( c_24__type__121957___24t(Vvar__0__X__121884,Vvar__1__lt__121885,Vvar__2__eq__121890,Vvar__3__x__121895,Vvar__4__y__121896,Vvar__1__lt__121885)
       => ( c_24__type__121976___24t(Vvar__0__X__121884,Vvar__1__lt__121885,Vvar__2__eq__121890,Vvar__3__x__121895,Vvar__4__y__121896,Vvar__2__eq__121890)
         => ( t(Vvar__3__x__121895,Vvar__0__X__121884)
           => ( t(Vvar__4__y__121896,Vvar__0__X__121884)
             => ( cCoq_2eStructures_2eOrderedType_2eCompare___24t(Vvar__0__X__121884,Vvar__1__lt__121885,Vvar__2__eq__121890,Vvar__3__x__121895,Vvar__4__y__121896,VX121897)
               => ( ( p(happ(happ(Vvar__1__lt__121885,Vvar__3__x__121895),Vvar__4__y__121896))
                    & VX121897 = cCoq_2eStructures_2eOrderedType_2eLT___24a5(Vvar__0__X__121884,Vvar__1__lt__121885,Vvar__2__eq__121890,Vvar__3__x__121895,Vvar__4__y__121896) )
                  | ( p(happ(happ(Vvar__2__eq__121890,Vvar__3__x__121895),Vvar__4__y__121896))
                    & VX121897 = cCoq_2eStructures_2eOrderedType_2eEQ___24a5(Vvar__0__X__121884,Vvar__1__lt__121885,Vvar__2__eq__121890,Vvar__3__x__121895,Vvar__4__y__121896) )
                  | ( p(happ(happ(Vvar__1__lt__121885,Vvar__4__y__121896),Vvar__3__x__121895))
                    & VX121897 = cCoq_2eStructures_2eOrderedType_2eGT___24a5(Vvar__0__X__121884,Vvar__1__lt__121885,Vvar__2__eq__121890,Vvar__3__x__121895,Vvar__4__y__121896) ) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.Structures.OrderedTypeEx.String_as_OT.lts',axiom,
    ! [Vvar__0___24Anonymous__88326,Vvar__1___24Anonymous__88327] :
      ( cCoq_2eStrings_2eString_2estring___24t(Vvar__0___24Anonymous__88326)
     => ( cCoq_2eStrings_2eString_2estring___24t(Vvar__1___24Anonymous__88327)
       => ( cCoq_2eStructures_2eOrderedTypeEx_2eString__as__OT_2elts___24a2(Vvar__0___24Anonymous__88326,Vvar__1___24Anonymous__88327)
         => ( ? [Vvar__0__a__88329] :
                ( cCoq_2eStrings_2eAscii_2eascii___24t(Vvar__0__a__88329)
                & ? [Vvar__1__s__88330] :
                    ( cCoq_2eStrings_2eString_2estring___24t(Vvar__1__s__88330)
                    & Vvar__1___24Anonymous__88327 = cCoq_2eStrings_2eString_2eString___24a2(Vvar__0__a__88329,Vvar__1__s__88330)
                    & Vvar__0___24Anonymous__88326 = cCoq_2eStrings_2eString_2eEmptyString ) )
            | ? [Vvar__0__a__88331] :
                ( cCoq_2eStrings_2eAscii_2eascii___24t(Vvar__0__a__88331)
                & ? [Vvar__1__s1__88332] :
                    ( cCoq_2eStrings_2eString_2estring___24t(Vvar__1__s1__88332)
                    & ? [Vvar__2__s2__88333] :
                        ( cCoq_2eStrings_2eString_2estring___24t(Vvar__2__s2__88333)
                        & cCoq_2eStructures_2eOrderedTypeEx_2eString__as__OT_2elts___24a2(Vvar__1__s1__88332,Vvar__2__s2__88333)
                        & Vvar__1___24Anonymous__88327 = cCoq_2eStrings_2eString_2eString___24a2(Vvar__0__a__88331,Vvar__2__s2__88333)
                        & Vvar__0___24Anonymous__88326 = cCoq_2eStrings_2eString_2eString___24a2(Vvar__0__a__88331,Vvar__1__s1__88332) ) ) )
            | ? [Vvar__0__a__88335] :
                ( cCoq_2eStrings_2eAscii_2eascii___24t(Vvar__0__a__88335)
                & ? [Vvar__1__b__88336] :
                    ( cCoq_2eStrings_2eAscii_2eascii___24t(Vvar__1__b__88336)
                    & ? [Vvar__2__s1__88337] :
                        ( cCoq_2eStrings_2eString_2estring___24t(Vvar__2__s1__88337)
                        & ? [Vvar__3__s2__88338] :
                            ( cCoq_2eStrings_2eString_2estring___24t(Vvar__3__s2__88338)
                            & cCoq_2eInit_2ePeano_2elt___24a2(cCoq_2eStrings_2eAscii_2enat__of__ascii___24a1(Vvar__0__a__88335),cCoq_2eStrings_2eAscii_2enat__of__ascii___24a1(Vvar__1__b__88336))
                            & Vvar__1___24Anonymous__88327 = cCoq_2eStrings_2eString_2eString___24a2(Vvar__1__b__88336,Vvar__3__s2__88338)
                            & Vvar__0___24Anonymous__88326 = cCoq_2eStrings_2eString_2eString___24a2(Vvar__0__a__88335,Vvar__2__s1__88337) ) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.Structures.OrdersTac.ord',axiom,
    ! [VX5164] :
      ( cCoq_2eStructures_2eOrdersTac_2eord___24t(VX5164)
     => ( VX5164 = cCoq_2eStructures_2eOrdersTac_2eOEQ
        | VX5164 = cCoq_2eStructures_2eOrdersTac_2eOLT
        | VX5164 = cCoq_2eStructures_2eOrdersTac_2eOLE ) ) ).

fof('$_inversion_Coq.Vectors.Fin.t',axiom,
    ! [Vvar__0___24Anonymous__1975,VX1976] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__1975)
     => ( cCoq_2eVectors_2eFin_2et___24t(Vvar__0___24Anonymous__1975,VX1976)
       => ( ? [Vvar__0__n__1977] :
              ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0__n__1977)
              & Vvar__0___24Anonymous__1975 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0__n__1977)
              & VX1976 = cCoq_2eVectors_2eFin_2eF1___24a1(Vvar__0__n__1977) )
          | ? [Vvar__0__n__1978] :
              ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0__n__1978)
              & ? [Vvar__1___24Anonymous__1979] :
                  ( cCoq_2eVectors_2eFin_2et___24t(Vvar__0__n__1978,Vvar__1___24Anonymous__1979)
                  & Vvar__0___24Anonymous__1975 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0__n__1978)
                  & VX1976 = cCoq_2eVectors_2eFin_2eFS___24a2(Vvar__0__n__1978,Vvar__1___24Anonymous__1979) ) ) ) ) ) ).

fof('$_inversion_Coq.Vectors.VectorDef.Exists',axiom,
    ! [Vvar__0__A__135726,Vvar__1__P__135727,Vvar__2__n__135730,Vvar__3___24Anonymous__135731] :
      ( cType___24t(Vvar__0__A__135726)
     => ( c_24__type__135754___24t(Vvar__0__A__135726,Vvar__1__P__135727,Vvar__2__n__135730,Vvar__3___24Anonymous__135731,Vvar__1__P__135727)
       => ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__2__n__135730)
         => ( cCoq_2eVectors_2eVectorDef_2et___24t(Vvar__0__A__135726,Vvar__2__n__135730,Vvar__3___24Anonymous__135731)
           => ( cCoq_2eVectors_2eVectorDef_2eExists___24a4(Vvar__0__A__135726,Vvar__1__P__135727,Vvar__2__n__135730,Vvar__3___24Anonymous__135731)
             => ( ? [Vvar__2__m__135737] :
                    ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__2__m__135737)
                    & ? [Vvar__3__x__135738] :
                        ( t(Vvar__3__x__135738,Vvar__0__A__135726)
                        & ? [Vvar__4__v__135739] :
                            ( cCoq_2eVectors_2eVectorDef_2et___24t(Vvar__0__A__135726,Vvar__2__m__135737,Vvar__4__v__135739)
                            & p(happ(Vvar__1__P__135727,Vvar__3__x__135738))
                            & Vvar__3___24Anonymous__135731 = cCoq_2eVectors_2eVectorDef_2econs___24a4(Vvar__0__A__135726,Vvar__3__x__135738,Vvar__2__m__135737,Vvar__4__v__135739)
                            & Vvar__2__n__135730 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__2__m__135737) ) ) )
                | ? [Vvar__2__m__135745] :
                    ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__2__m__135745)
                    & ? [Vvar__3__x__135746] :
                        ( t(Vvar__3__x__135746,Vvar__0__A__135726)
                        & ? [Vvar__4__v__135747] :
                            ( cCoq_2eVectors_2eVectorDef_2et___24t(Vvar__0__A__135726,Vvar__2__m__135745,Vvar__4__v__135747)
                            & cCoq_2eVectors_2eVectorDef_2eExists___24a4(Vvar__0__A__135726,Vvar__1__P__135727,Vvar__2__m__135745,Vvar__4__v__135747)
                            & Vvar__3___24Anonymous__135731 = cCoq_2eVectors_2eVectorDef_2econs___24a4(Vvar__0__A__135726,Vvar__3__x__135746,Vvar__2__m__135745,Vvar__4__v__135747)
                            & Vvar__2__n__135730 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__2__m__135745) ) ) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.Vectors.VectorDef.Exists2',axiom,
    ! [Vvar__0__A__135771,Vvar__1__B__135772,Vvar__2__P__135773,Vvar__3__n__135778,Vvar__4___24Anonymous__135779,Vvar__5___24Anonymous__135780] :
      ( cType___24t(Vvar__0__A__135771)
     => ( cType___24t(Vvar__1__B__135772)
       => ( c_24__type__135825___24t(Vvar__0__A__135771,Vvar__1__B__135772,Vvar__2__P__135773,Vvar__3__n__135778,Vvar__4___24Anonymous__135779,Vvar__5___24Anonymous__135780,Vvar__2__P__135773)
         => ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__3__n__135778)
           => ( cCoq_2eVectors_2eVectorDef_2et___24t(Vvar__0__A__135771,Vvar__3__n__135778,Vvar__4___24Anonymous__135779)
             => ( cCoq_2eVectors_2eVectorDef_2et___24t(Vvar__1__B__135772,Vvar__3__n__135778,Vvar__5___24Anonymous__135780)
               => ( cCoq_2eVectors_2eVectorDef_2eExists2___24a6(Vvar__0__A__135771,Vvar__1__B__135772,Vvar__2__P__135773,Vvar__3__n__135778,Vvar__4___24Anonymous__135779,Vvar__5___24Anonymous__135780)
                 => ( ? [Vvar__3__m__135789] :
                        ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__3__m__135789)
                        & ? [Vvar__4__x1__135790] :
                            ( t(Vvar__4__x1__135790,Vvar__0__A__135771)
                            & ? [Vvar__5__x2__135791] :
                                ( t(Vvar__5__x2__135791,Vvar__1__B__135772)
                                & ? [Vvar__6__v1__135792] :
                                    ( cCoq_2eVectors_2eVectorDef_2et___24t(Vvar__0__A__135771,Vvar__3__m__135789,Vvar__6__v1__135792)
                                    & ? [Vvar__7__v2__135793] :
                                        ( cCoq_2eVectors_2eVectorDef_2et___24t(Vvar__1__B__135772,Vvar__3__m__135789,Vvar__7__v2__135793)
                                        & p(happ(happ(Vvar__2__P__135773,Vvar__4__x1__135790),Vvar__5__x2__135791))
                                        & Vvar__5___24Anonymous__135780 = cCoq_2eVectors_2eVectorDef_2econs___24a4(Vvar__1__B__135772,Vvar__5__x2__135791,Vvar__3__m__135789,Vvar__7__v2__135793)
                                        & Vvar__4___24Anonymous__135779 = cCoq_2eVectors_2eVectorDef_2econs___24a4(Vvar__0__A__135771,Vvar__4__x1__135790,Vvar__3__m__135789,Vvar__6__v1__135792)
                                        & Vvar__3__n__135778 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__3__m__135789) ) ) ) ) )
                    | ? [Vvar__3__m__135802] :
                        ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__3__m__135802)
                        & ? [Vvar__4__x1__135803] :
                            ( t(Vvar__4__x1__135803,Vvar__0__A__135771)
                            & ? [Vvar__5__x2__135804] :
                                ( t(Vvar__5__x2__135804,Vvar__1__B__135772)
                                & ? [Vvar__6__v1__135805] :
                                    ( cCoq_2eVectors_2eVectorDef_2et___24t(Vvar__0__A__135771,Vvar__3__m__135802,Vvar__6__v1__135805)
                                    & ? [Vvar__7__v2__135806] :
                                        ( cCoq_2eVectors_2eVectorDef_2et___24t(Vvar__1__B__135772,Vvar__3__m__135802,Vvar__7__v2__135806)
                                        & cCoq_2eVectors_2eVectorDef_2eExists2___24a6(Vvar__0__A__135771,Vvar__1__B__135772,Vvar__2__P__135773,Vvar__3__m__135802,Vvar__6__v1__135805,Vvar__7__v2__135806)
                                        & Vvar__5___24Anonymous__135780 = cCoq_2eVectors_2eVectorDef_2econs___24a4(Vvar__1__B__135772,Vvar__5__x2__135804,Vvar__3__m__135802,Vvar__7__v2__135806)
                                        & Vvar__4___24Anonymous__135779 = cCoq_2eVectors_2eVectorDef_2econs___24a4(Vvar__0__A__135771,Vvar__4__x1__135803,Vvar__3__m__135802,Vvar__6__v1__135805)
                                        & Vvar__3__n__135778 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__3__m__135802) ) ) ) ) ) ) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.Vectors.VectorDef.Forall',axiom,
    ! [Vvar__0__A__85018,Vvar__1__P__85019,Vvar__2__n__85022,Vvar__3__v__85023] :
      ( cType___24t(Vvar__0__A__85018)
     => ( c_24__type__85043___24t(Vvar__0__A__85018,Vvar__1__P__85019,Vvar__2__n__85022,Vvar__3__v__85023,Vvar__1__P__85019)
       => ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__2__n__85022)
         => ( cCoq_2eVectors_2eVectorDef_2et___24t(Vvar__0__A__85018,Vvar__2__n__85022,Vvar__3__v__85023)
           => ( cCoq_2eVectors_2eVectorDef_2eForall___24a4(Vvar__0__A__85018,Vvar__1__P__85019,Vvar__2__n__85022,Vvar__3__v__85023)
             => ( ( Vvar__3__v__85023 = cCoq_2eVectors_2eVectorDef_2enil___24a1(Vvar__0__A__85018)
                  & Vvar__2__n__85022 = cCoq_2eInit_2eDatatypes_2eO )
                | ? [Vvar__2__n__85033] :
                    ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__2__n__85033)
                    & ? [Vvar__3__x__85034] :
                        ( t(Vvar__3__x__85034,Vvar__0__A__85018)
                        & ? [Vvar__4__v__85035] :
                            ( cCoq_2eVectors_2eVectorDef_2et___24t(Vvar__0__A__85018,Vvar__2__n__85033,Vvar__4__v__85035)
                            & p(happ(Vvar__1__P__85019,Vvar__3__x__85034))
                            & cCoq_2eVectors_2eVectorDef_2eForall___24a4(Vvar__0__A__85018,Vvar__1__P__85019,Vvar__2__n__85033,Vvar__4__v__85035)
                            & Vvar__3__v__85023 = cCoq_2eVectors_2eVectorDef_2econs___24a4(Vvar__0__A__85018,Vvar__3__x__85034,Vvar__2__n__85033,Vvar__4__v__85035)
                            & Vvar__2__n__85022 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__2__n__85033) ) ) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.Vectors.VectorDef.Forall2',axiom,
    ! [Vvar__0__A__85065,Vvar__1__B__85066,Vvar__2__P__85067,Vvar__3__n__85072,Vvar__4___24Anonymous__85073,Vvar__5___24Anonymous__85074] :
      ( cType___24t(Vvar__0__A__85065)
     => ( cType___24t(Vvar__1__B__85066)
       => ( c_24__type__85114___24t(Vvar__0__A__85065,Vvar__1__B__85066,Vvar__2__P__85067,Vvar__3__n__85072,Vvar__4___24Anonymous__85073,Vvar__5___24Anonymous__85074,Vvar__2__P__85067)
         => ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__3__n__85072)
           => ( cCoq_2eVectors_2eVectorDef_2et___24t(Vvar__0__A__85065,Vvar__3__n__85072,Vvar__4___24Anonymous__85073)
             => ( cCoq_2eVectors_2eVectorDef_2et___24t(Vvar__1__B__85066,Vvar__3__n__85072,Vvar__5___24Anonymous__85074)
               => ( cCoq_2eVectors_2eVectorDef_2eForall2___24a6(Vvar__0__A__85065,Vvar__1__B__85066,Vvar__2__P__85067,Vvar__3__n__85072,Vvar__4___24Anonymous__85073,Vvar__5___24Anonymous__85074)
                 => ( ( Vvar__5___24Anonymous__85074 = cCoq_2eVectors_2eVectorDef_2enil___24a1(Vvar__1__B__85066)
                      & Vvar__4___24Anonymous__85073 = cCoq_2eVectors_2eVectorDef_2enil___24a1(Vvar__0__A__85065)
                      & Vvar__3__n__85072 = cCoq_2eInit_2eDatatypes_2eO )
                    | ? [Vvar__3__m__85090] :
                        ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__3__m__85090)
                        & ? [Vvar__4__x1__85091] :
                            ( t(Vvar__4__x1__85091,Vvar__0__A__85065)
                            & ? [Vvar__5__x2__85092] :
                                ( t(Vvar__5__x2__85092,Vvar__1__B__85066)
                                & ? [Vvar__6__v1__85093] :
                                    ( cCoq_2eVectors_2eVectorDef_2et___24t(Vvar__0__A__85065,Vvar__3__m__85090,Vvar__6__v1__85093)
                                    & ? [Vvar__7__v2__85094] :
                                        ( cCoq_2eVectors_2eVectorDef_2et___24t(Vvar__1__B__85066,Vvar__3__m__85090,Vvar__7__v2__85094)
                                        & p(happ(happ(Vvar__2__P__85067,Vvar__4__x1__85091),Vvar__5__x2__85092))
                                        & cCoq_2eVectors_2eVectorDef_2eForall2___24a6(Vvar__0__A__85065,Vvar__1__B__85066,Vvar__2__P__85067,Vvar__3__m__85090,Vvar__6__v1__85093,Vvar__7__v2__85094)
                                        & Vvar__5___24Anonymous__85074 = cCoq_2eVectors_2eVectorDef_2econs___24a4(Vvar__1__B__85066,Vvar__5__x2__85092,Vvar__3__m__85090,Vvar__7__v2__85094)
                                        & Vvar__4___24Anonymous__85073 = cCoq_2eVectors_2eVectorDef_2econs___24a4(Vvar__0__A__85065,Vvar__4__x1__85091,Vvar__3__m__85090,Vvar__6__v1__85093)
                                        & Vvar__3__n__85072 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__3__m__85090) ) ) ) ) ) ) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.Vectors.VectorDef.In',axiom,
    ! [Vvar__0__A__135756,Vvar__1__a__135757,Vvar__2__n__135758,Vvar__3___24Anonymous__135759] :
      ( cType___24t(Vvar__0__A__135756)
     => ( t(Vvar__1__a__135757,Vvar__0__A__135756)
       => ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__2__n__135758)
         => ( cCoq_2eVectors_2eVectorDef_2et___24t(Vvar__0__A__135756,Vvar__2__n__135758,Vvar__3___24Anonymous__135759)
           => ( cCoq_2eVectors_2eVectorDef_2eIn___24a4(Vvar__0__A__135756,Vvar__1__a__135757,Vvar__2__n__135758,Vvar__3___24Anonymous__135759)
             => ( ? [Vvar__2__m__135763] :
                    ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__2__m__135763)
                    & ? [Vvar__3__v__135764] :
                        ( cCoq_2eVectors_2eVectorDef_2et___24t(Vvar__0__A__135756,Vvar__2__m__135763,Vvar__3__v__135764)
                        & Vvar__3___24Anonymous__135759 = cCoq_2eVectors_2eVectorDef_2econs___24a4(Vvar__0__A__135756,Vvar__1__a__135757,Vvar__2__m__135763,Vvar__3__v__135764)
                        & Vvar__2__n__135758 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__2__m__135763) ) )
                | ? [Vvar__2__m__135767] :
                    ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__2__m__135767)
                    & ? [Vvar__3__x__135768] :
                        ( t(Vvar__3__x__135768,Vvar__0__A__135756)
                        & ? [Vvar__4__v__135769] :
                            ( cCoq_2eVectors_2eVectorDef_2et___24t(Vvar__0__A__135756,Vvar__2__m__135767,Vvar__4__v__135769)
                            & cCoq_2eVectors_2eVectorDef_2eIn___24a4(Vvar__0__A__135756,Vvar__1__a__135757,Vvar__2__m__135767,Vvar__4__v__135769)
                            & Vvar__3___24Anonymous__135759 = cCoq_2eVectors_2eVectorDef_2econs___24a4(Vvar__0__A__135756,Vvar__3__x__135768,Vvar__2__m__135767,Vvar__4__v__135769)
                            & Vvar__2__n__135758 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__2__m__135767) ) ) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.Vectors.VectorDef.t',axiom,
    ! [Vvar__0__A__3835,Vvar__1___24Anonymous__3836,VX3837] :
      ( cType___24t(Vvar__0__A__3835)
     => ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__1___24Anonymous__3836)
       => ( cCoq_2eVectors_2eVectorDef_2et___24t(Vvar__0__A__3835,Vvar__1___24Anonymous__3836,VX3837)
         => ( ( Vvar__1___24Anonymous__3836 = cCoq_2eInit_2eDatatypes_2eO
              & VX3837 = cCoq_2eVectors_2eVectorDef_2enil___24a1(Vvar__0__A__3835) )
            | ? [Vvar__1__h__3840] :
                ( t(Vvar__1__h__3840,Vvar__0__A__3835)
                & ? [Vvar__2__n__3841] :
                    ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__2__n__3841)
                    & ? [Vvar__3___24Anonymous__3842] :
                        ( cCoq_2eVectors_2eVectorDef_2et___24t(Vvar__0__A__3835,Vvar__2__n__3841,Vvar__3___24Anonymous__3842)
                        & Vvar__1___24Anonymous__3836 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__2__n__3841)
                        & VX3837 = cCoq_2eVectors_2eVectorDef_2econs___24a4(Vvar__0__A__3835,Vvar__1__h__3840,Vvar__2__n__3841,Vvar__3___24Anonymous__3842) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.ZArith.Znumtheory.Bezout',axiom,
    ! [Vvar__0__a__149747,Vvar__1__b__149748,Vvar__2__d__149749] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__0__a__149747)
     => ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__1__b__149748)
       => ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__2__d__149749)
         => ( cCoq_2eZArith_2eZnumtheory_2eBezout___24a3(Vvar__0__a__149747,Vvar__1__b__149748,Vvar__2__d__149749)
           => ? [Vvar__3__u__149754] :
                ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__3__u__149754)
                & ? [Vvar__4__v__149755] :
                    ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__4__v__149755)
                    & cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(Vvar__3__u__149754,Vvar__0__a__149747),cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(Vvar__4__v__149755,Vvar__1__b__149748)) = Vvar__2__d__149749
                    & p(c_24True) ) ) ) ) ) ) ).

fof('$_inversion_Coq.ZArith.Znumtheory.Euclid',axiom,
    ! [Vvar__0__a__143422,Vvar__1__b__143423,VX143424] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__0__a__143422)
     => ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__1__b__143423)
       => ( cCoq_2eZArith_2eZnumtheory_2eEuclid___24t(Vvar__0__a__143422,Vvar__1__b__143423,VX143424)
         => ? [Vvar__2__u__143427] :
              ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__2__u__143427)
              & ? [Vvar__3__v__143428] :
                  ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__3__v__143428)
                  & ? [Vvar__4__d__143429] :
                      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__4__d__143429)
                      & cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(Vvar__2__u__143427,Vvar__0__a__143422),cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(Vvar__3__v__143428,Vvar__1__b__143423)) = Vvar__4__d__143429
                      & cCoq_2eZArith_2eZnumtheory_2eZis__gcd___24a3(Vvar__0__a__143422,Vvar__1__b__143423,Vvar__4__d__143429)
                      & VX143424 = cCoq_2eZArith_2eZnumtheory_2eEuclid__intro___24a5(Vvar__0__a__143422,Vvar__1__b__143423,Vvar__2__u__143427,Vvar__3__v__143428,Vvar__4__d__143429) ) ) ) ) ) ) ).

fof('$_inversion_Coq.ZArith.Znumtheory.Zis_gcd',axiom,
    ! [Vvar__0__a__143391,Vvar__1__b__143392,Vvar__2__g__143393] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__0__a__143391)
     => ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__1__b__143392)
       => ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__2__g__143393)
         => ( cCoq_2eZArith_2eZnumtheory_2eZis__gcd___24a3(Vvar__0__a__143391,Vvar__1__b__143392,Vvar__2__g__143393)
           => ( cCoq_2eZArith_2eBinInt_2eZ_2edivide___24a2(Vvar__2__g__143393,Vvar__0__a__143391)
              & cCoq_2eZArith_2eBinInt_2eZ_2edivide___24a2(Vvar__2__g__143393,Vvar__1__b__143392)
              & ! [Vvar__var__var__var__var__5__x__143401__143404__143407__143410__143413] :
                  ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__var__var__var__var__5__x__143401__143404__143407__143410__143413)
                 => ( cCoq_2eZArith_2eBinInt_2eZ_2edivide___24a2(Vvar__var__var__var__var__5__x__143401__143404__143407__143410__143413,Vvar__0__a__143391)
                   => ( cCoq_2eZArith_2eBinInt_2eZ_2edivide___24a2(Vvar__var__var__var__var__5__x__143401__143404__143407__143410__143413,Vvar__1__b__143392)
                     => cCoq_2eZArith_2eBinInt_2eZ_2edivide___24a2(Vvar__var__var__var__var__5__x__143401__143404__143407__143410__143413,Vvar__2__g__143393) ) ) )
              & p(c_24True) ) ) ) ) ) ).

fof('$_inversion_Coq.ZArith.Znumtheory.prime',axiom,
    ! [Vvar__0__p__143471] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__0__p__143471)
     => ( cCoq_2eZArith_2eZnumtheory_2eprime___24a1(Vvar__0__p__143471)
       => ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH),Vvar__0__p__143471))
          & ! [Vvar__var__var__2__n__143476__143478__143480] :
              ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__var__var__2__n__143476__143478__143480)
             => ( ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH),Vvar__var__var__2__n__143476__143478__143480))
                  & p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(Vvar__var__var__2__n__143476__143478__143480,Vvar__0__p__143471)) )
               => cCoq_2eZArith_2eZnumtheory_2erel__prime___24a2(Vvar__var__var__2__n__143476__143478__143480,Vvar__0__p__143471) ) )
          & p(c_24True) ) ) ) ).

fof('$_inversion_Coq.ZArith.Zpower.Zdiv_rest_proofs',axiom,
    ! [Vvar__0__x__149757,Vvar__1__p__149758,VX149759] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__0__x__149757)
     => ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1__p__149758)
       => ( cCoq_2eZArith_2eZpower_2eZdiv__rest__proofs___24t(Vvar__0__x__149757,Vvar__1__p__149758,VX149759)
         => ? [Vvar__2__q__149762] :
              ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__2__q__149762)
              & ? [Vvar__3__r__149763] :
                  ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__3__r__149763)
                  & Vvar__0__x__149757 = cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(Vvar__2__q__149762,cCoq_2eZArith_2eZpower_2etwo__power__pos___24a1(Vvar__1__p__149758)),Vvar__3__r__149763)
                  & p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,Vvar__3__r__149763))
                  & p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(Vvar__3__r__149763,cCoq_2eZArith_2eZpower_2etwo__power__pos___24a1(Vvar__1__p__149758)))
                  & VX149759 = cCoq_2eZArith_2eZpower_2eZdiv__rest__proof___24a4(Vvar__0__x__149757,Vvar__1__p__149758,Vvar__2__q__149762,Vvar__3__r__149763) ) ) ) ) ) ).

fof('$_inversion_Coq.micromega.DeclConstant.DeclaredConstant',axiom,
    ! [Vvar__0__T__124047,Vvar__1__F__124048] :
      ( cType___24t(Vvar__0__T__124047)
     => ( t(Vvar__1__F__124048,Vvar__0__T__124047)
       => ( cCoq_2emicromega_2eDeclConstant_2eDeclaredConstant___24a2(Vvar__0__T__124047,Vvar__1__F__124048)
         => p(c_24True) ) ) ) ).

fof('$_inversion_Coq.micromega.DeclConstant.GT',axiom,
    ! [Vvar__0__T__145742,Vvar__1__F__145743] :
      ( cType___24t(Vvar__0__T__145742)
     => ( t(Vvar__1__F__145743,Vvar__0__T__145742)
       => ( cCoq_2emicromega_2eDeclConstant_2eGT___24a2(Vvar__0__T__145742,Vvar__1__F__145743)
         => p(c_24True) ) ) ) ).

fof('$_inversion_Coq.micromega.EnvRing.Mon',axiom,
    ! [VX124269] :
      ( cCoq_2emicromega_2eEnvRing_2eMon___24t(VX124269)
     => ( VX124269 = cCoq_2emicromega_2eEnvRing_2emon0
        | ? [Vvar__0___24Anonymous__124270] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__124270)
            & ? [Vvar__1___24Anonymous__124271] :
                ( cCoq_2emicromega_2eEnvRing_2eMon___24t(Vvar__1___24Anonymous__124271)
                & VX124269 = cCoq_2emicromega_2eEnvRing_2ezmon___24a2(Vvar__0___24Anonymous__124270,Vvar__1___24Anonymous__124271) ) )
        | ? [Vvar__0___24Anonymous__124272] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__124272)
            & ? [Vvar__1___24Anonymous__124273] :
                ( cCoq_2emicromega_2eEnvRing_2eMon___24t(Vvar__1___24Anonymous__124273)
                & VX124269 = cCoq_2emicromega_2eEnvRing_2evmon___24a2(Vvar__0___24Anonymous__124272,Vvar__1___24Anonymous__124273) ) ) ) ) ).

fof('$_inversion_Coq.micromega.EnvRing.PExpr',axiom,
    ! [Vvar__0__C__124055,VX124056] :
      ( cType___24t(Vvar__0__C__124055)
     => ( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__C__124055,VX124056)
       => ( ? [Vvar__1___24Anonymous__124058] :
              ( t(Vvar__1___24Anonymous__124058,Vvar__0__C__124055)
              & VX124056 = cCoq_2emicromega_2eEnvRing_2ePEc___24a2(Vvar__0__C__124055,Vvar__1___24Anonymous__124058) )
          | ? [Vvar__1___24Anonymous__124060] :
              ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__124060)
              & VX124056 = cCoq_2emicromega_2eEnvRing_2ePEX___24a2(Vvar__0__C__124055,Vvar__1___24Anonymous__124060) )
          | ? [Vvar__1___24Anonymous__124062] :
              ( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__C__124055,Vvar__1___24Anonymous__124062)
              & ? [Vvar__2___24Anonymous__124063] :
                  ( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__C__124055,Vvar__2___24Anonymous__124063)
                  & VX124056 = cCoq_2emicromega_2eEnvRing_2ePEadd___24a3(Vvar__0__C__124055,Vvar__1___24Anonymous__124062,Vvar__2___24Anonymous__124063) ) )
          | ? [Vvar__1___24Anonymous__124065] :
              ( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__C__124055,Vvar__1___24Anonymous__124065)
              & ? [Vvar__2___24Anonymous__124066] :
                  ( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__C__124055,Vvar__2___24Anonymous__124066)
                  & VX124056 = cCoq_2emicromega_2eEnvRing_2ePEsub___24a3(Vvar__0__C__124055,Vvar__1___24Anonymous__124065,Vvar__2___24Anonymous__124066) ) )
          | ? [Vvar__1___24Anonymous__124068] :
              ( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__C__124055,Vvar__1___24Anonymous__124068)
              & ? [Vvar__2___24Anonymous__124069] :
                  ( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__C__124055,Vvar__2___24Anonymous__124069)
                  & VX124056 = cCoq_2emicromega_2eEnvRing_2ePEmul___24a3(Vvar__0__C__124055,Vvar__1___24Anonymous__124068,Vvar__2___24Anonymous__124069) ) )
          | ? [Vvar__1___24Anonymous__124071] :
              ( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__C__124055,Vvar__1___24Anonymous__124071)
              & VX124056 = cCoq_2emicromega_2eEnvRing_2ePEopp___24a2(Vvar__0__C__124055,Vvar__1___24Anonymous__124071) )
          | ? [Vvar__1___24Anonymous__124073] :
              ( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__C__124055,Vvar__1___24Anonymous__124073)
              & ? [Vvar__2___24Anonymous__124074] :
                  ( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__2___24Anonymous__124074)
                  & VX124056 = cCoq_2emicromega_2eEnvRing_2ePEpow___24a3(Vvar__0__C__124055,Vvar__1___24Anonymous__124073,Vvar__2___24Anonymous__124074) ) ) ) ) ) ).

fof('$_inversion_Coq.micromega.EnvRing.Pol',axiom,
    ! [Vvar__0__C__124219,VX124220] :
      ( cType___24t(Vvar__0__C__124219)
     => ( cCoq_2emicromega_2eEnvRing_2ePol___24t(Vvar__0__C__124219,VX124220)
       => ( ? [Vvar__1___24Anonymous__124222] :
              ( t(Vvar__1___24Anonymous__124222,Vvar__0__C__124219)
              & VX124220 = cCoq_2emicromega_2eEnvRing_2ePc___24a2(Vvar__0__C__124219,Vvar__1___24Anonymous__124222) )
          | ? [Vvar__1___24Anonymous__124224] :
              ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__124224)
              & ? [Vvar__2___24Anonymous__124225] :
                  ( cCoq_2emicromega_2eEnvRing_2ePol___24t(Vvar__0__C__124219,Vvar__2___24Anonymous__124225)
                  & VX124220 = cCoq_2emicromega_2eEnvRing_2ePinj___24a3(Vvar__0__C__124219,Vvar__1___24Anonymous__124224,Vvar__2___24Anonymous__124225) ) )
          | ? [Vvar__1___24Anonymous__124227] :
              ( cCoq_2emicromega_2eEnvRing_2ePol___24t(Vvar__0__C__124219,Vvar__1___24Anonymous__124227)
              & ? [Vvar__2___24Anonymous__124228] :
                  ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2___24Anonymous__124228)
                  & ? [Vvar__3___24Anonymous__124229] :
                      ( cCoq_2emicromega_2eEnvRing_2ePol___24t(Vvar__0__C__124219,Vvar__3___24Anonymous__124229)
                      & VX124220 = cCoq_2emicromega_2eEnvRing_2ePX___24a4(Vvar__0__C__124219,Vvar__1___24Anonymous__124227,Vvar__2___24Anonymous__124228,Vvar__3___24Anonymous__124229) ) ) ) ) ) ) ).

fof('$_inversion_Coq.micromega.OrderedRing.SOR',axiom,
    ! [Vvar__0__R__125149,Vvar__1__rO__125150,Vvar__2__rI__125151,Vvar__3__rplus__125152,Vvar__4__rtimes__125157,Vvar__5__rminus__125162,Vvar__6__ropp__125167,Vvar__7__req__125170,Vvar__8__rle__125175,Vvar__9__rlt__125180] :
      ( cType___24t(Vvar__0__R__125149)
     => ( t(Vvar__1__rO__125150,Vvar__0__R__125149)
       => ( t(Vvar__2__rI__125151,Vvar__0__R__125149)
         => ( c_24__type__125581___24t(Vvar__0__R__125149,Vvar__1__rO__125150,Vvar__2__rI__125151,Vvar__3__rplus__125152,Vvar__4__rtimes__125157,Vvar__5__rminus__125162,Vvar__6__ropp__125167,Vvar__7__req__125170,Vvar__8__rle__125175,Vvar__9__rlt__125180,Vvar__3__rplus__125152)
           => ( c_24__type__125682___24t(Vvar__0__R__125149,Vvar__1__rO__125150,Vvar__2__rI__125151,Vvar__3__rplus__125152,Vvar__4__rtimes__125157,Vvar__5__rminus__125162,Vvar__6__ropp__125167,Vvar__7__req__125170,Vvar__8__rle__125175,Vvar__9__rlt__125180,Vvar__4__rtimes__125157)
             => ( c_24__type__125783___24t(Vvar__0__R__125149,Vvar__1__rO__125150,Vvar__2__rI__125151,Vvar__3__rplus__125152,Vvar__4__rtimes__125157,Vvar__5__rminus__125162,Vvar__6__ropp__125167,Vvar__7__req__125170,Vvar__8__rle__125175,Vvar__9__rlt__125180,Vvar__5__rminus__125162)
               => ( c_24__type__125873___24t(Vvar__0__R__125149,Vvar__1__rO__125150,Vvar__2__rI__125151,Vvar__3__rplus__125152,Vvar__4__rtimes__125157,Vvar__5__rminus__125162,Vvar__6__ropp__125167,Vvar__7__req__125170,Vvar__8__rle__125175,Vvar__9__rlt__125180,Vvar__6__ropp__125167)
                 => ( c_24__type__125974___24t(Vvar__0__R__125149,Vvar__1__rO__125150,Vvar__2__rI__125151,Vvar__3__rplus__125152,Vvar__4__rtimes__125157,Vvar__5__rminus__125162,Vvar__6__ropp__125167,Vvar__7__req__125170,Vvar__8__rle__125175,Vvar__9__rlt__125180,Vvar__7__req__125170)
                   => ( c_24__type__126075___24t(Vvar__0__R__125149,Vvar__1__rO__125150,Vvar__2__rI__125151,Vvar__3__rplus__125152,Vvar__4__rtimes__125157,Vvar__5__rminus__125162,Vvar__6__ropp__125167,Vvar__7__req__125170,Vvar__8__rle__125175,Vvar__9__rlt__125180,Vvar__8__rle__125175)
                     => ( c_24__type__126176___24t(Vvar__0__R__125149,Vvar__1__rO__125150,Vvar__2__rI__125151,Vvar__3__rplus__125152,Vvar__4__rtimes__125157,Vvar__5__rminus__125162,Vvar__6__ropp__125167,Vvar__7__req__125170,Vvar__8__rle__125175,Vvar__9__rlt__125180,Vvar__9__rlt__125180)
                       => ( cCoq_2emicromega_2eOrderedRing_2eSOR___24a10(Vvar__0__R__125149,Vvar__1__rO__125150,Vvar__2__rI__125151,Vvar__3__rplus__125152,Vvar__4__rtimes__125157,Vvar__5__rminus__125162,Vvar__6__ropp__125167,Vvar__7__req__125170,Vvar__8__rle__125175,Vvar__9__rlt__125180)
                         => ( cCoq_2eSetoids_2eSetoid_2eSetoid__Theory___24a2(Vvar__0__R__125149,Vvar__7__req__125170)
                            & ! [Vvar__var__var__var__var__11__x1__125224__125230__125335__125341__125347] :
                                ( t(Vvar__var__var__var__var__11__x1__125224__125230__125335__125341__125347,Vvar__0__R__125149)
                               => ! [Vvar__var__var__var__var__12__x2__125225__125231__125336__125342__125348] :
                                    ( t(Vvar__var__var__var__var__12__x2__125225__125231__125336__125342__125348,Vvar__0__R__125149)
                                   => ( p(happ(happ(Vvar__7__req__125170,Vvar__var__var__var__var__11__x1__125224__125230__125335__125341__125347),Vvar__var__var__var__var__12__x2__125225__125231__125336__125342__125348))
                                     => ! [Vvar__var__var__var__var__14__y1__125226__125232__125337__125343__125349] :
                                          ( t(Vvar__var__var__var__var__14__y1__125226__125232__125337__125343__125349,Vvar__0__R__125149)
                                         => ! [Vvar__var__var__var__var__15__y2__125227__125233__125338__125344__125350] :
                                              ( t(Vvar__var__var__var__var__15__y2__125227__125233__125338__125344__125350,Vvar__0__R__125149)
                                             => ( p(happ(happ(Vvar__7__req__125170,Vvar__var__var__var__var__14__y1__125226__125232__125337__125343__125349),Vvar__var__var__var__var__15__y2__125227__125233__125338__125344__125350))
                                               => p(happ(happ(Vvar__7__req__125170,happ(happ(Vvar__3__rplus__125152,Vvar__var__var__var__var__11__x1__125224__125230__125335__125341__125347),Vvar__var__var__var__var__14__y1__125226__125232__125337__125343__125349)),happ(happ(Vvar__3__rplus__125152,Vvar__var__var__var__var__12__x2__125225__125231__125336__125342__125348),Vvar__var__var__var__var__15__y2__125227__125233__125338__125344__125350))) ) ) ) ) ) )
                            & ! [Vvar__var__var__var__var__12__x1__125237__125243__125353__125359__125365] :
                                ( t(Vvar__var__var__var__var__12__x1__125237__125243__125353__125359__125365,Vvar__0__R__125149)
                               => ! [Vvar__var__var__var__var__13__x2__125238__125244__125354__125360__125366] :
                                    ( t(Vvar__var__var__var__var__13__x2__125238__125244__125354__125360__125366,Vvar__0__R__125149)
                                   => ( p(happ(happ(Vvar__7__req__125170,Vvar__var__var__var__var__12__x1__125237__125243__125353__125359__125365),Vvar__var__var__var__var__13__x2__125238__125244__125354__125360__125366))
                                     => ! [Vvar__var__var__var__var__15__y1__125239__125245__125355__125361__125367] :
                                          ( t(Vvar__var__var__var__var__15__y1__125239__125245__125355__125361__125367,Vvar__0__R__125149)
                                         => ! [Vvar__var__var__var__var__16__y2__125240__125246__125356__125362__125368] :
                                              ( t(Vvar__var__var__var__var__16__y2__125240__125246__125356__125362__125368,Vvar__0__R__125149)
                                             => ( p(happ(happ(Vvar__7__req__125170,Vvar__var__var__var__var__15__y1__125239__125245__125355__125361__125367),Vvar__var__var__var__var__16__y2__125240__125246__125356__125362__125368))
                                               => p(happ(happ(Vvar__7__req__125170,happ(happ(Vvar__4__rtimes__125157,Vvar__var__var__var__var__12__x1__125237__125243__125353__125359__125365),Vvar__var__var__var__var__15__y1__125239__125245__125355__125361__125367)),happ(happ(Vvar__4__rtimes__125157,Vvar__var__var__var__var__13__x2__125238__125244__125354__125360__125366),Vvar__var__var__var__var__16__y2__125240__125246__125356__125362__125368))) ) ) ) ) ) )
                            & ! [Vvar__var__var__var__var__13__x1__125250__125253__125371__125374__125377] :
                                ( t(Vvar__var__var__var__var__13__x1__125250__125253__125371__125374__125377,Vvar__0__R__125149)
                               => ! [Vvar__var__var__var__var__14__x2__125251__125254__125372__125375__125378] :
                                    ( t(Vvar__var__var__var__var__14__x2__125251__125254__125372__125375__125378,Vvar__0__R__125149)
                                   => ( p(happ(happ(Vvar__7__req__125170,Vvar__var__var__var__var__13__x1__125250__125253__125371__125374__125377),Vvar__var__var__var__var__14__x2__125251__125254__125372__125375__125378))
                                     => p(happ(happ(Vvar__7__req__125170,happ(Vvar__6__ropp__125167,Vvar__var__var__var__var__13__x1__125250__125253__125371__125374__125377)),happ(Vvar__6__ropp__125167,Vvar__var__var__var__var__14__x2__125251__125254__125372__125375__125378))) ) ) )
                            & ! [Vvar__var__var__var__var__14__x1__125257__125263__125380__125386__125392] :
                                ( t(Vvar__var__var__var__var__14__x1__125257__125263__125380__125386__125392,Vvar__0__R__125149)
                               => ! [Vvar__var__var__var__var__15__x2__125258__125264__125381__125387__125393] :
                                    ( t(Vvar__var__var__var__var__15__x2__125258__125264__125381__125387__125393,Vvar__0__R__125149)
                                   => ( p(happ(happ(Vvar__7__req__125170,Vvar__var__var__var__var__14__x1__125257__125263__125380__125386__125392),Vvar__var__var__var__var__15__x2__125258__125264__125381__125387__125393))
                                     => ! [Vvar__var__var__var__var__17__y1__125259__125265__125382__125388__125394] :
                                          ( t(Vvar__var__var__var__var__17__y1__125259__125265__125382__125388__125394,Vvar__0__R__125149)
                                         => ! [Vvar__var__var__var__var__18__y2__125260__125266__125383__125389__125395] :
                                              ( t(Vvar__var__var__var__var__18__y2__125260__125266__125383__125389__125395,Vvar__0__R__125149)
                                             => ( p(happ(happ(Vvar__7__req__125170,Vvar__var__var__var__var__17__y1__125259__125265__125382__125388__125394),Vvar__var__var__var__var__18__y2__125260__125266__125383__125389__125395))
                                               => ( p(happ(happ(Vvar__8__rle__125175,Vvar__var__var__var__var__14__x1__125257__125263__125380__125386__125392),Vvar__var__var__var__var__17__y1__125259__125265__125382__125388__125394))
                                                <=> p(happ(happ(Vvar__8__rle__125175,Vvar__var__var__var__var__15__x2__125258__125264__125381__125387__125393),Vvar__var__var__var__var__18__y2__125260__125266__125383__125389__125395)) ) ) ) ) ) ) )
                            & ! [Vvar__var__var__var__var__15__x1__125270__125276__125398__125404__125410] :
                                ( t(Vvar__var__var__var__var__15__x1__125270__125276__125398__125404__125410,Vvar__0__R__125149)
                               => ! [Vvar__var__var__var__var__16__x2__125271__125277__125399__125405__125411] :
                                    ( t(Vvar__var__var__var__var__16__x2__125271__125277__125399__125405__125411,Vvar__0__R__125149)
                                   => ( p(happ(happ(Vvar__7__req__125170,Vvar__var__var__var__var__15__x1__125270__125276__125398__125404__125410),Vvar__var__var__var__var__16__x2__125271__125277__125399__125405__125411))
                                     => ! [Vvar__var__var__var__var__18__y1__125272__125278__125400__125406__125412] :
                                          ( t(Vvar__var__var__var__var__18__y1__125272__125278__125400__125406__125412,Vvar__0__R__125149)
                                         => ! [Vvar__var__var__var__var__19__y2__125273__125279__125401__125407__125413] :
                                              ( t(Vvar__var__var__var__var__19__y2__125273__125279__125401__125407__125413,Vvar__0__R__125149)
                                             => ( p(happ(happ(Vvar__7__req__125170,Vvar__var__var__var__var__18__y1__125272__125278__125400__125406__125412),Vvar__var__var__var__var__19__y2__125273__125279__125401__125407__125413))
                                               => ( p(happ(happ(Vvar__9__rlt__125180,Vvar__var__var__var__var__15__x1__125270__125276__125398__125404__125410),Vvar__var__var__var__var__18__y1__125272__125278__125400__125406__125412))
                                                <=> p(happ(happ(Vvar__9__rlt__125180,Vvar__var__var__var__var__16__x2__125271__125277__125399__125405__125411),Vvar__var__var__var__var__19__y2__125273__125279__125401__125407__125413)) ) ) ) ) ) ) )
                            & cCoq_2esetoid__ring_2eRing__theory_2ering__theory___24a8(Vvar__0__R__125149,Vvar__1__rO__125150,Vvar__2__rI__125151,Vvar__3__rplus__125152,Vvar__4__rtimes__125157,Vvar__5__rminus__125162,Vvar__6__ropp__125167,Vvar__7__req__125170)
                            & ! [Vvar__var__var__var__17__n__125284__125285__125416__125417] :
                                ( t(Vvar__var__var__var__17__n__125284__125285__125416__125417,Vvar__0__R__125149)
                               => p(happ(happ(Vvar__8__rle__125175,Vvar__var__var__var__17__n__125284__125285__125416__125417),Vvar__var__var__var__17__n__125284__125285__125416__125417)) )
                            & ! [Vvar__var__var__var__var__18__n__125287__125291__125418__125422__125426] :
                                ( t(Vvar__var__var__var__var__18__n__125287__125291__125418__125422__125426,Vvar__0__R__125149)
                               => ! [Vvar__var__var__var__var__19__m__125288__125292__125419__125423__125427] :
                                    ( t(Vvar__var__var__var__var__19__m__125288__125292__125419__125423__125427,Vvar__0__R__125149)
                                   => ( p(happ(happ(Vvar__8__rle__125175,Vvar__var__var__var__var__18__n__125287__125291__125418__125422__125426),Vvar__var__var__var__var__19__m__125288__125292__125419__125423__125427))
                                     => ( p(happ(happ(Vvar__8__rle__125175,Vvar__var__var__var__var__19__m__125288__125292__125419__125423__125427),Vvar__var__var__var__var__18__n__125287__125291__125418__125422__125426))
                                       => p(happ(happ(Vvar__7__req__125170,Vvar__var__var__var__var__18__n__125287__125291__125418__125422__125426),Vvar__var__var__var__var__19__m__125288__125292__125419__125423__125427)) ) ) ) )
                            & ! [Vvar__var__var__var__19__n__125296__125301__125430__125435] :
                                ( t(Vvar__var__var__var__19__n__125296__125301__125430__125435,Vvar__0__R__125149)
                               => ! [Vvar__var__var__var__20__m__125297__125302__125431__125436] :
                                    ( t(Vvar__var__var__var__20__m__125297__125302__125431__125436,Vvar__0__R__125149)
                                   => ! [Vvar__var__var__var__21__p__125298__125303__125432__125437] :
                                        ( t(Vvar__var__var__var__21__p__125298__125303__125432__125437,Vvar__0__R__125149)
                                       => ( p(happ(happ(Vvar__8__rle__125175,Vvar__var__var__var__19__n__125296__125301__125430__125435),Vvar__var__var__var__20__m__125297__125302__125431__125436))
                                         => ( p(happ(happ(Vvar__8__rle__125175,Vvar__var__var__var__20__m__125297__125302__125431__125436),Vvar__var__var__var__21__p__125298__125303__125432__125437))
                                           => p(happ(happ(Vvar__8__rle__125175,Vvar__var__var__var__19__n__125296__125301__125430__125435),Vvar__var__var__var__21__p__125298__125303__125432__125437)) ) ) ) ) )
                            & ! [Vvar__var__var__var__var__var__20__n__125307__125309__125440__125442__125444__125446] :
                                ( t(Vvar__var__var__var__var__var__20__n__125307__125309__125440__125442__125444__125446,Vvar__0__R__125149)
                               => ! [Vvar__var__var__var__var__var__21__m__125308__125310__125441__125443__125445__125447] :
                                    ( t(Vvar__var__var__var__var__var__21__m__125308__125310__125441__125443__125445__125447,Vvar__0__R__125149)
                                   => ( p(happ(happ(Vvar__9__rlt__125180,Vvar__var__var__var__var__var__20__n__125307__125309__125440__125442__125444__125446),Vvar__var__var__var__var__var__21__m__125308__125310__125441__125443__125445__125447))
                                    <=> ( p(happ(happ(Vvar__8__rle__125175,Vvar__var__var__var__var__var__20__n__125307__125309__125440__125442__125444__125446),Vvar__var__var__var__var__var__21__m__125308__125310__125441__125443__125445__125447))
                                        & ~ p(happ(happ(Vvar__7__req__125170,Vvar__var__var__var__var__var__20__n__125307__125309__125440__125442__125444__125446),Vvar__var__var__var__var__var__21__m__125308__125310__125441__125443__125445__125447)) ) ) ) )
                            & ! [Vvar__var__var__var__var__21__n__125312__125314__125448__125450__125452] :
                                ( t(Vvar__var__var__var__var__21__n__125312__125314__125448__125450__125452,Vvar__0__R__125149)
                               => ! [Vvar__var__var__var__var__22__m__125313__125315__125449__125451__125453] :
                                    ( t(Vvar__var__var__var__var__22__m__125313__125315__125449__125451__125453,Vvar__0__R__125149)
                                   => ( p(happ(happ(Vvar__9__rlt__125180,Vvar__var__var__var__var__21__n__125312__125314__125448__125450__125452),Vvar__var__var__var__var__22__m__125313__125315__125449__125451__125453))
                                      | p(happ(happ(Vvar__7__req__125170,Vvar__var__var__var__var__21__n__125312__125314__125448__125450__125452),Vvar__var__var__var__var__22__m__125313__125315__125449__125451__125453))
                                      | p(happ(happ(Vvar__9__rlt__125180,Vvar__var__var__var__var__22__m__125313__125315__125449__125451__125453),Vvar__var__var__var__var__21__n__125312__125314__125448__125450__125452)) ) ) )
                            & ! [Vvar__var__var__var__var__22__n__125317__125321__125454__125458__125462] :
                                ( t(Vvar__var__var__var__var__22__n__125317__125321__125454__125458__125462,Vvar__0__R__125149)
                               => ! [Vvar__var__var__var__var__23__m__125318__125322__125455__125459__125463] :
                                    ( t(Vvar__var__var__var__var__23__m__125318__125322__125455__125459__125463,Vvar__0__R__125149)
                                   => ! [Vvar__var__var__var__var__24__p__125319__125323__125456__125460__125464] :
                                        ( t(Vvar__var__var__var__var__24__p__125319__125323__125456__125460__125464,Vvar__0__R__125149)
                                       => ( p(happ(happ(Vvar__8__rle__125175,Vvar__var__var__var__var__22__n__125317__125321__125454__125458__125462),Vvar__var__var__var__var__23__m__125318__125322__125455__125459__125463))
                                         => p(happ(happ(Vvar__8__rle__125175,happ(happ(Vvar__3__rplus__125152,Vvar__var__var__var__var__24__p__125319__125323__125456__125460__125464),Vvar__var__var__var__var__22__n__125317__125321__125454__125458__125462)),happ(happ(Vvar__3__rplus__125152,Vvar__var__var__var__var__24__p__125319__125323__125456__125460__125464),Vvar__var__var__var__var__23__m__125318__125322__125455__125459__125463))) ) ) ) )
                            & ! [Vvar__var__var__var__var__var__23__n__125326__125330__125466__125470__125474__125478] :
                                ( t(Vvar__var__var__var__var__var__23__n__125326__125330__125466__125470__125474__125478,Vvar__0__R__125149)
                               => ! [Vvar__var__var__var__var__var__24__m__125327__125331__125467__125471__125475__125479] :
                                    ( t(Vvar__var__var__var__var__var__24__m__125327__125331__125467__125471__125475__125479,Vvar__0__R__125149)
                                   => ( p(happ(happ(Vvar__9__rlt__125180,Vvar__1__rO__125150),Vvar__var__var__var__var__var__23__n__125326__125330__125466__125470__125474__125478))
                                     => ( p(happ(happ(Vvar__9__rlt__125180,Vvar__1__rO__125150),Vvar__var__var__var__var__var__24__m__125327__125331__125467__125471__125475__125479))
                                       => p(happ(happ(Vvar__9__rlt__125180,Vvar__1__rO__125150),happ(happ(Vvar__4__rtimes__125157,Vvar__var__var__var__var__var__23__n__125326__125330__125466__125470__125474__125478),Vvar__var__var__var__var__var__24__m__125327__125331__125467__125471__125475__125479))) ) ) ) )
                            & ~ p(happ(happ(Vvar__7__req__125170,Vvar__1__rO__125150),Vvar__2__rI__125151))
                            & p(c_24True) ) ) ) ) ) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.micromega.RMicromega.Rcst',axiom,
    ! [VX122187] :
      ( cCoq_2emicromega_2eRMicromega_2eRcst___24t(VX122187)
     => ( VX122187 = cCoq_2emicromega_2eRMicromega_2eC0
        | VX122187 = cCoq_2emicromega_2eRMicromega_2eC1
        | ? [Vvar__0__r__122188] :
            ( cCoq_2eQArith_2eQArith__base_2eQ___24t(Vvar__0__r__122188)
            & VX122187 = cCoq_2emicromega_2eRMicromega_2eCQ___24a1(Vvar__0__r__122188) )
        | ? [Vvar__0__r__122189] :
            ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__0__r__122189)
            & VX122187 = cCoq_2emicromega_2eRMicromega_2eCZ___24a1(Vvar__0__r__122189) )
        | ? [Vvar__0__r1__122190] :
            ( cCoq_2emicromega_2eRMicromega_2eRcst___24t(Vvar__0__r1__122190)
            & ? [Vvar__1__r2__122191] :
                ( cCoq_2emicromega_2eRMicromega_2eRcst___24t(Vvar__1__r2__122191)
                & VX122187 = cCoq_2emicromega_2eRMicromega_2eCPlus___24a2(Vvar__0__r1__122190,Vvar__1__r2__122191) ) )
        | ? [Vvar__0__r1__122192] :
            ( cCoq_2emicromega_2eRMicromega_2eRcst___24t(Vvar__0__r1__122192)
            & ? [Vvar__1__r2__122193] :
                ( cCoq_2emicromega_2eRMicromega_2eRcst___24t(Vvar__1__r2__122193)
                & VX122187 = cCoq_2emicromega_2eRMicromega_2eCMinus___24a2(Vvar__0__r1__122192,Vvar__1__r2__122193) ) )
        | ? [Vvar__0__r1__122194] :
            ( cCoq_2emicromega_2eRMicromega_2eRcst___24t(Vvar__0__r1__122194)
            & ? [Vvar__1__r2__122195] :
                ( cCoq_2emicromega_2eRMicromega_2eRcst___24t(Vvar__1__r2__122195)
                & VX122187 = cCoq_2emicromega_2eRMicromega_2eCMult___24a2(Vvar__0__r1__122194,Vvar__1__r2__122195) ) )
        | ? [Vvar__0__r1__122196] :
            ( cCoq_2emicromega_2eRMicromega_2eRcst___24t(Vvar__0__r1__122196)
            & ? [Vvar__1__z__122197] :
                ( cCoq_2eInit_2eDatatypes_2esum___24t(cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eInit_2eDatatypes_2enat,Vvar__1__z__122197)
                & VX122187 = cCoq_2emicromega_2eRMicromega_2eCPow___24a2(Vvar__0__r1__122196,Vvar__1__z__122197) ) )
        | ? [Vvar__0__r__122198] :
            ( cCoq_2emicromega_2eRMicromega_2eRcst___24t(Vvar__0__r__122198)
            & VX122187 = cCoq_2emicromega_2eRMicromega_2eCInv___24a1(Vvar__0__r__122198) )
        | ? [Vvar__0__r__122199] :
            ( cCoq_2emicromega_2eRMicromega_2eRcst___24t(Vvar__0__r__122199)
            & VX122187 = cCoq_2emicromega_2eRMicromega_2eCOpp___24a1(Vvar__0__r__122199) ) ) ) ).

fof('$_inversion_Coq.micromega.RingMicromega.Formula',axiom,
    ! [Vvar__0__T__131793,VX131794] :
      ( cType___24t(Vvar__0__T__131793)
     => ( cCoq_2emicromega_2eRingMicromega_2eFormula___24t(Vvar__0__T__131793,VX131794)
       => ? [Vvar__1__Flhs__131796] :
            ( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__T__131793,Vvar__1__Flhs__131796)
            & ? [Vvar__2__Fop__131797] :
                ( cCoq_2emicromega_2eRingMicromega_2eOp2___24t(Vvar__2__Fop__131797)
                & ? [Vvar__3__Frhs__131798] :
                    ( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__T__131793,Vvar__3__Frhs__131798)
                    & VX131794 = cCoq_2emicromega_2eRingMicromega_2eBuild__Formula___24a4(Vvar__0__T__131793,Vvar__1__Flhs__131796,Vvar__2__Fop__131797,Vvar__3__Frhs__131798) ) ) ) ) ) ).

fof('$_inversion_Coq.micromega.RingMicromega.Op1',axiom,
    ! [VX131631] :
      ( cCoq_2emicromega_2eRingMicromega_2eOp1___24t(VX131631)
     => ( VX131631 = cCoq_2emicromega_2eRingMicromega_2eEqual
        | VX131631 = cCoq_2emicromega_2eRingMicromega_2eNonEqual
        | VX131631 = cCoq_2emicromega_2eRingMicromega_2eStrict
        | VX131631 = cCoq_2emicromega_2eRingMicromega_2eNonStrict ) ) ).

fof('$_inversion_Coq.micromega.RingMicromega.Op2',axiom,
    ! [VX148628] :
      ( cCoq_2emicromega_2eRingMicromega_2eOp2___24t(VX148628)
     => ( VX148628 = cCoq_2emicromega_2eRingMicromega_2eOpEq
        | VX148628 = cCoq_2emicromega_2eRingMicromega_2eOpNEq
        | VX148628 = cCoq_2emicromega_2eRingMicromega_2eOpLe
        | VX148628 = cCoq_2emicromega_2eRingMicromega_2eOpGe
        | VX148628 = cCoq_2emicromega_2eRingMicromega_2eOpLt
        | VX148628 = cCoq_2emicromega_2eRingMicromega_2eOpGt ) ) ).

fof('$_inversion_Coq.micromega.RingMicromega.Psatz',axiom,
    ! [Vvar__0__C__131632,VX131633] :
      ( cType___24t(Vvar__0__C__131632)
     => ( cCoq_2emicromega_2eRingMicromega_2ePsatz___24t(Vvar__0__C__131632,VX131633)
       => ( ? [Vvar__1___24Anonymous__131635] :
              ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__1___24Anonymous__131635)
              & VX131633 = cCoq_2emicromega_2eRingMicromega_2ePsatzIn___24a2(Vvar__0__C__131632,Vvar__1___24Anonymous__131635) )
          | ? [Vvar__1___24Anonymous__131637] :
              ( cCoq_2emicromega_2eRingMicromega_2ePolC___24t(Vvar__0__C__131632,Vvar__1___24Anonymous__131637)
              & VX131633 = cCoq_2emicromega_2eRingMicromega_2ePsatzSquare___24a2(Vvar__0__C__131632,Vvar__1___24Anonymous__131637) )
          | ? [Vvar__1___24Anonymous__131639] :
              ( cCoq_2emicromega_2eRingMicromega_2ePolC___24t(Vvar__0__C__131632,Vvar__1___24Anonymous__131639)
              & ? [Vvar__2___24Anonymous__131640] :
                  ( cCoq_2emicromega_2eRingMicromega_2ePsatz___24t(Vvar__0__C__131632,Vvar__2___24Anonymous__131640)
                  & VX131633 = cCoq_2emicromega_2eRingMicromega_2ePsatzMulC___24a3(Vvar__0__C__131632,Vvar__1___24Anonymous__131639,Vvar__2___24Anonymous__131640) ) )
          | ? [Vvar__1___24Anonymous__131642] :
              ( cCoq_2emicromega_2eRingMicromega_2ePsatz___24t(Vvar__0__C__131632,Vvar__1___24Anonymous__131642)
              & ? [Vvar__2___24Anonymous__131643] :
                  ( cCoq_2emicromega_2eRingMicromega_2ePsatz___24t(Vvar__0__C__131632,Vvar__2___24Anonymous__131643)
                  & VX131633 = cCoq_2emicromega_2eRingMicromega_2ePsatzMulE___24a3(Vvar__0__C__131632,Vvar__1___24Anonymous__131642,Vvar__2___24Anonymous__131643) ) )
          | ? [Vvar__1___24Anonymous__131645] :
              ( cCoq_2emicromega_2eRingMicromega_2ePsatz___24t(Vvar__0__C__131632,Vvar__1___24Anonymous__131645)
              & ? [Vvar__2___24Anonymous__131646] :
                  ( cCoq_2emicromega_2eRingMicromega_2ePsatz___24t(Vvar__0__C__131632,Vvar__2___24Anonymous__131646)
                  & VX131633 = cCoq_2emicromega_2eRingMicromega_2ePsatzAdd___24a3(Vvar__0__C__131632,Vvar__1___24Anonymous__131645,Vvar__2___24Anonymous__131646) ) )
          | ? [Vvar__1___24Anonymous__131648] :
              ( t(Vvar__1___24Anonymous__131648,Vvar__0__C__131632)
              & VX131633 = cCoq_2emicromega_2eRingMicromega_2ePsatzC___24a2(Vvar__0__C__131632,Vvar__1___24Anonymous__131648) )
          | VX131633 = cCoq_2emicromega_2eRingMicromega_2ePsatzZ___24a1(Vvar__0__C__131632) ) ) ) ).

fof('$_inversion_Coq.micromega.RingMicromega.SORaddon',axiom,
    ! [Vvar__0__R__126338,Vvar__1__rO__126339,Vvar__2__rI__126340,Vvar__3__rplus__126341,Vvar__4__rtimes__126346,Vvar__5__rminus__126351,Vvar__6__ropp__126356,Vvar__7__req__126359,Vvar__8__rle__126364,Vvar__9__C__126369,Vvar__10__cO__126370,Vvar__11__cI__126371,Vvar__12__cplus__126372,Vvar__13__ctimes__126377,Vvar__14__cminus__126382,Vvar__15__copp__126387,Vvar__16__ceqb__126390,Vvar__17__cleb__126395,Vvar__18__phi__126400,Vvar__19__E__126403,Vvar__20__pow__phi__126404,Vvar__21__rpow__126407] :
      ( cType___24t(Vvar__0__R__126338)
     => ( t(Vvar__1__rO__126339,Vvar__0__R__126338)
       => ( t(Vvar__2__rI__126340,Vvar__0__R__126338)
         => ( c_24__type__126871___24t(Vvar__0__R__126338,Vvar__1__rO__126339,Vvar__2__rI__126340,Vvar__3__rplus__126341,Vvar__4__rtimes__126346,Vvar__5__rminus__126351,Vvar__6__ropp__126356,Vvar__7__req__126359,Vvar__8__rle__126364,Vvar__9__C__126369,Vvar__10__cO__126370,Vvar__11__cI__126371,Vvar__12__cplus__126372,Vvar__13__ctimes__126377,Vvar__14__cminus__126382,Vvar__15__copp__126387,Vvar__16__ceqb__126390,Vvar__17__cleb__126395,Vvar__18__phi__126400,Vvar__19__E__126403,Vvar__20__pow__phi__126404,Vvar__21__rpow__126407,Vvar__3__rplus__126341)
           => ( c_24__type__127217___24t(Vvar__0__R__126338,Vvar__1__rO__126339,Vvar__2__rI__126340,Vvar__3__rplus__126341,Vvar__4__rtimes__126346,Vvar__5__rminus__126351,Vvar__6__ropp__126356,Vvar__7__req__126359,Vvar__8__rle__126364,Vvar__9__C__126369,Vvar__10__cO__126370,Vvar__11__cI__126371,Vvar__12__cplus__126372,Vvar__13__ctimes__126377,Vvar__14__cminus__126382,Vvar__15__copp__126387,Vvar__16__ceqb__126390,Vvar__17__cleb__126395,Vvar__18__phi__126400,Vvar__19__E__126403,Vvar__20__pow__phi__126404,Vvar__21__rpow__126407,Vvar__4__rtimes__126346)
             => ( c_24__type__127563___24t(Vvar__0__R__126338,Vvar__1__rO__126339,Vvar__2__rI__126340,Vvar__3__rplus__126341,Vvar__4__rtimes__126346,Vvar__5__rminus__126351,Vvar__6__ropp__126356,Vvar__7__req__126359,Vvar__8__rle__126364,Vvar__9__C__126369,Vvar__10__cO__126370,Vvar__11__cI__126371,Vvar__12__cplus__126372,Vvar__13__ctimes__126377,Vvar__14__cminus__126382,Vvar__15__copp__126387,Vvar__16__ceqb__126390,Vvar__17__cleb__126395,Vvar__18__phi__126400,Vvar__19__E__126403,Vvar__20__pow__phi__126404,Vvar__21__rpow__126407,Vvar__5__rminus__126351)
               => ( c_24__type__127886___24t(Vvar__0__R__126338,Vvar__1__rO__126339,Vvar__2__rI__126340,Vvar__3__rplus__126341,Vvar__4__rtimes__126346,Vvar__5__rminus__126351,Vvar__6__ropp__126356,Vvar__7__req__126359,Vvar__8__rle__126364,Vvar__9__C__126369,Vvar__10__cO__126370,Vvar__11__cI__126371,Vvar__12__cplus__126372,Vvar__13__ctimes__126377,Vvar__14__cminus__126382,Vvar__15__copp__126387,Vvar__16__ceqb__126390,Vvar__17__cleb__126395,Vvar__18__phi__126400,Vvar__19__E__126403,Vvar__20__pow__phi__126404,Vvar__21__rpow__126407,Vvar__6__ropp__126356)
                 => ( c_24__type__128232___24t(Vvar__0__R__126338,Vvar__1__rO__126339,Vvar__2__rI__126340,Vvar__3__rplus__126341,Vvar__4__rtimes__126346,Vvar__5__rminus__126351,Vvar__6__ropp__126356,Vvar__7__req__126359,Vvar__8__rle__126364,Vvar__9__C__126369,Vvar__10__cO__126370,Vvar__11__cI__126371,Vvar__12__cplus__126372,Vvar__13__ctimes__126377,Vvar__14__cminus__126382,Vvar__15__copp__126387,Vvar__16__ceqb__126390,Vvar__17__cleb__126395,Vvar__18__phi__126400,Vvar__19__E__126403,Vvar__20__pow__phi__126404,Vvar__21__rpow__126407,Vvar__7__req__126359)
                   => ( c_24__type__128578___24t(Vvar__0__R__126338,Vvar__1__rO__126339,Vvar__2__rI__126340,Vvar__3__rplus__126341,Vvar__4__rtimes__126346,Vvar__5__rminus__126351,Vvar__6__ropp__126356,Vvar__7__req__126359,Vvar__8__rle__126364,Vvar__9__C__126369,Vvar__10__cO__126370,Vvar__11__cI__126371,Vvar__12__cplus__126372,Vvar__13__ctimes__126377,Vvar__14__cminus__126382,Vvar__15__copp__126387,Vvar__16__ceqb__126390,Vvar__17__cleb__126395,Vvar__18__phi__126400,Vvar__19__E__126403,Vvar__20__pow__phi__126404,Vvar__21__rpow__126407,Vvar__8__rle__126364)
                     => ( cType___24t(Vvar__9__C__126369)
                       => ( t(Vvar__10__cO__126370,Vvar__9__C__126369)
                         => ( t(Vvar__11__cI__126371,Vvar__9__C__126369)
                           => ( c_24__type__128924___24t(Vvar__0__R__126338,Vvar__1__rO__126339,Vvar__2__rI__126340,Vvar__3__rplus__126341,Vvar__4__rtimes__126346,Vvar__5__rminus__126351,Vvar__6__ropp__126356,Vvar__7__req__126359,Vvar__8__rle__126364,Vvar__9__C__126369,Vvar__10__cO__126370,Vvar__11__cI__126371,Vvar__12__cplus__126372,Vvar__13__ctimes__126377,Vvar__14__cminus__126382,Vvar__15__copp__126387,Vvar__16__ceqb__126390,Vvar__17__cleb__126395,Vvar__18__phi__126400,Vvar__19__E__126403,Vvar__20__pow__phi__126404,Vvar__21__rpow__126407,Vvar__12__cplus__126372)
                             => ( c_24__type__129270___24t(Vvar__0__R__126338,Vvar__1__rO__126339,Vvar__2__rI__126340,Vvar__3__rplus__126341,Vvar__4__rtimes__126346,Vvar__5__rminus__126351,Vvar__6__ropp__126356,Vvar__7__req__126359,Vvar__8__rle__126364,Vvar__9__C__126369,Vvar__10__cO__126370,Vvar__11__cI__126371,Vvar__12__cplus__126372,Vvar__13__ctimes__126377,Vvar__14__cminus__126382,Vvar__15__copp__126387,Vvar__16__ceqb__126390,Vvar__17__cleb__126395,Vvar__18__phi__126400,Vvar__19__E__126403,Vvar__20__pow__phi__126404,Vvar__21__rpow__126407,Vvar__13__ctimes__126377)
                               => ( c_24__type__129616___24t(Vvar__0__R__126338,Vvar__1__rO__126339,Vvar__2__rI__126340,Vvar__3__rplus__126341,Vvar__4__rtimes__126346,Vvar__5__rminus__126351,Vvar__6__ropp__126356,Vvar__7__req__126359,Vvar__8__rle__126364,Vvar__9__C__126369,Vvar__10__cO__126370,Vvar__11__cI__126371,Vvar__12__cplus__126372,Vvar__13__ctimes__126377,Vvar__14__cminus__126382,Vvar__15__copp__126387,Vvar__16__ceqb__126390,Vvar__17__cleb__126395,Vvar__18__phi__126400,Vvar__19__E__126403,Vvar__20__pow__phi__126404,Vvar__21__rpow__126407,Vvar__14__cminus__126382)
                                 => ( c_24__type__129939___24t(Vvar__0__R__126338,Vvar__1__rO__126339,Vvar__2__rI__126340,Vvar__3__rplus__126341,Vvar__4__rtimes__126346,Vvar__5__rminus__126351,Vvar__6__ropp__126356,Vvar__7__req__126359,Vvar__8__rle__126364,Vvar__9__C__126369,Vvar__10__cO__126370,Vvar__11__cI__126371,Vvar__12__cplus__126372,Vvar__13__ctimes__126377,Vvar__14__cminus__126382,Vvar__15__copp__126387,Vvar__16__ceqb__126390,Vvar__17__cleb__126395,Vvar__18__phi__126400,Vvar__19__E__126403,Vvar__20__pow__phi__126404,Vvar__21__rpow__126407,Vvar__15__copp__126387)
                                   => ( c_24__type__130285___24t(Vvar__0__R__126338,Vvar__1__rO__126339,Vvar__2__rI__126340,Vvar__3__rplus__126341,Vvar__4__rtimes__126346,Vvar__5__rminus__126351,Vvar__6__ropp__126356,Vvar__7__req__126359,Vvar__8__rle__126364,Vvar__9__C__126369,Vvar__10__cO__126370,Vvar__11__cI__126371,Vvar__12__cplus__126372,Vvar__13__ctimes__126377,Vvar__14__cminus__126382,Vvar__15__copp__126387,Vvar__16__ceqb__126390,Vvar__17__cleb__126395,Vvar__18__phi__126400,Vvar__19__E__126403,Vvar__20__pow__phi__126404,Vvar__21__rpow__126407,Vvar__16__ceqb__126390)
                                     => ( c_24__type__130631___24t(Vvar__0__R__126338,Vvar__1__rO__126339,Vvar__2__rI__126340,Vvar__3__rplus__126341,Vvar__4__rtimes__126346,Vvar__5__rminus__126351,Vvar__6__ropp__126356,Vvar__7__req__126359,Vvar__8__rle__126364,Vvar__9__C__126369,Vvar__10__cO__126370,Vvar__11__cI__126371,Vvar__12__cplus__126372,Vvar__13__ctimes__126377,Vvar__14__cminus__126382,Vvar__15__copp__126387,Vvar__16__ceqb__126390,Vvar__17__cleb__126395,Vvar__18__phi__126400,Vvar__19__E__126403,Vvar__20__pow__phi__126404,Vvar__21__rpow__126407,Vvar__17__cleb__126395)
                                       => ( c_24__type__130954___24t(Vvar__0__R__126338,Vvar__1__rO__126339,Vvar__2__rI__126340,Vvar__3__rplus__126341,Vvar__4__rtimes__126346,Vvar__5__rminus__126351,Vvar__6__ropp__126356,Vvar__7__req__126359,Vvar__8__rle__126364,Vvar__9__C__126369,Vvar__10__cO__126370,Vvar__11__cI__126371,Vvar__12__cplus__126372,Vvar__13__ctimes__126377,Vvar__14__cminus__126382,Vvar__15__copp__126387,Vvar__16__ceqb__126390,Vvar__17__cleb__126395,Vvar__18__phi__126400,Vvar__19__E__126403,Vvar__20__pow__phi__126404,Vvar__21__rpow__126407,Vvar__18__phi__126400)
                                         => ( cType___24t(Vvar__19__E__126403)
                                           => ( c_24__type__131277___24t(Vvar__0__R__126338,Vvar__1__rO__126339,Vvar__2__rI__126340,Vvar__3__rplus__126341,Vvar__4__rtimes__126346,Vvar__5__rminus__126351,Vvar__6__ropp__126356,Vvar__7__req__126359,Vvar__8__rle__126364,Vvar__9__C__126369,Vvar__10__cO__126370,Vvar__11__cI__126371,Vvar__12__cplus__126372,Vvar__13__ctimes__126377,Vvar__14__cminus__126382,Vvar__15__copp__126387,Vvar__16__ceqb__126390,Vvar__17__cleb__126395,Vvar__18__phi__126400,Vvar__19__E__126403,Vvar__20__pow__phi__126404,Vvar__21__rpow__126407,Vvar__20__pow__phi__126404)
                                             => ( c_24__type__131623___24t(Vvar__0__R__126338,Vvar__1__rO__126339,Vvar__2__rI__126340,Vvar__3__rplus__126341,Vvar__4__rtimes__126346,Vvar__5__rminus__126351,Vvar__6__ropp__126356,Vvar__7__req__126359,Vvar__8__rle__126364,Vvar__9__C__126369,Vvar__10__cO__126370,Vvar__11__cI__126371,Vvar__12__cplus__126372,Vvar__13__ctimes__126377,Vvar__14__cminus__126382,Vvar__15__copp__126387,Vvar__16__ceqb__126390,Vvar__17__cleb__126395,Vvar__18__phi__126400,Vvar__19__E__126403,Vvar__20__pow__phi__126404,Vvar__21__rpow__126407,Vvar__21__rpow__126407)
                                               => ( cCoq_2emicromega_2eRingMicromega_2eSORaddon___24a22(Vvar__0__R__126338,Vvar__1__rO__126339,Vvar__2__rI__126340,Vvar__3__rplus__126341,Vvar__4__rtimes__126346,Vvar__5__rminus__126351,Vvar__6__ropp__126356,Vvar__7__req__126359,Vvar__8__rle__126364,Vvar__9__C__126369,Vvar__10__cO__126370,Vvar__11__cI__126371,Vvar__12__cplus__126372,Vvar__13__ctimes__126377,Vvar__14__cminus__126382,Vvar__15__copp__126387,Vvar__16__ceqb__126390,Vvar__17__cleb__126395,Vvar__18__phi__126400,Vvar__19__E__126403,Vvar__20__pow__phi__126404,Vvar__21__rpow__126407)
                                                 => ( cCoq_2esetoid__ring_2eRing__theory_2ering__morph___24a17(Vvar__0__R__126338,Vvar__1__rO__126339,Vvar__2__rI__126340,Vvar__3__rplus__126341,Vvar__4__rtimes__126346,Vvar__5__rminus__126351,Vvar__6__ropp__126356,Vvar__7__req__126359,Vvar__9__C__126369,Vvar__10__cO__126370,Vvar__11__cI__126371,Vvar__12__cplus__126372,Vvar__13__ctimes__126377,Vvar__14__cminus__126382,Vvar__15__copp__126387,Vvar__16__ceqb__126390,Vvar__18__phi__126400)
                                                    & cCoq_2esetoid__ring_2eRing__theory_2epower__theory___24a7(Vvar__0__R__126338,Vvar__2__rI__126340,Vvar__4__rtimes__126346,Vvar__7__req__126359,Vvar__19__E__126403,Vvar__20__pow__phi__126404,Vvar__21__rpow__126407)
                                                    & ! [Vvar__var__var__var__var__var__24__x__126490__126493__126503__126506__126509__126512] :
                                                        ( t(Vvar__var__var__var__var__var__24__x__126490__126493__126503__126506__126509__126512,Vvar__9__C__126369)
                                                       => ! [Vvar__var__var__var__var__var__25__y__126491__126494__126504__126507__126510__126513] :
                                                            ( t(Vvar__var__var__var__var__var__25__y__126491__126494__126504__126507__126510__126513,Vvar__9__C__126369)
                                                           => ( happ(happ(Vvar__16__ceqb__126390,Vvar__var__var__var__var__var__24__x__126490__126493__126503__126506__126509__126512),Vvar__var__var__var__var__var__25__y__126491__126494__126504__126507__126510__126513) = cCoq_2eInit_2eDatatypes_2efalse
                                                             => ~ p(happ(happ(Vvar__7__req__126359,happ(Vvar__18__phi__126400,Vvar__var__var__var__var__var__24__x__126490__126493__126503__126506__126509__126512)),happ(Vvar__18__phi__126400,Vvar__var__var__var__var__var__25__y__126491__126494__126504__126507__126510__126513))) ) ) )
                                                    & ! [Vvar__var__var__var__var__var__25__x__126497__126500__126515__126518__126521__126524] :
                                                        ( t(Vvar__var__var__var__var__var__25__x__126497__126500__126515__126518__126521__126524,Vvar__9__C__126369)
                                                       => ! [Vvar__var__var__var__var__var__26__y__126498__126501__126516__126519__126522__126525] :
                                                            ( t(Vvar__var__var__var__var__var__26__y__126498__126501__126516__126519__126522__126525,Vvar__9__C__126369)
                                                           => ( happ(happ(Vvar__17__cleb__126395,Vvar__var__var__var__var__var__25__x__126497__126500__126515__126518__126521__126524),Vvar__var__var__var__var__var__26__y__126498__126501__126516__126519__126522__126525) = cCoq_2eInit_2eDatatypes_2etrue
                                                             => p(happ(happ(Vvar__8__rle__126364,happ(Vvar__18__phi__126400,Vvar__var__var__var__var__var__25__x__126497__126500__126515__126518__126521__126524)),happ(Vvar__18__phi__126400,Vvar__var__var__var__var__var__26__y__126498__126501__126516__126519__126522__126525))) ) ) )
                                                    & p(c_24True) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.micromega.Tauto.GFormula',axiom,
    ! [Vvar__0__TA__149171,Vvar__1__TX__149172,Vvar__2__AA__149173,Vvar__3__AF__149174,VX149175] :
      ( cType___24t(Vvar__0__TA__149171)
     => ( cType___24t(Vvar__1__TX__149172)
       => ( cType___24t(Vvar__2__AA__149173)
         => ( cType___24t(Vvar__3__AF__149174)
           => ( cCoq_2emicromega_2eTauto_2eGFormula___24t(Vvar__0__TA__149171,Vvar__1__TX__149172,Vvar__2__AA__149173,Vvar__3__AF__149174,VX149175)
             => ( VX149175 = cCoq_2emicromega_2eTauto_2eTT___24a4(Vvar__0__TA__149171,Vvar__1__TX__149172,Vvar__2__AA__149173,Vvar__3__AF__149174)
                | VX149175 = cCoq_2emicromega_2eTauto_2eFF___24a4(Vvar__0__TA__149171,Vvar__1__TX__149172,Vvar__2__AA__149173,Vvar__3__AF__149174)
                | ? [Vvar__4___24Anonymous__149188] :
                    ( t(Vvar__4___24Anonymous__149188,Vvar__1__TX__149172)
                    & VX149175 = cCoq_2emicromega_2eTauto_2eX___24a5(Vvar__0__TA__149171,Vvar__1__TX__149172,Vvar__2__AA__149173,Vvar__3__AF__149174,Vvar__4___24Anonymous__149188) )
                | ? [Vvar__4___24Anonymous__149193] :
                    ( t(Vvar__4___24Anonymous__149193,Vvar__0__TA__149171)
                    & ? [Vvar__5___24Anonymous__149194] :
                        ( t(Vvar__5___24Anonymous__149194,Vvar__2__AA__149173)
                        & VX149175 = cCoq_2emicromega_2eTauto_2eA___24a6(Vvar__0__TA__149171,Vvar__1__TX__149172,Vvar__2__AA__149173,Vvar__3__AF__149174,Vvar__4___24Anonymous__149193,Vvar__5___24Anonymous__149194) ) )
                | ? [Vvar__4___24Anonymous__149199] :
                    ( cCoq_2emicromega_2eTauto_2eGFormula___24t(Vvar__0__TA__149171,Vvar__1__TX__149172,Vvar__2__AA__149173,Vvar__3__AF__149174,Vvar__4___24Anonymous__149199)
                    & ? [Vvar__5___24Anonymous__149200] :
                        ( cCoq_2emicromega_2eTauto_2eGFormula___24t(Vvar__0__TA__149171,Vvar__1__TX__149172,Vvar__2__AA__149173,Vvar__3__AF__149174,Vvar__5___24Anonymous__149200)
                        & VX149175 = cCoq_2emicromega_2eTauto_2eCj___24a6(Vvar__0__TA__149171,Vvar__1__TX__149172,Vvar__2__AA__149173,Vvar__3__AF__149174,Vvar__4___24Anonymous__149199,Vvar__5___24Anonymous__149200) ) )
                | ? [Vvar__4___24Anonymous__149205] :
                    ( cCoq_2emicromega_2eTauto_2eGFormula___24t(Vvar__0__TA__149171,Vvar__1__TX__149172,Vvar__2__AA__149173,Vvar__3__AF__149174,Vvar__4___24Anonymous__149205)
                    & ? [Vvar__5___24Anonymous__149206] :
                        ( cCoq_2emicromega_2eTauto_2eGFormula___24t(Vvar__0__TA__149171,Vvar__1__TX__149172,Vvar__2__AA__149173,Vvar__3__AF__149174,Vvar__5___24Anonymous__149206)
                        & VX149175 = cCoq_2emicromega_2eTauto_2eD___24a6(Vvar__0__TA__149171,Vvar__1__TX__149172,Vvar__2__AA__149173,Vvar__3__AF__149174,Vvar__4___24Anonymous__149205,Vvar__5___24Anonymous__149206) ) )
                | ? [Vvar__4___24Anonymous__149211] :
                    ( cCoq_2emicromega_2eTauto_2eGFormula___24t(Vvar__0__TA__149171,Vvar__1__TX__149172,Vvar__2__AA__149173,Vvar__3__AF__149174,Vvar__4___24Anonymous__149211)
                    & VX149175 = cCoq_2emicromega_2eTauto_2eN___24a5(Vvar__0__TA__149171,Vvar__1__TX__149172,Vvar__2__AA__149173,Vvar__3__AF__149174,Vvar__4___24Anonymous__149211) )
                | ? [Vvar__4___24Anonymous__149216] :
                    ( cCoq_2emicromega_2eTauto_2eGFormula___24t(Vvar__0__TA__149171,Vvar__1__TX__149172,Vvar__2__AA__149173,Vvar__3__AF__149174,Vvar__4___24Anonymous__149216)
                    & ? [Vvar__5___24Anonymous__149217] :
                        ( cCoq_2eInit_2eDatatypes_2eoption___24t(Vvar__3__AF__149174,Vvar__5___24Anonymous__149217)
                        & ? [Vvar__6___24Anonymous__149218] :
                            ( cCoq_2emicromega_2eTauto_2eGFormula___24t(Vvar__0__TA__149171,Vvar__1__TX__149172,Vvar__2__AA__149173,Vvar__3__AF__149174,Vvar__6___24Anonymous__149218)
                            & VX149175 = cCoq_2emicromega_2eTauto_2eI___24a7(Vvar__0__TA__149171,Vvar__1__TX__149172,Vvar__2__AA__149173,Vvar__3__AF__149174,Vvar__4___24Anonymous__149216,Vvar__5___24Anonymous__149217,Vvar__6___24Anonymous__149218) ) ) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.micromega.VarMap.t',axiom,
    ! [Vvar__0__A__142712,VX142713] :
      ( cType___24t(Vvar__0__A__142712)
     => ( cCoq_2emicromega_2eVarMap_2et___24t(Vvar__0__A__142712,VX142713)
       => ( VX142713 = cCoq_2emicromega_2eVarMap_2eEmpty___24a1(Vvar__0__A__142712)
          | ? [Vvar__1___24Anonymous__142716] :
              ( t(Vvar__1___24Anonymous__142716,Vvar__0__A__142712)
              & VX142713 = cCoq_2emicromega_2eVarMap_2eElt___24a2(Vvar__0__A__142712,Vvar__1___24Anonymous__142716) )
          | ? [Vvar__1___24Anonymous__142718] :
              ( cCoq_2emicromega_2eVarMap_2et___24t(Vvar__0__A__142712,Vvar__1___24Anonymous__142718)
              & ? [Vvar__2___24Anonymous__142719] :
                  ( t(Vvar__2___24Anonymous__142719,Vvar__0__A__142712)
                  & ? [Vvar__3___24Anonymous__142720] :
                      ( cCoq_2emicromega_2eVarMap_2et___24t(Vvar__0__A__142712,Vvar__3___24Anonymous__142720)
                      & VX142713 = cCoq_2emicromega_2eVarMap_2eBranch___24a4(Vvar__0__A__142712,Vvar__1___24Anonymous__142718,Vvar__2___24Anonymous__142719,Vvar__3___24Anonymous__142720) ) ) ) ) ) ) ).

fof('$_inversion_Coq.micromega.ZMicromega.Vars.Facts.MP.Dec.FSetDecideAuxiliary.FSet_Prop',axiom,
    ! [Vvar__0___24Anonymous__149922] :
      ( cProp___24t(Vvar__0___24Anonymous__149922)
     => ( cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__Prop___24a1(Vvar__0___24Anonymous__149922)
       => ( ? [Vvar__0__P__149924] :
              ( cProp___24t(Vvar__0__P__149924)
              & cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__elt__Prop___24a1(Vvar__0__P__149924)
              & Vvar__0___24Anonymous__149922 = Vvar__0__P__149924 )
          | ? [Vvar__0__s__149926] :
              ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(Vvar__0__s__149926)
              & Vvar__0___24Anonymous__149922 = c_24__prop__149935___24a2(Vvar__0___24Anonymous__149922,Vvar__0__s__149926) )
          | ? [Vvar__0__s1__149928] :
              ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(Vvar__0__s1__149928)
              & ? [Vvar__1__s2__149929] :
                  ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(Vvar__1__s2__149929)
                  & Vvar__0___24Anonymous__149922 = c_24__prop__149936___24a3(Vvar__0___24Anonymous__149922,Vvar__0__s1__149928,Vvar__1__s2__149929) ) )
          | ? [Vvar__0__s1__149932] :
              ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(Vvar__0__s1__149932)
              & ? [Vvar__1__s2__149933] :
                  ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(Vvar__1__s2__149933)
                  & Vvar__0___24Anonymous__149922 = c_24__prop__149937___24a3(Vvar__0___24Anonymous__149922,Vvar__0__s1__149932,Vvar__1__s2__149933) ) ) ) ) ) ).

fof('$_inversion_Coq.micromega.ZMicromega.Vars.Facts.MP.Dec.FSetDecideAuxiliary.FSet_elt_Prop',axiom,
    ! [Vvar__0___24Anonymous__149891] :
      ( cProp___24t(Vvar__0___24Anonymous__149891)
     => ( cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__elt__Prop___24a1(Vvar__0___24Anonymous__149891)
       => ( ? [Vvar__0__S__149893] :
              ( cType___24t(Vvar__0__S__149893)
              & ? [Vvar__1__x__149894] :
                  ( t(Vvar__1__x__149894,Vvar__0__S__149893)
                  & ? [Vvar__2__y__149895] :
                      ( t(Vvar__2__y__149895,Vvar__0__S__149893)
                      & Vvar__0___24Anonymous__149891 = c_24__prop__149915___24a4(Vvar__0___24Anonymous__149891,Vvar__0__S__149893,Vvar__1__x__149894,Vvar__2__y__149895) ) ) )
          | ? [Vvar__0__x__149896] :
              ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0__x__149896)
              & ? [Vvar__1__y__149897] :
                  ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1__y__149897)
                  & Vvar__0___24Anonymous__149891 = c_24__prop__149916___24a3(Vvar__0___24Anonymous__149891,Vvar__0__x__149896,Vvar__1__y__149897) ) )
          | ? [Vvar__0__x__149898] :
              ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(Vvar__0__x__149898)
              & ? [Vvar__1__s__149899] :
                  ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(Vvar__1__s__149899)
                  & Vvar__0___24Anonymous__149891 = c_24__prop__149917___24a3(Vvar__0___24Anonymous__149891,Vvar__0__x__149898,Vvar__1__s__149899) ) )
          | Vvar__0___24Anonymous__149891 = c_24True
          | Vvar__0___24Anonymous__149891 = c_24False
          | ? [Vvar__0__P__149900] :
              ( cProp___24t(Vvar__0__P__149900)
              & ? [Vvar__1__Q__149901] :
                  ( cProp___24t(Vvar__1__Q__149901)
                  & cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__elt__Prop___24a1(Vvar__0__P__149900)
                  & cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__elt__Prop___24a1(Vvar__1__Q__149901)
                  & Vvar__0___24Anonymous__149891 = c_24__prop__149918___24a3(Vvar__0___24Anonymous__149891,Vvar__0__P__149900,Vvar__1__Q__149901) ) )
          | ? [Vvar__0__P__149904] :
              ( cProp___24t(Vvar__0__P__149904)
              & ? [Vvar__1__Q__149905] :
                  ( cProp___24t(Vvar__1__Q__149905)
                  & cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__elt__Prop___24a1(Vvar__0__P__149904)
                  & cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__elt__Prop___24a1(Vvar__1__Q__149905)
                  & Vvar__0___24Anonymous__149891 = c_24__prop__149919___24a3(Vvar__0___24Anonymous__149891,Vvar__0__P__149904,Vvar__1__Q__149905) ) )
          | ? [Vvar__0__P__149908] :
              ( cProp___24t(Vvar__0__P__149908)
              & ? [Vvar__1__Q__149909] :
                  ( cProp___24t(Vvar__1__Q__149909)
                  & cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__elt__Prop___24a1(Vvar__0__P__149908)
                  & cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__elt__Prop___24a1(Vvar__1__Q__149909)
                  & Vvar__0___24Anonymous__149891 = c_24__prop__149920___24a3(Vvar__0___24Anonymous__149891,Vvar__0__P__149908,Vvar__1__Q__149909) ) )
          | ? [Vvar__0__P__149913] :
              ( cProp___24t(Vvar__0__P__149913)
              & cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__elt__Prop___24a1(Vvar__0__P__149913)
              & Vvar__0___24Anonymous__149891 = c_24__prop__149921___24a2(Vvar__0___24Anonymous__149891,Vvar__0__P__149913) ) ) ) ) ).

fof('$_inversion_Coq.micromega.ZMicromega.ZArithProof',axiom,
    ! [VX135946] :
      ( cCoq_2emicromega_2eZMicromega_2eZArithProof___24t(VX135946)
     => ( VX135946 = cCoq_2emicromega_2eZMicromega_2eDoneProof
        | ? [Vvar__0___24Anonymous__135947] :
            ( cCoq_2emicromega_2eZMicromega_2eZWitness___24t(Vvar__0___24Anonymous__135947)
            & ? [Vvar__1___24Anonymous__135948] :
                ( cCoq_2emicromega_2eZMicromega_2eZArithProof___24t(Vvar__1___24Anonymous__135948)
                & VX135946 = cCoq_2emicromega_2eZMicromega_2eRatProof___24a2(Vvar__0___24Anonymous__135947,Vvar__1___24Anonymous__135948) ) )
        | ? [Vvar__0___24Anonymous__135949] :
            ( cCoq_2emicromega_2eZMicromega_2eZWitness___24t(Vvar__0___24Anonymous__135949)
            & ? [Vvar__1___24Anonymous__135950] :
                ( cCoq_2emicromega_2eZMicromega_2eZArithProof___24t(Vvar__1___24Anonymous__135950)
                & VX135946 = cCoq_2emicromega_2eZMicromega_2eCutProof___24a2(Vvar__0___24Anonymous__135949,Vvar__1___24Anonymous__135950) ) )
        | ? [Vvar__0___24Anonymous__135951] :
            ( cCoq_2emicromega_2eZMicromega_2eZWitness___24t(Vvar__0___24Anonymous__135951)
            & ? [Vvar__1___24Anonymous__135952] :
                ( cCoq_2emicromega_2eZMicromega_2eZWitness___24t(Vvar__1___24Anonymous__135952)
                & ? [Vvar__2___24Anonymous__135953] :
                    ( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2emicromega_2eZMicromega_2eZArithProof,Vvar__2___24Anonymous__135953)
                    & VX135946 = cCoq_2emicromega_2eZMicromega_2eEnumProof___24a3(Vvar__0___24Anonymous__135951,Vvar__1___24Anonymous__135952,Vvar__2___24Anonymous__135953) ) ) ) ) ) ).

fof('$_inversion_Coq.micromega.ZMicromega.Zdivide_pol',axiom,
    ! [Vvar__0__x__143349,Vvar__1___24Anonymous__143350] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__0__x__143349)
     => ( cCoq_2emicromega_2eRingMicromega_2ePolC___24t(cCoq_2eNumbers_2eBinNums_2eZ,Vvar__1___24Anonymous__143350)
       => ( cCoq_2emicromega_2eZMicromega_2eZdivide__pol___24a2(Vvar__0__x__143349,Vvar__1___24Anonymous__143350)
         => ( ? [Vvar__1__c__143353] :
                ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__1__c__143353)
                & cCoq_2eZArith_2eBinInt_2eZ_2edivide___24a2(Vvar__0__x__143349,Vvar__1__c__143353)
                & Vvar__1___24Anonymous__143350 = cCoq_2emicromega_2eEnvRing_2ePc___24a2(cCoq_2eNumbers_2eBinNums_2eZ,Vvar__1__c__143353) )
            | ? [Vvar__1__p__143356] :
                ( cCoq_2emicromega_2eRingMicromega_2ePolC___24t(cCoq_2eNumbers_2eBinNums_2eZ,Vvar__1__p__143356)
                & cCoq_2emicromega_2eZMicromega_2eZdivide__pol___24a2(Vvar__0__x__143349,Vvar__1__p__143356)
                & ? [Vvar__3__j__143358] :
                    ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__3__j__143358)
                    & Vvar__1___24Anonymous__143350 = cCoq_2emicromega_2eEnvRing_2ePinj___24a3(cCoq_2eNumbers_2eBinNums_2eZ,Vvar__3__j__143358,Vvar__1__p__143356) ) )
            | ? [Vvar__1__p__143360] :
                ( cCoq_2emicromega_2eRingMicromega_2ePolC___24t(cCoq_2eNumbers_2eBinNums_2eZ,Vvar__1__p__143360)
                & ? [Vvar__2__q__143361] :
                    ( cCoq_2emicromega_2eRingMicromega_2ePolC___24t(cCoq_2eNumbers_2eBinNums_2eZ,Vvar__2__q__143361)
                    & cCoq_2emicromega_2eZMicromega_2eZdivide__pol___24a2(Vvar__0__x__143349,Vvar__1__p__143360)
                    & cCoq_2emicromega_2eZMicromega_2eZdivide__pol___24a2(Vvar__0__x__143349,Vvar__2__q__143361)
                    & ? [Vvar__5__j__143364] :
                        ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__5__j__143364)
                        & Vvar__1___24Anonymous__143350 = cCoq_2emicromega_2eEnvRing_2ePX___24a4(cCoq_2eNumbers_2eBinNums_2eZ,Vvar__1__p__143360,Vvar__5__j__143364,Vvar__2__q__143361) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.micromega.ZMicromega.is_diff_env_elt',axiom,
    ! [Vvar__0__fr__149695,Vvar__1__env__149696,Vvar__2__env_27__149699,Vvar__3__x__149702] :
      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0__fr__149695)
     => ( c_24__type__149723___24t(Vvar__0__fr__149695,Vvar__1__env__149696,Vvar__2__env_27__149699,Vvar__3__x__149702,Vvar__1__env__149696)
       => ( c_24__type__149732___24t(Vvar__0__fr__149695,Vvar__1__env__149696,Vvar__2__env_27__149699,Vvar__3__x__149702,Vvar__2__env_27__149699)
         => ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__3__x__149702)
           => ( cCoq_2emicromega_2eZMicromega_2eis__diff__env__elt___24a4(Vvar__0__fr__149695,Vvar__1__env__149696,Vvar__2__env_27__149699,Vvar__3__x__149702)
             => ( happ(Vvar__1__env__149696,Vvar__3__x__149702) = happ(Vvar__2__env_27__149699,Vvar__3__x__149702)
                & happ(Vvar__1__env__149696,Vvar__3__x__149702) = cCoq_2eZArith_2eBinIntDef_2eZ_2esub___24a2(happ(Vvar__2__env_27__149699,cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(Vvar__0__fr__149695,Vvar__3__x__149702))),happ(Vvar__2__env_27__149699,cCoq_2eNumbers_2eBinNums_2exI___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(Vvar__0__fr__149695,Vvar__3__x__149702))))
                & cCoq_2eZArith_2eBinInt_2eZ_2ege___24a2(happ(Vvar__2__env_27__149699,cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(Vvar__0__fr__149695,Vvar__3__x__149702))),cCoq_2eNumbers_2eBinNums_2eZ0)
                & cCoq_2eZArith_2eBinInt_2eZ_2ege___24a2(happ(Vvar__2__env_27__149699,cCoq_2eNumbers_2eBinNums_2exI___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(Vvar__0__fr__149695,Vvar__3__x__149702))),cCoq_2eNumbers_2eBinNums_2eZ0)
                & p(c_24True) ) ) ) ) ) ) ).

fof('$_inversion_Coq.setoid_ring.Field_theory.FExpr',axiom,
    ! [Vvar__0__C__119471,VX119472] :
      ( cType___24t(Vvar__0__C__119471)
     => ( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__119471,VX119472)
       => ( VX119472 = cCoq_2esetoid__ring_2eField__theory_2eFEO___24a1(Vvar__0__C__119471)
          | VX119472 = cCoq_2esetoid__ring_2eField__theory_2eFEI___24a1(Vvar__0__C__119471)
          | ? [Vvar__1___24Anonymous__119476] :
              ( t(Vvar__1___24Anonymous__119476,Vvar__0__C__119471)
              & VX119472 = cCoq_2esetoid__ring_2eField__theory_2eFEc___24a2(Vvar__0__C__119471,Vvar__1___24Anonymous__119476) )
          | ? [Vvar__1___24Anonymous__119478] :
              ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__119478)
              & VX119472 = cCoq_2esetoid__ring_2eField__theory_2eFEX___24a2(Vvar__0__C__119471,Vvar__1___24Anonymous__119478) )
          | ? [Vvar__1___24Anonymous__119480] :
              ( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__119471,Vvar__1___24Anonymous__119480)
              & ? [Vvar__2___24Anonymous__119481] :
                  ( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__119471,Vvar__2___24Anonymous__119481)
                  & VX119472 = cCoq_2esetoid__ring_2eField__theory_2eFEadd___24a3(Vvar__0__C__119471,Vvar__1___24Anonymous__119480,Vvar__2___24Anonymous__119481) ) )
          | ? [Vvar__1___24Anonymous__119483] :
              ( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__119471,Vvar__1___24Anonymous__119483)
              & ? [Vvar__2___24Anonymous__119484] :
                  ( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__119471,Vvar__2___24Anonymous__119484)
                  & VX119472 = cCoq_2esetoid__ring_2eField__theory_2eFEsub___24a3(Vvar__0__C__119471,Vvar__1___24Anonymous__119483,Vvar__2___24Anonymous__119484) ) )
          | ? [Vvar__1___24Anonymous__119486] :
              ( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__119471,Vvar__1___24Anonymous__119486)
              & ? [Vvar__2___24Anonymous__119487] :
                  ( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__119471,Vvar__2___24Anonymous__119487)
                  & VX119472 = cCoq_2esetoid__ring_2eField__theory_2eFEmul___24a3(Vvar__0__C__119471,Vvar__1___24Anonymous__119486,Vvar__2___24Anonymous__119487) ) )
          | ? [Vvar__1___24Anonymous__119489] :
              ( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__119471,Vvar__1___24Anonymous__119489)
              & VX119472 = cCoq_2esetoid__ring_2eField__theory_2eFEopp___24a2(Vvar__0__C__119471,Vvar__1___24Anonymous__119489) )
          | ? [Vvar__1___24Anonymous__119491] :
              ( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__119471,Vvar__1___24Anonymous__119491)
              & VX119472 = cCoq_2esetoid__ring_2eField__theory_2eFEinv___24a2(Vvar__0__C__119471,Vvar__1___24Anonymous__119491) )
          | ? [Vvar__1___24Anonymous__119493] :
              ( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__119471,Vvar__1___24Anonymous__119493)
              & ? [Vvar__2___24Anonymous__119494] :
                  ( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__119471,Vvar__2___24Anonymous__119494)
                  & VX119472 = cCoq_2esetoid__ring_2eField__theory_2eFEdiv___24a3(Vvar__0__C__119471,Vvar__1___24Anonymous__119493,Vvar__2___24Anonymous__119494) ) )
          | ? [Vvar__1___24Anonymous__119496] :
              ( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__119471,Vvar__1___24Anonymous__119496)
              & ? [Vvar__2___24Anonymous__119497] :
                  ( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__2___24Anonymous__119497)
                  & VX119472 = cCoq_2esetoid__ring_2eField__theory_2eFEpow___24a3(Vvar__0__C__119471,Vvar__1___24Anonymous__119496,Vvar__2___24Anonymous__119497) ) ) ) ) ) ).

fof('$_inversion_Coq.setoid_ring.Field_theory.almost_field_theory',axiom,
    ! [Vvar__0__R__124290,Vvar__1__rO__124291,Vvar__2__rI__124292,Vvar__3__radd__124293,Vvar__4__rmul__124298,Vvar__5__rsub__124303,Vvar__6__ropp__124308,Vvar__7__rdiv__124311,Vvar__8__rinv__124316,Vvar__9__req__124319] :
      ( cType___24t(Vvar__0__R__124290)
     => ( t(Vvar__1__rO__124291,Vvar__0__R__124290)
       => ( t(Vvar__2__rI__124292,Vvar__0__R__124290)
         => ( c_24__type__124484___24t(Vvar__0__R__124290,Vvar__1__rO__124291,Vvar__2__rI__124292,Vvar__3__radd__124293,Vvar__4__rmul__124298,Vvar__5__rsub__124303,Vvar__6__ropp__124308,Vvar__7__rdiv__124311,Vvar__8__rinv__124316,Vvar__9__req__124319,Vvar__3__radd__124293)
           => ( c_24__type__124577___24t(Vvar__0__R__124290,Vvar__1__rO__124291,Vvar__2__rI__124292,Vvar__3__radd__124293,Vvar__4__rmul__124298,Vvar__5__rsub__124303,Vvar__6__ropp__124308,Vvar__7__rdiv__124311,Vvar__8__rinv__124316,Vvar__9__req__124319,Vvar__4__rmul__124298)
             => ( c_24__type__124670___24t(Vvar__0__R__124290,Vvar__1__rO__124291,Vvar__2__rI__124292,Vvar__3__radd__124293,Vvar__4__rmul__124298,Vvar__5__rsub__124303,Vvar__6__ropp__124308,Vvar__7__rdiv__124311,Vvar__8__rinv__124316,Vvar__9__req__124319,Vvar__5__rsub__124303)
               => ( c_24__type__124752___24t(Vvar__0__R__124290,Vvar__1__rO__124291,Vvar__2__rI__124292,Vvar__3__radd__124293,Vvar__4__rmul__124298,Vvar__5__rsub__124303,Vvar__6__ropp__124308,Vvar__7__rdiv__124311,Vvar__8__rinv__124316,Vvar__9__req__124319,Vvar__6__ropp__124308)
                 => ( c_24__type__124845___24t(Vvar__0__R__124290,Vvar__1__rO__124291,Vvar__2__rI__124292,Vvar__3__radd__124293,Vvar__4__rmul__124298,Vvar__5__rsub__124303,Vvar__6__ropp__124308,Vvar__7__rdiv__124311,Vvar__8__rinv__124316,Vvar__9__req__124319,Vvar__7__rdiv__124311)
                   => ( c_24__type__124927___24t(Vvar__0__R__124290,Vvar__1__rO__124291,Vvar__2__rI__124292,Vvar__3__radd__124293,Vvar__4__rmul__124298,Vvar__5__rsub__124303,Vvar__6__ropp__124308,Vvar__7__rdiv__124311,Vvar__8__rinv__124316,Vvar__9__req__124319,Vvar__8__rinv__124316)
                     => ( c_24__type__125020___24t(Vvar__0__R__124290,Vvar__1__rO__124291,Vvar__2__rI__124292,Vvar__3__radd__124293,Vvar__4__rmul__124298,Vvar__5__rsub__124303,Vvar__6__ropp__124308,Vvar__7__rdiv__124311,Vvar__8__rinv__124316,Vvar__9__req__124319,Vvar__9__req__124319)
                       => ( cCoq_2esetoid__ring_2eField__theory_2ealmost__field__theory___24a10(Vvar__0__R__124290,Vvar__1__rO__124291,Vvar__2__rI__124292,Vvar__3__radd__124293,Vvar__4__rmul__124298,Vvar__5__rsub__124303,Vvar__6__ropp__124308,Vvar__7__rdiv__124311,Vvar__8__rinv__124316,Vvar__9__req__124319)
                         => ( cCoq_2esetoid__ring_2eRing__theory_2ealmost__ring__theory___24a8(Vvar__0__R__124290,Vvar__1__rO__124291,Vvar__2__rI__124292,Vvar__3__radd__124293,Vvar__4__rmul__124298,Vvar__5__rsub__124303,Vvar__6__ropp__124308,Vvar__9__req__124319)
                            & ~ p(happ(happ(Vvar__9__req__124319,Vvar__2__rI__124292),Vvar__1__rO__124291))
                            & ! [Vvar__var__var__var__var__var__var__12__p__124362__124364__124371__124373__124375__124377__124379] :
                                ( t(Vvar__var__var__var__var__var__var__12__p__124362__124364__124371__124373__124375__124377__124379,Vvar__0__R__124290)
                               => ! [Vvar__var__var__var__var__var__var__13__q__124363__124365__124372__124374__124376__124378__124380] :
                                    ( t(Vvar__var__var__var__var__var__var__13__q__124363__124365__124372__124374__124376__124378__124380,Vvar__0__R__124290)
                                   => p(happ(happ(Vvar__9__req__124319,happ(happ(Vvar__7__rdiv__124311,Vvar__var__var__var__var__var__var__12__p__124362__124364__124371__124373__124375__124377__124379),Vvar__var__var__var__var__var__var__13__q__124363__124365__124372__124374__124376__124378__124380)),happ(happ(Vvar__4__rmul__124298,Vvar__var__var__var__var__var__var__12__p__124362__124364__124371__124373__124375__124377__124379),happ(Vvar__8__rinv__124316,Vvar__var__var__var__var__var__var__13__q__124363__124365__124372__124374__124376__124378__124380)))) ) )
                            & ! [Vvar__var__var__var__var__var__var__var__13__p__124367__124369__124381__124383__124385__124387__124389__124391] :
                                ( t(Vvar__var__var__var__var__var__var__var__13__p__124367__124369__124381__124383__124385__124387__124389__124391,Vvar__0__R__124290)
                               => ( ~ p(happ(happ(Vvar__9__req__124319,Vvar__var__var__var__var__var__var__var__13__p__124367__124369__124381__124383__124385__124387__124389__124391),Vvar__1__rO__124291))
                                 => p(happ(happ(Vvar__9__req__124319,happ(happ(Vvar__4__rmul__124298,happ(Vvar__8__rinv__124316,Vvar__var__var__var__var__var__var__var__13__p__124367__124369__124381__124383__124385__124387__124389__124391)),Vvar__var__var__var__var__var__var__var__13__p__124367__124369__124381__124383__124385__124387__124389__124391)),Vvar__2__rI__124292)) ) )
                            & p(c_24True) ) ) ) ) ) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.setoid_ring.Field_theory.field_theory',axiom,
    ! [Vvar__0__R__145808,Vvar__1__rO__145809,Vvar__2__rI__145810,Vvar__3__radd__145811,Vvar__4__rmul__145816,Vvar__5__rsub__145821,Vvar__6__ropp__145826,Vvar__7__rdiv__145829,Vvar__8__rinv__145834,Vvar__9__req__145837] :
      ( cType___24t(Vvar__0__R__145808)
     => ( t(Vvar__1__rO__145809,Vvar__0__R__145808)
       => ( t(Vvar__2__rI__145810,Vvar__0__R__145808)
         => ( c_24__type__146002___24t(Vvar__0__R__145808,Vvar__1__rO__145809,Vvar__2__rI__145810,Vvar__3__radd__145811,Vvar__4__rmul__145816,Vvar__5__rsub__145821,Vvar__6__ropp__145826,Vvar__7__rdiv__145829,Vvar__8__rinv__145834,Vvar__9__req__145837,Vvar__3__radd__145811)
           => ( c_24__type__146095___24t(Vvar__0__R__145808,Vvar__1__rO__145809,Vvar__2__rI__145810,Vvar__3__radd__145811,Vvar__4__rmul__145816,Vvar__5__rsub__145821,Vvar__6__ropp__145826,Vvar__7__rdiv__145829,Vvar__8__rinv__145834,Vvar__9__req__145837,Vvar__4__rmul__145816)
             => ( c_24__type__146188___24t(Vvar__0__R__145808,Vvar__1__rO__145809,Vvar__2__rI__145810,Vvar__3__radd__145811,Vvar__4__rmul__145816,Vvar__5__rsub__145821,Vvar__6__ropp__145826,Vvar__7__rdiv__145829,Vvar__8__rinv__145834,Vvar__9__req__145837,Vvar__5__rsub__145821)
               => ( c_24__type__146270___24t(Vvar__0__R__145808,Vvar__1__rO__145809,Vvar__2__rI__145810,Vvar__3__radd__145811,Vvar__4__rmul__145816,Vvar__5__rsub__145821,Vvar__6__ropp__145826,Vvar__7__rdiv__145829,Vvar__8__rinv__145834,Vvar__9__req__145837,Vvar__6__ropp__145826)
                 => ( c_24__type__146363___24t(Vvar__0__R__145808,Vvar__1__rO__145809,Vvar__2__rI__145810,Vvar__3__radd__145811,Vvar__4__rmul__145816,Vvar__5__rsub__145821,Vvar__6__ropp__145826,Vvar__7__rdiv__145829,Vvar__8__rinv__145834,Vvar__9__req__145837,Vvar__7__rdiv__145829)
                   => ( c_24__type__146445___24t(Vvar__0__R__145808,Vvar__1__rO__145809,Vvar__2__rI__145810,Vvar__3__radd__145811,Vvar__4__rmul__145816,Vvar__5__rsub__145821,Vvar__6__ropp__145826,Vvar__7__rdiv__145829,Vvar__8__rinv__145834,Vvar__9__req__145837,Vvar__8__rinv__145834)
                     => ( c_24__type__146538___24t(Vvar__0__R__145808,Vvar__1__rO__145809,Vvar__2__rI__145810,Vvar__3__radd__145811,Vvar__4__rmul__145816,Vvar__5__rsub__145821,Vvar__6__ropp__145826,Vvar__7__rdiv__145829,Vvar__8__rinv__145834,Vvar__9__req__145837,Vvar__9__req__145837)
                       => ( cCoq_2esetoid__ring_2eField__theory_2efield__theory___24a10(Vvar__0__R__145808,Vvar__1__rO__145809,Vvar__2__rI__145810,Vvar__3__radd__145811,Vvar__4__rmul__145816,Vvar__5__rsub__145821,Vvar__6__ropp__145826,Vvar__7__rdiv__145829,Vvar__8__rinv__145834,Vvar__9__req__145837)
                         => ( cCoq_2esetoid__ring_2eRing__theory_2ering__theory___24a8(Vvar__0__R__145808,Vvar__1__rO__145809,Vvar__2__rI__145810,Vvar__3__radd__145811,Vvar__4__rmul__145816,Vvar__5__rsub__145821,Vvar__6__ropp__145826,Vvar__9__req__145837)
                            & ~ p(happ(happ(Vvar__9__req__145837,Vvar__2__rI__145810),Vvar__1__rO__145809))
                            & ! [Vvar__var__var__var__var__var__var__12__p__145880__145882__145889__145891__145893__145895__145897] :
                                ( t(Vvar__var__var__var__var__var__var__12__p__145880__145882__145889__145891__145893__145895__145897,Vvar__0__R__145808)
                               => ! [Vvar__var__var__var__var__var__var__13__q__145881__145883__145890__145892__145894__145896__145898] :
                                    ( t(Vvar__var__var__var__var__var__var__13__q__145881__145883__145890__145892__145894__145896__145898,Vvar__0__R__145808)
                                   => p(happ(happ(Vvar__9__req__145837,happ(happ(Vvar__7__rdiv__145829,Vvar__var__var__var__var__var__var__12__p__145880__145882__145889__145891__145893__145895__145897),Vvar__var__var__var__var__var__var__13__q__145881__145883__145890__145892__145894__145896__145898)),happ(happ(Vvar__4__rmul__145816,Vvar__var__var__var__var__var__var__12__p__145880__145882__145889__145891__145893__145895__145897),happ(Vvar__8__rinv__145834,Vvar__var__var__var__var__var__var__13__q__145881__145883__145890__145892__145894__145896__145898)))) ) )
                            & ! [Vvar__var__var__var__var__var__var__var__13__p__145885__145887__145899__145901__145903__145905__145907__145909] :
                                ( t(Vvar__var__var__var__var__var__var__var__13__p__145885__145887__145899__145901__145903__145905__145907__145909,Vvar__0__R__145808)
                               => ( ~ p(happ(happ(Vvar__9__req__145837,Vvar__var__var__var__var__var__var__var__13__p__145885__145887__145899__145901__145903__145905__145907__145909),Vvar__1__rO__145809))
                                 => p(happ(happ(Vvar__9__req__145837,happ(happ(Vvar__4__rmul__145816,happ(Vvar__8__rinv__145834,Vvar__var__var__var__var__var__var__var__13__p__145885__145887__145899__145901__145903__145905__145907__145909)),Vvar__var__var__var__var__var__var__var__13__p__145885__145887__145899__145901__145903__145905__145907__145909)),Vvar__2__rI__145810)) ) )
                            & p(c_24True) ) ) ) ) ) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.setoid_ring.Field_theory.linear',axiom,
    ! [Vvar__0__C__120083,VX120084] :
      ( cType___24t(Vvar__0__C__120083)
     => ( cCoq_2esetoid__ring_2eField__theory_2elinear___24t(Vvar__0__C__120083,VX120084)
       => ? [Vvar__1__num__120086] :
            ( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__120083,Vvar__1__num__120086)
            & ? [Vvar__2__denum__120087] :
                ( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__120083,Vvar__2__denum__120087)
                & ? [Vvar__3__condition__120088] :
                    ( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(Vvar__0__C__120083),Vvar__3__condition__120088)
                    & VX120084 = cCoq_2esetoid__ring_2eField__theory_2emk__linear___24a4(Vvar__0__C__120083,Vvar__1__num__120086,Vvar__2__denum__120087,Vvar__3__condition__120088) ) ) ) ) ) ).

fof('$_inversion_Coq.setoid_ring.Field_theory.rsplit',axiom,
    ! [Vvar__0__C__120372,VX120373] :
      ( cType___24t(Vvar__0__C__120372)
     => ( cCoq_2esetoid__ring_2eField__theory_2ersplit___24t(Vvar__0__C__120372,VX120373)
       => ? [Vvar__1__rsplit__left__120375] :
            ( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__120372,Vvar__1__rsplit__left__120375)
            & ? [Vvar__2__rsplit__common__120376] :
                ( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__120372,Vvar__2__rsplit__common__120376)
                & ? [Vvar__3__rsplit__right__120377] :
                    ( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__120372,Vvar__3__rsplit__right__120377)
                    & VX120373 = cCoq_2esetoid__ring_2eField__theory_2emk__rsplit___24a4(Vvar__0__C__120372,Vvar__1__rsplit__left__120375,Vvar__2__rsplit__common__120376,Vvar__3__rsplit__right__120377) ) ) ) ) ) ).

fof('$_inversion_Coq.setoid_ring.Field_theory.semi_field_theory',axiom,
    ! [Vvar__0__R__146544,Vvar__1__rO__146545,Vvar__2__rI__146546,Vvar__3__radd__146547,Vvar__4__rmul__146552,Vvar__5__rdiv__146557,Vvar__6__rinv__146562,Vvar__7__req__146565] :
      ( cType___24t(Vvar__0__R__146544)
     => ( t(Vvar__1__rO__146545,Vvar__0__R__146544)
       => ( t(Vvar__2__rI__146546,Vvar__0__R__146544)
         => ( c_24__type__146692___24t(Vvar__0__R__146544,Vvar__1__rO__146545,Vvar__2__rI__146546,Vvar__3__radd__146547,Vvar__4__rmul__146552,Vvar__5__rdiv__146557,Vvar__6__rinv__146562,Vvar__7__req__146565,Vvar__3__radd__146547)
           => ( c_24__type__146755___24t(Vvar__0__R__146544,Vvar__1__rO__146545,Vvar__2__rI__146546,Vvar__3__radd__146547,Vvar__4__rmul__146552,Vvar__5__rdiv__146557,Vvar__6__rinv__146562,Vvar__7__req__146565,Vvar__4__rmul__146552)
             => ( c_24__type__146818___24t(Vvar__0__R__146544,Vvar__1__rO__146545,Vvar__2__rI__146546,Vvar__3__radd__146547,Vvar__4__rmul__146552,Vvar__5__rdiv__146557,Vvar__6__rinv__146562,Vvar__7__req__146565,Vvar__5__rdiv__146557)
               => ( c_24__type__146872___24t(Vvar__0__R__146544,Vvar__1__rO__146545,Vvar__2__rI__146546,Vvar__3__radd__146547,Vvar__4__rmul__146552,Vvar__5__rdiv__146557,Vvar__6__rinv__146562,Vvar__7__req__146565,Vvar__6__rinv__146562)
                 => ( c_24__type__146935___24t(Vvar__0__R__146544,Vvar__1__rO__146545,Vvar__2__rI__146546,Vvar__3__radd__146547,Vvar__4__rmul__146552,Vvar__5__rdiv__146557,Vvar__6__rinv__146562,Vvar__7__req__146565,Vvar__7__req__146565)
                   => ( cCoq_2esetoid__ring_2eField__theory_2esemi__field__theory___24a8(Vvar__0__R__146544,Vvar__1__rO__146545,Vvar__2__rI__146546,Vvar__3__radd__146547,Vvar__4__rmul__146552,Vvar__5__rdiv__146557,Vvar__6__rinv__146562,Vvar__7__req__146565)
                     => ( cCoq_2esetoid__ring_2eRing__theory_2esemi__ring__theory___24a6(Vvar__0__R__146544,Vvar__1__rO__146545,Vvar__2__rI__146546,Vvar__3__radd__146547,Vvar__4__rmul__146552,Vvar__7__req__146565)
                        & ~ p(happ(happ(Vvar__7__req__146565,Vvar__2__rI__146546),Vvar__1__rO__146545))
                        & ! [Vvar__var__var__var__var__var__var__10__p__146600__146602__146609__146611__146613__146615__146617] :
                            ( t(Vvar__var__var__var__var__var__var__10__p__146600__146602__146609__146611__146613__146615__146617,Vvar__0__R__146544)
                           => ! [Vvar__var__var__var__var__var__var__11__q__146601__146603__146610__146612__146614__146616__146618] :
                                ( t(Vvar__var__var__var__var__var__var__11__q__146601__146603__146610__146612__146614__146616__146618,Vvar__0__R__146544)
                               => p(happ(happ(Vvar__7__req__146565,happ(happ(Vvar__5__rdiv__146557,Vvar__var__var__var__var__var__var__10__p__146600__146602__146609__146611__146613__146615__146617),Vvar__var__var__var__var__var__var__11__q__146601__146603__146610__146612__146614__146616__146618)),happ(happ(Vvar__4__rmul__146552,Vvar__var__var__var__var__var__var__10__p__146600__146602__146609__146611__146613__146615__146617),happ(Vvar__6__rinv__146562,Vvar__var__var__var__var__var__var__11__q__146601__146603__146610__146612__146614__146616__146618)))) ) )
                        & ! [Vvar__var__var__var__var__var__var__var__11__p__146605__146607__146619__146621__146623__146625__146627__146629] :
                            ( t(Vvar__var__var__var__var__var__var__var__11__p__146605__146607__146619__146621__146623__146625__146627__146629,Vvar__0__R__146544)
                           => ( ~ p(happ(happ(Vvar__7__req__146565,Vvar__var__var__var__var__var__var__var__11__p__146605__146607__146619__146621__146623__146625__146627__146629),Vvar__1__rO__146545))
                             => p(happ(happ(Vvar__7__req__146565,happ(happ(Vvar__4__rmul__146552,happ(Vvar__6__rinv__146562,Vvar__var__var__var__var__var__var__var__11__p__146605__146607__146619__146621__146623__146625__146627__146629)),Vvar__var__var__var__var__var__var__var__11__p__146605__146607__146619__146621__146623__146625__146627__146629)),Vvar__2__rI__146546)) ) )
                        & p(c_24True) ) ) ) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.setoid_ring.InitialRing.hypo',axiom,
    ! [VX147096] :
      ( cCoq_2esetoid__ring_2eInitialRing_2ehypo___24t(VX147096)
     => ? [Vvar__0__hypo__type__147097] :
          ( cType___24t(Vvar__0__hypo__type__147097)
          & ? [Vvar__1__hypo__proof__147098] :
              ( t(Vvar__1__hypo__proof__147098,Vvar__0__hypo__type__147097)
              & VX147096 = cCoq_2esetoid__ring_2eInitialRing_2emkhypo___24a2(Vvar__0__hypo__type__147097,Vvar__1__hypo__proof__147098) ) ) ) ).

fof('$_inversion_Coq.setoid_ring.Ring_polynom.Mon',axiom,
    ! [VX3046] :
      ( cCoq_2esetoid__ring_2eRing__polynom_2eMon___24t(VX3046)
     => ( VX3046 = cCoq_2esetoid__ring_2eRing__polynom_2emon0
        | ? [Vvar__0___24Anonymous__3047] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__3047)
            & ? [Vvar__1___24Anonymous__3048] :
                ( cCoq_2esetoid__ring_2eRing__polynom_2eMon___24t(Vvar__1___24Anonymous__3048)
                & VX3046 = cCoq_2esetoid__ring_2eRing__polynom_2ezmon___24a2(Vvar__0___24Anonymous__3047,Vvar__1___24Anonymous__3048) ) )
        | ? [Vvar__0___24Anonymous__3049] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__3049)
            & ? [Vvar__1___24Anonymous__3050] :
                ( cCoq_2esetoid__ring_2eRing__polynom_2eMon___24t(Vvar__1___24Anonymous__3050)
                & VX3046 = cCoq_2esetoid__ring_2eRing__polynom_2evmon___24a2(Vvar__0___24Anonymous__3049,Vvar__1___24Anonymous__3050) ) ) ) ) ).

fof('$_inversion_Coq.setoid_ring.Ring_polynom.PExpr',axiom,
    ! [Vvar__0__C__3067,VX3068] :
      ( cType___24t(Vvar__0__C__3067)
     => ( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__3067,VX3068)
       => ( VX3068 = cCoq_2esetoid__ring_2eRing__polynom_2ePEO___24a1(Vvar__0__C__3067)
          | VX3068 = cCoq_2esetoid__ring_2eRing__polynom_2ePEI___24a1(Vvar__0__C__3067)
          | ? [Vvar__1___24Anonymous__3072] :
              ( t(Vvar__1___24Anonymous__3072,Vvar__0__C__3067)
              & VX3068 = cCoq_2esetoid__ring_2eRing__polynom_2ePEc___24a2(Vvar__0__C__3067,Vvar__1___24Anonymous__3072) )
          | ? [Vvar__1___24Anonymous__3074] :
              ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__3074)
              & VX3068 = cCoq_2esetoid__ring_2eRing__polynom_2ePEX___24a2(Vvar__0__C__3067,Vvar__1___24Anonymous__3074) )
          | ? [Vvar__1___24Anonymous__3076] :
              ( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__3067,Vvar__1___24Anonymous__3076)
              & ? [Vvar__2___24Anonymous__3077] :
                  ( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__3067,Vvar__2___24Anonymous__3077)
                  & VX3068 = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(Vvar__0__C__3067,Vvar__1___24Anonymous__3076,Vvar__2___24Anonymous__3077) ) )
          | ? [Vvar__1___24Anonymous__3079] :
              ( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__3067,Vvar__1___24Anonymous__3079)
              & ? [Vvar__2___24Anonymous__3080] :
                  ( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__3067,Vvar__2___24Anonymous__3080)
                  & VX3068 = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(Vvar__0__C__3067,Vvar__1___24Anonymous__3079,Vvar__2___24Anonymous__3080) ) )
          | ? [Vvar__1___24Anonymous__3082] :
              ( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__3067,Vvar__1___24Anonymous__3082)
              & ? [Vvar__2___24Anonymous__3083] :
                  ( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__3067,Vvar__2___24Anonymous__3083)
                  & VX3068 = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(Vvar__0__C__3067,Vvar__1___24Anonymous__3082,Vvar__2___24Anonymous__3083) ) )
          | ? [Vvar__1___24Anonymous__3085] :
              ( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__3067,Vvar__1___24Anonymous__3085)
              & VX3068 = cCoq_2esetoid__ring_2eRing__polynom_2ePEopp___24a2(Vvar__0__C__3067,Vvar__1___24Anonymous__3085) )
          | ? [Vvar__1___24Anonymous__3087] :
              ( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__3067,Vvar__1___24Anonymous__3087)
              & ? [Vvar__2___24Anonymous__3088] :
                  ( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__2___24Anonymous__3088)
                  & VX3068 = cCoq_2esetoid__ring_2eRing__polynom_2ePEpow___24a3(Vvar__0__C__3067,Vvar__1___24Anonymous__3087,Vvar__2___24Anonymous__3088) ) ) ) ) ) ).

fof('$_inversion_Coq.setoid_ring.Ring_polynom.Pol',axiom,
    ! [Vvar__0__C__2865,VX2866] :
      ( cType___24t(Vvar__0__C__2865)
     => ( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vvar__0__C__2865,VX2866)
       => ( ? [Vvar__1___24Anonymous__2868] :
              ( t(Vvar__1___24Anonymous__2868,Vvar__0__C__2865)
              & VX2866 = cCoq_2esetoid__ring_2eRing__polynom_2ePc___24a2(Vvar__0__C__2865,Vvar__1___24Anonymous__2868) )
          | ? [Vvar__1___24Anonymous__2870] :
              ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__2870)
              & ? [Vvar__2___24Anonymous__2871] :
                  ( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vvar__0__C__2865,Vvar__2___24Anonymous__2871)
                  & VX2866 = cCoq_2esetoid__ring_2eRing__polynom_2ePinj___24a3(Vvar__0__C__2865,Vvar__1___24Anonymous__2870,Vvar__2___24Anonymous__2871) ) )
          | ? [Vvar__1___24Anonymous__2873] :
              ( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vvar__0__C__2865,Vvar__1___24Anonymous__2873)
              & ? [Vvar__2___24Anonymous__2874] :
                  ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2___24Anonymous__2874)
                  & ? [Vvar__3___24Anonymous__2875] :
                      ( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vvar__0__C__2865,Vvar__3___24Anonymous__2875)
                      & VX2866 = cCoq_2esetoid__ring_2eRing__polynom_2ePX___24a4(Vvar__0__C__2865,Vvar__1___24Anonymous__2873,Vvar__2___24Anonymous__2874,Vvar__3___24Anonymous__2875) ) ) ) ) ) ) ).

fof('$_inversion_Coq.setoid_ring.Ring_theory.almost_ring_theory',axiom,
    ! [Vvar__0__R__131828,Vvar__1__rO__131829,Vvar__2__rI__131830,Vvar__3__radd__131831,Vvar__4__rmul__131836,Vvar__5__rsub__131841,Vvar__6__ropp__131846,Vvar__7__req__131849] :
      ( cType___24t(Vvar__0__R__131828)
     => ( t(Vvar__1__rO__131829,Vvar__0__R__131828)
       => ( t(Vvar__2__rI__131830,Vvar__0__R__131828)
         => ( c_24__type__132077___24t(Vvar__0__R__131828,Vvar__1__rO__131829,Vvar__2__rI__131830,Vvar__3__radd__131831,Vvar__4__rmul__131836,Vvar__5__rsub__131841,Vvar__6__ropp__131846,Vvar__7__req__131849,Vvar__3__radd__131831)
           => ( c_24__type__132140___24t(Vvar__0__R__131828,Vvar__1__rO__131829,Vvar__2__rI__131830,Vvar__3__radd__131831,Vvar__4__rmul__131836,Vvar__5__rsub__131841,Vvar__6__ropp__131846,Vvar__7__req__131849,Vvar__4__rmul__131836)
             => ( c_24__type__132203___24t(Vvar__0__R__131828,Vvar__1__rO__131829,Vvar__2__rI__131830,Vvar__3__radd__131831,Vvar__4__rmul__131836,Vvar__5__rsub__131841,Vvar__6__ropp__131846,Vvar__7__req__131849,Vvar__5__rsub__131841)
               => ( c_24__type__132257___24t(Vvar__0__R__131828,Vvar__1__rO__131829,Vvar__2__rI__131830,Vvar__3__radd__131831,Vvar__4__rmul__131836,Vvar__5__rsub__131841,Vvar__6__ropp__131846,Vvar__7__req__131849,Vvar__6__ropp__131846)
                 => ( c_24__type__132320___24t(Vvar__0__R__131828,Vvar__1__rO__131829,Vvar__2__rI__131830,Vvar__3__radd__131831,Vvar__4__rmul__131836,Vvar__5__rsub__131841,Vvar__6__ropp__131846,Vvar__7__req__131849,Vvar__7__req__131849)
                   => ( cCoq_2esetoid__ring_2eRing__theory_2ealmost__ring__theory___24a8(Vvar__0__R__131828,Vvar__1__rO__131829,Vvar__2__rI__131830,Vvar__3__radd__131831,Vvar__4__rmul__131836,Vvar__5__rsub__131841,Vvar__6__ropp__131846,Vvar__7__req__131849)
                     => ( ! [Vvar__var__var__var__var__var__8__x__131882__131883__131936__131937__131938__131939] :
                            ( t(Vvar__var__var__var__var__var__8__x__131882__131883__131936__131937__131938__131939,Vvar__0__R__131828)
                           => p(happ(happ(Vvar__7__req__131849,happ(happ(Vvar__3__radd__131831,Vvar__1__rO__131829),Vvar__var__var__var__var__var__8__x__131882__131883__131936__131937__131938__131939)),Vvar__var__var__var__var__var__8__x__131882__131883__131936__131937__131938__131939)) )
                        & ! [Vvar__var__var__var__var__9__x__131885__131887__131940__131942__131944] :
                            ( t(Vvar__var__var__var__var__9__x__131885__131887__131940__131942__131944,Vvar__0__R__131828)
                           => ! [Vvar__var__var__var__var__10__y__131886__131888__131941__131943__131945] :
                                ( t(Vvar__var__var__var__var__10__y__131886__131888__131941__131943__131945,Vvar__0__R__131828)
                               => p(happ(happ(Vvar__7__req__131849,happ(happ(Vvar__3__radd__131831,Vvar__var__var__var__var__9__x__131885__131887__131940__131942__131944),Vvar__var__var__var__var__10__y__131886__131888__131941__131943__131945)),happ(happ(Vvar__3__radd__131831,Vvar__var__var__var__var__10__y__131886__131888__131941__131943__131945),Vvar__var__var__var__var__9__x__131885__131887__131940__131942__131944))) ) )
                        & ! [Vvar__var__var__var__var__10__x__131890__131893__131946__131949__131952] :
                            ( t(Vvar__var__var__var__var__10__x__131890__131893__131946__131949__131952,Vvar__0__R__131828)
                           => ! [Vvar__var__var__var__var__11__y__131891__131894__131947__131950__131953] :
                                ( t(Vvar__var__var__var__var__11__y__131891__131894__131947__131950__131953,Vvar__0__R__131828)
                               => ! [Vvar__var__var__var__var__12__z__131892__131895__131948__131951__131954] :
                                    ( t(Vvar__var__var__var__var__12__z__131892__131895__131948__131951__131954,Vvar__0__R__131828)
                                   => p(happ(happ(Vvar__7__req__131849,happ(happ(Vvar__3__radd__131831,Vvar__var__var__var__var__10__x__131890__131893__131946__131949__131952),happ(happ(Vvar__3__radd__131831,Vvar__var__var__var__var__11__y__131891__131894__131947__131950__131953),Vvar__var__var__var__var__12__z__131892__131895__131948__131951__131954))),happ(happ(Vvar__3__radd__131831,happ(happ(Vvar__3__radd__131831,Vvar__var__var__var__var__10__x__131890__131893__131946__131949__131952),Vvar__var__var__var__var__11__y__131891__131894__131947__131950__131953)),Vvar__var__var__var__var__12__z__131892__131895__131948__131951__131954))) ) ) )
                        & ! [Vvar__var__var__var__var__var__11__x__131897__131898__131955__131956__131957__131958] :
                            ( t(Vvar__var__var__var__var__var__11__x__131897__131898__131955__131956__131957__131958,Vvar__0__R__131828)
                           => p(happ(happ(Vvar__7__req__131849,happ(happ(Vvar__4__rmul__131836,Vvar__2__rI__131830),Vvar__var__var__var__var__var__11__x__131897__131898__131955__131956__131957__131958)),Vvar__var__var__var__var__var__11__x__131897__131898__131955__131956__131957__131958)) )
                        & ! [Vvar__var__var__var__var__var__12__x__131900__131901__131959__131960__131961__131962] :
                            ( t(Vvar__var__var__var__var__var__12__x__131900__131901__131959__131960__131961__131962,Vvar__0__R__131828)
                           => p(happ(happ(Vvar__7__req__131849,happ(happ(Vvar__4__rmul__131836,Vvar__1__rO__131829),Vvar__var__var__var__var__var__12__x__131900__131901__131959__131960__131961__131962)),Vvar__1__rO__131829)) )
                        & ! [Vvar__var__var__var__var__13__x__131903__131905__131963__131965__131967] :
                            ( t(Vvar__var__var__var__var__13__x__131903__131905__131963__131965__131967,Vvar__0__R__131828)
                           => ! [Vvar__var__var__var__var__14__y__131904__131906__131964__131966__131968] :
                                ( t(Vvar__var__var__var__var__14__y__131904__131906__131964__131966__131968,Vvar__0__R__131828)
                               => p(happ(happ(Vvar__7__req__131849,happ(happ(Vvar__4__rmul__131836,Vvar__var__var__var__var__13__x__131903__131905__131963__131965__131967),Vvar__var__var__var__var__14__y__131904__131906__131964__131966__131968)),happ(happ(Vvar__4__rmul__131836,Vvar__var__var__var__var__14__y__131904__131906__131964__131966__131968),Vvar__var__var__var__var__13__x__131903__131905__131963__131965__131967))) ) )
                        & ! [Vvar__var__var__var__var__14__x__131908__131911__131969__131972__131975] :
                            ( t(Vvar__var__var__var__var__14__x__131908__131911__131969__131972__131975,Vvar__0__R__131828)
                           => ! [Vvar__var__var__var__var__15__y__131909__131912__131970__131973__131976] :
                                ( t(Vvar__var__var__var__var__15__y__131909__131912__131970__131973__131976,Vvar__0__R__131828)
                               => ! [Vvar__var__var__var__var__16__z__131910__131913__131971__131974__131977] :
                                    ( t(Vvar__var__var__var__var__16__z__131910__131913__131971__131974__131977,Vvar__0__R__131828)
                                   => p(happ(happ(Vvar__7__req__131849,happ(happ(Vvar__4__rmul__131836,Vvar__var__var__var__var__14__x__131908__131911__131969__131972__131975),happ(happ(Vvar__4__rmul__131836,Vvar__var__var__var__var__15__y__131909__131912__131970__131973__131976),Vvar__var__var__var__var__16__z__131910__131913__131971__131974__131977))),happ(happ(Vvar__4__rmul__131836,happ(happ(Vvar__4__rmul__131836,Vvar__var__var__var__var__14__x__131908__131911__131969__131972__131975),Vvar__var__var__var__var__15__y__131909__131912__131970__131973__131976)),Vvar__var__var__var__var__16__z__131910__131913__131971__131974__131977))) ) ) )
                        & ! [Vvar__var__var__var__var__var__15__x__131915__131918__131978__131981__131984__131987] :
                            ( t(Vvar__var__var__var__var__var__15__x__131915__131918__131978__131981__131984__131987,Vvar__0__R__131828)
                           => ! [Vvar__var__var__var__var__var__16__y__131916__131919__131979__131982__131985__131988] :
                                ( t(Vvar__var__var__var__var__var__16__y__131916__131919__131979__131982__131985__131988,Vvar__0__R__131828)
                               => ! [Vvar__var__var__var__var__var__17__z__131917__131920__131980__131983__131986__131989] :
                                    ( t(Vvar__var__var__var__var__var__17__z__131917__131920__131980__131983__131986__131989,Vvar__0__R__131828)
                                   => p(happ(happ(Vvar__7__req__131849,happ(happ(Vvar__4__rmul__131836,happ(happ(Vvar__3__radd__131831,Vvar__var__var__var__var__var__15__x__131915__131918__131978__131981__131984__131987),Vvar__var__var__var__var__var__16__y__131916__131919__131979__131982__131985__131988)),Vvar__var__var__var__var__var__17__z__131917__131920__131980__131983__131986__131989)),happ(happ(Vvar__3__radd__131831,happ(happ(Vvar__4__rmul__131836,Vvar__var__var__var__var__var__15__x__131915__131918__131978__131981__131984__131987),Vvar__var__var__var__var__var__17__z__131917__131920__131980__131983__131986__131989)),happ(happ(Vvar__4__rmul__131836,Vvar__var__var__var__var__var__16__y__131916__131919__131979__131982__131985__131988),Vvar__var__var__var__var__var__17__z__131917__131920__131980__131983__131986__131989)))) ) ) )
                        & ! [Vvar__var__var__var__var__var__16__x__131922__131924__131990__131992__131994__131996] :
                            ( t(Vvar__var__var__var__var__var__16__x__131922__131924__131990__131992__131994__131996,Vvar__0__R__131828)
                           => ! [Vvar__var__var__var__var__var__17__y__131923__131925__131991__131993__131995__131997] :
                                ( t(Vvar__var__var__var__var__var__17__y__131923__131925__131991__131993__131995__131997,Vvar__0__R__131828)
                               => p(happ(happ(Vvar__7__req__131849,happ(Vvar__6__ropp__131846,happ(happ(Vvar__4__rmul__131836,Vvar__var__var__var__var__var__16__x__131922__131924__131990__131992__131994__131996),Vvar__var__var__var__var__var__17__y__131923__131925__131991__131993__131995__131997))),happ(happ(Vvar__4__rmul__131836,happ(Vvar__6__ropp__131846,Vvar__var__var__var__var__var__16__x__131922__131924__131990__131992__131994__131996)),Vvar__var__var__var__var__var__17__y__131923__131925__131991__131993__131995__131997))) ) )
                        & ! [Vvar__var__var__var__var__var__17__x__131927__131929__131998__132000__132002__132004] :
                            ( t(Vvar__var__var__var__var__var__17__x__131927__131929__131998__132000__132002__132004,Vvar__0__R__131828)
                           => ! [Vvar__var__var__var__var__var__18__y__131928__131930__131999__132001__132003__132005] :
                                ( t(Vvar__var__var__var__var__var__18__y__131928__131930__131999__132001__132003__132005,Vvar__0__R__131828)
                               => p(happ(happ(Vvar__7__req__131849,happ(Vvar__6__ropp__131846,happ(happ(Vvar__3__radd__131831,Vvar__var__var__var__var__var__17__x__131927__131929__131998__132000__132002__132004),Vvar__var__var__var__var__var__18__y__131928__131930__131999__132001__132003__132005))),happ(happ(Vvar__3__radd__131831,happ(Vvar__6__ropp__131846,Vvar__var__var__var__var__var__17__x__131927__131929__131998__132000__132002__132004)),happ(Vvar__6__ropp__131846,Vvar__var__var__var__var__var__18__y__131928__131930__131999__132001__132003__132005)))) ) )
                        & ! [Vvar__var__var__var__var__var__var__18__x__131932__131934__132006__132008__132010__132012__132014] :
                            ( t(Vvar__var__var__var__var__var__var__18__x__131932__131934__132006__132008__132010__132012__132014,Vvar__0__R__131828)
                           => ! [Vvar__var__var__var__var__var__var__19__y__131933__131935__132007__132009__132011__132013__132015] :
                                ( t(Vvar__var__var__var__var__var__var__19__y__131933__131935__132007__132009__132011__132013__132015,Vvar__0__R__131828)
                               => p(happ(happ(Vvar__7__req__131849,happ(happ(Vvar__5__rsub__131841,Vvar__var__var__var__var__var__var__18__x__131932__131934__132006__132008__132010__132012__132014),Vvar__var__var__var__var__var__var__19__y__131933__131935__132007__132009__132011__132013__132015)),happ(happ(Vvar__3__radd__131831,Vvar__var__var__var__var__var__var__18__x__131932__131934__132006__132008__132010__132012__132014),happ(Vvar__6__ropp__131846,Vvar__var__var__var__var__var__var__19__y__131933__131935__132007__132009__132011__132013__132015)))) ) )
                        & p(c_24True) ) ) ) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.setoid_ring.Ring_theory.div_theory',axiom,
    ! [Vvar__0__R__139155,Vvar__1__req__139156,Vvar__2__C__139161,Vvar__3__cadd__139162,Vvar__4__cmul__139167,Vvar__5__phi__139172,Vvar__6__cdiv__139175] :
      ( cType___24t(Vvar__0__R__139155)
     => ( c_24__type__139295___24t(Vvar__0__R__139155,Vvar__1__req__139156,Vvar__2__C__139161,Vvar__3__cadd__139162,Vvar__4__cmul__139167,Vvar__5__phi__139172,Vvar__6__cdiv__139175,Vvar__1__req__139156)
       => ( cType___24t(Vvar__2__C__139161)
         => ( c_24__type__139345___24t(Vvar__0__R__139155,Vvar__1__req__139156,Vvar__2__C__139161,Vvar__3__cadd__139162,Vvar__4__cmul__139167,Vvar__5__phi__139172,Vvar__6__cdiv__139175,Vvar__3__cadd__139162)
           => ( c_24__type__139395___24t(Vvar__0__R__139155,Vvar__1__req__139156,Vvar__2__C__139161,Vvar__3__cadd__139162,Vvar__4__cmul__139167,Vvar__5__phi__139172,Vvar__6__cdiv__139175,Vvar__4__cmul__139167)
             => ( c_24__type__139437___24t(Vvar__0__R__139155,Vvar__1__req__139156,Vvar__2__C__139161,Vvar__3__cadd__139162,Vvar__4__cmul__139167,Vvar__5__phi__139172,Vvar__6__cdiv__139175,Vvar__5__phi__139172)
               => ( c_24__type__139487___24t(Vvar__0__R__139155,Vvar__1__req__139156,Vvar__2__C__139161,Vvar__3__cadd__139162,Vvar__4__cmul__139167,Vvar__5__phi__139172,Vvar__6__cdiv__139175,Vvar__6__cdiv__139175)
                 => ( cCoq_2esetoid__ring_2eRing__theory_2ediv__theory___24a7(Vvar__0__R__139155,Vvar__1__req__139156,Vvar__2__C__139161,Vvar__3__cadd__139162,Vvar__4__cmul__139167,Vvar__5__phi__139172,Vvar__6__cdiv__139175)
                   => ( ! [Vvar__var__var__var__var__var__var__var__7__a__139207__139212__139217__139222__139227__139232__139237__139242] :
                          ( t(Vvar__var__var__var__var__var__var__var__7__a__139207__139212__139217__139222__139227__139232__139237__139242,Vvar__2__C__139161)
                         => ! [Vvar__var__var__var__var__var__var__var__8__b__139208__139213__139218__139223__139228__139233__139238__139243] :
                              ( t(Vvar__var__var__var__var__var__var__var__8__b__139208__139213__139218__139223__139228__139233__139238__139243,Vvar__2__C__139161)
                             => c_24__case__Coq_2eInit_2eDatatypes_2eprod_24139550___24a9(Vvar__0__R__139155,Vvar__1__req__139156,Vvar__2__C__139161,Vvar__3__cadd__139162,Vvar__4__cmul__139167,Vvar__5__phi__139172,Vvar__6__cdiv__139175,Vvar__var__var__var__var__var__var__var__7__a__139207__139212__139217__139222__139227__139232__139237__139242,Vvar__var__var__var__var__var__var__var__8__b__139208__139213__139218__139223__139228__139233__139238__139243) ) )
                      & p(c_24True) ) ) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.setoid_ring.Ring_theory.power_theory',axiom,
    ! [Vvar__0__R__135381,Vvar__1__rI__135382,Vvar__2__rmul__135383,Vvar__3__req__135388,Vvar__4__Cpow__135393,Vvar__5__Cp__phi__135394,Vvar__6__rpow__135397] :
      ( cType___24t(Vvar__0__R__135381)
     => ( t(Vvar__1__rI__135382,Vvar__0__R__135381)
       => ( c_24__type__135483___24t(Vvar__0__R__135381,Vvar__1__rI__135382,Vvar__2__rmul__135383,Vvar__3__req__135388,Vvar__4__Cpow__135393,Vvar__5__Cp__phi__135394,Vvar__6__rpow__135397,Vvar__2__rmul__135383)
         => ( c_24__type__135527___24t(Vvar__0__R__135381,Vvar__1__rI__135382,Vvar__2__rmul__135383,Vvar__3__req__135388,Vvar__4__Cpow__135393,Vvar__5__Cp__phi__135394,Vvar__6__rpow__135397,Vvar__3__req__135388)
           => ( cType___24t(Vvar__4__Cpow__135393)
             => ( c_24__type__135563___24t(Vvar__0__R__135381,Vvar__1__rI__135382,Vvar__2__rmul__135383,Vvar__3__req__135388,Vvar__4__Cpow__135393,Vvar__5__Cp__phi__135394,Vvar__6__rpow__135397,Vvar__5__Cp__phi__135394)
               => ( c_24__type__135607___24t(Vvar__0__R__135381,Vvar__1__rI__135382,Vvar__2__rmul__135383,Vvar__3__req__135388,Vvar__4__Cpow__135393,Vvar__5__Cp__phi__135394,Vvar__6__rpow__135397,Vvar__6__rpow__135397)
                 => ( cCoq_2esetoid__ring_2eRing__theory_2epower__theory___24a7(Vvar__0__R__135381,Vvar__1__rI__135382,Vvar__2__rmul__135383,Vvar__3__req__135388,Vvar__4__Cpow__135393,Vvar__5__Cp__phi__135394,Vvar__6__rpow__135397)
                   => ( ! [Vvar__var__var__var__var__var__var__var__7__r__135425__135427__135429__135431__135433__135435__135437__135439] :
                          ( t(Vvar__var__var__var__var__var__var__var__7__r__135425__135427__135429__135431__135433__135435__135437__135439,Vvar__0__R__135381)
                         => ! [Vvar__var__var__var__var__var__var__var__8__n__135426__135428__135430__135432__135434__135436__135438__135440] :
                              ( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__var__var__var__var__var__var__var__8__n__135426__135428__135430__135432__135434__135436__135438__135440)
                             => p(happ(happ(Vvar__3__req__135388,happ(happ(Vvar__6__rpow__135397,Vvar__var__var__var__var__var__var__var__7__r__135425__135427__135429__135431__135433__135435__135437__135439),happ(Vvar__5__Cp__phi__135394,Vvar__var__var__var__var__var__var__var__8__n__135426__135428__135430__135432__135434__135436__135438__135440))),cCoq_2esetoid__ring_2eRing__theory_2epow__N___24a5(Vvar__0__R__135381,Vvar__1__rI__135382,Vvar__2__rmul__135383,Vvar__var__var__var__var__var__var__var__7__r__135425__135427__135429__135431__135433__135435__135437__135439,Vvar__var__var__var__var__var__var__var__8__n__135426__135428__135430__135432__135434__135436__135438__135440))) ) )
                      & p(c_24True) ) ) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.setoid_ring.Ring_theory.ring_eq_ext',axiom,
    ! [Vvar__0__R__132566,Vvar__1__radd__132567,Vvar__2__rmul__132572,Vvar__3__ropp__132577,Vvar__4__req__132580] :
      ( cType___24t(Vvar__0__R__132566)
     => ( c_24__type__132671___24t(Vvar__0__R__132566,Vvar__1__radd__132567,Vvar__2__rmul__132572,Vvar__3__ropp__132577,Vvar__4__req__132580,Vvar__1__radd__132567)
       => ( c_24__type__132701___24t(Vvar__0__R__132566,Vvar__1__radd__132567,Vvar__2__rmul__132572,Vvar__3__ropp__132577,Vvar__4__req__132580,Vvar__2__rmul__132572)
         => ( c_24__type__132725___24t(Vvar__0__R__132566,Vvar__1__radd__132567,Vvar__2__rmul__132572,Vvar__3__ropp__132577,Vvar__4__req__132580,Vvar__3__ropp__132577)
           => ( c_24__type__132755___24t(Vvar__0__R__132566,Vvar__1__radd__132567,Vvar__2__rmul__132572,Vvar__3__ropp__132577,Vvar__4__req__132580,Vvar__4__req__132580)
             => ( cCoq_2esetoid__ring_2eRing__theory_2ering__eq__ext___24a5(Vvar__0__R__132566,Vvar__1__radd__132567,Vvar__2__rmul__132572,Vvar__3__ropp__132577,Vvar__4__req__132580)
               => ( cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__132785___24a5(Vvar__0__R__132566,Vvar__1__radd__132567,Vvar__2__rmul__132572,Vvar__3__ropp__132577,Vvar__4__req__132580),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(Vvar__0__R__132566,c_24__type__132809___24a5(Vvar__0__R__132566,Vvar__1__radd__132567,Vvar__2__rmul__132572,Vvar__3__ropp__132577,Vvar__4__req__132580),Vvar__4__req__132580,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(Vvar__0__R__132566,Vvar__0__R__132566,Vvar__4__req__132580,Vvar__4__req__132580)),Vvar__1__radd__132567)
                  & cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__132842___24a5(Vvar__0__R__132566,Vvar__1__radd__132567,Vvar__2__rmul__132572,Vvar__3__ropp__132577,Vvar__4__req__132580),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(Vvar__0__R__132566,c_24__type__132866___24a5(Vvar__0__R__132566,Vvar__1__radd__132567,Vvar__2__rmul__132572,Vvar__3__ropp__132577,Vvar__4__req__132580),Vvar__4__req__132580,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(Vvar__0__R__132566,Vvar__0__R__132566,Vvar__4__req__132580,Vvar__4__req__132580)),Vvar__2__rmul__132572)
                  & cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__132893___24a5(Vvar__0__R__132566,Vvar__1__radd__132567,Vvar__2__rmul__132572,Vvar__3__ropp__132577,Vvar__4__req__132580),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(Vvar__0__R__132566,Vvar__0__R__132566,Vvar__4__req__132580,Vvar__4__req__132580),Vvar__3__ropp__132577)
                  & p(c_24True) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.setoid_ring.Ring_theory.ring_kind',axiom,
    ! [VX148653] :
      ( cCoq_2esetoid__ring_2eRing__theory_2ering__kind___24t(VX148653)
     => ( VX148653 = cCoq_2esetoid__ring_2eRing__theory_2eAbstract
        | ? [Vvar__0__R__148654] :
            ( cType___24t(Vvar__0__R__148654)
            & ? [Vvar__1__req__148655] :
                ( c_24__type__2863___24t(Vvar__0__R__148654,Vvar__1__req__148655)
                & ? [Vvar__2__reqb__148660] :
                    ( c_24__type__3030___24t(Vvar__0__R__148654,Vvar__2__reqb__148660)
                    & ! [Vvar__var__3__x__148666__148669] :
                        ( t(Vvar__var__3__x__148666__148669,Vvar__0__R__148654)
                       => ! [Vvar__var__4__y__148667__148670] :
                            ( t(Vvar__var__4__y__148667__148670,Vvar__0__R__148654)
                           => ( happ(happ(Vvar__2__reqb__148660,Vvar__var__3__x__148666__148669),Vvar__var__4__y__148667__148670) = cCoq_2eInit_2eDatatypes_2etrue
                             => p(happ(happ(Vvar__1__req__148655,Vvar__var__3__x__148666__148669),Vvar__var__4__y__148667__148670)) ) ) )
                    & VX148653 = cCoq_2esetoid__ring_2eRing__theory_2eComputational___24a3(Vvar__0__R__148654,Vvar__1__req__148655,Vvar__2__reqb__148660) ) ) )
        | ? [Vvar__0__R__148672] :
            ( cType___24t(Vvar__0__R__148672)
            & ? [Vvar__1__rO__148673] :
                ( t(Vvar__1__rO__148673,Vvar__0__R__148672)
                & ? [Vvar__2__rI__148674] :
                    ( t(Vvar__2__rI__148674,Vvar__0__R__148672)
                    & ? [Vvar__3__radd__148675] :
                        ( c_24__type__3514___24t(Vvar__0__R__148672,Vvar__3__radd__148675)
                        & ? [Vvar__4__rmul__148680] :
                            ( c_24__type__3514___24t(Vvar__0__R__148672,Vvar__4__rmul__148680)
                            & ? [Vvar__5__rsub__148685] :
                                ( c_24__type__3514___24t(Vvar__0__R__148672,Vvar__5__rsub__148685)
                                & ? [Vvar__6__ropp__148690] :
                                    ( c_24__type__3523___24t(Vvar__0__R__148672,Vvar__6__ropp__148690)
                                    & ? [Vvar__7__req__148693] :
                                        ( c_24__type__2863___24t(Vvar__0__R__148672,Vvar__7__req__148693)
                                        & ? [Vvar__8__C__148698] :
                                            ( cType___24t(Vvar__8__C__148698)
                                            & ? [Vvar__9__cO__148699] :
                                                ( t(Vvar__9__cO__148699,Vvar__8__C__148698)
                                                & ? [Vvar__10__cI__148700] :
                                                    ( t(Vvar__10__cI__148700,Vvar__8__C__148698)
                                                    & ? [Vvar__11__cadd__148701] :
                                                        ( c_24__type__6690___24t(Vvar__0__R__148672,Vvar__8__C__148698,Vvar__11__cadd__148701)
                                                        & ? [Vvar__12__cmul__148706] :
                                                            ( c_24__type__6690___24t(Vvar__0__R__148672,Vvar__8__C__148698,Vvar__12__cmul__148706)
                                                            & ? [Vvar__13__csub__148711] :
                                                                ( c_24__type__6690___24t(Vvar__0__R__148672,Vvar__8__C__148698,Vvar__13__csub__148711)
                                                                & ? [Vvar__14__copp__148716] :
                                                                    ( c_24__type__6791___24t(Vvar__0__R__148672,Vvar__8__C__148698,Vvar__14__copp__148716)
                                                                    & ? [Vvar__15__ceqb__148719] :
                                                                        ( c_24__type__6702___24t(Vvar__0__R__148672,Vvar__8__C__148698,Vvar__15__ceqb__148719)
                                                                        & ? [Vvar__16__phi__148724] :
                                                                            ( c_24__type__5375___24t(Vvar__0__R__148672,Vvar__8__C__148698,Vvar__16__phi__148724)
                                                                            & cCoq_2esetoid__ring_2eRing__theory_2ering__morph___24a17(Vvar__0__R__148672,Vvar__1__rO__148673,Vvar__2__rI__148674,Vvar__3__radd__148675,Vvar__4__rmul__148680,Vvar__5__rsub__148685,Vvar__6__ropp__148690,Vvar__7__req__148693,Vvar__8__C__148698,Vvar__9__cO__148699,Vvar__10__cI__148700,Vvar__11__cadd__148701,Vvar__12__cmul__148706,Vvar__13__csub__148711,Vvar__14__copp__148716,Vvar__15__ceqb__148719,Vvar__16__phi__148724)
                                                                            & VX148653 = cCoq_2esetoid__ring_2eRing__theory_2eMorphism___24a17(Vvar__0__R__148672,Vvar__1__rO__148673,Vvar__2__rI__148674,Vvar__3__radd__148675,Vvar__4__rmul__148680,Vvar__5__rsub__148685,Vvar__6__ropp__148690,Vvar__7__req__148693,Vvar__8__C__148698,Vvar__9__cO__148699,Vvar__10__cI__148700,Vvar__11__cadd__148701,Vvar__12__cmul__148706,Vvar__13__csub__148711,Vvar__14__copp__148716,Vvar__15__ceqb__148719,Vvar__16__phi__148724) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.setoid_ring.Ring_theory.ring_morph',axiom,
    ! [Vvar__0__R__132896,Vvar__1__rO__132897,Vvar__2__rI__132898,Vvar__3__radd__132899,Vvar__4__rmul__132904,Vvar__5__rsub__132909,Vvar__6__ropp__132914,Vvar__7__req__132917,Vvar__8__C__132922,Vvar__9__cO__132923,Vvar__10__cI__132924,Vvar__11__cadd__132925,Vvar__12__cmul__132930,Vvar__13__csub__132935,Vvar__14__copp__132940,Vvar__15__ceqb__132943,Vvar__16__phi__132948] :
      ( cType___24t(Vvar__0__R__132896)
     => ( t(Vvar__1__rO__132897,Vvar__0__R__132896)
       => ( t(Vvar__2__rI__132898,Vvar__0__R__132896)
         => ( c_24__type__133292___24t(Vvar__0__R__132896,Vvar__1__rO__132897,Vvar__2__rI__132898,Vvar__3__radd__132899,Vvar__4__rmul__132904,Vvar__5__rsub__132909,Vvar__6__ropp__132914,Vvar__7__req__132917,Vvar__8__C__132922,Vvar__9__cO__132923,Vvar__10__cI__132924,Vvar__11__cadd__132925,Vvar__12__cmul__132930,Vvar__13__csub__132935,Vvar__14__copp__132940,Vvar__15__ceqb__132943,Vvar__16__phi__132948,Vvar__3__radd__132899)
           => ( c_24__type__133505___24t(Vvar__0__R__132896,Vvar__1__rO__132897,Vvar__2__rI__132898,Vvar__3__radd__132899,Vvar__4__rmul__132904,Vvar__5__rsub__132909,Vvar__6__ropp__132914,Vvar__7__req__132917,Vvar__8__C__132922,Vvar__9__cO__132923,Vvar__10__cI__132924,Vvar__11__cadd__132925,Vvar__12__cmul__132930,Vvar__13__csub__132935,Vvar__14__copp__132940,Vvar__15__ceqb__132943,Vvar__16__phi__132948,Vvar__4__rmul__132904)
             => ( c_24__type__133718___24t(Vvar__0__R__132896,Vvar__1__rO__132897,Vvar__2__rI__132898,Vvar__3__radd__132899,Vvar__4__rmul__132904,Vvar__5__rsub__132909,Vvar__6__ropp__132914,Vvar__7__req__132917,Vvar__8__C__132922,Vvar__9__cO__132923,Vvar__10__cI__132924,Vvar__11__cadd__132925,Vvar__12__cmul__132930,Vvar__13__csub__132935,Vvar__14__copp__132940,Vvar__15__ceqb__132943,Vvar__16__phi__132948,Vvar__5__rsub__132909)
               => ( c_24__type__133913___24t(Vvar__0__R__132896,Vvar__1__rO__132897,Vvar__2__rI__132898,Vvar__3__radd__132899,Vvar__4__rmul__132904,Vvar__5__rsub__132909,Vvar__6__ropp__132914,Vvar__7__req__132917,Vvar__8__C__132922,Vvar__9__cO__132923,Vvar__10__cI__132924,Vvar__11__cadd__132925,Vvar__12__cmul__132930,Vvar__13__csub__132935,Vvar__14__copp__132940,Vvar__15__ceqb__132943,Vvar__16__phi__132948,Vvar__6__ropp__132914)
                 => ( c_24__type__134126___24t(Vvar__0__R__132896,Vvar__1__rO__132897,Vvar__2__rI__132898,Vvar__3__radd__132899,Vvar__4__rmul__132904,Vvar__5__rsub__132909,Vvar__6__ropp__132914,Vvar__7__req__132917,Vvar__8__C__132922,Vvar__9__cO__132923,Vvar__10__cI__132924,Vvar__11__cadd__132925,Vvar__12__cmul__132930,Vvar__13__csub__132935,Vvar__14__copp__132940,Vvar__15__ceqb__132943,Vvar__16__phi__132948,Vvar__7__req__132917)
                   => ( cType___24t(Vvar__8__C__132922)
                     => ( t(Vvar__9__cO__132923,Vvar__8__C__132922)
                       => ( t(Vvar__10__cI__132924,Vvar__8__C__132922)
                         => ( c_24__type__134339___24t(Vvar__0__R__132896,Vvar__1__rO__132897,Vvar__2__rI__132898,Vvar__3__radd__132899,Vvar__4__rmul__132904,Vvar__5__rsub__132909,Vvar__6__ropp__132914,Vvar__7__req__132917,Vvar__8__C__132922,Vvar__9__cO__132923,Vvar__10__cI__132924,Vvar__11__cadd__132925,Vvar__12__cmul__132930,Vvar__13__csub__132935,Vvar__14__copp__132940,Vvar__15__ceqb__132943,Vvar__16__phi__132948,Vvar__11__cadd__132925)
                           => ( c_24__type__134552___24t(Vvar__0__R__132896,Vvar__1__rO__132897,Vvar__2__rI__132898,Vvar__3__radd__132899,Vvar__4__rmul__132904,Vvar__5__rsub__132909,Vvar__6__ropp__132914,Vvar__7__req__132917,Vvar__8__C__132922,Vvar__9__cO__132923,Vvar__10__cI__132924,Vvar__11__cadd__132925,Vvar__12__cmul__132930,Vvar__13__csub__132935,Vvar__14__copp__132940,Vvar__15__ceqb__132943,Vvar__16__phi__132948,Vvar__12__cmul__132930)
                             => ( c_24__type__134765___24t(Vvar__0__R__132896,Vvar__1__rO__132897,Vvar__2__rI__132898,Vvar__3__radd__132899,Vvar__4__rmul__132904,Vvar__5__rsub__132909,Vvar__6__ropp__132914,Vvar__7__req__132917,Vvar__8__C__132922,Vvar__9__cO__132923,Vvar__10__cI__132924,Vvar__11__cadd__132925,Vvar__12__cmul__132930,Vvar__13__csub__132935,Vvar__14__copp__132940,Vvar__15__ceqb__132943,Vvar__16__phi__132948,Vvar__13__csub__132935)
                               => ( c_24__type__134960___24t(Vvar__0__R__132896,Vvar__1__rO__132897,Vvar__2__rI__132898,Vvar__3__radd__132899,Vvar__4__rmul__132904,Vvar__5__rsub__132909,Vvar__6__ropp__132914,Vvar__7__req__132917,Vvar__8__C__132922,Vvar__9__cO__132923,Vvar__10__cI__132924,Vvar__11__cadd__132925,Vvar__12__cmul__132930,Vvar__13__csub__132935,Vvar__14__copp__132940,Vvar__15__ceqb__132943,Vvar__16__phi__132948,Vvar__14__copp__132940)
                                 => ( c_24__type__135173___24t(Vvar__0__R__132896,Vvar__1__rO__132897,Vvar__2__rI__132898,Vvar__3__radd__132899,Vvar__4__rmul__132904,Vvar__5__rsub__132909,Vvar__6__ropp__132914,Vvar__7__req__132917,Vvar__8__C__132922,Vvar__9__cO__132923,Vvar__10__cI__132924,Vvar__11__cadd__132925,Vvar__12__cmul__132930,Vvar__13__csub__132935,Vvar__14__copp__132940,Vvar__15__ceqb__132943,Vvar__16__phi__132948,Vvar__15__ceqb__132943)
                                   => ( c_24__type__135368___24t(Vvar__0__R__132896,Vvar__1__rO__132897,Vvar__2__rI__132898,Vvar__3__radd__132899,Vvar__4__rmul__132904,Vvar__5__rsub__132909,Vvar__6__ropp__132914,Vvar__7__req__132917,Vvar__8__C__132922,Vvar__9__cO__132923,Vvar__10__cI__132924,Vvar__11__cadd__132925,Vvar__12__cmul__132930,Vvar__13__csub__132935,Vvar__14__copp__132940,Vvar__15__ceqb__132943,Vvar__16__phi__132948,Vvar__16__phi__132948)
                                     => ( cCoq_2esetoid__ring_2eRing__theory_2ering__morph___24a17(Vvar__0__R__132896,Vvar__1__rO__132897,Vvar__2__rI__132898,Vvar__3__radd__132899,Vvar__4__rmul__132904,Vvar__5__rsub__132909,Vvar__6__ropp__132914,Vvar__7__req__132917,Vvar__8__C__132922,Vvar__9__cO__132923,Vvar__10__cI__132924,Vvar__11__cadd__132925,Vvar__12__cmul__132930,Vvar__13__csub__132935,Vvar__14__copp__132940,Vvar__15__ceqb__132943,Vvar__16__phi__132948)
                                       => ( p(happ(happ(Vvar__7__req__132917,happ(Vvar__16__phi__132948,Vvar__9__cO__132923)),Vvar__1__rO__132897))
                                          & p(happ(happ(Vvar__7__req__132917,happ(Vvar__16__phi__132948,Vvar__10__cI__132924)),Vvar__2__rI__132898))
                                          & ! [Vvar__var__var__var__var__var__var__19__x__133010__133012__133034__133036__133038__133040__133042] :
                                              ( t(Vvar__var__var__var__var__var__var__19__x__133010__133012__133034__133036__133038__133040__133042,Vvar__8__C__132922)
                                             => ! [Vvar__var__var__var__var__var__var__20__y__133011__133013__133035__133037__133039__133041__133043] :
                                                  ( t(Vvar__var__var__var__var__var__var__20__y__133011__133013__133035__133037__133039__133041__133043,Vvar__8__C__132922)
                                                 => p(happ(happ(Vvar__7__req__132917,happ(Vvar__16__phi__132948,happ(happ(Vvar__11__cadd__132925,Vvar__var__var__var__var__var__var__19__x__133010__133012__133034__133036__133038__133040__133042),Vvar__var__var__var__var__var__var__20__y__133011__133013__133035__133037__133039__133041__133043))),happ(happ(Vvar__3__radd__132899,happ(Vvar__16__phi__132948,Vvar__var__var__var__var__var__var__19__x__133010__133012__133034__133036__133038__133040__133042)),happ(Vvar__16__phi__132948,Vvar__var__var__var__var__var__var__20__y__133011__133013__133035__133037__133039__133041__133043)))) ) )
                                          & ! [Vvar__var__var__var__var__var__var__20__x__133015__133017__133044__133046__133048__133050__133052] :
                                              ( t(Vvar__var__var__var__var__var__var__20__x__133015__133017__133044__133046__133048__133050__133052,Vvar__8__C__132922)
                                             => ! [Vvar__var__var__var__var__var__var__21__y__133016__133018__133045__133047__133049__133051__133053] :
                                                  ( t(Vvar__var__var__var__var__var__var__21__y__133016__133018__133045__133047__133049__133051__133053,Vvar__8__C__132922)
                                                 => p(happ(happ(Vvar__7__req__132917,happ(Vvar__16__phi__132948,happ(happ(Vvar__13__csub__132935,Vvar__var__var__var__var__var__var__20__x__133015__133017__133044__133046__133048__133050__133052),Vvar__var__var__var__var__var__var__21__y__133016__133018__133045__133047__133049__133051__133053))),happ(happ(Vvar__5__rsub__132909,happ(Vvar__16__phi__132948,Vvar__var__var__var__var__var__var__20__x__133015__133017__133044__133046__133048__133050__133052)),happ(Vvar__16__phi__132948,Vvar__var__var__var__var__var__var__21__y__133016__133018__133045__133047__133049__133051__133053)))) ) )
                                          & ! [Vvar__var__var__var__var__var__var__21__x__133020__133022__133054__133056__133058__133060__133062] :
                                              ( t(Vvar__var__var__var__var__var__var__21__x__133020__133022__133054__133056__133058__133060__133062,Vvar__8__C__132922)
                                             => ! [Vvar__var__var__var__var__var__var__22__y__133021__133023__133055__133057__133059__133061__133063] :
                                                  ( t(Vvar__var__var__var__var__var__var__22__y__133021__133023__133055__133057__133059__133061__133063,Vvar__8__C__132922)
                                                 => p(happ(happ(Vvar__7__req__132917,happ(Vvar__16__phi__132948,happ(happ(Vvar__12__cmul__132930,Vvar__var__var__var__var__var__var__21__x__133020__133022__133054__133056__133058__133060__133062),Vvar__var__var__var__var__var__var__22__y__133021__133023__133055__133057__133059__133061__133063))),happ(happ(Vvar__4__rmul__132904,happ(Vvar__16__phi__132948,Vvar__var__var__var__var__var__var__21__x__133020__133022__133054__133056__133058__133060__133062)),happ(Vvar__16__phi__132948,Vvar__var__var__var__var__var__var__22__y__133021__133023__133055__133057__133059__133061__133063)))) ) )
                                          & ! [Vvar__var__var__var__var__var__var__22__x__133025__133026__133064__133065__133066__133067__133068] :
                                              ( t(Vvar__var__var__var__var__var__var__22__x__133025__133026__133064__133065__133066__133067__133068,Vvar__8__C__132922)
                                             => p(happ(happ(Vvar__7__req__132917,happ(Vvar__16__phi__132948,happ(Vvar__14__copp__132940,Vvar__var__var__var__var__var__var__22__x__133025__133026__133064__133065__133066__133067__133068))),happ(Vvar__6__ropp__132914,happ(Vvar__16__phi__132948,Vvar__var__var__var__var__var__var__22__x__133025__133026__133064__133065__133066__133067__133068)))) )
                                          & ! [Vvar__var__var__var__var__var__23__x__133028__133031__133069__133072__133075__133078] :
                                              ( t(Vvar__var__var__var__var__var__23__x__133028__133031__133069__133072__133075__133078,Vvar__8__C__132922)
                                             => ! [Vvar__var__var__var__var__var__24__y__133029__133032__133070__133073__133076__133079] :
                                                  ( t(Vvar__var__var__var__var__var__24__y__133029__133032__133070__133073__133076__133079,Vvar__8__C__132922)
                                                 => ( happ(happ(Vvar__15__ceqb__132943,Vvar__var__var__var__var__var__23__x__133028__133031__133069__133072__133075__133078),Vvar__var__var__var__var__var__24__y__133029__133032__133070__133073__133076__133079) = cCoq_2eInit_2eDatatypes_2etrue
                                                   => p(happ(happ(Vvar__7__req__132917,happ(Vvar__16__phi__132948,Vvar__var__var__var__var__var__23__x__133028__133031__133069__133072__133075__133078)),happ(Vvar__16__phi__132948,Vvar__var__var__var__var__var__24__y__133029__133032__133070__133073__133076__133079))) ) ) )
                                          & p(c_24True) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.setoid_ring.Ring_theory.ring_theory',axiom,
    ! [Vvar__0__R__138463,Vvar__1__rO__138464,Vvar__2__rI__138465,Vvar__3__radd__138466,Vvar__4__rmul__138471,Vvar__5__rsub__138476,Vvar__6__ropp__138481,Vvar__7__req__138484] :
      ( cType___24t(Vvar__0__R__138463)
     => ( t(Vvar__1__rO__138464,Vvar__0__R__138463)
       => ( t(Vvar__2__rI__138465,Vvar__0__R__138463)
         => ( c_24__type__138687___24t(Vvar__0__R__138463,Vvar__1__rO__138464,Vvar__2__rI__138465,Vvar__3__radd__138466,Vvar__4__rmul__138471,Vvar__5__rsub__138476,Vvar__6__ropp__138481,Vvar__7__req__138484,Vvar__3__radd__138466)
           => ( c_24__type__138750___24t(Vvar__0__R__138463,Vvar__1__rO__138464,Vvar__2__rI__138465,Vvar__3__radd__138466,Vvar__4__rmul__138471,Vvar__5__rsub__138476,Vvar__6__ropp__138481,Vvar__7__req__138484,Vvar__4__rmul__138471)
             => ( c_24__type__138813___24t(Vvar__0__R__138463,Vvar__1__rO__138464,Vvar__2__rI__138465,Vvar__3__radd__138466,Vvar__4__rmul__138471,Vvar__5__rsub__138476,Vvar__6__ropp__138481,Vvar__7__req__138484,Vvar__5__rsub__138476)
               => ( c_24__type__138867___24t(Vvar__0__R__138463,Vvar__1__rO__138464,Vvar__2__rI__138465,Vvar__3__radd__138466,Vvar__4__rmul__138471,Vvar__5__rsub__138476,Vvar__6__ropp__138481,Vvar__7__req__138484,Vvar__6__ropp__138481)
                 => ( c_24__type__138930___24t(Vvar__0__R__138463,Vvar__1__rO__138464,Vvar__2__rI__138465,Vvar__3__radd__138466,Vvar__4__rmul__138471,Vvar__5__rsub__138476,Vvar__6__ropp__138481,Vvar__7__req__138484,Vvar__7__req__138484)
                   => ( cCoq_2esetoid__ring_2eRing__theory_2ering__theory___24a8(Vvar__0__R__138463,Vvar__1__rO__138464,Vvar__2__rI__138465,Vvar__3__radd__138466,Vvar__4__rmul__138471,Vvar__5__rsub__138476,Vvar__6__ropp__138481,Vvar__7__req__138484)
                     => ( ! [Vvar__var__var__var__var__var__8__x__138517__138518__138561__138562__138563__138564] :
                            ( t(Vvar__var__var__var__var__var__8__x__138517__138518__138561__138562__138563__138564,Vvar__0__R__138463)
                           => p(happ(happ(Vvar__7__req__138484,happ(happ(Vvar__3__radd__138466,Vvar__1__rO__138464),Vvar__var__var__var__var__var__8__x__138517__138518__138561__138562__138563__138564)),Vvar__var__var__var__var__var__8__x__138517__138518__138561__138562__138563__138564)) )
                        & ! [Vvar__var__var__var__var__9__x__138520__138522__138565__138567__138569] :
                            ( t(Vvar__var__var__var__var__9__x__138520__138522__138565__138567__138569,Vvar__0__R__138463)
                           => ! [Vvar__var__var__var__var__10__y__138521__138523__138566__138568__138570] :
                                ( t(Vvar__var__var__var__var__10__y__138521__138523__138566__138568__138570,Vvar__0__R__138463)
                               => p(happ(happ(Vvar__7__req__138484,happ(happ(Vvar__3__radd__138466,Vvar__var__var__var__var__9__x__138520__138522__138565__138567__138569),Vvar__var__var__var__var__10__y__138521__138523__138566__138568__138570)),happ(happ(Vvar__3__radd__138466,Vvar__var__var__var__var__10__y__138521__138523__138566__138568__138570),Vvar__var__var__var__var__9__x__138520__138522__138565__138567__138569))) ) )
                        & ! [Vvar__var__var__var__var__10__x__138525__138528__138571__138574__138577] :
                            ( t(Vvar__var__var__var__var__10__x__138525__138528__138571__138574__138577,Vvar__0__R__138463)
                           => ! [Vvar__var__var__var__var__11__y__138526__138529__138572__138575__138578] :
                                ( t(Vvar__var__var__var__var__11__y__138526__138529__138572__138575__138578,Vvar__0__R__138463)
                               => ! [Vvar__var__var__var__var__12__z__138527__138530__138573__138576__138579] :
                                    ( t(Vvar__var__var__var__var__12__z__138527__138530__138573__138576__138579,Vvar__0__R__138463)
                                   => p(happ(happ(Vvar__7__req__138484,happ(happ(Vvar__3__radd__138466,Vvar__var__var__var__var__10__x__138525__138528__138571__138574__138577),happ(happ(Vvar__3__radd__138466,Vvar__var__var__var__var__11__y__138526__138529__138572__138575__138578),Vvar__var__var__var__var__12__z__138527__138530__138573__138576__138579))),happ(happ(Vvar__3__radd__138466,happ(happ(Vvar__3__radd__138466,Vvar__var__var__var__var__10__x__138525__138528__138571__138574__138577),Vvar__var__var__var__var__11__y__138526__138529__138572__138575__138578)),Vvar__var__var__var__var__12__z__138527__138530__138573__138576__138579))) ) ) )
                        & ! [Vvar__var__var__var__var__var__11__x__138532__138533__138580__138581__138582__138583] :
                            ( t(Vvar__var__var__var__var__var__11__x__138532__138533__138580__138581__138582__138583,Vvar__0__R__138463)
                           => p(happ(happ(Vvar__7__req__138484,happ(happ(Vvar__4__rmul__138471,Vvar__2__rI__138465),Vvar__var__var__var__var__var__11__x__138532__138533__138580__138581__138582__138583)),Vvar__var__var__var__var__var__11__x__138532__138533__138580__138581__138582__138583)) )
                        & ! [Vvar__var__var__var__var__12__x__138535__138537__138584__138586__138588] :
                            ( t(Vvar__var__var__var__var__12__x__138535__138537__138584__138586__138588,Vvar__0__R__138463)
                           => ! [Vvar__var__var__var__var__13__y__138536__138538__138585__138587__138589] :
                                ( t(Vvar__var__var__var__var__13__y__138536__138538__138585__138587__138589,Vvar__0__R__138463)
                               => p(happ(happ(Vvar__7__req__138484,happ(happ(Vvar__4__rmul__138471,Vvar__var__var__var__var__12__x__138535__138537__138584__138586__138588),Vvar__var__var__var__var__13__y__138536__138538__138585__138587__138589)),happ(happ(Vvar__4__rmul__138471,Vvar__var__var__var__var__13__y__138536__138538__138585__138587__138589),Vvar__var__var__var__var__12__x__138535__138537__138584__138586__138588))) ) )
                        & ! [Vvar__var__var__var__var__13__x__138540__138543__138590__138593__138596] :
                            ( t(Vvar__var__var__var__var__13__x__138540__138543__138590__138593__138596,Vvar__0__R__138463)
                           => ! [Vvar__var__var__var__var__14__y__138541__138544__138591__138594__138597] :
                                ( t(Vvar__var__var__var__var__14__y__138541__138544__138591__138594__138597,Vvar__0__R__138463)
                               => ! [Vvar__var__var__var__var__15__z__138542__138545__138592__138595__138598] :
                                    ( t(Vvar__var__var__var__var__15__z__138542__138545__138592__138595__138598,Vvar__0__R__138463)
                                   => p(happ(happ(Vvar__7__req__138484,happ(happ(Vvar__4__rmul__138471,Vvar__var__var__var__var__13__x__138540__138543__138590__138593__138596),happ(happ(Vvar__4__rmul__138471,Vvar__var__var__var__var__14__y__138541__138544__138591__138594__138597),Vvar__var__var__var__var__15__z__138542__138545__138592__138595__138598))),happ(happ(Vvar__4__rmul__138471,happ(happ(Vvar__4__rmul__138471,Vvar__var__var__var__var__13__x__138540__138543__138590__138593__138596),Vvar__var__var__var__var__14__y__138541__138544__138591__138594__138597)),Vvar__var__var__var__var__15__z__138542__138545__138592__138595__138598))) ) ) )
                        & ! [Vvar__var__var__var__var__var__14__x__138547__138550__138599__138602__138605__138608] :
                            ( t(Vvar__var__var__var__var__var__14__x__138547__138550__138599__138602__138605__138608,Vvar__0__R__138463)
                           => ! [Vvar__var__var__var__var__var__15__y__138548__138551__138600__138603__138606__138609] :
                                ( t(Vvar__var__var__var__var__var__15__y__138548__138551__138600__138603__138606__138609,Vvar__0__R__138463)
                               => ! [Vvar__var__var__var__var__var__16__z__138549__138552__138601__138604__138607__138610] :
                                    ( t(Vvar__var__var__var__var__var__16__z__138549__138552__138601__138604__138607__138610,Vvar__0__R__138463)
                                   => p(happ(happ(Vvar__7__req__138484,happ(happ(Vvar__4__rmul__138471,happ(happ(Vvar__3__radd__138466,Vvar__var__var__var__var__var__14__x__138547__138550__138599__138602__138605__138608),Vvar__var__var__var__var__var__15__y__138548__138551__138600__138603__138606__138609)),Vvar__var__var__var__var__var__16__z__138549__138552__138601__138604__138607__138610)),happ(happ(Vvar__3__radd__138466,happ(happ(Vvar__4__rmul__138471,Vvar__var__var__var__var__var__14__x__138547__138550__138599__138602__138605__138608),Vvar__var__var__var__var__var__16__z__138549__138552__138601__138604__138607__138610)),happ(happ(Vvar__4__rmul__138471,Vvar__var__var__var__var__var__15__y__138548__138551__138600__138603__138606__138609),Vvar__var__var__var__var__var__16__z__138549__138552__138601__138604__138607__138610)))) ) ) )
                        & ! [Vvar__var__var__var__var__var__var__15__x__138554__138556__138611__138613__138615__138617__138619] :
                            ( t(Vvar__var__var__var__var__var__var__15__x__138554__138556__138611__138613__138615__138617__138619,Vvar__0__R__138463)
                           => ! [Vvar__var__var__var__var__var__var__16__y__138555__138557__138612__138614__138616__138618__138620] :
                                ( t(Vvar__var__var__var__var__var__var__16__y__138555__138557__138612__138614__138616__138618__138620,Vvar__0__R__138463)
                               => p(happ(happ(Vvar__7__req__138484,happ(happ(Vvar__5__rsub__138476,Vvar__var__var__var__var__var__var__15__x__138554__138556__138611__138613__138615__138617__138619),Vvar__var__var__var__var__var__var__16__y__138555__138557__138612__138614__138616__138618__138620)),happ(happ(Vvar__3__radd__138466,Vvar__var__var__var__var__var__var__15__x__138554__138556__138611__138613__138615__138617__138619),happ(Vvar__6__ropp__138481,Vvar__var__var__var__var__var__var__16__y__138555__138557__138612__138614__138616__138618__138620)))) ) )
                        & ! [Vvar__var__var__var__var__var__var__16__x__138559__138560__138621__138622__138623__138624__138625] :
                            ( t(Vvar__var__var__var__var__var__var__16__x__138559__138560__138621__138622__138623__138624__138625,Vvar__0__R__138463)
                           => p(happ(happ(Vvar__7__req__138484,happ(happ(Vvar__3__radd__138466,Vvar__var__var__var__var__var__var__16__x__138559__138560__138621__138622__138623__138624__138625),happ(Vvar__6__ropp__138481,Vvar__var__var__var__var__var__var__16__x__138559__138560__138621__138622__138623__138624__138625))),Vvar__1__rO__138464)) )
                        & p(c_24True) ) ) ) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.setoid_ring.Ring_theory.semi_morph',axiom,
    ! [Vvar__0__R__5678,Vvar__1__rO__5679,Vvar__2__rI__5680,Vvar__3__radd__5681,Vvar__4__rmul__5686,Vvar__5__req__5691,Vvar__6__C__5696,Vvar__7__cO__5697,Vvar__8__cI__5698,Vvar__9__cadd__5699,Vvar__10__cmul__5704,Vvar__11__ceqb__5709,Vvar__12__phi__5714] :
      ( cType___24t(Vvar__0__R__5678)
     => ( t(Vvar__1__rO__5679,Vvar__0__R__5678)
       => ( t(Vvar__2__rI__5680,Vvar__0__R__5678)
         => ( c_24__type__5931___24t(Vvar__0__R__5678,Vvar__1__rO__5679,Vvar__2__rI__5680,Vvar__3__radd__5681,Vvar__4__rmul__5686,Vvar__5__req__5691,Vvar__6__C__5696,Vvar__7__cO__5697,Vvar__8__cI__5698,Vvar__9__cadd__5699,Vvar__10__cmul__5704,Vvar__11__ceqb__5709,Vvar__12__phi__5714,Vvar__3__radd__5681)
           => ( c_24__type__6056___24t(Vvar__0__R__5678,Vvar__1__rO__5679,Vvar__2__rI__5680,Vvar__3__radd__5681,Vvar__4__rmul__5686,Vvar__5__req__5691,Vvar__6__C__5696,Vvar__7__cO__5697,Vvar__8__cI__5698,Vvar__9__cadd__5699,Vvar__10__cmul__5704,Vvar__11__ceqb__5709,Vvar__12__phi__5714,Vvar__4__rmul__5686)
             => ( c_24__type__6181___24t(Vvar__0__R__5678,Vvar__1__rO__5679,Vvar__2__rI__5680,Vvar__3__radd__5681,Vvar__4__rmul__5686,Vvar__5__req__5691,Vvar__6__C__5696,Vvar__7__cO__5697,Vvar__8__cI__5698,Vvar__9__cadd__5699,Vvar__10__cmul__5704,Vvar__11__ceqb__5709,Vvar__12__phi__5714,Vvar__5__req__5691)
               => ( cType___24t(Vvar__6__C__5696)
                 => ( t(Vvar__7__cO__5697,Vvar__6__C__5696)
                   => ( t(Vvar__8__cI__5698,Vvar__6__C__5696)
                     => ( c_24__type__6306___24t(Vvar__0__R__5678,Vvar__1__rO__5679,Vvar__2__rI__5680,Vvar__3__radd__5681,Vvar__4__rmul__5686,Vvar__5__req__5691,Vvar__6__C__5696,Vvar__7__cO__5697,Vvar__8__cI__5698,Vvar__9__cadd__5699,Vvar__10__cmul__5704,Vvar__11__ceqb__5709,Vvar__12__phi__5714,Vvar__9__cadd__5699)
                       => ( c_24__type__6431___24t(Vvar__0__R__5678,Vvar__1__rO__5679,Vvar__2__rI__5680,Vvar__3__radd__5681,Vvar__4__rmul__5686,Vvar__5__req__5691,Vvar__6__C__5696,Vvar__7__cO__5697,Vvar__8__cI__5698,Vvar__9__cadd__5699,Vvar__10__cmul__5704,Vvar__11__ceqb__5709,Vvar__12__phi__5714,Vvar__10__cmul__5704)
                         => ( c_24__type__6556___24t(Vvar__0__R__5678,Vvar__1__rO__5679,Vvar__2__rI__5680,Vvar__3__radd__5681,Vvar__4__rmul__5686,Vvar__5__req__5691,Vvar__6__C__5696,Vvar__7__cO__5697,Vvar__8__cI__5698,Vvar__9__cadd__5699,Vvar__10__cmul__5704,Vvar__11__ceqb__5709,Vvar__12__phi__5714,Vvar__11__ceqb__5709)
                           => ( c_24__type__6667___24t(Vvar__0__R__5678,Vvar__1__rO__5679,Vvar__2__rI__5680,Vvar__3__radd__5681,Vvar__4__rmul__5686,Vvar__5__req__5691,Vvar__6__C__5696,Vvar__7__cO__5697,Vvar__8__cI__5698,Vvar__9__cadd__5699,Vvar__10__cmul__5704,Vvar__11__ceqb__5709,Vvar__12__phi__5714,Vvar__12__phi__5714)
                             => ( cCoq_2esetoid__ring_2eRing__theory_2esemi__morph___24a13(Vvar__0__R__5678,Vvar__1__rO__5679,Vvar__2__rI__5680,Vvar__3__radd__5681,Vvar__4__rmul__5686,Vvar__5__req__5691,Vvar__6__C__5696,Vvar__7__cO__5697,Vvar__8__cI__5698,Vvar__9__cadd__5699,Vvar__10__cmul__5704,Vvar__11__ceqb__5709,Vvar__12__phi__5714)
                               => ( p(happ(happ(Vvar__5__req__5691,happ(Vvar__12__phi__5714,Vvar__7__cO__5697)),Vvar__1__rO__5679))
                                  & p(happ(happ(Vvar__5__req__5691,happ(Vvar__12__phi__5714,Vvar__8__cI__5698)),Vvar__2__rI__5680))
                                  & ! [Vvar__var__var__var__var__var__var__15__x__5760__5762__5776__5778__5780__5782__5784] :
                                      ( t(Vvar__var__var__var__var__var__var__15__x__5760__5762__5776__5778__5780__5782__5784,Vvar__6__C__5696)
                                     => ! [Vvar__var__var__var__var__var__var__16__y__5761__5763__5777__5779__5781__5783__5785] :
                                          ( t(Vvar__var__var__var__var__var__var__16__y__5761__5763__5777__5779__5781__5783__5785,Vvar__6__C__5696)
                                         => p(happ(happ(Vvar__5__req__5691,happ(Vvar__12__phi__5714,happ(happ(Vvar__9__cadd__5699,Vvar__var__var__var__var__var__var__15__x__5760__5762__5776__5778__5780__5782__5784),Vvar__var__var__var__var__var__var__16__y__5761__5763__5777__5779__5781__5783__5785))),happ(happ(Vvar__3__radd__5681,happ(Vvar__12__phi__5714,Vvar__var__var__var__var__var__var__15__x__5760__5762__5776__5778__5780__5782__5784)),happ(Vvar__12__phi__5714,Vvar__var__var__var__var__var__var__16__y__5761__5763__5777__5779__5781__5783__5785)))) ) )
                                  & ! [Vvar__var__var__var__var__var__var__16__x__5765__5767__5786__5788__5790__5792__5794] :
                                      ( t(Vvar__var__var__var__var__var__var__16__x__5765__5767__5786__5788__5790__5792__5794,Vvar__6__C__5696)
                                     => ! [Vvar__var__var__var__var__var__var__17__y__5766__5768__5787__5789__5791__5793__5795] :
                                          ( t(Vvar__var__var__var__var__var__var__17__y__5766__5768__5787__5789__5791__5793__5795,Vvar__6__C__5696)
                                         => p(happ(happ(Vvar__5__req__5691,happ(Vvar__12__phi__5714,happ(happ(Vvar__10__cmul__5704,Vvar__var__var__var__var__var__var__16__x__5765__5767__5786__5788__5790__5792__5794),Vvar__var__var__var__var__var__var__17__y__5766__5768__5787__5789__5791__5793__5795))),happ(happ(Vvar__4__rmul__5686,happ(Vvar__12__phi__5714,Vvar__var__var__var__var__var__var__16__x__5765__5767__5786__5788__5790__5792__5794)),happ(Vvar__12__phi__5714,Vvar__var__var__var__var__var__var__17__y__5766__5768__5787__5789__5791__5793__5795)))) ) )
                                  & ! [Vvar__var__var__var__var__var__17__x__5770__5773__5796__5799__5802__5805] :
                                      ( t(Vvar__var__var__var__var__var__17__x__5770__5773__5796__5799__5802__5805,Vvar__6__C__5696)
                                     => ! [Vvar__var__var__var__var__var__18__y__5771__5774__5797__5800__5803__5806] :
                                          ( t(Vvar__var__var__var__var__var__18__y__5771__5774__5797__5800__5803__5806,Vvar__6__C__5696)
                                         => ( happ(happ(Vvar__11__ceqb__5709,Vvar__var__var__var__var__var__17__x__5770__5773__5796__5799__5802__5805),Vvar__var__var__var__var__var__18__y__5771__5774__5797__5800__5803__5806) = cCoq_2eInit_2eDatatypes_2etrue
                                           => p(happ(happ(Vvar__5__req__5691,happ(Vvar__12__phi__5714,Vvar__var__var__var__var__var__17__x__5770__5773__5796__5799__5802__5805)),happ(Vvar__12__phi__5714,Vvar__var__var__var__var__var__18__y__5771__5774__5797__5800__5803__5806))) ) ) )
                                  & p(c_24True) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.setoid_ring.Ring_theory.semi_ring_theory',axiom,
    ! [Vvar__0__R__5414,Vvar__1__rO__5415,Vvar__2__rI__5416,Vvar__3__radd__5417,Vvar__4__rmul__5422,Vvar__5__req__5427] :
      ( cType___24t(Vvar__0__R__5414)
     => ( t(Vvar__1__rO__5415,Vvar__0__R__5414)
       => ( t(Vvar__2__rI__5416,Vvar__0__R__5414)
         => ( c_24__type__5582___24t(Vvar__0__R__5414,Vvar__1__rO__5415,Vvar__2__rI__5416,Vvar__3__radd__5417,Vvar__4__rmul__5422,Vvar__5__req__5427,Vvar__3__radd__5417)
           => ( c_24__type__5621___24t(Vvar__0__R__5414,Vvar__1__rO__5415,Vvar__2__rI__5416,Vvar__3__radd__5417,Vvar__4__rmul__5422,Vvar__5__req__5427,Vvar__4__rmul__5422)
             => ( c_24__type__5660___24t(Vvar__0__R__5414,Vvar__1__rO__5415,Vvar__2__rI__5416,Vvar__3__radd__5417,Vvar__4__rmul__5422,Vvar__5__req__5427,Vvar__5__req__5427)
               => ( cCoq_2esetoid__ring_2eRing__theory_2esemi__ring__theory___24a6(Vvar__0__R__5414,Vvar__1__rO__5415,Vvar__2__rI__5416,Vvar__3__radd__5417,Vvar__4__rmul__5422,Vvar__5__req__5427)
                 => ( ! [Vvar__var__var__var__var__var__6__n__5452__5453__5491__5492__5493__5494] :
                        ( t(Vvar__var__var__var__var__var__6__n__5452__5453__5491__5492__5493__5494,Vvar__0__R__5414)
                       => p(happ(happ(Vvar__5__req__5427,happ(happ(Vvar__3__radd__5417,Vvar__1__rO__5415),Vvar__var__var__var__var__var__6__n__5452__5453__5491__5492__5493__5494)),Vvar__var__var__var__var__var__6__n__5452__5453__5491__5492__5493__5494)) )
                    & ! [Vvar__var__var__var__var__7__n__5455__5457__5495__5497__5499] :
                        ( t(Vvar__var__var__var__var__7__n__5455__5457__5495__5497__5499,Vvar__0__R__5414)
                       => ! [Vvar__var__var__var__var__8__m__5456__5458__5496__5498__5500] :
                            ( t(Vvar__var__var__var__var__8__m__5456__5458__5496__5498__5500,Vvar__0__R__5414)
                           => p(happ(happ(Vvar__5__req__5427,happ(happ(Vvar__3__radd__5417,Vvar__var__var__var__var__7__n__5455__5457__5495__5497__5499),Vvar__var__var__var__var__8__m__5456__5458__5496__5498__5500)),happ(happ(Vvar__3__radd__5417,Vvar__var__var__var__var__8__m__5456__5458__5496__5498__5500),Vvar__var__var__var__var__7__n__5455__5457__5495__5497__5499))) ) )
                    & ! [Vvar__var__var__var__var__8__n__5460__5463__5501__5504__5507] :
                        ( t(Vvar__var__var__var__var__8__n__5460__5463__5501__5504__5507,Vvar__0__R__5414)
                       => ! [Vvar__var__var__var__var__9__m__5461__5464__5502__5505__5508] :
                            ( t(Vvar__var__var__var__var__9__m__5461__5464__5502__5505__5508,Vvar__0__R__5414)
                           => ! [Vvar__var__var__var__var__10__p__5462__5465__5503__5506__5509] :
                                ( t(Vvar__var__var__var__var__10__p__5462__5465__5503__5506__5509,Vvar__0__R__5414)
                               => p(happ(happ(Vvar__5__req__5427,happ(happ(Vvar__3__radd__5417,Vvar__var__var__var__var__8__n__5460__5463__5501__5504__5507),happ(happ(Vvar__3__radd__5417,Vvar__var__var__var__var__9__m__5461__5464__5502__5505__5508),Vvar__var__var__var__var__10__p__5462__5465__5503__5506__5509))),happ(happ(Vvar__3__radd__5417,happ(happ(Vvar__3__radd__5417,Vvar__var__var__var__var__8__n__5460__5463__5501__5504__5507),Vvar__var__var__var__var__9__m__5461__5464__5502__5505__5508)),Vvar__var__var__var__var__10__p__5462__5465__5503__5506__5509))) ) ) )
                    & ! [Vvar__var__var__var__var__var__9__n__5467__5468__5510__5511__5512__5513] :
                        ( t(Vvar__var__var__var__var__var__9__n__5467__5468__5510__5511__5512__5513,Vvar__0__R__5414)
                       => p(happ(happ(Vvar__5__req__5427,happ(happ(Vvar__4__rmul__5422,Vvar__2__rI__5416),Vvar__var__var__var__var__var__9__n__5467__5468__5510__5511__5512__5513)),Vvar__var__var__var__var__var__9__n__5467__5468__5510__5511__5512__5513)) )
                    & ! [Vvar__var__var__var__var__var__10__n__5470__5471__5514__5515__5516__5517] :
                        ( t(Vvar__var__var__var__var__var__10__n__5470__5471__5514__5515__5516__5517,Vvar__0__R__5414)
                       => p(happ(happ(Vvar__5__req__5427,happ(happ(Vvar__4__rmul__5422,Vvar__1__rO__5415),Vvar__var__var__var__var__var__10__n__5470__5471__5514__5515__5516__5517)),Vvar__1__rO__5415)) )
                    & ! [Vvar__var__var__var__var__11__n__5473__5475__5518__5520__5522] :
                        ( t(Vvar__var__var__var__var__11__n__5473__5475__5518__5520__5522,Vvar__0__R__5414)
                       => ! [Vvar__var__var__var__var__12__m__5474__5476__5519__5521__5523] :
                            ( t(Vvar__var__var__var__var__12__m__5474__5476__5519__5521__5523,Vvar__0__R__5414)
                           => p(happ(happ(Vvar__5__req__5427,happ(happ(Vvar__4__rmul__5422,Vvar__var__var__var__var__11__n__5473__5475__5518__5520__5522),Vvar__var__var__var__var__12__m__5474__5476__5519__5521__5523)),happ(happ(Vvar__4__rmul__5422,Vvar__var__var__var__var__12__m__5474__5476__5519__5521__5523),Vvar__var__var__var__var__11__n__5473__5475__5518__5520__5522))) ) )
                    & ! [Vvar__var__var__var__var__12__n__5478__5481__5524__5527__5530] :
                        ( t(Vvar__var__var__var__var__12__n__5478__5481__5524__5527__5530,Vvar__0__R__5414)
                       => ! [Vvar__var__var__var__var__13__m__5479__5482__5525__5528__5531] :
                            ( t(Vvar__var__var__var__var__13__m__5479__5482__5525__5528__5531,Vvar__0__R__5414)
                           => ! [Vvar__var__var__var__var__14__p__5480__5483__5526__5529__5532] :
                                ( t(Vvar__var__var__var__var__14__p__5480__5483__5526__5529__5532,Vvar__0__R__5414)
                               => p(happ(happ(Vvar__5__req__5427,happ(happ(Vvar__4__rmul__5422,Vvar__var__var__var__var__12__n__5478__5481__5524__5527__5530),happ(happ(Vvar__4__rmul__5422,Vvar__var__var__var__var__13__m__5479__5482__5525__5528__5531),Vvar__var__var__var__var__14__p__5480__5483__5526__5529__5532))),happ(happ(Vvar__4__rmul__5422,happ(happ(Vvar__4__rmul__5422,Vvar__var__var__var__var__12__n__5478__5481__5524__5527__5530),Vvar__var__var__var__var__13__m__5479__5482__5525__5528__5531)),Vvar__var__var__var__var__14__p__5480__5483__5526__5529__5532))) ) ) )
                    & ! [Vvar__var__var__var__var__var__13__n__5485__5488__5533__5536__5539__5542] :
                        ( t(Vvar__var__var__var__var__var__13__n__5485__5488__5533__5536__5539__5542,Vvar__0__R__5414)
                       => ! [Vvar__var__var__var__var__var__14__m__5486__5489__5534__5537__5540__5543] :
                            ( t(Vvar__var__var__var__var__var__14__m__5486__5489__5534__5537__5540__5543,Vvar__0__R__5414)
                           => ! [Vvar__var__var__var__var__var__15__p__5487__5490__5535__5538__5541__5544] :
                                ( t(Vvar__var__var__var__var__var__15__p__5487__5490__5535__5538__5541__5544,Vvar__0__R__5414)
                               => p(happ(happ(Vvar__5__req__5427,happ(happ(Vvar__4__rmul__5422,happ(happ(Vvar__3__radd__5417,Vvar__var__var__var__var__var__13__n__5485__5488__5533__5536__5539__5542),Vvar__var__var__var__var__var__14__m__5486__5489__5534__5537__5540__5543)),Vvar__var__var__var__var__var__15__p__5487__5490__5535__5538__5541__5544)),happ(happ(Vvar__3__radd__5417,happ(happ(Vvar__4__rmul__5422,Vvar__var__var__var__var__var__13__n__5485__5488__5533__5536__5539__5542),Vvar__var__var__var__var__var__15__p__5487__5490__5535__5538__5541__5544)),happ(happ(Vvar__4__rmul__5422,Vvar__var__var__var__var__var__14__m__5486__5489__5534__5537__5540__5543),Vvar__var__var__var__var__var__15__p__5487__5490__5535__5538__5541__5544)))) ) ) )
                    & p(c_24True) ) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.setoid_ring.Ring_theory.sign_theory',axiom,
    ! [Vvar__0__C__139061,Vvar__1__copp__139062,Vvar__2__ceqb__139065,Vvar__3__get__sign__139070] :
      ( cType___24t(Vvar__0__C__139061)
     => ( c_24__type__139117___24t(Vvar__0__C__139061,Vvar__1__copp__139062,Vvar__2__ceqb__139065,Vvar__3__get__sign__139070,Vvar__1__copp__139062)
       => ( c_24__type__139136___24t(Vvar__0__C__139061,Vvar__1__copp__139062,Vvar__2__ceqb__139065,Vvar__3__get__sign__139070,Vvar__2__ceqb__139065)
         => ( c_24__type__139150___24t(Vvar__0__C__139061,Vvar__1__copp__139062,Vvar__2__ceqb__139065,Vvar__3__get__sign__139070,Vvar__3__get__sign__139070)
           => ( cCoq_2esetoid__ring_2eRing__theory_2esign__theory___24a4(Vvar__0__C__139061,Vvar__1__copp__139062,Vvar__2__ceqb__139065,Vvar__3__get__sign__139070)
             => ( ! [Vvar__var__var__var__var__var__4__c__139087__139090__139093__139096__139099__139102] :
                    ( t(Vvar__var__var__var__var__var__4__c__139087__139090__139093__139096__139099__139102,Vvar__0__C__139061)
                   => ! [Vvar__var__var__var__var__var__5__c_27__139088__139091__139094__139097__139100__139103] :
                        ( t(Vvar__var__var__var__var__var__5__c_27__139088__139091__139094__139097__139100__139103,Vvar__0__C__139061)
                       => ( happ(Vvar__3__get__sign__139070,Vvar__var__var__var__var__var__4__c__139087__139090__139093__139096__139099__139102) = cCoq_2eInit_2eDatatypes_2eSome___24a2(Vvar__0__C__139061,Vvar__var__var__var__var__var__5__c_27__139088__139091__139094__139097__139100__139103)
                         => happ(happ(Vvar__2__ceqb__139065,Vvar__var__var__var__var__var__4__c__139087__139090__139093__139096__139099__139102),happ(Vvar__1__copp__139062,Vvar__var__var__var__var__var__5__c_27__139088__139091__139094__139097__139100__139103)) = cCoq_2eInit_2eDatatypes_2etrue ) ) )
                & p(c_24True) ) ) ) ) ) ) ).

fof('$_inversion_Coq.setoid_ring.Ring_theory.sring_eq_ext',axiom,
    ! [Vvar__0__R__132344,Vvar__1__radd__132345,Vvar__2__rmul__132350,Vvar__3__req__132355] :
      ( cType___24t(Vvar__0__R__132344)
     => ( c_24__type__132430___24t(Vvar__0__R__132344,Vvar__1__radd__132345,Vvar__2__rmul__132350,Vvar__3__req__132355,Vvar__1__radd__132345)
       => ( c_24__type__132453___24t(Vvar__0__R__132344,Vvar__1__radd__132345,Vvar__2__rmul__132350,Vvar__3__req__132355,Vvar__2__rmul__132350)
         => ( c_24__type__132476___24t(Vvar__0__R__132344,Vvar__1__radd__132345,Vvar__2__rmul__132350,Vvar__3__req__132355,Vvar__3__req__132355)
           => ( cCoq_2esetoid__ring_2eRing__theory_2esring__eq__ext___24a4(Vvar__0__R__132344,Vvar__1__radd__132345,Vvar__2__rmul__132350,Vvar__3__req__132355)
             => ( cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__132499___24a4(Vvar__0__R__132344,Vvar__1__radd__132345,Vvar__2__rmul__132350,Vvar__3__req__132355),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(Vvar__0__R__132344,c_24__type__132517___24a4(Vvar__0__R__132344,Vvar__1__radd__132345,Vvar__2__rmul__132350,Vvar__3__req__132355),Vvar__3__req__132355,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(Vvar__0__R__132344,Vvar__0__R__132344,Vvar__3__req__132355,Vvar__3__req__132355)),Vvar__1__radd__132345)
                & cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__132543___24a4(Vvar__0__R__132344,Vvar__1__radd__132345,Vvar__2__rmul__132350,Vvar__3__req__132355),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(Vvar__0__R__132344,c_24__type__132561___24a4(Vvar__0__R__132344,Vvar__1__radd__132345,Vvar__2__rmul__132350,Vvar__3__req__132355),Vvar__3__req__132355,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(Vvar__0__R__132344,Vvar__0__R__132344,Vvar__3__req__132355,Vvar__3__req__132355)),Vvar__2__rmul__132350)
                & p(c_24True) ) ) ) ) ) ) ).

fof('$_inversion_Hammer.Tactics.Reconstr.ReconstrT',axiom,
    ! [VX147837] :
      ( cHammer_2eTactics_2eReconstr_2eReconstrT___24t(VX147837)
     => ( VX147837 = cHammer_2eTactics_2eReconstr_2eEmpty
        | VX147837 = cHammer_2eTactics_2eReconstr_2eAllHyps ) ) ).

fof('$_inversion_Hoare2.dcom',axiom,
    ! [VX150320] :
      ( cHoare2_2edcom___24t(VX150320)
     => ( ? [Vvar__0___24Anonymous__150321] :
            ( cPLF_2eHoare_2eAssertion___24t(Vvar__0___24Anonymous__150321)
            & VX150320 = cHoare2_2eDCSkip___24a1(Vvar__0___24Anonymous__150321) )
        | ? [Vvar__0___24Anonymous__150322] :
            ( cHoare2_2edcom___24t(Vvar__0___24Anonymous__150322)
            & ? [Vvar__1___24Anonymous__150323] :
                ( cHoare2_2edcom___24t(Vvar__1___24Anonymous__150323)
                & VX150320 = cHoare2_2eDCSeq___24a2(Vvar__0___24Anonymous__150322,Vvar__1___24Anonymous__150323) ) )
        | ? [Vvar__0___24Anonymous__150324] :
            ( cCoq_2eStrings_2eString_2estring___24t(Vvar__0___24Anonymous__150324)
            & ? [Vvar__1___24Anonymous__150325] :
                ( cPLF_2eImp_2eaexp___24t(Vvar__1___24Anonymous__150325)
                & ? [Vvar__2___24Anonymous__150326] :
                    ( cPLF_2eHoare_2eAssertion___24t(Vvar__2___24Anonymous__150326)
                    & VX150320 = cHoare2_2eDCAsgn___24a3(Vvar__0___24Anonymous__150324,Vvar__1___24Anonymous__150325,Vvar__2___24Anonymous__150326) ) ) )
        | ? [Vvar__0___24Anonymous__150327] :
            ( cPLF_2eImp_2ebexp___24t(Vvar__0___24Anonymous__150327)
            & ? [Vvar__1___24Anonymous__150328] :
                ( cPLF_2eHoare_2eAssertion___24t(Vvar__1___24Anonymous__150328)
                & ? [Vvar__2___24Anonymous__150329] :
                    ( cHoare2_2edcom___24t(Vvar__2___24Anonymous__150329)
                    & ? [Vvar__3___24Anonymous__150330] :
                        ( cPLF_2eHoare_2eAssertion___24t(Vvar__3___24Anonymous__150330)
                        & ? [Vvar__4___24Anonymous__150331] :
                            ( cHoare2_2edcom___24t(Vvar__4___24Anonymous__150331)
                            & ? [Vvar__5___24Anonymous__150332] :
                                ( cPLF_2eHoare_2eAssertion___24t(Vvar__5___24Anonymous__150332)
                                & VX150320 = cHoare2_2eDCIf___24a6(Vvar__0___24Anonymous__150327,Vvar__1___24Anonymous__150328,Vvar__2___24Anonymous__150329,Vvar__3___24Anonymous__150330,Vvar__4___24Anonymous__150331,Vvar__5___24Anonymous__150332) ) ) ) ) ) )
        | ? [Vvar__0___24Anonymous__150333] :
            ( cPLF_2eImp_2ebexp___24t(Vvar__0___24Anonymous__150333)
            & ? [Vvar__1___24Anonymous__150334] :
                ( cPLF_2eHoare_2eAssertion___24t(Vvar__1___24Anonymous__150334)
                & ? [Vvar__2___24Anonymous__150335] :
                    ( cHoare2_2edcom___24t(Vvar__2___24Anonymous__150335)
                    & ? [Vvar__3___24Anonymous__150336] :
                        ( cPLF_2eHoare_2eAssertion___24t(Vvar__3___24Anonymous__150336)
                        & VX150320 = cHoare2_2eDCWhile___24a4(Vvar__0___24Anonymous__150333,Vvar__1___24Anonymous__150334,Vvar__2___24Anonymous__150335,Vvar__3___24Anonymous__150336) ) ) ) )
        | ? [Vvar__0___24Anonymous__150337] :
            ( cPLF_2eHoare_2eAssertion___24t(Vvar__0___24Anonymous__150337)
            & ? [Vvar__1___24Anonymous__150338] :
                ( cHoare2_2edcom___24t(Vvar__1___24Anonymous__150338)
                & VX150320 = cHoare2_2eDCPre___24a2(Vvar__0___24Anonymous__150337,Vvar__1___24Anonymous__150338) ) )
        | ? [Vvar__0___24Anonymous__150339] :
            ( cHoare2_2edcom___24t(Vvar__0___24Anonymous__150339)
            & ? [Vvar__1___24Anonymous__150340] :
                ( cPLF_2eHoare_2eAssertion___24t(Vvar__1___24Anonymous__150340)
                & VX150320 = cHoare2_2eDCPost___24a2(Vvar__0___24Anonymous__150339,Vvar__1___24Anonymous__150340) ) ) ) ) ).

fof('$_inversion_Hoare2.decorated',axiom,
    ! [VX150313] :
      ( cHoare2_2edecorated___24t(VX150313)
     => ? [Vvar__0___24Anonymous__150314] :
          ( cPLF_2eHoare_2eAssertion___24t(Vvar__0___24Anonymous__150314)
          & ? [Vvar__1___24Anonymous__150315] :
              ( cHoare2_2edcom___24t(Vvar__1___24Anonymous__150315)
              & VX150313 = cHoare2_2eDecorated___24a2(Vvar__0___24Anonymous__150314,Vvar__1___24Anonymous__150315) ) ) ) ).

fof('$_inversion_PLF.Hoare.Himp.ceval',axiom,
    ! [Vvar__0___24Anonymous__880,Vvar__1___24Anonymous__881,Vvar__2___24Anonymous__882] :
      ( cPLF_2eHoare_2eHimp_2ecom___24t(Vvar__0___24Anonymous__880)
     => ( cPLF_2eImp_2estate___24t(Vvar__1___24Anonymous__881)
       => ( cPLF_2eImp_2estate___24t(Vvar__2___24Anonymous__882)
         => ( cPLF_2eHoare_2eHimp_2eceval___24a3(Vvar__0___24Anonymous__880,Vvar__1___24Anonymous__881,Vvar__2___24Anonymous__882)
           => ( ? [Vvar__0__st__884] :
                  ( cPLF_2eImp_2estate___24t(Vvar__0__st__884)
                  & Vvar__2___24Anonymous__882 = Vvar__0__st__884
                  & Vvar__1___24Anonymous__881 = Vvar__0__st__884
                  & Vvar__0___24Anonymous__880 = cPLF_2eHoare_2eHimp_2eCSkip )
              | ? [Vvar__0__st__885] :
                  ( cPLF_2eImp_2estate___24t(Vvar__0__st__885)
                  & ? [Vvar__1__a1__886] :
                      ( cPLF_2eImp_2eaexp___24t(Vvar__1__a1__886)
                      & ? [Vvar__2__n__887] :
                          ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__2__n__887)
                          & ? [Vvar__3__x__888] :
                              ( cCoq_2eStrings_2eString_2estring___24t(Vvar__3__x__888)
                              & cPLF_2eImp_2eaeval___24a2(Vvar__0__st__885,Vvar__1__a1__886) = Vvar__2__n__887
                              & Vvar__2___24Anonymous__882 = c_24__lam__943___24a6(Vvar__0___24Anonymous__880,Vvar__1___24Anonymous__881,Vvar__2___24Anonymous__882,Vvar__0__st__885,Vvar__2__n__887,Vvar__3__x__888)
                              & Vvar__1___24Anonymous__881 = Vvar__0__st__885
                              & Vvar__0___24Anonymous__880 = cPLF_2eHoare_2eHimp_2eCAsgn___24a2(Vvar__3__x__888,Vvar__1__a1__886) ) ) ) )
              | ? [Vvar__0__c1__892] :
                  ( cPLF_2eHoare_2eHimp_2ecom___24t(Vvar__0__c1__892)
                  & ? [Vvar__1__c2__893] :
                      ( cPLF_2eHoare_2eHimp_2ecom___24t(Vvar__1__c2__893)
                      & ? [Vvar__2__st__894] :
                          ( cPLF_2eImp_2estate___24t(Vvar__2__st__894)
                          & ? [Vvar__3__st_27__895] :
                              ( cPLF_2eImp_2estate___24t(Vvar__3__st_27__895)
                              & ? [Vvar__4__st_27_27__896] :
                                  ( cPLF_2eImp_2estate___24t(Vvar__4__st_27_27__896)
                                  & cPLF_2eHoare_2eHimp_2eceval___24a3(Vvar__0__c1__892,Vvar__2__st__894,Vvar__3__st_27__895)
                                  & cPLF_2eHoare_2eHimp_2eceval___24a3(Vvar__1__c2__893,Vvar__3__st_27__895,Vvar__4__st_27_27__896)
                                  & Vvar__2___24Anonymous__882 = Vvar__4__st_27_27__896
                                  & Vvar__1___24Anonymous__881 = Vvar__2__st__894
                                  & Vvar__0___24Anonymous__880 = cPLF_2eHoare_2eHimp_2eCSeq___24a2(Vvar__0__c1__892,Vvar__1__c2__893) ) ) ) ) )
              | ? [Vvar__0__st__899] :
                  ( cPLF_2eImp_2estate___24t(Vvar__0__st__899)
                  & ? [Vvar__1__st_27__900] :
                      ( cPLF_2eImp_2estate___24t(Vvar__1__st_27__900)
                      & ? [Vvar__2__b__901] :
                          ( cPLF_2eImp_2ebexp___24t(Vvar__2__b__901)
                          & ? [Vvar__3__c1__902] :
                              ( cPLF_2eHoare_2eHimp_2ecom___24t(Vvar__3__c1__902)
                              & ? [Vvar__4__c2__903] :
                                  ( cPLF_2eHoare_2eHimp_2ecom___24t(Vvar__4__c2__903)
                                  & cPLF_2eImp_2ebeval___24a2(Vvar__0__st__899,Vvar__2__b__901) = cCoq_2eInit_2eDatatypes_2etrue
                                  & cPLF_2eHoare_2eHimp_2eceval___24a3(Vvar__3__c1__902,Vvar__0__st__899,Vvar__1__st_27__900)
                                  & Vvar__2___24Anonymous__882 = Vvar__1__st_27__900
                                  & Vvar__1___24Anonymous__881 = Vvar__0__st__899
                                  & Vvar__0___24Anonymous__880 = cPLF_2eHoare_2eHimp_2eCIf___24a3(Vvar__2__b__901,Vvar__3__c1__902,Vvar__4__c2__903) ) ) ) ) )
              | ? [Vvar__0__st__906] :
                  ( cPLF_2eImp_2estate___24t(Vvar__0__st__906)
                  & ? [Vvar__1__st_27__907] :
                      ( cPLF_2eImp_2estate___24t(Vvar__1__st_27__907)
                      & ? [Vvar__2__b__908] :
                          ( cPLF_2eImp_2ebexp___24t(Vvar__2__b__908)
                          & ? [Vvar__3__c1__909] :
                              ( cPLF_2eHoare_2eHimp_2ecom___24t(Vvar__3__c1__909)
                              & ? [Vvar__4__c2__910] :
                                  ( cPLF_2eHoare_2eHimp_2ecom___24t(Vvar__4__c2__910)
                                  & cPLF_2eImp_2ebeval___24a2(Vvar__0__st__906,Vvar__2__b__908) = cCoq_2eInit_2eDatatypes_2efalse
                                  & cPLF_2eHoare_2eHimp_2eceval___24a3(Vvar__4__c2__910,Vvar__0__st__906,Vvar__1__st_27__907)
                                  & Vvar__2___24Anonymous__882 = Vvar__1__st_27__907
                                  & Vvar__1___24Anonymous__881 = Vvar__0__st__906
                                  & Vvar__0___24Anonymous__880 = cPLF_2eHoare_2eHimp_2eCIf___24a3(Vvar__2__b__908,Vvar__3__c1__909,Vvar__4__c2__910) ) ) ) ) )
              | ? [Vvar__0__b__913] :
                  ( cPLF_2eImp_2ebexp___24t(Vvar__0__b__913)
                  & ? [Vvar__1__st__914] :
                      ( cPLF_2eImp_2estate___24t(Vvar__1__st__914)
                      & ? [Vvar__2__c__915] :
                          ( cPLF_2eHoare_2eHimp_2ecom___24t(Vvar__2__c__915)
                          & cPLF_2eImp_2ebeval___24a2(Vvar__1__st__914,Vvar__0__b__913) = cCoq_2eInit_2eDatatypes_2efalse
                          & Vvar__2___24Anonymous__882 = Vvar__1__st__914
                          & Vvar__1___24Anonymous__881 = Vvar__1__st__914
                          & Vvar__0___24Anonymous__880 = cPLF_2eHoare_2eHimp_2eCWhile___24a2(Vvar__0__b__913,Vvar__2__c__915) ) ) )
              | ? [Vvar__0__st__917] :
                  ( cPLF_2eImp_2estate___24t(Vvar__0__st__917)
                  & ? [Vvar__1__st_27__918] :
                      ( cPLF_2eImp_2estate___24t(Vvar__1__st_27__918)
                      & ? [Vvar__2__st_27_27__919] :
                          ( cPLF_2eImp_2estate___24t(Vvar__2__st_27_27__919)
                          & ? [Vvar__3__b__920] :
                              ( cPLF_2eImp_2ebexp___24t(Vvar__3__b__920)
                              & ? [Vvar__4__c__921] :
                                  ( cPLF_2eHoare_2eHimp_2ecom___24t(Vvar__4__c__921)
                                  & cPLF_2eImp_2ebeval___24a2(Vvar__0__st__917,Vvar__3__b__920) = cCoq_2eInit_2eDatatypes_2etrue
                                  & cPLF_2eHoare_2eHimp_2eceval___24a3(Vvar__4__c__921,Vvar__0__st__917,Vvar__1__st_27__918)
                                  & cPLF_2eHoare_2eHimp_2eceval___24a3(cPLF_2eHoare_2eHimp_2eCWhile___24a2(Vvar__3__b__920,Vvar__4__c__921),Vvar__1__st_27__918,Vvar__2__st_27_27__919)
                                  & Vvar__2___24Anonymous__882 = Vvar__2__st_27_27__919
                                  & Vvar__1___24Anonymous__881 = Vvar__0__st__917
                                  & Vvar__0___24Anonymous__880 = cPLF_2eHoare_2eHimp_2eCWhile___24a2(Vvar__3__b__920,Vvar__4__c__921) ) ) ) ) )
              | ? [Vvar__0__st__925] :
                  ( cPLF_2eImp_2estate___24t(Vvar__0__st__925)
                  & ? [Vvar__1__X__926] :
                      ( cCoq_2eStrings_2eString_2estring___24t(Vvar__1__X__926)
                      & ? [Vvar__2__n__927] :
                          ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__2__n__927)
                          & Vvar__2___24Anonymous__882 = c_24__lam__957___24a6(Vvar__0___24Anonymous__880,Vvar__1___24Anonymous__881,Vvar__2___24Anonymous__882,Vvar__0__st__925,Vvar__1__X__926,Vvar__2__n__927)
                          & Vvar__1___24Anonymous__881 = Vvar__0__st__925
                          & Vvar__0___24Anonymous__880 = cPLF_2eHoare_2eHimp_2eCHavoc___24a1(Vvar__1__X__926) ) ) ) ) ) ) ) ) ).

fof('$_inversion_PLF.Hoare.Himp.com',axiom,
    ! [VX783] :
      ( cPLF_2eHoare_2eHimp_2ecom___24t(VX783)
     => ( VX783 = cPLF_2eHoare_2eHimp_2eCSkip
        | ? [Vvar__0___24Anonymous__784] :
            ( cCoq_2eStrings_2eString_2estring___24t(Vvar__0___24Anonymous__784)
            & ? [Vvar__1___24Anonymous__785] :
                ( cPLF_2eImp_2eaexp___24t(Vvar__1___24Anonymous__785)
                & VX783 = cPLF_2eHoare_2eHimp_2eCAsgn___24a2(Vvar__0___24Anonymous__784,Vvar__1___24Anonymous__785) ) )
        | ? [Vvar__0___24Anonymous__786] :
            ( cPLF_2eHoare_2eHimp_2ecom___24t(Vvar__0___24Anonymous__786)
            & ? [Vvar__1___24Anonymous__787] :
                ( cPLF_2eHoare_2eHimp_2ecom___24t(Vvar__1___24Anonymous__787)
                & VX783 = cPLF_2eHoare_2eHimp_2eCSeq___24a2(Vvar__0___24Anonymous__786,Vvar__1___24Anonymous__787) ) )
        | ? [Vvar__0___24Anonymous__788] :
            ( cPLF_2eImp_2ebexp___24t(Vvar__0___24Anonymous__788)
            & ? [Vvar__1___24Anonymous__789] :
                ( cPLF_2eHoare_2eHimp_2ecom___24t(Vvar__1___24Anonymous__789)
                & ? [Vvar__2___24Anonymous__790] :
                    ( cPLF_2eHoare_2eHimp_2ecom___24t(Vvar__2___24Anonymous__790)
                    & VX783 = cPLF_2eHoare_2eHimp_2eCIf___24a3(Vvar__0___24Anonymous__788,Vvar__1___24Anonymous__789,Vvar__2___24Anonymous__790) ) ) )
        | ? [Vvar__0___24Anonymous__791] :
            ( cPLF_2eImp_2ebexp___24t(Vvar__0___24Anonymous__791)
            & ? [Vvar__1___24Anonymous__792] :
                ( cPLF_2eHoare_2eHimp_2ecom___24t(Vvar__1___24Anonymous__792)
                & VX783 = cPLF_2eHoare_2eHimp_2eCWhile___24a2(Vvar__0___24Anonymous__791,Vvar__1___24Anonymous__792) ) )
        | ? [Vvar__0___24Anonymous__793] :
            ( cCoq_2eStrings_2eString_2estring___24t(Vvar__0___24Anonymous__793)
            & VX783 = cPLF_2eHoare_2eHimp_2eCHavoc___24a1(Vvar__0___24Anonymous__793) ) ) ) ).

fof('$_inversion_PLF.Hoare.HoareAssertAssume.com',axiom,
    ! [VX1011] :
      ( cPLF_2eHoare_2eHoareAssertAssume_2ecom___24t(VX1011)
     => ( VX1011 = cPLF_2eHoare_2eHoareAssertAssume_2eCSkip
        | ? [Vvar__0___24Anonymous__1012] :
            ( cCoq_2eStrings_2eString_2estring___24t(Vvar__0___24Anonymous__1012)
            & ? [Vvar__1___24Anonymous__1013] :
                ( cPLF_2eImp_2eaexp___24t(Vvar__1___24Anonymous__1013)
                & VX1011 = cPLF_2eHoare_2eHoareAssertAssume_2eCAss___24a2(Vvar__0___24Anonymous__1012,Vvar__1___24Anonymous__1013) ) )
        | ? [Vvar__0___24Anonymous__1014] :
            ( cPLF_2eHoare_2eHoareAssertAssume_2ecom___24t(Vvar__0___24Anonymous__1014)
            & ? [Vvar__1___24Anonymous__1015] :
                ( cPLF_2eHoare_2eHoareAssertAssume_2ecom___24t(Vvar__1___24Anonymous__1015)
                & VX1011 = cPLF_2eHoare_2eHoareAssertAssume_2eCSeq___24a2(Vvar__0___24Anonymous__1014,Vvar__1___24Anonymous__1015) ) )
        | ? [Vvar__0___24Anonymous__1016] :
            ( cPLF_2eImp_2ebexp___24t(Vvar__0___24Anonymous__1016)
            & ? [Vvar__1___24Anonymous__1017] :
                ( cPLF_2eHoare_2eHoareAssertAssume_2ecom___24t(Vvar__1___24Anonymous__1017)
                & ? [Vvar__2___24Anonymous__1018] :
                    ( cPLF_2eHoare_2eHoareAssertAssume_2ecom___24t(Vvar__2___24Anonymous__1018)
                    & VX1011 = cPLF_2eHoare_2eHoareAssertAssume_2eCIf___24a3(Vvar__0___24Anonymous__1016,Vvar__1___24Anonymous__1017,Vvar__2___24Anonymous__1018) ) ) )
        | ? [Vvar__0___24Anonymous__1019] :
            ( cPLF_2eImp_2ebexp___24t(Vvar__0___24Anonymous__1019)
            & ? [Vvar__1___24Anonymous__1020] :
                ( cPLF_2eHoare_2eHoareAssertAssume_2ecom___24t(Vvar__1___24Anonymous__1020)
                & VX1011 = cPLF_2eHoare_2eHoareAssertAssume_2eCWhile___24a2(Vvar__0___24Anonymous__1019,Vvar__1___24Anonymous__1020) ) )
        | ? [Vvar__0___24Anonymous__1021] :
            ( cPLF_2eImp_2ebexp___24t(Vvar__0___24Anonymous__1021)
            & VX1011 = cPLF_2eHoare_2eHoareAssertAssume_2eCAssert___24a1(Vvar__0___24Anonymous__1021) )
        | ? [Vvar__0___24Anonymous__1022] :
            ( cPLF_2eImp_2ebexp___24t(Vvar__0___24Anonymous__1022)
            & VX1011 = cPLF_2eHoare_2eHoareAssertAssume_2eCAssume___24a1(Vvar__0___24Anonymous__1022) ) ) ) ).

fof('$_inversion_PLF.Hoare.HoareAssertAssume.result',axiom,
    ! [VX1127] :
      ( cPLF_2eHoare_2eHoareAssertAssume_2eresult___24t(VX1127)
     => ( ? [Vvar__0___24Anonymous__1128] :
            ( cPLF_2eImp_2estate___24t(Vvar__0___24Anonymous__1128)
            & VX1127 = cPLF_2eHoare_2eHoareAssertAssume_2eRNormal___24a1(Vvar__0___24Anonymous__1128) )
        | VX1127 = cPLF_2eHoare_2eHoareAssertAssume_2eRError ) ) ).

fof('$_inversion_PLF.Hoare.If1.ceval',axiom,
    ! [Vvar__0___24Anonymous__1429,Vvar__1___24Anonymous__1430,Vvar__2___24Anonymous__1431] :
      ( cPLF_2eHoare_2eIf1_2ecom___24t(Vvar__0___24Anonymous__1429)
     => ( cPLF_2eImp_2estate___24t(Vvar__1___24Anonymous__1430)
       => ( cPLF_2eImp_2estate___24t(Vvar__2___24Anonymous__1431)
         => ( cPLF_2eHoare_2eIf1_2eceval___24a3(Vvar__0___24Anonymous__1429,Vvar__1___24Anonymous__1430,Vvar__2___24Anonymous__1431)
           => ( ? [Vvar__0__st__1433] :
                  ( cPLF_2eImp_2estate___24t(Vvar__0__st__1433)
                  & Vvar__2___24Anonymous__1431 = Vvar__0__st__1433
                  & Vvar__1___24Anonymous__1430 = Vvar__0__st__1433
                  & Vvar__0___24Anonymous__1429 = cPLF_2eHoare_2eIf1_2eCSkip )
              | ? [Vvar__0__st__1434] :
                  ( cPLF_2eImp_2estate___24t(Vvar__0__st__1434)
                  & ? [Vvar__1__a1__1435] :
                      ( cPLF_2eImp_2eaexp___24t(Vvar__1__a1__1435)
                      & ? [Vvar__2__n__1436] :
                          ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__2__n__1436)
                          & ? [Vvar__3__x__1437] :
                              ( cCoq_2eStrings_2eString_2estring___24t(Vvar__3__x__1437)
                              & cPLF_2eImp_2eaeval___24a2(Vvar__0__st__1434,Vvar__1__a1__1435) = Vvar__2__n__1436
                              & Vvar__2___24Anonymous__1431 = c_24__lam__1487___24a6(Vvar__0___24Anonymous__1429,Vvar__1___24Anonymous__1430,Vvar__2___24Anonymous__1431,Vvar__0__st__1434,Vvar__2__n__1436,Vvar__3__x__1437)
                              & Vvar__1___24Anonymous__1430 = Vvar__0__st__1434
                              & Vvar__0___24Anonymous__1429 = cPLF_2eHoare_2eIf1_2eCAss___24a2(Vvar__3__x__1437,Vvar__1__a1__1435) ) ) ) )
              | ? [Vvar__0__c1__1441] :
                  ( cPLF_2eHoare_2eIf1_2ecom___24t(Vvar__0__c1__1441)
                  & ? [Vvar__1__c2__1442] :
                      ( cPLF_2eHoare_2eIf1_2ecom___24t(Vvar__1__c2__1442)
                      & ? [Vvar__2__st__1443] :
                          ( cPLF_2eImp_2estate___24t(Vvar__2__st__1443)
                          & ? [Vvar__3__st_27__1444] :
                              ( cPLF_2eImp_2estate___24t(Vvar__3__st_27__1444)
                              & ? [Vvar__4__st_27_27__1445] :
                                  ( cPLF_2eImp_2estate___24t(Vvar__4__st_27_27__1445)
                                  & cPLF_2eHoare_2eIf1_2eceval___24a3(Vvar__0__c1__1441,Vvar__2__st__1443,Vvar__3__st_27__1444)
                                  & cPLF_2eHoare_2eIf1_2eceval___24a3(Vvar__1__c2__1442,Vvar__3__st_27__1444,Vvar__4__st_27_27__1445)
                                  & Vvar__2___24Anonymous__1431 = Vvar__4__st_27_27__1445
                                  & Vvar__1___24Anonymous__1430 = Vvar__2__st__1443
                                  & Vvar__0___24Anonymous__1429 = cPLF_2eHoare_2eIf1_2eCSeq___24a2(Vvar__0__c1__1441,Vvar__1__c2__1442) ) ) ) ) )
              | ? [Vvar__0__st__1448] :
                  ( cPLF_2eImp_2estate___24t(Vvar__0__st__1448)
                  & ? [Vvar__1__st_27__1449] :
                      ( cPLF_2eImp_2estate___24t(Vvar__1__st_27__1449)
                      & ? [Vvar__2__b__1450] :
                          ( cPLF_2eImp_2ebexp___24t(Vvar__2__b__1450)
                          & ? [Vvar__3__c1__1451] :
                              ( cPLF_2eHoare_2eIf1_2ecom___24t(Vvar__3__c1__1451)
                              & ? [Vvar__4__c2__1452] :
                                  ( cPLF_2eHoare_2eIf1_2ecom___24t(Vvar__4__c2__1452)
                                  & cPLF_2eImp_2ebeval___24a2(Vvar__0__st__1448,Vvar__2__b__1450) = cCoq_2eInit_2eDatatypes_2etrue
                                  & cPLF_2eHoare_2eIf1_2eceval___24a3(Vvar__3__c1__1451,Vvar__0__st__1448,Vvar__1__st_27__1449)
                                  & Vvar__2___24Anonymous__1431 = Vvar__1__st_27__1449
                                  & Vvar__1___24Anonymous__1430 = Vvar__0__st__1448
                                  & Vvar__0___24Anonymous__1429 = cPLF_2eHoare_2eIf1_2eCIf___24a3(Vvar__2__b__1450,Vvar__3__c1__1451,Vvar__4__c2__1452) ) ) ) ) )
              | ? [Vvar__0__st__1455] :
                  ( cPLF_2eImp_2estate___24t(Vvar__0__st__1455)
                  & ? [Vvar__1__st_27__1456] :
                      ( cPLF_2eImp_2estate___24t(Vvar__1__st_27__1456)
                      & ? [Vvar__2__b__1457] :
                          ( cPLF_2eImp_2ebexp___24t(Vvar__2__b__1457)
                          & ? [Vvar__3__c1__1458] :
                              ( cPLF_2eHoare_2eIf1_2ecom___24t(Vvar__3__c1__1458)
                              & ? [Vvar__4__c2__1459] :
                                  ( cPLF_2eHoare_2eIf1_2ecom___24t(Vvar__4__c2__1459)
                                  & cPLF_2eImp_2ebeval___24a2(Vvar__0__st__1455,Vvar__2__b__1457) = cCoq_2eInit_2eDatatypes_2efalse
                                  & cPLF_2eHoare_2eIf1_2eceval___24a3(Vvar__4__c2__1459,Vvar__0__st__1455,Vvar__1__st_27__1456)
                                  & Vvar__2___24Anonymous__1431 = Vvar__1__st_27__1456
                                  & Vvar__1___24Anonymous__1430 = Vvar__0__st__1455
                                  & Vvar__0___24Anonymous__1429 = cPLF_2eHoare_2eIf1_2eCIf___24a3(Vvar__2__b__1457,Vvar__3__c1__1458,Vvar__4__c2__1459) ) ) ) ) )
              | ? [Vvar__0__b__1462] :
                  ( cPLF_2eImp_2ebexp___24t(Vvar__0__b__1462)
                  & ? [Vvar__1__st__1463] :
                      ( cPLF_2eImp_2estate___24t(Vvar__1__st__1463)
                      & ? [Vvar__2__c__1464] :
                          ( cPLF_2eHoare_2eIf1_2ecom___24t(Vvar__2__c__1464)
                          & cPLF_2eImp_2ebeval___24a2(Vvar__1__st__1463,Vvar__0__b__1462) = cCoq_2eInit_2eDatatypes_2efalse
                          & Vvar__2___24Anonymous__1431 = Vvar__1__st__1463
                          & Vvar__1___24Anonymous__1430 = Vvar__1__st__1463
                          & Vvar__0___24Anonymous__1429 = cPLF_2eHoare_2eIf1_2eCWhile___24a2(Vvar__0__b__1462,Vvar__2__c__1464) ) ) )
              | ? [Vvar__0__st__1466] :
                  ( cPLF_2eImp_2estate___24t(Vvar__0__st__1466)
                  & ? [Vvar__1__st_27__1467] :
                      ( cPLF_2eImp_2estate___24t(Vvar__1__st_27__1467)
                      & ? [Vvar__2__st_27_27__1468] :
                          ( cPLF_2eImp_2estate___24t(Vvar__2__st_27_27__1468)
                          & ? [Vvar__3__b__1469] :
                              ( cPLF_2eImp_2ebexp___24t(Vvar__3__b__1469)
                              & ? [Vvar__4__c__1470] :
                                  ( cPLF_2eHoare_2eIf1_2ecom___24t(Vvar__4__c__1470)
                                  & cPLF_2eImp_2ebeval___24a2(Vvar__0__st__1466,Vvar__3__b__1469) = cCoq_2eInit_2eDatatypes_2etrue
                                  & cPLF_2eHoare_2eIf1_2eceval___24a3(Vvar__4__c__1470,Vvar__0__st__1466,Vvar__1__st_27__1467)
                                  & cPLF_2eHoare_2eIf1_2eceval___24a3(cPLF_2eHoare_2eIf1_2eCWhile___24a2(Vvar__3__b__1469,Vvar__4__c__1470),Vvar__1__st_27__1467,Vvar__2__st_27_27__1468)
                                  & Vvar__2___24Anonymous__1431 = Vvar__2__st_27_27__1468
                                  & Vvar__1___24Anonymous__1430 = Vvar__0__st__1466
                                  & Vvar__0___24Anonymous__1429 = cPLF_2eHoare_2eIf1_2eCWhile___24a2(Vvar__3__b__1469,Vvar__4__c__1470) ) ) ) ) ) ) ) ) ) ) ).

fof('$_inversion_PLF.Hoare.If1.com',axiom,
    ! [VX1325] :
      ( cPLF_2eHoare_2eIf1_2ecom___24t(VX1325)
     => ( VX1325 = cPLF_2eHoare_2eIf1_2eCSkip
        | ? [Vvar__0___24Anonymous__1326] :
            ( cCoq_2eStrings_2eString_2estring___24t(Vvar__0___24Anonymous__1326)
            & ? [Vvar__1___24Anonymous__1327] :
                ( cPLF_2eImp_2eaexp___24t(Vvar__1___24Anonymous__1327)
                & VX1325 = cPLF_2eHoare_2eIf1_2eCAss___24a2(Vvar__0___24Anonymous__1326,Vvar__1___24Anonymous__1327) ) )
        | ? [Vvar__0___24Anonymous__1328] :
            ( cPLF_2eHoare_2eIf1_2ecom___24t(Vvar__0___24Anonymous__1328)
            & ? [Vvar__1___24Anonymous__1329] :
                ( cPLF_2eHoare_2eIf1_2ecom___24t(Vvar__1___24Anonymous__1329)
                & VX1325 = cPLF_2eHoare_2eIf1_2eCSeq___24a2(Vvar__0___24Anonymous__1328,Vvar__1___24Anonymous__1329) ) )
        | ? [Vvar__0___24Anonymous__1330] :
            ( cPLF_2eImp_2ebexp___24t(Vvar__0___24Anonymous__1330)
            & ? [Vvar__1___24Anonymous__1331] :
                ( cPLF_2eHoare_2eIf1_2ecom___24t(Vvar__1___24Anonymous__1331)
                & ? [Vvar__2___24Anonymous__1332] :
                    ( cPLF_2eHoare_2eIf1_2ecom___24t(Vvar__2___24Anonymous__1332)
                    & VX1325 = cPLF_2eHoare_2eIf1_2eCIf___24a3(Vvar__0___24Anonymous__1330,Vvar__1___24Anonymous__1331,Vvar__2___24Anonymous__1332) ) ) )
        | ? [Vvar__0___24Anonymous__1333] :
            ( cPLF_2eImp_2ebexp___24t(Vvar__0___24Anonymous__1333)
            & ? [Vvar__1___24Anonymous__1334] :
                ( cPLF_2eHoare_2eIf1_2ecom___24t(Vvar__1___24Anonymous__1334)
                & VX1325 = cPLF_2eHoare_2eIf1_2eCWhile___24a2(Vvar__0___24Anonymous__1333,Vvar__1___24Anonymous__1334) ) )
        | ? [Vvar__0___24Anonymous__1335] :
            ( cPLF_2eImp_2ebexp___24t(Vvar__0___24Anonymous__1335)
            & ? [Vvar__1___24Anonymous__1336] :
                ( cPLF_2eHoare_2eIf1_2ecom___24t(Vvar__1___24Anonymous__1336)
                & VX1325 = cPLF_2eHoare_2eIf1_2eCIf1___24a2(Vvar__0___24Anonymous__1335,Vvar__1___24Anonymous__1336) ) ) ) ) ).

fof('$_inversion_PLF.Hoare.RepeatExercise.ceval',axiom,
    ! [Vvar__0___24Anonymous__1659,Vvar__1___24Anonymous__1660,Vvar__2___24Anonymous__1661] :
      ( cPLF_2eImp_2estate___24t(Vvar__0___24Anonymous__1659)
     => ( cPLF_2eHoare_2eRepeatExercise_2ecom___24t(Vvar__1___24Anonymous__1660)
       => ( cPLF_2eImp_2estate___24t(Vvar__2___24Anonymous__1661)
         => ( cPLF_2eHoare_2eRepeatExercise_2eceval___24a3(Vvar__0___24Anonymous__1659,Vvar__1___24Anonymous__1660,Vvar__2___24Anonymous__1661)
           => ( ? [Vvar__0__st__1663] :
                  ( cPLF_2eImp_2estate___24t(Vvar__0__st__1663)
                  & Vvar__2___24Anonymous__1661 = Vvar__0__st__1663
                  & Vvar__1___24Anonymous__1660 = cPLF_2eHoare_2eRepeatExercise_2eCSkip
                  & Vvar__0___24Anonymous__1659 = Vvar__0__st__1663 )
              | ? [Vvar__0__st__1664] :
                  ( cPLF_2eImp_2estate___24t(Vvar__0__st__1664)
                  & ? [Vvar__1__a1__1665] :
                      ( cPLF_2eImp_2eaexp___24t(Vvar__1__a1__1665)
                      & ? [Vvar__2__n__1666] :
                          ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__2__n__1666)
                          & ? [Vvar__3__x__1667] :
                              ( cCoq_2eStrings_2eString_2estring___24t(Vvar__3__x__1667)
                              & cPLF_2eImp_2eaeval___24a2(Vvar__0__st__1664,Vvar__1__a1__1665) = Vvar__2__n__1666
                              & Vvar__2___24Anonymous__1661 = c_24__lam__1717___24a6(Vvar__0___24Anonymous__1659,Vvar__1___24Anonymous__1660,Vvar__2___24Anonymous__1661,Vvar__0__st__1664,Vvar__2__n__1666,Vvar__3__x__1667)
                              & Vvar__1___24Anonymous__1660 = cPLF_2eHoare_2eRepeatExercise_2eCAsgn___24a2(Vvar__3__x__1667,Vvar__1__a1__1665)
                              & Vvar__0___24Anonymous__1659 = Vvar__0__st__1664 ) ) ) )
              | ? [Vvar__0__c1__1671] :
                  ( cPLF_2eHoare_2eRepeatExercise_2ecom___24t(Vvar__0__c1__1671)
                  & ? [Vvar__1__c2__1672] :
                      ( cPLF_2eHoare_2eRepeatExercise_2ecom___24t(Vvar__1__c2__1672)
                      & ? [Vvar__2__st__1673] :
                          ( cPLF_2eImp_2estate___24t(Vvar__2__st__1673)
                          & ? [Vvar__3__st_27__1674] :
                              ( cPLF_2eImp_2estate___24t(Vvar__3__st_27__1674)
                              & ? [Vvar__4__st_27_27__1675] :
                                  ( cPLF_2eImp_2estate___24t(Vvar__4__st_27_27__1675)
                                  & cPLF_2eHoare_2eRepeatExercise_2eceval___24a3(Vvar__2__st__1673,Vvar__0__c1__1671,Vvar__3__st_27__1674)
                                  & cPLF_2eHoare_2eRepeatExercise_2eceval___24a3(Vvar__3__st_27__1674,Vvar__1__c2__1672,Vvar__4__st_27_27__1675)
                                  & Vvar__2___24Anonymous__1661 = Vvar__4__st_27_27__1675
                                  & Vvar__1___24Anonymous__1660 = cPLF_2eHoare_2eRepeatExercise_2eCSeq___24a2(Vvar__0__c1__1671,Vvar__1__c2__1672)
                                  & Vvar__0___24Anonymous__1659 = Vvar__2__st__1673 ) ) ) ) )
              | ? [Vvar__0__st__1678] :
                  ( cPLF_2eImp_2estate___24t(Vvar__0__st__1678)
                  & ? [Vvar__1__st_27__1679] :
                      ( cPLF_2eImp_2estate___24t(Vvar__1__st_27__1679)
                      & ? [Vvar__2__b__1680] :
                          ( cPLF_2eImp_2ebexp___24t(Vvar__2__b__1680)
                          & ? [Vvar__3__c1__1681] :
                              ( cPLF_2eHoare_2eRepeatExercise_2ecom___24t(Vvar__3__c1__1681)
                              & ? [Vvar__4__c2__1682] :
                                  ( cPLF_2eHoare_2eRepeatExercise_2ecom___24t(Vvar__4__c2__1682)
                                  & cPLF_2eImp_2ebeval___24a2(Vvar__0__st__1678,Vvar__2__b__1680) = cCoq_2eInit_2eDatatypes_2etrue
                                  & cPLF_2eHoare_2eRepeatExercise_2eceval___24a3(Vvar__0__st__1678,Vvar__3__c1__1681,Vvar__1__st_27__1679)
                                  & Vvar__2___24Anonymous__1661 = Vvar__1__st_27__1679
                                  & Vvar__1___24Anonymous__1660 = cPLF_2eHoare_2eRepeatExercise_2eCIf___24a3(Vvar__2__b__1680,Vvar__3__c1__1681,Vvar__4__c2__1682)
                                  & Vvar__0___24Anonymous__1659 = Vvar__0__st__1678 ) ) ) ) )
              | ? [Vvar__0__st__1685] :
                  ( cPLF_2eImp_2estate___24t(Vvar__0__st__1685)
                  & ? [Vvar__1__st_27__1686] :
                      ( cPLF_2eImp_2estate___24t(Vvar__1__st_27__1686)
                      & ? [Vvar__2__b__1687] :
                          ( cPLF_2eImp_2ebexp___24t(Vvar__2__b__1687)
                          & ? [Vvar__3__c1__1688] :
                              ( cPLF_2eHoare_2eRepeatExercise_2ecom___24t(Vvar__3__c1__1688)
                              & ? [Vvar__4__c2__1689] :
                                  ( cPLF_2eHoare_2eRepeatExercise_2ecom___24t(Vvar__4__c2__1689)
                                  & cPLF_2eImp_2ebeval___24a2(Vvar__0__st__1685,Vvar__2__b__1687) = cCoq_2eInit_2eDatatypes_2efalse
                                  & cPLF_2eHoare_2eRepeatExercise_2eceval___24a3(Vvar__0__st__1685,Vvar__4__c2__1689,Vvar__1__st_27__1686)
                                  & Vvar__2___24Anonymous__1661 = Vvar__1__st_27__1686
                                  & Vvar__1___24Anonymous__1660 = cPLF_2eHoare_2eRepeatExercise_2eCIf___24a3(Vvar__2__b__1687,Vvar__3__c1__1688,Vvar__4__c2__1689)
                                  & Vvar__0___24Anonymous__1659 = Vvar__0__st__1685 ) ) ) ) )
              | ? [Vvar__0__b__1692] :
                  ( cPLF_2eImp_2ebexp___24t(Vvar__0__b__1692)
                  & ? [Vvar__1__st__1693] :
                      ( cPLF_2eImp_2estate___24t(Vvar__1__st__1693)
                      & ? [Vvar__2__c__1694] :
                          ( cPLF_2eHoare_2eRepeatExercise_2ecom___24t(Vvar__2__c__1694)
                          & cPLF_2eImp_2ebeval___24a2(Vvar__1__st__1693,Vvar__0__b__1692) = cCoq_2eInit_2eDatatypes_2efalse
                          & Vvar__2___24Anonymous__1661 = Vvar__1__st__1693
                          & Vvar__1___24Anonymous__1660 = cPLF_2eHoare_2eRepeatExercise_2eCWhile___24a2(Vvar__0__b__1692,Vvar__2__c__1694)
                          & Vvar__0___24Anonymous__1659 = Vvar__1__st__1693 ) ) )
              | ? [Vvar__0__st__1696] :
                  ( cPLF_2eImp_2estate___24t(Vvar__0__st__1696)
                  & ? [Vvar__1__st_27__1697] :
                      ( cPLF_2eImp_2estate___24t(Vvar__1__st_27__1697)
                      & ? [Vvar__2__st_27_27__1698] :
                          ( cPLF_2eImp_2estate___24t(Vvar__2__st_27_27__1698)
                          & ? [Vvar__3__b__1699] :
                              ( cPLF_2eImp_2ebexp___24t(Vvar__3__b__1699)
                              & ? [Vvar__4__c__1700] :
                                  ( cPLF_2eHoare_2eRepeatExercise_2ecom___24t(Vvar__4__c__1700)
                                  & cPLF_2eImp_2ebeval___24a2(Vvar__0__st__1696,Vvar__3__b__1699) = cCoq_2eInit_2eDatatypes_2etrue
                                  & cPLF_2eHoare_2eRepeatExercise_2eceval___24a3(Vvar__0__st__1696,Vvar__4__c__1700,Vvar__1__st_27__1697)
                                  & cPLF_2eHoare_2eRepeatExercise_2eceval___24a3(Vvar__1__st_27__1697,cPLF_2eHoare_2eRepeatExercise_2eCWhile___24a2(Vvar__3__b__1699,Vvar__4__c__1700),Vvar__2__st_27_27__1698)
                                  & Vvar__2___24Anonymous__1661 = Vvar__2__st_27_27__1698
                                  & Vvar__1___24Anonymous__1660 = cPLF_2eHoare_2eRepeatExercise_2eCWhile___24a2(Vvar__3__b__1699,Vvar__4__c__1700)
                                  & Vvar__0___24Anonymous__1659 = Vvar__0__st__1696 ) ) ) ) ) ) ) ) ) ) ).

fof('$_inversion_PLF.Hoare.RepeatExercise.com',axiom,
    ! [VX1553] :
      ( cPLF_2eHoare_2eRepeatExercise_2ecom___24t(VX1553)
     => ( VX1553 = cPLF_2eHoare_2eRepeatExercise_2eCSkip
        | ? [Vvar__0___24Anonymous__1554] :
            ( cCoq_2eStrings_2eString_2estring___24t(Vvar__0___24Anonymous__1554)
            & ? [Vvar__1___24Anonymous__1555] :
                ( cPLF_2eImp_2eaexp___24t(Vvar__1___24Anonymous__1555)
                & VX1553 = cPLF_2eHoare_2eRepeatExercise_2eCAsgn___24a2(Vvar__0___24Anonymous__1554,Vvar__1___24Anonymous__1555) ) )
        | ? [Vvar__0___24Anonymous__1556] :
            ( cPLF_2eHoare_2eRepeatExercise_2ecom___24t(Vvar__0___24Anonymous__1556)
            & ? [Vvar__1___24Anonymous__1557] :
                ( cPLF_2eHoare_2eRepeatExercise_2ecom___24t(Vvar__1___24Anonymous__1557)
                & VX1553 = cPLF_2eHoare_2eRepeatExercise_2eCSeq___24a2(Vvar__0___24Anonymous__1556,Vvar__1___24Anonymous__1557) ) )
        | ? [Vvar__0___24Anonymous__1558] :
            ( cPLF_2eImp_2ebexp___24t(Vvar__0___24Anonymous__1558)
            & ? [Vvar__1___24Anonymous__1559] :
                ( cPLF_2eHoare_2eRepeatExercise_2ecom___24t(Vvar__1___24Anonymous__1559)
                & ? [Vvar__2___24Anonymous__1560] :
                    ( cPLF_2eHoare_2eRepeatExercise_2ecom___24t(Vvar__2___24Anonymous__1560)
                    & VX1553 = cPLF_2eHoare_2eRepeatExercise_2eCIf___24a3(Vvar__0___24Anonymous__1558,Vvar__1___24Anonymous__1559,Vvar__2___24Anonymous__1560) ) ) )
        | ? [Vvar__0___24Anonymous__1561] :
            ( cPLF_2eImp_2ebexp___24t(Vvar__0___24Anonymous__1561)
            & ? [Vvar__1___24Anonymous__1562] :
                ( cPLF_2eHoare_2eRepeatExercise_2ecom___24t(Vvar__1___24Anonymous__1562)
                & VX1553 = cPLF_2eHoare_2eRepeatExercise_2eCWhile___24a2(Vvar__0___24Anonymous__1561,Vvar__1___24Anonymous__1562) ) )
        | ? [Vvar__0___24Anonymous__1563] :
            ( cPLF_2eHoare_2eRepeatExercise_2ecom___24t(Vvar__0___24Anonymous__1563)
            & ? [Vvar__1___24Anonymous__1564] :
                ( cPLF_2eImp_2ebexp___24t(Vvar__1___24Anonymous__1564)
                & VX1553 = cPLF_2eHoare_2eRepeatExercise_2eCRepeat___24a2(Vvar__0___24Anonymous__1563,Vvar__1___24Anonymous__1564) ) ) ) ) ).

fof('$_inversion_PLF.Imp.AExp.aevalR',axiom,
    ! [Vvar__0___24Anonymous__82762,Vvar__1___24Anonymous__82763] :
      ( cPLF_2eImp_2eAExp_2eaexp___24t(Vvar__0___24Anonymous__82762)
     => ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__1___24Anonymous__82763)
       => ( cPLF_2eImp_2eAExp_2eaevalR___24a2(Vvar__0___24Anonymous__82762,Vvar__1___24Anonymous__82763)
         => ( ? [Vvar__0__n__82765] :
                ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0__n__82765)
                & Vvar__1___24Anonymous__82763 = Vvar__0__n__82765
                & Vvar__0___24Anonymous__82762 = cPLF_2eImp_2eAExp_2eANum___24a1(Vvar__0__n__82765) )
            | ? [Vvar__0__e1__82766] :
                ( cPLF_2eImp_2eAExp_2eaexp___24t(Vvar__0__e1__82766)
                & ? [Vvar__1__e2__82767] :
                    ( cPLF_2eImp_2eAExp_2eaexp___24t(Vvar__1__e2__82767)
                    & ? [Vvar__2__n1__82768] :
                        ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__2__n1__82768)
                        & ? [Vvar__3__n2__82769] :
                            ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__3__n2__82769)
                            & cPLF_2eImp_2eAExp_2eaevalR___24a2(Vvar__0__e1__82766,Vvar__2__n1__82768)
                            & cPLF_2eImp_2eAExp_2eaevalR___24a2(Vvar__1__e2__82767,Vvar__3__n2__82769)
                            & Vvar__1___24Anonymous__82763 = c_24__case__Coq_2eInit_2eDatatypes_2enat_2482845___24a4(Vvar__0___24Anonymous__82762,Vvar__1___24Anonymous__82763,Vvar__2__n1__82768,Vvar__3__n2__82769)
                            & Vvar__0___24Anonymous__82762 = cPLF_2eImp_2eAExp_2eAPlus___24a2(Vvar__0__e1__82766,Vvar__1__e2__82767) ) ) ) )
            | ? [Vvar__0__e1__82774] :
                ( cPLF_2eImp_2eAExp_2eaexp___24t(Vvar__0__e1__82774)
                & ? [Vvar__1__e2__82775] :
                    ( cPLF_2eImp_2eAExp_2eaexp___24t(Vvar__1__e2__82775)
                    & ? [Vvar__2__n1__82776] :
                        ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__2__n1__82776)
                        & ? [Vvar__3__n2__82777] :
                            ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__3__n2__82777)
                            & cPLF_2eImp_2eAExp_2eaevalR___24a2(Vvar__0__e1__82774,Vvar__2__n1__82776)
                            & cPLF_2eImp_2eAExp_2eaevalR___24a2(Vvar__1__e2__82775,Vvar__3__n2__82777)
                            & Vvar__1___24Anonymous__82763 = c_24__case__Coq_2eInit_2eDatatypes_2enat_2482954___24a4(Vvar__0___24Anonymous__82762,Vvar__1___24Anonymous__82763,Vvar__2__n1__82776,Vvar__3__n2__82777)
                            & Vvar__0___24Anonymous__82762 = cPLF_2eImp_2eAExp_2eAMinus___24a2(Vvar__0__e1__82774,Vvar__1__e2__82775) ) ) ) )
            | ? [Vvar__0__e1__82784] :
                ( cPLF_2eImp_2eAExp_2eaexp___24t(Vvar__0__e1__82784)
                & ? [Vvar__1__e2__82785] :
                    ( cPLF_2eImp_2eAExp_2eaexp___24t(Vvar__1__e2__82785)
                    & ? [Vvar__2__n1__82786] :
                        ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__2__n1__82786)
                        & ? [Vvar__3__n2__82787] :
                            ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__3__n2__82787)
                            & cPLF_2eImp_2eAExp_2eaevalR___24a2(Vvar__0__e1__82784,Vvar__2__n1__82786)
                            & cPLF_2eImp_2eAExp_2eaevalR___24a2(Vvar__1__e2__82785,Vvar__3__n2__82787)
                            & Vvar__1___24Anonymous__82763 = c_24__case__Coq_2eInit_2eDatatypes_2enat_2483048___24a4(Vvar__0___24Anonymous__82762,Vvar__1___24Anonymous__82763,Vvar__2__n1__82786,Vvar__3__n2__82787)
                            & Vvar__0___24Anonymous__82762 = cPLF_2eImp_2eAExp_2eAMult___24a2(Vvar__0__e1__82784,Vvar__1__e2__82785) ) ) ) ) ) ) ) ) ).

fof('$_inversion_PLF.Imp.AExp.aevalR_first_try.TooHardToRead.aevalR',axiom,
    ! [Vvar__0___24Anonymous__83261,Vvar__1___24Anonymous__83262] :
      ( cPLF_2eImp_2eAExp_2eaexp___24t(Vvar__0___24Anonymous__83261)
     => ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__1___24Anonymous__83262)
       => ( cPLF_2eImp_2eAExp_2eaevalR__first__try_2eTooHardToRead_2eaevalR___24a2(Vvar__0___24Anonymous__83261,Vvar__1___24Anonymous__83262)
         => ( ? [Vvar__0__n__83264] :
                ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0__n__83264)
                & Vvar__1___24Anonymous__83262 = Vvar__0__n__83264
                & Vvar__0___24Anonymous__83261 = cPLF_2eImp_2eAExp_2eANum___24a1(Vvar__0__n__83264) )
            | ? [Vvar__0__e1__83265] :
                ( cPLF_2eImp_2eAExp_2eaexp___24t(Vvar__0__e1__83265)
                & ? [Vvar__1__e2__83266] :
                    ( cPLF_2eImp_2eAExp_2eaexp___24t(Vvar__1__e2__83266)
                    & ? [Vvar__2__n1__83267] :
                        ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__2__n1__83267)
                        & ? [Vvar__3__n2__83268] :
                            ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__3__n2__83268)
                            & cPLF_2eImp_2eAExp_2eaevalR__first__try_2eTooHardToRead_2eaevalR___24a2(Vvar__0__e1__83265,Vvar__2__n1__83267)
                            & cPLF_2eImp_2eAExp_2eaevalR__first__try_2eTooHardToRead_2eaevalR___24a2(Vvar__1__e2__83266,Vvar__3__n2__83268)
                            & Vvar__1___24Anonymous__83262 = c_24__case__Coq_2eInit_2eDatatypes_2enat_2482845___24a4(Vvar__0___24Anonymous__83261,Vvar__1___24Anonymous__83262,Vvar__2__n1__83267,Vvar__3__n2__83268)
                            & Vvar__0___24Anonymous__83261 = cPLF_2eImp_2eAExp_2eAPlus___24a2(Vvar__0__e1__83265,Vvar__1__e2__83266) ) ) ) )
            | ? [Vvar__0__e1__83273] :
                ( cPLF_2eImp_2eAExp_2eaexp___24t(Vvar__0__e1__83273)
                & ? [Vvar__1__e2__83274] :
                    ( cPLF_2eImp_2eAExp_2eaexp___24t(Vvar__1__e2__83274)
                    & ? [Vvar__2__n1__83275] :
                        ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__2__n1__83275)
                        & ? [Vvar__3__n2__83276] :
                            ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__3__n2__83276)
                            & cPLF_2eImp_2eAExp_2eaevalR__first__try_2eTooHardToRead_2eaevalR___24a2(Vvar__0__e1__83273,Vvar__2__n1__83275)
                            & cPLF_2eImp_2eAExp_2eaevalR__first__try_2eTooHardToRead_2eaevalR___24a2(Vvar__1__e2__83274,Vvar__3__n2__83276)
                            & Vvar__1___24Anonymous__83262 = c_24__case__Coq_2eInit_2eDatatypes_2enat_2482954___24a4(Vvar__0___24Anonymous__83261,Vvar__1___24Anonymous__83262,Vvar__2__n1__83275,Vvar__3__n2__83276)
                            & Vvar__0___24Anonymous__83261 = cPLF_2eImp_2eAExp_2eAMinus___24a2(Vvar__0__e1__83273,Vvar__1__e2__83274) ) ) ) )
            | ? [Vvar__0__e1__83283] :
                ( cPLF_2eImp_2eAExp_2eaexp___24t(Vvar__0__e1__83283)
                & ? [Vvar__1__e2__83284] :
                    ( cPLF_2eImp_2eAExp_2eaexp___24t(Vvar__1__e2__83284)
                    & ? [Vvar__2__n1__83285] :
                        ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__2__n1__83285)
                        & ? [Vvar__3__n2__83286] :
                            ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__3__n2__83286)
                            & cPLF_2eImp_2eAExp_2eaevalR__first__try_2eTooHardToRead_2eaevalR___24a2(Vvar__0__e1__83283,Vvar__2__n1__83285)
                            & cPLF_2eImp_2eAExp_2eaevalR__first__try_2eTooHardToRead_2eaevalR___24a2(Vvar__1__e2__83284,Vvar__3__n2__83286)
                            & Vvar__1___24Anonymous__83262 = c_24__case__Coq_2eInit_2eDatatypes_2enat_2483048___24a4(Vvar__0___24Anonymous__83261,Vvar__1___24Anonymous__83262,Vvar__2__n1__83285,Vvar__3__n2__83286)
                            & Vvar__0___24Anonymous__83261 = cPLF_2eImp_2eAExp_2eAMult___24a2(Vvar__0__e1__83283,Vvar__1__e2__83284) ) ) ) ) ) ) ) ) ).

fof('$_inversion_PLF.Imp.AExp.aevalR_first_try.aevalR',axiom,
    ! [Vvar__0___24Anonymous__83975,Vvar__1___24Anonymous__83976] :
      ( cPLF_2eImp_2eAExp_2eaexp___24t(Vvar__0___24Anonymous__83975)
     => ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__1___24Anonymous__83976)
       => ( cPLF_2eImp_2eAExp_2eaevalR__first__try_2eaevalR___24a2(Vvar__0___24Anonymous__83975,Vvar__1___24Anonymous__83976)
         => ( ? [Vvar__0__n__83978] :
                ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0__n__83978)
                & Vvar__1___24Anonymous__83976 = Vvar__0__n__83978
                & Vvar__0___24Anonymous__83975 = cPLF_2eImp_2eAExp_2eANum___24a1(Vvar__0__n__83978) )
            | ? [Vvar__0__e1__83979] :
                ( cPLF_2eImp_2eAExp_2eaexp___24t(Vvar__0__e1__83979)
                & ? [Vvar__1__e2__83980] :
                    ( cPLF_2eImp_2eAExp_2eaexp___24t(Vvar__1__e2__83980)
                    & ? [Vvar__2__n1__83981] :
                        ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__2__n1__83981)
                        & ? [Vvar__3__n2__83982] :
                            ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__3__n2__83982)
                            & cPLF_2eImp_2eAExp_2eaevalR__first__try_2eaevalR___24a2(Vvar__0__e1__83979,Vvar__2__n1__83981)
                            & cPLF_2eImp_2eAExp_2eaevalR__first__try_2eaevalR___24a2(Vvar__1__e2__83980,Vvar__3__n2__83982)
                            & Vvar__1___24Anonymous__83976 = c_24__case__Coq_2eInit_2eDatatypes_2enat_2482845___24a4(Vvar__0___24Anonymous__83975,Vvar__1___24Anonymous__83976,Vvar__2__n1__83981,Vvar__3__n2__83982)
                            & Vvar__0___24Anonymous__83975 = cPLF_2eImp_2eAExp_2eAPlus___24a2(Vvar__0__e1__83979,Vvar__1__e2__83980) ) ) ) )
            | ? [Vvar__0__e1__83987] :
                ( cPLF_2eImp_2eAExp_2eaexp___24t(Vvar__0__e1__83987)
                & ? [Vvar__1__e2__83988] :
                    ( cPLF_2eImp_2eAExp_2eaexp___24t(Vvar__1__e2__83988)
                    & ? [Vvar__2__n1__83989] :
                        ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__2__n1__83989)
                        & ? [Vvar__3__n2__83990] :
                            ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__3__n2__83990)
                            & cPLF_2eImp_2eAExp_2eaevalR__first__try_2eaevalR___24a2(Vvar__0__e1__83987,Vvar__2__n1__83989)
                            & cPLF_2eImp_2eAExp_2eaevalR__first__try_2eaevalR___24a2(Vvar__1__e2__83988,Vvar__3__n2__83990)
                            & Vvar__1___24Anonymous__83976 = c_24__case__Coq_2eInit_2eDatatypes_2enat_2482954___24a4(Vvar__0___24Anonymous__83975,Vvar__1___24Anonymous__83976,Vvar__2__n1__83989,Vvar__3__n2__83990)
                            & Vvar__0___24Anonymous__83975 = cPLF_2eImp_2eAExp_2eAMinus___24a2(Vvar__0__e1__83987,Vvar__1__e2__83988) ) ) ) )
            | ? [Vvar__0__e1__83997] :
                ( cPLF_2eImp_2eAExp_2eaexp___24t(Vvar__0__e1__83997)
                & ? [Vvar__1__e2__83998] :
                    ( cPLF_2eImp_2eAExp_2eaexp___24t(Vvar__1__e2__83998)
                    & ? [Vvar__2__n1__83999] :
                        ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__2__n1__83999)
                        & ? [Vvar__3__n2__84000] :
                            ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__3__n2__84000)
                            & cPLF_2eImp_2eAExp_2eaevalR__first__try_2eaevalR___24a2(Vvar__0__e1__83997,Vvar__2__n1__83999)
                            & cPLF_2eImp_2eAExp_2eaevalR__first__try_2eaevalR___24a2(Vvar__1__e2__83998,Vvar__3__n2__84000)
                            & Vvar__1___24Anonymous__83976 = c_24__case__Coq_2eInit_2eDatatypes_2enat_2483048___24a4(Vvar__0___24Anonymous__83975,Vvar__1___24Anonymous__83976,Vvar__2__n1__83999,Vvar__3__n2__84000)
                            & Vvar__0___24Anonymous__83975 = cPLF_2eImp_2eAExp_2eAMult___24a2(Vvar__0__e1__83997,Vvar__1__e2__83998) ) ) ) ) ) ) ) ) ).

fof('$_inversion_PLF.Imp.AExp.aexp',axiom,
    ! [VX6940] :
      ( cPLF_2eImp_2eAExp_2eaexp___24t(VX6940)
     => ( ? [Vvar__0__n__6941] :
            ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0__n__6941)
            & VX6940 = cPLF_2eImp_2eAExp_2eANum___24a1(Vvar__0__n__6941) )
        | ? [Vvar__0__a1__6942] :
            ( cPLF_2eImp_2eAExp_2eaexp___24t(Vvar__0__a1__6942)
            & ? [Vvar__1__a2__6943] :
                ( cPLF_2eImp_2eAExp_2eaexp___24t(Vvar__1__a2__6943)
                & VX6940 = cPLF_2eImp_2eAExp_2eAPlus___24a2(Vvar__0__a1__6942,Vvar__1__a2__6943) ) )
        | ? [Vvar__0__a1__6944] :
            ( cPLF_2eImp_2eAExp_2eaexp___24t(Vvar__0__a1__6944)
            & ? [Vvar__1__a2__6945] :
                ( cPLF_2eImp_2eAExp_2eaexp___24t(Vvar__1__a2__6945)
                & VX6940 = cPLF_2eImp_2eAExp_2eAMinus___24a2(Vvar__0__a1__6944,Vvar__1__a2__6945) ) )
        | ? [Vvar__0__a1__6946] :
            ( cPLF_2eImp_2eAExp_2eaexp___24t(Vvar__0__a1__6946)
            & ? [Vvar__1__a2__6947] :
                ( cPLF_2eImp_2eAExp_2eaexp___24t(Vvar__1__a2__6947)
                & VX6940 = cPLF_2eImp_2eAExp_2eAMult___24a2(Vvar__0__a1__6946,Vvar__1__a2__6947) ) ) ) ) ).

fof('$_inversion_PLF.Imp.AExp.bexp',axiom,
    ! [VX149795] :
      ( cPLF_2eImp_2eAExp_2ebexp___24t(VX149795)
     => ( VX149795 = cPLF_2eImp_2eAExp_2eBTrue
        | VX149795 = cPLF_2eImp_2eAExp_2eBFalse
        | ? [Vvar__0__a1__149796] :
            ( cPLF_2eImp_2eAExp_2eaexp___24t(Vvar__0__a1__149796)
            & ? [Vvar__1__a2__149797] :
                ( cPLF_2eImp_2eAExp_2eaexp___24t(Vvar__1__a2__149797)
                & VX149795 = cPLF_2eImp_2eAExp_2eBEq___24a2(Vvar__0__a1__149796,Vvar__1__a2__149797) ) )
        | ? [Vvar__0__a1__149798] :
            ( cPLF_2eImp_2eAExp_2eaexp___24t(Vvar__0__a1__149798)
            & ? [Vvar__1__a2__149799] :
                ( cPLF_2eImp_2eAExp_2eaexp___24t(Vvar__1__a2__149799)
                & VX149795 = cPLF_2eImp_2eAExp_2eBLe___24a2(Vvar__0__a1__149798,Vvar__1__a2__149799) ) )
        | ? [Vvar__0__b__149800] :
            ( cPLF_2eImp_2eAExp_2ebexp___24t(Vvar__0__b__149800)
            & VX149795 = cPLF_2eImp_2eAExp_2eBNot___24a1(Vvar__0__b__149800) )
        | ? [Vvar__0__b1__149801] :
            ( cPLF_2eImp_2eAExp_2ebexp___24t(Vvar__0__b1__149801)
            & ? [Vvar__1__b2__149802] :
                ( cPLF_2eImp_2eAExp_2ebexp___24t(Vvar__1__b2__149802)
                & VX149795 = cPLF_2eImp_2eAExp_2eBAnd___24a2(Vvar__0__b1__149801,Vvar__1__b2__149802) ) ) ) ) ).

fof('$_inversion_PLF.Imp.BreakImp.com',axiom,
    ! [VX688] :
      ( cPLF_2eImp_2eBreakImp_2ecom___24t(VX688)
     => ( VX688 = cPLF_2eImp_2eBreakImp_2eCSkip
        | VX688 = cPLF_2eImp_2eBreakImp_2eCBreak
        | ? [Vvar__0__x__689] :
            ( cCoq_2eStrings_2eString_2estring___24t(Vvar__0__x__689)
            & ? [Vvar__1__a__690] :
                ( cPLF_2eImp_2eaexp___24t(Vvar__1__a__690)
                & VX688 = cPLF_2eImp_2eBreakImp_2eCAss___24a2(Vvar__0__x__689,Vvar__1__a__690) ) )
        | ? [Vvar__0__c1__691] :
            ( cPLF_2eImp_2eBreakImp_2ecom___24t(Vvar__0__c1__691)
            & ? [Vvar__1__c2__692] :
                ( cPLF_2eImp_2eBreakImp_2ecom___24t(Vvar__1__c2__692)
                & VX688 = cPLF_2eImp_2eBreakImp_2eCSeq___24a2(Vvar__0__c1__691,Vvar__1__c2__692) ) )
        | ? [Vvar__0__b__693] :
            ( cPLF_2eImp_2ebexp___24t(Vvar__0__b__693)
            & ? [Vvar__1__c1__694] :
                ( cPLF_2eImp_2eBreakImp_2ecom___24t(Vvar__1__c1__694)
                & ? [Vvar__2__c2__695] :
                    ( cPLF_2eImp_2eBreakImp_2ecom___24t(Vvar__2__c2__695)
                    & VX688 = cPLF_2eImp_2eBreakImp_2eCIf___24a3(Vvar__0__b__693,Vvar__1__c1__694,Vvar__2__c2__695) ) ) )
        | ? [Vvar__0__b__696] :
            ( cPLF_2eImp_2ebexp___24t(Vvar__0__b__696)
            & ? [Vvar__1__c__697] :
                ( cPLF_2eImp_2eBreakImp_2ecom___24t(Vvar__1__c__697)
                & VX688 = cPLF_2eImp_2eBreakImp_2eCWhile___24a2(Vvar__0__b__696,Vvar__1__c__697) ) ) ) ) ).

fof('$_inversion_PLF.Imp.BreakImp.result',axiom,
    ! [VX767] :
      ( cPLF_2eImp_2eBreakImp_2eresult___24t(VX767)
     => ( VX767 = cPLF_2eImp_2eBreakImp_2eSContinue
        | VX767 = cPLF_2eImp_2eBreakImp_2eSBreak ) ) ).

fof('$_inversion_PLF.Imp.aevalR_division.aevalR',axiom,
    ! [Vvar__0___24Anonymous__4537,Vvar__1___24Anonymous__4538] :
      ( cPLF_2eImp_2eaevalR__division_2eaexp___24t(Vvar__0___24Anonymous__4537)
     => ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__1___24Anonymous__4538)
       => ( cPLF_2eImp_2eaevalR__division_2eaevalR___24a2(Vvar__0___24Anonymous__4537,Vvar__1___24Anonymous__4538)
         => ( ? [Vvar__0__n__4540] :
                ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0__n__4540)
                & Vvar__1___24Anonymous__4538 = Vvar__0__n__4540
                & Vvar__0___24Anonymous__4537 = cPLF_2eImp_2eaevalR__division_2eANum___24a1(Vvar__0__n__4540) )
            | ? [Vvar__0__a1__4541] :
                ( cPLF_2eImp_2eaevalR__division_2eaexp___24t(Vvar__0__a1__4541)
                & ? [Vvar__1__a2__4542] :
                    ( cPLF_2eImp_2eaevalR__division_2eaexp___24t(Vvar__1__a2__4542)
                    & ? [Vvar__2__n1__4543] :
                        ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__2__n1__4543)
                        & ? [Vvar__3__n2__4544] :
                            ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__3__n2__4544)
                            & cPLF_2eImp_2eaevalR__division_2eaevalR___24a2(Vvar__0__a1__4541,Vvar__2__n1__4543)
                            & cPLF_2eImp_2eaevalR__division_2eaevalR___24a2(Vvar__1__a2__4542,Vvar__3__n2__4544)
                            & Vvar__1___24Anonymous__4538 = c_24__case__Coq_2eInit_2eDatatypes_2enat_244629___24a4(Vvar__0___24Anonymous__4537,Vvar__1___24Anonymous__4538,Vvar__2__n1__4543,Vvar__3__n2__4544)
                            & Vvar__0___24Anonymous__4537 = cPLF_2eImp_2eaevalR__division_2eAPlus___24a2(Vvar__0__a1__4541,Vvar__1__a2__4542) ) ) ) )
            | ? [Vvar__0__a1__4549] :
                ( cPLF_2eImp_2eaevalR__division_2eaexp___24t(Vvar__0__a1__4549)
                & ? [Vvar__1__a2__4550] :
                    ( cPLF_2eImp_2eaevalR__division_2eaexp___24t(Vvar__1__a2__4550)
                    & ? [Vvar__2__n1__4551] :
                        ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__2__n1__4551)
                        & ? [Vvar__3__n2__4552] :
                            ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__3__n2__4552)
                            & cPLF_2eImp_2eaevalR__division_2eaevalR___24a2(Vvar__0__a1__4549,Vvar__2__n1__4551)
                            & cPLF_2eImp_2eaevalR__division_2eaevalR___24a2(Vvar__1__a2__4550,Vvar__3__n2__4552)
                            & Vvar__1___24Anonymous__4538 = c_24__case__Coq_2eInit_2eDatatypes_2enat_244740___24a4(Vvar__0___24Anonymous__4537,Vvar__1___24Anonymous__4538,Vvar__2__n1__4551,Vvar__3__n2__4552)
                            & Vvar__0___24Anonymous__4537 = cPLF_2eImp_2eaevalR__division_2eAMinus___24a2(Vvar__0__a1__4549,Vvar__1__a2__4550) ) ) ) )
            | ? [Vvar__0__a1__4559] :
                ( cPLF_2eImp_2eaevalR__division_2eaexp___24t(Vvar__0__a1__4559)
                & ? [Vvar__1__a2__4560] :
                    ( cPLF_2eImp_2eaevalR__division_2eaexp___24t(Vvar__1__a2__4560)
                    & ? [Vvar__2__n1__4561] :
                        ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__2__n1__4561)
                        & ? [Vvar__3__n2__4562] :
                            ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__3__n2__4562)
                            & cPLF_2eImp_2eaevalR__division_2eaevalR___24a2(Vvar__0__a1__4559,Vvar__2__n1__4561)
                            & cPLF_2eImp_2eaevalR__division_2eaevalR___24a2(Vvar__1__a2__4560,Vvar__3__n2__4562)
                            & Vvar__1___24Anonymous__4538 = c_24__case__Coq_2eInit_2eDatatypes_2enat_244839___24a4(Vvar__0___24Anonymous__4537,Vvar__1___24Anonymous__4538,Vvar__2__n1__4561,Vvar__3__n2__4562)
                            & Vvar__0___24Anonymous__4537 = cPLF_2eImp_2eaevalR__division_2eAMult___24a2(Vvar__0__a1__4559,Vvar__1__a2__4560) ) ) ) )
            | ? [Vvar__0__a1__4567] :
                ( cPLF_2eImp_2eaevalR__division_2eaexp___24t(Vvar__0__a1__4567)
                & ? [Vvar__1__a2__4568] :
                    ( cPLF_2eImp_2eaevalR__division_2eaexp___24t(Vvar__1__a2__4568)
                    & ? [Vvar__2__n1__4569] :
                        ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__2__n1__4569)
                        & ? [Vvar__3__n2__4570] :
                            ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__3__n2__4570)
                            & ? [Vvar__4__n3__4571] :
                                ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__4__n3__4571)
                                & cPLF_2eImp_2eaevalR__division_2eaevalR___24a2(Vvar__0__a1__4567,Vvar__2__n1__4569)
                                & cPLF_2eImp_2eaevalR__division_2eaevalR___24a2(Vvar__1__a2__4568,Vvar__3__n2__4570)
                                & cCoq_2eInit_2ePeano_2egt___24a2(Vvar__3__n2__4570,cCoq_2eInit_2eDatatypes_2eO)
                                & cCoq_2eInit_2eNat_2emul___24a2(Vvar__3__n2__4570,Vvar__4__n3__4571) = Vvar__2__n1__4569
                                & Vvar__1___24Anonymous__4538 = Vvar__4__n3__4571
                                & Vvar__0___24Anonymous__4537 = cPLF_2eImp_2eaevalR__division_2eADiv___24a2(Vvar__0__a1__4567,Vvar__1__a2__4568) ) ) ) ) ) ) ) ) ) ).

fof('$_inversion_PLF.Imp.aevalR_division.aexp',axiom,
    ! [VX4465] :
      ( cPLF_2eImp_2eaevalR__division_2eaexp___24t(VX4465)
     => ( ? [Vvar__0__n__4466] :
            ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0__n__4466)
            & VX4465 = cPLF_2eImp_2eaevalR__division_2eANum___24a1(Vvar__0__n__4466) )
        | ? [Vvar__0__a1__4467] :
            ( cPLF_2eImp_2eaevalR__division_2eaexp___24t(Vvar__0__a1__4467)
            & ? [Vvar__1__a2__4468] :
                ( cPLF_2eImp_2eaevalR__division_2eaexp___24t(Vvar__1__a2__4468)
                & VX4465 = cPLF_2eImp_2eaevalR__division_2eAPlus___24a2(Vvar__0__a1__4467,Vvar__1__a2__4468) ) )
        | ? [Vvar__0__a1__4469] :
            ( cPLF_2eImp_2eaevalR__division_2eaexp___24t(Vvar__0__a1__4469)
            & ? [Vvar__1__a2__4470] :
                ( cPLF_2eImp_2eaevalR__division_2eaexp___24t(Vvar__1__a2__4470)
                & VX4465 = cPLF_2eImp_2eaevalR__division_2eAMinus___24a2(Vvar__0__a1__4469,Vvar__1__a2__4470) ) )
        | ? [Vvar__0__a1__4471] :
            ( cPLF_2eImp_2eaevalR__division_2eaexp___24t(Vvar__0__a1__4471)
            & ? [Vvar__1__a2__4472] :
                ( cPLF_2eImp_2eaevalR__division_2eaexp___24t(Vvar__1__a2__4472)
                & VX4465 = cPLF_2eImp_2eaevalR__division_2eAMult___24a2(Vvar__0__a1__4471,Vvar__1__a2__4472) ) )
        | ? [Vvar__0__a1__4473] :
            ( cPLF_2eImp_2eaevalR__division_2eaexp___24t(Vvar__0__a1__4473)
            & ? [Vvar__1__a2__4474] :
                ( cPLF_2eImp_2eaevalR__division_2eaexp___24t(Vvar__1__a2__4474)
                & VX4465 = cPLF_2eImp_2eaevalR__division_2eADiv___24a2(Vvar__0__a1__4473,Vvar__1__a2__4474) ) ) ) ) ).

fof('$_inversion_PLF.Imp.aevalR_extended.aevalR',axiom,
    ! [Vvar__0___24Anonymous__83640,Vvar__1___24Anonymous__83641] :
      ( cPLF_2eImp_2eaevalR__extended_2eaexp___24t(Vvar__0___24Anonymous__83640)
     => ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__1___24Anonymous__83641)
       => ( cPLF_2eImp_2eaevalR__extended_2eaevalR___24a2(Vvar__0___24Anonymous__83640,Vvar__1___24Anonymous__83641)
         => ( ? [Vvar__0__n__83643] :
                ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0__n__83643)
                & Vvar__1___24Anonymous__83641 = Vvar__0__n__83643
                & Vvar__0___24Anonymous__83640 = cPLF_2eImp_2eaevalR__extended_2eAAny )
            | ? [Vvar__0__n__83644] :
                ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0__n__83644)
                & Vvar__1___24Anonymous__83641 = Vvar__0__n__83644
                & Vvar__0___24Anonymous__83640 = cPLF_2eImp_2eaevalR__extended_2eANum___24a1(Vvar__0__n__83644) )
            | ? [Vvar__0__a1__83645] :
                ( cPLF_2eImp_2eaevalR__extended_2eaexp___24t(Vvar__0__a1__83645)
                & ? [Vvar__1__a2__83646] :
                    ( cPLF_2eImp_2eaevalR__extended_2eaexp___24t(Vvar__1__a2__83646)
                    & ? [Vvar__2__n1__83647] :
                        ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__2__n1__83647)
                        & ? [Vvar__3__n2__83648] :
                            ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__3__n2__83648)
                            & cPLF_2eImp_2eaevalR__extended_2eaevalR___24a2(Vvar__0__a1__83645,Vvar__2__n1__83647)
                            & cPLF_2eImp_2eaevalR__extended_2eaevalR___24a2(Vvar__1__a2__83646,Vvar__3__n2__83648)
                            & Vvar__1___24Anonymous__83641 = c_24__case__Coq_2eInit_2eDatatypes_2enat_2483724___24a4(Vvar__0___24Anonymous__83640,Vvar__1___24Anonymous__83641,Vvar__2__n1__83647,Vvar__3__n2__83648)
                            & Vvar__0___24Anonymous__83640 = cPLF_2eImp_2eaevalR__extended_2eAPlus___24a2(Vvar__0__a1__83645,Vvar__1__a2__83646) ) ) ) )
            | ? [Vvar__0__a1__83653] :
                ( cPLF_2eImp_2eaevalR__extended_2eaexp___24t(Vvar__0__a1__83653)
                & ? [Vvar__1__a2__83654] :
                    ( cPLF_2eImp_2eaevalR__extended_2eaexp___24t(Vvar__1__a2__83654)
                    & ? [Vvar__2__n1__83655] :
                        ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__2__n1__83655)
                        & ? [Vvar__3__n2__83656] :
                            ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__3__n2__83656)
                            & cPLF_2eImp_2eaevalR__extended_2eaevalR___24a2(Vvar__0__a1__83653,Vvar__2__n1__83655)
                            & cPLF_2eImp_2eaevalR__extended_2eaevalR___24a2(Vvar__1__a2__83654,Vvar__3__n2__83656)
                            & Vvar__1___24Anonymous__83641 = c_24__case__Coq_2eInit_2eDatatypes_2enat_2483833___24a4(Vvar__0___24Anonymous__83640,Vvar__1___24Anonymous__83641,Vvar__2__n1__83655,Vvar__3__n2__83656)
                            & Vvar__0___24Anonymous__83640 = cPLF_2eImp_2eaevalR__extended_2eAMinus___24a2(Vvar__0__a1__83653,Vvar__1__a2__83654) ) ) ) )
            | ? [Vvar__0__a1__83663] :
                ( cPLF_2eImp_2eaevalR__extended_2eaexp___24t(Vvar__0__a1__83663)
                & ? [Vvar__1__a2__83664] :
                    ( cPLF_2eImp_2eaevalR__extended_2eaexp___24t(Vvar__1__a2__83664)
                    & ? [Vvar__2__n1__83665] :
                        ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__2__n1__83665)
                        & ? [Vvar__3__n2__83666] :
                            ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__3__n2__83666)
                            & cPLF_2eImp_2eaevalR__extended_2eaevalR___24a2(Vvar__0__a1__83663,Vvar__2__n1__83665)
                            & cPLF_2eImp_2eaevalR__extended_2eaevalR___24a2(Vvar__1__a2__83664,Vvar__3__n2__83666)
                            & Vvar__1___24Anonymous__83641 = c_24__case__Coq_2eInit_2eDatatypes_2enat_2483927___24a4(Vvar__0___24Anonymous__83640,Vvar__1___24Anonymous__83641,Vvar__2__n1__83665,Vvar__3__n2__83666)
                            & Vvar__0___24Anonymous__83640 = cPLF_2eImp_2eaevalR__extended_2eAMult___24a2(Vvar__0__a1__83663,Vvar__1__a2__83664) ) ) ) ) ) ) ) ) ).

fof('$_inversion_PLF.Imp.aevalR_extended.aexp',axiom,
    ! [VX83583] :
      ( cPLF_2eImp_2eaevalR__extended_2eaexp___24t(VX83583)
     => ( VX83583 = cPLF_2eImp_2eaevalR__extended_2eAAny
        | ? [Vvar__0__n__83584] :
            ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0__n__83584)
            & VX83583 = cPLF_2eImp_2eaevalR__extended_2eANum___24a1(Vvar__0__n__83584) )
        | ? [Vvar__0__a1__83585] :
            ( cPLF_2eImp_2eaevalR__extended_2eaexp___24t(Vvar__0__a1__83585)
            & ? [Vvar__1__a2__83586] :
                ( cPLF_2eImp_2eaevalR__extended_2eaexp___24t(Vvar__1__a2__83586)
                & VX83583 = cPLF_2eImp_2eaevalR__extended_2eAPlus___24a2(Vvar__0__a1__83585,Vvar__1__a2__83586) ) )
        | ? [Vvar__0__a1__83587] :
            ( cPLF_2eImp_2eaevalR__extended_2eaexp___24t(Vvar__0__a1__83587)
            & ? [Vvar__1__a2__83588] :
                ( cPLF_2eImp_2eaevalR__extended_2eaexp___24t(Vvar__1__a2__83588)
                & VX83583 = cPLF_2eImp_2eaevalR__extended_2eAMinus___24a2(Vvar__0__a1__83587,Vvar__1__a2__83588) ) )
        | ? [Vvar__0__a1__83589] :
            ( cPLF_2eImp_2eaevalR__extended_2eaexp___24t(Vvar__0__a1__83589)
            & ? [Vvar__1__a2__83590] :
                ( cPLF_2eImp_2eaevalR__extended_2eaexp___24t(Vvar__1__a2__83590)
                & VX83583 = cPLF_2eImp_2eaevalR__extended_2eAMult___24a2(Vvar__0__a1__83589,Vvar__1__a2__83590) ) ) ) ) ).

fof('$_inversion_PLF.Imp.aexp',axiom,
    ! [VX41] :
      ( cPLF_2eImp_2eaexp___24t(VX41)
     => ( ? [Vvar__0__n__42] :
            ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0__n__42)
            & VX41 = cPLF_2eImp_2eANum___24a1(Vvar__0__n__42) )
        | ? [Vvar__0__x__43] :
            ( cCoq_2eStrings_2eString_2estring___24t(Vvar__0__x__43)
            & VX41 = cPLF_2eImp_2eAId___24a1(Vvar__0__x__43) )
        | ? [Vvar__0__a1__44] :
            ( cPLF_2eImp_2eaexp___24t(Vvar__0__a1__44)
            & ? [Vvar__1__a2__45] :
                ( cPLF_2eImp_2eaexp___24t(Vvar__1__a2__45)
                & VX41 = cPLF_2eImp_2eAPlus___24a2(Vvar__0__a1__44,Vvar__1__a2__45) ) )
        | ? [Vvar__0__a1__46] :
            ( cPLF_2eImp_2eaexp___24t(Vvar__0__a1__46)
            & ? [Vvar__1__a2__47] :
                ( cPLF_2eImp_2eaexp___24t(Vvar__1__a2__47)
                & VX41 = cPLF_2eImp_2eAMinus___24a2(Vvar__0__a1__46,Vvar__1__a2__47) ) )
        | ? [Vvar__0__a1__48] :
            ( cPLF_2eImp_2eaexp___24t(Vvar__0__a1__48)
            & ? [Vvar__1__a2__49] :
                ( cPLF_2eImp_2eaexp___24t(Vvar__1__a2__49)
                & VX41 = cPLF_2eImp_2eAMult___24a2(Vvar__0__a1__48,Vvar__1__a2__49) ) ) ) ) ).

fof('$_inversion_PLF.Imp.bexp',axiom,
    ! [VX249] :
      ( cPLF_2eImp_2ebexp___24t(VX249)
     => ( VX249 = cPLF_2eImp_2eBTrue
        | VX249 = cPLF_2eImp_2eBFalse
        | ? [Vvar__0__a1__250] :
            ( cPLF_2eImp_2eaexp___24t(Vvar__0__a1__250)
            & ? [Vvar__1__a2__251] :
                ( cPLF_2eImp_2eaexp___24t(Vvar__1__a2__251)
                & VX249 = cPLF_2eImp_2eBEq___24a2(Vvar__0__a1__250,Vvar__1__a2__251) ) )
        | ? [Vvar__0__a1__252] :
            ( cPLF_2eImp_2eaexp___24t(Vvar__0__a1__252)
            & ? [Vvar__1__a2__253] :
                ( cPLF_2eImp_2eaexp___24t(Vvar__1__a2__253)
                & VX249 = cPLF_2eImp_2eBLe___24a2(Vvar__0__a1__252,Vvar__1__a2__253) ) )
        | ? [Vvar__0__b__254] :
            ( cPLF_2eImp_2ebexp___24t(Vvar__0__b__254)
            & VX249 = cPLF_2eImp_2eBNot___24a1(Vvar__0__b__254) )
        | ? [Vvar__0__b1__255] :
            ( cPLF_2eImp_2ebexp___24t(Vvar__0__b1__255)
            & ? [Vvar__1__b2__256] :
                ( cPLF_2eImp_2ebexp___24t(Vvar__1__b2__256)
                & VX249 = cPLF_2eImp_2eBAnd___24a2(Vvar__0__b1__255,Vvar__1__b2__256) ) ) ) ) ).

fof('$_inversion_PLF.Imp.ceval',axiom,
    ! [Vvar__0___24Anonymous__399,Vvar__1___24Anonymous__400,Vvar__2___24Anonymous__401] :
      ( cPLF_2eImp_2ecom___24t(Vvar__0___24Anonymous__399)
     => ( cPLF_2eImp_2estate___24t(Vvar__1___24Anonymous__400)
       => ( cPLF_2eImp_2estate___24t(Vvar__2___24Anonymous__401)
         => ( cPLF_2eImp_2eceval___24a3(Vvar__0___24Anonymous__399,Vvar__1___24Anonymous__400,Vvar__2___24Anonymous__401)
           => ( ? [Vvar__0__st__403] :
                  ( cPLF_2eImp_2estate___24t(Vvar__0__st__403)
                  & Vvar__2___24Anonymous__401 = Vvar__0__st__403
                  & Vvar__1___24Anonymous__400 = Vvar__0__st__403
                  & Vvar__0___24Anonymous__399 = cPLF_2eImp_2eCSkip )
              | ? [Vvar__0__st__404] :
                  ( cPLF_2eImp_2estate___24t(Vvar__0__st__404)
                  & ? [Vvar__1__a1__405] :
                      ( cPLF_2eImp_2eaexp___24t(Vvar__1__a1__405)
                      & ? [Vvar__2__n__406] :
                          ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__2__n__406)
                          & ? [Vvar__3__x__407] :
                              ( cCoq_2eStrings_2eString_2estring___24t(Vvar__3__x__407)
                              & cPLF_2eImp_2eaeval___24a2(Vvar__0__st__404,Vvar__1__a1__405) = Vvar__2__n__406
                              & Vvar__2___24Anonymous__401 = c_24__lam__457___24a6(Vvar__0___24Anonymous__399,Vvar__1___24Anonymous__400,Vvar__2___24Anonymous__401,Vvar__0__st__404,Vvar__2__n__406,Vvar__3__x__407)
                              & Vvar__1___24Anonymous__400 = Vvar__0__st__404
                              & Vvar__0___24Anonymous__399 = cPLF_2eImp_2eCAss___24a2(Vvar__3__x__407,Vvar__1__a1__405) ) ) ) )
              | ? [Vvar__0__c1__411] :
                  ( cPLF_2eImp_2ecom___24t(Vvar__0__c1__411)
                  & ? [Vvar__1__c2__412] :
                      ( cPLF_2eImp_2ecom___24t(Vvar__1__c2__412)
                      & ? [Vvar__2__st__413] :
                          ( cPLF_2eImp_2estate___24t(Vvar__2__st__413)
                          & ? [Vvar__3__st_27__414] :
                              ( cPLF_2eImp_2estate___24t(Vvar__3__st_27__414)
                              & ? [Vvar__4__st_27_27__415] :
                                  ( cPLF_2eImp_2estate___24t(Vvar__4__st_27_27__415)
                                  & cPLF_2eImp_2eceval___24a3(Vvar__0__c1__411,Vvar__2__st__413,Vvar__3__st_27__414)
                                  & cPLF_2eImp_2eceval___24a3(Vvar__1__c2__412,Vvar__3__st_27__414,Vvar__4__st_27_27__415)
                                  & Vvar__2___24Anonymous__401 = Vvar__4__st_27_27__415
                                  & Vvar__1___24Anonymous__400 = Vvar__2__st__413
                                  & Vvar__0___24Anonymous__399 = cPLF_2eImp_2eCSeq___24a2(Vvar__0__c1__411,Vvar__1__c2__412) ) ) ) ) )
              | ? [Vvar__0__st__418] :
                  ( cPLF_2eImp_2estate___24t(Vvar__0__st__418)
                  & ? [Vvar__1__st_27__419] :
                      ( cPLF_2eImp_2estate___24t(Vvar__1__st_27__419)
                      & ? [Vvar__2__b__420] :
                          ( cPLF_2eImp_2ebexp___24t(Vvar__2__b__420)
                          & ? [Vvar__3__c1__421] :
                              ( cPLF_2eImp_2ecom___24t(Vvar__3__c1__421)
                              & ? [Vvar__4__c2__422] :
                                  ( cPLF_2eImp_2ecom___24t(Vvar__4__c2__422)
                                  & cPLF_2eImp_2ebeval___24a2(Vvar__0__st__418,Vvar__2__b__420) = cCoq_2eInit_2eDatatypes_2etrue
                                  & cPLF_2eImp_2eceval___24a3(Vvar__3__c1__421,Vvar__0__st__418,Vvar__1__st_27__419)
                                  & Vvar__2___24Anonymous__401 = Vvar__1__st_27__419
                                  & Vvar__1___24Anonymous__400 = Vvar__0__st__418
                                  & Vvar__0___24Anonymous__399 = cPLF_2eImp_2eCIf___24a3(Vvar__2__b__420,Vvar__3__c1__421,Vvar__4__c2__422) ) ) ) ) )
              | ? [Vvar__0__st__425] :
                  ( cPLF_2eImp_2estate___24t(Vvar__0__st__425)
                  & ? [Vvar__1__st_27__426] :
                      ( cPLF_2eImp_2estate___24t(Vvar__1__st_27__426)
                      & ? [Vvar__2__b__427] :
                          ( cPLF_2eImp_2ebexp___24t(Vvar__2__b__427)
                          & ? [Vvar__3__c1__428] :
                              ( cPLF_2eImp_2ecom___24t(Vvar__3__c1__428)
                              & ? [Vvar__4__c2__429] :
                                  ( cPLF_2eImp_2ecom___24t(Vvar__4__c2__429)
                                  & cPLF_2eImp_2ebeval___24a2(Vvar__0__st__425,Vvar__2__b__427) = cCoq_2eInit_2eDatatypes_2efalse
                                  & cPLF_2eImp_2eceval___24a3(Vvar__4__c2__429,Vvar__0__st__425,Vvar__1__st_27__426)
                                  & Vvar__2___24Anonymous__401 = Vvar__1__st_27__426
                                  & Vvar__1___24Anonymous__400 = Vvar__0__st__425
                                  & Vvar__0___24Anonymous__399 = cPLF_2eImp_2eCIf___24a3(Vvar__2__b__427,Vvar__3__c1__428,Vvar__4__c2__429) ) ) ) ) )
              | ? [Vvar__0__b__432] :
                  ( cPLF_2eImp_2ebexp___24t(Vvar__0__b__432)
                  & ? [Vvar__1__st__433] :
                      ( cPLF_2eImp_2estate___24t(Vvar__1__st__433)
                      & ? [Vvar__2__c__434] :
                          ( cPLF_2eImp_2ecom___24t(Vvar__2__c__434)
                          & cPLF_2eImp_2ebeval___24a2(Vvar__1__st__433,Vvar__0__b__432) = cCoq_2eInit_2eDatatypes_2efalse
                          & Vvar__2___24Anonymous__401 = Vvar__1__st__433
                          & Vvar__1___24Anonymous__400 = Vvar__1__st__433
                          & Vvar__0___24Anonymous__399 = cPLF_2eImp_2eCWhile___24a2(Vvar__0__b__432,Vvar__2__c__434) ) ) )
              | ? [Vvar__0__st__436] :
                  ( cPLF_2eImp_2estate___24t(Vvar__0__st__436)
                  & ? [Vvar__1__st_27__437] :
                      ( cPLF_2eImp_2estate___24t(Vvar__1__st_27__437)
                      & ? [Vvar__2__st_27_27__438] :
                          ( cPLF_2eImp_2estate___24t(Vvar__2__st_27_27__438)
                          & ? [Vvar__3__b__439] :
                              ( cPLF_2eImp_2ebexp___24t(Vvar__3__b__439)
                              & ? [Vvar__4__c__440] :
                                  ( cPLF_2eImp_2ecom___24t(Vvar__4__c__440)
                                  & cPLF_2eImp_2ebeval___24a2(Vvar__0__st__436,Vvar__3__b__439) = cCoq_2eInit_2eDatatypes_2etrue
                                  & cPLF_2eImp_2eceval___24a3(Vvar__4__c__440,Vvar__0__st__436,Vvar__1__st_27__437)
                                  & cPLF_2eImp_2eceval___24a3(cPLF_2eImp_2eCWhile___24a2(Vvar__3__b__439,Vvar__4__c__440),Vvar__1__st_27__437,Vvar__2__st_27_27__438)
                                  & Vvar__2___24Anonymous__401 = Vvar__2__st_27_27__438
                                  & Vvar__1___24Anonymous__400 = Vvar__0__st__436
                                  & Vvar__0___24Anonymous__399 = cPLF_2eImp_2eCWhile___24a2(Vvar__3__b__439,Vvar__4__c__440) ) ) ) ) ) ) ) ) ) ) ).

fof('$_inversion_PLF.Imp.com',axiom,
    ! [VX115] :
      ( cPLF_2eImp_2ecom___24t(VX115)
     => ( VX115 = cPLF_2eImp_2eCSkip
        | ? [Vvar__0__x__116] :
            ( cCoq_2eStrings_2eString_2estring___24t(Vvar__0__x__116)
            & ? [Vvar__1__a__117] :
                ( cPLF_2eImp_2eaexp___24t(Vvar__1__a__117)
                & VX115 = cPLF_2eImp_2eCAss___24a2(Vvar__0__x__116,Vvar__1__a__117) ) )
        | ? [Vvar__0__c1__118] :
            ( cPLF_2eImp_2ecom___24t(Vvar__0__c1__118)
            & ? [Vvar__1__c2__119] :
                ( cPLF_2eImp_2ecom___24t(Vvar__1__c2__119)
                & VX115 = cPLF_2eImp_2eCSeq___24a2(Vvar__0__c1__118,Vvar__1__c2__119) ) )
        | ? [Vvar__0__b__120] :
            ( cPLF_2eImp_2ebexp___24t(Vvar__0__b__120)
            & ? [Vvar__1__c1__121] :
                ( cPLF_2eImp_2ecom___24t(Vvar__1__c1__121)
                & ? [Vvar__2__c2__122] :
                    ( cPLF_2eImp_2ecom___24t(Vvar__2__c2__122)
                    & VX115 = cPLF_2eImp_2eCIf___24a3(Vvar__0__b__120,Vvar__1__c1__121,Vvar__2__c2__122) ) ) )
        | ? [Vvar__0__b__123] :
            ( cPLF_2eImp_2ebexp___24t(Vvar__0__b__123)
            & ? [Vvar__1__c__124] :
                ( cPLF_2eImp_2ecom___24t(Vvar__1__c__124)
                & VX115 = cPLF_2eImp_2eCWhile___24a2(Vvar__0__b__123,Vvar__1__c__124) ) ) ) ) ).

fof('$_inversion_PLF.Imp.sinstr',axiom,
    ! [VX653] :
      ( cPLF_2eImp_2esinstr___24t(VX653)
     => ( ? [Vvar__0__n__654] :
            ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0__n__654)
            & VX653 = cPLF_2eImp_2eSPush___24a1(Vvar__0__n__654) )
        | ? [Vvar__0__x__655] :
            ( cCoq_2eStrings_2eString_2estring___24t(Vvar__0__x__655)
            & VX653 = cPLF_2eImp_2eSLoad___24a1(Vvar__0__x__655) )
        | VX653 = cPLF_2eImp_2eSPlus
        | VX653 = cPLF_2eImp_2eSMinus
        | VX653 = cPLF_2eImp_2eSMult ) ) ).

fof('$_lam_146985',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] : c_24__lam__146985___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = happ(Vv__CANONICAL__2,Vv__CANONICAL__3) ).

fof('$_lam_146993',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] : c_24__lam__146993___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = happ(Vv__CANONICAL__2,Vv__CANONICAL__3) ).

fof('$_lam_1487',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6] :
      ( cCoq_2eStrings_2eString_2estring___24t(Vv__CANONICAL__5)
     => ( cCoq_2eStrings_2eString_2estring___24t(Vv__CANONICAL__6)
       => ( ( cPLF_2eMaps_2eeqb__string___24a2(Vv__CANONICAL__5,Vv__CANONICAL__6) = cCoq_2eInit_2eDatatypes_2etrue
            & c_24__lam__1487___24a7(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6) = Vv__CANONICAL__4 )
          | ( cPLF_2eMaps_2eeqb__string___24a2(Vv__CANONICAL__5,Vv__CANONICAL__6) = cCoq_2eInit_2eDatatypes_2efalse
            & c_24__lam__1487___24a7(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6) = happ(Vv__CANONICAL__3,Vv__CANONICAL__6) ) ) ) ) ).

fof('$_lam_152854',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1] : c_24__lam__152854___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = Vv__CANONICAL__0 ).

fof('$_lam_155201',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] :
      ( c_24__lam__155201___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_155209',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] :
      ( c_24__lam__155209___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_155217',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] :
      ( c_24__lam__155217___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_155225',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] :
      ( c_24__lam__155225___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_1717',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6] :
      ( cCoq_2eStrings_2eString_2estring___24t(Vv__CANONICAL__5)
     => ( cCoq_2eStrings_2eString_2estring___24t(Vv__CANONICAL__6)
       => ( ( cPLF_2eMaps_2eeqb__string___24a2(Vv__CANONICAL__5,Vv__CANONICAL__6) = cCoq_2eInit_2eDatatypes_2etrue
            & c_24__lam__1717___24a7(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6) = Vv__CANONICAL__4 )
          | ( cPLF_2eMaps_2eeqb__string___24a2(Vv__CANONICAL__5,Vv__CANONICAL__6) = cCoq_2eInit_2eDatatypes_2efalse
            & c_24__lam__1717___24a7(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6) = happ(Vv__CANONICAL__3,Vv__CANONICAL__6) ) ) ) ) ).

fof('$_lam_457',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6] :
      ( cCoq_2eStrings_2eString_2estring___24t(Vv__CANONICAL__5)
     => ( cCoq_2eStrings_2eString_2estring___24t(Vv__CANONICAL__6)
       => ( ( cPLF_2eMaps_2eeqb__string___24a2(Vv__CANONICAL__5,Vv__CANONICAL__6) = cCoq_2eInit_2eDatatypes_2etrue
            & c_24__lam__457___24a7(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6) = Vv__CANONICAL__4 )
          | ( cPLF_2eMaps_2eeqb__string___24a2(Vv__CANONICAL__5,Vv__CANONICAL__6) = cCoq_2eInit_2eDatatypes_2efalse
            & c_24__lam__457___24a7(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6) = happ(Vv__CANONICAL__3,Vv__CANONICAL__6) ) ) ) ) ).

fof('$_lam_7029',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1] : c_24__lam__7029___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = Vv__CANONICAL__0 ).

fof('$_lam_83190',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__83190___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = cCoq_2eInit_2eDatatypes_2etrue )
        | ? [Vvar__0___24Anonymous__83191] :
            ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__83191)
            & Vv__CANONICAL__1 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__83191)
            & c_24__lam__83190___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = cCoq_2ePArith_2eBinPosDef_2ePos_2etestbit__nat___24a2(Vv__CANONICAL__0,Vvar__0___24Anonymous__83191) ) ) ) ).

fof('$_lam_83197',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__83197___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = cCoq_2eInit_2eDatatypes_2efalse )
        | ? [Vvar__0___24Anonymous__83198] :
            ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__83198)
            & Vv__CANONICAL__1 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__83198)
            & c_24__lam__83197___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = cCoq_2ePArith_2eBinPosDef_2ePos_2etestbit__nat___24a2(Vv__CANONICAL__0,Vvar__0___24Anonymous__83198) ) ) ) ).

fof('$_lam_83201',axiom,
    ! [Vv__CANONICAL__0] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
     => ( ( Vv__CANONICAL__0 = cCoq_2eInit_2eDatatypes_2eO
          & c_24__lam__83201___24a1(Vv__CANONICAL__0) = cCoq_2eInit_2eDatatypes_2etrue )
        | ? [Vvar__0___24Anonymous__83202] :
            ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__83202)
            & Vv__CANONICAL__0 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__83202)
            & c_24__lam__83201___24a1(Vv__CANONICAL__0) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ).

fof('$_lam_943',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6] :
      ( cCoq_2eStrings_2eString_2estring___24t(Vv__CANONICAL__5)
     => ( cCoq_2eStrings_2eString_2estring___24t(Vv__CANONICAL__6)
       => ( ( cPLF_2eMaps_2eeqb__string___24a2(Vv__CANONICAL__5,Vv__CANONICAL__6) = cCoq_2eInit_2eDatatypes_2etrue
            & c_24__lam__943___24a7(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6) = Vv__CANONICAL__4 )
          | ( cPLF_2eMaps_2eeqb__string___24a2(Vv__CANONICAL__5,Vv__CANONICAL__6) = cCoq_2eInit_2eDatatypes_2efalse
            & c_24__lam__943___24a7(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6) = happ(Vv__CANONICAL__3,Vv__CANONICAL__6) ) ) ) ) ).

fof('$_lam_957',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6] :
      ( cCoq_2eStrings_2eString_2estring___24t(Vv__CANONICAL__4)
     => ( cCoq_2eStrings_2eString_2estring___24t(Vv__CANONICAL__6)
       => ( ( cPLF_2eMaps_2eeqb__string___24a2(Vv__CANONICAL__4,Vv__CANONICAL__6) = cCoq_2eInit_2eDatatypes_2etrue
            & c_24__lam__957___24a7(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6) = Vv__CANONICAL__5 )
          | ( cPLF_2eMaps_2eeqb__string___24a2(Vv__CANONICAL__4,Vv__CANONICAL__6) = cCoq_2eInit_2eDatatypes_2efalse
            & c_24__lam__957___24a7(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6) = happ(Vv__CANONICAL__3,Vv__CANONICAL__6) ) ) ) ) ).

fof('$_prop_149915',axiom,
    ! [Vvar__0___24Anonymous__149891,Vvar__0__S__149893,Vvar__1__x__149894,Vvar__2__y__149895] :
      ( p(c_24__prop__149915___24a4(Vvar__0___24Anonymous__149891,Vvar__0__S__149893,Vvar__1__x__149894,Vvar__2__y__149895))
    <=> Vvar__1__x__149894 = Vvar__2__y__149895 ) ).

fof('$_prop_149916',axiom,
    ! [Vvar__0___24Anonymous__149891,Vvar__0__x__149896,Vvar__1__y__149897] :
      ( p(c_24__prop__149916___24a3(Vvar__0___24Anonymous__149891,Vvar__0__x__149896,Vvar__1__y__149897))
    <=> Vvar__0__x__149896 = Vvar__1__y__149897 ) ).

fof('$_prop_149917',axiom,
    ! [Vvar__0___24Anonymous__149891,Vvar__0__x__149898,Vvar__1__s__149899] :
      ( p(c_24__prop__149917___24a3(Vvar__0___24Anonymous__149891,Vvar__0__x__149898,Vvar__1__s__149899))
    <=> cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2emem___24a2(Vvar__0__x__149898,Vvar__1__s__149899) = cCoq_2eInit_2eDatatypes_2etrue ) ).

fof('$_prop_149918',axiom,
    ! [Vvar__0___24Anonymous__149891,Vvar__0__P__149900,Vvar__1__Q__149901] :
      ( p(c_24__prop__149918___24a3(Vvar__0___24Anonymous__149891,Vvar__0__P__149900,Vvar__1__Q__149901))
    <=> ( p(Vvar__0__P__149900)
        & p(Vvar__1__Q__149901) ) ) ).

fof('$_prop_149919',axiom,
    ! [Vvar__0___24Anonymous__149891,Vvar__0__P__149904,Vvar__1__Q__149905] :
      ( p(c_24__prop__149919___24a3(Vvar__0___24Anonymous__149891,Vvar__0__P__149904,Vvar__1__Q__149905))
    <=> ( p(Vvar__0__P__149904)
        | p(Vvar__1__Q__149905) ) ) ).

fof('$_prop_149920',axiom,
    ! [Vvar__0___24Anonymous__149891,Vvar__0__P__149908,Vvar__1__Q__149909] :
      ( p(c_24__prop__149920___24a3(Vvar__0___24Anonymous__149891,Vvar__0__P__149908,Vvar__1__Q__149909))
    <=> ( p(Vvar__0__P__149908)
       => p(Vvar__1__Q__149909) ) ) ).

fof('$_prop_149921',axiom,
    ! [Vvar__0___24Anonymous__149891,Vvar__0__P__149913] :
      ( p(c_24__prop__149921___24a2(Vvar__0___24Anonymous__149891,Vvar__0__P__149913))
    <=> ~ p(Vvar__0__P__149913) ) ).

fof('$_prop_149935',axiom,
    ! [Vvar__0___24Anonymous__149922,Vvar__0__s__149926] :
      ( p(c_24__prop__149935___24a2(Vvar__0___24Anonymous__149922,Vvar__0__s__149926))
    <=> ! [Vvar__1__a__149927] :
          ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(Vvar__1__a__149927)
         => ~ cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eIn___24a2(Vvar__1__a__149927,Vvar__0__s__149926) ) ) ).

fof('$_prop_149936',axiom,
    ! [Vvar__0___24Anonymous__149922,Vvar__0__s1__149928,Vvar__1__s2__149929] :
      ( p(c_24__prop__149936___24a3(Vvar__0___24Anonymous__149922,Vvar__0__s1__149928,Vvar__1__s2__149929))
    <=> ! [Vvar__2__a__149930] :
          ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(Vvar__2__a__149930)
         => ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eIn___24a2(Vvar__2__a__149930,Vvar__0__s1__149928)
           => cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eIn___24a2(Vvar__2__a__149930,Vvar__1__s2__149929) ) ) ) ).

fof('$_prop_149937',axiom,
    ! [Vvar__0___24Anonymous__149922,Vvar__0__s1__149932,Vvar__1__s2__149933] :
      ( p(c_24__prop__149937___24a3(Vvar__0___24Anonymous__149922,Vvar__0__s1__149932,Vvar__1__s2__149933))
    <=> ! [Vvar__2__a__149934] :
          ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(Vvar__2__a__149934)
         => ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eIn___24a2(Vvar__2__a__149934,Vvar__0__s1__149932)
          <=> cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eIn___24a2(Vvar__2__a__149934,Vvar__1__s2__149933) ) ) ) ).

fof('$_prop_152873',axiom,
    ! [V0__n,V1__m] :
      ( p(c_24__prop__152873___24a2(V0__n,V1__m))
    <=> V0__n = V1__m ) ).

fof('$_type_1115',axiom,
    ! [Vvar__1116] :
      ( c_24__type__1115___24t(Vvar__1116)
    <=> ! [Vv__CANONICAL__0] :
          ( cPLF_2eHoare_2eHoareAssertAssume_2ecom___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cPLF_2eHoare_2eHoareAssertAssume_2ecom___24t(Vv__CANONICAL__1)
             => cPLF_2eHoare_2eHoareAssertAssume_2ecom___24t(happ(happ(Vvar__1116,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_1120',axiom,
    ! [Vvar__1121] :
      ( c_24__type__1120___24t(Vvar__1121)
    <=> ! [Vv__CANONICAL__0] :
          ( cPLF_2eImp_2ebexp___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cPLF_2eHoare_2eHoareAssertAssume_2ecom___24t(Vv__CANONICAL__1)
             => ! [Vv__CANONICAL__2] :
                  ( cPLF_2eHoare_2eHoareAssertAssume_2ecom___24t(Vv__CANONICAL__2)
                 => cPLF_2eHoare_2eHoareAssertAssume_2ecom___24t(happ(happ(happ(Vvar__1121,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).

fof('$_type_1123',axiom,
    ! [Vvar__1124] :
      ( c_24__type__1123___24t(Vvar__1124)
    <=> ! [Vv__CANONICAL__0] :
          ( cPLF_2eImp_2ebexp___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cPLF_2eHoare_2eHoareAssertAssume_2ecom___24t(Vv__CANONICAL__1)
             => cPLF_2eHoare_2eHoareAssertAssume_2ecom___24t(happ(happ(Vvar__1124,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_1125',axiom,
    ! [Vvar__1126] :
      ( c_24__type__1125___24t(Vvar__1126)
    <=> ! [Vv__CANONICAL__0] :
          ( cPLF_2eImp_2ebexp___24t(Vv__CANONICAL__0)
         => cPLF_2eHoare_2eHoareAssertAssume_2ecom___24t(happ(Vvar__1126,Vv__CANONICAL__0)) ) ) ).

fof('$_type_1132',axiom,
    ! [Vvar__1133] :
      ( c_24__type__1132___24t(Vvar__1133)
    <=> ! [Vv__CANONICAL__0] :
          ( cPLF_2eImp_2estate___24t(Vv__CANONICAL__0)
         => cPLF_2eHoare_2eHoareAssertAssume_2eresult___24t(happ(Vvar__1133,Vv__CANONICAL__0)) ) ) ).

fof('$_type_119461',axiom,
    ! [Vvar__119462] :
      ( c_24__type__119461___24t(Vvar__119462)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eInit_2eDecimal_2eint___24t(Vv__CANONICAL__0)
         => cCoq_2eInit_2eDecimal_2eint___24t(happ(Vvar__119462,Vv__CANONICAL__0)) ) ) ).

fof('$_type_121772',axiom,
    ! [Vvar__121773] :
      ( c_24__type__121772___24t(Vvar__121773)
    <=> ! [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__3514___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
                     => ! [Vv__CANONICAL__4] :
                          ( c_24__type__3514___24t(Vv__CANONICAL__0,Vv__CANONICAL__4)
                         => ! [Vv__CANONICAL__5] :
                              ( c_24__type__3523___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__121773,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_121957',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__121958] :
      ( c_24__type__121957___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__121958)
    <=> ! [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__121958,Vv__CANONICAL__5),Vv__CANONICAL__6)) ) ) ) ).

fof('$_type_121976',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__121977] :
      ( c_24__type__121976___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__121977)
    <=> ! [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__121977,Vv__CANONICAL__5),Vv__CANONICAL__6)) ) ) ) ).

fof('$_type_121996',axiom,
    ! [Vvar__121997] :
      ( c_24__type__121996___24t(Vvar__121997)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( c_24__type__2863___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
             => ! [Vv__CANONICAL__2] :
                  ( c_24__type__2863___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__121997,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ) ) ) ).

fof('$_type_122332',axiom,
    ! [Vvar__122333] :
      ( c_24__type__122332___24t(Vvar__122333)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eQArith_2eQArith__base_2eQ___24t(Vv__CANONICAL__0)
         => cCoq_2emicromega_2eRMicromega_2eRcst___24t(happ(Vvar__122333,Vv__CANONICAL__0)) ) ) ).

fof('$_type_122334',axiom,
    ! [Vvar__122335] :
      ( c_24__type__122334___24t(Vvar__122335)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
         => cCoq_2emicromega_2eRMicromega_2eRcst___24t(happ(Vvar__122335,Vv__CANONICAL__0)) ) ) ).

fof('$_type_122337',axiom,
    ! [Vvar__122338] :
      ( c_24__type__122337___24t(Vvar__122338)
    <=> ! [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__122338,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_122344',axiom,
    ! [Vvar__122345] :
      ( c_24__type__122344___24t(Vvar__122345)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2emicromega_2eRMicromega_2eRcst___24t(Vv__CANONICAL__0)
         => cCoq_2emicromega_2eRMicromega_2eRcst___24t(happ(Vvar__122345,Vv__CANONICAL__0)) ) ) ).

fof('$_type_123915',axiom,
    ! [Vvar__123916] :
      ( c_24__type__123915___24t(Vvar__123916)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__0)
         => cCoq_2eInit_2eDatatypes_2ebool___24t(happ(Vvar__123916,Vv__CANONICAL__0)) ) ) ).

fof('$_type_124022',axiom,
    ! [Vvar__124023] :
      ( c_24__type__124022___24t(Vvar__124023)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eInit_2eDecimal_2euint___24t(Vv__CANONICAL__0)
         => cCoq_2eInit_2eDecimal_2euint___24t(happ(Vvar__124023,Vv__CANONICAL__0)) ) ) ).

fof('$_type_124024',axiom,
    ! [Vvar__124025] :
      ( c_24__type__124024___24t(Vvar__124025)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eInit_2eDecimal_2euint___24t(Vv__CANONICAL__0)
         => cCoq_2eInit_2eDecimal_2eint___24t(happ(Vvar__124025,Vv__CANONICAL__0)) ) ) ).

fof('$_type_124053',axiom,
    ! [Vv__CANONICAL__0,Vvar__124054] :
      ( c_24__type__124053___24t(Vv__CANONICAL__0,Vvar__124054)
    <=> ! [Vv__CANONICAL__1] :
          ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__1)
         => t(happ(Vvar__124054,Vv__CANONICAL__1),Vv__CANONICAL__0) ) ) ).

fof('$_type_124267',axiom,
    ! [Vvar__124268] :
      ( c_24__type__124267___24t(Vvar__124268)
    <=> ! [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__124268,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_124484',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,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__124485] :
      ( c_24__type__124484___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,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__124485)
    <=> ! [Vv__CANONICAL__10] :
          ( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__11] :
              ( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
             => t(happ(happ(Vvar__124485,Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_124577',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,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__124578] :
      ( c_24__type__124577___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,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__124578)
    <=> ! [Vv__CANONICAL__10] :
          ( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__11] :
              ( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
             => t(happ(happ(Vvar__124578,Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_124670',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,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__124671] :
      ( c_24__type__124670___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,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__124671)
    <=> ! [Vv__CANONICAL__10] :
          ( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__11] :
              ( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
             => t(happ(happ(Vvar__124671,Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_124752',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,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__124753] :
      ( c_24__type__124752___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,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__124753)
    <=> ! [Vv__CANONICAL__10] :
          ( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
         => t(happ(Vvar__124753,Vv__CANONICAL__10),Vv__CANONICAL__0) ) ) ).

fof('$_type_124845',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,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__124846] :
      ( c_24__type__124845___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,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__124846)
    <=> ! [Vv__CANONICAL__10] :
          ( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__11] :
              ( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
             => t(happ(happ(Vvar__124846,Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_124927',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,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__124928] :
      ( c_24__type__124927___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,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__124928)
    <=> ! [Vv__CANONICAL__10] :
          ( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
         => t(happ(Vvar__124928,Vv__CANONICAL__10),Vv__CANONICAL__0) ) ) ).

fof('$_type_125020',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,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__125021] :
      ( c_24__type__125020___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,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__125021)
    <=> ! [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__125021,Vv__CANONICAL__10),Vv__CANONICAL__11)) ) ) ) ).

fof('$_type_125073',axiom,
    ! [Vvar__125074] :
      ( c_24__type__125073___24t(Vvar__125074)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cType___24t(Vv__CANONICAL__1)
             => ! [Vv__CANONICAL__2] :
                  ( c_24__type__125080___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__125074,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__0) ) ) ) ) ) ) ).

fof('$_type_125080',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__125081] :
      ( c_24__type__125080___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__125081)
    <=> ! [Vv__CANONICAL__2] :
          ( t(Vv__CANONICAL__2,Vv__CANONICAL__1)
         => ! [Vv__CANONICAL__3] :
              ( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
             => t(happ(happ(Vvar__125081,Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_125581',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,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__125582] :
      ( c_24__type__125581___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,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__125582)
    <=> ! [Vv__CANONICAL__10] :
          ( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__11] :
              ( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
             => t(happ(happ(Vvar__125582,Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_125682',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,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__125683] :
      ( c_24__type__125682___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,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__125683)
    <=> ! [Vv__CANONICAL__10] :
          ( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__11] :
              ( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
             => t(happ(happ(Vvar__125683,Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_125783',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,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__125784] :
      ( c_24__type__125783___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,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__125784)
    <=> ! [Vv__CANONICAL__10] :
          ( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__11] :
              ( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
             => t(happ(happ(Vvar__125784,Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_125873',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,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__125874] :
      ( c_24__type__125873___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,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__125874)
    <=> ! [Vv__CANONICAL__10] :
          ( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
         => t(happ(Vvar__125874,Vv__CANONICAL__10),Vv__CANONICAL__0) ) ) ).

fof('$_type_125974',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,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__125975] :
      ( c_24__type__125974___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,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__125975)
    <=> ! [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__125975,Vv__CANONICAL__10),Vv__CANONICAL__11)) ) ) ) ).

fof('$_type_126075',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,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__126076] :
      ( c_24__type__126075___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,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__126076)
    <=> ! [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__126076,Vv__CANONICAL__10),Vv__CANONICAL__11)) ) ) ) ).

fof('$_type_126176',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,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__126177] :
      ( c_24__type__126176___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,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__126177)
    <=> ! [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__126177,Vv__CANONICAL__10),Vv__CANONICAL__11)) ) ) ) ).

fof('$_type_126232',axiom,
    ! [Vvar__126233] :
      ( c_24__type__126232___24t(Vvar__126233)
    <=> ! [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__126233,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_126237',axiom,
    ! [Vvar__126238] :
      ( c_24__type__126237___24t(Vvar__126238)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eQArith_2eQArith__base_2eQ___24t(Vv__CANONICAL__0)
         => cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(Vvar__126238,Vv__CANONICAL__0)) ) ) ).

fof('$_type_126242',axiom,
    ! [Vvar__126243] :
      ( c_24__type__126242___24t(Vvar__126243)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eQArith_2eQArith__base_2eQ___24t(Vv__CANONICAL__0)
         => cCoq_2eNumbers_2eBinNums_2epositive___24t(happ(Vvar__126243,Vv__CANONICAL__0)) ) ) ).

fof('$_type_126244',axiom,
    ! [Vvar__126245] :
      ( c_24__type__126244___24t(Vvar__126245)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__0)
         => cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(Vvar__126245,Vv__CANONICAL__0)) ) ) ).

fof('$_type_126302',axiom,
    ! [Vvar__126303] :
      ( c_24__type__126302___24t(Vvar__126303)
    <=> ! [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__126303,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_126871',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,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__126872] :
      ( c_24__type__126871___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,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__126872)
    <=> ! [Vv__CANONICAL__22] :
          ( t(Vv__CANONICAL__22,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__23] :
              ( t(Vv__CANONICAL__23,Vv__CANONICAL__0)
             => t(happ(happ(Vvar__126872,Vv__CANONICAL__22),Vv__CANONICAL__23),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_127217',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,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__127218] :
      ( c_24__type__127217___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,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__127218)
    <=> ! [Vv__CANONICAL__22] :
          ( t(Vv__CANONICAL__22,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__23] :
              ( t(Vv__CANONICAL__23,Vv__CANONICAL__0)
             => t(happ(happ(Vvar__127218,Vv__CANONICAL__22),Vv__CANONICAL__23),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_127563',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,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__127564] :
      ( c_24__type__127563___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,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__127564)
    <=> ! [Vv__CANONICAL__22] :
          ( t(Vv__CANONICAL__22,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__23] :
              ( t(Vv__CANONICAL__23,Vv__CANONICAL__0)
             => t(happ(happ(Vvar__127564,Vv__CANONICAL__22),Vv__CANONICAL__23),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_127886',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,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__127887] :
      ( c_24__type__127886___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,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__127887)
    <=> ! [Vv__CANONICAL__22] :
          ( t(Vv__CANONICAL__22,Vv__CANONICAL__0)
         => t(happ(Vvar__127887,Vv__CANONICAL__22),Vv__CANONICAL__0) ) ) ).

fof('$_type_128232',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,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__128233] :
      ( c_24__type__128232___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,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__128233)
    <=> ! [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__128233,Vv__CANONICAL__22),Vv__CANONICAL__23)) ) ) ) ).

fof('$_type_128578',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,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__128579] :
      ( c_24__type__128578___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,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__128579)
    <=> ! [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__128579,Vv__CANONICAL__22),Vv__CANONICAL__23)) ) ) ) ).

fof('$_type_128924',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,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__128925] :
      ( c_24__type__128924___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,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__128925)
    <=> ! [Vv__CANONICAL__22] :
          ( t(Vv__CANONICAL__22,Vv__CANONICAL__9)
         => ! [Vv__CANONICAL__23] :
              ( t(Vv__CANONICAL__23,Vv__CANONICAL__9)
             => t(happ(happ(Vvar__128925,Vv__CANONICAL__22),Vv__CANONICAL__23),Vv__CANONICAL__9) ) ) ) ).

fof('$_type_129270',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,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__129271] :
      ( c_24__type__129270___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,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__129271)
    <=> ! [Vv__CANONICAL__22] :
          ( t(Vv__CANONICAL__22,Vv__CANONICAL__9)
         => ! [Vv__CANONICAL__23] :
              ( t(Vv__CANONICAL__23,Vv__CANONICAL__9)
             => t(happ(happ(Vvar__129271,Vv__CANONICAL__22),Vv__CANONICAL__23),Vv__CANONICAL__9) ) ) ) ).

fof('$_type_129616',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,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__129617] :
      ( c_24__type__129616___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,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__129617)
    <=> ! [Vv__CANONICAL__22] :
          ( t(Vv__CANONICAL__22,Vv__CANONICAL__9)
         => ! [Vv__CANONICAL__23] :
              ( t(Vv__CANONICAL__23,Vv__CANONICAL__9)
             => t(happ(happ(Vvar__129617,Vv__CANONICAL__22),Vv__CANONICAL__23),Vv__CANONICAL__9) ) ) ) ).

fof('$_type_129939',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,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__129940] :
      ( c_24__type__129939___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,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__129940)
    <=> ! [Vv__CANONICAL__22] :
          ( t(Vv__CANONICAL__22,Vv__CANONICAL__9)
         => t(happ(Vvar__129940,Vv__CANONICAL__22),Vv__CANONICAL__9) ) ) ).

fof('$_type_130285',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,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__130286] :
      ( c_24__type__130285___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,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__130286)
    <=> ! [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__130286,Vv__CANONICAL__22),Vv__CANONICAL__23)) ) ) ) ).

fof('$_type_130631',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,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__130632] :
      ( c_24__type__130631___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,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__130632)
    <=> ! [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__130632,Vv__CANONICAL__22),Vv__CANONICAL__23)) ) ) ) ).

fof('$_type_130954',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,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__130955] :
      ( c_24__type__130954___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,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__130955)
    <=> ! [Vv__CANONICAL__22] :
          ( t(Vv__CANONICAL__22,Vv__CANONICAL__9)
         => t(happ(Vvar__130955,Vv__CANONICAL__22),Vv__CANONICAL__0) ) ) ).

fof('$_type_131277',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,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__131278] :
      ( c_24__type__131277___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,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__131278)
    <=> ! [Vv__CANONICAL__22] :
          ( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__22)
         => t(happ(Vvar__131278,Vv__CANONICAL__22),Vv__CANONICAL__19) ) ) ).

fof('$_type_131623',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,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__131624] :
      ( c_24__type__131623___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,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__131624)
    <=> ! [Vv__CANONICAL__22] :
          ( t(Vv__CANONICAL__22,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__23] :
              ( t(Vv__CANONICAL__23,Vv__CANONICAL__19)
             => t(happ(happ(Vvar__131624,Vv__CANONICAL__22),Vv__CANONICAL__23),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_131823',axiom,
    ! [Vvar__131824] :
      ( c_24__type__131823___24t(Vvar__131824)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( c_24__type__3514___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__131824,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__0) ) ) ) ) ) ).

fof('$_type_132077',axiom,
    ! [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__132078] :
      ( c_24__type__132077___24t(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__132078)
    <=> ! [Vv__CANONICAL__8] :
          ( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__9] :
              ( t(Vv__CANONICAL__9,Vv__CANONICAL__0)
             => t(happ(happ(Vvar__132078,Vv__CANONICAL__8),Vv__CANONICAL__9),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_132140',axiom,
    ! [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__132141] :
      ( c_24__type__132140___24t(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__132141)
    <=> ! [Vv__CANONICAL__8] :
          ( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__9] :
              ( t(Vv__CANONICAL__9,Vv__CANONICAL__0)
             => t(happ(happ(Vvar__132141,Vv__CANONICAL__8),Vv__CANONICAL__9),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_132203',axiom,
    ! [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__132204] :
      ( c_24__type__132203___24t(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__132204)
    <=> ! [Vv__CANONICAL__8] :
          ( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__9] :
              ( t(Vv__CANONICAL__9,Vv__CANONICAL__0)
             => t(happ(happ(Vvar__132204,Vv__CANONICAL__8),Vv__CANONICAL__9),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_132257',axiom,
    ! [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__132258] :
      ( c_24__type__132257___24t(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__132258)
    <=> ! [Vv__CANONICAL__8] :
          ( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
         => t(happ(Vvar__132258,Vv__CANONICAL__8),Vv__CANONICAL__0) ) ) ).

fof('$_type_132320',axiom,
    ! [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__132321] :
      ( c_24__type__132320___24t(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__132321)
    <=> ! [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__132321,Vv__CANONICAL__8),Vv__CANONICAL__9)) ) ) ) ).

fof('$_type_132430',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__132431] :
      ( c_24__type__132430___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__132431)
    <=> ! [Vv__CANONICAL__4] :
          ( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__5] :
              ( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
             => t(happ(happ(Vvar__132431,Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_132453',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__132454] :
      ( c_24__type__132453___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__132454)
    <=> ! [Vv__CANONICAL__4] :
          ( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__5] :
              ( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
             => t(happ(happ(Vvar__132454,Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_132476',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__132477] :
      ( c_24__type__132476___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__132477)
    <=> ! [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__132477,Vv__CANONICAL__4),Vv__CANONICAL__5)) ) ) ) ).

fof('$_type_132499',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__132500] :
      ( c_24__type__132499___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__132500)
    <=> ! [Vv__CANONICAL__4] :
          ( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__5] :
              ( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
             => t(happ(happ(Vvar__132500,Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_132517',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__132518] :
      ( c_24__type__132517___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__132518)
    <=> ! [Vv__CANONICAL__4] :
          ( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
         => t(happ(Vvar__132518,Vv__CANONICAL__4),Vv__CANONICAL__0) ) ) ).

fof('$_type_132543',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__132544] :
      ( c_24__type__132543___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__132544)
    <=> ! [Vv__CANONICAL__4] :
          ( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__5] :
              ( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
             => t(happ(happ(Vvar__132544,Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_132561',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__132562] :
      ( c_24__type__132561___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__132562)
    <=> ! [Vv__CANONICAL__4] :
          ( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
         => t(happ(Vvar__132562,Vv__CANONICAL__4),Vv__CANONICAL__0) ) ) ).

fof('$_type_132671',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__132672] :
      ( c_24__type__132671___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__132672)
    <=> ! [Vv__CANONICAL__5] :
          ( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__6] :
              ( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
             => t(happ(happ(Vvar__132672,Vv__CANONICAL__5),Vv__CANONICAL__6),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_132701',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__132702] :
      ( c_24__type__132701___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__132702)
    <=> ! [Vv__CANONICAL__5] :
          ( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__6] :
              ( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
             => t(happ(happ(Vvar__132702,Vv__CANONICAL__5),Vv__CANONICAL__6),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_132725',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__132726] :
      ( c_24__type__132725___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__132726)
    <=> ! [Vv__CANONICAL__5] :
          ( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
         => t(happ(Vvar__132726,Vv__CANONICAL__5),Vv__CANONICAL__0) ) ) ).

fof('$_type_132755',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__132756] :
      ( c_24__type__132755___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__132756)
    <=> ! [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__132756,Vv__CANONICAL__5),Vv__CANONICAL__6)) ) ) ) ).

fof('$_type_132785',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__132786] :
      ( c_24__type__132785___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__132786)
    <=> ! [Vv__CANONICAL__5] :
          ( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__6] :
              ( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
             => t(happ(happ(Vvar__132786,Vv__CANONICAL__5),Vv__CANONICAL__6),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_132809',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__132810] :
      ( c_24__type__132809___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__132810)
    <=> ! [Vv__CANONICAL__5] :
          ( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
         => t(happ(Vvar__132810,Vv__CANONICAL__5),Vv__CANONICAL__0) ) ) ).

fof('$_type_132842',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__132843] :
      ( c_24__type__132842___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__132843)
    <=> ! [Vv__CANONICAL__5] :
          ( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__6] :
              ( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
             => t(happ(happ(Vvar__132843,Vv__CANONICAL__5),Vv__CANONICAL__6),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_132866',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__132867] :
      ( c_24__type__132866___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__132867)
    <=> ! [Vv__CANONICAL__5] :
          ( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
         => t(happ(Vvar__132867,Vv__CANONICAL__5),Vv__CANONICAL__0) ) ) ).

fof('$_type_132893',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__132894] :
      ( c_24__type__132893___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__132894)
    <=> ! [Vv__CANONICAL__5] :
          ( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
         => t(happ(Vvar__132894,Vv__CANONICAL__5),Vv__CANONICAL__0) ) ) ).

fof('$_type_133292',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,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__133293] :
      ( c_24__type__133292___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,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__133293)
    <=> ! [Vv__CANONICAL__17] :
          ( t(Vv__CANONICAL__17,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__18] :
              ( t(Vv__CANONICAL__18,Vv__CANONICAL__0)
             => t(happ(happ(Vvar__133293,Vv__CANONICAL__17),Vv__CANONICAL__18),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_133505',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,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__133506] :
      ( c_24__type__133505___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,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__133506)
    <=> ! [Vv__CANONICAL__17] :
          ( t(Vv__CANONICAL__17,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__18] :
              ( t(Vv__CANONICAL__18,Vv__CANONICAL__0)
             => t(happ(happ(Vvar__133506,Vv__CANONICAL__17),Vv__CANONICAL__18),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_133718',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,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__133719] :
      ( c_24__type__133718___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,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__133719)
    <=> ! [Vv__CANONICAL__17] :
          ( t(Vv__CANONICAL__17,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__18] :
              ( t(Vv__CANONICAL__18,Vv__CANONICAL__0)
             => t(happ(happ(Vvar__133719,Vv__CANONICAL__17),Vv__CANONICAL__18),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_133913',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,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__133914] :
      ( c_24__type__133913___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,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__133914)
    <=> ! [Vv__CANONICAL__17] :
          ( t(Vv__CANONICAL__17,Vv__CANONICAL__0)
         => t(happ(Vvar__133914,Vv__CANONICAL__17),Vv__CANONICAL__0) ) ) ).

fof('$_type_134126',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,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__134127] :
      ( c_24__type__134126___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,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__134127)
    <=> ! [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__134127,Vv__CANONICAL__17),Vv__CANONICAL__18)) ) ) ) ).

fof('$_type_134339',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,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__134340] :
      ( c_24__type__134339___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,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__134340)
    <=> ! [Vv__CANONICAL__17] :
          ( t(Vv__CANONICAL__17,Vv__CANONICAL__8)
         => ! [Vv__CANONICAL__18] :
              ( t(Vv__CANONICAL__18,Vv__CANONICAL__8)
             => t(happ(happ(Vvar__134340,Vv__CANONICAL__17),Vv__CANONICAL__18),Vv__CANONICAL__8) ) ) ) ).

fof('$_type_134552',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,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__134553] :
      ( c_24__type__134552___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,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__134553)
    <=> ! [Vv__CANONICAL__17] :
          ( t(Vv__CANONICAL__17,Vv__CANONICAL__8)
         => ! [Vv__CANONICAL__18] :
              ( t(Vv__CANONICAL__18,Vv__CANONICAL__8)
             => t(happ(happ(Vvar__134553,Vv__CANONICAL__17),Vv__CANONICAL__18),Vv__CANONICAL__8) ) ) ) ).

fof('$_type_134765',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,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__134766] :
      ( c_24__type__134765___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,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__134766)
    <=> ! [Vv__CANONICAL__17] :
          ( t(Vv__CANONICAL__17,Vv__CANONICAL__8)
         => ! [Vv__CANONICAL__18] :
              ( t(Vv__CANONICAL__18,Vv__CANONICAL__8)
             => t(happ(happ(Vvar__134766,Vv__CANONICAL__17),Vv__CANONICAL__18),Vv__CANONICAL__8) ) ) ) ).

fof('$_type_134960',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,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__134961] :
      ( c_24__type__134960___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,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__134961)
    <=> ! [Vv__CANONICAL__17] :
          ( t(Vv__CANONICAL__17,Vv__CANONICAL__8)
         => t(happ(Vvar__134961,Vv__CANONICAL__17),Vv__CANONICAL__8) ) ) ).

fof('$_type_135173',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,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__135174] :
      ( c_24__type__135173___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,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__135174)
    <=> ! [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__135174,Vv__CANONICAL__17),Vv__CANONICAL__18)) ) ) ) ).

fof('$_type_135368',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,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__135369] :
      ( c_24__type__135368___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,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__135369)
    <=> ! [Vv__CANONICAL__17] :
          ( t(Vv__CANONICAL__17,Vv__CANONICAL__8)
         => t(happ(Vvar__135369,Vv__CANONICAL__17),Vv__CANONICAL__0) ) ) ).

fof('$_type_135483',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__135484] :
      ( c_24__type__135483___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__135484)
    <=> ! [Vv__CANONICAL__7] :
          ( t(Vv__CANONICAL__7,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__8] :
              ( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
             => t(happ(happ(Vvar__135484,Vv__CANONICAL__7),Vv__CANONICAL__8),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_135527',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__135528] :
      ( c_24__type__135527___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__135528)
    <=> ! [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__135528,Vv__CANONICAL__7),Vv__CANONICAL__8)) ) ) ) ).

fof('$_type_135563',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__135564] :
      ( c_24__type__135563___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__135564)
    <=> ! [Vv__CANONICAL__7] :
          ( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__7)
         => t(happ(Vvar__135564,Vv__CANONICAL__7),Vv__CANONICAL__4) ) ) ).

fof('$_type_135607',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__135608] :
      ( c_24__type__135607___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__135608)
    <=> ! [Vv__CANONICAL__7] :
          ( t(Vv__CANONICAL__7,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__8] :
              ( t(Vv__CANONICAL__8,Vv__CANONICAL__4)
             => t(happ(happ(Vvar__135608,Vv__CANONICAL__7),Vv__CANONICAL__8),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_135644',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__135645] :
      ( c_24__type__135644___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__135645)
    <=> ! [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__135645,Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ).

fof('$_type_135684',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__135685] :
      ( c_24__type__135684___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__135685)
    <=> ! [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__135685,Vv__CANONICAL__4),Vv__CANONICAL__5)) ) ) ) ).

fof('$_type_135754',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__135755] :
      ( c_24__type__135754___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__135755)
    <=> ! [Vv__CANONICAL__4] :
          ( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
         => cProp___24t(happ(Vvar__135755,Vv__CANONICAL__4)) ) ) ).

fof('$_type_135825',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__135826] :
      ( c_24__type__135825___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__135826)
    <=> ! [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__135826,Vv__CANONICAL__6),Vv__CANONICAL__7)) ) ) ) ).

fof('$_type_135834',axiom,
    ! [Vvar__135835] :
      ( c_24__type__135834___24t(Vvar__135835)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( c_24__type__135837___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__135835,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).

fof('$_type_135837',axiom,
    ! [Vv__CANONICAL__0,Vvar__135838] :
      ( c_24__type__135837___24t(Vv__CANONICAL__0,Vvar__135838)
    <=> ! [Vv__CANONICAL__1] :
          ( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
         => cCoq_2eInit_2eDatatypes_2enat___24t(happ(Vvar__135838,Vv__CANONICAL__1)) ) ) ).

fof('$_type_136016',axiom,
    ! [Vvar__136017] :
      ( c_24__type__136016___24t(Vvar__136017)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( c_24__type__3523___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__136017,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__0) ) ) ) ) ) ).

fof('$_type_136028',axiom,
    ! [Vvar__136029] :
      ( c_24__type__136028___24t(Vvar__136029)
    <=> ! [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__136029,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).

fof('$_type_138033',axiom,
    ! [Vvar__138034] :
      ( c_24__type__138033___24t(Vvar__138034)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( c_24__type__3735___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__138034,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).

fof('$_type_138323',axiom,
    ! [Vvar__138324] :
      ( c_24__type__138323___24t(Vvar__138324)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vv__CANONICAL__0,happ(Vvar__138324,Vv__CANONICAL__0)) ) ) ).

fof('$_type_138326',axiom,
    ! [Vvar__138327] :
      ( c_24__type__138326___24t(Vvar__138327)
    <=> ! [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__138327,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_138687',axiom,
    ! [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__138688] :
      ( c_24__type__138687___24t(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__138688)
    <=> ! [Vv__CANONICAL__8] :
          ( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__9] :
              ( t(Vv__CANONICAL__9,Vv__CANONICAL__0)
             => t(happ(happ(Vvar__138688,Vv__CANONICAL__8),Vv__CANONICAL__9),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_138750',axiom,
    ! [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__138751] :
      ( c_24__type__138750___24t(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__138751)
    <=> ! [Vv__CANONICAL__8] :
          ( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__9] :
              ( t(Vv__CANONICAL__9,Vv__CANONICAL__0)
             => t(happ(happ(Vvar__138751,Vv__CANONICAL__8),Vv__CANONICAL__9),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_138813',axiom,
    ! [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__138814] :
      ( c_24__type__138813___24t(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__138814)
    <=> ! [Vv__CANONICAL__8] :
          ( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__9] :
              ( t(Vv__CANONICAL__9,Vv__CANONICAL__0)
             => t(happ(happ(Vvar__138814,Vv__CANONICAL__8),Vv__CANONICAL__9),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_138867',axiom,
    ! [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__138868] :
      ( c_24__type__138867___24t(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__138868)
    <=> ! [Vv__CANONICAL__8] :
          ( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
         => t(happ(Vvar__138868,Vv__CANONICAL__8),Vv__CANONICAL__0) ) ) ).

fof('$_type_138930',axiom,
    ! [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__138931] :
      ( c_24__type__138930___24t(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__138931)
    <=> ! [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__138931,Vv__CANONICAL__8),Vv__CANONICAL__9)) ) ) ) ).

fof('$_type_139117',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__139118] :
      ( c_24__type__139117___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__139118)
    <=> ! [Vv__CANONICAL__4] :
          ( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
         => t(happ(Vvar__139118,Vv__CANONICAL__4),Vv__CANONICAL__0) ) ) ).

fof('$_type_139136',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__139137] :
      ( c_24__type__139136___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__139137)
    <=> ! [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__139137,Vv__CANONICAL__4),Vv__CANONICAL__5)) ) ) ) ).

fof('$_type_139150',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__139151] :
      ( c_24__type__139150___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__139151)
    <=> ! [Vv__CANONICAL__4] :
          ( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
         => cCoq_2eInit_2eDatatypes_2eoption___24t(Vv__CANONICAL__0,happ(Vvar__139151,Vv__CANONICAL__4)) ) ) ).

fof('$_type_139295',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__139296] :
      ( c_24__type__139295___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__139296)
    <=> ! [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__139296,Vv__CANONICAL__7),Vv__CANONICAL__8)) ) ) ) ).

fof('$_type_139345',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__139346] :
      ( c_24__type__139345___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__139346)
    <=> ! [Vv__CANONICAL__7] :
          ( t(Vv__CANONICAL__7,Vv__CANONICAL__2)
         => ! [Vv__CANONICAL__8] :
              ( t(Vv__CANONICAL__8,Vv__CANONICAL__2)
             => t(happ(happ(Vvar__139346,Vv__CANONICAL__7),Vv__CANONICAL__8),Vv__CANONICAL__2) ) ) ) ).

fof('$_type_139395',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__139396] :
      ( c_24__type__139395___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__139396)
    <=> ! [Vv__CANONICAL__7] :
          ( t(Vv__CANONICAL__7,Vv__CANONICAL__2)
         => ! [Vv__CANONICAL__8] :
              ( t(Vv__CANONICAL__8,Vv__CANONICAL__2)
             => t(happ(happ(Vvar__139396,Vv__CANONICAL__7),Vv__CANONICAL__8),Vv__CANONICAL__2) ) ) ) ).

fof('$_type_139437',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__139438] :
      ( c_24__type__139437___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__139438)
    <=> ! [Vv__CANONICAL__7] :
          ( t(Vv__CANONICAL__7,Vv__CANONICAL__2)
         => t(happ(Vvar__139438,Vv__CANONICAL__7),Vv__CANONICAL__0) ) ) ).

fof('$_type_139487',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__139488] :
      ( c_24__type__139487___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__139488)
    <=> ! [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__139488,Vv__CANONICAL__7),Vv__CANONICAL__8)) ) ) ) ).

fof('$_type_139563',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__139564] :
      ( c_24__type__139563___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__139564)
    <=> ! [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__139564,Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ).

fof('$_type_139638',axiom,
    ! [Vvar__139639] :
      ( c_24__type__139638___24t(Vvar__139639)
    <=> ! [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__139639,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_139657',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__139658] :
      ( c_24__type__139657___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__139658)
    <=> ! [Vv__CANONICAL__2] :
          ( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
         => cType___24t(happ(Vvar__139658,Vv__CANONICAL__2)) ) ) ).

fof('$_type_139661',axiom,
    ! [Vvar__139662] :
      ( c_24__type__139661___24t(Vvar__139662)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( c_24__type__139664___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
             => cType___24t(happ(happ(Vvar__139662,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_139664',axiom,
    ! [Vv__CANONICAL__0,Vvar__139665] :
      ( c_24__type__139664___24t(Vv__CANONICAL__0,Vvar__139665)
    <=> ! [Vv__CANONICAL__1] :
          ( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
         => cType___24t(happ(Vvar__139665,Vv__CANONICAL__1)) ) ) ).

fof('$_type_139681',axiom,
    ! [Vvar__139682] :
      ( c_24__type__139681___24t(Vvar__139682)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( c_24__type__139664___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__139682,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).

fof('$_type_139708',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__139709] :
      ( c_24__type__139708___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__139709)
    <=> ! [Vv__CANONICAL__3] :
          ( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
         => cType___24t(happ(Vvar__139709,Vv__CANONICAL__3)) ) ) ).

fof('$_type_139716',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__139717] :
      ( c_24__type__139716___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__139717)
    <=> ! [Vv__CANONICAL__3] :
          ( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
         => cType___24t(happ(Vvar__139717,Vv__CANONICAL__3)) ) ) ).

fof('$_type_139724',axiom,
    ! [Vvar__139725] :
      ( c_24__type__139724___24t(Vvar__139725)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( c_24__type__139664___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
             => ! [Vv__CANONICAL__2] :
                  ( c_24__type__139664___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
                 => cType___24t(happ(happ(happ(Vvar__139725,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).

fof('$_type_139754',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__139755] :
      ( c_24__type__139754___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__139755)
    <=> ! [Vv__CANONICAL__2] :
          ( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
         => cType___24t(happ(Vvar__139755,Vv__CANONICAL__2)) ) ) ).

fof('$_type_139760',axiom,
    ! [Vvar__139761] :
      ( c_24__type__139760___24t(Vvar__139761)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( c_24__type__139664___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__139761,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__0) ) ) ) ) ).

fof('$_type_14',axiom,
    ! [Vvar__15] :
      ( c_24__type__14___24t(Vvar__15)
    <=> ! [Vv__CANONICAL__0] :
          ( cPLF_2eHoare_2eAssertion___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cPLF_2eHoare_2eAssertion___24t(Vv__CANONICAL__1)
             => cProp___24t(happ(happ(Vvar__15,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_1418',axiom,
    ! [Vvar__1419] :
      ( c_24__type__1418___24t(Vvar__1419)
    <=> ! [Vv__CANONICAL__0] :
          ( cPLF_2eHoare_2eIf1_2ecom___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cPLF_2eHoare_2eIf1_2ecom___24t(Vv__CANONICAL__1)
             => cPLF_2eHoare_2eIf1_2ecom___24t(happ(happ(Vvar__1419,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_145158',axiom,
    ! [Vvar__145159] :
      ( c_24__type__145158___24t(Vvar__145159)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__0)
         => cType___24t(happ(Vvar__145159,Vv__CANONICAL__0)) ) ) ).

fof('$_type_145681',axiom,
    ! [Vvar__145682] :
      ( c_24__type__145681___24t(Vvar__145682)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
         => cCoq_2eInit_2eDatatypes_2ebool___24t(happ(Vvar__145682,Vv__CANONICAL__0)) ) ) ).

fof('$_type_145711',axiom,
    ! [Vvar__145712] :
      ( c_24__type__145711___24t(Vvar__145712)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__0)
         => cProp___24t(happ(Vvar__145712,Vv__CANONICAL__0)) ) ) ).

fof('$_type_145716',axiom,
    ! [Vvar__145717] :
      ( c_24__type__145716___24t(Vvar__145717)
    <=> ! [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__145717,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).

fof('$_type_145718',axiom,
    ! [Vvar__145719] :
      ( c_24__type__145718___24t(Vvar__145719)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eInit_2eByte_2ebyte___24t(Vv__CANONICAL__0)
         => cCoq_2eInit_2eByte_2ebyte___24t(happ(Vvar__145719,Vv__CANONICAL__0)) ) ) ).

fof('$_type_145748',axiom,
    ! [Vvar__145749] :
      ( c_24__type__145748___24t(Vvar__145749)
    <=> ! [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__145749,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_145772',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__145773] :
      ( c_24__type__145772___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__145773)
    <=> ! [Vv__CANONICAL__6] :
          ( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
         => cType___24t(happ(Vvar__145773,Vv__CANONICAL__6)) ) ) ).

fof('$_type_145800',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__145801] :
      ( c_24__type__145800___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__145801)
    <=> ! [Vv__CANONICAL__6] :
          ( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
         => cType___24t(happ(Vvar__145801,Vv__CANONICAL__6)) ) ) ).

fof('$_type_145803',axiom,
    ! [Vvar__145804] :
      ( c_24__type__145803___24t(Vvar__145804)
    <=> ! [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__145804,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_145806',axiom,
    ! [Vvar__145807] :
      ( c_24__type__145806___24t(Vvar__145807)
    <=> ! [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__145807,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_146002',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,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__146003] :
      ( c_24__type__146002___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,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__146003)
    <=> ! [Vv__CANONICAL__10] :
          ( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__11] :
              ( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
             => t(happ(happ(Vvar__146003,Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_146095',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,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__146096] :
      ( c_24__type__146095___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,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__146096)
    <=> ! [Vv__CANONICAL__10] :
          ( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__11] :
              ( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
             => t(happ(happ(Vvar__146096,Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_146188',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,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__146189] :
      ( c_24__type__146188___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,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__146189)
    <=> ! [Vv__CANONICAL__10] :
          ( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__11] :
              ( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
             => t(happ(happ(Vvar__146189,Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_146270',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,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__146271] :
      ( c_24__type__146270___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,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__146271)
    <=> ! [Vv__CANONICAL__10] :
          ( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
         => t(happ(Vvar__146271,Vv__CANONICAL__10),Vv__CANONICAL__0) ) ) ).

fof('$_type_146363',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,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__146364] :
      ( c_24__type__146363___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,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__146364)
    <=> ! [Vv__CANONICAL__10] :
          ( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__11] :
              ( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
             => t(happ(happ(Vvar__146364,Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_146445',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,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__146446] :
      ( c_24__type__146445___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,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__146446)
    <=> ! [Vv__CANONICAL__10] :
          ( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
         => t(happ(Vvar__146446,Vv__CANONICAL__10),Vv__CANONICAL__0) ) ) ).

fof('$_type_146538',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,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__146539] :
      ( c_24__type__146538___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,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__146539)
    <=> ! [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__146539,Vv__CANONICAL__10),Vv__CANONICAL__11)) ) ) ) ).

fof('$_type_146692',axiom,
    ! [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__146693] :
      ( c_24__type__146692___24t(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__146693)
    <=> ! [Vv__CANONICAL__8] :
          ( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__9] :
              ( t(Vv__CANONICAL__9,Vv__CANONICAL__0)
             => t(happ(happ(Vvar__146693,Vv__CANONICAL__8),Vv__CANONICAL__9),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_146755',axiom,
    ! [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__146756] :
      ( c_24__type__146755___24t(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__146756)
    <=> ! [Vv__CANONICAL__8] :
          ( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__9] :
              ( t(Vv__CANONICAL__9,Vv__CANONICAL__0)
             => t(happ(happ(Vvar__146756,Vv__CANONICAL__8),Vv__CANONICAL__9),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_146818',axiom,
    ! [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__146819] :
      ( c_24__type__146818___24t(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__146819)
    <=> ! [Vv__CANONICAL__8] :
          ( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__9] :
              ( t(Vv__CANONICAL__9,Vv__CANONICAL__0)
             => t(happ(happ(Vvar__146819,Vv__CANONICAL__8),Vv__CANONICAL__9),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_146872',axiom,
    ! [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__146873] :
      ( c_24__type__146872___24t(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__146873)
    <=> ! [Vv__CANONICAL__8] :
          ( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
         => t(happ(Vvar__146873,Vv__CANONICAL__8),Vv__CANONICAL__0) ) ) ).

fof('$_type_146935',axiom,
    ! [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__146936] :
      ( c_24__type__146935___24t(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__146936)
    <=> ! [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__146936,Vv__CANONICAL__8),Vv__CANONICAL__9)) ) ) ) ).

fof('$_type_146949',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__146950] :
      ( c_24__type__146949___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__146950)
    <=> ! [Vv__CANONICAL__2] :
          ( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
         => t(happ(Vvar__146950,Vv__CANONICAL__2),happ(Vv__CANONICAL__1,Vv__CANONICAL__2)) ) ) ).

fof('$_type_14695',axiom,
    ! [Vvar__14696] :
      ( c_24__type__14695___24t(Vvar__14696)
    <=> ! [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__14696,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).

fof('$_type_146954',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__146955] :
      ( c_24__type__146954___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__146955)
    <=> ! [Vv__CANONICAL__2] :
          ( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
         => t(happ(Vvar__146955,Vv__CANONICAL__2),happ(Vv__CANONICAL__1,Vv__CANONICAL__2)) ) ) ).

fof('$_type_146960',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__146961] :
      ( c_24__type__146960___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__146961)
    <=> ! [Vv__CANONICAL__2] :
          ( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
         => t(happ(Vvar__146961,Vv__CANONICAL__2),happ(Vv__CANONICAL__1,Vv__CANONICAL__2)) ) ) ).

fof('$_type_146965',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__146966] :
      ( c_24__type__146965___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__146966)
    <=> ! [Vv__CANONICAL__2] :
          ( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
         => t(happ(Vvar__146966,Vv__CANONICAL__2),happ(Vv__CANONICAL__1,Vv__CANONICAL__2)) ) ) ).

fof('$_type_146977',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__146978] :
      ( c_24__type__146977___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__146978)
    <=> ! [Vv__CANONICAL__2] :
          ( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
         => t(happ(Vvar__146978,Vv__CANONICAL__2),happ(Vv__CANONICAL__1,Vv__CANONICAL__2)) ) ) ).

fof('$_type_146997',axiom,
    ! [Vv__CANONICAL__0,Vvar__146998] :
      ( c_24__type__146997___24t(Vv__CANONICAL__0,Vvar__146998)
    <=> ! [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__146998,Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ).

fof('$_type_147008',axiom,
    ! [Vvar__147009] :
      ( c_24__type__147008___24t(Vvar__147009)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( c_24__type__146997___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__147009,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__0) ) ) ) ) ) ).

fof('$_type_147052',axiom,
    ! [Vvar__147053] :
      ( c_24__type__147052___24t(Vvar__147053)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
             => ! [Vv__CANONICAL__2] :
                  ( c_24__type__3514___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
                 => ! [Vv__CANONICAL__3] :
                      ( c_24__type__3514___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__147053,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__0) ) ) ) ) ) ) ).

fof('$_type_147104',axiom,
    ! [Vvar__147105] :
      ( c_24__type__147104___24t(Vvar__147105)
    <=> ! [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__147105,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_147115',axiom,
    ! [Vvar__147116] :
      ( c_24__type__147115___24t(Vvar__147116)
    <=> ! [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__147116,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__0) ) ) ) ) ).

fof('$_type_147141',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__147142] :
      ( c_24__type__147141___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__147142)
    <=> ! [Vv__CANONICAL__3] :
          ( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
         => cProp___24t(happ(Vvar__147142,Vv__CANONICAL__3)) ) ) ).

fof('$_type_147165',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__147166] :
      ( c_24__type__147165___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__147166)
    <=> ! [Vv__CANONICAL__3] :
          ( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
         => cProp___24t(happ(Vvar__147166,Vv__CANONICAL__3)) ) ) ).

fof('$_type_147212',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__147213] :
      ( c_24__type__147212___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__147213)
    <=> ! [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__147213,Vv__CANONICAL__5),Vv__CANONICAL__6)) ) ) ) ).

fof('$_type_147247',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__147248] :
      ( c_24__type__147247___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__147248)
    <=> ! [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__147248,Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ).

fof('$_type_147249',axiom,
    ! [Vvar__147250] :
      ( c_24__type__147249___24t(Vvar__147250)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => cProp___24t(happ(Vvar__147250,Vv__CANONICAL__0)) ) ) ).

fof('$_type_147839',axiom,
    ! [Vvar__147840] :
      ( c_24__type__147839___24t(Vvar__147840)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
             => cProp___24t(happ(happ(Vvar__147840,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_147857',axiom,
    ! [Vvar__147858] :
      ( c_24__type__147857___24t(Vvar__147858)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( c_24__type__3735___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__147858,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).

fof('$_type_147986',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__147987] :
      ( c_24__type__147986___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__147987)
    <=> ! [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__147987,Vv__CANONICAL__6),Vv__CANONICAL__7)) ) ) ) ).

fof('$_type_148011',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__148012] :
      ( c_24__type__148011___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__148012)
    <=> ! [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__148012,Vv__CANONICAL__6),Vv__CANONICAL__7)) ) ) ) ).

fof('$_type_148053',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__148054] :
      ( c_24__type__148053___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__148054)
    <=> ! [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__148054,Vv__CANONICAL__4),Vv__CANONICAL__5)) ) ) ) ).

fof('$_type_148104',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__148105] :
      ( c_24__type__148104___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__148105)
    <=> ! [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__148105,Vv__CANONICAL__4),Vv__CANONICAL__5)) ) ) ) ).

fof('$_type_148202',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__148203] :
      ( c_24__type__148202___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__148203)
    <=> ! [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__148203,Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ).

fof('$_type_14831',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__14832] :
      ( c_24__type__14831___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__14832)
    <=> ! [Vv__CANONICAL__3] :
          ( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__3)
         => cProp___24t(happ(Vvar__14832,Vv__CANONICAL__3)) ) ) ).

fof('$_type_148630',axiom,
    ! [Vvar__148631] :
      ( c_24__type__148630___24t(Vvar__148631)
    <=> ! [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__148631,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_148648',axiom,
    ! [Vvar__148649] :
      ( c_24__type__148648___24t(Vvar__148649)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( c_24__type__3514___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__148649,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__0) ) ) ) ) ) ) ).

fof('$_type_148893',axiom,
    ! [Vvar__148894] :
      ( c_24__type__148893___24t(Vvar__148894)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cType___24t(Vv__CANONICAL__1)
             => ! [Vv__CANONICAL__2] :
                  ( c_24__type__2863___24t(Vv__CANONICAL__1,Vv__CANONICAL__2)
                 => ! [Vv__CANONICAL__3] :
                      ( c_24__type__148903___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__3)
                     => ! [Vv__CANONICAL__4] :
                          ( c_24__type__6765___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__4)
                         => cProp___24t(happ(happ(happ(happ(happ(Vvar__148894,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ) ) ) ).

fof('$_type_148903',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__148904] :
      ( c_24__type__148903___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__148904)
    <=> ! [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__148904,Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ).

fof('$_type_149000',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__149001] :
      ( c_24__type__149000___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__149001)
    <=> ! [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__149001,Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ).

fof('$_type_149039',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__149040] :
      ( c_24__type__149039___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__149040)
    <=> ! [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__149040,Vv__CANONICAL__4),Vv__CANONICAL__5)) ) ) ) ).

fof('$_type_149074',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__149075] :
      ( c_24__type__149074___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__149075)
    <=> ! [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__149075,Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ).

fof('$_type_149109',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__149110] :
      ( c_24__type__149109___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__149110)
    <=> ! [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__149110,Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ).

fof('$_type_149135',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__149136] :
      ( c_24__type__149135___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__149136)
    <=> ! [Vv__CANONICAL__3] :
          ( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
         => cProp___24t(happ(Vvar__149136,Vv__CANONICAL__3)) ) ) ).

fof('$_type_149143',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__149144] :
      ( c_24__type__149143___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__149144)
    <=> ! [Vv__CANONICAL__3] :
          ( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
         => cProp___24t(happ(Vvar__149144,Vv__CANONICAL__3)) ) ) ).

fof('$_type_149151',axiom,
    ! [Vvar__149152] :
      ( c_24__type__149151___24t(Vvar__149152)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( c_24__type__3735___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
             => ! [Vv__CANONICAL__2] :
                  ( c_24__type__3735___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
                 => cType___24t(happ(happ(happ(Vvar__149152,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).

fof('$_type_149168',axiom,
    ! [Vvar__149169] :
      ( c_24__type__149168___24t(Vvar__149169)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ( p(c_24False)
           => t(happ(Vvar__149169,Vv__CANONICAL__0),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_149225',axiom,
    ! [Vvar__149226] :
      ( c_24__type__149225___24t(Vvar__149226)
    <=> ! [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__149226,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).

fof('$_type_149723',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__149724] :
      ( c_24__type__149723___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__149724)
    <=> ! [Vv__CANONICAL__4] :
          ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__4)
         => cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(Vvar__149724,Vv__CANONICAL__4)) ) ) ).

fof('$_type_149732',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__149733] :
      ( c_24__type__149732___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__149733)
    <=> ! [Vv__CANONICAL__4] :
          ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__4)
         => cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(Vvar__149733,Vv__CANONICAL__4)) ) ) ).

fof('$_type_149779',axiom,
    ! [Vvar__149780] :
      ( c_24__type__149779___24t(Vvar__149780)
    <=> ! [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__149780,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_149942',axiom,
    ! [Vvar__149943] :
      ( c_24__type__149942___24t(Vvar__149943)
    <=> ! [Vv__CANONICAL__0] :
          ( c_24__type__123915___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( c_24__type__123915___24t(Vv__CANONICAL__1)
             => cProp___24t(happ(happ(Vvar__149943,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_150092',axiom,
    ! [Vvar__150093] :
      ( c_24__type__150092___24t(Vvar__150093)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
         => cCoq_2eNumbers_2eBinNums_2epositive___24t(happ(Vvar__150093,Vv__CANONICAL__0)) ) ) ).

fof('$_type_150097',axiom,
    ! [Vvar__150098] :
      ( c_24__type__150097___24t(Vvar__150098)
    <=> ! [Vv__CANONICAL__0] :
          ( c_24__type__145681___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( c_24__type__145681___24t(Vv__CANONICAL__1)
             => cProp___24t(happ(happ(Vvar__150098,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_150501',axiom,
    ! [Vvar__150502] :
      ( c_24__type__150501___24t(Vvar__150502)
    <=> ! [Vv__CANONICAL__0] :
          ( cHoare2_2edecorated___24t(Vv__CANONICAL__0)
         => cProp___24t(happ(Vvar__150502,Vv__CANONICAL__0)) ) ) ).

fof('$_type_151112',axiom,
    ! [Vvar__151113] :
      ( c_24__type__151112___24t(Vvar__151113)
    <=> ! [Vv__CANONICAL__0] :
          ( cPLF_2eHoare_2eAssertion___24t(Vv__CANONICAL__0)
         => cHoare2_2edcom___24t(happ(Vvar__151113,Vv__CANONICAL__0)) ) ) ).

fof('$_type_151115',axiom,
    ! [Vvar__151116] :
      ( c_24__type__151115___24t(Vvar__151116)
    <=> ! [Vv__CANONICAL__0] :
          ( cHoare2_2edcom___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cHoare2_2edcom___24t(Vv__CANONICAL__1)
             => cHoare2_2edcom___24t(happ(happ(Vvar__151116,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_151195',axiom,
    ! [Vvar__151196] :
      ( c_24__type__151195___24t(Vvar__151196)
    <=> ! [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__151196,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).

fof('$_type_151198',axiom,
    ! [Vvar__151199] :
      ( c_24__type__151198___24t(Vvar__151199)
    <=> ! [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__151199,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_152488',axiom,
    ! [Vvar__152489] :
      ( c_24__type__152488___24t(Vvar__152489)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__0)
         => cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(Vvar__152489,Vv__CANONICAL__0)) ) ) ).

fof('$_type_152498',axiom,
    ! [Vvar__152499] :
      ( c_24__type__152498___24t(Vvar__152499)
    <=> ! [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__152499,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).

fof('$_type_152503',axiom,
    ! [Vvar__152504] :
      ( c_24__type__152503___24t(Vvar__152504)
    <=> ! [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__152504,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).

fof('$_type_152506',axiom,
    ! [Vvar__152507] :
      ( c_24__type__152506___24t(Vvar__152507)
    <=> ! [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__152507,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_152511',axiom,
    ! [Vvar__152512] :
      ( c_24__type__152511___24t(Vvar__152512)
    <=> ! [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__152512,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).

fof('$_type_152519',axiom,
    ! [Vvar__152520] :
      ( c_24__type__152519___24t(Vvar__152520)
    <=> ! [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__152520,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).

fof('$_type_152522',axiom,
    ! [Vvar__152523] :
      ( c_24__type__152522___24t(Vvar__152523)
    <=> ! [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__152523,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_152531',axiom,
    ! [Vvar__152532] :
      ( c_24__type__152531___24t(Vvar__152532)
    <=> ! [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__152532,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ) ).

fof('$_type_152555',axiom,
    ! [Vvar__152556] :
      ( c_24__type__152555___24t(Vvar__152556)
    <=> ! [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__152556,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__0) ) ) ) ) ).

fof('$_type_152713',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__152714] :
      ( c_24__type__152713___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__152714)
    <=> ! [Vv__CANONICAL__6] :
          ( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
         => cType___24t(happ(Vvar__152714,Vv__CANONICAL__6)) ) ) ).

fof('$_type_152742',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__152743] :
      ( c_24__type__152742___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__152743)
    <=> ! [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__152743,Vv__CANONICAL__6),Vv__CANONICAL__7)) ) ) ) ).

fof('$_type_152779',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__152780] :
      ( c_24__type__152779___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__152780)
    <=> ! [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__152780,Vv__CANONICAL__6),Vv__CANONICAL__7),Vv__CANONICAL__8)) ) ) ) ) ).

fof('$_type_152782',axiom,
    ! [Vvar__152783] :
      ( c_24__type__152782___24t(Vvar__152783)
    <=> ! [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__152783,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_152822',axiom,
    ! [Vvar__152823] :
      ( c_24__type__152822___24t(Vvar__152823)
    <=> ! [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__152823,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).

fof('$_type_152839',axiom,
    ! [Vvar__152840] :
      ( c_24__type__152839___24t(Vvar__152840)
    <=> ! [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__152840,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5)) ) ) ) ) ) ) ) ).

fof('$_type_152847',axiom,
    ! [Vvar__152848] :
      ( c_24__type__152847___24t(Vvar__152848)
    <=> ! [Vv__CANONICAL__0] :
          ( cPLF_2eImp_2eAExp_2ebexp___24t(Vv__CANONICAL__0)
         => cPLF_2eImp_2eAExp_2ebexp___24t(happ(Vvar__152848,Vv__CANONICAL__0)) ) ) ).

fof('$_type_152850',axiom,
    ! [Vvar__152851] :
      ( c_24__type__152850___24t(Vvar__152851)
    <=> ! [Vv__CANONICAL__0] :
          ( cPLF_2eImp_2eAExp_2ebexp___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cPLF_2eImp_2eAExp_2ebexp___24t(Vv__CANONICAL__1)
             => cPLF_2eImp_2eAExp_2ebexp___24t(happ(happ(Vvar__152851,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_152866',axiom,
    ! [Vvar__152867] :
      ( c_24__type__152866___24t(Vvar__152867)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
             => ! [Vv__CANONICAL__2] :
                  ( c_24__type__152871___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
                 => ! [Vv__CANONICAL__3] :
                      ( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__3)
                     => t(happ(happ(happ(happ(Vvar__152867,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__0) ) ) ) ) ) ).

fof('$_type_152871',axiom,
    ! [Vv__CANONICAL__0,Vvar__152872] :
      ( c_24__type__152871___24t(Vv__CANONICAL__0,Vvar__152872)
    <=> ! [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__152872,Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_154230',axiom,
    ! [Vvar__154231] :
      ( c_24__type__154230___24t(Vvar__154231)
    <=> ! [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__154231,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).

fof('$_type_1547',axiom,
    ! [Vvar__1548] :
      ( c_24__type__1547___24t(Vvar__1548)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
         => cCoq_2eInit_2eDatatypes_2ebool___24t(happ(Vvar__1548,Vv__CANONICAL__0)) ) ) ).

fof('$_type_155062',axiom,
    ! [Vvar__155063] :
      ( c_24__type__155062___24t(Vvar__155063)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vv__CANONICAL__0,happ(Vvar__155063,Vv__CANONICAL__0)) ) ) ).

fof('$_type_1551',axiom,
    ! [Vvar__1552] :
      ( c_24__type__1551___24t(Vvar__1552)
    <=> ! [Vv__CANONICAL__0] :
          ( c_24__type__1547___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( c_24__type__1547___24t(Vv__CANONICAL__1)
             => cProp___24t(happ(happ(Vvar__1552,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_155153',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__155154] :
      ( c_24__type__155153___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__155154)
    <=> ! [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__155154,Vv__CANONICAL__6),Vv__CANONICAL__7)) ) ) ) ).

fof('$_type_155178',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__155179] :
      ( c_24__type__155178___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__155179)
    <=> ! [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__155179,Vv__CANONICAL__6),Vv__CANONICAL__7)) ) ) ) ).

fof('$_type_155189',axiom,
    ! [Vvar__155190] :
      ( c_24__type__155189___24t(Vvar__155190)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( c_24__type__3030___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__155190,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).

fof('$_type_155268',axiom,
    ! [Vvar__155269] :
      ( c_24__type__155268___24t(Vvar__155269)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
             => ! [Vv__CANONICAL__2] :
                  ( c_24__type__2863___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
                 => ! [Vv__CANONICAL__3] :
                      ( c_24__type__2863___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
                     => ! [Vv__CANONICAL__4] :
                          ( c_24__type__2863___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__155269,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__6)) ) ) ) ) ) ) ) ) ).

fof('$_type_155282',axiom,
    ! [Vvar__155283] :
      ( c_24__type__155282___24t(Vvar__155283)
    <=> ! [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__155283,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).

fof('$_type_155290',axiom,
    ! [Vvar__155291] :
      ( c_24__type__155290___24t(Vvar__155291)
    <=> ! [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__155291,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).

fof('$_type_155382',axiom,
    ! [Vvar__155383] :
      ( c_24__type__155382___24t(Vvar__155383)
    <=> ! [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__155383,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ) ) ) ).

fof('$_type_155388',axiom,
    ! [Vvar__155389] :
      ( c_24__type__155388___24t(Vvar__155389)
    <=> ! [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__155389,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_155453',axiom,
    ! [Vvar__155454] :
      ( c_24__type__155453___24t(Vvar__155454)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__0)
         => cCoq_2eNumbers_2eBinNums_2epositive___24t(happ(Vvar__155454,Vv__CANONICAL__0)) ) ) ).

fof('$_type_1646',axiom,
    ! [Vvar__1647] :
      ( c_24__type__1646___24t(Vvar__1647)
    <=> ! [Vv__CANONICAL__0] :
          ( cPLF_2eHoare_2eRepeatExercise_2ecom___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cPLF_2eHoare_2eRepeatExercise_2ecom___24t(Vv__CANONICAL__1)
             => cPLF_2eHoare_2eRepeatExercise_2ecom___24t(happ(happ(Vvar__1647,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_1781',axiom,
    ! [Vvar__1782] :
      ( c_24__type__1781___24t(Vvar__1782)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__0)
         => cCoq_2eNumbers_2eBinNums_2eN___24t(happ(Vvar__1782,Vv__CANONICAL__0)) ) ) ).

fof('$_type_180',axiom,
    ! [Vvar__181] :
      ( c_24__type__180___24t(Vvar__181)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eStrings_2eString_2estring___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cPLF_2eImp_2eaexp___24t(Vv__CANONICAL__1)
             => cPLF_2eImp_2ecom___24t(happ(happ(Vvar__181,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_183',axiom,
    ! [Vvar__184] :
      ( c_24__type__183___24t(Vvar__184)
    <=> ! [Vv__CANONICAL__0] :
          ( cPLF_2eImp_2ecom___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cPLF_2eImp_2ecom___24t(Vv__CANONICAL__1)
             => cPLF_2eImp_2ecom___24t(happ(happ(Vvar__184,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_1856',axiom,
    ! [Vvar__1857] :
      ( c_24__type__1856___24t(Vvar__1857)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
         => cProp___24t(happ(Vvar__1857,Vv__CANONICAL__0)) ) ) ).

fof('$_type_1871',axiom,
    ! [Vvar__1872] :
      ( c_24__type__1871___24t(Vvar__1872)
    <=> ! [Vv__CANONICAL__0] :
          ( c_24__type__1873___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__1878___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
                 => ! [Vv__CANONICAL__3] :
                      ( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__3)
                     => t(happ(happ(happ(happ(Vvar__1872,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),happ(Vv__CANONICAL__0,Vv__CANONICAL__3)) ) ) ) ) ) ).

fof('$_type_1873',axiom,
    ! [Vvar__1874] :
      ( c_24__type__1873___24t(Vvar__1874)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
         => cType___24t(happ(Vvar__1874,Vv__CANONICAL__0)) ) ) ).

fof('$_type_1878',axiom,
    ! [Vv__CANONICAL__0,Vvar__1879] :
      ( c_24__type__1878___24t(Vv__CANONICAL__0,Vvar__1879)
    <=> ! [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__1879,Vv__CANONICAL__1),Vv__CANONICAL__2),happ(Vv__CANONICAL__0,cCoq_2eInit_2eDatatypes_2eS___24a1(Vv__CANONICAL__1))) ) ) ) ).

fof('$_type_1888',axiom,
    ! [Vvar__1889] :
      ( c_24__type__1888___24t(Vvar__1889)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cType___24t(Vv__CANONICAL__1)
             => cType___24t(happ(happ(Vvar__1889,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_1904',axiom,
    ! [Vvar__1905] :
      ( c_24__type__1904___24t(Vvar__1905)
    <=> ! [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__1905,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).

fof('$_type_1916',axiom,
    ! [Vvar__1917] :
      ( c_24__type__1916___24t(Vvar__1917)
    <=> ! [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__1917,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__0) ) ) ) ) ).

fof('$_type_1928',axiom,
    ! [Vvar__1929] :
      ( c_24__type__1928___24t(Vvar__1929)
    <=> ! [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__1929,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__1) ) ) ) ) ).

fof('$_type_1944',axiom,
    ! [Vvar__1945] :
      ( c_24__type__1944___24t(Vvar__1945)
    <=> ! [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__1945,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_1963',axiom,
    ! [Vvar__1964] :
      ( c_24__type__1963___24t(Vvar__1964)
    <=> ! [Vv__CANONICAL__0] :
          ( cProp___24t(Vv__CANONICAL__0)
         => cProp___24t(happ(Vvar__1964,Vv__CANONICAL__0)) ) ) ).

fof('$_type_220',axiom,
    ! [Vvar__221] :
      ( c_24__type__220___24t(Vvar__221)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__0)
         => cCoq_2eNumbers_2eBinNums_2epositive___24t(happ(Vvar__221,Vv__CANONICAL__0)) ) ) ).

fof('$_type_233',axiom,
    ! [Vvar__234] :
      ( c_24__type__233___24t(Vvar__234)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__0)
         => cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(Vvar__234,Vv__CANONICAL__0)) ) ) ).

fof('$_type_244',axiom,
    ! [Vvar__245] :
      ( c_24__type__244___24t(Vvar__245)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eStrings_2eString_2estring___24t(Vv__CANONICAL__0)
         => cPLF_2eImp_2eaexp___24t(happ(Vvar__245,Vv__CANONICAL__0)) ) ) ).

fof('$_type_247',axiom,
    ! [Vvar__248] :
      ( c_24__type__247___24t(Vvar__248)
    <=> ! [Vv__CANONICAL__0] :
          ( cPLF_2eImp_2eaexp___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cPLF_2eImp_2eaexp___24t(Vv__CANONICAL__1)
             => cPLF_2eImp_2eaexp___24t(happ(happ(Vvar__248,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_2576',axiom,
    ! [Vvar__2577] :
      ( c_24__type__2576___24t(Vvar__2577)
    <=> ! [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__2577,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).

fof('$_type_2671',axiom,
    ! [Vvar__2672] :
      ( c_24__type__2671___24t(Vvar__2672)
    <=> ! [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__2672,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_2846',axiom,
    ! [Vvar__2847] :
      ( c_24__type__2846___24t(Vvar__2847)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__0)
         => cCoq_2eReals_2eRdefinitions_2eR___24t(happ(Vvar__2847,Vv__CANONICAL__0)) ) ) ).

fof('$_type_2849',axiom,
    ! [Vvar__2850] :
      ( c_24__type__2849___24t(Vvar__2850)
    <=> ! [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__2850,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_2853',axiom,
    ! [Vvar__2854] :
      ( c_24__type__2853___24t(Vvar__2854)
    <=> ! [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__2854,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_2858',axiom,
    ! [Vvar__2859] :
      ( c_24__type__2858___24t(Vvar__2859)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
         => cCoq_2eReals_2eRdefinitions_2eR___24t(happ(Vvar__2859,Vv__CANONICAL__0)) ) ) ).

fof('$_type_2863',axiom,
    ! [Vv__CANONICAL__0,Vvar__2864] :
      ( c_24__type__2863___24t(Vv__CANONICAL__0,Vvar__2864)
    <=> ! [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__2864,Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ).

fof('$_type_3030',axiom,
    ! [Vv__CANONICAL__0,Vvar__3031] :
      ( c_24__type__3030___24t(Vv__CANONICAL__0,Vvar__3031)
    <=> ! [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__3031,Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ).

fof('$_type_3041',axiom,
    ! [Vvar__3042] :
      ( c_24__type__3041___24t(Vvar__3042)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( c_24__type__3030___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__3042,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).

fof('$_type_307',axiom,
    ! [Vvar__308] :
      ( c_24__type__307___24t(Vvar__308)
    <=> ! [Vv__CANONICAL__0] :
          ( cPLF_2eImp_2eaexp___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cPLF_2eImp_2eaexp___24t(Vv__CANONICAL__1)
             => cPLF_2eImp_2ebexp___24t(happ(happ(Vvar__308,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_324',axiom,
    ! [Vvar__325] :
      ( c_24__type__324___24t(Vvar__325)
    <=> ! [Vv__CANONICAL__0] :
          ( cPLF_2eImp_2ebexp___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cPLF_2eImp_2ecom___24t(Vv__CANONICAL__1)
             => cPLF_2eImp_2ecom___24t(happ(happ(Vvar__325,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_329',axiom,
    ! [Vvar__330] :
      ( c_24__type__329___24t(Vvar__330)
    <=> ! [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__330,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_3290',axiom,
    ! [Vvar__3291] :
      ( c_24__type__3290___24t(Vvar__3291)
    <=> ! [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__3291,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_3293',axiom,
    ! [Vvar__3294] :
      ( c_24__type__3293___24t(Vvar__3294)
    <=> ! [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__3294,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_3298',axiom,
    ! [Vvar__3299] :
      ( c_24__type__3298___24t(Vvar__3299)
    <=> ! [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__3299,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).

fof('$_type_337',axiom,
    ! [Vvar__338] :
      ( c_24__type__337___24t(Vvar__338)
    <=> ! [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__338,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_339',axiom,
    ! [Vvar__340] :
      ( c_24__type__339___24t(Vvar__340)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
         => cProp___24t(happ(Vvar__340,Vv__CANONICAL__0)) ) ) ).

fof('$_type_349',axiom,
    ! [Vvar__350] :
      ( c_24__type__349___24t(Vvar__350)
    <=> ! [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__350,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_3514',axiom,
    ! [Vv__CANONICAL__0,Vvar__3515] :
      ( c_24__type__3514___24t(Vv__CANONICAL__0,Vvar__3515)
    <=> ! [Vv__CANONICAL__1] :
          ( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__2] :
              ( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
             => t(happ(happ(Vvar__3515,Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_3523',axiom,
    ! [Vv__CANONICAL__0,Vvar__3524] :
      ( c_24__type__3523___24t(Vv__CANONICAL__0,Vvar__3524)
    <=> ! [Vv__CANONICAL__1] :
          ( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
         => t(happ(Vvar__3524,Vv__CANONICAL__1),Vv__CANONICAL__0) ) ) ).

fof('$_type_3728',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__3729] :
      ( c_24__type__3728___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__3729)
    <=> ! [Vv__CANONICAL__2] :
          ( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
         => cProp___24t(happ(Vvar__3729,Vv__CANONICAL__2)) ) ) ).

fof('$_type_3732',axiom,
    ! [Vvar__3733] :
      ( c_24__type__3732___24t(Vvar__3733)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( c_24__type__3735___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
             => cType___24t(happ(happ(Vvar__3733,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_3735',axiom,
    ! [Vv__CANONICAL__0,Vvar__3736] :
      ( c_24__type__3735___24t(Vv__CANONICAL__0,Vvar__3736)
    <=> ! [Vv__CANONICAL__1] :
          ( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
         => cProp___24t(happ(Vvar__3736,Vv__CANONICAL__1)) ) ) ).

fof('$_type_3752',axiom,
    ! [Vvar__3753] :
      ( c_24__type__3752___24t(Vvar__3753)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( c_24__type__3735___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__3753,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ) ).

fof('$_type_3765',axiom,
    ! [Vvar__3766] :
      ( c_24__type__3765___24t(Vvar__3766)
    <=> ! [Vv__CANONICAL__0] :
          ( cProp___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cProp___24t(Vv__CANONICAL__1)
             => cType___24t(happ(happ(Vvar__3766,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_3788',axiom,
    ! [Vvar__3789] :
      ( c_24__type__3788___24t(Vvar__3789)
    <=> ! [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__3789,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ) ).

fof('$_type_3793',axiom,
    ! [Vvar__3794] :
      ( c_24__type__3793___24t(Vvar__3794)
    <=> ! [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__3794,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ) ).

fof('$_type_3805',axiom,
    ! [Vvar__3806] :
      ( c_24__type__3805___24t(Vvar__3806)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cProp___24t(Vv__CANONICAL__1)
             => cType___24t(happ(happ(Vvar__3806,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_3828',axiom,
    ! [Vvar__3829] :
      ( c_24__type__3828___24t(Vvar__3829)
    <=> ! [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__3829,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).

fof('$_type_3833',axiom,
    ! [Vvar__3834] :
      ( c_24__type__3833___24t(Vvar__3834)
    <=> ! [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__3834,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ) ).

fof('$_type_3844',axiom,
    ! [Vvar__3845] :
      ( c_24__type__3844___24t(Vvar__3845)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
             => cType___24t(happ(happ(Vvar__3845,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_3861',axiom,
    ! [Vvar__3862] :
      ( c_24__type__3861___24t(Vvar__3862)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => cCoq_2eVectors_2eVectorDef_2et___24t(Vv__CANONICAL__0,cCoq_2eInit_2eDatatypes_2eO,happ(Vvar__3862,Vv__CANONICAL__0)) ) ) ).

fof('$_type_397',axiom,
    ! [Vvar__398] :
      ( c_24__type__397___24t(Vvar__398)
    <=> ! [Vv__CANONICAL__0] :
          ( cPLF_2eImp_2ebexp___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cPLF_2eImp_2ecom___24t(Vv__CANONICAL__1)
             => ! [Vv__CANONICAL__2] :
                  ( cPLF_2eImp_2ecom___24t(Vv__CANONICAL__2)
                 => cPLF_2eImp_2ecom___24t(happ(happ(happ(Vvar__398,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).

fof('$_type_4087',axiom,
    ! [Vvar__4088] :
      ( c_24__type__4087___24t(Vvar__4088)
    <=> ! [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__4088,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_4125',axiom,
    ! [Vvar__4126] :
      ( c_24__type__4125___24t(Vvar__4126)
    <=> ! [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__4126,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_4139',axiom,
    ! [Vvar__4140] :
      ( c_24__type__4139___24t(Vvar__4140)
    <=> ! [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__4140,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_4338',axiom,
    ! [Vvar__4339] :
      ( c_24__type__4338___24t(Vvar__4339)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__0)
         => cCoq_2eInit_2eDatatypes_2enat___24t(happ(Vvar__4339,Vv__CANONICAL__0)) ) ) ).

fof('$_type_4380',axiom,
    ! [Vvar__4381] :
      ( c_24__type__4380___24t(Vvar__4381)
    <=> ! [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__4381,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_4389',axiom,
    ! [Vvar__4390] :
      ( c_24__type__4389___24t(Vvar__4390)
    <=> ! [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__4390,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_4391',axiom,
    ! [Vvar__4392] :
      ( c_24__type__4391___24t(Vvar__4392)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__0)
         => cCoq_2eInit_2eDatatypes_2enat___24t(happ(Vvar__4392,Vv__CANONICAL__0)) ) ) ).

fof('$_type_4398',axiom,
    ! [Vvar__4399] :
      ( c_24__type__4398___24t(Vvar__4399)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
         => cCoq_2eNumbers_2eBinNums_2epositive___24t(happ(Vvar__4399,Vv__CANONICAL__0)) ) ) ).

fof('$_type_4433',axiom,
    ! [Vvar__4434] :
      ( c_24__type__4433___24t(Vvar__4434)
    <=> ! [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__4434,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_4445',axiom,
    ! [Vvar__4446] :
      ( c_24__type__4445___24t(Vvar__4446)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
         => cCoq_2eInit_2eDatatypes_2enat___24t(happ(Vvar__4446,Vv__CANONICAL__0)) ) ) ).

fof('$_type_4529',axiom,
    ! [Vvar__4530] :
      ( c_24__type__4529___24t(Vvar__4530)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
         => cPLF_2eImp_2eaevalR__division_2eaexp___24t(happ(Vvar__4530,Vv__CANONICAL__0)) ) ) ).

fof('$_type_4532',axiom,
    ! [Vvar__4533] :
      ( c_24__type__4532___24t(Vvar__4533)
    <=> ! [Vv__CANONICAL__0] :
          ( cPLF_2eImp_2eaevalR__division_2eaexp___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cPLF_2eImp_2eaevalR__division_2eaexp___24t(Vv__CANONICAL__1)
             => cPLF_2eImp_2eaevalR__division_2eaexp___24t(happ(happ(Vvar__4533,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_4943',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__4944] :
      ( c_24__type__4943___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__4944)
    <=> ! [Vv__CANONICAL__3] :
          ( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__3)
         => cProp___24t(happ(Vvar__4944,Vv__CANONICAL__3)) ) ) ).

fof('$_type_4953',axiom,
    ! [Vvar__4954] :
      ( c_24__type__4953___24t(Vvar__4954)
    <=> ! [Vv__CANONICAL__0] :
          ( cProp___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__1)
             => cType___24t(happ(happ(Vvar__4954,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_4983',axiom,
    ! [Vv__CANONICAL__0,Vvar__4984] :
      ( c_24__type__4983___24t(Vv__CANONICAL__0,Vvar__4984)
    <=> ! [Vv__CANONICAL__1] :
          ( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
         => cType___24t(happ(Vvar__4984,Vv__CANONICAL__1)) ) ) ).

fof('$_type_5011',axiom,
    ! [Vvar__5012] :
      ( c_24__type__5011___24t(Vvar__5012)
    <=> ! [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__5012,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_5013',axiom,
    ! [Vvar__5014] :
      ( c_24__type__5013___24t(Vvar__5014)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => cCoq_2eInit_2eDatatypes_2eoption___24t(Vv__CANONICAL__0,happ(Vvar__5014,Vv__CANONICAL__0)) ) ) ).

fof('$_type_5025',axiom,
    ! [Vvar__5026] :
      ( c_24__type__5025___24t(Vvar__5026)
    <=> ! [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__5026,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).

fof('$_type_5057',axiom,
    ! [Vvar__5058] :
      ( c_24__type__5057___24t(Vvar__5058)
    <=> ! [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__5058,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__0) ) ) ) ) ) ).

fof('$_type_5081',axiom,
    ! [Vvar__5082] :
      ( c_24__type__5081___24t(Vvar__5082)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cType___24t(Vv__CANONICAL__1)
             => ! [Vv__CANONICAL__2] :
                  ( c_24__type__5088___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__5082,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__0) ) ) ) ) ) ) ).

fof('$_type_5088',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__5089] :
      ( c_24__type__5088___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__5089)
    <=> ! [Vv__CANONICAL__2] :
          ( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__3] :
              ( t(Vv__CANONICAL__3,Vv__CANONICAL__1)
             => t(happ(happ(Vvar__5089,Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_5130',axiom,
    ! [Vv__CANONICAL__0,Vvar__5131] :
      ( c_24__type__5130___24t(Vv__CANONICAL__0,Vvar__5131)
    <=> ! [Vv__CANONICAL__1] :
          ( cCoq_2eStrings_2eString_2estring___24t(Vv__CANONICAL__1)
         => t(happ(Vvar__5131,Vv__CANONICAL__1),Vv__CANONICAL__0) ) ) ).

fof('$_type_528',axiom,
    ! [Vvar__529] :
      ( c_24__type__528___24t(Vvar__529)
    <=> ! [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__529,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_5375',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__5376] :
      ( c_24__type__5375___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__5376)
    <=> ! [Vv__CANONICAL__2] :
          ( t(Vv__CANONICAL__2,Vv__CANONICAL__1)
         => t(happ(Vvar__5376,Vv__CANONICAL__2),Vv__CANONICAL__0) ) ) ).

fof('$_type_5407',axiom,
    ! [Vvar__5408] :
      ( c_24__type__5407___24t(Vvar__5408)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
             => ! [Vv__CANONICAL__2] :
                  ( c_24__type__3514___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__5408,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__0) ) ) ) ) ) ) ).

fof('$_type_5412',axiom,
    ! [Vvar__5413] :
      ( c_24__type__5412___24t(Vvar__5413)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__0)
         => cCoq_2eNumbers_2eBinNums_2eN___24t(happ(Vvar__5413,Vv__CANONICAL__0)) ) ) ).

fof('$_type_546',axiom,
    ! [Vvar__547] :
      ( c_24__type__546___24t(Vvar__547)
    <=> ! [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__547,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_550',axiom,
    ! [Vvar__551] :
      ( c_24__type__550___24t(Vvar__551)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
         => cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(Vvar__551,Vv__CANONICAL__0)) ) ) ).

fof('$_type_5582',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__5583] :
      ( c_24__type__5582___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__5583)
    <=> ! [Vv__CANONICAL__6] :
          ( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__7] :
              ( t(Vv__CANONICAL__7,Vv__CANONICAL__0)
             => t(happ(happ(Vvar__5583,Vv__CANONICAL__6),Vv__CANONICAL__7),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_5621',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__5622] :
      ( c_24__type__5621___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__5622)
    <=> ! [Vv__CANONICAL__6] :
          ( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__7] :
              ( t(Vv__CANONICAL__7,Vv__CANONICAL__0)
             => t(happ(happ(Vvar__5622,Vv__CANONICAL__6),Vv__CANONICAL__7),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_5660',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__5661] :
      ( c_24__type__5660___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__5661)
    <=> ! [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__5661,Vv__CANONICAL__6),Vv__CANONICAL__7)) ) ) ) ).

fof('$_type_580',axiom,
    ! [Vvar__581] :
      ( c_24__type__580___24t(Vvar__581)
    <=> ! [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__581,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_583',axiom,
    ! [Vvar__584] :
      ( c_24__type__583___24t(Vvar__584)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
         => cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(Vvar__584,Vv__CANONICAL__0)) ) ) ).

fof('$_type_591',axiom,
    ! [Vvar__592] :
      ( c_24__type__591___24t(Vvar__592)
    <=> ! [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__592,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_593',axiom,
    ! [Vvar__594] :
      ( c_24__type__593___24t(Vvar__594)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__0)
         => cCoq_2eInit_2eDatatypes_2ebool___24t(happ(Vvar__594,Vv__CANONICAL__0)) ) ) ).

fof('$_type_5931',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,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__5932] :
      ( c_24__type__5931___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,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__5932)
    <=> ! [Vv__CANONICAL__13] :
          ( t(Vv__CANONICAL__13,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__14] :
              ( t(Vv__CANONICAL__14,Vv__CANONICAL__0)
             => t(happ(happ(Vvar__5932,Vv__CANONICAL__13),Vv__CANONICAL__14),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_601',axiom,
    ! [Vvar__602] :
      ( c_24__type__601___24t(Vvar__602)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => cType___24t(happ(Vvar__602,Vv__CANONICAL__0)) ) ) ).

fof('$_type_6056',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,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__6057] :
      ( c_24__type__6056___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,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__6057)
    <=> ! [Vv__CANONICAL__13] :
          ( t(Vv__CANONICAL__13,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__14] :
              ( t(Vv__CANONICAL__14,Vv__CANONICAL__0)
             => t(happ(happ(Vvar__6057,Vv__CANONICAL__13),Vv__CANONICAL__14),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_615',axiom,
    ! [Vvar__616] :
      ( c_24__type__615___24t(Vvar__616)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,happ(Vvar__616,Vv__CANONICAL__0)) ) ) ).

fof('$_type_6181',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,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__6182] :
      ( c_24__type__6181___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,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__6182)
    <=> ! [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__6182,Vv__CANONICAL__13),Vv__CANONICAL__14)) ) ) ) ).

fof('$_type_620',axiom,
    ! [Vvar__621] :
      ( c_24__type__620___24t(Vvar__621)
    <=> ! [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__621,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).

fof('$_type_623',axiom,
    ! [Vvar__624] :
      ( c_24__type__623___24t(Vvar__624)
    <=> ! [Vv__CANONICAL__0] :
          ( cPLF_2eImp_2ebexp___24t(Vv__CANONICAL__0)
         => cPLF_2eImp_2ebexp___24t(happ(Vvar__624,Vv__CANONICAL__0)) ) ) ).

fof('$_type_626',axiom,
    ! [Vvar__627] :
      ( c_24__type__626___24t(Vvar__627)
    <=> ! [Vv__CANONICAL__0] :
          ( cPLF_2eImp_2ebexp___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cPLF_2eImp_2ebexp___24t(Vv__CANONICAL__1)
             => cPLF_2eImp_2ebexp___24t(happ(happ(Vvar__627,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_6306',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,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__6307] :
      ( c_24__type__6306___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,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__6307)
    <=> ! [Vv__CANONICAL__13] :
          ( t(Vv__CANONICAL__13,Vv__CANONICAL__6)
         => ! [Vv__CANONICAL__14] :
              ( t(Vv__CANONICAL__14,Vv__CANONICAL__6)
             => t(happ(happ(Vvar__6307,Vv__CANONICAL__13),Vv__CANONICAL__14),Vv__CANONICAL__6) ) ) ) ).

fof('$_type_6431',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,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__6432] :
      ( c_24__type__6431___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,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__6432)
    <=> ! [Vv__CANONICAL__13] :
          ( t(Vv__CANONICAL__13,Vv__CANONICAL__6)
         => ! [Vv__CANONICAL__14] :
              ( t(Vv__CANONICAL__14,Vv__CANONICAL__6)
             => t(happ(happ(Vvar__6432,Vv__CANONICAL__13),Vv__CANONICAL__14),Vv__CANONICAL__6) ) ) ) ).

fof('$_type_6556',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,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__6557] :
      ( c_24__type__6556___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,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__6557)
    <=> ! [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__6557,Vv__CANONICAL__13),Vv__CANONICAL__14)) ) ) ) ).

fof('$_type_6667',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,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__6668] :
      ( c_24__type__6667___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,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__6668)
    <=> ! [Vv__CANONICAL__13] :
          ( t(Vv__CANONICAL__13,Vv__CANONICAL__6)
         => t(happ(Vvar__6668,Vv__CANONICAL__13),Vv__CANONICAL__0) ) ) ).

fof('$_type_668',axiom,
    ! [Vvar__669] :
      ( c_24__type__668___24t(Vvar__669)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
         => cPLF_2eImp_2esinstr___24t(happ(Vvar__669,Vv__CANONICAL__0)) ) ) ).

fof('$_type_6690',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__6691] :
      ( c_24__type__6690___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__6691)
    <=> ! [Vv__CANONICAL__2] :
          ( t(Vv__CANONICAL__2,Vv__CANONICAL__1)
         => ! [Vv__CANONICAL__3] :
              ( t(Vv__CANONICAL__3,Vv__CANONICAL__1)
             => t(happ(happ(Vvar__6691,Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__1) ) ) ) ).

fof('$_type_670',axiom,
    ! [Vvar__671] :
      ( c_24__type__670___24t(Vvar__671)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eStrings_2eString_2estring___24t(Vv__CANONICAL__0)
         => cPLF_2eImp_2esinstr___24t(happ(Vvar__671,Vv__CANONICAL__0)) ) ) ).

fof('$_type_6702',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__6703] :
      ( c_24__type__6702___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__6703)
    <=> ! [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__6703,Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ).

fof('$_type_6721',axiom,
    ! [Vvar__6722] :
      ( c_24__type__6721___24t(Vvar__6722)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
             => t(happ(happ(Vvar__6722,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_6732',axiom,
    ! [Vvar__6733] :
      ( c_24__type__6732___24t(Vvar__6733)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( c_24__type__3514___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__6733,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__0) ) ) ) ) ) ).

fof('$_type_6755',axiom,
    ! [Vvar__6756] :
      ( c_24__type__6755___24t(Vvar__6756)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cType___24t(Vv__CANONICAL__1)
             => ! [Vv__CANONICAL__2] :
                  ( c_24__type__2863___24t(Vv__CANONICAL__1,Vv__CANONICAL__2)
                 => ! [Vv__CANONICAL__3] :
                      ( c_24__type__6765___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__3)
                     => cProp___24t(happ(happ(happ(happ(Vvar__6756,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).

fof('$_type_6765',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__6766] :
      ( c_24__type__6765___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__6766)
    <=> ! [Vv__CANONICAL__2] :
          ( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__3] :
              ( t(Vv__CANONICAL__3,Vv__CANONICAL__1)
             => t(happ(happ(Vvar__6766,Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__1) ) ) ) ).

fof('$_type_6791',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__6792] :
      ( c_24__type__6791___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__6792)
    <=> ! [Vv__CANONICAL__2] :
          ( t(Vv__CANONICAL__2,Vv__CANONICAL__1)
         => t(happ(Vvar__6792,Vv__CANONICAL__2),Vv__CANONICAL__1) ) ) ).

fof('$_type_6855',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__6856] :
      ( c_24__type__6855___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__6856)
    <=> ! [Vv__CANONICAL__2] :
          ( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
         => cProp___24t(happ(Vvar__6856,Vv__CANONICAL__2)) ) ) ).

fof('$_type_6861',axiom,
    ! [Vvar__6862] :
      ( c_24__type__6861___24t(Vvar__6862)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( c_24__type__3735___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__6862,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__0) ) ) ) ) ).

fof('$_type_6865',axiom,
    ! [Vvar__6866] :
      ( c_24__type__6865___24t(Vvar__6866)
    <=> ! [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__6866,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_6935',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__6936] :
      ( c_24__type__6935___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__6936)
    <=> ! [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__6936,Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ).

fof('$_type_6983',axiom,
    ! [Vvar__6984] :
      ( c_24__type__6983___24t(Vvar__6984)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
         => cPLF_2eImp_2eAExp_2eaexp___24t(happ(Vvar__6984,Vv__CANONICAL__0)) ) ) ).

fof('$_type_6986',axiom,
    ! [Vvar__6987] :
      ( c_24__type__6986___24t(Vvar__6987)
    <=> ! [Vv__CANONICAL__0] :
          ( cPLF_2eImp_2eAExp_2eaexp___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cPLF_2eImp_2eAExp_2eaexp___24t(Vv__CANONICAL__1)
             => cPLF_2eImp_2eAExp_2eaexp___24t(happ(happ(Vvar__6987,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_7004',axiom,
    ! [Vvar__7005] :
      ( c_24__type__7004___24t(Vvar__7005)
    <=> ! [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__7005,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).

fof('$_type_7022',axiom,
    ! [Vvar__7023] :
      ( c_24__type__7022___24t(Vvar__7023)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__0)
         => cCoq_2eInit_2eDatatypes_2enat___24t(happ(Vvar__7023,Vv__CANONICAL__0)) ) ) ).

fof('$_type_7026',axiom,
    ! [Vvar__7027] :
      ( c_24__type__7026___24t(Vvar__7027)
    <=> ! [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__7027,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_7041',axiom,
    ! [Vvar__7042] :
      ( c_24__type__7041___24t(Vvar__7042)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
             => ! [Vv__CANONICAL__2] :
                  ( c_24__type__7046___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
                 => ! [Vv__CANONICAL__3] :
                      ( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__3)
                     => t(happ(happ(happ(happ(Vvar__7042,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__0) ) ) ) ) ) ).

fof('$_type_7046',axiom,
    ! [Vv__CANONICAL__0,Vvar__7047] :
      ( c_24__type__7046___24t(Vv__CANONICAL__0,Vvar__7047)
    <=> ! [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__7047,Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_7054',axiom,
    ! [Vvar__7055] :
      ( c_24__type__7054___24t(Vvar__7055)
    <=> ! [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__7055,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).

fof('$_type_7083',axiom,
    ! [Vvar__7084] :
      ( c_24__type__7083___24t(Vvar__7084)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( c_24__type__3514___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__7084,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__0) ) ) ) ) ) ).

fof('$_type_7089',axiom,
    ! [Vvar__7090] :
      ( c_24__type__7089___24t(Vvar__7090)
    <=> ! [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__7090,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_7124',axiom,
    ! [Vvar__7125] :
      ( c_24__type__7124___24t(Vvar__7125)
    <=> ! [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__7125,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_7201',axiom,
    ! [Vvar__7202] :
      ( c_24__type__7201___24t(Vvar__7202)
    <=> ! [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__7202,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_7208',axiom,
    ! [Vvar__7209] :
      ( c_24__type__7208___24t(Vvar__7209)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
         => cCoq_2eNumbers_2eBinNums_2eN___24t(happ(Vvar__7209,Vv__CANONICAL__0)) ) ) ).

fof('$_type_7211',axiom,
    ! [Vvar__7212] :
      ( c_24__type__7211___24t(Vvar__7212)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__0)
         => cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(Vvar__7212,Vv__CANONICAL__0)) ) ) ).

fof('$_type_7323',axiom,
    ! [Vvar__7324] :
      ( c_24__type__7323___24t(Vvar__7324)
    <=> ! [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__7324,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_7469',axiom,
    ! [Vvar__7470] :
      ( c_24__type__7469___24t(Vvar__7470)
    <=> ! [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__7470,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_762',axiom,
    ! [Vvar__763] :
      ( c_24__type__762___24t(Vvar__763)
    <=> ! [Vv__CANONICAL__0] :
          ( cPLF_2eImp_2eBreakImp_2ecom___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cPLF_2eImp_2eBreakImp_2ecom___24t(Vv__CANONICAL__1)
             => cPLF_2eImp_2eBreakImp_2ecom___24t(happ(happ(Vvar__763,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_80524',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__80525] :
      ( c_24__type__80524___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__80525)
    <=> ! [Vv__CANONICAL__2] :
          ( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
         => t(happ(Vvar__80525,Vv__CANONICAL__2),Vv__CANONICAL__1) ) ) ).

fof('$_type_83121',axiom,
    ! [Vvar__83122] :
      ( c_24__type__83121___24t(Vvar__83122)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__0)
         => cCoq_2ePArith_2eBinPosDef_2ePos_2emask___24t(happ(Vvar__83122,Vv__CANONICAL__0)) ) ) ).

fof('$_type_83174',axiom,
    ! [Vvar__83175] :
      ( c_24__type__83174___24t(Vvar__83175)
    <=> ! [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__83175,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_83204',axiom,
    ! [Vvar__83205] :
      ( c_24__type__83204___24t(Vvar__83205)
    <=> ! [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__83205,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_83633',axiom,
    ! [Vvar__83634] :
      ( c_24__type__83633___24t(Vvar__83634)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
         => cPLF_2eImp_2eaevalR__extended_2eaexp___24t(happ(Vvar__83634,Vv__CANONICAL__0)) ) ) ).

fof('$_type_83636',axiom,
    ! [Vvar__83637] :
      ( c_24__type__83636___24t(Vvar__83637)
    <=> ! [Vv__CANONICAL__0] :
          ( cPLF_2eImp_2eaevalR__extended_2eaexp___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cPLF_2eImp_2eaevalR__extended_2eaexp___24t(Vv__CANONICAL__1)
             => cPLF_2eImp_2eaevalR__extended_2eaexp___24t(happ(happ(Vvar__83637,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_84269',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__84270] :
      ( c_24__type__84269___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__84270)
    <=> ! [Vv__CANONICAL__5] :
          ( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__5)
         => cProp___24t(happ(Vvar__84270,Vv__CANONICAL__5)) ) ) ).

fof('$_type_84277',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__84278] :
      ( c_24__type__84277___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__84278)
    <=> ! [Vv__CANONICAL__5] :
          ( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__5)
         => cProp___24t(happ(Vvar__84278,Vv__CANONICAL__5)) ) ) ).

fof('$_type_84288',axiom,
    ! [Vvar__84289] :
      ( c_24__type__84288___24t(Vvar__84289)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( c_24__type__2863___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
             => cProp___24t(happ(happ(Vvar__84289,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_84433',axiom,
    ! [Vvar__84434] :
      ( c_24__type__84433___24t(Vvar__84434)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eInit_2eDatatypes_2ecomparison___24t(Vv__CANONICAL__0)
         => cCoq_2eInit_2eDatatypes_2ecomparison___24t(happ(Vvar__84434,Vv__CANONICAL__0)) ) ) ).

fof('$_type_85043',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__85044] :
      ( c_24__type__85043___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__85044)
    <=> ! [Vv__CANONICAL__4] :
          ( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
         => cProp___24t(happ(Vvar__85044,Vv__CANONICAL__4)) ) ) ).

fof('$_type_85114',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__85115] :
      ( c_24__type__85114___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__85115)
    <=> ! [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__85115,Vv__CANONICAL__6),Vv__CANONICAL__7)) ) ) ) ).

fof('$_type_85245',axiom,
    ! [Vvar__85246] :
      ( c_24__type__85245___24t(Vvar__85246)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__0)
         => cProp___24t(happ(Vvar__85246,Vv__CANONICAL__0)) ) ) ).

fof('$_type_85274',axiom,
    ! [Vvar__85275] :
      ( c_24__type__85274___24t(Vvar__85275)
    <=> ! [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__85275,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).

fof('$_type_85364',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__85365] :
      ( c_24__type__85364___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__85365)
    <=> ! [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__85365,Vv__CANONICAL__4),Vv__CANONICAL__5)) ) ) ) ).

fof('$_type_868',axiom,
    ! [Vvar__869] :
      ( c_24__type__868___24t(Vvar__869)
    <=> ! [Vv__CANONICAL__0] :
          ( cPLF_2eHoare_2eHimp_2ecom___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cPLF_2eHoare_2eHimp_2ecom___24t(Vv__CANONICAL__1)
             => cPLF_2eHoare_2eHimp_2ecom___24t(happ(happ(Vvar__869,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_878',axiom,
    ! [Vvar__879] :
      ( c_24__type__878___24t(Vvar__879)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eStrings_2eString_2estring___24t(Vv__CANONICAL__0)
         => cPLF_2eHoare_2eHimp_2ecom___24t(happ(Vvar__879,Vv__CANONICAL__0)) ) ) ).

fof('$_type_88324',axiom,
    ! [Vvar__88325] :
      ( c_24__type__88324___24t(Vvar__88325)
    <=> ! [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__88325,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_9',axiom,
    ! [Vvar__10] :
      ( c_24__type__9___24t(Vvar__10)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
         => cCoq_2eInit_2eDatatypes_2enat___24t(happ(Vvar__10,Vv__CANONICAL__0)) ) ) ).

fof('$_type_98',axiom,
    ! [Vvar__99] :
      ( c_24__type__98___24t(Vvar__99)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
         => cPLF_2eImp_2eaexp___24t(happ(Vvar__99,Vv__CANONICAL__0)) ) ) ).

fof('$_typeof_Coq.Arith.Between.in_int',axiom,
    c_24__type__7054___24t(cCoq_2eArith_2eBetween_2ein__int) ).

fof('$_typeof_Coq.Arith.EqNat.eq_nat',axiom,
    c_24__type__528___24t(cCoq_2eArith_2eEqNat_2eeq__nat) ).

fof('$_typeof_Coq.Arith.PeanoNat.Nat.b2n',axiom,
    c_24__type__4338___24t(cCoq_2eArith_2ePeanoNat_2eNat_2eb2n) ).

fof('$_typeof_Coq.Arith.PeanoNat.Nat.divide',axiom,
    c_24__type__528___24t(cCoq_2eArith_2ePeanoNat_2eNat_2edivide) ).

fof('$_typeof_Coq.Arith.PeanoNat.Nat.eq',axiom,
    c_24__type__528___24t(cCoq_2eArith_2ePeanoNat_2eNat_2eeq) ).

fof('$_typeof_Coq.Arith.PeanoNat.Nat.eqf',axiom,
    c_24__type__1551___24t(cCoq_2eArith_2ePeanoNat_2eNat_2eeqf) ).

fof('$_typeof_Coq.Arith.PeanoNat.Nat.le',axiom,
    c_24__type__528___24t(cCoq_2eArith_2ePeanoNat_2eNat_2ele) ).

fof('$_typeof_Coq.Arith.PeanoNat.Nat.lt',axiom,
    c_24__type__528___24t(cCoq_2eArith_2ePeanoNat_2eNat_2elt) ).

fof('$_typeof_Coq.Arith.PeanoNat.Nat.recursion',axiom,
    c_24__type__7041___24t(cCoq_2eArith_2ePeanoNat_2eNat_2erecursion) ).

fof('$_typeof_Coq.Arith.Plus.tail_plus',axiom,
    c_24__type__329___24t(cCoq_2eArith_2ePlus_2etail__plus) ).

fof('$_typeof_Coq.Arith.Wf_nat.gtof',axiom,
    c_24__type__135834___24t(cCoq_2eArith_2eWf__nat_2egtof) ).

fof('$_typeof_Coq.Arith.Wf_nat.ltof',axiom,
    c_24__type__135834___24t(cCoq_2eArith_2eWf__nat_2eltof) ).

fof('$_typeof_Coq.Bool.Bool.Is_true',axiom,
    c_24__type__145711___24t(cCoq_2eBool_2eBool_2eIs__true) ).

fof('$_typeof_Coq.Bool.Bool.eqb',axiom,
    c_24__type__591___24t(cCoq_2eBool_2eBool_2eeqb) ).

fof('$_typeof_Coq.Bool.Bool.ifb',axiom,
    c_24__type__145716___24t(cCoq_2eBool_2eBool_2eifb) ).

fof('$_typeof_Coq.Bool.Bool.reflect',axiom,
    c_24__type__4953___24t(cCoq_2eBool_2eBool_2ereflect) ).

fof('$_typeof_Coq.Bool.Bvector.Bvector',axiom,
    c_24__type__1873___24t(cCoq_2eBool_2eBvector_2eBvector) ).

fof('$_typeof_Coq.Bool.Zerob.zerob',axiom,
    c_24__type__1547___24t(cCoq_2eBool_2eZerob_2ezerob) ).

fof('$_typeof_Coq.FSets.FSetPositive.PositiveSet.Equal',axiom,
    c_24__type__7201___24t(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eEqual) ).

fof('$_typeof_Coq.FSets.FSetPositive.PositiveSet.In',axiom,
    c_24__type__4433___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__136028___24t(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eNode) ).

fof('$_typeof_Coq.FSets.FSetPositive.PositiveSet.Subset',axiom,
    c_24__type__7201___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__7201___24t(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eeq) ).

fof('$_typeof_Coq.FSets.FSetPositive.PositiveSet.mem',axiom,
    c_24__type__7124___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__145718___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__84433___24t(cCoq_2eInit_2eDatatypes_2eCompOpp) ).

fof('$_typeof_Coq.Init.Datatypes.CompareSpecT',axiom,
    c_24__type__85274___24t(cCoq_2eInit_2eDatatypes_2eCompareSpecT) ).

fof('$_typeof_Coq.Init.Datatypes.Empty_set',axiom,
    cType___24t(cCoq_2eInit_2eDatatypes_2eEmpty__set) ).

fof('$_typeof_Coq.Init.Datatypes.Eq',axiom,
    cCoq_2eInit_2eDatatypes_2ecomparison___24t(cCoq_2eInit_2eDatatypes_2eEq) ).

fof('$_typeof_Coq.Init.Datatypes.Gt',axiom,
    cCoq_2eInit_2eDatatypes_2ecomparison___24t(cCoq_2eInit_2eDatatypes_2eGt) ).

fof('$_typeof_Coq.Init.Datatypes.ID',axiom,
    cType___24t(cCoq_2eInit_2eDatatypes_2eID) ).

fof('$_typeof_Coq.Init.Datatypes.IDProp',axiom,
    cProp___24t(cCoq_2eInit_2eDatatypes_2eIDProp) ).

fof('$_typeof_Coq.Init.Datatypes.Lt',axiom,
    cCoq_2eInit_2eDatatypes_2ecomparison___24t(cCoq_2eInit_2eDatatypes_2eLt) ).

fof('$_typeof_Coq.Init.Datatypes.None',axiom,
    c_24__type__5013___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__9___24t(cCoq_2eInit_2eDatatypes_2eS) ).

fof('$_typeof_Coq.Init.Datatypes.Some',axiom,
    c_24__type__5011___24t(cCoq_2eInit_2eDatatypes_2eSome) ).

fof('$_typeof_Coq.Init.Datatypes.andb',axiom,
    c_24__type__591___24t(cCoq_2eInit_2eDatatypes_2eandb) ).

fof('$_typeof_Coq.Init.Datatypes.app',axiom,
    c_24__type__5025___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__620___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__1916___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__591___24t(cCoq_2eInit_2eDatatypes_2eimplb) ).

fof('$_typeof_Coq.Init.Datatypes.inl',axiom,
    c_24__type__152498___24t(cCoq_2eInit_2eDatatypes_2einl) ).

fof('$_typeof_Coq.Init.Datatypes.inr',axiom,
    c_24__type__152503___24t(cCoq_2eInit_2eDatatypes_2einr) ).

fof('$_typeof_Coq.Init.Datatypes.length',axiom,
    c_24__type__1944___24t(cCoq_2eInit_2eDatatypes_2elength) ).

fof('$_typeof_Coq.Init.Datatypes.list',axiom,
    c_24__type__601___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__1871___24t(cCoq_2eInit_2eDatatypes_2enat__rect) ).

fof('$_typeof_Coq.Init.Datatypes.negb',axiom,
    c_24__type__593___24t(cCoq_2eInit_2eDatatypes_2enegb) ).

fof('$_typeof_Coq.Init.Datatypes.nil',axiom,
    c_24__type__615___24t(cCoq_2eInit_2eDatatypes_2enil) ).

fof('$_typeof_Coq.Init.Datatypes.option',axiom,
    c_24__type__601___24t(cCoq_2eInit_2eDatatypes_2eoption) ).

fof('$_typeof_Coq.Init.Datatypes.orb',axiom,
    c_24__type__591___24t(cCoq_2eInit_2eDatatypes_2eorb) ).

fof('$_typeof_Coq.Init.Datatypes.pair',axiom,
    c_24__type__1904___24t(cCoq_2eInit_2eDatatypes_2epair) ).

fof('$_typeof_Coq.Init.Datatypes.prod',axiom,
    c_24__type__1888___24t(cCoq_2eInit_2eDatatypes_2eprod) ).

fof('$_typeof_Coq.Init.Datatypes.snd',axiom,
    c_24__type__1928___24t(cCoq_2eInit_2eDatatypes_2esnd) ).

fof('$_typeof_Coq.Init.Datatypes.sum',axiom,
    c_24__type__1888___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__591___24t(cCoq_2eInit_2eDatatypes_2exorb) ).

fof('$_typeof_Coq.Init.Decimal.D0',axiom,
    c_24__type__124022___24t(cCoq_2eInit_2eDecimal_2eD0) ).

fof('$_typeof_Coq.Init.Decimal.D1',axiom,
    c_24__type__124022___24t(cCoq_2eInit_2eDecimal_2eD1) ).

fof('$_typeof_Coq.Init.Decimal.D2',axiom,
    c_24__type__124022___24t(cCoq_2eInit_2eDecimal_2eD2) ).

fof('$_typeof_Coq.Init.Decimal.D3',axiom,
    c_24__type__124022___24t(cCoq_2eInit_2eDecimal_2eD3) ).

fof('$_typeof_Coq.Init.Decimal.D4',axiom,
    c_24__type__124022___24t(cCoq_2eInit_2eDecimal_2eD4) ).

fof('$_typeof_Coq.Init.Decimal.D5',axiom,
    c_24__type__124022___24t(cCoq_2eInit_2eDecimal_2eD5) ).

fof('$_typeof_Coq.Init.Decimal.D6',axiom,
    c_24__type__124022___24t(cCoq_2eInit_2eDecimal_2eD6) ).

fof('$_typeof_Coq.Init.Decimal.D7',axiom,
    c_24__type__124022___24t(cCoq_2eInit_2eDecimal_2eD7) ).

fof('$_typeof_Coq.Init.Decimal.D8',axiom,
    c_24__type__124022___24t(cCoq_2eInit_2eDecimal_2eD8) ).

fof('$_typeof_Coq.Init.Decimal.D9',axiom,
    c_24__type__124022___24t(cCoq_2eInit_2eDecimal_2eD9) ).

fof('$_typeof_Coq.Init.Decimal.Neg',axiom,
    c_24__type__124024___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__124024___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__119461___24t(cCoq_2eInit_2eDecimal_2eint__of__int) ).

fof('$_typeof_Coq.Init.Decimal.nzhead',axiom,
    c_24__type__124022___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__124022___24t(cCoq_2eInit_2eDecimal_2euint__of__uint) ).

fof('$_typeof_Coq.Init.Logic_Type.notT',axiom,
    c_24__type__147249___24t(cCoq_2eInit_2eLogic__Type_2enotT) ).

fof('$_typeof_Coq.Init.Nat.add',axiom,
    c_24__type__329___24t(cCoq_2eInit_2eNat_2eadd) ).

fof('$_typeof_Coq.Init.Nat.compare',axiom,
    c_24__type__2671___24t(cCoq_2eInit_2eNat_2ecompare) ).

fof('$_typeof_Coq.Init.Nat.div2',axiom,
    c_24__type__9___24t(cCoq_2eInit_2eNat_2ediv2) ).

fof('$_typeof_Coq.Init.Nat.double',axiom,
    c_24__type__9___24t(cCoq_2eInit_2eNat_2edouble) ).

fof('$_typeof_Coq.Init.Nat.eqb',axiom,
    c_24__type__337___24t(cCoq_2eInit_2eNat_2eeqb) ).

fof('$_typeof_Coq.Init.Nat.even',axiom,
    c_24__type__1547___24t(cCoq_2eInit_2eNat_2eeven) ).

fof('$_typeof_Coq.Init.Nat.leb',axiom,
    c_24__type__337___24t(cCoq_2eInit_2eNat_2eleb) ).

fof('$_typeof_Coq.Init.Nat.log2_iter',axiom,
    c_24__type__14695___24t(cCoq_2eInit_2eNat_2elog2__iter) ).

fof('$_typeof_Coq.Init.Nat.max',axiom,
    c_24__type__329___24t(cCoq_2eInit_2eNat_2emax) ).

fof('$_typeof_Coq.Init.Nat.min',axiom,
    c_24__type__329___24t(cCoq_2eInit_2eNat_2emin) ).

fof('$_typeof_Coq.Init.Nat.mul',axiom,
    c_24__type__329___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__329___24t(cCoq_2eInit_2eNat_2epow) ).

fof('$_typeof_Coq.Init.Nat.pred',axiom,
    c_24__type__9___24t(cCoq_2eInit_2eNat_2epred) ).

fof('$_typeof_Coq.Init.Nat.sqrt_iter',axiom,
    c_24__type__14695___24t(cCoq_2eInit_2eNat_2esqrt__iter) ).

fof('$_typeof_Coq.Init.Nat.square',axiom,
    c_24__type__9___24t(cCoq_2eInit_2eNat_2esquare) ).

fof('$_typeof_Coq.Init.Nat.sub',axiom,
    c_24__type__329___24t(cCoq_2eInit_2eNat_2esub) ).

fof('$_typeof_Coq.Init.Nat.succ',axiom,
    c_24__type__9___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__329___24t(cCoq_2eInit_2eNat_2etail__add) ).

fof('$_typeof_Coq.Init.Nat.testbit',axiom,
    c_24__type__337___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__1856___24t(cCoq_2eInit_2ePeano_2eIsSucc) ).

fof('$_typeof_Coq.Init.Peano.ge',axiom,
    c_24__type__528___24t(cCoq_2eInit_2ePeano_2ege) ).

fof('$_typeof_Coq.Init.Peano.gt',axiom,
    c_24__type__528___24t(cCoq_2eInit_2ePeano_2egt) ).

fof('$_typeof_Coq.Init.Peano.lt',axiom,
    c_24__type__528___24t(cCoq_2eInit_2ePeano_2elt) ).

fof('$_typeof_Coq.Init.Specif.Exc',axiom,
    c_24__type__601___24t(cCoq_2eInit_2eSpecif_2eExc) ).

fof('$_typeof_Coq.Init.Specif.except',axiom,
    c_24__type__149168___24t(cCoq_2eInit_2eSpecif_2eexcept) ).

fof('$_typeof_Coq.Init.Specif.exist',axiom,
    c_24__type__3752___24t(cCoq_2eInit_2eSpecif_2eexist) ).

fof('$_typeof_Coq.Init.Specif.existT',axiom,
    c_24__type__139681___24t(cCoq_2eInit_2eSpecif_2eexistT) ).

fof('$_typeof_Coq.Init.Specif.inleft',axiom,
    c_24__type__3828___24t(cCoq_2eInit_2eSpecif_2einleft) ).

fof('$_typeof_Coq.Init.Specif.inright',axiom,
    c_24__type__3833___24t(cCoq_2eInit_2eSpecif_2einright) ).

fof('$_typeof_Coq.Init.Specif.left',axiom,
    c_24__type__3788___24t(cCoq_2eInit_2eSpecif_2eleft) ).

fof('$_typeof_Coq.Init.Specif.proj1_sig',axiom,
    c_24__type__6861___24t(cCoq_2eInit_2eSpecif_2eproj1__sig) ).

fof('$_typeof_Coq.Init.Specif.projT1',axiom,
    c_24__type__139760___24t(cCoq_2eInit_2eSpecif_2eprojT1) ).

fof('$_typeof_Coq.Init.Specif.right',axiom,
    c_24__type__3793___24t(cCoq_2eInit_2eSpecif_2eright) ).

fof('$_typeof_Coq.Init.Specif.sig',axiom,
    c_24__type__3732___24t(cCoq_2eInit_2eSpecif_2esig) ).

fof('$_typeof_Coq.Init.Specif.sig2',axiom,
    c_24__type__149151___24t(cCoq_2eInit_2eSpecif_2esig2) ).

fof('$_typeof_Coq.Init.Specif.sigT',axiom,
    c_24__type__139661___24t(cCoq_2eInit_2eSpecif_2esigT) ).

fof('$_typeof_Coq.Init.Specif.sigT2',axiom,
    c_24__type__139724___24t(cCoq_2eInit_2eSpecif_2esigT2) ).

fof('$_typeof_Coq.Init.Specif.sumbool',axiom,
    c_24__type__3765___24t(cCoq_2eInit_2eSpecif_2esumbool) ).

fof('$_typeof_Coq.Init.Specif.sumor',axiom,
    c_24__type__3805___24t(cCoq_2eInit_2eSpecif_2esumor) ).

fof('$_typeof_Coq.Init.Wf.well_founded',axiom,
    c_24__type__84288___24t(cCoq_2eInit_2eWf_2ewell__founded) ).

fof('$_typeof_Coq.Lists.List.In',axiom,
    c_24__type__2576___24t(cCoq_2eLists_2eList_2eIn) ).

fof('$_typeof_Coq.Lists.List.fold_left',axiom,
    c_24__type__5081___24t(cCoq_2eLists_2eList_2efold__left) ).

fof('$_typeof_Coq.Lists.List.fold_right',axiom,
    c_24__type__125073___24t(cCoq_2eLists_2eList_2efold__right) ).

fof('$_typeof_Coq.Lists.List.hd',axiom,
    c_24__type__147115___24t(cCoq_2eLists_2eList_2ehd) ).

fof('$_typeof_Coq.Lists.List.last',axiom,
    c_24__type__152555___24t(cCoq_2eLists_2eList_2elast) ).

fof('$_typeof_Coq.Lists.List.nth',axiom,
    c_24__type__5057___24t(cCoq_2eLists_2eList_2enth) ).

fof('$_typeof_Coq.Lists.List.tl',axiom,
    c_24__type__7323___24t(cCoq_2eLists_2eList_2etl) ).

fof('$_typeof_Coq.Lists.SetoidList.transpose',axiom,
    c_24__type__6755___24t(cCoq_2eLists_2eSetoidList_2etranspose) ).

fof('$_typeof_Coq.Lists.SetoidList.transpose2',axiom,
    c_24__type__6755___24t(cCoq_2eLists_2eSetoidList_2etranspose2) ).

fof('$_typeof_Coq.Lists.SetoidList.transpose_restr',axiom,
    c_24__type__148893___24t(cCoq_2eLists_2eSetoidList_2etranspose__restr) ).

fof('$_typeof_Coq.Lists.SetoidList.transpose_restr2',axiom,
    c_24__type__148893___24t(cCoq_2eLists_2eSetoidList_2etranspose__restr2) ).

fof('$_typeof_Coq.Logic.Decidable.decidable',axiom,
    c_24__type__1963___24t(cCoq_2eLogic_2eDecidable_2edecidable) ).

fof('$_typeof_Coq.Logic.EqdepFacts.UIP_on_',axiom,
    c_24__type__152531___24t(cCoq_2eLogic_2eEqdepFacts_2eUIP__on__) ).

fof('$_typeof_Coq.NArith.BinNat.N.divide',axiom,
    c_24__type__7026___24t(cCoq_2eNArith_2eBinNat_2eN_2edivide) ).

fof('$_typeof_Coq.NArith.BinNat.N.eq',axiom,
    c_24__type__7026___24t(cCoq_2eNArith_2eBinNat_2eN_2eeq) ).

fof('$_typeof_Coq.NArith.BinNat.N.eqf',axiom,
    c_24__type__149942___24t(cCoq_2eNArith_2eBinNat_2eN_2eeqf) ).

fof('$_typeof_Coq.NArith.BinNat.N.le',axiom,
    c_24__type__7026___24t(cCoq_2eNArith_2eBinNat_2eN_2ele) ).

fof('$_typeof_Coq.NArith.BinNat.N.lt',axiom,
    c_24__type__7026___24t(cCoq_2eNArith_2eBinNat_2eN_2elt) ).

fof('$_typeof_Coq.NArith.BinNat.N.recursion',axiom,
    c_24__type__152866___24t(cCoq_2eNArith_2eBinNat_2eN_2erecursion) ).

fof('$_typeof_Coq.NArith.BinNatDef.N.add',axiom,
    c_24__type__4125___24t(cCoq_2eNArith_2eBinNatDef_2eN_2eadd) ).

fof('$_typeof_Coq.NArith.BinNatDef.N.div2',axiom,
    c_24__type__5412___24t(cCoq_2eNArith_2eBinNatDef_2eN_2ediv2) ).

fof('$_typeof_Coq.NArith.BinNatDef.N.double',axiom,
    c_24__type__5412___24t(cCoq_2eNArith_2eBinNatDef_2eN_2edouble) ).

fof('$_typeof_Coq.NArith.BinNatDef.N.eqb',axiom,
    c_24__type__4139___24t(cCoq_2eNArith_2eBinNatDef_2eN_2eeqb) ).

fof('$_typeof_Coq.NArith.BinNatDef.N.even',axiom,
    c_24__type__123915___24t(cCoq_2eNArith_2eBinNatDef_2eN_2eeven) ).

fof('$_typeof_Coq.NArith.BinNatDef.N.lxor',axiom,
    c_24__type__4125___24t(cCoq_2eNArith_2eBinNatDef_2eN_2elxor) ).

fof('$_typeof_Coq.NArith.BinNatDef.N.max',axiom,
    c_24__type__4125___24t(cCoq_2eNArith_2eBinNatDef_2eN_2emax) ).

fof('$_typeof_Coq.NArith.BinNatDef.N.min',axiom,
    c_24__type__4125___24t(cCoq_2eNArith_2eBinNatDef_2eN_2emin) ).

fof('$_typeof_Coq.NArith.BinNatDef.N.mul',axiom,
    c_24__type__4125___24t(cCoq_2eNArith_2eBinNatDef_2eN_2emul) ).

fof('$_typeof_Coq.NArith.BinNatDef.N.pred',axiom,
    c_24__type__5412___24t(cCoq_2eNArith_2eBinNatDef_2eN_2epred) ).

fof('$_typeof_Coq.NArith.BinNatDef.N.succ',axiom,
    c_24__type__5412___24t(cCoq_2eNArith_2eBinNatDef_2eN_2esucc) ).

fof('$_typeof_Coq.NArith.BinNatDef.N.succ_pos',axiom,
    c_24__type__155453___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__4139___24t(cCoq_2eNArith_2eBinNatDef_2eN_2etestbit) ).

fof('$_typeof_Coq.NArith.BinNatDef.N.to_nat',axiom,
    c_24__type__7022___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__1551___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__1781___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__233___24t(cCoq_2eNumbers_2eBinNums_2eZneg) ).

fof('$_typeof_Coq.Numbers.BinNums.Zpos',axiom,
    c_24__type__233___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__220___24t(cCoq_2eNumbers_2eBinNums_2exI) ).

fof('$_typeof_Coq.Numbers.BinNums.xO',axiom,
    c_24__type__220___24t(cCoq_2eNumbers_2eBinNums_2exO) ).

fof('$_typeof_Coq.PArith.BinPos.Pos.PeanoView',axiom,
    c_24__type__145158___24t(cCoq_2ePArith_2eBinPos_2ePos_2ePeanoView) ).

fof('$_typeof_Coq.PArith.BinPos.Pos.eq',axiom,
    c_24__type__7089___24t(cCoq_2ePArith_2eBinPos_2ePos_2eeq) ).

fof('$_typeof_Coq.PArith.BinPos.Pos.lt',axiom,
    c_24__type__7089___24t(cCoq_2ePArith_2eBinPos_2ePos_2elt) ).

fof('$_typeof_Coq.PArith.BinPos.Pos.switch_Eq',axiom,
    c_24__type__155388___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__83121___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2eIsPos) ).

fof('$_typeof_Coq.PArith.BinPosDef.Pos.compare',axiom,
    c_24__type__4389___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare) ).

fof('$_typeof_Coq.PArith.BinPosDef.Pos.div2',axiom,
    c_24__type__220___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2ediv2) ).

fof('$_typeof_Coq.PArith.BinPosDef.Pos.eqb',axiom,
    c_24__type__83174___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2eeqb) ).

fof('$_typeof_Coq.PArith.BinPosDef.Pos.iter',axiom,
    c_24__type__136016___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2eiter) ).

fof('$_typeof_Coq.PArith.BinPosDef.Pos.iter_op',axiom,
    c_24__type__7083___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__4380___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2emax) ).

fof('$_typeof_Coq.PArith.BinPosDef.Pos.min',axiom,
    c_24__type__4380___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2emin) ).

fof('$_typeof_Coq.PArith.BinPosDef.Pos.mul',axiom,
    c_24__type__4380___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2emul) ).

fof('$_typeof_Coq.PArith.BinPosDef.Pos.of_nat',axiom,
    c_24__type__4398___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2eof__nat) ).

fof('$_typeof_Coq.PArith.BinPosDef.Pos.of_succ_nat',axiom,
    c_24__type__4398___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2eof__succ__nat) ).

fof('$_typeof_Coq.PArith.BinPosDef.Pos.size',axiom,
    c_24__type__220___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2esize) ).

fof('$_typeof_Coq.PArith.BinPosDef.Pos.size_nat',axiom,
    c_24__type__4391___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2esize__nat) ).

fof('$_typeof_Coq.PArith.BinPosDef.Pos.sub',axiom,
    c_24__type__4380___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2esub) ).

fof('$_typeof_Coq.PArith.BinPosDef.Pos.succ',axiom,
    c_24__type__220___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__83204___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__126242___24t(cCoq_2eQArith_2eQArith__base_2eQden) ).

fof('$_typeof_Coq.QArith.QArith_base.Qmake',axiom,
    c_24__type__126232___24t(cCoq_2eQArith_2eQArith__base_2eQmake) ).

fof('$_typeof_Coq.QArith.QArith_base.Qnum',axiom,
    c_24__type__126237___24t(cCoq_2eQArith_2eQArith__base_2eQnum) ).

fof('$_typeof_Coq.Reals.RIneq.Rsqr',axiom,
    c_24__type__2846___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__2858___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__2853___24t(cCoq_2eReals_2eRdefinitions_2eRge) ).

fof('$_typeof_Coq.Reals.Rdefinitions.Rgt',axiom,
    c_24__type__2853___24t(cCoq_2eReals_2eRdefinitions_2eRgt) ).

fof('$_typeof_Coq.Reals.Rdefinitions.Rinv',axiom,
    c_24__type__2846___24t(cCoq_2eReals_2eRdefinitions_2eRinv) ).

fof('$_typeof_Coq.Reals.Rdefinitions.Rle',axiom,
    c_24__type__2853___24t(cCoq_2eReals_2eRdefinitions_2eRle) ).

fof('$_typeof_Coq.Reals.Rdefinitions.Rlt',axiom,
    c_24__type__2853___24t(cCoq_2eReals_2eRdefinitions_2eRlt) ).

fof('$_typeof_Coq.Reals.Rdefinitions.Rmult',axiom,
    c_24__type__2849___24t(cCoq_2eReals_2eRdefinitions_2eRmult) ).

fof('$_typeof_Coq.Reals.Rdefinitions.Ropp',axiom,
    c_24__type__2846___24t(cCoq_2eReals_2eRdefinitions_2eRopp) ).

fof('$_typeof_Coq.Reals.Rdefinitions.Rplus',axiom,
    c_24__type__2849___24t(cCoq_2eReals_2eRdefinitions_2eRplus) ).

fof('$_typeof_Coq.Reals.Rdefinitions.up',axiom,
    c_24__type__126244___24t(cCoq_2eReals_2eRdefinitions_2eup) ).

fof('$_typeof_Coq.Reals.Rfunctions.Z_spec',axiom,
    c_24__type__126302___24t(cCoq_2eReals_2eRfunctions_2eZ__spec) ).

fof('$_typeof_Coq.Relations.Relation_Definitions.relation',axiom,
    c_24__type__601___24t(cCoq_2eRelations_2eRelation__Definitions_2erelation) ).

fof('$_typeof_Coq.Setoids.Setoid.Setoid_Theory',axiom,
    c_24__type__139638___24t(cCoq_2eSetoids_2eSetoid_2eSetoid__Theory) ).

fof('$_typeof_Coq.Sets.Relations_1.Relation',axiom,
    c_24__type__601___24t(cCoq_2eSets_2eRelations__1_2eRelation) ).

fof('$_typeof_Coq.Strings.Ascii.Ascii',axiom,
    c_24__type__7469___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__6865___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__147008___24t(cCoq_2eStructures_2eGenericMinMax_2egmax) ).

fof('$_typeof_Coq.Structures.GenericMinMax.gmin',axiom,
    c_24__type__147008___24t(cCoq_2eStructures_2eGenericMinMax_2egmin) ).

fof('$_typeof_Coq.Structures.OrderedType.Compare',axiom,
    c_24__type__121996___24t(cCoq_2eStructures_2eOrderedType_2eCompare) ).

fof('$_typeof_Coq.Structures.OrderedTypeEx.N_as_OT.eq',axiom,
    c_24__type__7026___24t(cCoq_2eStructures_2eOrderedTypeEx_2eN__as__OT_2eeq) ).

fof('$_typeof_Coq.Structures.OrderedTypeEx.N_as_OT.lt',axiom,
    c_24__type__7026___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__528___24t(cCoq_2eStructures_2eOrderedTypeEx_2eNat__as__OT_2eeq) ).

fof('$_typeof_Coq.Structures.OrderedTypeEx.Nat_as_OT.lt',axiom,
    c_24__type__528___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__7089___24t(cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2ebits__lt) ).

fof('$_typeof_Coq.Structures.OrderedTypeEx.PositiveOrderedTypeBits.eq',axiom,
    c_24__type__7089___24t(cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2eeq) ).

fof('$_typeof_Coq.Structures.OrderedTypeEx.PositiveOrderedTypeBits.lt',axiom,
    c_24__type__7089___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__7089___24t(cCoq_2eStructures_2eOrderedTypeEx_2ePositive__as__OT_2eeq) ).

fof('$_typeof_Coq.Structures.OrderedTypeEx.Positive_as_OT.lt',axiom,
    c_24__type__7089___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__88324___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__349___24t(cCoq_2eStructures_2eOrderedTypeEx_2eZ__as__OT_2eeq) ).

fof('$_typeof_Coq.Structures.OrderedTypeEx.Z_as_OT.lt',axiom,
    c_24__type__349___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__1873___24t(cCoq_2eVectors_2eFin_2et) ).

fof('$_typeof_Coq.Vectors.VectorDef.nil',axiom,
    c_24__type__3861___24t(cCoq_2eVectors_2eVectorDef_2enil) ).

fof('$_typeof_Coq.Vectors.VectorDef.t',axiom,
    c_24__type__3844___24t(cCoq_2eVectors_2eVectorDef_2et) ).

fof('$_typeof_Coq.ZArith.BinInt.Z.Private_Div.Quot2Div.div',axiom,
    c_24__type__546___24t(cCoq_2eZArith_2eBinInt_2eZ_2ePrivate__Div_2eQuot2Div_2ediv) ).

fof('$_typeof_Coq.ZArith.BinInt.Z.Private_Div.Quot2Div.modulo',axiom,
    c_24__type__546___24t(cCoq_2eZArith_2eBinInt_2eZ_2ePrivate__Div_2eQuot2Div_2emodulo) ).

fof('$_typeof_Coq.ZArith.BinInt.Z.b2z',axiom,
    c_24__type__152488___24t(cCoq_2eZArith_2eBinInt_2eZ_2eb2z) ).

fof('$_typeof_Coq.ZArith.BinInt.Z.divide',axiom,
    c_24__type__349___24t(cCoq_2eZArith_2eBinInt_2eZ_2edivide) ).

fof('$_typeof_Coq.ZArith.BinInt.Z.eq',axiom,
    c_24__type__349___24t(cCoq_2eZArith_2eBinInt_2eZ_2eeq) ).

fof('$_typeof_Coq.ZArith.BinInt.Z.eqf',axiom,
    c_24__type__150097___24t(cCoq_2eZArith_2eBinInt_2eZ_2eeqf) ).

fof('$_typeof_Coq.ZArith.BinInt.Z.gt',axiom,
    c_24__type__349___24t(cCoq_2eZArith_2eBinInt_2eZ_2egt) ).

fof('$_typeof_Coq.ZArith.BinInt.Z.le',axiom,
    c_24__type__349___24t(cCoq_2eZArith_2eBinInt_2eZ_2ele) ).

fof('$_typeof_Coq.ZArith.BinInt.Z.lt',axiom,
    c_24__type__349___24t(cCoq_2eZArith_2eBinInt_2eZ_2elt) ).

fof('$_typeof_Coq.ZArith.BinInt.Zne',axiom,
    c_24__type__349___24t(cCoq_2eZArith_2eBinInt_2eZne) ).

fof('$_typeof_Coq.ZArith.BinIntDef.Z.abs',axiom,
    c_24__type__550___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2eabs) ).

fof('$_typeof_Coq.ZArith.BinIntDef.Z.abs_N',axiom,
    c_24__type__7208___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2eabs__N) ).

fof('$_typeof_Coq.ZArith.BinIntDef.Z.abs_nat',axiom,
    c_24__type__4445___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2eabs__nat) ).

fof('$_typeof_Coq.ZArith.BinIntDef.Z.add',axiom,
    c_24__type__546___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2eadd) ).

fof('$_typeof_Coq.ZArith.BinIntDef.Z.compare',axiom,
    c_24__type__580___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare) ).

fof('$_typeof_Coq.ZArith.BinIntDef.Z.div',axiom,
    c_24__type__546___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2ediv) ).

fof('$_typeof_Coq.ZArith.BinIntDef.Z.even',axiom,
    c_24__type__145681___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2eeven) ).

fof('$_typeof_Coq.ZArith.BinIntDef.Z.leb',axiom,
    c_24__type__4087___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2eleb) ).

fof('$_typeof_Coq.ZArith.BinIntDef.Z.max',axiom,
    c_24__type__546___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2emax) ).

fof('$_typeof_Coq.ZArith.BinIntDef.Z.min',axiom,
    c_24__type__546___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2emin) ).

fof('$_typeof_Coq.ZArith.BinIntDef.Z.modulo',axiom,
    c_24__type__546___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2emodulo) ).

fof('$_typeof_Coq.ZArith.BinIntDef.Z.mul',axiom,
    c_24__type__546___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2emul) ).

fof('$_typeof_Coq.ZArith.BinIntDef.Z.odd',axiom,
    c_24__type__145681___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2eodd) ).

fof('$_typeof_Coq.ZArith.BinIntDef.Z.of_N',axiom,
    c_24__type__7211___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2eof__N) ).

fof('$_typeof_Coq.ZArith.BinIntDef.Z.of_nat',axiom,
    c_24__type__583___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat) ).

fof('$_typeof_Coq.ZArith.BinIntDef.Z.opp',axiom,
    c_24__type__550___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2eopp) ).

fof('$_typeof_Coq.ZArith.BinIntDef.Z.pow',axiom,
    c_24__type__546___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2epow) ).

fof('$_typeof_Coq.ZArith.BinIntDef.Z.pred',axiom,
    c_24__type__550___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2epred) ).

fof('$_typeof_Coq.ZArith.BinIntDef.Z.sub',axiom,
    c_24__type__546___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2esub) ).

fof('$_typeof_Coq.ZArith.BinIntDef.Z.succ',axiom,
    c_24__type__550___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__7208___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2eto__N) ).

fof('$_typeof_Coq.ZArith.BinIntDef.Z.to_nat',axiom,
    c_24__type__4445___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2eto__nat) ).

fof('$_typeof_Coq.ZArith.BinIntDef.Z.to_pos',axiom,
    c_24__type__150092___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__4087___24t(cCoq_2eZArith_2eZbool_2eZeq__bool) ).

fof('$_typeof_Coq.ZArith.Zeven.Zeven',axiom,
    c_24__type__339___24t(cCoq_2eZArith_2eZeven_2eZeven) ).

fof('$_typeof_Coq.ZArith.Zeven.Zodd',axiom,
    c_24__type__339___24t(cCoq_2eZArith_2eZeven_2eZodd) ).

fof('$_typeof_Coq.ZArith.Zlogarithm.Is_power',axiom,
    c_24__type__85245___24t(cCoq_2eZArith_2eZlogarithm_2eIs__power) ).

fof('$_typeof_Coq.ZArith.Zlogarithm.log_inf',axiom,
    c_24__type__233___24t(cCoq_2eZArith_2eZlogarithm_2elog__inf) ).

fof('$_typeof_Coq.ZArith.Znumtheory.Euclid',axiom,
    c_24__type__126302___24t(cCoq_2eZArith_2eZnumtheory_2eEuclid) ).

fof('$_typeof_Coq.ZArith.Zpower.Zdiv_rest_proofs',axiom,
    c_24__type__149779___24t(cCoq_2eZArith_2eZpower_2eZdiv__rest__proofs) ).

fof('$_typeof_Coq.micromega.Env.Env',axiom,
    c_24__type__601___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__152506___24t(cCoq_2emicromega_2eEnvRing_2ePEX) ).

fof('$_typeof_Coq.micromega.EnvRing.PEc',axiom,
    c_24__type__145748___24t(cCoq_2emicromega_2eEnvRing_2ePEc) ).

fof('$_typeof_Coq.micromega.EnvRing.PExpr',axiom,
    c_24__type__601___24t(cCoq_2emicromega_2eEnvRing_2ePExpr) ).

fof('$_typeof_Coq.micromega.EnvRing.PX',axiom,
    c_24__type__152519___24t(cCoq_2emicromega_2eEnvRing_2ePX) ).

fof('$_typeof_Coq.micromega.EnvRing.Pc',axiom,
    c_24__type__124267___24t(cCoq_2emicromega_2eEnvRing_2ePc) ).

fof('$_typeof_Coq.micromega.EnvRing.Pinj',axiom,
    c_24__type__152511___24t(cCoq_2emicromega_2eEnvRing_2ePinj) ).

fof('$_typeof_Coq.micromega.EnvRing.Pol',axiom,
    c_24__type__601___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__152522___24t(cCoq_2emicromega_2eEnvRing_2evmon) ).

fof('$_typeof_Coq.micromega.EnvRing.zmon',axiom,
    c_24__type__152522___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__122344___24t(cCoq_2emicromega_2eRMicromega_2eCInv) ).

fof('$_typeof_Coq.micromega.RMicromega.CMinus',axiom,
    c_24__type__122337___24t(cCoq_2emicromega_2eRMicromega_2eCMinus) ).

fof('$_typeof_Coq.micromega.RMicromega.CMult',axiom,
    c_24__type__122337___24t(cCoq_2emicromega_2eRMicromega_2eCMult) ).

fof('$_typeof_Coq.micromega.RMicromega.COpp',axiom,
    c_24__type__122344___24t(cCoq_2emicromega_2eRMicromega_2eCOpp) ).

fof('$_typeof_Coq.micromega.RMicromega.CPlus',axiom,
    c_24__type__122337___24t(cCoq_2emicromega_2eRMicromega_2eCPlus) ).

fof('$_typeof_Coq.micromega.RMicromega.CQ',axiom,
    c_24__type__122332___24t(cCoq_2emicromega_2eRMicromega_2eCQ) ).

fof('$_typeof_Coq.micromega.RMicromega.CZ',axiom,
    c_24__type__122334___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__138033___24t(cCoq_2emicromega_2eRefl_2emake__conj) ).

fof('$_typeof_Coq.micromega.Refl.make_impl',axiom,
    c_24__type__147857___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__601___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__601___24t(cCoq_2emicromega_2eRingMicromega_2ePolC) ).

fof('$_typeof_Coq.micromega.RingMicromega.PolEnv',axiom,
    c_24__type__601___24t(cCoq_2emicromega_2eRingMicromega_2ePolEnv) ).

fof('$_typeof_Coq.micromega.RingMicromega.Psatz',axiom,
    c_24__type__601___24t(cCoq_2emicromega_2eRingMicromega_2ePsatz) ).

fof('$_typeof_Coq.micromega.RingMicromega.Strict',axiom,
    cCoq_2emicromega_2eRingMicromega_2eOp1___24t(cCoq_2emicromega_2eRingMicromega_2eStrict) ).

fof('$_typeof_Coq.micromega.RingMicromega.cneqb',axiom,
    c_24__type__155189___24t(cCoq_2emicromega_2eRingMicromega_2ecneqb) ).

fof('$_typeof_Coq.micromega.RingMicromega.eval_op1',axiom,
    c_24__type__155268___24t(cCoq_2emicromega_2eRingMicromega_2eeval__op1) ).

fof('$_typeof_Coq.micromega.RingMicromega.ge_bool',axiom,
    c_24__type__337___24t(cCoq_2emicromega_2eRingMicromega_2ege__bool) ).

fof('$_typeof_Coq.micromega.Tauto.A',axiom,
    c_24__type__152839___24t(cCoq_2emicromega_2eTauto_2eA) ).

fof('$_typeof_Coq.micromega.Tauto.FF',axiom,
    c_24__type__152822___24t(cCoq_2emicromega_2eTauto_2eFF) ).

fof('$_typeof_Coq.micromega.Tauto.GFormula',axiom,
    c_24__type__149225___24t(cCoq_2emicromega_2eTauto_2eGFormula) ).

fof('$_typeof_Coq.micromega.Tauto.TFormula',axiom,
    c_24__type__149225___24t(cCoq_2emicromega_2eTauto_2eTFormula) ).

fof('$_typeof_Coq.micromega.Tauto.TT',axiom,
    c_24__type__152822___24t(cCoq_2emicromega_2eTauto_2eTT) ).

fof('$_typeof_Coq.micromega.Tauto.X',axiom,
    c_24__type__155382___24t(cCoq_2emicromega_2eTauto_2eX) ).

fof('$_typeof_Coq.micromega.Tauto.clause',axiom,
    c_24__type__1888___24t(cCoq_2emicromega_2eTauto_2eclause) ).

fof('$_typeof_Coq.micromega.VarMap.t',axiom,
    c_24__type__601___24t(cCoq_2emicromega_2eVarMap_2et) ).

fof('$_typeof_Coq.micromega.ZCoeff.gen_order_phi_Z',axiom,
    c_24__type__121772___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__7004___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.omega.PreOmega.Z_of_N\'',axiom,
    c_24__type__7211___24t(cCoq_2eomega_2ePreOmega_2eZ__of__N_27) ).

fof('$_typeof_Coq.omega.PreOmega.Z_of_nat\'',axiom,
    c_24__type__583___24t(cCoq_2eomega_2ePreOmega_2eZ__of__nat_27) ).

fof('$_typeof_Coq.omega.PreOmega.Zneg\'',axiom,
    c_24__type__233___24t(cCoq_2eomega_2ePreOmega_2eZneg_27) ).

fof('$_typeof_Coq.omega.PreOmega.Zpos\'',axiom,
    c_24__type__233___24t(cCoq_2eomega_2ePreOmega_2eZpos_27) ).

fof('$_typeof_Coq.setoid_ring.ArithRing.protected_to_nat',axiom,
    c_24__type__7022___24t(cCoq_2esetoid__ring_2eArithRing_2eprotected__to__nat) ).

fof('$_typeof_Coq.setoid_ring.Field_theory.FEI',axiom,
    c_24__type__155062___24t(cCoq_2esetoid__ring_2eField__theory_2eFEI) ).

fof('$_typeof_Coq.setoid_ring.Field_theory.FEO',axiom,
    c_24__type__155062___24t(cCoq_2esetoid__ring_2eField__theory_2eFEO) ).

fof('$_typeof_Coq.setoid_ring.Field_theory.FEX',axiom,
    c_24__type__145806___24t(cCoq_2esetoid__ring_2eField__theory_2eFEX) ).

fof('$_typeof_Coq.setoid_ring.Field_theory.FEc',axiom,
    c_24__type__145803___24t(cCoq_2esetoid__ring_2eField__theory_2eFEc) ).

fof('$_typeof_Coq.setoid_ring.Field_theory.FEinv',axiom,
    c_24__type__151198___24t(cCoq_2esetoid__ring_2eField__theory_2eFEinv) ).

fof('$_typeof_Coq.setoid_ring.Field_theory.FEmul',axiom,
    c_24__type__151195___24t(cCoq_2esetoid__ring_2eField__theory_2eFEmul) ).

fof('$_typeof_Coq.setoid_ring.Field_theory.FExpr',axiom,
    c_24__type__601___24t(cCoq_2esetoid__ring_2eField__theory_2eFExpr) ).

fof('$_typeof_Coq.setoid_ring.Field_theory.linear',axiom,
    c_24__type__601___24t(cCoq_2esetoid__ring_2eField__theory_2elinear) ).

fof('$_typeof_Coq.setoid_ring.Field_theory.rsplit',axiom,
    c_24__type__601___24t(cCoq_2esetoid__ring_2eField__theory_2ersplit) ).

fof('$_typeof_Coq.setoid_ring.InitialRing.Nopp',axiom,
    c_24__type__5412___24t(cCoq_2esetoid__ring_2eInitialRing_2eNopp) ).

fof('$_typeof_Coq.setoid_ring.InitialRing.NotConstant',axiom,
    cCoq_2eInit_2eDatatypes_2ebool___24t(cCoq_2esetoid__ring_2eInitialRing_2eNotConstant) ).

fof('$_typeof_Coq.setoid_ring.InitialRing.Nword',axiom,
    cType___24t(cCoq_2esetoid__ring_2eInitialRing_2eNword) ).

fof('$_typeof_Coq.setoid_ring.InitialRing.gen_phiPOS',axiom,
    c_24__type__147052___24t(cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS) ).

fof('$_typeof_Coq.setoid_ring.InitialRing.gen_phiPOS1',axiom,
    c_24__type__147052___24t(cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS1) ).

fof('$_typeof_Coq.setoid_ring.InitialRing.gen_phiZ',axiom,
    c_24__type__121772___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.mkhypo',axiom,
    c_24__type__147104___24t(cCoq_2esetoid__ring_2eInitialRing_2emkhypo) ).

fof('$_typeof_Coq.setoid_ring.Ring_polynom.Mon',axiom,
    cType___24t(cCoq_2esetoid__ring_2eRing__polynom_2eMon) ).

fof('$_typeof_Coq.setoid_ring.Ring_polynom.PEI',axiom,
    c_24__type__138323___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePEI) ).

fof('$_typeof_Coq.setoid_ring.Ring_polynom.PEO',axiom,
    c_24__type__138323___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePEO) ).

fof('$_typeof_Coq.setoid_ring.Ring_polynom.PEX',axiom,
    c_24__type__3293___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePEX) ).

fof('$_typeof_Coq.setoid_ring.Ring_polynom.PEadd',axiom,
    c_24__type__3298___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePEadd) ).

fof('$_typeof_Coq.setoid_ring.Ring_polynom.PEc',axiom,
    c_24__type__3290___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePEc) ).

fof('$_typeof_Coq.setoid_ring.Ring_polynom.PEmul',axiom,
    c_24__type__3298___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePEmul) ).

fof('$_typeof_Coq.setoid_ring.Ring_polynom.PEopp',axiom,
    c_24__type__138326___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePEopp) ).

fof('$_typeof_Coq.setoid_ring.Ring_polynom.PEpow',axiom,
    c_24__type__154230___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePEpow) ).

fof('$_typeof_Coq.setoid_ring.Ring_polynom.PEsub',axiom,
    c_24__type__3298___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePEsub) ).

fof('$_typeof_Coq.setoid_ring.Ring_polynom.PExpr',axiom,
    c_24__type__601___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr) ).

fof('$_typeof_Coq.setoid_ring.Ring_polynom.PX',axiom,
    c_24__type__155290___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePX) ).

fof('$_typeof_Coq.setoid_ring.Ring_polynom.Pc',axiom,
    c_24__type__148630___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePc) ).

fof('$_typeof_Coq.setoid_ring.Ring_polynom.Peq',axiom,
    c_24__type__3041___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePeq) ).

fof('$_typeof_Coq.setoid_ring.Ring_polynom.Pinj',axiom,
    c_24__type__155282___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePinj) ).

fof('$_typeof_Coq.setoid_ring.Ring_polynom.Pol',axiom,
    c_24__type__601___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePol) ).

fof('$_typeof_Coq.setoid_ring.Ring_polynom.mkmult_pow',axiom,
    c_24__type__148648___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__152782___24t(cCoq_2esetoid__ring_2eRing__polynom_2evmon) ).

fof('$_typeof_Coq.setoid_ring.Ring_polynom.zmon',axiom,
    c_24__type__152782___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__6721___24t(cCoq_2esetoid__ring_2eRing__theory_2eIDphi) ).

fof('$_typeof_Coq.setoid_ring.Ring_theory.SRopp',axiom,
    c_24__type__6721___24t(cCoq_2esetoid__ring_2eRing__theory_2eSRopp) ).

fof('$_typeof_Coq.setoid_ring.Ring_theory.SRsub',axiom,
    c_24__type__6732___24t(cCoq_2esetoid__ring_2eRing__theory_2eSRsub) ).

fof('$_typeof_Coq.setoid_ring.Ring_theory.id_phi_N',axiom,
    c_24__type__5412___24t(cCoq_2esetoid__ring_2eRing__theory_2eid__phi__N) ).

fof('$_typeof_Coq.setoid_ring.Ring_theory.pow_N',axiom,
    c_24__type__5407___24t(cCoq_2esetoid__ring_2eRing__theory_2epow__N) ).

fof('$_typeof_Coq.setoid_ring.Ring_theory.pow_pos',axiom,
    c_24__type__131823___24t(cCoq_2esetoid__ring_2eRing__theory_2epow__pos) ).

fof('$_typeof_Coq.setoid_ring.Ring_theory.ring_kind',axiom,
    cType___24t(cCoq_2esetoid__ring_2eRing__theory_2ering__kind) ).

fof('$_typeof_Hammer.Tactics.Reconstr.AllHyps',axiom,
    cHammer_2eTactics_2eReconstr_2eReconstrT___24t(cHammer_2eTactics_2eReconstr_2eAllHyps) ).

fof('$_typeof_Hammer.Tactics.Reconstr.Empty',axiom,
    cHammer_2eTactics_2eReconstr_2eReconstrT___24t(cHammer_2eTactics_2eReconstr_2eEmpty) ).

fof('$_typeof_Hammer.Tactics.Reconstr.ReconstrT',axiom,
    cType___24t(cHammer_2eTactics_2eReconstr_2eReconstrT) ).

fof('$_typeof_Hammer.Tactics.Reconstr.rdone',axiom,
    c_24__type__147839___24t(cHammer_2eTactics_2eReconstr_2erdone) ).

fof('$_typeof_Hammer.Tactics.Tactics.rdone',axiom,
    c_24__type__147839___24t(cHammer_2eTactics_2eTactics_2erdone) ).

fof('$_typeof_Hoare2.DCSeq',axiom,
    c_24__type__151115___24t(cHoare2_2eDCSeq) ).

fof('$_typeof_Hoare2.DCSkip',axiom,
    c_24__type__151112___24t(cHoare2_2eDCSkip) ).

fof('$_typeof_Hoare2.dcom',axiom,
    cType___24t(cHoare2_2edcom) ).

fof('$_typeof_Hoare2.dec_correct',axiom,
    c_24__type__150501___24t(cHoare2_2edec__correct) ).

fof('$_typeof_Hoare2.decorated',axiom,
    cType___24t(cHoare2_2edecorated) ).

fof('$_typeof_Hoare2.parity',axiom,
    c_24__type__9___24t(cHoare2_2eparity) ).

fof('$_typeof_Hoare2.verification_conditions_dec',axiom,
    c_24__type__150501___24t(cHoare2_2everification__conditions__dec) ).

fof('$_typeof_PLF.Hoare.Assertion',axiom,
    cType___24t(cPLF_2eHoare_2eAssertion) ).

fof('$_typeof_PLF.Hoare.ExAssertions.as5',axiom,
    cPLF_2eHoare_2eAssertion___24t(cPLF_2eHoare_2eExAssertions_2eas5) ).

fof('$_typeof_PLF.Hoare.ExAssertions.as6',axiom,
    cPLF_2eHoare_2eAssertion___24t(cPLF_2eHoare_2eExAssertions_2eas6) ).

fof('$_typeof_PLF.Hoare.Himp.CHavoc',axiom,
    c_24__type__878___24t(cPLF_2eHoare_2eHimp_2eCHavoc) ).

fof('$_typeof_PLF.Hoare.Himp.CSeq',axiom,
    c_24__type__868___24t(cPLF_2eHoare_2eHimp_2eCSeq) ).

fof('$_typeof_PLF.Hoare.Himp.CSkip',axiom,
    cPLF_2eHoare_2eHimp_2ecom___24t(cPLF_2eHoare_2eHimp_2eCSkip) ).

fof('$_typeof_PLF.Hoare.Himp.com',axiom,
    cType___24t(cPLF_2eHoare_2eHimp_2ecom) ).

fof('$_typeof_PLF.Hoare.HoareAssertAssume.CAssert',axiom,
    c_24__type__1125___24t(cPLF_2eHoare_2eHoareAssertAssume_2eCAssert) ).

fof('$_typeof_PLF.Hoare.HoareAssertAssume.CAssume',axiom,
    c_24__type__1125___24t(cPLF_2eHoare_2eHoareAssertAssume_2eCAssume) ).

fof('$_typeof_PLF.Hoare.HoareAssertAssume.CIf',axiom,
    c_24__type__1120___24t(cPLF_2eHoare_2eHoareAssertAssume_2eCIf) ).

fof('$_typeof_PLF.Hoare.HoareAssertAssume.CSeq',axiom,
    c_24__type__1115___24t(cPLF_2eHoare_2eHoareAssertAssume_2eCSeq) ).

fof('$_typeof_PLF.Hoare.HoareAssertAssume.CSkip',axiom,
    cPLF_2eHoare_2eHoareAssertAssume_2ecom___24t(cPLF_2eHoare_2eHoareAssertAssume_2eCSkip) ).

fof('$_typeof_PLF.Hoare.HoareAssertAssume.CWhile',axiom,
    c_24__type__1123___24t(cPLF_2eHoare_2eHoareAssertAssume_2eCWhile) ).

fof('$_typeof_PLF.Hoare.HoareAssertAssume.RError',axiom,
    cPLF_2eHoare_2eHoareAssertAssume_2eresult___24t(cPLF_2eHoare_2eHoareAssertAssume_2eRError) ).

fof('$_typeof_PLF.Hoare.HoareAssertAssume.RNormal',axiom,
    c_24__type__1132___24t(cPLF_2eHoare_2eHoareAssertAssume_2eRNormal) ).

fof('$_typeof_PLF.Hoare.HoareAssertAssume.com',axiom,
    cType___24t(cPLF_2eHoare_2eHoareAssertAssume_2ecom) ).

fof('$_typeof_PLF.Hoare.HoareAssertAssume.result',axiom,
    cType___24t(cPLF_2eHoare_2eHoareAssertAssume_2eresult) ).

fof('$_typeof_PLF.Hoare.If1.CSeq',axiom,
    c_24__type__1418___24t(cPLF_2eHoare_2eIf1_2eCSeq) ).

fof('$_typeof_PLF.Hoare.If1.CSkip',axiom,
    cPLF_2eHoare_2eIf1_2ecom___24t(cPLF_2eHoare_2eIf1_2eCSkip) ).

fof('$_typeof_PLF.Hoare.If1.com',axiom,
    cType___24t(cPLF_2eHoare_2eIf1_2ecom) ).

fof('$_typeof_PLF.Hoare.RepeatExercise.CSeq',axiom,
    c_24__type__1646___24t(cPLF_2eHoare_2eRepeatExercise_2eCSeq) ).

fof('$_typeof_PLF.Hoare.RepeatExercise.CSkip',axiom,
    cPLF_2eHoare_2eRepeatExercise_2ecom___24t(cPLF_2eHoare_2eRepeatExercise_2eCSkip) ).

fof('$_typeof_PLF.Hoare.RepeatExercise.com',axiom,
    cType___24t(cPLF_2eHoare_2eRepeatExercise_2ecom) ).

fof('$_typeof_PLF.Hoare.assert_implies',axiom,
    c_24__type__14___24t(cPLF_2eHoare_2eassert__implies) ).

fof('$_typeof_PLF.Hoare.swap_program',axiom,
    cPLF_2eImp_2ecom___24t(cPLF_2eHoare_2eswap__program) ).

fof('$_typeof_PLF.Imp.AExp.AMinus',axiom,
    c_24__type__6986___24t(cPLF_2eImp_2eAExp_2eAMinus) ).

fof('$_typeof_PLF.Imp.AExp.AMult',axiom,
    c_24__type__6986___24t(cPLF_2eImp_2eAExp_2eAMult) ).

fof('$_typeof_PLF.Imp.AExp.ANum',axiom,
    c_24__type__6983___24t(cPLF_2eImp_2eAExp_2eANum) ).

fof('$_typeof_PLF.Imp.AExp.APlus',axiom,
    c_24__type__6986___24t(cPLF_2eImp_2eAExp_2eAPlus) ).

fof('$_typeof_PLF.Imp.AExp.BAnd',axiom,
    c_24__type__152850___24t(cPLF_2eImp_2eAExp_2eBAnd) ).

fof('$_typeof_PLF.Imp.AExp.BFalse',axiom,
    cPLF_2eImp_2eAExp_2ebexp___24t(cPLF_2eImp_2eAExp_2eBFalse) ).

fof('$_typeof_PLF.Imp.AExp.BNot',axiom,
    c_24__type__152847___24t(cPLF_2eImp_2eAExp_2eBNot) ).

fof('$_typeof_PLF.Imp.AExp.BTrue',axiom,
    cPLF_2eImp_2eAExp_2ebexp___24t(cPLF_2eImp_2eAExp_2eBTrue) ).

fof('$_typeof_PLF.Imp.AExp.aexp',axiom,
    cType___24t(cPLF_2eImp_2eAExp_2eaexp) ).

fof('$_typeof_PLF.Imp.AExp.bexp',axiom,
    cType___24t(cPLF_2eImp_2eAExp_2ebexp) ).

fof('$_typeof_PLF.Imp.AExp.optimize_0plus_b',axiom,
    c_24__type__152847___24t(cPLF_2eImp_2eAExp_2eoptimize__0plus__b) ).

fof('$_typeof_PLF.Imp.AId',axiom,
    c_24__type__244___24t(cPLF_2eImp_2eAId) ).

fof('$_typeof_PLF.Imp.AMinus',axiom,
    c_24__type__247___24t(cPLF_2eImp_2eAMinus) ).

fof('$_typeof_PLF.Imp.AMult',axiom,
    c_24__type__247___24t(cPLF_2eImp_2eAMult) ).

fof('$_typeof_PLF.Imp.ANum',axiom,
    c_24__type__98___24t(cPLF_2eImp_2eANum) ).

fof('$_typeof_PLF.Imp.APlus',axiom,
    c_24__type__247___24t(cPLF_2eImp_2eAPlus) ).

fof('$_typeof_PLF.Imp.BAnd',axiom,
    c_24__type__626___24t(cPLF_2eImp_2eBAnd) ).

fof('$_typeof_PLF.Imp.BEq',axiom,
    c_24__type__307___24t(cPLF_2eImp_2eBEq) ).

fof('$_typeof_PLF.Imp.BFalse',axiom,
    cPLF_2eImp_2ebexp___24t(cPLF_2eImp_2eBFalse) ).

fof('$_typeof_PLF.Imp.BLe',axiom,
    c_24__type__307___24t(cPLF_2eImp_2eBLe) ).

fof('$_typeof_PLF.Imp.BNot',axiom,
    c_24__type__623___24t(cPLF_2eImp_2eBNot) ).

fof('$_typeof_PLF.Imp.BTrue',axiom,
    cPLF_2eImp_2ebexp___24t(cPLF_2eImp_2eBTrue) ).

fof('$_typeof_PLF.Imp.BreakImp.CBreak',axiom,
    cPLF_2eImp_2eBreakImp_2ecom___24t(cPLF_2eImp_2eBreakImp_2eCBreak) ).

fof('$_typeof_PLF.Imp.BreakImp.CSeq',axiom,
    c_24__type__762___24t(cPLF_2eImp_2eBreakImp_2eCSeq) ).

fof('$_typeof_PLF.Imp.BreakImp.CSkip',axiom,
    cPLF_2eImp_2eBreakImp_2ecom___24t(cPLF_2eImp_2eBreakImp_2eCSkip) ).

fof('$_typeof_PLF.Imp.BreakImp.SBreak',axiom,
    cPLF_2eImp_2eBreakImp_2eresult___24t(cPLF_2eImp_2eBreakImp_2eSBreak) ).

fof('$_typeof_PLF.Imp.BreakImp.SContinue',axiom,
    cPLF_2eImp_2eBreakImp_2eresult___24t(cPLF_2eImp_2eBreakImp_2eSContinue) ).

fof('$_typeof_PLF.Imp.BreakImp.com',axiom,
    cType___24t(cPLF_2eImp_2eBreakImp_2ecom) ).

fof('$_typeof_PLF.Imp.BreakImp.result',axiom,
    cType___24t(cPLF_2eImp_2eBreakImp_2eresult) ).

fof('$_typeof_PLF.Imp.CAss',axiom,
    c_24__type__180___24t(cPLF_2eImp_2eCAss) ).

fof('$_typeof_PLF.Imp.CIf',axiom,
    c_24__type__397___24t(cPLF_2eImp_2eCIf) ).

fof('$_typeof_PLF.Imp.CSeq',axiom,
    c_24__type__183___24t(cPLF_2eImp_2eCSeq) ).

fof('$_typeof_PLF.Imp.CSkip',axiom,
    cPLF_2eImp_2ecom___24t(cPLF_2eImp_2eCSkip) ).

fof('$_typeof_PLF.Imp.CWhile',axiom,
    c_24__type__324___24t(cPLF_2eImp_2eCWhile) ).

fof('$_typeof_PLF.Imp.SLoad',axiom,
    c_24__type__670___24t(cPLF_2eImp_2eSLoad) ).

fof('$_typeof_PLF.Imp.SMinus',axiom,
    cPLF_2eImp_2esinstr___24t(cPLF_2eImp_2eSMinus) ).

fof('$_typeof_PLF.Imp.SMult',axiom,
    cPLF_2eImp_2esinstr___24t(cPLF_2eImp_2eSMult) ).

fof('$_typeof_PLF.Imp.SPlus',axiom,
    cPLF_2eImp_2esinstr___24t(cPLF_2eImp_2eSPlus) ).

fof('$_typeof_PLF.Imp.SPush',axiom,
    c_24__type__668___24t(cPLF_2eImp_2eSPush) ).

fof('$_typeof_PLF.Imp.aevalR_division.ADiv',axiom,
    c_24__type__4532___24t(cPLF_2eImp_2eaevalR__division_2eADiv) ).

fof('$_typeof_PLF.Imp.aevalR_division.AMinus',axiom,
    c_24__type__4532___24t(cPLF_2eImp_2eaevalR__division_2eAMinus) ).

fof('$_typeof_PLF.Imp.aevalR_division.AMult',axiom,
    c_24__type__4532___24t(cPLF_2eImp_2eaevalR__division_2eAMult) ).

fof('$_typeof_PLF.Imp.aevalR_division.ANum',axiom,
    c_24__type__4529___24t(cPLF_2eImp_2eaevalR__division_2eANum) ).

fof('$_typeof_PLF.Imp.aevalR_division.APlus',axiom,
    c_24__type__4532___24t(cPLF_2eImp_2eaevalR__division_2eAPlus) ).

fof('$_typeof_PLF.Imp.aevalR_division.aexp',axiom,
    cType___24t(cPLF_2eImp_2eaevalR__division_2eaexp) ).

fof('$_typeof_PLF.Imp.aevalR_extended.AAny',axiom,
    cPLF_2eImp_2eaevalR__extended_2eaexp___24t(cPLF_2eImp_2eaevalR__extended_2eAAny) ).

fof('$_typeof_PLF.Imp.aevalR_extended.AMinus',axiom,
    c_24__type__83636___24t(cPLF_2eImp_2eaevalR__extended_2eAMinus) ).

fof('$_typeof_PLF.Imp.aevalR_extended.AMult',axiom,
    c_24__type__83636___24t(cPLF_2eImp_2eaevalR__extended_2eAMult) ).

fof('$_typeof_PLF.Imp.aevalR_extended.ANum',axiom,
    c_24__type__83633___24t(cPLF_2eImp_2eaevalR__extended_2eANum) ).

fof('$_typeof_PLF.Imp.aevalR_extended.APlus',axiom,
    c_24__type__83636___24t(cPLF_2eImp_2eaevalR__extended_2eAPlus) ).

fof('$_typeof_PLF.Imp.aevalR_extended.aexp',axiom,
    cType___24t(cPLF_2eImp_2eaevalR__extended_2eaexp) ).

fof('$_typeof_PLF.Imp.aexp',axiom,
    cType___24t(cPLF_2eImp_2eaexp) ).

fof('$_typeof_PLF.Imp.bexp',axiom,
    cType___24t(cPLF_2eImp_2ebexp) ).

fof('$_typeof_PLF.Imp.com',axiom,
    cType___24t(cPLF_2eImp_2ecom) ).

fof('$_typeof_PLF.Imp.pup_to_n',axiom,
    cPLF_2eImp_2ecom___24t(cPLF_2eImp_2epup__to__n) ).

fof('$_typeof_PLF.Imp.sinstr',axiom,
    cType___24t(cPLF_2eImp_2esinstr) ).

fof('$_typeof_PLF.Imp.state',axiom,
    cType___24t(cPLF_2eImp_2estate) ).

fof('$_typeof_PLF.Maps.total_map',axiom,
    c_24__type__601___24t(cPLF_2eMaps_2etotal__map) ).

fof('Coq.Arith.PeanoNat.Nat.Private_OrderTac.Tac.eq_refl',axiom,
    ! [V0__x] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)
     => V0__x = V0__x ) ).

fof('Coq.Arith.PeanoNat.Nat.Private_OrderTac.Tac.eq_sym',axiom,
    ! [V0__x] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)
     => ! [V1__y] :
          ( cCoq_2eInit_2eDatatypes_2enat___24t(V1__y)
         => ( V0__x = V1__y
           => V1__y = V0__x ) ) ) ).

fof('Coq.Arith.PeanoNat.Nat.Private_OrderTac.Tac.le_antisym',axiom,
    ! [V0__x] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)
     => ! [V1__y] :
          ( cCoq_2eInit_2eDatatypes_2enat___24t(V1__y)
         => ( cCoq_2eInit_2ePeano_2ele___24a2(V0__x,V1__y)
           => ( cCoq_2eInit_2ePeano_2ele___24a2(V1__y,V0__x)
             => V0__x = V1__y ) ) ) ) ).

fof('Coq.Arith.PeanoNat.Nat.Private_OrderTac.Tac.le_refl',axiom,
    ! [V0__x] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)
     => cCoq_2eInit_2ePeano_2ele___24a2(V0__x,V0__x) ) ).

fof('Coq.Arith.PeanoNat.Nat.Private_OrderTac.Tac.lt_irrefl',axiom,
    ! [V0__x] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)
     => ~ cCoq_2eInit_2ePeano_2elt___24a2(V0__x,V0__x) ) ).

fof('Coq.Arith.PeanoNat.Nat.Private_OrderTac.Tac.not_ge_lt',axiom,
    ! [V0__x] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)
     => ! [V1__y] :
          ( cCoq_2eInit_2eDatatypes_2enat___24t(V1__y)
         => ( ~ cCoq_2eInit_2ePeano_2ele___24a2(V1__y,V0__x)
           => cCoq_2eInit_2ePeano_2elt___24a2(V0__x,V1__y) ) ) ) ).

fof('Coq.Arith.PeanoNat.Nat.Private_OrderTac.Tac.not_gt_le',axiom,
    ! [V0__x] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)
     => ! [V1__y] :
          ( cCoq_2eInit_2eDatatypes_2enat___24t(V1__y)
         => ( ~ cCoq_2eInit_2ePeano_2elt___24a2(V1__y,V0__x)
           => cCoq_2eInit_2ePeano_2ele___24a2(V0__x,V1__y) ) ) ) ).

fof('Coq.Arith.PeanoNat.Nat.Private_Tac.eq_refl',axiom,
    ! [V0__x] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)
     => V0__x = V0__x ) ).

fof('Coq.Arith.PeanoNat.Nat.Private_Tac.eq_sym',axiom,
    ! [V0__x] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)
     => ! [V1__y] :
          ( cCoq_2eInit_2eDatatypes_2enat___24t(V1__y)
         => ( V0__x = V1__y
           => V1__y = V0__x ) ) ) ).

fof('Coq.Arith.PeanoNat.Nat.Private_Tac.le_refl',axiom,
    ! [V0__x] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)
     => cCoq_2eInit_2ePeano_2ele___24a2(V0__x,V0__x) ) ).

fof('Coq.Arith.PeanoNat.Nat.Private_Tac.lt_irrefl',axiom,
    ! [V0__x] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)
     => ~ cCoq_2eInit_2ePeano_2elt___24a2(V0__x,V0__x) ) ).

fof('Coq.Arith.PeanoNat.Nat.add_comm',axiom,
    ! [V0__n] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
     => ! [V1__m] :
          ( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
         => cCoq_2eInit_2eNat_2eadd___24a2(V0__n,V1__m) = cCoq_2eInit_2eNat_2eadd___24a2(V1__m,V0__n) ) ) ).

fof('Coq.Arith.PeanoNat.Nat.divide_refl',axiom,
    ! [V0__n] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
     => cCoq_2eArith_2ePeanoNat_2eNat_2edivide___24a2(V0__n,V0__n) ) ).

fof('Coq.Arith.PeanoNat.Nat.eq_equiv',axiom,
    cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(cCoq_2eInit_2eDatatypes_2enat,c_3d___24a1(cCoq_2eInit_2eDatatypes_2enat)) ).

fof('Coq.Arith.PeanoNat.Nat.eq_le_incl',axiom,
    ! [V0__n] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
     => ! [V1__m] :
          ( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
         => ( V0__n = V1__m
           => cCoq_2eInit_2ePeano_2ele___24a2(V0__n,V1__m) ) ) ) ).

fof('Coq.Arith.PeanoNat.Nat.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.le_0_l',axiom,
    ! [V0__n] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
     => cCoq_2eInit_2ePeano_2ele___24a2(cCoq_2eInit_2eDatatypes_2eO,V0__n) ) ).

fof('Coq.Arith.PeanoNat.Nat.le_antisymm',axiom,
    ! [V0__n] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
     => ! [V1__m] :
          ( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
         => ( cCoq_2eInit_2ePeano_2ele___24a2(V0__n,V1__m)
           => ( cCoq_2eInit_2ePeano_2ele___24a2(V1__m,V0__n)
             => V0__n = V1__m ) ) ) ) ).

fof('Coq.Arith.PeanoNat.Nat.le_ge_cases',axiom,
    ! [V0__n] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
     => ! [V1__m] :
          ( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
         => ( cCoq_2eInit_2ePeano_2ele___24a2(V0__n,V1__m)
            | cCoq_2eInit_2ePeano_2ele___24a2(V1__m,V0__n) ) ) ) ).

fof('Coq.Arith.PeanoNat.Nat.le_gt_cases',axiom,
    ! [V0__n] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
     => ! [V1__m] :
          ( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
         => ( cCoq_2eInit_2ePeano_2ele___24a2(V0__n,V1__m)
            | cCoq_2eInit_2ePeano_2elt___24a2(V1__m,V0__n) ) ) ) ).

fof('Coq.Arith.PeanoNat.Nat.le_refl',axiom,
    ! [V0__n] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
     => cCoq_2eInit_2ePeano_2ele___24a2(V0__n,V0__n) ) ).

fof('Coq.Arith.PeanoNat.Nat.le_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.mul_comm',axiom,
    ! [V0__n] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
     => ! [V1__m] :
          ( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
         => cCoq_2eInit_2eNat_2emul___24a2(V0__n,V1__m) = cCoq_2eInit_2eNat_2emul___24a2(V1__m,V0__n) ) ) ).

fof('Coq.Arith.PeanoNat.Nat.one_succ',axiom,
    cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO) = cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO) ).

fof('Coq.Arith.Wf_nat.lt_wf_double_ind',axiom,
    ! [V0__P] :
      ( c_24__type__528___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__1856___24t(V1__P)
         => ( ! [V2__n] :
                ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__n)
               => ( ! [V3__m] :
                      ( cCoq_2eInit_2eDatatypes_2enat___24t(V3__m)
                     => ( cCoq_2eInit_2ePeano_2elt___24a2(V3__m,V2__n)
                       => p(happ(V1__P,V3__m)) ) )
                 => p(happ(V1__P,V2__n)) ) )
           => p(happ(V1__P,V0__n)) ) ) ) ).

fof('Coq.Bool.Bool.absurd_eq_bool',axiom,
    ! [V0__b] :
      ( cCoq_2eInit_2eDatatypes_2ebool___24t(V0__b)
     => ! [V1__b_27] :
          ( cCoq_2eInit_2eDatatypes_2ebool___24t(V1__b_27)
         => ( p(c_24False)
           => V0__b = V1__b_27 ) ) ) ).

fof('Coq.Init.Datatypes.idProp',axiom,
    p(cCoq_2eInit_2eDatatypes_2eIDProp) ).

fof('Coq.Init.Datatypes.nat_ind',axiom,
    ! [V0__P] :
      ( c_24__type__1856___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__528___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.Logic.Decidable.dec_not_not',axiom,
    ! [V0__P] :
      ( cProp___24t(V0__P)
     => ( cCoq_2eLogic_2eDecidable_2edecidable___24a1(V0__P)
       => ( ( ~ p(V0__P)
           => p(c_24False) )
         => p(V0__P) ) ) ) ).

fof('Coq.Logic.Decidable.not_and_iff',axiom,
    ! [V0__A] :
      ( cProp___24t(V0__A)
     => ! [V1__B] :
          ( cProp___24t(V1__B)
         => ( ( ( p(V0__A)
                & p(V1__B) )
             => p(c_24False) )
          <=> ( p(V0__A)
             => ( p(V1__B)
               => p(c_24False) ) ) ) ) ) ).

fof('Coq.Logic.Decidable.not_false_iff',axiom,
    ( ( p(c_24False)
     => p(c_24False) )
  <=> p(c_24True) ) ).

fof('Coq.Logic.Decidable.not_or_iff',axiom,
    ! [V0__A] :
      ( cProp___24t(V0__A)
     => ! [V1__B] :
          ( cProp___24t(V1__B)
         => ( ( ( p(V0__A)
                | p(V1__B) )
             => p(c_24False) )
          <=> ( ( p(V0__A)
               => p(c_24False) )
              & ( p(V1__B)
               => p(c_24False) ) ) ) ) ) ).

fof('Coq.Logic.Decidable.not_true_iff',axiom,
    ( ( p(c_24True)
     => p(c_24False) )
  <=> p(c_24False) ) ).

fof('Coq.Logic.EqdepFacts.eq_dep_intro',axiom,
    ! [V0__U] :
      ( cType___24t(V0__U)
     => ! [V1__P] :
          ( c_24__type__139664___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.Logic.FunctionalExtensionality.equal_f',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__B] :
          ( cType___24t(V1__B)
         => ! [V2__f] :
              ( c_24__type__80524___24t(V0__A,V1__B,V2__f)
             => ! [V3__g] :
                  ( c_24__type__80524___24t(V0__A,V1__B,V3__g)
                 => ( V2__f = V3__g
                   => ! [V5__x] :
                        ( t(V5__x,V0__A)
                       => happ(V2__f,V5__x) = happ(V3__g,V5__x) ) ) ) ) ) ) ).

fof('Coq.Logic.FunctionalExtensionality.equal_f_dep',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__B] :
          ( c_24__type__139664___24t(V0__A,V1__B)
         => ! [V2__f] :
              ( c_24__type__146949___24t(V0__A,V1__B,V2__f)
             => ! [V3__g] :
                  ( c_24__type__146954___24t(V0__A,V1__B,V3__g)
                 => ( V2__f = V3__g
                   => ! [V5__x] :
                        ( t(V5__x,V0__A)
                       => happ(V2__f,V5__x) = happ(V3__g,V5__x) ) ) ) ) ) ) ).

fof('Coq.Logic.FunctionalExtensionality.eta_expansion',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__B] :
          ( cType___24t(V1__B)
         => ! [V2__f] :
              ( c_24__type__80524___24t(V0__A,V1__B,V2__f)
             => V2__f = c_24__lam__146993___24a3(V0__A,V1__B,V2__f) ) ) ) ).

fof('Coq.Logic.FunctionalExtensionality.eta_expansion_dep',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__B] :
          ( c_24__type__139664___24t(V0__A,V1__B)
         => ! [V2__f] :
              ( c_24__type__146977___24t(V0__A,V1__B,V2__f)
             => V2__f = c_24__lam__146985___24a3(V0__A,V1__B,V2__f) ) ) ) ).

fof('Coq.Logic.FunctionalExtensionality.functional_extensionality',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__B] :
          ( cType___24t(V1__B)
         => ! [V2__f] :
              ( c_24__type__80524___24t(V0__A,V1__B,V2__f)
             => ! [V3__g] :
                  ( c_24__type__80524___24t(V0__A,V1__B,V3__g)
                 => ( ! [V4__x] :
                        ( t(V4__x,V0__A)
                       => happ(V2__f,V4__x) = happ(V3__g,V4__x) )
                   => V2__f = V3__g ) ) ) ) ) ).

fof('Coq.Logic.FunctionalExtensionality.functional_extensionality_dep',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__B] :
          ( c_24__type__139664___24t(V0__A,V1__B)
         => ! [V2__f] :
              ( c_24__type__146960___24t(V0__A,V1__B,V2__f)
             => ! [V3__g] :
                  ( c_24__type__146965___24t(V0__A,V1__B,V3__g)
                 => ( ! [V4__x] :
                        ( t(V4__x,V0__A)
                       => happ(V2__f,V4__x) = happ(V3__g,V4__x) )
                   => V2__f = V3__g ) ) ) ) ) ).

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.le_0_l',axiom,
    ! [V0__n] :
      ( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
     => cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eN0,V0__n) ) ).

fof('Coq.NArith.BinNat.N.le_ge_cases',axiom,
    ! [V0__n] :
      ( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
     => ! [V1__m] :
          ( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
         => ( cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(V0__n,V1__m)
            | cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(V1__m,V0__n) ) ) ) ).

fof('Coq.NArith.BinNat.N.le_gt_cases',axiom,
    ! [V0__n] :
      ( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
     => ! [V1__m] :
          ( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
         => ( cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(V0__n,V1__m)
            | cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V1__m,V0__n) ) ) ) ).

fof('Coq.NArith.BinNat.N.le_refl',axiom,
    ! [V0__n] :
      ( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
     => cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(V0__n,V0__n) ) ).

fof('Coq.NArith.BinNat.N.le_trans',axiom,
    ! [V0__n] :
      ( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
     => ! [V1__m] :
          ( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
         => ! [V2__p] :
              ( cCoq_2eNumbers_2eBinNums_2eN___24t(V2__p)
             => ( cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(V0__n,V1__m)
               => ( cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(V1__m,V2__p)
                 => cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(V0__n,V2__p) ) ) ) ) ) ).

fof('Coq.NArith.BinNat.N.lt_ge_cases',axiom,
    ! [V0__n] :
      ( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
     => ! [V1__m] :
          ( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
         => ( cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V0__n,V1__m)
            | cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(V1__m,V0__n) ) ) ) ).

fof('Coq.NArith.BinNat.N.lt_le_incl',axiom,
    ! [V0__n] :
      ( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
     => ! [V1__m] :
          ( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
         => ( cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V0__n,V1__m)
           => cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(V0__n,V1__m) ) ) ) ).

fof('Coq.NArith.BinNat.N.lt_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.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.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.le_refl',axiom,
    ! [V0__p] :
      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V0__p)
     => cCoq_2ePArith_2eBinPos_2ePos_2ele___24a2(V0__p,V0__p) ) ).

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__339___24t(V0__A)
     => ! [V1__z] :
          ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__z)
         => ( ! [V2__n] :
                ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__n)
               => ! [Vvar__4__m__155390] :
                    ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__4__m__155390)
                   => ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(Vvar__4__m__155390,V1__z))
                     => ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V2__n,Vvar__4__m__155390))
                       => p(happ(V0__A,Vvar__4__m__155390)) ) ) ) )
           => ! [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_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_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.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.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_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__152873___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.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_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.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.mul_comm',axiom,
    ! [V0__n] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
     => ! [V1__m] :
          ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
         => cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n,V1__m) = cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__m,V0__n) ) ) ).

fof('Coq.micromega.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__3514___24t(V0__R,V3__rplus)
                 => ! [V4__rtimes] :
                      ( c_24__type__3514___24t(V0__R,V4__rtimes)
                     => ! [V5__rminus] :
                          ( c_24__type__3514___24t(V0__R,V5__rminus)
                         => ! [V6__ropp] :
                              ( c_24__type__3523___24t(V0__R,V6__ropp)
                             => ! [V7__req] :
                                  ( c_24__type__2863___24t(V0__R,V7__req)
                                 => ! [V8__rle] :
                                      ( c_24__type__2863___24t(V0__R,V8__rle)
                                     => ! [V9__rlt] :
                                          ( c_24__type__2863___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__3514___24t(V0__R,V3__rplus)
                 => ! [V4__rtimes] :
                      ( c_24__type__3514___24t(V0__R,V4__rtimes)
                     => ! [V5__rminus] :
                          ( c_24__type__3514___24t(V0__R,V5__rminus)
                         => ! [V6__ropp] :
                              ( c_24__type__3523___24t(V0__R,V6__ropp)
                             => ! [V7__req] :
                                  ( c_24__type__2863___24t(V0__R,V7__req)
                                 => ! [V8__rle] :
                                      ( c_24__type__2863___24t(V0__R,V8__rle)
                                     => ! [V9__rlt] :
                                          ( c_24__type__2863___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__3514___24t(V0__R,V3__rplus)
                 => ! [V4__rtimes] :
                      ( c_24__type__3514___24t(V0__R,V4__rtimes)
                     => ! [V5__rminus] :
                          ( c_24__type__3514___24t(V0__R,V5__rminus)
                         => ! [V6__ropp] :
                              ( c_24__type__3523___24t(V0__R,V6__ropp)
                             => ! [V7__req] :
                                  ( c_24__type__2863___24t(V0__R,V7__req)
                                 => ! [V8__rle] :
                                      ( c_24__type__2863___24t(V0__R,V8__rle)
                                     => ! [V9__rlt] :
                                          ( c_24__type__2863___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__3514___24t(V0__R,V3__rplus)
                 => ! [V4__rtimes] :
                      ( c_24__type__3514___24t(V0__R,V4__rtimes)
                     => ! [V5__rminus] :
                          ( c_24__type__3514___24t(V0__R,V5__rminus)
                         => ! [V6__ropp] :
                              ( c_24__type__3523___24t(V0__R,V6__ropp)
                             => ! [V7__req] :
                                  ( c_24__type__2863___24t(V0__R,V7__req)
                                 => ! [V8__rle] :
                                      ( c_24__type__2863___24t(V0__R,V8__rle)
                                     => ! [V9__rlt] :
                                          ( c_24__type__2863___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__3514___24t(V0__R,V3__rplus)
                 => ! [V4__rtimes] :
                      ( c_24__type__3514___24t(V0__R,V4__rtimes)
                     => ! [V5__rminus] :
                          ( c_24__type__3514___24t(V0__R,V5__rminus)
                         => ! [V6__ropp] :
                              ( c_24__type__3523___24t(V0__R,V6__ropp)
                             => ! [V7__req] :
                                  ( c_24__type__2863___24t(V0__R,V7__req)
                                 => ! [V8__rle] :
                                      ( c_24__type__2863___24t(V0__R,V8__rle)
                                     => ! [V9__rlt] :
                                          ( c_24__type__2863___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__3514___24t(V0__R,V3__rplus)
                 => ! [V4__rtimes] :
                      ( c_24__type__3514___24t(V0__R,V4__rtimes)
                     => ! [V5__rminus] :
                          ( c_24__type__3514___24t(V0__R,V5__rminus)
                         => ! [V6__ropp] :
                              ( c_24__type__3523___24t(V0__R,V6__ropp)
                             => ! [V7__req] :
                                  ( c_24__type__2863___24t(V0__R,V7__req)
                                 => ! [V8__rle] :
                                      ( c_24__type__2863___24t(V0__R,V8__rle)
                                     => ! [V9__rlt] :
                                          ( c_24__type__2863___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__3514___24t(V0__R,V3__rplus)
                 => ! [V4__rtimes] :
                      ( c_24__type__3514___24t(V0__R,V4__rtimes)
                     => ! [V5__rminus] :
                          ( c_24__type__3514___24t(V0__R,V5__rminus)
                         => ! [V6__ropp] :
                              ( c_24__type__3523___24t(V0__R,V6__ropp)
                             => ! [V7__req] :
                                  ( c_24__type__2863___24t(V0__R,V7__req)
                                 => ! [V8__rle] :
                                      ( c_24__type__2863___24t(V0__R,V8__rle)
                                     => ! [V9__rlt] :
                                          ( c_24__type__2863___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__3514___24t(V0__R,V3__rplus)
                 => ! [V4__rtimes] :
                      ( c_24__type__3514___24t(V0__R,V4__rtimes)
                     => ! [V5__rminus] :
                          ( c_24__type__3514___24t(V0__R,V5__rminus)
                         => ! [V6__ropp] :
                              ( c_24__type__3523___24t(V0__R,V6__ropp)
                             => ! [V7__req] :
                                  ( c_24__type__2863___24t(V0__R,V7__req)
                                 => ! [V8__rle] :
                                      ( c_24__type__2863___24t(V0__R,V8__rle)
                                     => ! [V9__rlt] :
                                          ( c_24__type__2863___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__3514___24t(V0__R,V3__rplus)
                 => ! [V4__rtimes] :
                      ( c_24__type__3514___24t(V0__R,V4__rtimes)
                     => ! [V5__rminus] :
                          ( c_24__type__3514___24t(V0__R,V5__rminus)
                         => ! [V6__ropp] :
                              ( c_24__type__3523___24t(V0__R,V6__ropp)
                             => ! [V7__req] :
                                  ( c_24__type__2863___24t(V0__R,V7__req)
                                 => ! [V8__rle] :
                                      ( c_24__type__2863___24t(V0__R,V8__rle)
                                     => ! [V9__rlt] :
                                          ( c_24__type__2863___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__3514___24t(V0__R,V3__rplus)
                 => ! [V4__rtimes] :
                      ( c_24__type__3514___24t(V0__R,V4__rtimes)
                     => ! [V5__rminus] :
                          ( c_24__type__3514___24t(V0__R,V5__rminus)
                         => ! [V6__ropp] :
                              ( c_24__type__3523___24t(V0__R,V6__ropp)
                             => ! [V7__req] :
                                  ( c_24__type__2863___24t(V0__R,V7__req)
                                 => ! [V8__rle] :
                                      ( c_24__type__2863___24t(V0__R,V8__rle)
                                     => ! [V9__rlt] :
                                          ( c_24__type__2863___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__3514___24t(V0__R,V3__rplus)
                 => ! [V4__rtimes] :
                      ( c_24__type__3514___24t(V0__R,V4__rtimes)
                     => ! [V5__rminus] :
                          ( c_24__type__3514___24t(V0__R,V5__rminus)
                         => ! [V6__ropp] :
                              ( c_24__type__3523___24t(V0__R,V6__ropp)
                             => ! [V7__req] :
                                  ( c_24__type__2863___24t(V0__R,V7__req)
                                 => ! [V8__rle] :
                                      ( c_24__type__2863___24t(V0__R,V8__rle)
                                     => ! [V9__rlt] :
                                          ( c_24__type__2863___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__3514___24t(V0__R,V3__rplus)
                 => ! [V4__rtimes] :
                      ( c_24__type__3514___24t(V0__R,V4__rtimes)
                     => ! [V5__rminus] :
                          ( c_24__type__3514___24t(V0__R,V5__rminus)
                         => ! [V6__ropp] :
                              ( c_24__type__3523___24t(V0__R,V6__ropp)
                             => ! [V7__req] :
                                  ( c_24__type__2863___24t(V0__R,V7__req)
                                 => ! [V8__rle] :
                                      ( c_24__type__2863___24t(V0__R,V8__rle)
                                     => ! [V9__rlt] :
                                          ( c_24__type__2863___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__3514___24t(V0__R,V3__rplus)
                 => ! [V4__rtimes] :
                      ( c_24__type__3514___24t(V0__R,V4__rtimes)
                     => ! [V5__rminus] :
                          ( c_24__type__3514___24t(V0__R,V5__rminus)
                         => ! [V6__ropp] :
                              ( c_24__type__3523___24t(V0__R,V6__ropp)
                             => ! [V7__req] :
                                  ( c_24__type__2863___24t(V0__R,V7__req)
                                 => ! [V8__rle] :
                                      ( c_24__type__2863___24t(V0__R,V8__rle)
                                     => ! [V9__rlt] :
                                          ( c_24__type__2863___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__3514___24t(V0__R,V3__rplus)
                 => ! [V4__rtimes] :
                      ( c_24__type__3514___24t(V0__R,V4__rtimes)
                     => ! [V5__rminus] :
                          ( c_24__type__3514___24t(V0__R,V5__rminus)
                         => ! [V6__ropp] :
                              ( c_24__type__3523___24t(V0__R,V6__ropp)
                             => ! [V7__req] :
                                  ( c_24__type__2863___24t(V0__R,V7__req)
                                 => ! [V8__rle] :
                                      ( c_24__type__2863___24t(V0__R,V8__rle)
                                     => ! [V9__rlt] :
                                          ( c_24__type__2863___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__3514___24t(V0__R,V3__rplus)
                 => ! [V4__rtimes] :
                      ( c_24__type__3514___24t(V0__R,V4__rtimes)
                     => ! [V5__rminus] :
                          ( c_24__type__3514___24t(V0__R,V5__rminus)
                         => ! [V6__ropp] :
                              ( c_24__type__3523___24t(V0__R,V6__ropp)
                             => ! [V7__req] :
                                  ( c_24__type__2863___24t(V0__R,V7__req)
                                 => ! [V8__rle] :
                                      ( c_24__type__2863___24t(V0__R,V8__rle)
                                     => ! [V9__rlt] :
                                          ( c_24__type__2863___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__3514___24t(V0__R,V3__rplus)
                 => ! [V4__rtimes] :
                      ( c_24__type__3514___24t(V0__R,V4__rtimes)
                     => ! [V5__rminus] :
                          ( c_24__type__3514___24t(V0__R,V5__rminus)
                         => ! [V6__ropp] :
                              ( c_24__type__3523___24t(V0__R,V6__ropp)
                             => ! [V7__req] :
                                  ( c_24__type__2863___24t(V0__R,V7__req)
                                 => ! [V8__rle] :
                                      ( c_24__type__2863___24t(V0__R,V8__rle)
                                     => ! [V9__rlt] :
                                          ( c_24__type__2863___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__3514___24t(V0__R,V3__rplus)
                 => ! [V4__rtimes] :
                      ( c_24__type__3514___24t(V0__R,V4__rtimes)
                     => ! [V5__rminus] :
                          ( c_24__type__3514___24t(V0__R,V5__rminus)
                         => ! [V6__ropp] :
                              ( c_24__type__3523___24t(V0__R,V6__ropp)
                             => ! [V7__req] :
                                  ( c_24__type__2863___24t(V0__R,V7__req)
                                 => ! [V8__rle] :
                                      ( c_24__type__2863___24t(V0__R,V8__rle)
                                     => ! [V9__rlt] :
                                          ( c_24__type__2863___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__3514___24t(V0__R,V3__rplus)
                 => ! [V4__rtimes] :
                      ( c_24__type__3514___24t(V0__R,V4__rtimes)
                     => ! [V5__rminus] :
                          ( c_24__type__3514___24t(V0__R,V5__rminus)
                         => ! [V6__ropp] :
                              ( c_24__type__3523___24t(V0__R,V6__ropp)
                             => ! [V7__req] :
                                  ( c_24__type__2863___24t(V0__R,V7__req)
                                 => ! [V8__rle] :
                                      ( c_24__type__2863___24t(V0__R,V8__rle)
                                     => ! [V9__rlt] :
                                          ( c_24__type__2863___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__3514___24t(V0__R,V3__rplus)
                 => ! [V4__rtimes] :
                      ( c_24__type__3514___24t(V0__R,V4__rtimes)
                     => ! [V5__rminus] :
                          ( c_24__type__3514___24t(V0__R,V5__rminus)
                         => ! [V6__ropp] :
                              ( c_24__type__3523___24t(V0__R,V6__ropp)
                             => ! [V7__req] :
                                  ( c_24__type__2863___24t(V0__R,V7__req)
                                 => ! [V8__rle] :
                                      ( c_24__type__2863___24t(V0__R,V8__rle)
                                     => ! [V9__rlt] :
                                          ( c_24__type__2863___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__3514___24t(V0__R,V3__rplus)
                 => ! [V4__rtimes] :
                      ( c_24__type__3514___24t(V0__R,V4__rtimes)
                     => ! [V5__rminus] :
                          ( c_24__type__3514___24t(V0__R,V5__rminus)
                         => ! [V6__ropp] :
                              ( c_24__type__3523___24t(V0__R,V6__ropp)
                             => ! [V7__req] :
                                  ( c_24__type__2863___24t(V0__R,V7__req)
                                 => ! [V8__rle] :
                                      ( c_24__type__2863___24t(V0__R,V8__rle)
                                     => ! [V9__rlt] :
                                          ( c_24__type__2863___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__3514___24t(V0__R,V3__rplus)
                 => ! [V4__rtimes] :
                      ( c_24__type__3514___24t(V0__R,V4__rtimes)
                     => ! [V5__rminus] :
                          ( c_24__type__3514___24t(V0__R,V5__rminus)
                         => ! [V6__ropp] :
                              ( c_24__type__3523___24t(V0__R,V6__ropp)
                             => ! [V7__req] :
                                  ( c_24__type__2863___24t(V0__R,V7__req)
                                 => ! [V8__rle] :
                                      ( c_24__type__2863___24t(V0__R,V8__rle)
                                     => ! [V9__rlt] :
                                          ( c_24__type__2863___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__3514___24t(V0__R,V3__rplus)
                 => ! [V4__rtimes] :
                      ( c_24__type__3514___24t(V0__R,V4__rtimes)
                     => ! [V5__rminus] :
                          ( c_24__type__3514___24t(V0__R,V5__rminus)
                         => ! [V6__ropp] :
                              ( c_24__type__3523___24t(V0__R,V6__ropp)
                             => ! [V7__req] :
                                  ( c_24__type__2863___24t(V0__R,V7__req)
                                 => ! [V8__rle] :
                                      ( c_24__type__2863___24t(V0__R,V8__rle)
                                     => ! [V9__rlt] :
                                          ( c_24__type__2863___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__3514___24t(V0__R,V3__rplus)
                 => ! [V4__rtimes] :
                      ( c_24__type__3514___24t(V0__R,V4__rtimes)
                     => ! [V5__rminus] :
                          ( c_24__type__3514___24t(V0__R,V5__rminus)
                         => ! [V6__ropp] :
                              ( c_24__type__3523___24t(V0__R,V6__ropp)
                             => ! [V7__req] :
                                  ( c_24__type__2863___24t(V0__R,V7__req)
                                 => ! [V8__rle] :
                                      ( c_24__type__2863___24t(V0__R,V8__rle)
                                     => ! [V9__rlt] :
                                          ( c_24__type__2863___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__3514___24t(V0__R,V3__rplus)
                 => ! [V4__rtimes] :
                      ( c_24__type__3514___24t(V0__R,V4__rtimes)
                     => ! [V5__rminus] :
                          ( c_24__type__3514___24t(V0__R,V5__rminus)
                         => ! [V6__ropp] :
                              ( c_24__type__3523___24t(V0__R,V6__ropp)
                             => ! [V7__req] :
                                  ( c_24__type__2863___24t(V0__R,V7__req)
                                 => ! [V8__rle] :
                                      ( c_24__type__2863___24t(V0__R,V8__rle)
                                     => ! [V9__rlt] :
                                          ( c_24__type__2863___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__3514___24t(V0__R,V3__rplus)
                 => ! [V4__rtimes] :
                      ( c_24__type__3514___24t(V0__R,V4__rtimes)
                     => ! [V5__rminus] :
                          ( c_24__type__3514___24t(V0__R,V5__rminus)
                         => ! [V6__ropp] :
                              ( c_24__type__3523___24t(V0__R,V6__ropp)
                             => ! [V7__req] :
                                  ( c_24__type__2863___24t(V0__R,V7__req)
                                 => ! [V8__rle] :
                                      ( c_24__type__2863___24t(V0__R,V8__rle)
                                     => ! [V9__rlt] :
                                          ( c_24__type__2863___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__3514___24t(V0__R,V3__rplus)
                 => ! [V4__rtimes] :
                      ( c_24__type__3514___24t(V0__R,V4__rtimes)
                     => ! [V5__rminus] :
                          ( c_24__type__3514___24t(V0__R,V5__rminus)
                         => ! [V6__ropp] :
                              ( c_24__type__3523___24t(V0__R,V6__ropp)
                             => ! [V7__req] :
                                  ( c_24__type__2863___24t(V0__R,V7__req)
                                 => ! [V8__rle] :
                                      ( c_24__type__2863___24t(V0__R,V8__rle)
                                     => ! [V9__rlt] :
                                          ( c_24__type__2863___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__3514___24t(V0__R,V3__rplus)
                 => ! [V4__rtimes] :
                      ( c_24__type__3514___24t(V0__R,V4__rtimes)
                     => ! [V5__rminus] :
                          ( c_24__type__3514___24t(V0__R,V5__rminus)
                         => ! [V6__ropp] :
                              ( c_24__type__3523___24t(V0__R,V6__ropp)
                             => ! [V7__req] :
                                  ( c_24__type__2863___24t(V0__R,V7__req)
                                 => ! [V8__rle] :
                                      ( c_24__type__2863___24t(V0__R,V8__rle)
                                     => ! [V9__rlt] :
                                          ( c_24__type__2863___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__3514___24t(V0__R,V3__rplus)
                 => ! [V4__rtimes] :
                      ( c_24__type__3514___24t(V0__R,V4__rtimes)
                     => ! [V5__rminus] :
                          ( c_24__type__3514___24t(V0__R,V5__rminus)
                         => ! [V6__ropp] :
                              ( c_24__type__3523___24t(V0__R,V6__ropp)
                             => ! [V7__req] :
                                  ( c_24__type__2863___24t(V0__R,V7__req)
                                 => ! [V8__rle] :
                                      ( c_24__type__2863___24t(V0__R,V8__rle)
                                     => ! [V9__rlt] :
                                          ( c_24__type__2863___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__3514___24t(V0__R,V3__rplus)
                 => ! [V4__rtimes] :
                      ( c_24__type__3514___24t(V0__R,V4__rtimes)
                     => ! [V5__rminus] :
                          ( c_24__type__3514___24t(V0__R,V5__rminus)
                         => ! [V6__ropp] :
                              ( c_24__type__3523___24t(V0__R,V6__ropp)
                             => ! [V7__req] :
                                  ( c_24__type__2863___24t(V0__R,V7__req)
                                 => ! [V8__rle] :
                                      ( c_24__type__2863___24t(V0__R,V8__rle)
                                     => ! [V9__rlt] :
                                          ( c_24__type__2863___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__3514___24t(V0__R,V3__rplus)
                 => ! [V4__rtimes] :
                      ( c_24__type__3514___24t(V0__R,V4__rtimes)
                     => ! [V5__rminus] :
                          ( c_24__type__3514___24t(V0__R,V5__rminus)
                         => ! [V6__ropp] :
                              ( c_24__type__3523___24t(V0__R,V6__ropp)
                             => ! [V7__req] :
                                  ( c_24__type__2863___24t(V0__R,V7__req)
                                 => ! [V8__rle] :
                                      ( c_24__type__2863___24t(V0__R,V8__rle)
                                     => ! [V9__rlt] :
                                          ( c_24__type__2863___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__3514___24t(V0__R,V3__rplus)
                 => ! [V4__rtimes] :
                      ( c_24__type__3514___24t(V0__R,V4__rtimes)
                     => ! [V5__rminus] :
                          ( c_24__type__3514___24t(V0__R,V5__rminus)
                         => ! [V6__ropp] :
                              ( c_24__type__3523___24t(V0__R,V6__ropp)
                             => ! [V7__req] :
                                  ( c_24__type__2863___24t(V0__R,V7__req)
                                 => ! [V8__rle] :
                                      ( c_24__type__2863___24t(V0__R,V8__rle)
                                     => ! [V9__rlt] :
                                          ( c_24__type__2863___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__3514___24t(V0__R,V3__rplus)
                 => ! [V4__rtimes] :
                      ( c_24__type__3514___24t(V0__R,V4__rtimes)
                     => ! [V5__rminus] :
                          ( c_24__type__3514___24t(V0__R,V5__rminus)
                         => ! [V6__ropp] :
                              ( c_24__type__3523___24t(V0__R,V6__ropp)
                             => ! [V7__req] :
                                  ( c_24__type__2863___24t(V0__R,V7__req)
                                 => ! [V8__rle] :
                                      ( c_24__type__2863___24t(V0__R,V8__rle)
                                     => ! [V9__rlt] :
                                          ( c_24__type__2863___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__3514___24t(V0__R,V3__rplus)
                 => ! [V4__rtimes] :
                      ( c_24__type__3514___24t(V0__R,V4__rtimes)
                     => ! [V5__rminus] :
                          ( c_24__type__3514___24t(V0__R,V5__rminus)
                         => ! [V6__ropp] :
                              ( c_24__type__3523___24t(V0__R,V6__ropp)
                             => ! [V7__req] :
                                  ( c_24__type__2863___24t(V0__R,V7__req)
                                 => ! [V8__rle] :
                                      ( c_24__type__2863___24t(V0__R,V8__rle)
                                     => ! [V9__rlt] :
                                          ( c_24__type__2863___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.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__3514___24t(V0__R,V3__radd)
                 => ! [V4__rmul] :
                      ( c_24__type__3514___24t(V0__R,V4__rmul)
                     => ! [V5__rsub] :
                          ( c_24__type__3514___24t(V0__R,V5__rsub)
                         => ! [V6__ropp] :
                              ( c_24__type__3523___24t(V0__R,V6__ropp)
                             => ! [V7__req] :
                                  ( c_24__type__2863___24t(V0__R,V7__req)
                                 => ( cCoq_2esetoid__ring_2eRing__theory_2ealmost__ring__theory___24a8(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__req)
                                   => ! [V9__x] :
                                        ( t(V9__x,V0__R)
                                       => p(happ(happ(V7__req,happ(happ(V3__radd,V1__rO),V9__x)),V9__x)) ) ) ) ) ) ) ) ) ) ) ).

fof('Coq.setoid_ring.Ring_theory.ARadd_assoc',axiom,
    ! [V0__R] :
      ( cType___24t(V0__R)
     => ! [V1__rO] :
          ( t(V1__rO,V0__R)
         => ! [V2__rI] :
              ( t(V2__rI,V0__R)
             => ! [V3__radd] :
                  ( c_24__type__3514___24t(V0__R,V3__radd)
                 => ! [V4__rmul] :
                      ( c_24__type__3514___24t(V0__R,V4__rmul)
                     => ! [V5__rsub] :
                          ( c_24__type__3514___24t(V0__R,V5__rsub)
                         => ! [V6__ropp] :
                              ( c_24__type__3523___24t(V0__R,V6__ropp)
                             => ! [V7__req] :
                                  ( c_24__type__2863___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__3514___24t(V0__R,V3__radd)
                 => ! [V4__rmul] :
                      ( c_24__type__3514___24t(V0__R,V4__rmul)
                     => ! [V5__rsub] :
                          ( c_24__type__3514___24t(V0__R,V5__rsub)
                         => ! [V6__ropp] :
                              ( c_24__type__3523___24t(V0__R,V6__ropp)
                             => ! [V7__req] :
                                  ( c_24__type__2863___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.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__3514___24t(V0__R,V3__radd)
                 => ! [V4__rmul] :
                      ( c_24__type__3514___24t(V0__R,V4__rmul)
                     => ! [V5__rsub] :
                          ( c_24__type__3514___24t(V0__R,V5__rsub)
                         => ! [V6__ropp] :
                              ( c_24__type__3523___24t(V0__R,V6__ropp)
                             => ! [V7__req] :
                                  ( c_24__type__2863___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__3514___24t(V0__R,V3__radd)
                 => ! [V4__rmul] :
                      ( c_24__type__3514___24t(V0__R,V4__rmul)
                     => ! [V5__rsub] :
                          ( c_24__type__3514___24t(V0__R,V5__rsub)
                         => ! [V6__ropp] :
                              ( c_24__type__3523___24t(V0__R,V6__ropp)
                             => ! [V7__req] :
                                  ( c_24__type__2863___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__3514___24t(V0__R,V3__radd)
                 => ! [V4__rmul] :
                      ( c_24__type__3514___24t(V0__R,V4__rmul)
                     => ! [V5__rsub] :
                          ( c_24__type__3514___24t(V0__R,V5__rsub)
                         => ! [V6__ropp] :
                              ( c_24__type__3523___24t(V0__R,V6__ropp)
                             => ! [V7__req] :
                                  ( c_24__type__2863___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__3514___24t(V0__R,V3__radd)
                 => ! [V4__rmul] :
                      ( c_24__type__3514___24t(V0__R,V4__rmul)
                     => ! [V5__rsub] :
                          ( c_24__type__3514___24t(V0__R,V5__rsub)
                         => ! [V6__ropp] :
                              ( c_24__type__3523___24t(V0__R,V6__ropp)
                             => ! [V7__req] :
                                  ( c_24__type__2863___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__3514___24t(V0__R,V3__radd)
                 => ! [V4__rmul] :
                      ( c_24__type__3514___24t(V0__R,V4__rmul)
                     => ! [V5__rsub] :
                          ( c_24__type__3514___24t(V0__R,V5__rsub)
                         => ! [V6__ropp] :
                              ( c_24__type__3523___24t(V0__R,V6__ropp)
                             => ! [V7__req] :
                                  ( c_24__type__2863___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__3514___24t(V0__R,V3__radd)
                 => ! [V4__rmul] :
                      ( c_24__type__3514___24t(V0__R,V4__rmul)
                     => ! [V5__rsub] :
                          ( c_24__type__3514___24t(V0__R,V5__rsub)
                         => ! [V6__ropp] :
                              ( c_24__type__3523___24t(V0__R,V6__ropp)
                             => ! [V7__req] :
                                  ( c_24__type__2863___24t(V0__R,V7__req)
                                 => ( cCoq_2esetoid__ring_2eRing__theory_2ealmost__ring__theory___24a8(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__req)
                                   => ! [V9__x] :
                                        ( t(V9__x,V0__R)
                                       => ! [V10__y] :
                                            ( t(V10__y,V0__R)
                                           => p(happ(happ(V7__req,happ(happ(V4__rmul,V9__x),V10__y)),happ(happ(V4__rmul,V10__y),V9__x))) ) ) ) ) ) ) ) ) ) ) ) ).

fof('Coq.setoid_ring.Ring_theory.ARopp_mul_l',axiom,
    ! [V0__R] :
      ( cType___24t(V0__R)
     => ! [V1__rO] :
          ( t(V1__rO,V0__R)
         => ! [V2__rI] :
              ( t(V2__rI,V0__R)
             => ! [V3__radd] :
                  ( c_24__type__3514___24t(V0__R,V3__radd)
                 => ! [V4__rmul] :
                      ( c_24__type__3514___24t(V0__R,V4__rmul)
                     => ! [V5__rsub] :
                          ( c_24__type__3514___24t(V0__R,V5__rsub)
                         => ! [V6__ropp] :
                              ( c_24__type__3523___24t(V0__R,V6__ropp)
                             => ! [V7__req] :
                                  ( c_24__type__2863___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__3514___24t(V0__R,V3__radd)
                 => ! [V4__rmul] :
                      ( c_24__type__3514___24t(V0__R,V4__rmul)
                     => ! [V5__rsub] :
                          ( c_24__type__3514___24t(V0__R,V5__rsub)
                         => ! [V6__ropp] :
                              ( c_24__type__3523___24t(V0__R,V6__ropp)
                             => ! [V7__req] :
                                  ( c_24__type__2863___24t(V0__R,V7__req)
                                 => ( cCoq_2esetoid__ring_2eRing__theory_2ealmost__ring__theory___24a8(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__req)
                                   => ! [V9__x] :
                                        ( t(V9__x,V0__R)
                                       => ! [V10__y] :
                                            ( t(V10__y,V0__R)
                                           => p(happ(happ(V7__req,happ(happ(V5__rsub,V9__x),V10__y)),happ(happ(V3__radd,V9__x),happ(V6__ropp,V10__y)))) ) ) ) ) ) ) ) ) ) ) ) ).

fof('Coq.setoid_ring.Ring_theory.mk_art',axiom,
    ! [V0__R] :
      ( cType___24t(V0__R)
     => ! [V1__rO] :
          ( t(V1__rO,V0__R)
         => ! [V2__rI] :
              ( t(V2__rI,V0__R)
             => ! [V3__radd] :
                  ( c_24__type__3514___24t(V0__R,V3__radd)
                 => ! [V4__rmul] :
                      ( c_24__type__3514___24t(V0__R,V4__rmul)
                     => ! [V5__rsub] :
                          ( c_24__type__3514___24t(V0__R,V5__rsub)
                         => ! [V6__ropp] :
                              ( c_24__type__3523___24t(V0__R,V6__ropp)
                             => ! [V7__req] :
                                  ( c_24__type__2863___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__3514___24t(V0__R,V3__radd)
                 => ! [V4__rmul] :
                      ( c_24__type__3514___24t(V0__R,V4__rmul)
                     => ! [V5__rsub] :
                          ( c_24__type__3514___24t(V0__R,V5__rsub)
                         => ! [V6__ropp] :
                              ( c_24__type__3523___24t(V0__R,V6__ropp)
                             => ! [V7__req] :
                                  ( c_24__type__2863___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('Hoare2.verification_correct',axiom,
    ! [V0__d] :
      ( cHoare2_2edcom___24t(V0__d)
     => ! [V1__P] :
          ( cPLF_2eHoare_2eAssertion___24t(V1__P)
         => ( cHoare2_2everification__conditions___24a2(V1__P,V0__d)
           => cPLF_2eHoare_2ehoare__triple___24a3(V1__P,cHoare2_2eextract___24a1(V0__d),cHoare2_2epost___24a1(V0__d)) ) ) ) ).

fof('Hoare2.verification_correct_dec',axiom,
    ! [V0__dec] :
      ( cHoare2_2edecorated___24t(V0__dec)
     => ( cHoare2_2everification__conditions__dec___24a1(V0__dec)
       => cHoare2_2edec__correct___24a1(V0__dec) ) ) ).

fof('PLF.Imp.AExp.silly2',axiom,
    ! [V0__P] :
      ( cProp___24t(V0__P)
     => ( p(V0__P)
       => p(V0__P) ) ) ).

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('$adef_$_let_var_6_p_131811_131813_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__let__var__6__p__131811__131813,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__let__var__6__p__131811__131813___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('$adef_Coq.PArith.BinPos.Pos.PeanoSucc_$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('$adef_Coq.Reals.Rdefinitions.IZR_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eReals_2eRdefinitions_2eIZR,V_24X1) = cCoq_2eReals_2eRdefinitions_2eIZR___24a1(V_24X1) ).

fof('$adef_$_case_Coq.Numbers.BinNums.Z$126290_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__case__Coq_2eNumbers_2eBinNums_2eZ_24126290,V_24X1),V_24X2),V_24X3) = c_24__case__Coq_2eNumbers_2eBinNums_2eZ_24126290___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_Hoare2.verification_conditions_dec_$a1',axiom,
    ! [V_24X1] :
      ( p(happ(cHoare2_2everification__conditions__dec,V_24X1))
    <=> cHoare2_2everification__conditions__dec___24a1(V_24X1) ) ).

fof('$adef_Coq.Relations.Relation_Definitions.preorder_$a2',axiom,
    ! [V_24X1,V_24X2] :
      ( p(happ(happ(cCoq_2eRelations_2eRelation__Definitions_2epreorder,V_24X1),V_24X2))
    <=> cCoq_2eRelations_2eRelation__Definitions_2epreorder___24a2(V_24X1,V_24X2) ) ).

fof('$adef_Coq.Init.Datatypes.None_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eInit_2eDatatypes_2eNone,V_24X1) = cCoq_2eInit_2eDatatypes_2eNone___24a1(V_24X1) ).

fof('$adef_Coq.ZArith.BinIntDef.Z.to_nat_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eZArith_2eBinIntDef_2eZ_2eto__nat,V_24X1) = cCoq_2eZArith_2eBinIntDef_2eZ_2eto__nat___24a1(V_24X1) ).

fof('$adef_Coq.NArith.BinNat.N.lt_$a2',axiom,
    ! [V_24X1,V_24X2] :
      ( p(happ(happ(cCoq_2eNArith_2eBinNat_2eN_2elt,V_24X1),V_24X2))
    <=> cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V_24X1,V_24X2) ) ).

fof('$adef_Coq.Vectors.VectorDef.cons_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2eVectors_2eVectorDef_2econs,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2eVectors_2eVectorDef_2econs___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).

fof('$adef_Coq.ZArith.BinIntDef.Z.of_N_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eZArith_2eBinIntDef_2eZ_2eof__N,V_24X1) = cCoq_2eZArith_2eBinIntDef_2eZ_2eof__N___24a1(V_24X1) ).

fof('$adef_PLF.Hoare.RepeatExercise.CRepeat_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cPLF_2eHoare_2eRepeatExercise_2eCRepeat,V_24X1),V_24X2) = cPLF_2eHoare_2eRepeatExercise_2eCRepeat___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('$adef_$_case_Coq.Init.Datatypes.nat$83833_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__case__Coq_2eInit_2eDatatypes_2enat_2483833,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__case__Coq_2eInit_2eDatatypes_2enat_2483833___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).

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('$adef_$_case_Coq.Init.Datatypes.nat$4839_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__case__Coq_2eInit_2eDatatypes_2enat_244839,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__case__Coq_2eInit_2eDatatypes_2enat_244839___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).

fof('$adef_PLF.Imp.beval_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cPLF_2eImp_2ebeval,V_24X1),V_24X2) = cPLF_2eImp_2ebeval___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.setoid_ring.Ring_theory.SRopp_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2esetoid__ring_2eRing__theory_2eSRopp,V_24X1),V_24X2) = cCoq_2esetoid__ring_2eRing__theory_2eSRopp___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.micromega.VarMap.t_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2emicromega_2eVarMap_2et,V_24X1) = cCoq_2emicromega_2eVarMap_2et___24a1(V_24X1) ).

fof('$adef_Coq.PArith.BinPosDef.Pos.of_nat_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2ePArith_2eBinPosDef_2ePos_2eof__nat,V_24X1) = cCoq_2ePArith_2eBinPosDef_2ePos_2eof__nat___24a1(V_24X1) ).

fof('$adef_Coq.Init.Decimal.nzhead_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eInit_2eDecimal_2enzhead,V_24X1) = cCoq_2eInit_2eDecimal_2enzhead___24a1(V_24X1) ).

fof('$adef_Coq.Lists.List.Exists_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] :
      ( p(happ(happ(happ(cCoq_2eLists_2eList_2eExists,V_24X1),V_24X2),V_24X3))
    <=> cCoq_2eLists_2eList_2eExists___24a3(V_24X1,V_24X2,V_24X3) ) ).

fof('$adef_Coq.micromega.RingMicromega.PsatzMulC_$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('$adef_PLF.Imp.aevalR_division.APlus_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cPLF_2eImp_2eaevalR__division_2eAPlus,V_24X1),V_24X2) = cPLF_2eImp_2eaevalR__division_2eAPlus___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.Reals.Rfunctions.ZintPos_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2eReals_2eRfunctions_2eZintPos,V_24X1),V_24X2) = cCoq_2eReals_2eRfunctions_2eZintPos___24a2(V_24X1,V_24X2) ).

fof('$adef_Hoare2.Decorated_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cHoare2_2eDecorated,V_24X1),V_24X2) = cHoare2_2eDecorated___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.setoid_ring.Ring_theory.sring_eq_ext_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] :
      ( p(happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__theory_2esring__eq__ext,V_24X1),V_24X2),V_24X3),V_24X4))
    <=> cCoq_2esetoid__ring_2eRing__theory_2esring__eq__ext___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).

fof('$adef_$_lam_155209_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__155209,V_24X1),V_24X2),V_24X3) = c_24__lam__155209___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_$_lam_155201_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__155201,V_24X1),V_24X2),V_24X3) = c_24__lam__155201___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_Coq.setoid_ring.Ring_polynom.PEc_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2ePEc,V_24X1),V_24X2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEc___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.Vectors.VectorDef.Forall_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] :
      ( p(happ(happ(happ(happ(cCoq_2eVectors_2eVectorDef_2eForall,V_24X1),V_24X2),V_24X3),V_24X4))
    <=> cCoq_2eVectors_2eVectorDef_2eForall___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).

fof('$adef_Coq.Init.Datatypes.implb_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eDatatypes_2eimplb,V_24X1),V_24X2) = cCoq_2eInit_2eDatatypes_2eimplb___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.micromega.ZCoeff.gen_order_phi_Z_$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('$adef_$_prop_149936_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__prop__149936,V_24X1),V_24X2),V_24X3) = c_24__prop__149936___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_Coq.setoid_ring.Ring_polynom.PEmul_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2ePEmul,V_24X1),V_24X2),V_24X3) = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_Coq.Relations.Relation_Operators.clos_refl_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] :
      ( p(happ(happ(happ(happ(cCoq_2eRelations_2eRelation__Operators_2eclos__refl,V_24X1),V_24X2),V_24X3),V_24X4))
    <=> cCoq_2eRelations_2eRelation__Operators_2eclos__refl___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).

fof('$adef_Coq.setoid_ring.Ring_polynom.Pc_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2ePc,V_24X1),V_24X2) = cCoq_2esetoid__ring_2eRing__polynom_2ePc___24a2(V_24X1,V_24X2) ).

fof('$adef_$_lam_1717_$a6',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(c_24__lam__1717,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = c_24__lam__1717___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).

fof('$adef_Coq.micromega.RMicromega.CMult_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2emicromega_2eRMicromega_2eCMult,V_24X1),V_24X2) = cCoq_2emicromega_2eRMicromega_2eCMult___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.micromega.DeclConstant.GT_$a2',axiom,
    ! [V_24X1,V_24X2] :
      ( p(happ(happ(cCoq_2emicromega_2eDeclConstant_2eGT,V_24X1),V_24X2))
    <=> cCoq_2emicromega_2eDeclConstant_2eGT___24a2(V_24X1,V_24X2) ) ).

fof('$adef_Coq.Init.Nat.log2_iter_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2eInit_2eNat_2elog2__iter,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2eInit_2eNat_2elog2__iter___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).

fof('$adef_Coq.setoid_ring.InitialRing.gen_phiZ_$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('$adef_$_lam_1487_$a6',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(c_24__lam__1487,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = c_24__lam__1487___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).

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('$adef_$_lam_1717_$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__1717,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7) = c_24__lam__1717___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7) ).

fof('$adef_Coq.Arith.Between.P_nth_$a5',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] :
      ( p(happ(happ(happ(happ(happ(cCoq_2eArith_2eBetween_2eP__nth,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5))
    <=> cCoq_2eArith_2eBetween_2eP__nth___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ) ).

fof('$adef_Coq.Relations.Relation_Operators.clos_refl_sym_trans_n1_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] :
      ( p(happ(happ(happ(happ(cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans__n1,V_24X1),V_24X2),V_24X3),V_24X4))
    <=> cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans__n1___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).

fof('$adef_Coq.Reals.Rdefinitions.IPR_$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('$adef_PLF.Imp.AExp.BNot_$a1',axiom,
    ! [V_24X1] : happ(cPLF_2eImp_2eAExp_2eBNot,V_24X1) = cPLF_2eImp_2eAExp_2eBNot___24a1(V_24X1) ).

fof('$adef_Coq.Init.Datatypes.CompareSpecT_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2eInit_2eDatatypes_2eCompareSpecT,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2eInit_2eDatatypes_2eCompareSpecT___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).

fof('$adef_Coq.ZArith.BinIntDef.Z.pred_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eZArith_2eBinIntDef_2eZ_2epred,V_24X1) = cCoq_2eZArith_2eBinIntDef_2eZ_2epred___24a1(V_24X1) ).

fof('$adef_Coq.micromega.ZMicromega.Vars.Facts.MP.Dec.FSetDecideAuxiliary.FSet_elt_Prop_$a1',axiom,
    ! [V_24X1] :
      ( p(happ(cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__elt__Prop,V_24X1))
    <=> cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__elt__Prop___24a1(V_24X1) ) ).

fof('$adef_Coq.setoid_ring.Field_theory.FEdiv_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2esetoid__ring_2eField__theory_2eFEdiv,V_24X1),V_24X2),V_24X3) = cCoq_2esetoid__ring_2eField__theory_2eFEdiv___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_Coq.Init.Nat.compare_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eNat_2ecompare,V_24X1),V_24X2) = cCoq_2eInit_2eNat_2ecompare___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.setoid_ring.Ring_theory.almost_ring_theory_$a8',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8] :
      ( p(happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__theory_2ealmost__ring__theory,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8))
    <=> cCoq_2esetoid__ring_2eRing__theory_2ealmost__ring__theory___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8) ) ).

fof('$adef_Coq.Init.Datatypes.app_$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('$adef_Coq.setoid_ring.InitialRing.gen_phiZ_$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('$adef_Coq.Init.Specif.sig_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eSpecif_2esig,V_24X1),V_24X2) = cCoq_2eInit_2eSpecif_2esig___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.ZArith.BinIntDef.Z.leb_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eBinIntDef_2eZ_2eleb,V_24X1),V_24X2) = cCoq_2eZArith_2eBinIntDef_2eZ_2eleb___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.Relations.Relation_Operators.lexprod_$a6',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] :
      ( p(happ(happ(happ(happ(happ(happ(cCoq_2eRelations_2eRelation__Operators_2elexprod,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6))
    <=> cCoq_2eRelations_2eRelation__Operators_2elexprod___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ) ).

fof('$adef_Coq.setoid_ring.Field_theory.FEmul_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2esetoid__ring_2eField__theory_2eFEmul,V_24X1),V_24X2),V_24X3) = cCoq_2esetoid__ring_2eField__theory_2eFEmul___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_Coq.ZArith.BinIntDef.Z.mul_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eBinIntDef_2eZ_2emul,V_24X1),V_24X2) = cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V_24X1,V_24X2) ).

fof('$adef_PLF.Hoare.Himp.CIf_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cPLF_2eHoare_2eHimp_2eCIf,V_24X1),V_24X2),V_24X3) = cPLF_2eHoare_2eHimp_2eCIf___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_Coq.micromega.ZMicromega.EnumProof_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2emicromega_2eZMicromega_2eEnumProof,V_24X1),V_24X2),V_24X3) = cCoq_2emicromega_2eZMicromega_2eEnumProof___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_Coq.PArith.BinPosDef.Pos.iter_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2ePArith_2eBinPosDef_2ePos_2eiter,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2ePArith_2eBinPosDef_2ePos_2eiter___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).

fof('$adef_Coq.Relations.Relation_Operators.symprod_$a6',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] :
      ( p(happ(happ(happ(happ(happ(happ(cCoq_2eRelations_2eRelation__Operators_2esymprod,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6))
    <=> cCoq_2eRelations_2eRelation__Operators_2esymprod___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ) ).

fof('$adef_$_fix_4648_v_CANONICAL_0_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(c_24__fix__4648__v__CANONICAL__0,V_24X1),V_24X2) = c_24__fix__4648__v__CANONICAL__0___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('$adef_Coq.micromega.RingMicromega.Build_Formula_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2emicromega_2eRingMicromega_2eBuild__Formula,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2emicromega_2eRingMicromega_2eBuild__Formula___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).

fof('$adef_Coq.setoid_ring.Ring_polynom.mkmult_pow_$a5',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2emkmult__pow,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2esetoid__ring_2eRing__polynom_2emkmult__pow___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).

fof('$adef_Coq.Init.Specif.sumbool_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eSpecif_2esumbool,V_24X1),V_24X2) = cCoq_2eInit_2eSpecif_2esumbool___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.setoid_ring.Field_theory.mk_rsplit_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2esetoid__ring_2eField__theory_2emk__rsplit,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2esetoid__ring_2eField__theory_2emk__rsplit___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).

fof('$adef_PLF.Imp.BLe_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cPLF_2eImp_2eBLe,V_24X1),V_24X2) = cPLF_2eImp_2eBLe___24a2(V_24X1,V_24X2) ).

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('$adef_Coq.Sets.Relations_1.Relation_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eSets_2eRelations__1_2eRelation,V_24X1) = cCoq_2eSets_2eRelations__1_2eRelation___24a1(V_24X1) ).

fof('$adef_Coq.setoid_ring.Ring_theory.semi_ring_theory_$a6',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] :
      ( p(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__theory_2esemi__ring__theory,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6))
    <=> cCoq_2esetoid__ring_2eRing__theory_2esemi__ring__theory___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ) ).

fof('$adef_Coq.Reals.RIneq.mknonposreal_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eReals_2eRIneq_2emknonposreal,V_24X1) = cCoq_2eReals_2eRIneq_2emknonposreal___24a1(V_24X1) ).

fof('$adef_PLF.Imp.aeval_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cPLF_2eImp_2eaeval,V_24X1),V_24X2) = cPLF_2eImp_2eaeval___24a2(V_24X1,V_24X2) ).

fof('$adef_Hoare2.DCAsgn_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cHoare2_2eDCAsgn,V_24X1),V_24X2),V_24X3) = cHoare2_2eDCAsgn___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_Coq.Lists.SetoidList.transpose_restr2_$a5',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] :
      ( p(happ(happ(happ(happ(happ(cCoq_2eLists_2eSetoidList_2etranspose__restr2,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5))
    <=> cCoq_2eLists_2eSetoidList_2etranspose__restr2___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ) ).

fof('$adef_PLF.Imp.ceval_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] :
      ( p(happ(happ(happ(cPLF_2eImp_2eceval,V_24X1),V_24X2),V_24X3))
    <=> cPLF_2eImp_2eceval___24a3(V_24X1,V_24X2,V_24X3) ) ).

fof('$adef_PLF.Imp.AMinus_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cPLF_2eImp_2eAMinus,V_24X1),V_24X2) = cPLF_2eImp_2eAMinus___24a2(V_24X1,V_24X2) ).

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('$adef_PLF.Hoare.HoareAssertAssume.CSeq_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cPLF_2eHoare_2eHoareAssertAssume_2eCSeq,V_24X1),V_24X2) = cPLF_2eHoare_2eHoareAssertAssume_2eCSeq___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.FSets.FSetPositive.PositiveSet.ct_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] :
      ( p(happ(happ(happ(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2ect,V_24X1),V_24X2),V_24X3))
    <=> cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2ect___24a3(V_24X1,V_24X2,V_24X3) ) ).

fof('$adef_Coq.Init.Nat.max_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eNat_2emax,V_24X1),V_24X2) = cCoq_2eInit_2eNat_2emax___24a2(V_24X1,V_24X2) ).

fof('$adef_$_case_Coq.Init.Datatypes.list$148487_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__case__Coq_2eInit_2eDatatypes_2elist_24148487,V_24X1),V_24X2),V_24X3) = c_24__case__Coq_2eInit_2eDatatypes_2elist_24148487___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_$_fix_4781_v_CANONICAL_0_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(c_24__fix__4781__v__CANONICAL__0,V_24X1),V_24X2) = c_24__fix__4781__v__CANONICAL__0___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.PArith.BinPosDef.Pos.pred_N_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2ePArith_2eBinPosDef_2ePos_2epred__N,V_24X1) = cCoq_2ePArith_2eBinPosDef_2ePos_2epred__N___24a1(V_24X1) ).

fof('$adef_PLF.Imp.BreakImp.CIf_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cPLF_2eImp_2eBreakImp_2eCIf,V_24X1),V_24X2),V_24X3) = cPLF_2eImp_2eBreakImp_2eCIf___24a3(V_24X1,V_24X2,V_24X3) ).

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('$adef_$_lam_146985_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__146985,V_24X1),V_24X2),V_24X3) = c_24__lam__146985___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_Coq.Init.Datatypes.option_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eInit_2eDatatypes_2eoption,V_24X1) = cCoq_2eInit_2eDatatypes_2eoption___24a1(V_24X1) ).

fof('$adef_Coq.Relations.Relation_Definitions.relation_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eRelations_2eRelation__Definitions_2erelation,V_24X1) = cCoq_2eRelations_2eRelation__Definitions_2erelation___24a1(V_24X1) ).

fof('$adef_PLF.Imp.BNot_$a1',axiom,
    ! [V_24X1] : happ(cPLF_2eImp_2eBNot,V_24X1) = cPLF_2eImp_2eBNot___24a1(V_24X1) ).

fof('$adef_PLF.Imp.BAnd_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cPLF_2eImp_2eBAnd,V_24X1),V_24X2) = cPLF_2eImp_2eBAnd___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('$adef_Coq.Structures.OrderedType.LT_$a5',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2eStructures_2eOrderedType_2eLT,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2eStructures_2eOrderedType_2eLT___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).

fof('$adef_Coq.Vectors.VectorDef.t_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2eVectors_2eVectorDef_2et,V_24X1),V_24X2) = cCoq_2eVectors_2eVectorDef_2et___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.setoid_ring.Ring_polynom.PExpr_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr,V_24X1) = cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V_24X1) ).

fof('$adef_Coq.Init.Datatypes.orb_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eDatatypes_2eorb,V_24X1),V_24X2) = cCoq_2eInit_2eDatatypes_2eorb___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.Arith.Plus.tail_plus_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2eArith_2ePlus_2etail__plus,V_24X1),V_24X2) = cCoq_2eArith_2ePlus_2etail__plus___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.setoid_ring.Ring_theory.ring_morph_$a17',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17] :
      ( p(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__theory_2ering__morph,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9),V_24X10),V_24X11),V_24X12),V_24X13),V_24X14),V_24X15),V_24X16),V_24X17))
    <=> cCoq_2esetoid__ring_2eRing__theory_2ering__morph___24a17(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17) ) ).

fof('$adef_Coq.Init.Datatypes.CompOpp_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eInit_2eDatatypes_2eCompOpp,V_24X1) = cCoq_2eInit_2eDatatypes_2eCompOpp___24a1(V_24X1) ).

fof('$adef_$_lam_152854_$a1',axiom,
    ! [V_24X1] : happ(c_24__lam__152854,V_24X1) = c_24__lam__152854___24a1(V_24X1) ).

fof('$adef_Coq.micromega.EnvRing.PEopp_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2emicromega_2eEnvRing_2ePEopp,V_24X1),V_24X2) = cCoq_2emicromega_2eEnvRing_2ePEopp___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.micromega.RingMicromega.SORaddon_$a22',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22] :
      ( p(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2emicromega_2eRingMicromega_2eSORaddon,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9),V_24X10),V_24X11),V_24X12),V_24X13),V_24X14),V_24X15),V_24X16),V_24X17),V_24X18),V_24X19),V_24X20),V_24X21),V_24X22))
    <=> cCoq_2emicromega_2eRingMicromega_2eSORaddon___24a22(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22) ) ).

fof('$adef_Coq.ZArith.Zpower.two_power_pos_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eZArith_2eZpower_2etwo__power__pos,V_24X1) = cCoq_2eZArith_2eZpower_2etwo__power__pos___24a1(V_24X1) ).

fof('$adef_$_let_var_6_p_131809_131812_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__let__var__6__p__131809__131812,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__let__var__6__p__131809__131812___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).

fof('$adef_Coq.Arith.Between.exists_between_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] :
      ( p(happ(happ(happ(cCoq_2eArith_2eBetween_2eexists__between,V_24X1),V_24X2),V_24X3))
    <=> cCoq_2eArith_2eBetween_2eexists__between___24a3(V_24X1,V_24X2,V_24X3) ) ).

fof('$adef_Coq.Init.Nat.square_$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('$adef_Coq.micromega.RingMicromega.PolEnv_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2emicromega_2eRingMicromega_2ePolEnv,V_24X1) = cCoq_2emicromega_2eRingMicromega_2ePolEnv___24a1(V_24X1) ).

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('$adef_PLF.Imp.ANum_$a1',axiom,
    ! [V_24X1] : happ(cPLF_2eImp_2eANum,V_24X1) = cPLF_2eImp_2eANum___24a1(V_24X1) ).

fof('$adef_Coq.Init.Datatypes.id_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eDatatypes_2eid,V_24X1),V_24X2) = cCoq_2eInit_2eDatatypes_2eid___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.Reals.Rdefinitions.Rle_$a2',axiom,
    ! [V_24X1,V_24X2] :
      ( p(happ(happ(cCoq_2eReals_2eRdefinitions_2eRle,V_24X1),V_24X2))
    <=> cCoq_2eReals_2eRdefinitions_2eRle___24a2(V_24X1,V_24X2) ) ).

fof('$adef_Coq.Relations.Relation_Definitions.order_$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('$adef_$_lam_7029_$a1',axiom,
    ! [V_24X1] : happ(c_24__lam__7029,V_24X1) = c_24__lam__7029___24a1(V_24X1) ).

fof('$adef_PLF.Imp.aevalR_extended.APlus_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cPLF_2eImp_2eaevalR__extended_2eAPlus,V_24X1),V_24X2) = cPLF_2eImp_2eaevalR__extended_2eAPlus___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.micromega.EnvRing.zmon_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2emicromega_2eEnvRing_2ezmon,V_24X1),V_24X2) = cCoq_2emicromega_2eEnvRing_2ezmon___24a2(V_24X1,V_24X2) ).

fof('$adef_$_prop_149916_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__prop__149916,V_24X1),V_24X2),V_24X3) = c_24__prop__149916___24a3(V_24X1,V_24X2,V_24X3) ).

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('$adef_Coq.Arith.Between.in_int_$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('$adef_$_lam_83197_$a1',axiom,
    ! [V_24X1] : happ(c_24__lam__83197,V_24X1) = c_24__lam__83197___24a1(V_24X1) ).

fof('$adef_Coq.Init.Nat.eqb_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eNat_2eeqb,V_24X1),V_24X2) = cCoq_2eInit_2eNat_2eeqb___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.setoid_ring.Ring_theory.div_theory_$a7',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7] :
      ( p(happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__theory_2ediv__theory,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7))
    <=> cCoq_2esetoid__ring_2eRing__theory_2ediv__theory___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7) ) ).

fof('$adef_Coq.Sorting.Sorted.HdRel_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] :
      ( p(happ(happ(happ(happ(cCoq_2eSorting_2eSorted_2eHdRel,V_24X1),V_24X2),V_24X3),V_24X4))
    <=> cCoq_2eSorting_2eSorted_2eHdRel___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).

fof('$adef_Hammer.Tactics.Reconstr.rdone_$a2',axiom,
    ! [V_24X1,V_24X2] :
      ( p(happ(happ(cHammer_2eTactics_2eReconstr_2erdone,V_24X1),V_24X2))
    <=> cHammer_2eTactics_2eReconstr_2erdone___24a2(V_24X1,V_24X2) ) ).

fof('$adef_Coq.Reals.Rfunctions.Z_spec_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2eReals_2eRfunctions_2eZ__spec,V_24X1),V_24X2) = cCoq_2eReals_2eRfunctions_2eZ__spec___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.Init.Datatypes.inl_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eInit_2eDatatypes_2einl,V_24X1),V_24X2),V_24X3) = cCoq_2eInit_2eDatatypes_2einl___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_Hoare2.DCPre_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cHoare2_2eDCPre,V_24X1),V_24X2) = cHoare2_2eDCPre___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.NArith.BinNat.N.divide_$a2',axiom,
    ! [V_24X1,V_24X2] :
      ( p(happ(happ(cCoq_2eNArith_2eBinNat_2eN_2edivide,V_24X1),V_24X2))
    <=> cCoq_2eNArith_2eBinNat_2eN_2edivide___24a2(V_24X1,V_24X2) ) ).

fof('$adef_Coq.Lists.SetoidList.transpose2_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] :
      ( p(happ(happ(happ(happ(cCoq_2eLists_2eSetoidList_2etranspose2,V_24X1),V_24X2),V_24X3),V_24X4))
    <=> cCoq_2eLists_2eSetoidList_2etranspose2___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).

fof('$adef_Coq.PArith.BinPosDef.Pos.testbit_nat_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2ePArith_2eBinPosDef_2ePos_2etestbit__nat,V_24X1) = cCoq_2ePArith_2eBinPosDef_2ePos_2etestbit__nat___24a1(V_24X1) ).

fof('$adef_Coq.setoid_ring.Ring_theory.ring_eq_ext_$a5',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] :
      ( p(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__theory_2ering__eq__ext,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5))
    <=> cCoq_2esetoid__ring_2eRing__theory_2ering__eq__ext___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ) ).

fof('$adef_$_lam_83190_$a1',axiom,
    ! [V_24X1] : happ(c_24__lam__83190,V_24X1) = c_24__lam__83190___24a1(V_24X1) ).

fof('$adef_PLF.Imp.AExp.BAnd_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cPLF_2eImp_2eAExp_2eBAnd,V_24X1),V_24X2) = cPLF_2eImp_2eAExp_2eBAnd___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('$adef_Coq.ZArith.BinInt.Z.b2z_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eZArith_2eBinInt_2eZ_2eb2z,V_24X1) = cCoq_2eZArith_2eBinInt_2eZ_2eb2z___24a1(V_24X1) ).

fof('$adef_Coq.Lists.List.Forall2_$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('$adef_Coq.Relations.Relation_Definitions.reflexive_$a2',axiom,
    ! [V_24X1,V_24X2] :
      ( p(happ(happ(cCoq_2eRelations_2eRelation__Definitions_2ereflexive,V_24X1),V_24X2))
    <=> cCoq_2eRelations_2eRelation__Definitions_2ereflexive___24a2(V_24X1,V_24X2) ) ).

fof('$adef_Coq.Init.Datatypes.nil_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eInit_2eDatatypes_2enil,V_24X1) = cCoq_2eInit_2eDatatypes_2enil___24a1(V_24X1) ).

fof('$adef_Coq.Logic.EqdepFacts.eq_dep1_$a6',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] :
      ( p(happ(happ(happ(happ(happ(happ(cCoq_2eLogic_2eEqdepFacts_2eeq__dep1,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6))
    <=> cCoq_2eLogic_2eEqdepFacts_2eeq__dep1___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ) ).

fof('$adef_Coq.NArith.BinNatDef.N.max_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2eNArith_2eBinNatDef_2eN_2emax,V_24X1),V_24X2) = cCoq_2eNArith_2eBinNatDef_2eN_2emax___24a2(V_24X1,V_24X2) ).

fof('$adef_PLF.Imp.aevalR_division.ANum_$a1',axiom,
    ! [V_24X1] : happ(cPLF_2eImp_2eaevalR__division_2eANum,V_24X1) = cPLF_2eImp_2eaevalR__division_2eANum___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('$adef_Coq.Init.Datatypes.CompGtT_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eInit_2eDatatypes_2eCompGtT,V_24X1),V_24X2),V_24X3) = cCoq_2eInit_2eDatatypes_2eCompGtT___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_Coq.Reals.Rdefinitions.Rmult_$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('$adef_$_case_Coq.Init.Datatypes.nat$83927_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__case__Coq_2eInit_2eDatatypes_2enat_2483927,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__case__Coq_2eInit_2eDatatypes_2enat_2483927___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('$adef_$_lam_155201_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] :
      ( p(happ(happ(happ(happ(c_24__lam__155201,V_24X1),V_24X2),V_24X3),V_24X4))
    <=> c_24__lam__155201___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).

fof('$adef_Coq.Numbers.BinNums.xI_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eNumbers_2eBinNums_2exI,V_24X1) = cCoq_2eNumbers_2eBinNums_2exI___24a1(V_24X1) ).

fof('$adef_Coq.ZArith.Zeven.Zodd_$a1',axiom,
    ! [V_24X1] :
      ( p(happ(cCoq_2eZArith_2eZeven_2eZodd,V_24X1))
    <=> cCoq_2eZArith_2eZeven_2eZodd___24a1(V_24X1) ) ).

fof('$adef_Coq.Structures.GenericMinMax.gmax_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2eStructures_2eGenericMinMax_2egmax,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2eStructures_2eGenericMinMax_2egmax___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).

fof('$adef_Coq.micromega.RMicromega.CPow_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2emicromega_2eRMicromega_2eCPow,V_24X1),V_24X2) = cCoq_2emicromega_2eRMicromega_2eCPow___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.ZArith.BinIntDef.Z.abs_nat_$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('$adef_$_case_Coq.Init.Datatypes.nat$126273_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__case__Coq_2eInit_2eDatatypes_2enat_24126273,V_24X1),V_24X2),V_24X3) = c_24__case__Coq_2eInit_2eDatatypes_2enat_24126273___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_Coq.Init.Decimal.D1_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eInit_2eDecimal_2eD1,V_24X1) = cCoq_2eInit_2eDecimal_2eD1___24a1(V_24X1) ).

fof('$adef_Coq.NArith.BinNat.N.recursion_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eNArith_2eBinNat_2eN_2erecursion,V_24X1) = cCoq_2eNArith_2eBinNat_2eN_2erecursion___24a1(V_24X1) ).

fof('$adef_Coq.ZArith.BinIntDef.Z.to_pos_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eZArith_2eBinIntDef_2eZ_2eto__pos,V_24X1) = cCoq_2eZArith_2eBinIntDef_2eZ_2eto__pos___24a1(V_24X1) ).

fof('$adef_Coq.Init.Nat.div2_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eInit_2eNat_2ediv2,V_24X1) = cCoq_2eInit_2eNat_2ediv2___24a1(V_24X1) ).

fof('$adef_Coq.Init.Datatypes.negb_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eInit_2eDatatypes_2enegb,V_24X1) = cCoq_2eInit_2eDatatypes_2enegb___24a1(V_24X1) ).

fof('$adef_Coq.micromega.RMicromega.COpp_$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('$adef_PLF.Imp.CIf_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cPLF_2eImp_2eCIf,V_24X1),V_24X2),V_24X3) = cPLF_2eImp_2eCIf___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_Coq.PArith.BinPosDef.Pos.div2_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2ePArith_2eBinPosDef_2ePos_2ediv2,V_24X1) = cCoq_2ePArith_2eBinPosDef_2ePos_2ediv2___24a1(V_24X1) ).

fof('$adef_Coq.Reals.Rdefinitions.Ropp_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eReals_2eRdefinitions_2eRopp,V_24X1) = cCoq_2eReals_2eRdefinitions_2eRopp___24a1(V_24X1) ).

fof('$adef_$_lam_1487_$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__1487,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7) = c_24__lam__1487___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7) ).

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('$adef_Hoare2.DCWhile_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cHoare2_2eDCWhile,V_24X1),V_24X2),V_24X3),V_24X4) = cHoare2_2eDCWhile___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).

fof('$adef_Coq.Arith.Even.odd_$a1',axiom,
    ! [V_24X1] :
      ( p(happ(cCoq_2eArith_2eEven_2eodd,V_24X1))
    <=> cCoq_2eArith_2eEven_2eodd___24a1(V_24X1) ) ).

fof('$adef_Coq.Lists.List.ForallOrdPairs_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] :
      ( p(happ(happ(happ(cCoq_2eLists_2eList_2eForallOrdPairs,V_24X1),V_24X2),V_24X3))
    <=> cCoq_2eLists_2eList_2eForallOrdPairs___24a3(V_24X1,V_24X2,V_24X3) ) ).

fof('$adef_Coq.ZArith.BinIntDef.Z.succ_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eZArith_2eBinIntDef_2eZ_2esucc,V_24X1) = cCoq_2eZArith_2eBinIntDef_2eZ_2esucc___24a1(V_24X1) ).

fof('$adef_Coq.Relations.Relation_Operators.clos_trans_1n_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] :
      ( p(happ(happ(happ(happ(cCoq_2eRelations_2eRelation__Operators_2eclos__trans__1n,V_24X1),V_24X2),V_24X3),V_24X4))
    <=> cCoq_2eRelations_2eRelation__Operators_2eclos__trans__1n___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).

fof('$adef_Coq.Init.Logic_Type.notT_$a1',axiom,
    ! [V_24X1] :
      ( p(happ(cCoq_2eInit_2eLogic__Type_2enotT,V_24X1))
    <=> cCoq_2eInit_2eLogic__Type_2enotT___24a1(V_24X1) ) ).

fof('$adef_$_case_Coq.Init.Datatypes.prod$139550_$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_24139550,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_24139550___24a9(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9) ) ).

fof('$adef_Coq.Init.Nat.add_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eNat_2eadd,V_24X1),V_24X2) = cCoq_2eInit_2eNat_2eadd___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.Init.Specif.sigT2_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eInit_2eSpecif_2esigT2,V_24X1),V_24X2),V_24X3) = cCoq_2eInit_2eSpecif_2esigT2___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_Hoare2.pre_dec_$a1',axiom,
    ! [V_24X1] : happ(cHoare2_2epre__dec,V_24X1) = cHoare2_2epre__dec___24a1(V_24X1) ).

fof('$adef_Coq.Structures.OrderedType.Compare_$a5',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2eStructures_2eOrderedType_2eCompare,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2eStructures_2eOrderedType_2eCompare___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).

fof('$adef_Coq.setoid_ring.Field_theory.FEc_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2esetoid__ring_2eField__theory_2eFEc,V_24X1),V_24X2) = cCoq_2esetoid__ring_2eField__theory_2eFEc___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.Classes.Morphisms.Proper_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] :
      ( p(happ(happ(happ(cCoq_2eClasses_2eMorphisms_2eProper,V_24X1),V_24X2),V_24X3))
    <=> cCoq_2eClasses_2eMorphisms_2eProper___24a3(V_24X1,V_24X2,V_24X3) ) ).

fof('$adef_Coq.ZArith.BinIntDef.Z.pos_sub_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eBinIntDef_2eZ_2epos__sub,V_24X1),V_24X2) = cCoq_2eZArith_2eBinIntDef_2eZ_2epos__sub___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.Init.Specif.right_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eSpecif_2eright,V_24X1),V_24X2) = cCoq_2eInit_2eSpecif_2eright___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.setoid_ring.Ring_theory.power_theory_$a7',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7] :
      ( p(happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__theory_2epower__theory,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7))
    <=> cCoq_2esetoid__ring_2eRing__theory_2epower__theory___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7) ) ).

fof('$adef_PLF.Imp.AExp.AMinus_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cPLF_2eImp_2eAExp_2eAMinus,V_24X1),V_24X2) = cPLF_2eImp_2eAExp_2eAMinus___24a2(V_24X1,V_24X2) ).

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_155225_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] :
      ( p(happ(happ(happ(happ(c_24__lam__155225,V_24X1),V_24X2),V_24X3),V_24X4))
    <=> c_24__lam__155225___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).

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('$adef_PLF.Imp.AExp.AMult_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cPLF_2eImp_2eAExp_2eAMult,V_24X1),V_24X2) = cPLF_2eImp_2eAExp_2eAMult___24a2(V_24X1,V_24X2) ).

fof('$adef_Hoare2.extract_dec_$a1',axiom,
    ! [V_24X1] : happ(cHoare2_2eextract__dec,V_24X1) = cHoare2_2eextract__dec___24a1(V_24X1) ).

fof('$adef_Coq.ZArith.BinIntDef.Z.div_eucl_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eBinIntDef_2eZ_2ediv__eucl,V_24X1),V_24X2) = cCoq_2eZArith_2eBinIntDef_2eZ_2ediv__eucl___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.Lists.List.Add_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] :
      ( p(happ(happ(happ(happ(cCoq_2eLists_2eList_2eAdd,V_24X1),V_24X2),V_24X3),V_24X4))
    <=> cCoq_2eLists_2eList_2eAdd___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).

fof('$adef_$_prop_149918_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__prop__149918,V_24X1),V_24X2),V_24X3) = c_24__prop__149918___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_$_case_Coq.Init.Datatypes.nat$4740_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__case__Coq_2eInit_2eDatatypes_2enat_244740,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__case__Coq_2eInit_2eDatatypes_2enat_244740___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).

fof('$adef_Coq.micromega.RMicromega.CMinus_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2emicromega_2eRMicromega_2eCMinus,V_24X1),V_24X2) = cCoq_2emicromega_2eRMicromega_2eCMinus___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.Bool.Bool.ifb_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eBool_2eBool_2eifb,V_24X1),V_24X2),V_24X3) = cCoq_2eBool_2eBool_2eifb___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_PLF.Hoare.HoareAssertAssume.CIf_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cPLF_2eHoare_2eHoareAssertAssume_2eCIf,V_24X1),V_24X2),V_24X3) = cPLF_2eHoare_2eHoareAssertAssume_2eCIf___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_Coq.setoid_ring.Field_theory.FEadd_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2esetoid__ring_2eField__theory_2eFEadd,V_24X1),V_24X2),V_24X3) = cCoq_2esetoid__ring_2eField__theory_2eFEadd___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_Coq.ZArith.BinIntDef.Z.odd_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eZArith_2eBinIntDef_2eZ_2eodd,V_24X1) = cCoq_2eZArith_2eBinIntDef_2eZ_2eodd___24a1(V_24X1) ).

fof('$adef_$_case_Coq.Numbers.BinNums.positive$145139_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(c_24__case__Coq_2eNumbers_2eBinNums_2epositive_24145139,V_24X1),V_24X2) = c_24__case__Coq_2eNumbers_2eBinNums_2epositive_24145139___24a2(V_24X1,V_24X2) ).

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('$adef_$_prop_149919_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__prop__149919,V_24X1),V_24X2),V_24X3) = c_24__prop__149919___24a3(V_24X1,V_24X2,V_24X3) ).

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('$adef_Coq.ZArith.BinIntDef.Z.add_$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('$adef_Coq.micromega.RingMicromega.Formula_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2emicromega_2eRingMicromega_2eFormula,V_24X1) = cCoq_2emicromega_2eRingMicromega_2eFormula___24a1(V_24X1) ).

fof('$adef_Coq.Reals.RIneq.mknegreal_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eReals_2eRIneq_2emknegreal,V_24X1) = cCoq_2eReals_2eRIneq_2emknegreal___24a1(V_24X1) ).

fof('$adef_Coq.setoid_ring.Ring_theory.SRsub_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__theory_2eSRsub,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2esetoid__ring_2eRing__theory_2eSRsub___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).

fof('$adef_Coq.setoid_ring.InitialRing.gen_phiPOS1_$a5',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS1,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS1___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).

fof('$adef_Coq.micromega.ZMicromega.RatProof_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2emicromega_2eZMicromega_2eRatProof,V_24X1),V_24X2) = cCoq_2emicromega_2eZMicromega_2eRatProof___24a2(V_24X1,V_24X2) ).

fof('$adef_PLF.Hoare.ExAssertions.as6_$a1',axiom,
    ! [V_24X1] :
      ( p(happ(cPLF_2eHoare_2eExAssertions_2eas6,V_24X1))
    <=> cPLF_2eHoare_2eExAssertions_2eas6___24a1(V_24X1) ) ).

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('$adef_$_fix_145155_v_CANONICAL_0_$a1',axiom,
    ! [V_24X1] : happ(c_24__fix__145155__v__CANONICAL__0,V_24X1) = c_24__fix__145155__v__CANONICAL__0___24a1(V_24X1) ).

fof('$adef_PLF.Hoare.If1.CSeq_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cPLF_2eHoare_2eIf1_2eCSeq,V_24X1),V_24X2) = cPLF_2eHoare_2eIf1_2eCSeq___24a2(V_24X1,V_24X2) ).

fof('$adef_PLF.Imp.AMult_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cPLF_2eImp_2eAMult,V_24X1),V_24X2) = cPLF_2eImp_2eAMult___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('$adef_$_prop_149917_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__prop__149917,V_24X1),V_24X2),V_24X3) = c_24__prop__149917___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_PLF.Imp.CSeq_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cPLF_2eImp_2eCSeq,V_24X1),V_24X2) = cPLF_2eImp_2eCSeq___24a2(V_24X1,V_24X2) ).

fof('$adef_PLF.Hoare.RepeatExercise.CSeq_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cPLF_2eHoare_2eRepeatExercise_2eCSeq,V_24X1),V_24X2) = cPLF_2eHoare_2eRepeatExercise_2eCSeq___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('$adef_Coq.ZArith.BinIntDef.Z.sub_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eBinIntDef_2eZ_2esub,V_24X1),V_24X2) = cCoq_2eZArith_2eBinIntDef_2eZ_2esub___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.setoid_ring.Ring_polynom.PEopp_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2ePEopp,V_24X1),V_24X2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEopp___24a2(V_24X1,V_24X2) ).

fof('$adef_$_fix_4858_v_CANONICAL_0_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(c_24__fix__4858__v__CANONICAL__0,V_24X1),V_24X2) = c_24__fix__4858__v__CANONICAL__0___24a2(V_24X1,V_24X2) ).

fof('$adef_Hoare2.post_dec_$a1',axiom,
    ! [V_24X1] : happ(cHoare2_2epost__dec,V_24X1) = cHoare2_2epost__dec___24a1(V_24X1) ).

fof('$adef_Hoare2.dec_correct_$a1',axiom,
    ! [V_24X1] :
      ( p(happ(cHoare2_2edec__correct,V_24X1))
    <=> cHoare2_2edec__correct___24a1(V_24X1) ) ).

fof('$adef_Coq.setoid_ring.Field_theory.mk_linear_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2esetoid__ring_2eField__theory_2emk__linear,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2esetoid__ring_2eField__theory_2emk__linear___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).

fof('$adef_Coq.setoid_ring.Ring_theory.pow_pos_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__theory_2epow__pos,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2esetoid__ring_2eRing__theory_2epow__pos___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).

fof('$adef_Coq.Relations.Relation_Operators.Ltl_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] :
      ( p(happ(happ(happ(happ(cCoq_2eRelations_2eRelation__Operators_2eLtl,V_24X1),V_24X2),V_24X3),V_24X4))
    <=> cCoq_2eRelations_2eRelation__Operators_2eLtl___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).

fof('$adef_Coq.Init.Nat.pow_$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('$adef_PLF.Imp.AExp.APlus_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cPLF_2eImp_2eAExp_2eAPlus,V_24X1),V_24X2) = cPLF_2eImp_2eAExp_2eAPlus___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.PArith.BinPos.Pos.switch_Eq_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2ePArith_2eBinPos_2ePos_2eswitch__Eq,V_24X1),V_24X2) = cCoq_2ePArith_2eBinPos_2ePos_2eswitch__Eq___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.ZArith.BinIntDef.Z.even_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eZArith_2eBinIntDef_2eZ_2eeven,V_24X1) = cCoq_2eZArith_2eBinIntDef_2eZ_2eeven___24a1(V_24X1) ).

fof('$adef_Coq.ZArith.BinInt.Z.gt_$a2',axiom,
    ! [V_24X1,V_24X2] :
      ( p(happ(happ(cCoq_2eZArith_2eBinInt_2eZ_2egt,V_24X1),V_24X2))
    <=> cCoq_2eZArith_2eBinInt_2eZ_2egt___24a2(V_24X1,V_24X2) ) ).

fof('$adef_Coq.Init.Logic.eq_rect_$a5',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2eInit_2eLogic_2eeq__rect,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2eInit_2eLogic_2eeq__rect___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).

fof('$adef_Coq.setoid_ring.Ring_polynom.PEO_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2esetoid__ring_2eRing__polynom_2ePEO,V_24X1) = cCoq_2esetoid__ring_2eRing__polynom_2ePEO___24a1(V_24X1) ).

fof('$adef_Coq.Numbers.BinNums.xO_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eNumbers_2eBinNums_2exO,V_24X1) = cCoq_2eNumbers_2eBinNums_2exO___24a1(V_24X1) ).

fof('$adef_$_case_Coq.Init.Datatypes.nat$82954_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__case__Coq_2eInit_2eDatatypes_2enat_2482954,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__case__Coq_2eInit_2eDatatypes_2enat_2482954___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).

fof('$adef_$_lam_155209_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] :
      ( p(happ(happ(happ(happ(c_24__lam__155209,V_24X1),V_24X2),V_24X3),V_24X4))
    <=> c_24__lam__155209___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).

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('$adef_PLF.Hoare.Himp.CHavoc_$a1',axiom,
    ! [V_24X1] : happ(cPLF_2eHoare_2eHimp_2eCHavoc,V_24X1) = cPLF_2eHoare_2eHimp_2eCHavoc___24a1(V_24X1) ).

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('$adef_$_prop_149921_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(c_24__prop__149921,V_24X1),V_24X2) = c_24__prop__149921___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.Init.Wf.Acc_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] :
      ( p(happ(happ(happ(cCoq_2eInit_2eWf_2eAcc,V_24X1),V_24X2),V_24X3))
    <=> cCoq_2eInit_2eWf_2eAcc___24a3(V_24X1,V_24X2,V_24X3) ) ).

fof('$adef_Coq.setoid_ring.Ring_theory.pow_N_$a5',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__theory_2epow__N,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2esetoid__ring_2eRing__theory_2epow__N___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).

fof('$adef_Coq.setoid_ring.Field_theory.semi_field_theory_$a8',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8] :
      ( p(happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eField__theory_2esemi__field__theory,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8))
    <=> cCoq_2esetoid__ring_2eField__theory_2esemi__field__theory___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8) ) ).

fof('$adef_Coq.Init.Decimal.D8_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eInit_2eDecimal_2eD8,V_24X1) = cCoq_2eInit_2eDecimal_2eD8___24a1(V_24X1) ).

fof('$adef_Coq.Relations.Relation_Operators.swapprod_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] :
      ( p(happ(happ(happ(happ(cCoq_2eRelations_2eRelation__Operators_2eswapprod,V_24X1),V_24X2),V_24X3),V_24X4))
    <=> cCoq_2eRelations_2eRelation__Operators_2eswapprod___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).

fof('$adef_Coq.ZArith.BinInt.Z.ge_$a2',axiom,
    ! [V_24X1,V_24X2] :
      ( p(happ(happ(cCoq_2eZArith_2eBinInt_2eZ_2ege,V_24X1),V_24X2))
    <=> cCoq_2eZArith_2eBinInt_2eZ_2ege___24a2(V_24X1,V_24X2) ) ).

fof('$adef_Coq.ZArith.Zbool.Zeq_bool_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eZbool_2eZeq__bool,V_24X1),V_24X2) = cCoq_2eZArith_2eZbool_2eZeq__bool___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.micromega.RMicromega.CQ_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2emicromega_2eRMicromega_2eCQ,V_24X1) = cCoq_2emicromega_2eRMicromega_2eCQ___24a1(V_24X1) ).

fof('$adef_Coq.QArith.QArith_base.Qmake_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2eQArith_2eQArith__base_2eQmake,V_24X1),V_24X2) = cCoq_2eQArith_2eQArith__base_2eQmake___24a2(V_24X1,V_24X2) ).

fof('$adef_Hoare2.post_$a1',axiom,
    ! [V_24X1] : happ(cHoare2_2epost,V_24X1) = cHoare2_2epost___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('$adef_Hoare2.DCSeq_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cHoare2_2eDCSeq,V_24X1),V_24X2) = cHoare2_2eDCSeq___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.NArith.BinNatDef.N.pred_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eNArith_2eBinNatDef_2eN_2epred,V_24X1) = cCoq_2eNArith_2eBinNatDef_2eN_2epred___24a1(V_24X1) ).

fof('$adef_Coq.micromega.OrderedRing.SOR_$a10',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10] :
      ( p(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2emicromega_2eOrderedRing_2eSOR,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9),V_24X10))
    <=> cCoq_2emicromega_2eOrderedRing_2eSOR___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10) ) ).

fof('$adef_Coq.Relations.Relation_Operators.clos_refl_trans_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] :
      ( p(happ(happ(happ(happ(cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans,V_24X1),V_24X2),V_24X3),V_24X4))
    <=> cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).

fof('$adef_Coq.Init.Datatypes.sum_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eDatatypes_2esum,V_24X1),V_24X2) = cCoq_2eInit_2eDatatypes_2esum___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.NArith.BinNatDef.N.min_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2eNArith_2eBinNatDef_2eN_2emin,V_24X1),V_24X2) = cCoq_2eNArith_2eBinNatDef_2eN_2emin___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.ZArith.Znumtheory.Zis_gcd_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] :
      ( p(happ(happ(happ(cCoq_2eZArith_2eZnumtheory_2eZis__gcd,V_24X1),V_24X2),V_24X3))
    <=> cCoq_2eZArith_2eZnumtheory_2eZis__gcd___24a3(V_24X1,V_24X2,V_24X3) ) ).

fof('$adef_Coq.PArith.BinPosDef.Pos.size_$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_146993_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__146993,V_24X1),V_24X2),V_24X3) = c_24__lam__146993___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_Coq.Relations.Relation_Operators.clos_trans_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] :
      ( p(happ(happ(happ(happ(cCoq_2eRelations_2eRelation__Operators_2eclos__trans,V_24X1),V_24X2),V_24X3),V_24X4))
    <=> cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).

fof('$adef_Coq.Relations.Relation_Operators.clos_refl_sym_trans_1n_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] :
      ( p(happ(happ(happ(happ(cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans__1n,V_24X1),V_24X2),V_24X3),V_24X4))
    <=> cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans__1n___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).

fof('$adef_Coq.Vectors.Fin.t_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eVectors_2eFin_2et,V_24X1) = cCoq_2eVectors_2eFin_2et___24a1(V_24X1) ).

fof('$adef_Coq.setoid_ring.Field_theory.FEO_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2esetoid__ring_2eField__theory_2eFEO,V_24X1) = cCoq_2esetoid__ring_2eField__theory_2eFEO___24a1(V_24X1) ).

fof('$adef_Coq.Lists.List.In_$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('$adef_Hoare2.DCIf_$a6',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(cHoare2_2eDCIf,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = cHoare2_2eDCIf___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).

fof('$adef_Coq.Init.Datatypes.andb_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eDatatypes_2eandb,V_24X1),V_24X2) = cCoq_2eInit_2eDatatypes_2eandb___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.Init.Peano.lt_$a2',axiom,
    ! [V_24X1,V_24X2] :
      ( p(happ(happ(cCoq_2eInit_2ePeano_2elt,V_24X1),V_24X2))
    <=> cCoq_2eInit_2ePeano_2elt___24a2(V_24X1,V_24X2) ) ).

fof('$adef_Coq.PArith.BinPos.Pos.le_$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('$adef_Coq.Init.Nat.mul_$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('$adef_Coq.setoid_ring.Field_theory.rsplit_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2esetoid__ring_2eField__theory_2ersplit,V_24X1) = cCoq_2esetoid__ring_2eField__theory_2ersplit___24a1(V_24X1) ).

fof('$adef_Coq.Init.Decimal.D2_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eInit_2eDecimal_2eD2,V_24X1) = cCoq_2eInit_2eDecimal_2eD2___24a1(V_24X1) ).

fof('$adef_Coq.Classes.RelationClasses.Equivalence_$a2',axiom,
    ! [V_24X1,V_24X2] :
      ( p(happ(happ(cCoq_2eClasses_2eRelationClasses_2eEquivalence,V_24X1),V_24X2))
    <=> cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(V_24X1,V_24X2) ) ).

fof('$adef_Coq.Arith.Even.even_$a1',axiom,
    ! [V_24X1] :
      ( p(happ(cCoq_2eArith_2eEven_2eeven,V_24X1))
    <=> cCoq_2eArith_2eEven_2eeven___24a1(V_24X1) ) ).

fof('$adef_Coq.micromega.Tauto.TT_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2emicromega_2eTauto_2eTT,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2emicromega_2eTauto_2eTT___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).

fof('$adef_Coq.Logic.Decidable.decidable_$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('$adef_Coq.Relations.Relation_Operators.le_AsB_$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('$adef_Coq.PArith.BinPos.Pos.lt_$a2',axiom,
    ! [V_24X1,V_24X2] :
      ( p(happ(happ(cCoq_2ePArith_2eBinPos_2ePos_2elt,V_24X1),V_24X2))
    <=> cCoq_2ePArith_2eBinPos_2ePos_2elt___24a2(V_24X1,V_24X2) ) ).

fof('$adef_$_lam_457_$a6',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(c_24__lam__457,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = c_24__lam__457___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).

fof('$adef_Coq.NArith.BinNatDef.N.testbit_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2eNArith_2eBinNatDef_2eN_2etestbit,V_24X1),V_24X2) = cCoq_2eNArith_2eBinNatDef_2eN_2etestbit___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.PArith.BinPosDef.Pos.to_nat_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2ePArith_2eBinPosDef_2ePos_2eto__nat,V_24X1) = cCoq_2ePArith_2eBinPosDef_2ePos_2eto__nat___24a1(V_24X1) ).

fof('$adef_Coq.Init.Decimal.D0_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eInit_2eDecimal_2eD0,V_24X1) = cCoq_2eInit_2eDecimal_2eD0___24a1(V_24X1) ).

fof('$adef_Coq.Relations.Relation_Definitions.antisymmetric_$a2',axiom,
    ! [V_24X1,V_24X2] :
      ( p(happ(happ(cCoq_2eRelations_2eRelation__Definitions_2eantisymmetric,V_24X1),V_24X2))
    <=> cCoq_2eRelations_2eRelation__Definitions_2eantisymmetric___24a2(V_24X1,V_24X2) ) ).

fof('$adef_Coq.ZArith.BinIntDef.Z.abs_N_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eZArith_2eBinIntDef_2eZ_2eabs__N,V_24X1) = cCoq_2eZArith_2eBinIntDef_2eZ_2eabs__N___24a1(V_24X1) ).

fof('$adef_PLF.Imp.BreakImp.CAss_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cPLF_2eImp_2eBreakImp_2eCAss,V_24X1),V_24X2) = cPLF_2eImp_2eBreakImp_2eCAss___24a2(V_24X1,V_24X2) ).

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('$adef_$_lam_152854_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(c_24__lam__152854,V_24X1),V_24X2) = c_24__lam__152854___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.Lists.List.nth_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2eLists_2eList_2enth,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2eLists_2eList_2enth___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).

fof('$adef_Coq.Lists.SetoidList.transpose_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] :
      ( p(happ(happ(happ(happ(cCoq_2eLists_2eSetoidList_2etranspose,V_24X1),V_24X2),V_24X3),V_24X4))
    <=> cCoq_2eLists_2eSetoidList_2etranspose___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).

fof('$adef_Coq.Init.Datatypes.nat_rect_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eInit_2eDatatypes_2enat__rect,V_24X1) = cCoq_2eInit_2eDatatypes_2enat__rect___24a1(V_24X1) ).

fof('$adef_$_case_Coq.Init.Datatypes.nat$83048_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__case__Coq_2eInit_2eDatatypes_2enat_2483048,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__case__Coq_2eInit_2eDatatypes_2enat_2483048___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).

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('$adef_Coq.NArith.BinNatDef.N.succ_pos_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eNArith_2eBinNatDef_2eN_2esucc__pos,V_24X1) = cCoq_2eNArith_2eBinNatDef_2eN_2esucc__pos___24a1(V_24X1) ).

fof('$adef_PLF.Imp.aevalR_division.AMinus_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cPLF_2eImp_2eaevalR__division_2eAMinus,V_24X1),V_24X2) = cPLF_2eImp_2eaevalR__division_2eAMinus___24a2(V_24X1,V_24X2) ).

fof('$adef_Hoare2.parity_$a1',axiom,
    ! [V_24X1] : happ(cHoare2_2eparity,V_24X1) = cHoare2_2eparity___24a1(V_24X1) ).

fof('$adef_Coq.Init.Datatypes.inr_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eInit_2eDatatypes_2einr,V_24X1),V_24X2),V_24X3) = cCoq_2eInit_2eDatatypes_2einr___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_Coq.micromega.VarMap.Branch_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2emicromega_2eVarMap_2eBranch,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2emicromega_2eVarMap_2eBranch___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).

fof('$adef_Coq.Reals.RIneq.mkposreal_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eReals_2eRIneq_2emkposreal,V_24X1) = cCoq_2eReals_2eRIneq_2emkposreal___24a1(V_24X1) ).

fof('$adef_Coq.Vectors.Fin.F1_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eVectors_2eFin_2eF1,V_24X1) = cCoq_2eVectors_2eFin_2eF1___24a1(V_24X1) ).

fof('$adef_Coq.QArith.QArith_base.Qnum_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eQArith_2eQArith__base_2eQnum,V_24X1) = cCoq_2eQArith_2eQArith__base_2eQnum___24a1(V_24X1) ).

fof('$adef_PLF.Hoare.Himp.CWhile_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cPLF_2eHoare_2eHimp_2eCWhile,V_24X1),V_24X2) = cPLF_2eHoare_2eHimp_2eCWhile___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('$adef_$_case_Coq.Init.Datatypes.nat$126295_$a1',axiom,
    ! [V_24X1] : happ(c_24__case__Coq_2eInit_2eDatatypes_2enat_24126295,V_24X1) = c_24__case__Coq_2eInit_2eDatatypes_2enat_24126295___24a1(V_24X1) ).

fof('$adef_$_lam_83197_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(c_24__lam__83197,V_24X1),V_24X2) = c_24__lam__83197___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('$adef_Hoare2.extract_$a1',axiom,
    ! [V_24X1] : happ(cHoare2_2eextract,V_24X1) = cHoare2_2eextract___24a1(V_24X1) ).

fof('$adef_Coq.Relations.Relation_Operators.Desc_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] :
      ( p(happ(happ(happ(cCoq_2eRelations_2eRelation__Operators_2eDesc,V_24X1),V_24X2),V_24X3))
    <=> cCoq_2eRelations_2eRelation__Operators_2eDesc___24a3(V_24X1,V_24X2,V_24X3) ) ).

fof('$adef_Coq.micromega.Tauto.D_$a6',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(cCoq_2emicromega_2eTauto_2eD,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = cCoq_2emicromega_2eTauto_2eD___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).

fof('$adef_Coq.Init.Datatypes.prod_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eDatatypes_2eprod,V_24X1),V_24X2) = cCoq_2eInit_2eDatatypes_2eprod___24a2(V_24X1,V_24X2) ).

fof('$adef_PLF.Maps.eqb_string_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cPLF_2eMaps_2eeqb__string,V_24X1),V_24X2) = cPLF_2eMaps_2eeqb__string___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.Init.Specif.Exc_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eInit_2eSpecif_2eExc,V_24X1) = cCoq_2eInit_2eSpecif_2eExc___24a1(V_24X1) ).

fof('$adef_Coq.Vectors.VectorDef.Forall2_$a6',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] :
      ( p(happ(happ(happ(happ(happ(happ(cCoq_2eVectors_2eVectorDef_2eForall2,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6))
    <=> cCoq_2eVectors_2eVectorDef_2eForall2___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ) ).

fof('$adef_$_lam_155217_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__155217,V_24X1),V_24X2),V_24X3) = c_24__lam__155217___24a3(V_24X1,V_24X2,V_24X3) ).

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('$adef_$_lam_155225_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__155225,V_24X1),V_24X2),V_24X3) = c_24__lam__155225___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_Coq.ZArith.BinIntDef.Z.compare_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare,V_24X1),V_24X2) = cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.setoid_ring.Ring_theory.ring_theory_$a8',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8] :
      ( p(happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__theory_2ering__theory,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8))
    <=> cCoq_2esetoid__ring_2eRing__theory_2ering__theory___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8) ) ).

fof('$adef_PLF.Imp.AExp.aevalR_first_try.TooHardToRead.aevalR_$a2',axiom,
    ! [V_24X1,V_24X2] :
      ( p(happ(happ(cPLF_2eImp_2eAExp_2eaevalR__first__try_2eTooHardToRead_2eaevalR,V_24X1),V_24X2))
    <=> cPLF_2eImp_2eAExp_2eaevalR__first__try_2eTooHardToRead_2eaevalR___24a2(V_24X1,V_24X2) ) ).

fof('$adef_$_lam_146993_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__lam__146993,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__lam__146993___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).

fof('$adef_Coq.QArith.QArith_base.Qden_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eQArith_2eQArith__base_2eQden,V_24X1) = cCoq_2eQArith_2eQArith__base_2eQden___24a1(V_24X1) ).

fof('$adef_PLF.Imp.BreakImp.CWhile_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cPLF_2eImp_2eBreakImp_2eCWhile,V_24X1),V_24X2) = cPLF_2eImp_2eBreakImp_2eCWhile___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.setoid_ring.InitialRing.gen_phiPOS_$a5',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).

fof('$adef_Coq.Init.Peano.IsSucc_$a1',axiom,
    ! [V_24X1] :
      ( p(happ(cCoq_2eInit_2ePeano_2eIsSucc,V_24X1))
    <=> cCoq_2eInit_2ePeano_2eIsSucc___24a1(V_24X1) ) ).

fof('$adef_Coq.NArith.BinNatDef.N.div2_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eNArith_2eBinNatDef_2eN_2ediv2,V_24X1) = cCoq_2eNArith_2eBinNatDef_2eN_2ediv2___24a1(V_24X1) ).

fof('$adef_Coq.Init.Datatypes.eq_true_$a1',axiom,
    ! [V_24X1] :
      ( p(happ(cCoq_2eInit_2eDatatypes_2eeq__true,V_24X1))
    <=> cCoq_2eInit_2eDatatypes_2eeq__true___24a1(V_24X1) ) ).

fof('$adef_Coq.micromega.VarMap.Elt_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2emicromega_2eVarMap_2eElt,V_24X1),V_24X2) = cCoq_2emicromega_2eVarMap_2eElt___24a2(V_24X1,V_24X2) ).

fof('$adef_$_lam_957_$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__957,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7) = c_24__lam__957___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7) ).

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('$adef_PLF.Hoare.If1.CIf_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cPLF_2eHoare_2eIf1_2eCIf,V_24X1),V_24X2),V_24X3) = cPLF_2eHoare_2eIf1_2eCIf___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_PLF.Hoare.RepeatExercise.ceval_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] :
      ( p(happ(happ(happ(cPLF_2eHoare_2eRepeatExercise_2eceval,V_24X1),V_24X2),V_24X3))
    <=> cPLF_2eHoare_2eRepeatExercise_2eceval___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('$adef_$_case_Coq.Init.Datatypes.nat$83724_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__case__Coq_2eInit_2eDatatypes_2enat_2483724,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__case__Coq_2eInit_2eDatatypes_2enat_2483724___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).

fof('$adef_$_lam_943_$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__943,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7) = c_24__lam__943___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7) ).

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('$adef_PLF.Imp.AExp.aevalR_$a2',axiom,
    ! [V_24X1,V_24X2] :
      ( p(happ(happ(cPLF_2eImp_2eAExp_2eaevalR,V_24X1),V_24X2))
    <=> cPLF_2eImp_2eAExp_2eaevalR___24a2(V_24X1,V_24X2) ) ).

fof('$adef_Coq.micromega.RMicromega.CZ_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2emicromega_2eRMicromega_2eCZ,V_24X1) = cCoq_2emicromega_2eRMicromega_2eCZ___24a1(V_24X1) ).

fof('$adef_Coq.ZArith.BinInt.Z.lt_$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('$adef_Coq.setoid_ring.Field_theory.linear_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2esetoid__ring_2eField__theory_2elinear,V_24X1) = cCoq_2esetoid__ring_2eField__theory_2elinear___24a1(V_24X1) ).

fof('$adef_$_case_Coq.Init.Datatypes.nat$4629_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__case__Coq_2eInit_2eDatatypes_2enat_244629,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__case__Coq_2eInit_2eDatatypes_2enat_244629___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).

fof('$adef_Coq.Arith.PeanoNat.Nat.b2n_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eArith_2ePeanoNat_2eNat_2eb2n,V_24X1) = cCoq_2eArith_2ePeanoNat_2eNat_2eb2n___24a1(V_24X1) ).

fof('$adef_Coq.Arith.PeanoNat.Nat.recursion_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eArith_2ePeanoNat_2eNat_2erecursion,V_24X1) = cCoq_2eArith_2ePeanoNat_2eNat_2erecursion___24a1(V_24X1) ).

fof('$adef_Coq.PArith.BinPosDef.Pos.eqb_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2ePArith_2eBinPosDef_2ePos_2eeqb,V_24X1),V_24X2) = cCoq_2ePArith_2eBinPosDef_2ePos_2eeqb___24a2(V_24X1,V_24X2) ).

fof('$adef_$_prop_149915_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__prop__149915,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__prop__149915___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).

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('$adef_Hoare2.DCPost_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cHoare2_2eDCPost,V_24X1),V_24X2) = cHoare2_2eDCPost___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.Numbers.BinNums.Zneg_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eNumbers_2eBinNums_2eZneg,V_24X1) = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(V_24X1) ).

fof('$adef_Coq.micromega.RingMicromega.ge_bool_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2emicromega_2eRingMicromega_2ege__bool,V_24X1),V_24X2) = cCoq_2emicromega_2eRingMicromega_2ege__bool___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.Reals.RIneq.mknonnegreal_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eReals_2eRIneq_2emknonnegreal,V_24X1) = cCoq_2eReals_2eRIneq_2emknonnegreal___24a1(V_24X1) ).

fof('$adef_Hoare2.verification_conditions_$a2',axiom,
    ! [V_24X1,V_24X2] :
      ( p(happ(happ(cHoare2_2everification__conditions,V_24X1),V_24X2))
    <=> cHoare2_2everification__conditions___24a2(V_24X1,V_24X2) ) ).

fof('$adef_Coq.Reals.Rdefinitions.Rgt_$a2',axiom,
    ! [V_24X1,V_24X2] :
      ( p(happ(happ(cCoq_2eReals_2eRdefinitions_2eRgt,V_24X1),V_24X2))
    <=> cCoq_2eReals_2eRdefinitions_2eRgt___24a2(V_24X1,V_24X2) ) ).

fof('$adef_Coq.setoid_ring.Ring_polynom.PEpow_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2ePEpow,V_24X1),V_24X2),V_24X3) = cCoq_2esetoid__ring_2eRing__polynom_2ePEpow___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_Coq.NArith.BinNatDef.N.to_nat_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eNArith_2eBinNatDef_2eN_2eto__nat,V_24X1) = cCoq_2eNArith_2eBinNatDef_2eN_2eto__nat___24a1(V_24X1) ).

fof('$adef_Coq.ZArith.Zeven.Zeven_$a1',axiom,
    ! [V_24X1] :
      ( p(happ(cCoq_2eZArith_2eZeven_2eZeven,V_24X1))
    <=> cCoq_2eZArith_2eZeven_2eZeven___24a1(V_24X1) ) ).

fof('$adef_Coq.Bool.Bool.reflect_$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('$adef_PLF.Imp.aevalR_division.AMult_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cPLF_2eImp_2eaevalR__division_2eAMult,V_24X1),V_24X2) = cPLF_2eImp_2eaevalR__division_2eAMult___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.setoid_ring.Ring_polynom.PX_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2ePX,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2esetoid__ring_2eRing__polynom_2ePX___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).

fof('$adef_PLF.Hoare.If1.CIf1_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cPLF_2eHoare_2eIf1_2eCIf1,V_24X1),V_24X2) = cPLF_2eHoare_2eIf1_2eCIf1___24a2(V_24X1,V_24X2) ).

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('$adef_$_prop_152873_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(c_24__prop__152873,V_24X1),V_24X2) = c_24__prop__152873___24a2(V_24X1,V_24X2) ).

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('$adef_PLF.Hoare.assert_implies_$a2',axiom,
    ! [V_24X1,V_24X2] :
      ( p(happ(happ(cPLF_2eHoare_2eassert__implies,V_24X1),V_24X2))
    <=> cPLF_2eHoare_2eassert__implies___24a2(V_24X1,V_24X2) ) ).

fof('$adef_Coq.PArith.BinPosDef.Pos.sub_mask_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2ePArith_2eBinPosDef_2ePos_2esub__mask,V_24X1),V_24X2) = cCoq_2ePArith_2eBinPosDef_2ePos_2esub__mask___24a2(V_24X1,V_24X2) ).

fof('$adef_PLF.Imp.AExp.ANum_$a1',axiom,
    ! [V_24X1] : happ(cPLF_2eImp_2eAExp_2eANum,V_24X1) = cPLF_2eImp_2eAExp_2eANum___24a1(V_24X1) ).

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('$adef_PLF.Imp.AExp.BEq_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cPLF_2eImp_2eAExp_2eBEq,V_24X1),V_24X2) = cPLF_2eImp_2eAExp_2eBEq___24a2(V_24X1,V_24X2) ).

fof('$adef_$_lam_155217_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] :
      ( p(happ(happ(happ(happ(c_24__lam__155217,V_24X1),V_24X2),V_24X3),V_24X4))
    <=> c_24__lam__155217___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).

fof('$adef_Coq.setoid_ring.Ring_polynom.PEadd_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2ePEadd,V_24X1),V_24X2),V_24X3) = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_$_case_Coq.Init.Datatypes.list$148400_$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_24148400,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = c_24__case__Coq_2eInit_2eDatatypes_2elist_24148400___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).

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('$adef_Coq.Init.Specif.exist2_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2eInit_2eSpecif_2eexist2,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2eInit_2eSpecif_2eexist2___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).

fof('$adef_Coq.Init.Datatypes.CompareSpec_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] :
      ( p(happ(happ(happ(happ(cCoq_2eInit_2eDatatypes_2eCompareSpec,V_24X1),V_24X2),V_24X3),V_24X4))
    <=> cCoq_2eInit_2eDatatypes_2eCompareSpec___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).

fof('$adef_Coq.Init.Datatypes.xorb_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eDatatypes_2exorb,V_24X1),V_24X2) = cCoq_2eInit_2eDatatypes_2exorb___24a2(V_24X1,V_24X2) ).

fof('$adef_PLF.Hoare.HoareAssertAssume.CAssert_$a1',axiom,
    ! [V_24X1] : happ(cPLF_2eHoare_2eHoareAssertAssume_2eCAssert,V_24X1) = cPLF_2eHoare_2eHoareAssertAssume_2eCAssert___24a1(V_24X1) ).

fof('$adef_Coq.Strings.String.String_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2eStrings_2eString_2eString,V_24X1),V_24X2) = cCoq_2eStrings_2eString_2eString___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.Relations.Relation_Definitions.equivalence_$a2',axiom,
    ! [V_24X1,V_24X2] :
      ( p(happ(happ(cCoq_2eRelations_2eRelation__Definitions_2eequivalence,V_24X1),V_24X2))
    <=> cCoq_2eRelations_2eRelation__Definitions_2eequivalence___24a2(V_24X1,V_24X2) ) ).

fof('$adef_Coq.ZArith.Znumtheory.Euclid_intro_$a5',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2eZArith_2eZnumtheory_2eEuclid__intro,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2eZArith_2eZnumtheory_2eEuclid__intro___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).

fof('$adef_Coq.Init.Datatypes.CompEqT_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eInit_2eDatatypes_2eCompEqT,V_24X1),V_24X2),V_24X3) = cCoq_2eInit_2eDatatypes_2eCompEqT___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_Coq.micromega.RingMicromega.PsatzMulE_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2emicromega_2eRingMicromega_2ePsatzMulE,V_24X1),V_24X2),V_24X3) = cCoq_2emicromega_2eRingMicromega_2ePsatzMulE___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_Coq.Classes.Morphisms.respectful_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2eClasses_2eMorphisms_2erespectful,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).

fof('$adef_PLF.Hoare.HoareAssertAssume.CAss_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cPLF_2eHoare_2eHoareAssertAssume_2eCAss,V_24X1),V_24X2) = cPLF_2eHoare_2eHoareAssertAssume_2eCAss___24a2(V_24X1,V_24X2) ).

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('$adef_Coq.micromega.Tauto.FF_$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('$adef_PLF.Hoare.If1.ceval_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] :
      ( p(happ(happ(happ(cPLF_2eHoare_2eIf1_2eceval,V_24X1),V_24X2),V_24X3))
    <=> cPLF_2eHoare_2eIf1_2eceval___24a3(V_24X1,V_24X2,V_24X3) ) ).

fof('$adef_PLF.Hoare.ExAssertions.as5_$a1',axiom,
    ! [V_24X1] :
      ( p(happ(cPLF_2eHoare_2eExAssertions_2eas5,V_24X1))
    <=> cPLF_2eHoare_2eExAssertions_2eas5___24a1(V_24X1) ) ).

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('$adef_Coq.NArith.BinNatDef.N.succ_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eNArith_2eBinNatDef_2eN_2esucc,V_24X1) = cCoq_2eNArith_2eBinNatDef_2eN_2esucc___24a1(V_24X1) ).

fof('$adef_Coq.Relations.Relation_Definitions.transitive_$a2',axiom,
    ! [V_24X1,V_24X2] :
      ( p(happ(happ(cCoq_2eRelations_2eRelation__Definitions_2etransitive,V_24X1),V_24X2))
    <=> cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2(V_24X1,V_24X2) ) ).

fof('$adef_Coq.Structures.OrderedType.GT_$a5',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2eStructures_2eOrderedType_2eGT,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2eStructures_2eOrderedType_2eGT___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).

fof('$adef_PLF.Imp.AExp.aevalR_first_try.aevalR_$a2',axiom,
    ! [V_24X1,V_24X2] :
      ( p(happ(happ(cPLF_2eImp_2eAExp_2eaevalR__first__try_2eaevalR,V_24X1),V_24X2))
    <=> cPLF_2eImp_2eAExp_2eaevalR__first__try_2eaevalR___24a2(V_24X1,V_24X2) ) ).

fof('$adef_PLF.Hoare.RepeatExercise.CWhile_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cPLF_2eHoare_2eRepeatExercise_2eCWhile,V_24X1),V_24X2) = cPLF_2eHoare_2eRepeatExercise_2eCWhile___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('$adef_PLF.Imp.aevalR_division.ADiv_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cPLF_2eImp_2eaevalR__division_2eADiv,V_24X1),V_24X2) = cPLF_2eImp_2eaevalR__division_2eADiv___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.setoid_ring.Ring_theory.id_phi_N_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2esetoid__ring_2eRing__theory_2eid__phi__N,V_24X1) = cCoq_2esetoid__ring_2eRing__theory_2eid__phi__N___24a1(V_24X1) ).

fof('$adef_Coq.Vectors.Fin.FS_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2eVectors_2eFin_2eFS,V_24X1),V_24X2) = cCoq_2eVectors_2eFin_2eFS___24a2(V_24X1,V_24X2) ).

fof('$adef_PLF.Hoare.RepeatExercise.CAsgn_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cPLF_2eHoare_2eRepeatExercise_2eCAsgn,V_24X1),V_24X2) = cPLF_2eHoare_2eRepeatExercise_2eCAsgn___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.micromega.EnvRing.PExpr_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2emicromega_2eEnvRing_2ePExpr,V_24X1) = cCoq_2emicromega_2eEnvRing_2ePExpr___24a1(V_24X1) ).

fof('$adef_$_lam_7029_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(c_24__lam__7029,V_24X1),V_24X2) = c_24__lam__7029___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.Setoids.Setoid.Setoid_Theory_$a2',axiom,
    ! [V_24X1,V_24X2] :
      ( p(happ(happ(cCoq_2eSetoids_2eSetoid_2eSetoid__Theory,V_24X1),V_24X2))
    <=> cCoq_2eSetoids_2eSetoid_2eSetoid__Theory___24a2(V_24X1,V_24X2) ) ).

fof('$adef_Coq.Init.Peano.ge_$a2',axiom,
    ! [V_24X1,V_24X2] :
      ( p(happ(happ(cCoq_2eInit_2ePeano_2ege,V_24X1),V_24X2))
    <=> cCoq_2eInit_2ePeano_2ege___24a2(V_24X1,V_24X2) ) ).

fof('$adef_Coq.Relations.Relation_Operators.clos_refl_trans_1n_$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('$adef_Coq.Vectors.VectorDef.In_$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('$adef_Coq.Lists.SetoidList.NoDupA_$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('$adef_PLF.Imp.SLoad_$a1',axiom,
    ! [V_24X1] : happ(cPLF_2eImp_2eSLoad,V_24X1) = cPLF_2eImp_2eSLoad___24a1(V_24X1) ).

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('$adef_PLF.Imp.aevalR_extended.AMult_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cPLF_2eImp_2eaevalR__extended_2eAMult,V_24X1),V_24X2) = cPLF_2eImp_2eaevalR__extended_2eAMult___24a2(V_24X1,V_24X2) ).

fof('$adef_PLF.Hoare.If1.CWhile_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cPLF_2eHoare_2eIf1_2eCWhile,V_24X1),V_24X2) = cPLF_2eHoare_2eIf1_2eCWhile___24a2(V_24X1,V_24X2) ).

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('$adef_Coq.Init.Byte.byte_of_byte_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eInit_2eByte_2ebyte__of__byte,V_24X1) = cCoq_2eInit_2eByte_2ebyte__of__byte___24a1(V_24X1) ).

fof('$adef_Coq.Arith.EqNat.eq_nat_$a2',axiom,
    ! [V_24X1,V_24X2] :
      ( p(happ(happ(cCoq_2eArith_2eEqNat_2eeq__nat,V_24X1),V_24X2))
    <=> cCoq_2eArith_2eEqNat_2eeq__nat___24a2(V_24X1,V_24X2) ) ).

fof('$adef_Coq.Init.Datatypes.nat_rect_$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('$adef_Coq.micromega.Tauto.A_$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('$adef_Coq.micromega.Tauto.X_$a5',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2emicromega_2eTauto_2eX,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2emicromega_2eTauto_2eX___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).

fof('$adef_Coq.setoid_ring.Field_theory.almost_field_theory_$a10',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10] :
      ( p(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eField__theory_2ealmost__field__theory,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9),V_24X10))
    <=> cCoq_2esetoid__ring_2eField__theory_2ealmost__field__theory___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10) ) ).

fof('$adef_Coq.Arith.Wf_nat.ltof_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] :
      ( p(happ(happ(happ(happ(cCoq_2eArith_2eWf__nat_2eltof,V_24X1),V_24X2),V_24X3),V_24X4))
    <=> cCoq_2eArith_2eWf__nat_2eltof___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).

fof('$adef_$_lam_83201_$a1',axiom,
    ! [V_24X1] : happ(c_24__lam__83201,V_24X1) = c_24__lam__83201___24a1(V_24X1) ).

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('$adef_PLF.Hoare.Himp.CSeq_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cPLF_2eHoare_2eHimp_2eCSeq,V_24X1),V_24X2) = cPLF_2eHoare_2eHimp_2eCSeq___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.micromega.RMicromega.CInv_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2emicromega_2eRMicromega_2eCInv,V_24X1) = cCoq_2emicromega_2eRMicromega_2eCInv___24a1(V_24X1) ).

fof('$adef_Coq.PArith.BinPosDef.Pos.mul_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2ePArith_2eBinPosDef_2ePos_2emul,V_24X1),V_24X2) = cCoq_2ePArith_2eBinPosDef_2ePos_2emul___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.PArith.BinPosDef.Pos.testbit_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2ePArith_2eBinPosDef_2ePos_2etestbit,V_24X1),V_24X2) = cCoq_2ePArith_2eBinPosDef_2ePos_2etestbit___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.ZArith.Znumtheory.rel_prime_$a2',axiom,
    ! [V_24X1,V_24X2] :
      ( p(happ(happ(cCoq_2eZArith_2eZnumtheory_2erel__prime,V_24X1),V_24X2))
    <=> cCoq_2eZArith_2eZnumtheory_2erel__prime___24a2(V_24X1,V_24X2) ) ).

fof('$adef_Coq.NArith.BinNatDef.N.mul_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2eNArith_2eBinNatDef_2eN_2emul,V_24X1),V_24X2) = cCoq_2eNArith_2eBinNatDef_2eN_2emul___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.Init.Nat.pred_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eInit_2eNat_2epred,V_24X1) = cCoq_2eInit_2eNat_2epred___24a1(V_24X1) ).

fof('$adef_Coq.Init.Specif.exist_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eInit_2eSpecif_2eexist,V_24X1),V_24X2),V_24X3) = cCoq_2eInit_2eSpecif_2eexist___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_Coq.ZArith.BinInt.Z.le_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eBinInt_2eZ_2ele,V_24X1),V_24X2) = cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V_24X1,V_24X2) ).

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('$adef_$_prop_149920_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__prop__149920,V_24X1),V_24X2),V_24X3) = c_24__prop__149920___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_PLF.Imp.aevalR_extended.AMinus_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cPLF_2eImp_2eaevalR__extended_2eAMinus,V_24X1),V_24X2) = cPLF_2eImp_2eaevalR__extended_2eAMinus___24a2(V_24X1,V_24X2) ).

fof('$adef_PLF.Imp.CWhile_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cPLF_2eImp_2eCWhile,V_24X1),V_24X2) = cPLF_2eImp_2eCWhile___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('$adef_PLF.Hoare.hoare_triple_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] :
      ( p(happ(happ(happ(cPLF_2eHoare_2ehoare__triple,V_24X1),V_24X2),V_24X3))
    <=> cPLF_2eHoare_2ehoare__triple___24a3(V_24X1,V_24X2,V_24X3) ) ).

fof('$adef_PLF.Imp.BEq_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cPLF_2eImp_2eBEq,V_24X1),V_24X2) = cPLF_2eImp_2eBEq___24a2(V_24X1,V_24X2) ).

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('$adef_PLF.Imp.BreakImp.CSeq_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cPLF_2eImp_2eBreakImp_2eCSeq,V_24X1),V_24X2) = cPLF_2eImp_2eBreakImp_2eCSeq___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.micromega.EnvRing.Pinj_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2emicromega_2eEnvRing_2ePinj,V_24X1),V_24X2),V_24X3) = cCoq_2emicromega_2eEnvRing_2ePinj___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_Coq.Init.Wf.well_founded_$a2',axiom,
    ! [V_24X1,V_24X2] :
      ( p(happ(happ(cCoq_2eInit_2eWf_2ewell__founded,V_24X1),V_24X2))
    <=> cCoq_2eInit_2eWf_2ewell__founded___24a2(V_24X1,V_24X2) ) ).

fof('$adef_Coq.Arith.Wf_nat.gtof_$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('$adef_Coq.Init.Datatypes.cons_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eInit_2eDatatypes_2econs,V_24X1),V_24X2),V_24X3) = cCoq_2eInit_2eDatatypes_2econs___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_Coq.setoid_ring.Field_theory.field_theory_$a10',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10] :
      ( p(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eField__theory_2efield__theory,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9),V_24X10))
    <=> cCoq_2esetoid__ring_2eField__theory_2efield__theory___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10) ) ).

fof('$adef_Coq.setoid_ring.Ring_theory.Computational_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2esetoid__ring_2eRing__theory_2eComputational,V_24X1),V_24X2),V_24X3) = cCoq_2esetoid__ring_2eRing__theory_2eComputational___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_Coq.micromega.RingMicromega.PsatzSquare_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2emicromega_2eRingMicromega_2ePsatzSquare,V_24X1),V_24X2) = cCoq_2emicromega_2eRingMicromega_2ePsatzSquare___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.ZArith.BinIntDef.Z.of_nat_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat,V_24X1) = cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat___24a1(V_24X1) ).

fof('$adef_Coq.Init.Datatypes.pair_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2eInit_2eDatatypes_2epair,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2eInit_2eDatatypes_2epair___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).

fof('$adef_Coq.Init.Decimal.int_of_int_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eInit_2eDecimal_2eint__of__int,V_24X1) = cCoq_2eInit_2eDecimal_2eint__of__int___24a1(V_24X1) ).

fof('$adef_Coq.PArith.BinPosDef.Pos.IsPos_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2ePArith_2eBinPosDef_2ePos_2eIsPos,V_24X1) = cCoq_2ePArith_2eBinPosDef_2ePos_2eIsPos___24a1(V_24X1) ).

fof('$adef_Coq.Init.Nat.sqrt_iter_$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('$adef_Coq.PArith.BinPosDef.Pos.max_$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('$adef_$_lam_957_$a6',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(c_24__lam__957,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = c_24__lam__957___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).

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('$adef_Coq.Structures.OrderedType.EQ_$a5',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2eStructures_2eOrderedType_2eEQ,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2eStructures_2eOrderedType_2eEQ___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).

fof('$adef_Coq.Numbers.BinNums.Zpos_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eNumbers_2eBinNums_2eZpos,V_24X1) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(V_24X1) ).

fof('$adef_Hoare2.DCSkip_$a1',axiom,
    ! [V_24X1] : happ(cHoare2_2eDCSkip,V_24X1) = cHoare2_2eDCSkip___24a1(V_24X1) ).

fof('$adef_Coq.NArith.BinNatDef.N.double_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eNArith_2eBinNatDef_2eN_2edouble,V_24X1) = cCoq_2eNArith_2eBinNatDef_2eN_2edouble___24a1(V_24X1) ).

fof('$adef_Coq.Init.Datatypes.list_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eInit_2eDatatypes_2elist,V_24X1) = cCoq_2eInit_2eDatatypes_2elist___24a1(V_24X1) ).

fof('$adef_Coq.Init.Nat.sub_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eNat_2esub,V_24X1),V_24X2) = cCoq_2eInit_2eNat_2esub___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.PArith.BinPos.Pos.SubMaskSpec_$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('$adef_PLF.Imp.AId_$a1',axiom,
    ! [V_24X1] : happ(cPLF_2eImp_2eAId,V_24X1) = cPLF_2eImp_2eAId___24a1(V_24X1) ).

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('$adef_$_lam_457_$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__457,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7) = c_24__lam__457___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7) ).

fof('$adef_Coq.Bool.Bool.ReflectF_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eBool_2eBool_2eReflectF,V_24X1) = cCoq_2eBool_2eBool_2eReflectF___24a1(V_24X1) ).

fof('$adef_Coq.micromega.ZMicromega.Vars.Facts.MP.Dec.FSetDecideAuxiliary.FSet_Prop_$a1',axiom,
    ! [V_24X1] :
      ( p(happ(cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__Prop,V_24X1))
    <=> cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__Prop___24a1(V_24X1) ) ).

fof('$adef_Coq.Reals.Rfunctions.ZintNull_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eReals_2eRfunctions_2eZintNull,V_24X1) = cCoq_2eReals_2eRfunctions_2eZintNull___24a1(V_24X1) ).

fof('$adef_Coq.setoid_ring.Field_theory.FEI_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2esetoid__ring_2eField__theory_2eFEI,V_24X1) = cCoq_2esetoid__ring_2eField__theory_2eFEI___24a1(V_24X1) ).

fof('$adef_Coq.micromega.EnvRing.PEX_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2emicromega_2eEnvRing_2ePEX,V_24X1),V_24X2) = cCoq_2emicromega_2eEnvRing_2ePEX___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.Bool.Bool.ReflectT_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eBool_2eBool_2eReflectT,V_24X1) = cCoq_2eBool_2eBool_2eReflectT___24a1(V_24X1) ).

fof('$adef_Coq.ZArith.Znumtheory.Euclid_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eZnumtheory_2eEuclid,V_24X1),V_24X2) = cCoq_2eZArith_2eZnumtheory_2eEuclid___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.Lists.List.Forall_$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('$adef_Coq.NArith.BinNatDef.N.lxor_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2eNArith_2eBinNatDef_2eN_2elxor,V_24X1),V_24X2) = cCoq_2eNArith_2eBinNatDef_2eN_2elxor___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.ZArith.Zlogarithm.log_inf_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eZArith_2eZlogarithm_2elog__inf,V_24X1) = cCoq_2eZArith_2eZlogarithm_2elog__inf___24a1(V_24X1) ).

fof('$adef_Coq.Init.Decimal.D5_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eInit_2eDecimal_2eD5,V_24X1) = cCoq_2eInit_2eDecimal_2eD5___24a1(V_24X1) ).

fof('$adef_Coq.PArith.BinPosDef.Pos.sub_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2ePArith_2eBinPosDef_2ePos_2esub,V_24X1),V_24X2) = cCoq_2ePArith_2eBinPosDef_2ePos_2esub___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.NArith.BinNatDef.N.compare_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2eNArith_2eBinNatDef_2eN_2ecompare,V_24X1),V_24X2) = cCoq_2eNArith_2eBinNatDef_2eN_2ecompare___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.Init.Decimal.uint_of_uint_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eInit_2eDecimal_2euint__of__uint,V_24X1) = cCoq_2eInit_2eDecimal_2euint__of__uint___24a1(V_24X1) ).

fof('$adef_Coq.PArith.BinPosDef.Pos.lxor_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2ePArith_2eBinPosDef_2ePos_2elxor,V_24X1),V_24X2) = cCoq_2ePArith_2eBinPosDef_2ePos_2elxor___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.Init.Datatypes.fst_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eInit_2eDatatypes_2efst,V_24X1),V_24X2),V_24X3) = cCoq_2eInit_2eDatatypes_2efst___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_PLF.Imp.aevalR_extended.aevalR_$a2',axiom,
    ! [V_24X1,V_24X2] :
      ( p(happ(happ(cPLF_2eImp_2eaevalR__extended_2eaevalR,V_24X1),V_24X2))
    <=> cPLF_2eImp_2eaevalR__extended_2eaevalR___24a2(V_24X1,V_24X2) ) ).

fof('$adef_Coq.micromega.VarMap.Empty_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2emicromega_2eVarMap_2eEmpty,V_24X1) = cCoq_2emicromega_2eVarMap_2eEmpty___24a1(V_24X1) ).

fof('$adef_Coq.micromega.RingMicromega.PsatzAdd_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2emicromega_2eRingMicromega_2ePsatzAdd,V_24X1),V_24X2),V_24X3) = cCoq_2emicromega_2eRingMicromega_2ePsatzAdd___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_Coq.PArith.BinPos.Pos.PeanoView_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2ePArith_2eBinPos_2ePos_2ePeanoView,V_24X1) = cCoq_2ePArith_2eBinPos_2ePos_2ePeanoView___24a1(V_24X1) ).

fof('$adef_Coq.Init.Decimal.DecimalExp_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eInit_2eDecimal_2eDecimalExp,V_24X1),V_24X2),V_24X3) = cCoq_2eInit_2eDecimal_2eDecimalExp___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_Coq.ZArith.BinIntDef.Z.min_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eBinIntDef_2eZ_2emin,V_24X1),V_24X2) = cCoq_2eZArith_2eBinIntDef_2eZ_2emin___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.micromega.Tauto.N_$a5',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2emicromega_2eTauto_2eN,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2emicromega_2eTauto_2eN___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).

fof('$adef_$_lam_146985_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__lam__146985,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__lam__146985___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).

fof('$adef_PLF.Hoare.HoareAssertAssume.CWhile_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cPLF_2eHoare_2eHoareAssertAssume_2eCWhile,V_24X1),V_24X2) = cPLF_2eHoare_2eHoareAssertAssume_2eCWhile___24a2(V_24X1,V_24X2) ).

fof('$adef_PLF.Imp.CAss_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cPLF_2eImp_2eCAss,V_24X1),V_24X2) = cPLF_2eImp_2eCAss___24a2(V_24X1,V_24X2) ).

fof('$adef_PLF.Hoare.Himp.ceval_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] :
      ( p(happ(happ(happ(cPLF_2eHoare_2eHimp_2eceval,V_24X1),V_24X2),V_24X3))
    <=> cPLF_2eHoare_2eHimp_2eceval___24a3(V_24X1,V_24X2,V_24X3) ) ).

fof('$adef_PLF.Hoare.HoareAssertAssume.CAssume_$a1',axiom,
    ! [V_24X1] : happ(cPLF_2eHoare_2eHoareAssertAssume_2eCAssume,V_24X1) = cPLF_2eHoare_2eHoareAssertAssume_2eCAssume___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('$adef_PLF.Imp.AExp.BLe_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cPLF_2eImp_2eAExp_2eBLe,V_24X1),V_24X2) = cPLF_2eImp_2eAExp_2eBLe___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.Init.Specif.existT2_$a6',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(cCoq_2eInit_2eSpecif_2eexistT2,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = cCoq_2eInit_2eSpecif_2eexistT2___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).

fof('$adef_Coq.micromega.RingMicromega.PsatzC_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2emicromega_2eRingMicromega_2ePsatzC,V_24X1),V_24X2) = cCoq_2emicromega_2eRingMicromega_2ePsatzC___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.ZArith.BinInt.Zne_$a2',axiom,
    ! [V_24X1,V_24X2] :
      ( p(happ(happ(cCoq_2eZArith_2eBinInt_2eZne,V_24X1),V_24X2))
    <=> cCoq_2eZArith_2eBinInt_2eZne___24a2(V_24X1,V_24X2) ) ).

fof('$adef_Coq.Reals.RIneq.Rsqr_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eReals_2eRIneq_2eRsqr,V_24X1) = cCoq_2eReals_2eRIneq_2eRsqr___24a1(V_24X1) ).

fof('$adef_Coq.PArith.BinPosDef.Pos.compare_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare,V_24X1),V_24X2) = cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.setoid_ring.InitialRing.mkhypo_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2esetoid__ring_2eInitialRing_2emkhypo,V_24X1),V_24X2) = cCoq_2esetoid__ring_2eInitialRing_2emkhypo___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.Reals.RIneq.mknonzeroreal_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eReals_2eRIneq_2emknonzeroreal,V_24X1) = cCoq_2eReals_2eRIneq_2emknonzeroreal___24a1(V_24X1) ).

fof('$adef_Coq.ZArith.BinIntDef.Z.div_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eBinIntDef_2eZ_2ediv,V_24X1),V_24X2) = cCoq_2eZArith_2eBinIntDef_2eZ_2ediv___24a2(V_24X1,V_24X2) ).

fof('$adef_PLF.Hoare.Himp.CAsgn_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cPLF_2eHoare_2eHimp_2eCAsgn,V_24X1),V_24X2) = cPLF_2eHoare_2eHimp_2eCAsgn___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('$adef_Coq.Lists.List.fold_right_$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('$adef_Coq.Init.Nat.odd_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eInit_2eNat_2eodd,V_24X1) = cCoq_2eInit_2eNat_2eodd___24a1(V_24X1) ).

fof('$adef_PLF.Imp.SPush_$a1',axiom,
    ! [V_24X1] : happ(cPLF_2eImp_2eSPush,V_24X1) = cPLF_2eImp_2eSPush___24a1(V_24X1) ).

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('$adef_Coq.setoid_ring.Ring_theory.sign_theory_$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('$adef_$_case_Coq.Init.Datatypes.nat$82845_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__case__Coq_2eInit_2eDatatypes_2enat_2482845,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__case__Coq_2eInit_2eDatatypes_2enat_2482845___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).

fof('$adef_$_lam_943_$a6',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(c_24__lam__943,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = c_24__lam__943___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).

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('$adef_PLF.Hoare.HoareAssertAssume.RNormal_$a1',axiom,
    ! [V_24X1] : happ(cPLF_2eHoare_2eHoareAssertAssume_2eRNormal,V_24X1) = cPLF_2eHoare_2eHoareAssertAssume_2eRNormal___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('$adef_PLF.Imp.APlus_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cPLF_2eImp_2eAPlus,V_24X1),V_24X2) = cPLF_2eImp_2eAPlus___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('$adef_PLF.Maps.total_map_$a1',axiom,
    ! [V_24X1] : happ(cPLF_2eMaps_2etotal__map,V_24X1) = cPLF_2eMaps_2etotal__map___24a1(V_24X1) ).

fof('$adef_Coq.Init.Specif.left_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eSpecif_2eleft,V_24X1),V_24X2) = cCoq_2eInit_2eSpecif_2eleft___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.Init.Specif.sigT_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eSpecif_2esigT,V_24X1),V_24X2) = cCoq_2eInit_2eSpecif_2esigT___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.Init.Decimal.D3_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eInit_2eDecimal_2eD3,V_24X1) = cCoq_2eInit_2eDecimal_2eD3___24a1(V_24X1) ).

fof('$adef_$_lam_83190_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(c_24__lam__83190,V_24X1),V_24X2) = c_24__lam__83190___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.ZArith.BinIntDef.Z.pow_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eBinIntDef_2eZ_2epow,V_24X1),V_24X2) = cCoq_2eZArith_2eBinIntDef_2eZ_2epow___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.Relations.Relation_Operators.clos_refl_trans_n1_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] :
      ( p(happ(happ(happ(happ(cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans__n1,V_24X1),V_24X2),V_24X3),V_24X4))
    <=> cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans__n1___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).

fof('$adef_$_prop_149937_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__prop__149937,V_24X1),V_24X2),V_24X3) = c_24__prop__149937___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_PLF.Hoare.If1.CAss_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cPLF_2eHoare_2eIf1_2eCAss,V_24X1),V_24X2) = cPLF_2eHoare_2eIf1_2eCAss___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('$adef_Coq.micromega.EnvRing.PEadd_$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('$adef_PLF.Imp.aevalR_division.aevalR_$a2',axiom,
    ! [V_24X1,V_24X2] :
      ( p(happ(happ(cPLF_2eImp_2eaevalR__division_2eaevalR,V_24X1),V_24X2))
    <=> cPLF_2eImp_2eaevalR__division_2eaevalR___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('$adef_$_fix_148532_v_CANONICAL_1_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__fix__148532__v__CANONICAL__1,V_24X1),V_24X2),V_24X3) = c_24__fix__148532__v__CANONICAL__1___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('$adef_Coq.NArith.BinNatDef.N.eqb_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2eNArith_2eBinNatDef_2eN_2eeqb,V_24X1),V_24X2) = cCoq_2eNArith_2eBinNatDef_2eN_2eeqb___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.NArith.BinNat.N.eqf_$a2',axiom,
    ! [V_24X1,V_24X2] :
      ( p(happ(happ(cCoq_2eNArith_2eBinNat_2eN_2eeqf,V_24X1),V_24X2))
    <=> cCoq_2eNArith_2eBinNat_2eN_2eeqf___24a2(V_24X1,V_24X2) ) ).

fof('$adef_Coq.micromega.ZMicromega.is_diff_env_elt_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] :
      ( p(happ(happ(happ(happ(cCoq_2emicromega_2eZMicromega_2eis__diff__env__elt,V_24X1),V_24X2),V_24X3),V_24X4))
    <=> cCoq_2emicromega_2eZMicromega_2eis__diff__env__elt___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).

fof('$adef_Coq.NArith.BinNat.N.le_$a2',axiom,
    ! [V_24X1,V_24X2] :
      ( p(happ(happ(cCoq_2eNArith_2eBinNat_2eN_2ele,V_24X1),V_24X2))
    <=> cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(V_24X1,V_24X2) ) ).

fof('$adef_$_prop_149935_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(c_24__prop__149935,V_24X1),V_24X2) = c_24__prop__149935___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.PArith.BinPosDef.Pos.testbit_nat_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2ePArith_2eBinPosDef_2ePos_2etestbit__nat,V_24X1),V_24X2) = cCoq_2ePArith_2eBinPosDef_2ePos_2etestbit__nat___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.ZArith.Zpower.Zdiv_rest_proofs_$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('$adef_PLF.Imp.aevalR_extended.ANum_$a1',axiom,
    ! [V_24X1] : happ(cPLF_2eImp_2eaevalR__extended_2eANum,V_24X1) = cPLF_2eImp_2eaevalR__extended_2eANum___24a1(V_24X1) ).

fof('$adef_Coq.PArith.BinPosDef.Pos.add_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2ePArith_2eBinPosDef_2ePos_2eadd,V_24X1),V_24X2) = cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.Init.Nat.double_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eInit_2eNat_2edouble,V_24X1) = cCoq_2eInit_2eNat_2edouble___24a1(V_24X1) ).

fof('$adef_Coq.Init.Peano.gt_$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('$adef_PLF.Hoare.RepeatExercise.CIf_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cPLF_2eHoare_2eRepeatExercise_2eCIf,V_24X1),V_24X2),V_24X3) = cPLF_2eHoare_2eRepeatExercise_2eCIf___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$tdef_$_type_145681',axiom,
    ! [V_24Y] :
      ( c_24__type__145681___24t(V_24Y)
    <=> t(V_24Y,c_24__type__145681) ) ).

fof('$tdef_PLF.Hoare.If1.com',axiom,
    ! [V_24Y] :
      ( cPLF_2eHoare_2eIf1_2ecom___24t(V_24Y)
    <=> t(V_24Y,cPLF_2eHoare_2eIf1_2ecom) ) ).

fof('$tdef_$_type_134126',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__134126___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__134126___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_2853',axiom,
    ! [V_24Y] :
      ( c_24__type__2853___24t(V_24Y)
    <=> t(V_24Y,c_24__type__2853) ) ).

fof('$tdef_$_type_152522',axiom,
    ! [V_24Y] :
      ( c_24__type__152522___24t(V_24Y)
    <=> t(V_24Y,c_24__type__152522) ) ).

fof('$tdef_$_type_122334',axiom,
    ! [V_24Y] :
      ( c_24__type__122334___24t(V_24Y)
    <=> t(V_24Y,c_24__type__122334) ) ).

fof('$tdef_$_type_124484',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__124484___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__124484___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).

fof('$tdef_$_type_128232',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__128232___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__128232___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_339',axiom,
    ! [V_24Y] :
      ( c_24__type__339___24t(V_24Y)
    <=> t(V_24Y,c_24__type__339) ) ).

fof('$tdef_$_type_138867',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
      ( c_24__type__138867___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__138867___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).

fof('$tdef_Coq.micromega.VarMap.t',axiom,
    ! [V_24X1,V_24Y] :
      ( cCoq_2emicromega_2eVarMap_2et___24t(V_24X1,V_24Y)
    <=> t(V_24Y,cCoq_2emicromega_2eVarMap_2et___24a1(V_24X1)) ) ).

fof('$tdef_$_type_329',axiom,
    ! [V_24Y] :
      ( c_24__type__329___24t(V_24Y)
    <=> t(V_24Y,c_24__type__329) ) ).

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_868',axiom,
    ! [V_24Y] :
      ( c_24__type__868___24t(V_24Y)
    <=> t(V_24Y,c_24__type__868) ) ).

fof('$tdef_$_type_139760',axiom,
    ! [V_24Y] :
      ( c_24__type__139760___24t(V_24Y)
    <=> t(V_24Y,c_24__type__139760) ) ).

fof('$tdef_$_type_134960',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__134960___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__134960___24a17(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17)) ) ).

fof('$tdef_Coq.Init.Datatypes.bool',axiom,
    ! [V_24Y] :
      ( cCoq_2eInit_2eDatatypes_2ebool___24t(V_24Y)
    <=> t(V_24Y,cCoq_2eInit_2eDatatypes_2ebool) ) ).

fof('$tdef_$_type_146095',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__146095___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__146095___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).

fof('$tdef_$_type_7022',axiom,
    ! [V_24Y] :
      ( c_24__type__7022___24t(V_24Y)
    <=> t(V_24Y,c_24__type__7022) ) ).

fof('$tdef_$_type_247',axiom,
    ! [V_24Y] :
      ( c_24__type__247___24t(V_24Y)
    <=> t(V_24Y,c_24__type__247) ) ).

fof('$tdef_$_type_6056',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__6056___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__6056___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_668',axiom,
    ! [V_24Y] :
      ( c_24__type__668___24t(V_24Y)
    <=> t(V_24Y,c_24__type__668) ) ).

fof('$tdef_$_type_152839',axiom,
    ! [V_24Y] :
      ( c_24__type__152839___24t(V_24Y)
    <=> t(V_24Y,c_24__type__152839) ) ).

fof('$tdef_$_type_135483',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y] :
      ( c_24__type__135483___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y)
    <=> t(V_24Y,c_24__type__135483___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7)) ) ).

fof('$tdef_Coq.Structures.OrdersTac.ord',axiom,
    ! [V_24Y] :
      ( cCoq_2eStructures_2eOrdersTac_2eord___24t(V_24Y)
    <=> t(V_24Y,cCoq_2eStructures_2eOrdersTac_2eord) ) ).

fof('$tdef_$_type_149074',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24Y] :
      ( c_24__type__149074___24t(V_24X1,V_24X2,V_24X3,V_24Y)
    <=> t(V_24Y,c_24__type__149074___24a3(V_24X1,V_24X2,V_24X3)) ) ).

fof('$tdef_$_type_7004',axiom,
    ! [V_24Y] :
      ( c_24__type__7004___24t(V_24Y)
    <=> t(V_24Y,c_24__type__7004) ) ).

fof('$tdef_Coq.micromega.EnvRing.PExpr',axiom,
    ! [V_24X1,V_24Y] :
      ( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(V_24X1,V_24Y)
    <=> t(V_24Y,cCoq_2emicromega_2eEnvRing_2ePExpr___24a1(V_24X1)) ) ).

fof('$tdef_$_type_139657',axiom,
    ! [V_24X1,V_24X2,V_24Y] :
      ( c_24__type__139657___24t(V_24X1,V_24X2,V_24Y)
    <=> t(V_24Y,c_24__type__139657___24a2(V_24X1,V_24X2)) ) ).

fof('$tdef_$_type_615',axiom,
    ! [V_24Y] :
      ( c_24__type__615___24t(V_24Y)
    <=> t(V_24Y,c_24__type__615) ) ).

fof('$tdef_$_type_139754',axiom,
    ! [V_24X1,V_24X2,V_24Y] :
      ( c_24__type__139754___24t(V_24X1,V_24X2,V_24Y)
    <=> t(V_24Y,c_24__type__139754___24a2(V_24X1,V_24X2)) ) ).

fof('$tdef_$_type_135173',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__135173___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__135173___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_83636',axiom,
    ! [V_24Y] :
      ( c_24__type__83636___24t(V_24Y)
    <=> t(V_24Y,c_24__type__83636) ) ).

fof('$tdef_$_type_155282',axiom,
    ! [V_24Y] :
      ( c_24__type__155282___24t(V_24Y)
    <=> t(V_24Y,c_24__type__155282) ) ).

fof('$tdef_$_type_152782',axiom,
    ! [V_24Y] :
      ( c_24__type__152782___24t(V_24Y)
    <=> t(V_24Y,c_24__type__152782) ) ).

fof('$tdef_$_type_155382',axiom,
    ! [V_24Y] :
      ( c_24__type__155382___24t(V_24Y)
    <=> t(V_24Y,c_24__type__155382) ) ).

fof('$tdef_Hoare2.decorated',axiom,
    ! [V_24Y] :
      ( cHoare2_2edecorated___24t(V_24Y)
    <=> t(V_24Y,cHoare2_2edecorated) ) ).

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_139345',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y] :
      ( c_24__type__139345___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y)
    <=> t(V_24Y,c_24__type__139345___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7)) ) ).

fof('$tdef_$_type_349',axiom,
    ! [V_24Y] :
      ( c_24__type__349___24t(V_24Y)
    <=> t(V_24Y,c_24__type__349) ) ).

fof('$tdef_$_type_149779',axiom,
    ! [V_24Y] :
      ( c_24__type__149779___24t(V_24Y)
    <=> t(V_24Y,c_24__type__149779) ) ).

fof('$tdef_$_type_9',axiom,
    ! [V_24Y] :
      ( c_24__type__9___24t(V_24Y)
    <=> t(V_24Y,c_24__type__9) ) ).

fof('$tdef_PLF.Imp.state',axiom,
    ! [V_24Y] :
      ( cPLF_2eImp_2estate___24t(V_24Y)
    <=> t(V_24Y,cPLF_2eImp_2estate) ) ).

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_151198',axiom,
    ! [V_24Y] :
      ( c_24__type__151198___24t(V_24Y)
    <=> t(V_24Y,c_24__type__151198) ) ).

fof('$tdef_$_type_85043',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
      ( c_24__type__85043___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
    <=> t(V_24Y,c_24__type__85043___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).

fof('$tdef_$_type_146954',axiom,
    ! [V_24X1,V_24X2,V_24Y] :
      ( c_24__type__146954___24t(V_24X1,V_24X2,V_24Y)
    <=> t(V_24Y,c_24__type__146954___24a2(V_24X1,V_24X2)) ) ).

fof('$tdef_PLF.Imp.BreakImp.com',axiom,
    ! [V_24Y] :
      ( cPLF_2eImp_2eBreakImp_2ecom___24t(V_24Y)
    <=> t(V_24Y,cPLF_2eImp_2eBreakImp_2ecom) ) ).

fof('$tdef_$_type_6306',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__6306___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__6306___24a13(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13)) ) ).

fof('$tdef_Coq.micromega.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_148202',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24Y] :
      ( c_24__type__148202___24t(V_24X1,V_24X2,V_24X3,V_24Y)
    <=> t(V_24Y,c_24__type__148202___24a3(V_24X1,V_24X2,V_24X3)) ) ).

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_5412',axiom,
    ! [V_24Y] :
      ( c_24__type__5412___24t(V_24Y)
    <=> t(V_24Y,c_24__type__5412) ) ).

fof('$tdef_$_type_6865',axiom,
    ! [V_24Y] :
      ( c_24__type__6865___24t(V_24Y)
    <=> t(V_24Y,c_24__type__6865) ) ).

fof('$tdef_$_type_397',axiom,
    ! [V_24Y] :
      ( c_24__type__397___24t(V_24Y)
    <=> t(V_24Y,c_24__type__397) ) ).

fof('$tdef_$_type_152871',axiom,
    ! [V_24X1,V_24Y] :
      ( c_24__type__152871___24t(V_24X1,V_24Y)
    <=> t(V_24Y,c_24__type__152871___24a1(V_24X1)) ) ).

fof('$tdef_$_type_147141',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24Y] :
      ( c_24__type__147141___24t(V_24X1,V_24X2,V_24X3,V_24Y)
    <=> t(V_24Y,c_24__type__147141___24a3(V_24X1,V_24X2,V_24X3)) ) ).

fof('$tdef_$_type_135754',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
      ( c_24__type__135754___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
    <=> t(V_24Y,c_24__type__135754___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).

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_125873',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__125873___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__125873___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).

fof('$tdef_$_type_4532',axiom,
    ! [V_24Y] :
      ( c_24__type__4532___24t(V_24Y)
    <=> t(V_24Y,c_24__type__4532) ) ).

fof('$tdef_$_type_135837',axiom,
    ! [V_24X1,V_24Y] :
      ( c_24__type__135837___24t(V_24X1,V_24Y)
    <=> t(V_24Y,c_24__type__135837___24a1(V_24X1)) ) ).

fof('$tdef_$_type_4389',axiom,
    ! [V_24Y] :
      ( c_24__type__4389___24t(V_24Y)
    <=> t(V_24Y,c_24__type__4389) ) ).

fof('$tdef_$_type_148903',axiom,
    ! [V_24X1,V_24X2,V_24Y] :
      ( c_24__type__148903___24t(V_24X1,V_24X2,V_24Y)
    <=> t(V_24Y,c_24__type__148903___24a2(V_24X1,V_24X2)) ) ).

fof('$tdef_$_type_122344',axiom,
    ! [V_24Y] :
      ( c_24__type__122344___24t(V_24Y)
    <=> t(V_24Y,c_24__type__122344) ) ).

fof('$tdef_$_type_132077',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
      ( c_24__type__132077___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__132077___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).

fof('$tdef_$_type_5057',axiom,
    ! [V_24Y] :
      ( c_24__type__5057___24t(V_24Y)
    <=> t(V_24Y,c_24__type__5057) ) ).

fof('$tdef_$_type_6755',axiom,
    ! [V_24Y] :
      ( c_24__type__6755___24t(V_24Y)
    <=> t(V_24Y,c_24__type__6755) ) ).

fof('$tdef_$_type_14',axiom,
    ! [V_24Y] :
      ( c_24__type__14___24t(V_24Y)
    <=> t(V_24Y,c_24__type__14) ) ).

fof('$tdef_$_type_132701',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
      ( c_24__type__132701___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
    <=> t(V_24Y,c_24__type__132701___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).

fof('$tdef_$_type_3765',axiom,
    ! [V_24Y] :
      ( c_24__type__3765___24t(V_24Y)
    <=> t(V_24Y,c_24__type__3765) ) ).

fof('$tdef_$_type_5931',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__5931___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__5931___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_PLF.Maps.total_map',axiom,
    ! [V_24X1,V_24Y] :
      ( cPLF_2eMaps_2etotal__map___24t(V_24X1,V_24Y)
    <=> t(V_24Y,cPLF_2eMaps_2etotal__map___24a1(V_24X1)) ) ).

fof('$tdef_$_type_146872',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
      ( c_24__type__146872___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__146872___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).

fof('$tdef_Coq.setoid_ring.Field_theory.FExpr',axiom,
    ! [V_24X1,V_24Y] :
      ( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(V_24X1,V_24Y)
    <=> t(V_24Y,cCoq_2esetoid__ring_2eField__theory_2eFExpr___24a1(V_24X1)) ) ).

fof('$tdef_$_type_6702',axiom,
    ! [V_24X1,V_24X2,V_24Y] :
      ( c_24__type__6702___24t(V_24X1,V_24X2,V_24Y)
    <=> t(V_24Y,c_24__type__6702___24a2(V_24X1,V_24X2)) ) ).

fof('$tdef_Coq.micromega.RMicromega.Rcst',axiom,
    ! [V_24Y] :
      ( cCoq_2emicromega_2eRMicromega_2eRcst___24t(V_24Y)
    <=> t(V_24Y,cCoq_2emicromega_2eRMicromega_2eRcst) ) ).

fof('$tdef_$_type_7046',axiom,
    ! [V_24X1,V_24Y] :
      ( c_24__type__7046___24t(V_24X1,V_24Y)
    <=> t(V_24Y,c_24__type__7046___24a1(V_24X1)) ) ).

fof('$tdef_$_type_1904',axiom,
    ! [V_24Y] :
      ( c_24__type__1904___24t(V_24Y)
    <=> t(V_24Y,c_24__type__1904) ) ).

fof('$tdef_$_type_147249',axiom,
    ! [V_24Y] :
      ( c_24__type__147249___24t(V_24Y)
    <=> t(V_24Y,c_24__type__147249) ) ).

fof('$tdef_$_type_7323',axiom,
    ! [V_24Y] :
      ( c_24__type__7323___24t(V_24Y)
    <=> t(V_24Y,c_24__type__7323) ) ).

fof('$tdef_$_type_138033',axiom,
    ! [V_24Y] :
      ( c_24__type__138033___24t(V_24Y)
    <=> t(V_24Y,c_24__type__138033) ) ).

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_4445',axiom,
    ! [V_24Y] :
      ( c_24__type__4445___24t(V_24Y)
    <=> t(V_24Y,c_24__type__4445) ) ).

fof('$tdef_$_type_6791',axiom,
    ! [V_24X1,V_24X2,V_24Y] :
      ( c_24__type__6791___24t(V_24X1,V_24X2,V_24Y)
    <=> t(V_24Y,c_24__type__6791___24a2(V_24X1,V_24X2)) ) ).

fof('$tdef_$_type_149000',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24Y] :
      ( c_24__type__149000___24t(V_24X1,V_24X2,V_24X3,V_24Y)
    <=> t(V_24Y,c_24__type__149000___24a3(V_24X1,V_24X2,V_24X3)) ) ).

fof('$tdef_$_type_124927',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__124927___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__124927___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).

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_138750',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
      ( c_24__type__138750___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__138750___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).

fof('$tdef_$_type_134765',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__134765___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__134765___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_139638',axiom,
    ! [V_24Y] :
      ( c_24__type__139638___24t(V_24Y)
    <=> t(V_24Y,c_24__type__139638) ) ).

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_7083',axiom,
    ! [V_24Y] :
      ( c_24__type__7083___24t(V_24Y)
    <=> t(V_24Y,c_24__type__7083) ) ).

fof('$tdef_$_type_1125',axiom,
    ! [V_24Y] :
      ( c_24__type__1125___24t(V_24Y)
    <=> t(V_24Y,c_24__type__1125) ) ).

fof('$tdef_$_type_3844',axiom,
    ! [V_24Y] :
      ( c_24__type__3844___24t(V_24Y)
    <=> t(V_24Y,c_24__type__3844) ) ).

fof('$tdef_$_type_148104',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
      ( c_24__type__148104___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
    <=> t(V_24Y,c_24__type__148104___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).

fof('$tdef_$_type_133913',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__133913___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__133913___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_6556',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__6556___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__6556___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_324',axiom,
    ! [V_24Y] :
      ( c_24__type__324___24t(V_24Y)
    <=> t(V_24Y,c_24__type__324) ) ).

fof('$tdef_$_type_139724',axiom,
    ! [V_24Y] :
      ( c_24__type__139724___24t(V_24Y)
    <=> t(V_24Y,c_24__type__139724) ) ).

fof('$tdef_$_type_14831',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24Y] :
      ( c_24__type__14831___24t(V_24X1,V_24X2,V_24X3,V_24Y)
    <=> t(V_24Y,c_24__type__14831___24a3(V_24X1,V_24X2,V_24X3)) ) ).

fof('$tdef_$_type_132725',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
      ( c_24__type__132725___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
    <=> t(V_24Y,c_24__type__132725___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).

fof('$tdef_$_type_128924',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__128924___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__128924___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_620',axiom,
    ! [V_24Y] :
      ( c_24__type__620___24t(V_24Y)
    <=> t(V_24Y,c_24__type__620) ) ).

fof('$tdef_$_type_152531',axiom,
    ! [V_24Y] :
      ( c_24__type__152531___24t(V_24Y)
    <=> t(V_24Y,c_24__type__152531) ) ).

fof('$tdef_$_type_124053',axiom,
    ! [V_24X1,V_24Y] :
      ( c_24__type__124053___24t(V_24X1,V_24Y)
    <=> t(V_24Y,c_24__type__124053___24a1(V_24X1)) ) ).

fof('$tdef_PLF.Imp.com',axiom,
    ! [V_24Y] :
      ( cPLF_2eImp_2ecom___24t(V_24Y)
    <=> t(V_24Y,cPLF_2eImp_2ecom) ) ).

fof('$tdef_$_type_132809',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
      ( c_24__type__132809___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
    <=> t(V_24Y,c_24__type__132809___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).

fof('$tdef_$_type_123915',axiom,
    ! [V_24Y] :
      ( c_24__type__123915___24t(V_24Y)
    <=> t(V_24Y,c_24__type__123915) ) ).

fof('$tdef_$_type_145806',axiom,
    ! [V_24Y] :
      ( c_24__type__145806___24t(V_24Y)
    <=> t(V_24Y,c_24__type__145806) ) ).

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_155153',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y] :
      ( c_24__type__155153___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y)
    <=> t(V_24Y,c_24__type__155153___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6)) ) ).

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_6855',axiom,
    ! [V_24X1,V_24X2,V_24Y] :
      ( c_24__type__6855___24t(V_24X1,V_24X2,V_24Y)
    <=> t(V_24Y,c_24__type__6855___24a2(V_24X1,V_24X2)) ) ).

fof('$tdef_$_type_148893',axiom,
    ! [V_24Y] :
      ( c_24__type__148893___24t(V_24Y)
    <=> t(V_24Y,c_24__type__148893) ) ).

fof('$tdef_$_type_128578',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__128578___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__128578___24a22(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22)) ) ).

fof('$tdef_Coq.Init.Byte.byte',axiom,
    ! [V_24Y] :
      ( cCoq_2eInit_2eByte_2ebyte___24t(V_24Y)
    <=> t(V_24Y,cCoq_2eInit_2eByte_2ebyte) ) ).

fof('$tdef_$_type_1928',axiom,
    ! [V_24Y] :
      ( c_24__type__1928___24t(V_24Y)
    <=> t(V_24Y,c_24__type__1928) ) ).

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('$tdef_$_type_1547',axiom,
    ! [V_24Y] :
      ( c_24__type__1547___24t(V_24Y)
    <=> t(V_24Y,c_24__type__1547) ) ).

fof('$tdef_$_type_151115',axiom,
    ! [V_24Y] :
      ( c_24__type__151115___24t(V_24Y)
    <=> t(V_24Y,c_24__type__151115) ) ).

fof('$tdef_PLF.Imp.aevalR_extended.aexp',axiom,
    ! [V_24Y] :
      ( cPLF_2eImp_2eaevalR__extended_2eaexp___24t(V_24Y)
    <=> t(V_24Y,cPLF_2eImp_2eaevalR__extended_2eaexp) ) ).

fof('$tdef_PLF.Imp.AExp.bexp',axiom,
    ! [V_24Y] :
      ( cPLF_2eImp_2eAExp_2ebexp___24t(V_24Y)
    <=> t(V_24Y,cPLF_2eImp_2eAExp_2ebexp) ) ).

fof('$tdef_$_type_307',axiom,
    ! [V_24Y] :
      ( c_24__type__307___24t(V_24Y)
    <=> t(V_24Y,c_24__type__307) ) ).

fof('$tdef_$_type_152519',axiom,
    ! [V_24Y] :
      ( c_24__type__152519___24t(V_24Y)
    <=> t(V_24Y,c_24__type__152519) ) ).

fof('$tdef_$_type_132893',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
      ( c_24__type__132893___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
    <=> t(V_24Y,c_24__type__132893___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).

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_155178',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y] :
      ( c_24__type__155178___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y)
    <=> t(V_24Y,c_24__type__155178___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6)) ) ).

fof('$tdef_$_type_122337',axiom,
    ! [V_24Y] :
      ( c_24__type__122337___24t(V_24Y)
    <=> t(V_24Y,c_24__type__122337) ) ).

fof('$tdef_$_type_4391',axiom,
    ! [V_24Y] :
      ( c_24__type__4391___24t(V_24Y)
    <=> t(V_24Y,c_24__type__4391) ) ).

fof('$tdef_$_type_4139',axiom,
    ! [V_24Y] :
      ( c_24__type__4139___24t(V_24Y)
    <=> t(V_24Y,c_24__type__4139) ) ).

fof('$tdef_$_type_2671',axiom,
    ! [V_24Y] :
      ( c_24__type__2671___24t(V_24Y)
    <=> t(V_24Y,c_24__type__2671) ) ).

fof('$tdef_$_type_145803',axiom,
    ! [V_24Y] :
      ( c_24__type__145803___24t(V_24Y)
    <=> t(V_24Y,c_24__type__145803) ) ).

fof('$tdef_$_type_121976',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
      ( c_24__type__121976___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
    <=> t(V_24Y,c_24__type__121976___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).

fof('$tdef_$_type_1878',axiom,
    ! [V_24X1,V_24Y] :
      ( c_24__type__1878___24t(V_24X1,V_24Y)
    <=> t(V_24Y,c_24__type__1878___24a1(V_24X1)) ) ).

fof('$tdef_$_type_126302',axiom,
    ! [V_24Y] :
      ( c_24__type__126302___24t(V_24Y)
    <=> t(V_24Y,c_24__type__126302) ) ).

fof('$tdef_$_type_132430',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
      ( c_24__type__132430___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
    <=> t(V_24Y,c_24__type__132430___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).

fof('$tdef_$_type_147165',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24Y] :
      ( c_24__type__147165___24t(V_24X1,V_24X2,V_24X3,V_24Y)
    <=> t(V_24Y,c_24__type__147165___24a3(V_24X1,V_24X2,V_24X3)) ) ).

fof('$tdef_Hoare2.dcom',axiom,
    ! [V_24Y] :
      ( cHoare2_2edcom___24t(V_24Y)
    <=> t(V_24Y,cHoare2_2edcom) ) ).

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_PLF.Imp.sinstr',axiom,
    ! [V_24Y] :
      ( cPLF_2eImp_2esinstr___24t(V_24Y)
    <=> t(V_24Y,cPLF_2eImp_2esinstr) ) ).

fof('$tdef_$_type_1123',axiom,
    ! [V_24Y] :
      ( c_24__type__1123___24t(V_24Y)
    <=> t(V_24Y,c_24__type__1123) ) ).

fof('$tdef_$_type_147857',axiom,
    ! [V_24Y] :
      ( c_24__type__147857___24t(V_24Y)
    <=> t(V_24Y,c_24__type__147857) ) ).

fof('$tdef_$_type_146965',axiom,
    ! [V_24X1,V_24X2,V_24Y] :
      ( c_24__type__146965___24t(V_24X1,V_24X2,V_24Y)
    <=> t(V_24Y,c_24__type__146965___24a2(V_24X1,V_24X2)) ) ).

fof('$tdef_$_type_124267',axiom,
    ! [V_24Y] :
      ( c_24__type__124267___24t(V_24Y)
    <=> t(V_24Y,c_24__type__124267) ) ).

fof('$tdef_$_type_135563',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y] :
      ( c_24__type__135563___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y)
    <=> t(V_24Y,c_24__type__135563___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7)) ) ).

fof('$tdef_$_type_5088',axiom,
    ! [V_24X1,V_24X2,V_24Y] :
      ( c_24__type__5088___24t(V_24X1,V_24X2,V_24Y)
    <=> t(V_24Y,c_24__type__5088___24a2(V_24X1,V_24X2)) ) ).

fof('$tdef_$_type_244',axiom,
    ! [V_24Y] :
      ( c_24__type__244___24t(V_24Y)
    <=> t(V_24Y,c_24__type__244) ) ).

fof('$tdef_$_type_152850',axiom,
    ! [V_24Y] :
      ( c_24__type__152850___24t(V_24Y)
    <=> t(V_24Y,c_24__type__152850) ) ).

fof('$tdef_$_type_145718',axiom,
    ! [V_24Y] :
      ( c_24__type__145718___24t(V_24Y)
    <=> t(V_24Y,c_24__type__145718) ) ).

fof('$tdef_$_type_1418',axiom,
    ! [V_24Y] :
      ( c_24__type__1418___24t(V_24Y)
    <=> t(V_24Y,c_24__type__1418) ) ).

fof('$tdef_$_type_152742',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y] :
      ( c_24__type__152742___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y)
    <=> t(V_24Y,c_24__type__152742___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6)) ) ).

fof('$tdef_$_type_147115',axiom,
    ! [V_24Y] :
      ( c_24__type__147115___24t(V_24Y)
    <=> t(V_24Y,c_24__type__147115) ) ).

fof('$tdef_$_type_2858',axiom,
    ! [V_24Y] :
      ( c_24__type__2858___24t(V_24Y)
    <=> t(V_24Y,c_24__type__2858) ) ).

fof('$tdef_$_type_1115',axiom,
    ! [V_24Y] :
      ( c_24__type__1115___24t(V_24Y)
    <=> t(V_24Y,c_24__type__1115) ) ).

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_131823',axiom,
    ! [V_24Y] :
      ( c_24__type__131823___24t(V_24Y)
    <=> t(V_24Y,c_24__type__131823) ) ).

fof('$tdef_$_type_134552',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__134552___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__134552___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_3523',axiom,
    ! [V_24X1,V_24Y] :
      ( c_24__type__3523___24t(V_24X1,V_24Y)
    <=> t(V_24Y,c_24__type__3523___24a1(V_24X1)) ) ).

fof('$tdef_$_type_152866',axiom,
    ! [V_24Y] :
      ( c_24__type__152866___24t(V_24Y)
    <=> t(V_24Y,c_24__type__152866) ) ).

fof('$tdef_$_type_147052',axiom,
    ! [V_24Y] :
      ( c_24__type__147052___24t(V_24Y)
    <=> t(V_24Y,c_24__type__147052) ) ).

fof('$tdef_$_type_3728',axiom,
    ! [V_24X1,V_24X2,V_24Y] :
      ( c_24__type__3728___24t(V_24X1,V_24X2,V_24Y)
    <=> t(V_24Y,c_24__type__3728___24a2(V_24X1,V_24X2)) ) ).

fof('$tdef_$_type_132755',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
      ( c_24__type__132755___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
    <=> t(V_24Y,c_24__type__132755___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).

fof('$tdef_$_type_1551',axiom,
    ! [V_24Y] :
      ( c_24__type__1551___24t(V_24Y)
    <=> t(V_24Y,c_24__type__1551) ) ).

fof('$tdef_$_type_125682',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__125682___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__125682___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).

fof('$tdef_$_type_1888',axiom,
    ! [V_24Y] :
      ( c_24__type__1888___24t(V_24Y)
    <=> t(V_24Y,c_24__type__1888) ) ).

fof('$tdef_$_type_601',axiom,
    ! [V_24Y] :
      ( c_24__type__601___24t(V_24Y)
    <=> t(V_24Y,c_24__type__601) ) ).

fof('$tdef_$_type_150501',axiom,
    ! [V_24Y] :
      ( c_24__type__150501___24t(V_24Y)
    <=> t(V_24Y,c_24__type__150501) ) ).

fof('$tdef_$_type_148648',axiom,
    ! [V_24Y] :
      ( c_24__type__148648___24t(V_24Y)
    <=> t(V_24Y,c_24__type__148648) ) ).

fof('$tdef_$_type_138326',axiom,
    ! [V_24Y] :
      ( c_24__type__138326___24t(V_24Y)
    <=> t(V_24Y,c_24__type__138326) ) ).

fof('$tdef_$_type_6983',axiom,
    ! [V_24Y] :
      ( c_24__type__6983___24t(V_24Y)
    <=> t(V_24Y,c_24__type__6983) ) ).

fof('$tdef_$_type_3805',axiom,
    ! [V_24Y] :
      ( c_24__type__3805___24t(V_24Y)
    <=> t(V_24Y,c_24__type__3805) ) ).

fof('$tdef_$_type_132499',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
      ( c_24__type__132499___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
    <=> t(V_24Y,c_24__type__132499___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).

fof('$tdef_$_type_4125',axiom,
    ! [V_24Y] :
      ( c_24__type__4125___24t(V_24Y)
    <=> t(V_24Y,c_24__type__4125) ) ).

fof('$tdef_$_type_149109',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24Y] :
      ( c_24__type__149109___24t(V_24X1,V_24X2,V_24X3,V_24Y)
    <=> t(V_24Y,c_24__type__149109___24a3(V_24X1,V_24X2,V_24X3)) ) ).

fof('$tdef_$_type_139661',axiom,
    ! [V_24Y] :
      ( c_24__type__139661___24t(V_24Y)
    <=> t(V_24Y,c_24__type__139661) ) ).

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_1871',axiom,
    ! [V_24Y] :
      ( c_24__type__1871___24t(V_24Y)
    <=> t(V_24Y,c_24__type__1871) ) ).

fof('$tdef_$_type_6986',axiom,
    ! [V_24Y] :
      ( c_24__type__6986___24t(V_24Y)
    <=> t(V_24Y,c_24__type__6986) ) ).

fof('$tdef_Coq.QArith.QArith_base.Q',axiom,
    ! [V_24Y] :
      ( cCoq_2eQArith_2eQArith__base_2eQ___24t(V_24Y)
    <=> t(V_24Y,cCoq_2eQArith_2eQArith__base_2eQ) ) ).

fof('$tdef_$_type_125020',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__125020___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__125020___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).

fof('$tdef_Coq.PArith.BinPos.Pos.PeanoView',axiom,
    ! [V_24X1,V_24Y] :
      ( cCoq_2ePArith_2eBinPos_2ePos_2ePeanoView___24t(V_24X1,V_24Y)
    <=> t(V_24Y,cCoq_2ePArith_2eBinPos_2ePos_2ePeanoView___24a1(V_24X1)) ) ).

fof('$tdef_Coq.Numbers.BinNums.positive',axiom,
    ! [V_24Y] :
      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V_24Y)
    <=> t(V_24Y,cCoq_2eNumbers_2eBinNums_2epositive) ) ).

fof('$tdef_$_type_2849',axiom,
    ! [V_24Y] :
      ( c_24__type__2849___24t(V_24Y)
    <=> t(V_24Y,c_24__type__2849) ) ).

fof('$tdef_$_type_149723',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
      ( c_24__type__149723___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
    <=> t(V_24Y,c_24__type__149723___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).

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_133718',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__133718___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__133718___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_3828',axiom,
    ! [V_24Y] :
      ( c_24__type__3828___24t(V_24Y)
    <=> t(V_24Y,c_24__type__3828) ) ).

fof('$tdef_$_type_155453',axiom,
    ! [V_24Y] :
      ( c_24__type__155453___24t(V_24Y)
    <=> t(V_24Y,c_24__type__155453) ) ).

fof('$tdef_$_type_119461',axiom,
    ! [V_24Y] :
      ( c_24__type__119461___24t(V_24Y)
    <=> t(V_24Y,c_24__type__119461) ) ).

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_1944',axiom,
    ! [V_24Y] :
      ( c_24__type__1944___24t(V_24Y)
    <=> t(V_24Y,c_24__type__1944) ) ).

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_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_149143',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24Y] :
      ( c_24__type__149143___24t(V_24X1,V_24X2,V_24X3,V_24Y)
    <=> t(V_24Y,c_24__type__149143___24a3(V_24X1,V_24X2,V_24X3)) ) ).

fof('$tdef_$_type_139136',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
      ( c_24__type__139136___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
    <=> t(V_24Y,c_24__type__139136___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).

fof('$tdef_$_type_83204',axiom,
    ! [V_24Y] :
      ( c_24__type__83204___24t(V_24Y)
    <=> t(V_24Y,c_24__type__83204) ) ).

fof('$tdef_$_type_146755',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
      ( c_24__type__146755___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__146755___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).

fof('$tdef_$_type_139708',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24Y] :
      ( c_24__type__139708___24t(V_24X1,V_24X2,V_24X3,V_24Y)
    <=> t(V_24Y,c_24__type__139708___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_2846',axiom,
    ! [V_24Y] :
      ( c_24__type__2846___24t(V_24Y)
    <=> t(V_24Y,c_24__type__2846) ) ).

fof('$tdef_PLF.Imp.bexp',axiom,
    ! [V_24Y] :
      ( cPLF_2eImp_2ebexp___24t(V_24Y)
    <=> t(V_24Y,cPLF_2eImp_2ebexp) ) ).

fof('$tdef_$_type_130631',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__130631___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__130631___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_152488',axiom,
    ! [V_24Y] :
      ( c_24__type__152488___24t(V_24Y)
    <=> t(V_24Y,c_24__type__152488) ) ).

fof('$tdef_$_type_152822',axiom,
    ! [V_24Y] :
      ( c_24__type__152822___24t(V_24Y)
    <=> t(V_24Y,c_24__type__152822) ) ).

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_127217',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__127217___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__127217___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.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_135607',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y] :
      ( c_24__type__135607___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y)
    <=> t(V_24Y,c_24__type__135607___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7)) ) ).

fof('$tdef_$_type_125581',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__125581___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__125581___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).

fof('$tdef_$_type_124024',axiom,
    ! [V_24Y] :
      ( c_24__type__124024___24t(V_24Y)
    <=> t(V_24Y,c_24__type__124024) ) ).

fof('$tdef_$_type_125080',axiom,
    ! [V_24X1,V_24X2,V_24Y] :
      ( c_24__type__125080___24t(V_24X1,V_24X2,V_24Y)
    <=> t(V_24Y,c_24__type__125080___24a2(V_24X1,V_24X2)) ) ).

fof('$tdef_$_type_6861',axiom,
    ! [V_24Y] :
      ( c_24__type__6861___24t(V_24Y)
    <=> t(V_24Y,c_24__type__6861) ) ).

fof('$tdef_$_type_129616',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__129616___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__129616___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_126871',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__126871___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__126871___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_88324',axiom,
    ! [V_24Y] :
      ( c_24__type__88324___24t(V_24Y)
    <=> t(V_24Y,c_24__type__88324) ) ).

fof('$tdef_$_type_83121',axiom,
    ! [V_24Y] :
      ( c_24__type__83121___24t(V_24Y)
    <=> t(V_24Y,c_24__type__83121) ) ).

fof('$tdef_$_type_147104',axiom,
    ! [V_24Y] :
      ( c_24__type__147104___24t(V_24Y)
    <=> t(V_24Y,c_24__type__147104) ) ).

fof('$tdef_$_type_3293',axiom,
    ! [V_24Y] :
      ( c_24__type__3293___24t(V_24Y)
    <=> t(V_24Y,c_24__type__3293) ) ).

fof('$tdef_$_type_150097',axiom,
    ! [V_24Y] :
      ( c_24__type__150097___24t(V_24Y)
    <=> t(V_24Y,c_24__type__150097) ) ).

fof('$tdef_$_type_139395',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y] :
      ( c_24__type__139395___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y)
    <=> t(V_24Y,c_24__type__139395___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7)) ) ).

fof('$tdef_$_type_132320',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
      ( c_24__type__132320___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__132320___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).

fof('$tdef_$_type_121957',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
      ( c_24__type__121957___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
    <=> t(V_24Y,c_24__type__121957___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).

fof('$tdef_Coq.Vectors.Fin.t',axiom,
    ! [V_24X1,V_24Y] :
      ( cCoq_2eVectors_2eFin_2et___24t(V_24X1,V_24Y)
    <=> t(V_24Y,cCoq_2eVectors_2eFin_2et___24a1(V_24X1)) ) ).

fof('$tdef_$_type_138323',axiom,
    ! [V_24Y] :
      ( c_24__type__138323___24t(V_24Y)
    <=> t(V_24Y,c_24__type__138323) ) ).

fof('$tdef_$_type_3514',axiom,
    ! [V_24X1,V_24Y] :
      ( c_24__type__3514___24t(V_24X1,V_24Y)
    <=> t(V_24Y,c_24__type__3514___24a1(V_24X1)) ) ).

fof('$tdef_$_type_145158',axiom,
    ! [V_24Y] :
      ( c_24__type__145158___24t(V_24Y)
    <=> t(V_24Y,c_24__type__145158) ) ).

fof('$tdef_$_type_593',axiom,
    ! [V_24Y] :
      ( c_24__type__593___24t(V_24Y)
    <=> t(V_24Y,c_24__type__593) ) ).

fof('$tdef_$_type_126244',axiom,
    ! [V_24Y] :
      ( c_24__type__126244___24t(V_24Y)
    <=> t(V_24Y,c_24__type__126244) ) ).

fof('$tdef_$_type_148011',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y] :
      ( c_24__type__148011___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y)
    <=> t(V_24Y,c_24__type__148011___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6)) ) ).

fof('$tdef_$_type_6690',axiom,
    ! [V_24X1,V_24X2,V_24Y] :
      ( c_24__type__6690___24t(V_24X1,V_24X2,V_24Y)
    <=> t(V_24Y,c_24__type__6690___24a2(V_24X1,V_24X2)) ) ).

fof('$tdef_$_type_147212',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
      ( c_24__type__147212___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
    <=> t(V_24Y,c_24__type__147212___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).

fof('$tdef_$_type_152511',axiom,
    ! [V_24Y] :
      ( c_24__type__152511___24t(V_24Y)
    <=> t(V_24Y,c_24__type__152511) ) ).

fof('$tdef_$_type_145748',axiom,
    ! [V_24Y] :
      ( c_24__type__145748___24t(V_24Y)
    <=> t(V_24Y,c_24__type__145748) ) ).

fof('$tdef_$_type_6181',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__6181___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__6181___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_183',axiom,
    ! [V_24Y] :
      ( c_24__type__183___24t(V_24Y)
    <=> t(V_24Y,c_24__type__183) ) ).

fof('$tdef_$_type_152847',axiom,
    ! [V_24Y] :
      ( c_24__type__152847___24t(V_24Y)
    <=> t(V_24Y,c_24__type__152847) ) ).

fof('$tdef_$_type_145711',axiom,
    ! [V_24Y] :
      ( c_24__type__145711___24t(V_24Y)
    <=> t(V_24Y,c_24__type__145711) ) ).

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_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_138813',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
      ( c_24__type__138813___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__138813___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).

fof('$tdef_$_type_84277',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
      ( c_24__type__84277___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
    <=> t(V_24Y,c_24__type__84277___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).

fof('$tdef_$_type_132203',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
      ( c_24__type__132203___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__132203___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).

fof('$tdef_$_type_146818',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
      ( c_24__type__146818___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__146818___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).

fof('$tdef_$_type_550',axiom,
    ! [V_24Y] :
      ( c_24__type__550___24t(V_24Y)
    <=> t(V_24Y,c_24__type__550) ) ).

fof('$tdef_$_type_180',axiom,
    ! [V_24Y] :
      ( c_24__type__180___24t(V_24Y)
    <=> t(V_24Y,c_24__type__180) ) ).

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_85364',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
      ( c_24__type__85364___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
    <=> t(V_24Y,c_24__type__85364___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).

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_146002',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__146002___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__146002___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).

fof('$tdef_$_type_7054',axiom,
    ! [V_24Y] :
      ( c_24__type__7054___24t(V_24Y)
    <=> t(V_24Y,c_24__type__7054) ) ).

fof('$tdef_$_type_1873',axiom,
    ! [V_24Y] :
      ( c_24__type__1873___24t(V_24Y)
    <=> t(V_24Y,c_24__type__1873) ) ).

fof('$tdef_$_type_3290',axiom,
    ! [V_24Y] :
      ( c_24__type__3290___24t(V_24Y)
    <=> t(V_24Y,c_24__type__3290) ) ).

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_PLF.Hoare.Himp.com',axiom,
    ! [V_24Y] :
      ( cPLF_2eHoare_2eHimp_2ecom___24t(V_24Y)
    <=> t(V_24Y,cPLF_2eHoare_2eHimp_2ecom) ) ).

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_132453',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
      ( c_24__type__132453___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
    <=> t(V_24Y,c_24__type__132453___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).

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_146692',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
      ( c_24__type__146692___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__146692___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).

fof('$tdef_$_type_6935',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24Y] :
      ( c_24__type__6935___24t(V_24X1,V_24X2,V_24X3,V_24Y)
    <=> t(V_24Y,c_24__type__6935___24a3(V_24X1,V_24X2,V_24X3)) ) ).

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_136016',axiom,
    ! [V_24Y] :
      ( c_24__type__136016___24t(V_24Y)
    <=> t(V_24Y,c_24__type__136016) ) ).

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_126242',axiom,
    ! [V_24Y] :
      ( c_24__type__126242___24t(V_24Y)
    <=> t(V_24Y,c_24__type__126242) ) ).

fof('$tdef_$_type_5130',axiom,
    ! [V_24X1,V_24Y] :
      ( c_24__type__5130___24t(V_24X1,V_24Y)
    <=> t(V_24Y,c_24__type__5130___24a1(V_24X1)) ) ).

fof('$tdef_$_type_3030',axiom,
    ! [V_24X1,V_24Y] :
      ( c_24__type__3030___24t(V_24X1,V_24Y)
    <=> t(V_24Y,c_24__type__3030___24a1(V_24X1)) ) ).

fof('$tdef_Coq.Structures.OrderedTypeEx.PositiveOrderedTypeBits.t',axiom,
    ! [V_24Y] :
      ( cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2et___24t(V_24Y)
    <=> t(V_24Y,cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2et) ) ).

fof('$tdef_$_type_1132',axiom,
    ! [V_24Y] :
      ( c_24__type__1132___24t(V_24Y)
    <=> t(V_24Y,c_24__type__1132) ) ).

fof('$tdef_$_type_152779',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y] :
      ( c_24__type__152779___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y)
    <=> t(V_24Y,c_24__type__152779___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6)) ) ).

fof('$tdef_$_type_122332',axiom,
    ! [V_24Y] :
      ( c_24__type__122332___24t(V_24Y)
    <=> t(V_24Y,c_24__type__122332) ) ).

fof('$tdef_$_type_546',axiom,
    ! [V_24Y] :
      ( c_24__type__546___24t(V_24Y)
    <=> t(V_24Y,c_24__type__546) ) ).

fof('$tdef_$_type_145716',axiom,
    ! [V_24Y] :
      ( c_24__type__145716___24t(V_24Y)
    <=> t(V_24Y,c_24__type__145716) ) ).

fof('$tdef_$_type_145800',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y] :
      ( c_24__type__145800___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y)
    <=> t(V_24Y,c_24__type__145800___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6)) ) ).

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_124577',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__124577___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__124577___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).

fof('$tdef_$_type_7211',axiom,
    ! [V_24Y] :
      ( c_24__type__7211___24t(V_24Y)
    <=> t(V_24Y,c_24__type__7211) ) ).

fof('$tdef_$_type_152498',axiom,
    ! [V_24Y] :
      ( c_24__type__152498___24t(V_24Y)
    <=> t(V_24Y,c_24__type__152498) ) ).

fof('$tdef_$_type_3041',axiom,
    ! [V_24Y] :
      ( c_24__type__3041___24t(V_24Y)
    <=> t(V_24Y,c_24__type__3041) ) ).

fof('$tdef_$_type_84269',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
      ( c_24__type__84269___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
    <=> t(V_24Y,c_24__type__84269___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).

fof('$tdef_$_type_84433',axiom,
    ! [V_24Y] :
      ( c_24__type__84433___24t(V_24Y)
    <=> t(V_24Y,c_24__type__84433) ) ).

fof('$tdef_$_type_1120',axiom,
    ! [V_24Y] :
      ( c_24__type__1120___24t(V_24Y)
    <=> t(V_24Y,c_24__type__1120) ) ).

fof('$tdef_$_type_135368',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__135368___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__135368___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_580',axiom,
    ! [V_24Y] :
      ( c_24__type__580___24t(V_24Y)
    <=> t(V_24Y,c_24__type__580) ) ).

fof('$tdef_PLF.Imp.aexp',axiom,
    ! [V_24Y] :
      ( cPLF_2eImp_2eaexp___24t(V_24Y)
    <=> t(V_24Y,cPLF_2eImp_2eaexp) ) ).

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_PLF.Imp.BreakImp.result',axiom,
    ! [V_24Y] :
      ( cPLF_2eImp_2eBreakImp_2eresult___24t(V_24Y)
    <=> t(V_24Y,cPLF_2eImp_2eBreakImp_2eresult) ) ).

fof('$tdef_$_type_130954',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__130954___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__130954___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.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_PLF.Hoare.RepeatExercise.com',axiom,
    ! [V_24Y] :
      ( cPLF_2eHoare_2eRepeatExercise_2ecom___24t(V_24Y)
    <=> t(V_24Y,cPLF_2eHoare_2eRepeatExercise_2ecom) ) ).

fof('$tdef_$_type_126075',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__126075___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__126075___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).

fof('$tdef_$_type_149135',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24Y] :
      ( c_24__type__149135___24t(V_24X1,V_24X2,V_24X3,V_24Y)
    <=> t(V_24Y,c_24__type__149135___24a3(V_24X1,V_24X2,V_24X3)) ) ).

fof('$tdef_$_type_146997',axiom,
    ! [V_24X1,V_24Y] :
      ( c_24__type__146997___24t(V_24X1,V_24Y)
    <=> t(V_24Y,c_24__type__146997___24a1(V_24X1)) ) ).

fof('$tdef_$_type_121996',axiom,
    ! [V_24Y] :
      ( c_24__type__121996___24t(V_24Y)
    <=> t(V_24Y,c_24__type__121996) ) ).

fof('$tdef_$_type_133505',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__133505___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__133505___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_135644',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24Y] :
      ( c_24__type__135644___24t(V_24X1,V_24X2,V_24X3,V_24Y)
    <=> t(V_24Y,c_24__type__135644___24a3(V_24X1,V_24X2,V_24X3)) ) ).

fof('$tdef_$_type_1856',axiom,
    ! [V_24Y] :
      ( c_24__type__1856___24t(V_24Y)
    <=> t(V_24Y,c_24__type__1856) ) ).

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_5621',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y] :
      ( c_24__type__5621___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y)
    <=> t(V_24Y,c_24__type__5621___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6)) ) ).

fof('$tdef_$_type_125783',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__125783___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__125783___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).

fof('$tdef_$_type_152713',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y] :
      ( c_24__type__152713___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y)
    <=> t(V_24Y,c_24__type__152713___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6)) ) ).

fof('$tdef_$_type_878',axiom,
    ! [V_24Y] :
      ( c_24__type__878___24t(V_24Y)
    <=> t(V_24Y,c_24__type__878) ) ).

fof('$tdef_$_type_154230',axiom,
    ! [V_24Y] :
      ( c_24__type__154230___24t(V_24Y)
    <=> t(V_24Y,c_24__type__154230) ) ).

fof('$tdef_$_type_132842',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
      ( c_24__type__132842___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
    <=> t(V_24Y,c_24__type__132842___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).

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_3788',axiom,
    ! [V_24Y] :
      ( c_24__type__3788___24t(V_24Y)
    <=> t(V_24Y,c_24__type__3788) ) ).

fof('$tdef_$_type_136028',axiom,
    ! [V_24Y] :
      ( c_24__type__136028___24t(V_24Y)
    <=> t(V_24Y,c_24__type__136028) ) ).

fof('$tdef_$_type_152555',axiom,
    ! [V_24Y] :
      ( c_24__type__152555___24t(V_24Y)
    <=> t(V_24Y,c_24__type__152555) ) ).

fof('$tdef_$_type_124670',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__124670___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__124670___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).

fof('$tdef_$_type_131623',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__131623___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__131623___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_PLF.Hoare.Assertion',axiom,
    ! [V_24Y] :
      ( cPLF_2eHoare_2eAssertion___24t(V_24Y)
    <=> t(V_24Y,cPLF_2eHoare_2eAssertion) ) ).

fof('$tdef_$_type_148053',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
      ( c_24__type__148053___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
    <=> t(V_24Y,c_24__type__148053___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).

fof('$tdef_$_type_146935',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
      ( c_24__type__146935___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__146935___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).

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_Coq.Reals.RIneq.nonnegreal',axiom,
    ! [V_24Y] :
      ( cCoq_2eReals_2eRIneq_2enonnegreal___24t(V_24Y)
    <=> t(V_24Y,cCoq_2eReals_2eRIneq_2enonnegreal) ) ).

fof('$tdef_$_type_85114',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y] :
      ( c_24__type__85114___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y)
    <=> t(V_24Y,c_24__type__85114___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6)) ) ).

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_151112',axiom,
    ! [V_24Y] :
      ( c_24__type__151112___24t(V_24Y)
    <=> t(V_24Y,c_24__type__151112) ) ).

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_3752',axiom,
    ! [V_24Y] :
      ( c_24__type__3752___24t(V_24Y)
    <=> t(V_24Y,c_24__type__3752) ) ).

fof('$tdef_$_type_134339',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__134339___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__134339___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_7469',axiom,
    ! [V_24Y] :
      ( c_24__type__7469___24t(V_24Y)
    <=> t(V_24Y,c_24__type__7469) ) ).

fof('$tdef_$_type_148630',axiom,
    ! [V_24Y] :
      ( c_24__type__148630___24t(V_24Y)
    <=> t(V_24Y,c_24__type__148630) ) ).

fof('$tdef_$_type_85245',axiom,
    ! [V_24Y] :
      ( c_24__type__85245___24t(V_24Y)
    <=> t(V_24Y,c_24__type__85245) ) ).

fof('$tdef_$_type_2576',axiom,
    ! [V_24Y] :
      ( c_24__type__2576___24t(V_24Y)
    <=> t(V_24Y,c_24__type__2576) ) ).

fof('$tdef_$_type_121772',axiom,
    ! [V_24Y] :
      ( c_24__type__121772___24t(V_24Y)
    <=> t(V_24Y,c_24__type__121772) ) ).

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_139117',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
      ( c_24__type__139117___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
    <=> t(V_24Y,c_24__type__139117___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).

fof('$tdef_$_type_762',axiom,
    ! [V_24Y] :
      ( c_24__type__762___24t(V_24Y)
    <=> t(V_24Y,c_24__type__762) ) ).

fof('$tdef_$_type_5660',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y] :
      ( c_24__type__5660___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y)
    <=> t(V_24Y,c_24__type__5660___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6)) ) ).

fof('$tdef_$_type_139664',axiom,
    ! [V_24X1,V_24Y] :
      ( c_24__type__139664___24t(V_24X1,V_24Y)
    <=> t(V_24Y,c_24__type__139664___24a1(V_24X1)) ) ).

fof('$tdef_Coq.FSets.FSetPositive.PositiveSet.tree',axiom,
    ! [V_24Y] :
      ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree___24t(V_24Y)
    <=> t(V_24Y,cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree) ) ).

fof('$tdef_$_type_5025',axiom,
    ! [V_24Y] :
      ( c_24__type__5025___24t(V_24Y)
    <=> t(V_24Y,c_24__type__5025) ) ).

fof('$tdef_$_type_591',axiom,
    ! [V_24Y] :
      ( c_24__type__591___24t(V_24Y)
    <=> t(V_24Y,c_24__type__591) ) ).

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_623',axiom,
    ! [V_24Y] :
      ( c_24__type__623___24t(V_24Y)
    <=> t(V_24Y,c_24__type__623) ) ).

fof('$tdef_$_type_132257',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
      ( c_24__type__132257___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__132257___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).

fof('$tdef_$_type_146188',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__146188___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__146188___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).

fof('$tdef_$_type_4398',axiom,
    ! [V_24Y] :
      ( c_24__type__4398___24t(V_24Y)
    <=> t(V_24Y,c_24__type__4398) ) ).

fof('$tdef_$_type_135684',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
      ( c_24__type__135684___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
    <=> t(V_24Y,c_24__type__135684___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).

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_6765',axiom,
    ! [V_24X1,V_24X2,V_24Y] :
      ( c_24__type__6765___24t(V_24X1,V_24X2,V_24Y)
    <=> t(V_24Y,c_24__type__6765___24a2(V_24X1,V_24X2)) ) ).

fof('$tdef_$_type_135527',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y] :
      ( c_24__type__135527___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y)
    <=> t(V_24Y,c_24__type__135527___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7)) ) ).

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_7208',axiom,
    ! [V_24Y] :
      ( c_24__type__7208___24t(V_24Y)
    <=> t(V_24Y,c_24__type__7208) ) ).

fof('$tdef_$_type_626',axiom,
    ! [V_24Y] :
      ( c_24__type__626___24t(V_24Y)
    <=> t(V_24Y,c_24__type__626) ) ).

fof('$tdef_$_type_146960',axiom,
    ! [V_24X1,V_24X2,V_24Y] :
      ( c_24__type__146960___24t(V_24X1,V_24X2,V_24Y)
    <=> t(V_24Y,c_24__type__146960___24a2(V_24X1,V_24X2)) ) ).

fof('$tdef_$_type_147247',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24Y] :
      ( c_24__type__147247___24t(V_24X1,V_24X2,V_24X3,V_24Y)
    <=> t(V_24Y,c_24__type__147247___24a3(V_24X1,V_24X2,V_24X3)) ) ).

fof('$tdef_$_type_80524',axiom,
    ! [V_24X1,V_24X2,V_24Y] :
      ( c_24__type__80524___24t(V_24X1,V_24X2,V_24Y)
    <=> t(V_24Y,c_24__type__80524___24a2(V_24X1,V_24X2)) ) ).

fof('$tdef_$_type_4529',axiom,
    ! [V_24Y] :
      ( c_24__type__4529___24t(V_24Y)
    <=> t(V_24Y,c_24__type__4529) ) ).

fof('$tdef_$_type_124022',axiom,
    ! [V_24Y] :
      ( c_24__type__124022___24t(V_24Y)
    <=> t(V_24Y,c_24__type__124022) ) ).

fof('$tdef_$_type_5582',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y] :
      ( c_24__type__5582___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y)
    <=> t(V_24Y,c_24__type__5582___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6)) ) ).

fof('$tdef_$_type_1916',axiom,
    ! [V_24Y] :
      ( c_24__type__1916___24t(V_24Y)
    <=> t(V_24Y,c_24__type__1916) ) ).

fof('$tdef_PLF.Imp.aevalR_division.aexp',axiom,
    ! [V_24Y] :
      ( cPLF_2eImp_2eaevalR__division_2eaexp___24t(V_24Y)
    <=> t(V_24Y,cPLF_2eImp_2eaevalR__division_2eaexp) ) ).

fof('$tdef_$_type_5375',axiom,
    ! [V_24X1,V_24X2,V_24Y] :
      ( c_24__type__5375___24t(V_24X1,V_24X2,V_24Y)
    <=> t(V_24Y,c_24__type__5375___24a2(V_24X1,V_24X2)) ) ).

fof('$tdef_$_type_126176',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__126176___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__126176___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).

fof('$tdef_$_type_155189',axiom,
    ! [V_24Y] :
      ( c_24__type__155189___24t(V_24Y)
    <=> t(V_24Y,c_24__type__155189) ) ).

fof('$tdef_$_type_1963',axiom,
    ! [V_24Y] :
      ( c_24__type__1963___24t(V_24Y)
    <=> t(V_24Y,c_24__type__1963) ) ).

fof('$tdef_$_type_146949',axiom,
    ! [V_24X1,V_24X2,V_24Y] :
      ( c_24__type__146949___24t(V_24X1,V_24X2,V_24Y)
    <=> t(V_24Y,c_24__type__146949___24a2(V_24X1,V_24X2)) ) ).

fof('$tdef_$_type_98',axiom,
    ! [V_24Y] :
      ( c_24__type__98___24t(V_24Y)
    <=> t(V_24Y,c_24__type__98) ) ).

fof('$tdef_$_type_7201',axiom,
    ! [V_24Y] :
      ( c_24__type__7201___24t(V_24Y)
    <=> t(V_24Y,c_24__type__7201) ) ).

fof('$tdef_$_type_132476',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
      ( c_24__type__132476___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
    <=> t(V_24Y,c_24__type__132476___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).

fof('$tdef_$_type_4943',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24Y] :
      ( c_24__type__4943___24t(V_24X1,V_24X2,V_24X3,V_24Y)
    <=> t(V_24Y,c_24__type__4943___24a3(V_24X1,V_24X2,V_24X3)) ) ).

fof('$tdef_$_type_14695',axiom,
    ! [V_24Y] :
      ( c_24__type__14695___24t(V_24Y)
    <=> t(V_24Y,c_24__type__14695) ) ).

fof('$tdef_$_type_139716',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24Y] :
      ( c_24__type__139716___24t(V_24X1,V_24X2,V_24X3,V_24Y)
    <=> t(V_24Y,c_24__type__139716___24a3(V_24X1,V_24X2,V_24X3)) ) ).

fof('$tdef_$_type_337',axiom,
    ! [V_24Y] :
      ( c_24__type__337___24t(V_24Y)
    <=> t(V_24Y,c_24__type__337) ) ).

fof('$tdef_$_type_124752',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__124752___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__124752___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).

fof('$tdef_$_type_152503',axiom,
    ! [V_24Y] :
      ( c_24__type__152503___24t(V_24Y)
    <=> t(V_24Y,c_24__type__152503) ) ).

fof('$tdef_$_type_149039',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
      ( c_24__type__149039___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
    <=> t(V_24Y,c_24__type__149039___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).

fof('$tdef_$_type_139437',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y] :
      ( c_24__type__139437___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y)
    <=> t(V_24Y,c_24__type__139437___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7)) ) ).

fof('$tdef_$_type_7041',axiom,
    ! [V_24Y] :
      ( c_24__type__7041___24t(V_24Y)
    <=> t(V_24Y,c_24__type__7041) ) ).

fof('$tdef_$_type_233',axiom,
    ! [V_24Y] :
      ( c_24__type__233___24t(V_24Y)
    <=> t(V_24Y,c_24__type__233) ) ).

fof('$tdef_$_type_127886',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__127886___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__127886___24a22(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22)) ) ).

fof('$tdef_Coq.Init.Datatypes.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_5081',axiom,
    ! [V_24Y] :
      ( c_24__type__5081___24t(V_24Y)
    <=> t(V_24Y,c_24__type__5081) ) ).

fof('$tdef_$_type_3833',axiom,
    ! [V_24Y] :
      ( c_24__type__3833___24t(V_24Y)
    <=> t(V_24Y,c_24__type__3833) ) ).

fof('$tdef_$_type_155388',axiom,
    ! [V_24Y] :
      ( c_24__type__155388___24t(V_24Y)
    <=> t(V_24Y,c_24__type__155388) ) ).

fof('$tdef_$_type_132671',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
      ( c_24__type__132671___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
    <=> t(V_24Y,c_24__type__132671___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).

fof('$tdef_$_type_1781',axiom,
    ! [V_24Y] :
      ( c_24__type__1781___24t(V_24Y)
    <=> t(V_24Y,c_24__type__1781) ) ).

fof('$tdef_$_type_132517',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
      ( c_24__type__132517___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
    <=> t(V_24Y,c_24__type__132517___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).

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_6667',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__6667___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__6667___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_4953',axiom,
    ! [V_24Y] :
      ( c_24__type__4953___24t(V_24Y)
    <=> t(V_24Y,c_24__type__4953) ) ).

fof('$tdef_$_type_149151',axiom,
    ! [V_24Y] :
      ( c_24__type__149151___24t(V_24Y)
    <=> t(V_24Y,c_24__type__149151) ) ).

fof('$tdef_$_type_146977',axiom,
    ! [V_24X1,V_24X2,V_24Y] :
      ( c_24__type__146977___24t(V_24X1,V_24X2,V_24Y)
    <=> t(V_24Y,c_24__type__146977___24a2(V_24X1,V_24X2)) ) ).

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_3298',axiom,
    ! [V_24Y] :
      ( c_24__type__3298___24t(V_24Y)
    <=> t(V_24Y,c_24__type__3298) ) ).

fof('$tdef_$_type_6431',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__6431___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__6431___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_PLF.Hoare.HoareAssertAssume.com',axiom,
    ! [V_24Y] :
      ( cPLF_2eHoare_2eHoareAssertAssume_2ecom___24t(V_24Y)
    <=> t(V_24Y,cPLF_2eHoare_2eHoareAssertAssume_2ecom) ) ).

fof('$tdef_$_type_7026',axiom,
    ! [V_24Y] :
      ( c_24__type__7026___24t(V_24Y)
    <=> t(V_24Y,c_24__type__7026) ) ).

fof('$tdef_$_type_149168',axiom,
    ! [V_24Y] :
      ( c_24__type__149168___24t(V_24Y)
    <=> t(V_24Y,c_24__type__149168) ) ).

fof('$tdef_$_type_124845',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__124845___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__124845___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).

fof('$tdef_$_type_84288',axiom,
    ! [V_24Y] :
      ( c_24__type__84288___24t(V_24Y)
    <=> t(V_24Y,c_24__type__84288) ) ).

fof('$tdef_$_type_583',axiom,
    ! [V_24Y] :
      ( c_24__type__583___24t(V_24Y)
    <=> t(V_24Y,c_24__type__583) ) ).

fof('$tdef_$_type_125073',axiom,
    ! [V_24Y] :
      ( c_24__type__125073___24t(V_24Y)
    <=> t(V_24Y,c_24__type__125073) ) ).

fof('$tdef_$_type_138930',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
      ( c_24__type__138930___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__138930___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).

fof('$tdef_$_type_135825',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y] :
      ( c_24__type__135825___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y)
    <=> t(V_24Y,c_24__type__135825___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6)) ) ).

fof('$tdef_$_type_3735',axiom,
    ! [V_24X1,V_24Y] :
      ( c_24__type__3735___24t(V_24X1,V_24Y)
    <=> t(V_24Y,c_24__type__3735___24a1(V_24X1)) ) ).

fof('$tdef_$_type_132140',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
      ( c_24__type__132140___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__132140___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).

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_149942',axiom,
    ! [V_24Y] :
      ( c_24__type__149942___24t(V_24Y)
    <=> t(V_24Y,c_24__type__149942) ) ).

fof('$tdef_PLF.Hoare.HoareAssertAssume.result',axiom,
    ! [V_24Y] :
      ( cPLF_2eHoare_2eHoareAssertAssume_2eresult___24t(V_24Y)
    <=> t(V_24Y,cPLF_2eHoare_2eHoareAssertAssume_2eresult) ) ).

fof('$tdef_$_type_139563',axiom,
    ! [V_24X1,V_24X2,V_24Y] :
      ( c_24__type__139563___24t(V_24X1,V_24X2,V_24Y)
    <=> t(V_24Y,c_24__type__139563___24a2(V_24X1,V_24X2)) ) ).

fof('$tdef_$_type_2863',axiom,
    ! [V_24X1,V_24Y] :
      ( c_24__type__2863___24t(V_24X1,V_24Y)
    <=> t(V_24Y,c_24__type__2863___24a1(V_24X1)) ) ).

fof('$tdef_$_type_155062',axiom,
    ! [V_24Y] :
      ( c_24__type__155062___24t(V_24Y)
    <=> t(V_24Y,c_24__type__155062) ) ).

fof('$tdef_$_type_146363',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__146363___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__146363___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).

fof('$tdef_Coq.Bool.Bool.reflect',axiom,
    ! [V_24X1,V_24X2,V_24Y] :
      ( cCoq_2eBool_2eBool_2ereflect___24t(V_24X1,V_24X2,V_24Y)
    <=> t(V_24Y,cCoq_2eBool_2eBool_2ereflect___24a2(V_24X1,V_24X2)) ) ).

fof('$tdef_Coq.setoid_ring.Ring_polynom.Pol',axiom,
    ! [V_24X1,V_24Y] :
      ( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V_24X1,V_24Y)
    <=> t(V_24Y,cCoq_2esetoid__ring_2eRing__polynom_2ePol___24a1(V_24X1)) ) ).

fof('$tdef_$_type_4338',axiom,
    ! [V_24Y] :
      ( c_24__type__4338___24t(V_24Y)
    <=> t(V_24Y,c_24__type__4338) ) ).

fof('$tdef_$_type_3793',axiom,
    ! [V_24Y] :
      ( c_24__type__3793___24t(V_24Y)
    <=> t(V_24Y,c_24__type__3793) ) ).

fof('$tdef_$_type_83633',axiom,
    ! [V_24Y] :
      ( c_24__type__83633___24t(V_24Y)
    <=> t(V_24Y,c_24__type__83633) ) ).

fof('$tdef_$_type_1646',axiom,
    ! [V_24Y] :
      ( c_24__type__1646___24t(V_24Y)
    <=> t(V_24Y,c_24__type__1646) ) ).

fof('$tdef_$_type_139150',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
      ( c_24__type__139150___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
    <=> t(V_24Y,c_24__type__139150___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).

fof('$tdef_$_type_670',axiom,
    ! [V_24Y] :
      ( c_24__type__670___24t(V_24Y)
    <=> t(V_24Y,c_24__type__670) ) ).

fof('$tdef_$_type_83174',axiom,
    ! [V_24Y] :
      ( c_24__type__83174___24t(V_24Y)
    <=> t(V_24Y,c_24__type__83174) ) ).

fof('$tdef_$_type_135834',axiom,
    ! [V_24Y] :
      ( c_24__type__135834___24t(V_24Y)
    <=> t(V_24Y,c_24__type__135834) ) ).

fof('$tdef_$_type_4433',axiom,
    ! [V_24Y] :
      ( c_24__type__4433___24t(V_24Y)
    <=> t(V_24Y,c_24__type__4433) ) ).

fof('$tdef_$_type_220',axiom,
    ! [V_24Y] :
      ( c_24__type__220___24t(V_24Y)
    <=> t(V_24Y,c_24__type__220) ) ).

fof('$tdef_$_type_139295',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y] :
      ( c_24__type__139295___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y)
    <=> t(V_24Y,c_24__type__139295___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7)) ) ).

fof('$tdef_$_type_130285',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__130285___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__130285___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_126237',axiom,
    ! [V_24Y] :
      ( c_24__type__126237___24t(V_24Y)
    <=> t(V_24Y,c_24__type__126237) ) ).

fof('$tdef_$_type_147986',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y] :
      ( c_24__type__147986___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y)
    <=> t(V_24Y,c_24__type__147986___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6)) ) ).

fof('$tdef_$_type_3861',axiom,
    ! [V_24Y] :
      ( c_24__type__3861___24t(V_24Y)
    <=> t(V_24Y,c_24__type__3861) ) ).

fof('$tdef_$_type_7089',axiom,
    ! [V_24Y] :
      ( c_24__type__7089___24t(V_24Y)
    <=> t(V_24Y,c_24__type__7089) ) ).

fof('$tdef_$_type_139681',axiom,
    ! [V_24Y] :
      ( c_24__type__139681___24t(V_24Y)
    <=> t(V_24Y,c_24__type__139681) ) ).

fof('$tdef_$_type_131277',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__131277___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__131277___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_4087',axiom,
    ! [V_24Y] :
      ( c_24__type__4087___24t(V_24Y)
    <=> t(V_24Y,c_24__type__4087) ) ).

fof('$tdef_$_type_155290',axiom,
    ! [V_24Y] :
      ( c_24__type__155290___24t(V_24Y)
    <=> t(V_24Y,c_24__type__155290) ) ).

fof('$tdef_$_type_146445',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__146445___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__146445___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).

fof('$tdef_$_type_129939',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__129939___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__129939___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_145772',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y] :
      ( c_24__type__145772___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y)
    <=> t(V_24Y,c_24__type__145772___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6)) ) ).

fof('$tdef_$_type_133292',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__133292___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__133292___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_6721',axiom,
    ! [V_24Y] :
      ( c_24__type__6721___24t(V_24Y)
    <=> t(V_24Y,c_24__type__6721) ) ).

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_129270',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__129270___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__129270___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_Hammer.Tactics.Reconstr.ReconstrT',axiom,
    ! [V_24Y] :
      ( cHammer_2eTactics_2eReconstr_2eReconstrT___24t(V_24Y)
    <=> t(V_24Y,cHammer_2eTactics_2eReconstr_2eReconstrT) ) ).

fof('$tdef_$_type_150092',axiom,
    ! [V_24Y] :
      ( c_24__type__150092___24t(V_24Y)
    <=> t(V_24Y,c_24__type__150092) ) ).

fof('$tdef_$_type_7124',axiom,
    ! [V_24Y] :
      ( c_24__type__7124___24t(V_24Y)
    <=> t(V_24Y,c_24__type__7124) ) ).

fof('$tdef_$_type_146538',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__146538___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__146538___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).

fof('$tdef_$_type_125974',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__125974___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__125974___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).

fof('$tdef_$_type_149225',axiom,
    ! [V_24Y] :
      ( c_24__type__149225___24t(V_24Y)
    <=> t(V_24Y,c_24__type__149225) ) ).

fof('$tdef_$_type_126232',axiom,
    ! [V_24Y] :
      ( c_24__type__126232___24t(V_24Y)
    <=> t(V_24Y,c_24__type__126232) ) ).

fof('$tdef_$_type_132866',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
      ( c_24__type__132866___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
    <=> t(V_24Y,c_24__type__132866___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).

fof('$tdef_$_type_147839',axiom,
    ! [V_24Y] :
      ( c_24__type__147839___24t(V_24Y)
    <=> t(V_24Y,c_24__type__147839) ) ).

fof('$tdef_$_type_138687',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
      ( c_24__type__138687___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__138687___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).

fof('$tdef_$_type_146270',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__146270___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__146270___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).

fof('$tdef_$_type_85274',axiom,
    ! [V_24Y] :
      ( c_24__type__85274___24t(V_24Y)
    <=> t(V_24Y,c_24__type__85274) ) ).

fof('$tdef_$_type_4983',axiom,
    ! [V_24X1,V_24Y] :
      ( c_24__type__4983___24t(V_24X1,V_24Y)
    <=> t(V_24Y,c_24__type__4983___24a1(V_24X1)) ) ).

fof('$tdef_$_type_155268',axiom,
    ! [V_24Y] :
      ( c_24__type__155268___24t(V_24Y)
    <=> t(V_24Y,c_24__type__155268) ) ).

fof('$tdef_$_type_5013',axiom,
    ! [V_24Y] :
      ( c_24__type__5013___24t(V_24Y)
    <=> t(V_24Y,c_24__type__5013) ) ).

fof('$tdef_Type',axiom,
    ! [V_24Y] :
      ( cType___24t(V_24Y)
    <=> t(V_24Y,cType) ) ).

fof('$tdef_$_type_5407',axiom,
    ! [V_24Y] :
      ( c_24__type__5407___24t(V_24Y)
    <=> t(V_24Y,c_24__type__5407) ) ).

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_5011',axiom,
    ! [V_24Y] :
      ( c_24__type__5011___24t(V_24Y)
    <=> t(V_24Y,c_24__type__5011) ) ).

fof('$tdef_$_type_132785',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
      ( c_24__type__132785___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
    <=> t(V_24Y,c_24__type__132785___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).

fof('$tdef_$_type_147008',axiom,
    ! [V_24Y] :
      ( c_24__type__147008___24t(V_24Y)
    <=> t(V_24Y,c_24__type__147008) ) ).

fof('$tdef_$_type_149732',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
      ( c_24__type__149732___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
    <=> t(V_24Y,c_24__type__149732___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).

fof('$tdef_$_type_132561',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
      ( c_24__type__132561___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
    <=> t(V_24Y,c_24__type__132561___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).

fof('$tdef_$_type_139487',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y] :
      ( c_24__type__139487___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y)
    <=> t(V_24Y,c_24__type__139487___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7)) ) ).

fof('$tdef_$_type_6732',axiom,
    ! [V_24Y] :
      ( c_24__type__6732___24t(V_24Y)
    <=> t(V_24Y,c_24__type__6732) ) ).

fof('$tdef_$_type_132543',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
      ( c_24__type__132543___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
    <=> t(V_24Y,c_24__type__132543___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).

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_528',axiom,
    ! [V_24Y] :
      ( c_24__type__528___24t(V_24Y)
    <=> t(V_24Y,c_24__type__528) ) ).

fof('$tdef_$_type_151195',axiom,
    ! [V_24Y] :
      ( c_24__type__151195___24t(V_24Y)
    <=> t(V_24Y,c_24__type__151195) ) ).

fof('$tdef_$_type_4380',axiom,
    ! [V_24Y] :
      ( c_24__type__4380___24t(V_24Y)
    <=> t(V_24Y,c_24__type__4380) ) ).

fof('$tdef_PLF.Imp.AExp.aexp',axiom,
    ! [V_24Y] :
      ( cPLF_2eImp_2eAExp_2eaexp___24t(V_24Y)
    <=> t(V_24Y,cPLF_2eImp_2eAExp_2eaexp) ) ).

fof('$tdef_$_type_127563',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__127563___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__127563___24a22(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22)) ) ).

fof('$tdef_Coq.setoid_ring.InitialRing.Nword',axiom,
    ! [V_24Y] :
      ( cCoq_2esetoid__ring_2eInitialRing_2eNword___24t(V_24Y)
    <=> t(V_24Y,cCoq_2esetoid__ring_2eInitialRing_2eNword) ) ).

fof('$tdef_Coq.Reals.RIneq.negreal',axiom,
    ! [V_24Y] :
      ( cCoq_2eReals_2eRIneq_2enegreal___24t(V_24Y)
    <=> t(V_24Y,cCoq_2eReals_2eRIneq_2enegreal) ) ).

fof('$tdef_$_type_3732',axiom,
    ! [V_24Y] :
      ( c_24__type__3732___24t(V_24Y)
    <=> t(V_24Y,c_24__type__3732) ) ).

fof('$tdef_$_type_152506',axiom,
    ! [V_24Y] :
      ( c_24__type__152506___24t(V_24Y)
    <=> t(V_24Y,c_24__type__152506) ) ).

fof('_HAMMER_GOAL',conjecture,
    cHoare2_2edec__correct___24a1(cHoare2_2edec__while) ).

%------------------------------------------------------------------------------